three essays on access and welfare in health care and

Three Essays on Access and Welfare in Health Care and Health Insurance Markets

Nathaniel Denison Mark

Submitted in partial fulfillment of therequirements for the degree of

Doctor of Philosophyunder the Executive Committee

of the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2021

Abstract

Three Essays on Access and Welfare in Health Care and Health Insurance Markets


This dissertation consists of three essays on access to primary care and the design of health

insurance markets. These essays share a methodological framework. In each, I estimate a model of

the market using detailed administrative data sets. Then, I employ the estimated model to answer

policy-relevant research questions.

The first chapter, entitled Access to Care in Equilibrium, studies consumer access to medical

care as an equilibrium outcome of a market without prices. I use data from the Northern Ontario

primary care market to estimate an empirical matching model where patients match with physicians.

The market is cleared by a non-price mechanism: the effort it takes to find a physician. I use the

model to study the distribution and determinants of access to care. By employing a model of the

market, I am able to define a measure of access to care that accounts for patient preferences and

market conditions: the probability that a patient who would attain care in a full access environment

currently attains care. I find that access to care is low and unevenly distributed. On average, a

patient who would attain care in a full access environment will receive care 73% of the time. The

issue is particularly acute in rural areas. Further, physicians discriminate in favor of patients with

higher expected utilization, thereby increasing access for older and sicker patients while decreasing

access for younger and healthier patients. The estimated model is used to decompose access into

its contributing factors. In rural areas, the geographic distribution of physicians is the primary

determinant of low access. In contrast, low access in urban areas is primarily driven by capacity

constraints of physicians. Interestingly, equating physician to population ratios across Northern

Ontario would not improve rural access.

In the second chapter, entitled Increasing Access to Care Through Policy: A Case Study of

Northern Ontario, Canada, I employ the estimated model from Chapter One to assess the impact of

policy on access to medical care. I study two policies: (1) grants to incentivize physicians to practice

in low-access areas and (2) a payment reform that provided incentives for physicians to increase

the numbers of patients on their books. Using the estimated model, I simulate market outcomes in

counterfactuals where each policy is removed. By comparing these simulations to outcomes in the

current market, I estimate policy impacts while accounting for equilibrium effects. I find that both

policies are effective at increasing access to care. However, the policies target different subsets of

the population. The grant program increases access most for rural patients, whereas the payment

reform increases urban access most.

Lastly, Chapter Three is a paper co-authored with Kate Ho and Michael Dickstein entitled

Market Segmentation and Competition in Health Insurance. We study the welfare consequences

of market segmentation in private health insurance in the US, where households obtain coverage

either through an employer or via an individual marketplace. We use comprehensive and detailed

data from Oregon’s small group and individual markets to demonstrate several facts. First, enrollees

in the small group market have lower health care spending than those in the individual market

conditional on plan coverage level. Second, small group enrollees benefit from tax exemptions

and employer premium subsidies that create a wedge between premiums charged by insurers and

the prices they face. However, these benefits are offset by relatively high plan markups over

costs, which generate premiums (prior to employer contributions) that are at least as high as those

in the individual market. These findings suggest that recent policies to merge the two markets,

allowing small group enrollees to shop on the individual exchanges while maintaining their tax

exemptions and employer contributions, may stabilize the individual market without much loss to

small group enrollees. However, the new equilibrium outcome depends crucially on the preferences

and characteristics of the two populations. We use a model of health plan choice and subsequent

utilization to estimate household preferences in both markets and predict premiums and costs under

a counterfactual pooled market. We find that integration mitigates adverse selection issues in the

individual market, while decreasing government and employer expenditures on premium subsidies.

Small group households benefit from lower premiums for low coverage plans in the merged market.

However, they face higher premiums for high coverage plans and are constrained to a smaller set of

insurance options. Thus, the effects of integration on small group households are heterogeneous.

Table of Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Chapter 1: Access to Care in Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Access To Care in Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Equilibrium Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 A Simplified Model: Effort as a Non-Price Market Clearing Mechanism . . 7

1.2.3 Complicating the Model: Heterogeneous Effort Costs . . . . . . . . . . . . 11

1.2.4 A Note on Markets with Prices and Non-Price Rationing . . . . . . . . . . 13

1.3 Matching Model: Patient and Physician Matching . . . . . . . . . . . . . . . . . . 14

1.3.1 Patient and Physician Preferences . . . . . . . . . . . . . . . . . . . . . . 14

1.3.2 Markets and Matchings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4 Empirical Setting: Primary Care in Northern Ontario . . . . . . . . . . . . . . . . 18

1.4.1 Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.5 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

i

1.5.1 Matching Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.5.2 Payment Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.6 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.6.1 Estimation of Matching Preferences . . . . . . . . . . . . . . . . . . . . . 37

1.6.2 Estimation of Unobserved Taste for Revenue . . . . . . . . . . . . . . . . 39

1.6.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

1.7 Results: Patient and Physician Preferences . . . . . . . . . . . . . . . . . . . . . . 41

1.7.1 Physician Choice of Payment Model . . . . . . . . . . . . . . . . . . . . . 41

1.7.2 Empirical Matching Model Estimates . . . . . . . . . . . . . . . . . . . . 44

1.7.3 Exposition of Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.7.4 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.8 Patterns And Determinants of Access to Care . . . . . . . . . . . . . . . . . . . . 49

1.8.1 Measures of Access to Care . . . . . . . . . . . . . . . . . . . . . . . . . 50

1.8.2 Patterns in Access to Care . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1.8.3 Determinants of Access Loss . . . . . . . . . . . . . . . . . . . . . . . . . 52

1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Chapter 2: Increasing Access to Care Through Policy: A Case Study of Northern Ontario,Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.2 An Empirical Model of the Primary Care Market in Northern Ontario, Canada . . . 66

2.2.1 The empirical setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.2.2 Model specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.2.3 Estimation and Key Model Results . . . . . . . . . . . . . . . . . . . . . . 70

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2.2.4 A Measure of Access to Care . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.3 Policy One: Practice Location Incentives . . . . . . . . . . . . . . . . . . . . . . . 73

2.3.1 Previous Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.3.2 Policy Counterfactual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.3.3 Gains in Access to Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

2.4 Policy Two: Physician Payment Reforms . . . . . . . . . . . . . . . . . . . . . . 80

2.4.1 Details of the Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.4.2 Reduced Form Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

2.4.3 Policy Impacts on Access . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

2.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Chapter 3: Market Segmentation and Competition in Health Insurance . . . . . . . . . . . 93

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.2 Institutional Detail and Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.2.1 Individual Insurance Market . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.2.2 Small group insurance market . . . . . . . . . . . . . . . . . . . . . . . . 102

3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.4 Descriptive Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3.4.1 Comparing the Small Group and Individual Markets . . . . . . . . . . . . 107

3.4.2 Potential Consequences of Market Pooling . . . . . . . . . . . . . . . . . . 110

3.5 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.5.1 Consumer Demand and Spending . . . . . . . . . . . . . . . . . . . . . . 111

3.5.2 Insurance Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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3.6 Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

3.6.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

3.6.2 Joint likelihood of plan choice and health spending . . . . . . . . . . . . . 116

3.6.3 Premium setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

3.7 Results and Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3.7.1 Demand Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3.7.2 Cost Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

3.7.3 Counterfactual Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 125

3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

3.9 Figures and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Appendix A: Appendix For Chapter One . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

A.1 Dataset Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

A.1.1 Sample Subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

A.1.2 Comorbidities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

A.1.3 Patient Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

A.1.4 Physician Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.1.5 Expected Revenue and Expected Number of Visits . . . . . . . . . . . . . 171

A.2 Details of the Physician Payment Models . . . . . . . . . . . . . . . . . . . . . . . 177

A.3 Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

A.4 Alternative Full Access Counterfactual Definitions . . . . . . . . . . . . . . . . . 183

A.5 A Simple Proof of Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

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A.6 Gradient and Standard Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

A.6.1 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

A.6.2 Standard Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Appendix B: Appendix For Chapter Two . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

B.1 Rurality Index for Ontario and Access . . . . . . . . . . . . . . . . . . . . . . . . 193

B.2 Other Incentive Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

B.3 Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Appendix C: Appendix For Chapter Three . . . . . . . . . . . . . . . . . . . . . . . . . . 200

C.1 Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

C.1.1 Individual Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

C.1.2 Small group insurance market . . . . . . . . . . . . . . . . . . . . . . . . 201

C.2 Dataset Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

C.2.1 Household Dataset Creation . . . . . . . . . . . . . . . . . . . . . . . . . 204

C.2.2 Switcher Dataset Creation . . . . . . . . . . . . . . . . . . . . . . . . . . 205

C.2.3 Household Demographic Variable Construction . . . . . . . . . . . . . . . 207

C.2.4 Household Plan Choice Variable Construction . . . . . . . . . . . . . . . . 211

C.2.5 Uninsured Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

C.3 Estimation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

C.3.1 Further details on deriving equations for estimation . . . . . . . . . . . . . 215

C.3.2 Likelihood derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

C.3.3 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

C.4 Consumer surplus calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

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C.5 Cost Censor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

C.6 Counterfactual algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

C.6.1 Steps in the equilibrium search . . . . . . . . . . . . . . . . . . . . . . . . 226

C.6.2 Counterfactual sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

C.7 Consumer Surplus in the Small Group Market . . . . . . . . . . . . . . . . . . . . 228

C.7.1 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

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List of Figures

1.1 Percent of Patients Who Do Not See a Primary Care Physician in 2014 . . . . . . . 7

1.2 Supply and Demand with Non-Price Market Clearing . . . . . . . . . . . . . . . . 9

1.3 An Increase in Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Alternative Payment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.5 Patient and Physician Summary Statistics . . . . . . . . . . . . . . . . . . . . . . 26

1.6 Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.7 Distribution of �̂� 𝑗 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.8 Preference Exposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.9 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.10 Distribution of Access in 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1.11 Share of Access Loss Attributed to Physician Capacities . . . . . . . . . . . . . . . 54

1.12 Access Loss Attributed to Characteristics of Physician Supply . . . . . . . . . . . 58

2.1 RIO Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.2 Entry and Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

2.3 Effect of Payment Reforms on Access to Care (By Patient Type) . . . . . . . . . . 90

2.4 Effect of Policies on the Distribution of Access in Northern Ontario . . . . . . . . 92

3.1 Market shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

3.2 Distribution of monthly medical costs . . . . . . . . . . . . . . . . . . . . . . . . 134

3.3 Kernel density of medical costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

3.4 Medical markup (total premiums over medical costs) . . . . . . . . . . . . . . . . 136

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3.5 Base monthly premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

3.6 Distribution of subsidies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

3.7 HH-sum risk score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

3.8 Number of enrollees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

A.1 Eligible Census Subdivisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

A.2 Rurality (SAC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.3 Heterogeneity in Physician Outputs . . . . . . . . . . . . . . . . . . . . . . . . . 179

A.4 Preferences: Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

B.1 Relationship Between Estimated Access to Care and Common Measures . . . . . . 194

B.2 Effect of NRRR on Access to Care (By Patient Type) . . . . . . . . . . . . . . . . 198

B.3 Entry and Access Scatterplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

C.1 Percent of Switchers to Ind. Market/Uninsurance . . . . . . . . . . . . . . . . . . 206

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List of Tables

1.1 Payment Model Selection Dataset Summary Statistics . . . . . . . . . . . . . . . . 23

1.2 Matching Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3 Matchings Within/Across Markets . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.4 Physician Choice of Payment Model Estimates . . . . . . . . . . . . . . . . . . . 43

1.5 Patient Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

1.6 Physician Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.1 Estimated Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.2 NRRR Grant Counterfactual Results (Access Gain) . . . . . . . . . . . . . . . . . 78

2.3 Characteristics of Payment Models . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.4 Regression Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.1 Summary statistics on demographics variables . . . . . . . . . . . . . . . . . . . . 141

3.2 Summary statistics on insurance variabels . . . . . . . . . . . . . . . . . . . . . . 142

3.3 Main parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

3.4 Derived parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

3.5 Derived parameters across markets . . . . . . . . . . . . . . . . . . . . . . . . . . 145

3.6 Premium setting equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

3.7 Administrative costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

3.8 Demographics of the switchers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

3.9 Demographics of the uninsured . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

3.10 Cost regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

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3.11 Cost distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

3.12 Counterfactual: Employees have premium subsidies . . . . . . . . . . . . . . . . . 152

3.13 Counterfactual: Employees have tax and employer subsidies . . . . . . . . . . . . 153

A.1 Charlson Comorbidity Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

A.2 CCPCP Payment Model Data Cleaning . . . . . . . . . . . . . . . . . . . . . . . . 171

A.3 Revenue and Visit Estimation Data Summary Statistics . . . . . . . . . . . . . . . 174

A.4 Revenue and Visits Estimation Regression Results . . . . . . . . . . . . . . . . . 175

A.5 Revenue and Visits Estimation Regression Results (Continued) . . . . . . . . . . . 176

A.6 Characteristics of Payment Models . . . . . . . . . . . . . . . . . . . . . . . . . . 177

A.7 Patient Characteristics Summary Statistics . . . . . . . . . . . . . . . . . . . . . . 180

A.8 Physician Characteristics Summary Statistics . . . . . . . . . . . . . . . . . . . . 181

A.9 Decomposition of Access Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.10 Average Access Loss Under Full Access Alternatives . . . . . . . . . . . . . . . . 185

B.1 NRRR Effect on Patient Access (By Base Access Level) . . . . . . . . . . . . . . 195

B.2 Effect of NRRR on Access to Care (By Patient Type) . . . . . . . . . . . . . . . . 196

B.3 Effect of NRRR on Percent of Patients With Care (By Patient Type) . . . . . . . . 197

B.4 Effect of Alternative Payment Models on Access to Care (By Patient Type) . . . . . 199

C.1 2014-16 real forced-out small group transitions . . . . . . . . . . . . . . . . . . . 207

C.2 Consumer Surplus Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

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Acknowledgements

I am grateful for the support and guidance of my advisors and co-authors: Bernard Salanié, Kate

Ho, Ashley Swanson, Mike Dickstein, and John Asker. I thank Simon Lee, Michael Riordan, Tobias

Salz, Andrea Prat, Adam Sacarny, José Luis Montiel Olea, Doug Almond, and seminar participants

at the IO colloquium, the IO workshop, the econometrics colloquium, and the Student Research

Breakfast at Columbia University, as well as participants at the Health Economics and Policy

Seminar at the Columbia Mailman School of Public Health for their useful comments. Without the

infinite patience and dedication of the staff at the Institute of Clinical and Evaluative Studies, this

dissertation would not have been possible. To this end, I especially thank Erin Graves, Eliane Kim,

Stefana Jovanovska, and Refik Saskin. For sticking with me through the Oregon data acquisition

process, I thank Sophia Johnson. For fielding our frequent server questions, I thank Robin Wurl

at NYU. For financial support, I thank the Program for Economic Research. Lastly, I am forever

grateful to my partner in life, Hannah Heyman, for reminding me to step outside and admire New

York City’s beautiful trees.

xi

Chapter 1: Access to Care in Equilibrium

Nathaniel Mark1

1.1 Introduction

Access to care is easy to spot when it is missing. In 2011, a Globe and Mail journalist, Gloria

Galloway, moved to the Ottawa area. At first, Ms. Galloway went without a regular primary care

physician because she could not find one that was accepting patients. After a change in health

status, she decided to put more effort into the search. She “phoned all 84 doctors who were listed

as practising within 10 kilometres of [her] home.” Every single physician rejected her. Finally,

after months of searching, a new clinic opened. The clinic was far from her home – 17 km – but

was accepting new patients. Ms Galloway went in person to register on opening day. She found

hundreds of people in line, but waited regardless (Galloway (2011)). It was the only option.

In this chapter, I use medical care utilization data to study access to care. Utilization is deter-

mined by both access and patient preferences. To measure access, I must account for preferences.

Ms. Galloway’s story illustrates this challenge. The data reflect only that Ms. Galloway did not

go to the physician for a span of time, then went to a physician who was 17 km away. Without

imposing further structure, the data analyst cannot determine whether these outcomes were driven

by low access to care.

I exploit observed matching patterns between patients and physicians to parse out the effects of

access to care and patient preferences for care. For example, I can attribute a difference between

1. This study made use of de-identified data from the ICES Data Repository, which is managed by the Institutefor Clinical Evaluative Sciences with support from its funders and partners: Canada’s Strategy for Patient-OrientedResearch (SPOR), the Ontario SPOR Support Unit, the Canadian Institutes of Health Research and the Government ofOntario. The opinions, results and conclusions reported are those of the authors. No endorsement by ICES or any of itsfunders or partners is intended or should be inferred. Parts of this material are based on data and information compiledand provided by CIHI. However, the analyses, conclusions, opinions and statements expressed herein are those of theauthor, and not necessarily those of CIHI.

1

regions in the share of patients who see a doctor to lower in access to care if, ceteris paribus, one

region has lower physician supply. In practice, the exercise is complicated by interactions between

regions, heterogeneous patients and physicians, and competition among market participants.

I take each of these factors into account. To do so, this chapter measures access to care as an

equilibrium outcome of a matching market between patients and physicians. Access to care is

defined as the share of patients who would attain care in a full access environment who already

attain care in the current equilibrium. Patients have heterogeneous preferences over physicians and

physicians have heterogeneous preferences over patients. I assume that observed matchings are

generated by a Rationing-by-Waiting equilibrium, which was introduced in the theoretical matching

literature by Galichon and Hsieh (2019). In a Rationing-by-Waiting equilibrium, the market is

cleared without prices by adjusting the effort it takes for one side of the market to match with the

other side. Patients, for example, must expend effort by waiting on wait lists or frequently calling

physicians in order to attain care.

The empirical setting is the primary care market in Northern Ontario, Canada. This setting has

several attractive features for the study of access to care. First, patients face zero user fees. Thus,

prices are exogenous to the equilibrium matching. Second, distinct markets for primary care can

be easily defined in Northern Ontario. Almost all primary care is provided by family physicians,

private practice is rare, and markets are geographically isolated. Third, the province makes detailed

deidentified billings data available to researchers. The main dataset consists of a panel of patient and

physician-level observations, importantly including measures of health and healthcare utilization,

physician characteristics, and patient-physician matches from 2004-2014.

Additionally, Northern Ontario contains rich variation in policies intended to increase access

to care. These allow me to trace out physician preferences and provide interesting settings for

policy counterfactuals. Specifically, the Ontario government implemented reforms to how they pay

primary care physicians from 2002 to 2006. The reforms introduced alternative payment models

for family physicians, including capitation payment models and enhanced fee-for-service payment

models. Alternative payment models are voluntary: family physicians are at liberty to participate

2

in any payment model they qualify for. The alternative payment models increased the average

revenue a physician received per visit, incentivizing physicians to accept more patients. Additionally,

both alternative payment models have capitation components (payments per patients regardless of

utilization). The capitation payments are coarsely risk-adjusted. Therefore, the alternative payment

models increased the incentive for physicians to select patients based on their characteristics. In the

empirical specification, I account for selection into payment models by modeling physician choice

behavior.

Access to care is defined as the probability that a patient who would attain care in a full access

environment already attains care in the current equilibrium. Defining a full access environment is

subjective. In the main specification, I define a full access environment as the hypothetical choice

conditions that patients would face if they lived in the largest city in Northern Ontario, Sudbury, and

all physicians in Sudbury were accepting patients. Sensitivity analyses are conducted by comparing

results under alternative definitions of full access. For ease of exposition, I define access loss as

1 − access, or the share of patients who would attain care in the full access environment who do not

attain care in the current equilibrium.

This chapter uses the proposed measure of access to care in the empirical setting. First, I show

the distribution of access to care across regions and patient types in Northern Ontario in 2014.

Second, I decompose estimated access loss into its determinants.

Access loss is large and unequally distributed. I find that average access loss for patients in 2014

is 27%. Healthier, younger, and more rural patients have higher access loss than sicker, older, and

more urban patients. Rural patients with no comorbidities and aged 0-34 have access loss of 51%,

while urban patients with comorbidities and aged 65+ have access loss of 5%. Competitive effects

drive the access loss of younger and healthier patients. I find that physicians discriminate in favor

of patients with higher expected utilization. This makes it harder for healthier and younger patients

to attain care.

The determinants of access loss vary by type of patient. In urban and semi-urban areas, access

loss is primarily driven by capacity constraints of physicians. I estimate that if physicians had

3

enough capacity to accept all patients, urban access loss would fall from 13% to 2%. In rural areas,

physician capacity constraints explain less of the access loss. Removing capacity constraints would

change access loss from 44% to 33% in rural areas. The remaining access loss is primarily caused

by distances needed to travel to a physician.

Related Literature

This chapter contributes to two main literatures. First, I advance the literature on measuring

access to care and decomposing the determinants of access to care by accounting for equilibrium

impacts. Second, I contribute to the literature on estimating decentralized non-transferable utility

(NTU) empirical matching models by applying a recent theoretical advancement to an empirical

setting.

The first set of results in this chapter describe the distribution of access to care across patient

characteristics and geography. The literature on measuring the distribution of access to care is wide

and interdisciplinary.

Measuring the distribution of access across patient characteristics is complex. Without estimat-

ing patient preferences, it is difficult to compare access across patient characteristics, as patient

characteristics are highly correlated with whether a patient wants to attain care. Thus, research on

this topic is sparse. An important exception is the body of literature that studies the distribution

of access to care across socioeconomic status. This work focuses on determining the extent to

which patients with the same healthcare needs receive different levels of healthcare (Wagstaff, Van

Doorslaer, and Paci (1991), Kakwani, Wagstaff, and Van Doorslaer (1997), and Pulok et al. (2020)).

Rather than estimate patient preferences for care, the literature uses regression techniques to decom-

pose healthcare utilization into utilization explained by health needs and utilization explained by

non-need factors. The object of interest is a measure similar to the Gini index for income inequality:

a horizontal inequity index (HI). In this chapter, I describe inequality of access across patient types.

Further, I estimate an absolute measure of access in contrast with the relative measures provided by

the horizontal inequity literature.

4

This chapter also contributes to the literature on measuring access across geographic space.

The matching model used in this chapter, although methodologically distinct, is related to gravity

models used by public health scholars to measure the spatial distribution of access. Gravity models,

such as the two-stage floating catchment model, define access as the ratio of supply to demand.

Supply (demand) in each location is determined by the observables of physicians (patients). Supply

and demand are redistributed according to a distance decay function such that patients demand

nearby physicians at higher rates than distant physicians (Luo and Wang (2003), Luo and Qi (2009),

McGrail and Humphreys (2015), and Kim, Byon, and Yeo (2018)).

The empirical matching model used in this chapter similarly allows demand to decay according

to distance and uses patient and physician characteristics to estimate supply and demand. However,

the matching model allows me to estimate the decay function rather than pre-specifying it. Further,

the matching model allows for greater complexity in access patterns. My measure of access to care

can be heterogeneous across patients in the same location and provides insight into the determinants

of access to care. However, the empirical matching model is more demanding than gravity models

in terms of computational complexity and data needs.

Secondly, this chapter adds to the empirical literature on decentralized matching markets

with non-transferable utility. Most empirical applications of decentralized non-transferable utility

matching markets use centralized non-transferable utility techniques to clear the market, then

estimate by simulated moment matching or analogous Bayesian techniques (Hitsch, Hortaçsu, and

Ariely (2010), Boyd et al. (2013), Vissing (2017), Agarwal (2015), and Matveyev (2013)). They

assume that equilibrium matchings are pairwise stable. However, pairwise stable equilibria are

generally not unique, so practitioners further assume that matchings are generated by a process

that mimics a centralized matchmaker’s algorithm, such as the Simulated Gale-Shapley deferred

acceptance algorithm. Simpler algorithms can be used when one side of the market is assumed to

have vertical preferences (Agarwal (2015) and Gazmuri (2019)).

By applying recent developments in the theoretical matching literature to an empirical applica-

tion, this chapter estimates a non-transferable utility matching model without imposing the deferred

5

acceptance algorithm. In doing so, I avoid the drawbacks of using the deferred acceptance algorithm.

Namely, the deferred acceptance algorithm is computationally demanding, potentially making

estimation intractable in markets with many participants, such as the Northern Ontario primary care

market. Further, the deferred acceptance algorithm has the unattractive feature that it allocates dif-

fering utilities in equilibrium to observably identical agents. Additionally, the Rationing-by-Waiting

equilibrium allows for estimating equilibrium effort costs – an object of interest. These effort costs

reflect the degree of rationing that takes place in the market due to physician capacity constraints.

Thus, they can be used to estimate the impact of capacity constraints on access.2

1.2 Access To Care in Equilibrium

Many people in Northern Ontario do not attain primary care. This is the outcome of a market for

primary care in equilibrium. To provide insight on how much this is determined by lack of access

and what mechanisms impact access to care, I present a model of the market for primary care. To

mirror the conditions of Northern Ontario, the market is cleared by a non-price mechanism: the

effort it takes for a patient (physician) to match with a physician (patient).

1.2.1 Equilibrium Outcomes

Figure 1.1 shows the percent of Northern Ontarians in 2014 who did not see a comprehensive

care primary care physician. 40% of the population do not attain care. As expected, younger and

healthier populations are less likely to attain care. Rural Ontarians are less likely to attain care than

their urban counterparts. By themselves, these results do not imply that access to care is low. To

determine whether patients do not attain care due to low access to care, we must account for patient

preferences.

2. A related literature focuses on estimating demand with unobserved capacity constraints. Goeree (2008), forexample, models the probability that a personal computer is in a consumer’s choice set at the time of a choice. Thismethodology could be used to model the probability that a physician is willing to accept a patient. Palma, Picard, andWaddell (2007) showed that this demand system could equivalently be modeled as consumers paying equilibrium effortcosts to attain capacity constrained goods, such as apartments in Parisian neighborhoods. Other studies of demand withcapacity constraints use data to determine bounds on capacity (Conlon and Mortimer (2013)) or choice sets (Gaynor,Propper, and Seiler (2016)).

6

Figure 1.1: Percent of Patients Who Do Not See a Primary Care Physician in 2014

(a) Healthier Patients (b) Sicker Patients

Survey evidence suggests that access to care does contribute to the high percentage of people

who do not attain care. In 2014, 56.1% of Canadians who stated that they did not have a regular

doctor attributed it to low access. They stated that either no doctor in their area was taking new

patients, their doctor had retired or left the area, or there were no doctors in their area (Statistics

Canada (2007)). In 2005, a survey found that only 11.4% of physicians were accepting new patients

in Ontario (News Staff (2006)). In 2017, 14.5% of patients in Ontario stated that they had to wait 8

days or longer to see their doctor. Waiting times are worse in Northern Ontario. 40.7% of patients

in the North West and 36.4% of patients in the North East reported wait times over 8 days (Health

Quality Ontario (2018)).3

1.2.2 A Simplified Model: Effort as a Non-Price Market Clearing Mechanism

This section presents a simplified model of supply and demand in a market with non-price

rationing. This model provides a stylized representation of how insufficient supply lowers access to

care. It also presents the main methodological concepts used in the rest of this chapter.

3. North East and North West refer to Local Integration Health Networks.

7

I define patient demand as the number of patients who demand care. Patient demand depends

on the characteristics that define the market 𝑿,𝒀 and the amount of effort a patient must expend

in order to attain care 𝜏𝑢. Effort 𝜏𝑢 only includes effort spent in the search process to attain care.

Market characteristics include the locations and characteristics of patients, 𝑿, and the locations and

characteristics of physicians, 𝒀 . The effort a patient expends to attain care 𝜏𝑢 can be interpreted as

waiting time, though other forms of effort may be present. It is assumed that demand is downward

sloping in 𝜏𝑢.

Supply is similarly defined as a function of market characteristics and the amount of effort

it takes a physician to attract one patient 𝜏𝑣. The effort a physician expends can be interpreted

as advertising costs, though this object can represent many different types of effort. Supply is

downward sloping in 𝜏𝑣.

Demand: 𝑄𝐷 = 𝐷 (𝜏𝑢; 𝑿,𝒀)

Supply: 𝑄𝑆 = 𝑆(𝜏𝑣; 𝑿,𝒀)

In equilibrium, two conditions hold. First, effort costs are such that the market clears. Second,

only one side of the market expends effort to match with the other. That is, if patients are expending

effort to match with physicians, then physicians are not expending effort to attract patients. In the

context of a waiting line, the intuition is clear. A line of patients forms. Physicians arrive at the line,

taking patients one at a time. If the rate of physician arrival exceeds the rate of patient arrival, then

the line of patients is soon replaced with a line of physicians waiting for patients to arrive.

Market Clearing: 𝑄𝐷 = 𝑄𝑆

One-Sided Effort Condition: 0 = 𝑚𝑖𝑛{𝜏𝑢, 𝜏𝑣}

Figure 1.2 presents the model graphically. To do so, I define net patient effort 𝜏 as the difference

8

between the effort expended by patients and the effort expended by physicians, 𝜏 = 𝜏𝑢 − 𝜏𝑣.

Importantly, transfers do not exist in this market. Physicians do not attain utility when patients

expend effort. Therefore, when physician capacity constraints are binding and 𝜏 > 0, supply is

perfectly inelastic with respect to net patient effort. Similarly, demand is perfectly inelastic with

respect to net patient effort when all patients who want care are receiving it. Thus, in all equilibria,

either physicians are operating at full capacity and patients are expending effort, or all patients who

want care are receiving care and physicians are expending effort.

Figure 1.2: Supply and Demand with Non-Price Market Clearing

(a) Patients Expend Effort

0

𝜏∗

𝜏

𝑄∗𝑄𝜏𝑢=0 𝑄

𝑆(𝜏)

𝐷 (𝜏)

(b) Physicians Expend Effort

0

𝜏∗

𝜏

𝑄∗ 𝑄

𝑆(𝜏)

𝐷 (𝜏)

Shifts in Supply are Correlated with Shifts in Demand

When physician locations and characteristics change, both supply and demand are affected.

Take, for example, the entry of a new physician into a town that previously did not have a doctor. The

entrant physician increases supply. Additionally, in the town where the entry occurred, patients have

expanded willingness to expend effort. The value of the care offered is higher now for these patients,

thus shifting demand. Other forms of changes in physician characteristics only affect supply. For

example, if an individual physician increases their capacity, the demand curve is unaffected.

Figure 1.3 presents a shift in supply and demand graphically. Allow a change in physician

9

characteristics from 𝒀 to 𝒀′. Demand then shifts from 𝐷 (𝜏) = 𝐷 (𝜏; 𝑿,𝒀) to 𝐷′(𝜏) = 𝐷 (𝜏; 𝑿,𝒀′)

and supply shifts from 𝑆(𝜏) = 𝑆(𝜏; 𝑿,𝒀) to 𝑆′(𝜏) = 𝑆(𝜏; 𝑿,𝒀′). Both shifts expand the number of

patients who attain care.

Figure 1.3: An Increase in Supply

0

𝜏∗

𝜏∗′

𝜏

𝑄∗𝑄𝜏𝑢=0 𝑄∗′

𝑆(𝜏) 𝑆′(𝜏)

𝐷 (𝜏) 𝐷′(𝜏)

Access to Care

I define access to care as the share of patients who would attain care in a full access environment

who already attain care in the current equilibrium. Access loss is defined as the share of patients

who would attain care in a full access environment who do not attain care in the current equilibrium.

In terms of model outputs, these objects are defined:

Access to Care =𝑄∗

𝑄𝐹𝐸

Access Loss =𝑄𝐹𝐸 −𝑄∗

𝑄𝐹𝐸

Where 𝑄𝐹𝐸 is the equilibrium number of patients who attain care under market characteristics

𝑿,𝒀𝐹𝐸 and 𝑄∗ is the equilibrium number of patients who attain care under the current market

characteristics.

In a market with non-price rationing, insufficient supply lowers access to care through two

10

mechanisms. First, in environments with insufficient supply, doctors are few and far between.

Patients must travel long distances to the nearest physician’s office and patients have difficulties

finding a physician who fits their needs. This decreases patient willingness to go to a doctor. Second,

insufficient supply makes it harder to attain care. Physicians are at capacity and thus cannot take on

any more patients. Care must be rationed. Patients face long waiting times for appointments, long

waiting lists to get on doctor’s rosters, and frustrating searches for physicians who are accepting

patients.

Using the simplified model, access loss can be graphically decomposed into its two mechanisms.

The effects of rationing-by-effort costs can be interpreted as the share of patients who do not attain

care because the effort it would take to attain care is greater than their willingness to expend effort,

𝑄𝜏𝑢=0−𝑄∗

𝑄𝐹𝐸. This effect could also be interpreted as the impact of physician capacity constraints on

access loss. As alluded to above, increasing capacity of existing physicians shifts the supply curve

but not the demand curve. Thus, removing physician capacity constraints would lead to a shift in

supply sufficient to allow all patients who want care to attain care. The remainder of access loss,

𝑄𝐹𝐸−𝑄𝜏𝑢=0

𝑄𝐹𝐸, can be attributed to the sparsity of the geographic distribution of physicians.

1.2.3 Complicating the Model: Heterogeneous Effort Costs

This simple model is complicated by the fact that not all patients face the same effort to attain

care. Physicians discriminate between patients, making it easier for some patients to attain care and

harder for others. Additionally, local variation in market characteristics affect effort.

Physicians discriminate between patients. Altruistic tendencies of physicians cause some

discrimination (Hennig-Schmidt, Selten, and Wiesen (2011)). Physicians prefer to treat patients

who need care and will provide special accommodations for those in particular need (McGuire

(2000)). This behavior, called positive prioritization by Gravelle and Siciliani (2008), can be

explained by a model of physician agency, where physicians treat patients with the highest expected

benefit of treatment until their capacity is reached. Under a general set of assumptions, positive

prioritization is welfare improving relative to non-discriminatory rationing (Iversen and Siciliani

11

(2011)).

Physicians may also discriminate to attain more profitable patients. The literature is large and

mixed on this topic.4 The implications for discrimination based on profitability depends on the

specifics of how physicians are paid. If physicians are paid by a fee-for-services model, physicians

will discriminate in favor of patients who are expected to attain high margin services. If physicians

are paid by capitation models, physicians will discriminate in favor of low-cost patients, conditional

on risk-adjustments.

In addition to physician discrimination, heterogeneity in patient effort arises from local variation

in market characteristics. Primary care physicians are distributed unevenly across geographic space

(Green et al. (2017)). Further, physician practices are very heterogeneous in size (see Figure A.3).

Thus, two identical patients in neighboring towns may face very different market conditions.

Importantly, however, the towns cannot be treated as separate markets, as patients are willing to

travel for care.

These complications suggest a natural extension of the simple model. Assume that patients

can be split into discrete types \ ∈ Θ. Types can be determined by health needs, location, and

other characteristics. A type \ patient must expend effort 𝜏𝑢\ 𝑗

to match with physician 𝑗 . Patients

choose among the physicians for whom their willingness to exert effort is greater than the effort cost.

Symmetrically, physician 𝑗 chooses patients according to their preferences and the effort costs 𝜏𝑣\ 𝑗

.

Define `\ 𝑗 to be the number of patients \ who attain care from physician 𝑗 . Supply and demand

can be written as a function of effort costs and market characteristics.

Demand: `𝐷\ 𝑗 = 𝐷\ 𝑗 (𝜏𝑢\ 𝑗 ; 𝝉𝑢\− 𝑗 , 𝑿,𝒀)

Supply: `𝑆\ 𝑗 = 𝑆\ 𝑗 (𝜏𝑣\ 𝑗 ; 𝝉

𝑣−\ 𝑗 , 𝑿,𝒀)

4. In the US, studies have found that both primary care physicians and hospitals select more profitable patients(Benson (2018) and Alexander (2020)). In the primary care market of Ontario, studies have found limited evidence ofselection (Rudoler et al. (2016) and Kantarevic and Kralj (2014)).

12

As before, an equilibrium exists when the market is cleared and the one-sided effort conditions

hold.

Market Clearing: `𝐷\ 𝑗 = `𝑆\ 𝑗 ∀\, 𝑗

One-Sided Effort Condition: 0 = 𝑚𝑖𝑛{𝜏𝑢\ 𝑗 , 𝜏𝑣\ 𝑗 } ∀\, 𝑗

1.2.4 A Note on Markets with Prices and Non-Price Rationing

Before turning to the matching model, it is useful to comment on the relationship between

prices and access to care in the context of this model. In markets where prices are flexible, they

may adjust to stimulate supply.5 In the United States, for example, family medicine physician

wages are 6% higher in non-metropolitan areas than metropolitan areas6, suggesting some role for

price adjustments in increasing supply (Lee (2010) and Newhouse et al. (1982)). However, even in

the multi-payer system of the US, over 39% of physician and clinical service expenditures are by

large public payers (CMS (2019)).7 Medicare, which accounts for 24% of expenditures, sets prices

according to input costs and the value of physician effort. Prices vary geographically according

to differences in the cost of supplying care, not the level of access (Chan and Dickstein (2019)),

except for periodic targeted add-ons (Mroz, Patterson, and Frogner (2020)).8 Further, Medicare’s

price setting practices influence prices paid by private payers (Clemens and Gottlieb (2017)).

In this chapter’s empirical setting – Ontario, Canada – prices are inflexible and set by the

5. Of course, prices add an additional mechanism through which access is restricted. Indeed, much of the literatureon access in the United States focuses on the negative impact of prices on access to care. As the focus of this chapter ison markets without flexible prices, I do not wade into the argument on the relative merits of regulated prices for accessto care.

6. Author’s calculation using BLS Occupational Employment Statistics (U.S. Bureau of Labor Statistics (2019)).Average wages in metropolitan and non-metropolitan areas are calculated as weighted averages of annual wages,weighted by employment. 48 areas have low numbers of employment (below 30). Employment for these areas isassumed to be 15. If these low employment areas are removed, non-metropolitan wages are found to equal 6.31%.

7. In 2018, 8.4% of physician and clinical services expenditures were out-of pocket payments. 43% were privateinsurance payments, 23.5% Medicare, 10.7% Medicaid, 4.8% Other federal Health Insurance Programs, and 9.7% otherthird party payers, some of which are also funded with federal funds.

8. The adjustments based on geography, Geographic Adjustment Factors, are negatively correlated with rurality, buthave not been found to be correlated with survey measures of access to care for Medicare beneficiaries (Committee onGAFs (2011)).

13

government at the provincial level. Globally, inflexible prices are the norm. Of the 29 countries in a

2009 OECD report, only 5 were found to have some aspect of primary care prices negotiated at the

local level (Paris, Devaux, and Wei (2010)). Without flexible prices, insufficient supply necessitates

rationing by other means. In medical care markets without a centralized rationing system, services

are distributed according to effort: those willing and able to wait in long lines or spend time calling

physicians are those who attain services (Iversen and Siciliani (2011)).

1.3 Matching Model: Patient and Physician Matching

This section formalizes the model described in section 2 using theory from the non-transferable

utility matching market literature. It follows a modified version of the Rationing-by-Waiting

framework developed by Galichon and Hsieh (2019).

1.3.1 Patient and Physician Preferences

Patients are indexed by 𝑖 and are members of a patient type, \ ∈ Θ𝑡 . Patients of type \ share

observable characteristics and location. Patient type \ has 𝑛\𝑡 members in market 𝑡. Physicians are

indexed by 𝑗 ∈ J𝑡 . Each physician can match with a maximum of 𝑚 𝑗 𝑡 patients in market 𝑡, which

varies by physician. I call this the physician’s panel capacity.

Patients derive utility from matching with physician 𝑗 in market 𝑡 as a function of distance 𝑑\ 𝑗𝑡

and match observables 𝒙\ 𝑗𝑡 . Match observables are physician characteristics, patient characteristics,

or interactions. Lastly, each patient 𝑖 of type \ has an additive taste shock, 𝜖𝑖\ 𝑗 𝑡 , for physician 𝑗 in

market 𝑡. Without loss of generality, patients derive zero mean latent utility if they do not match

with a physician. I use the empty set index to denote a match with no physicians.

𝑢𝑖\ 𝑗 𝑡 = 𝑢(𝑑\ 𝑗𝑡 , 𝒙\ 𝑗𝑡) + 𝜖𝑖\ 𝑗 𝑡

𝑢𝑖\∅𝑡 = 𝜖𝑖\∅𝑡

Physicians derive utility independently from each potential space in their patient panel, 𝑞 ∈

14

{1, ..., 𝑚 𝑗 𝑡}. The utility a physician derives from matching in panel space 𝑞 with a patient of type \

in market 𝑡 depends on observables 𝒚\ 𝑗𝑡 . These observables are a function of patient and physician

characteristics. Physicians have an additive taste shock, [\ 𝑗𝑞𝑡 , for each panel space 𝑞, patient type

\, and market 𝑡.

𝑣\ 𝑗𝑞𝑡 = 𝑣(𝒚\ 𝑗𝑡) + [\ 𝑗𝑞𝑡

𝑣∅ 𝑗𝑞𝑡 = [∅ 𝑗𝑞𝑡

Note that the model does not allow physicians to have idiosyncratic taste shocks over individual

patients. Physician latent utility is constant over all patients in the same patient type. This

assumption is common in the transferable utility matching literature (Choo and Siow (2006)), is

fairly reasonable in the empirical application, and provides the basis of a tractable functional form

of match probabilities between patient and physician types.

1.3.2 Markets and Matchings

A market is defined by the characteristics and preferences of patients and physicians, the

number of patients of each type, 𝑛\𝑡 , and each physician’s panel capacity, 𝑚 𝑗 𝑡 . If preferences can

be parameterized by a vector 𝜷, then a market is formally a tuple (𝜷, 𝒏𝑡 ,𝒎𝑡 , 𝑫𝑡 , 𝑿𝑡 ,𝒀𝑡) where

𝒏𝑡 = {𝑛\𝑡}∀\ , 𝒎𝑡 = {𝑚 𝑗 𝑡}∀ 𝑗 , 𝑫𝑡 = {𝑑\ 𝑗𝑡}∀\ 𝑗 , 𝑿𝑡 = {𝒙\ 𝑗𝑡}∀\ 𝑗 , and 𝒀𝑡 = {𝒚\ 𝑗𝑡}∀\ 𝑗 .

A matching, `𝑡 , defines which type of patients are matched with which physicians. Formally, a

matching is a measure over the set of patient types and the set of physicians.

`𝑡 : {Θ𝑡 , ∅} × {J𝑡 , ∅} → N

𝑠.𝑡.∑︁

𝑗∈{J𝑡 ,∅}`𝑡 (\, 𝑗) = 𝑛\𝑡∑︁

\∈{Θ𝑡 ,∅}`𝑡 (\, 𝑗) = 𝑚 𝑗 𝑡

The realization of a matching at a point (\, 𝑗) is the number of patients of type \ that are matched

15

with physician 𝑗 .

1.3.3 Equilibrium

Stability

Most of the decentralized non-transferable utility matching market literature focuses on stable

matchings. A matching is stable if:

1. No patient prefers to be unmatched than be matched with their current physician.

2. No physician prefers to leave a panel space empty that is currently occupied by a patient.

3. No patient and physician in one panel space would both prefer to match with each other than

keep their current matches.

The assumption that matchings are stable in a decentralized market is justified by Adachi (2003).

Adachi shows that a realistic dynamic search model, as search costs converge to 0, produces a set of

equilibria that coincides with the set of stable equilibria in a corresponding matching model.

Existing Methods to Predict a Unique Matching

The stability assumption alone does not predict a unique matching, which is needed for point-

identified estimation techniques. The empirical literature tends to use the Gale-Shapley deferred-

acceptance (DA) algorithm to choose a unique matching from the set of stable matchings (Gale and

Shapley (1962)). Hitsch, Hortaçsu, and Ariely (2010) show that the DA algorithm performs well

predicting outcomes in the online dating market.

Though conceptually simple, using the DA algorithm as an equilibrium concept has drawbacks.

First, the DA algorithm chooses a stable matching which is optimal for one side of the market. This

assumption can affect welfare predictions. Second, the DA algorithm is computationally demanding.

If used within an estimation routine, the algorithm must be run many times at each iteration of

the optimization algorithm. In a large market such as the Ontario primary care market, this can

16

be intractable (Chiappori and Salanie (2016); See Hsieh (2012) for a discussion). Third, the DA

algorithm has the unattractive feature that it allocates differing equilibrium utilities to observably

identical agents.

Alternatives to the DA algorithm to model decentralized markets have relied on assumptions

of very large markets and/or strictly vertical preferences on one side of the market (Azevedo and

Leshno (2016), Agarwal (2015), Gazmuri (2019), and Menzel (2015)).9 Such assumptions are

unreasonable in the Ontario primary care market. Markets in less populated parts of Northern

Ontario are not large. Physician preferences are horizontal, as physicians are paid under varying

payment models and homophily in age and sex are possible.

The Rationing-By-Waiting Equilibrium

I employ the Rationing-by-Waiting equilibrium concept proposed by Galichon and Hsieh (2019)

to predict unique matchings. To my knowledge, I am the first to apply this equilibrium concept to

an empirical setting. I first present the equilibrium concept, then I discuss its attributes.

Definition: Rationing-By-Waiting Equilibrium

A tuple (`𝑡 , 𝝉𝑣𝑡 , 𝝉𝑢𝑡 ) is a Rationing-by-Waiting Equilibrium if

`𝑡 : {Θ, ∅} × {J , ∅} → N ∀𝑡 (1.1)

𝑠.𝑡.∑︁𝑗

`\ 𝑗𝑡 + `\∅𝑡 = 𝑛\𝑡 ∀\∀𝑡 (1.2)∑︁\

`\ 𝑗𝑡 + `∅ 𝑗 𝑡 = 𝑚 𝑗 𝑡 ∀ 𝑗∀𝑡 (1.3)

`\ 𝑗𝑡 = 𝑛\𝑡𝑃(𝑢\ 𝑗𝑡 − 𝜏𝑢\ 𝑗𝑡 > 𝑢\ 𝑗 ′𝑡 − 𝜏𝑢\ 𝑗 ′𝑡 ∀ 𝑗

′ ≠ 𝑗 ∧ 𝑢\ 𝑗𝑡 − 𝜏𝑢\ 𝑗𝑡 > 𝑢\∅𝑡) (1.4)

= 𝑚 𝑗 𝑡𝑃(𝑣\ 𝑗𝑡 − 𝜏𝑣\ 𝑗𝑡 > 𝑣\ ′ 𝑗 𝑡 − 𝜏𝛾

\ ′ 𝑗 𝑡 ∀\′ ≠ \ ∧ 𝑣\ 𝑗𝑡 − 𝜏𝑣\ 𝑗𝑡 > 𝑣∅ 𝑗 𝑡) ∀\∀ 𝑗∀𝑡

𝑚𝑖𝑛(𝜏𝑢\ 𝑗𝑡 , 𝜏𝑣\ 𝑗𝑡) = 0 ∀\∀ 𝑗∀𝑡 (1.5)

9. Agarwal (2015) and Gazmuri (2019) impose a vertical preferences assumption, Menzel (2015) assumes infinitelylarge markets, and Azevedo and Leshno (2016) assume both.

17

`𝑡 is a matching in market 𝑡. `\ 𝑗𝑡 is shorthand for number of matches `𝑡 (\, 𝑗). 𝜏𝑢\ 𝑗𝑡 ∈ 𝝉𝑢𝑡 is the

additive effort cost (in utils) that a patient of type \ must incur to match with physician 𝑗 . 𝜏𝑣\ 𝑗𝑡

∈ 𝝉𝑣𝑡

is the effort cost that physician 𝑗 must incur to match with a patient of type \. The interpretation of

effort costs is discussed in Section 1.2.

Equations 1.1,1.2, and 1.3 define a matching. Equation 1.4 is the market clearing condition. In

equilibrium, the number of patients of type \ who choose physician 𝑗 must be equal to the number

of patients of type \ that physician 𝑗 chooses. Equation 1.5 is the one sided waiting condition:

either patients of type \ wait for physician 𝑗’s spaces or physician 𝑗 waits for patients of type \.

Rationing-by-Waiting equilibria are stable and unique (see Section A.5).10 Therefore, the

assumption that matchings are produced by Rationing-by-Waiting equilibria allows for point-

identified estimation of preferences. Further, computing a Rationing-by-Waiting equilibrium is

computationally easier than implementing the DA algorithm and it allows for the estimation of

equilibrium effort costs, which provide the basis of a method to determine the impact of physician

capacity constraints on patient access.

1.4 Empirical Setting: Primary Care in Northern Ontario

Northern Ontario was chosen as the empirical setting of this chapter for three reasons. First,

the prices that are paid to physicians are known and patients face zero user fees. Prices are

therefore exogenous to the matching process. Second, primary care markets are easy to define, both

according to physician specialties and geography. Lastly, reforms to physician payment models are

advantageous for this research. These policy reforms provide variation that helps identify physician

preferences over patients. Specifically, it provides quasi-exogenous variation in the revenue that

a physician would attain from matching with a patient. By exploiting this variation, I am able to

separately identify physicians preferences for the revenue a patient would provide and the patient’s

expected utilization of services.

The remainder of this section details the institutional environment of primary care in Northern

10. See Galichon and Hsieh (2019) for a detailed discussion of the Rationing-by-Waiting equilibrium’s properties.

18

Ontario then discusses the data used in the analysis.

1.4.1 Institutional Background

Zero User Fees

Primary Health Care in Ontario is a single payer, private practice system. The Ontario Health

Insurance Plan (OHIP) pays for all diagnostic and physician services that are deemed necessary

care. There are zero user fees for these services. The services are financed through provincial and

federal income taxation. Pharmaceutical and non-essential services are not covered by the single

payer. They are often funded by private insurance (Marchildon (2013) and Glazier et al. (2019)).

Definable Markets

An insignificant private primary health care market exists alongside the publicly funded market.

Private payment for necessary care is illegal, except in special circumstances (Ontario Legislature

(2004)). Users of the private primary health care system must pay out-of-pocket (Starfield (2010)).

Primary care clinics that sell access are rare in Ontario. There were 7 so-called “boutique” clinics in

2007 and 6 in 2017 (Mehra (2008, 2017)). None of these clinics are in Northern Ontario.11

Primary care in Ontario is provided almost exclusively by family physicians, with the exception

of some pediatricians and nurse practitioners. Unlike in the United States, internists “rarely provide

primary care, as they’re trained to be hospitalists and subspecialists” (Bernstein (2013)). Geria-

tricians, likewise, do not provide primary care services (Frank and Wilson (2015)). Pediatricians

are “encouraged to pursue subspecialties and act as ’consultants’ instead of providing primary care”

(Bernstein (2013)). In 2004, 30-40% of children’s primary care visits were to a pediatrician. These

visits were primarily in large urban areas outside of Northern Ontario (Canadian Paediatric Society

Public Education Subcommittee (2004)). Nurse Practitioners work alongside family physicians in

many primary care clinics. In these clinics, physicians are responsible for billing and the Nurse

Practitioners are salaried (NPAO (2020)). A small number of nurse practitioner-led clinics do exist

11. In 2017, all were in the highly urbanized Golden Horseshoe region.

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in Ontario in 2017, with the first such clinic opening in 2006 (College of Nurses of Ontario (2008)

and Heale and Butcher (2010)). Pediatricians who provide primary care and nurse practitioners

from nurse practitioner-led primary care clinics are excluded from the sample, as I am unable to

distinguish them from their non-primary care colleagues.

Alternative Payment Models

Before 2002, family physicians in Ontario were paid on a fee-for-service basis. For each service

provided (e.g. an office visit, a flu shot), a physician would attain a pre-specified fee from the

Ontario Health Insurance Plan (OHIP). From 2002 to 2006, the province introduced alternative

payment models for family physicians. Participation in alternative payment models is voluntary

and family physicians can participate in any payment model they qualify for. There were two main

categories of alternative payment models: capitation and enhanced fee-for-service. Section A.2

provides a detailed description of all alternative payment models.

Capitation payment models provide yearly and monthly payments for each patient on a physi-

cian’s roster, regardless of the services provided to the patient.12 These capitation payments are

risk-adjusted according to a patient’s sex and age in five-year bins. Physicians in capitation pay-

ment models are paid a fraction of the fee-for-service fee for a specified basket of services. Also,

physicians in capitation payment models receive bonuses for providing specific services to rostered

patients. The first capitation payment model was introduced in April 2002, and the most popular

capitation payment model was introduced in November 2006.

To incentivize physicians from rostering patients who do not actually go to their practice (and

go elsewhere), the capitation payment models have an “Access Bonus” structure: A physician group

is provided an access bonus of 18.59 percent of all capitation payments. If rostered patients receive

services from physicians outside of the group, the cost of those services are deducted from the

access bonus (Glazier et al. (2019)).

12. Note that I refer to the terms “panel” and “roster” to describe slightly different objects. A physician’s panel is allpatients who primarily go to that physician. A physician’s roster is all patients that are formally signed up to be thephysician’s patient. In the empirical work, these are assumed to be equivalent. They are, however, different with regardsto the institutional details.

20

Enhanced fee-for-service (EFFS) payment models provide small monthly capitation payments

for rostered patients and the same bonuses as physicians in the capitation models. In the more

popular enhanced fee-for-service model, physicians are paid fees that are 10% or 15% higher than

the fee-for-service fee for certain services provided to rostered patients. The most popular enhanced

fee-for-service payment model was introduced in October 2005 (Buckley et al. (2014a)).

The primary goal of these payment models was to increase access. Secondary goals were to

control costs and increase quality of care (Hutchison, Abelson, and Lavis (2001)). Physicians who

joined the alternative payment models are usually mandated to join as a group (at least 3 physicians),

though “physicians practicing in groups do not need to be co-located or share the same electronic

medical record” (Kiran et al. (2018)). This led to a decrease in solo practitioners from 37% in 2001

to 25% in 2010 (Hutchison and Glazier (2013)). As a group, physicians were expected to offer more

after-hours visit opportunities and provide more continuity of care.

Incentives Generated by the Alternative Payment Models

Alternative payment models increase the incentive for physicians to add patients and increase the

incentive for patient selection. Figure 1.4b illustrates both incentives. In this figure, the horizontal

axis is the expected utilization of a patient attaining care from a fee-for-service physician. The

vertical axis is the revenue a physician would expect to attain per patient visit. The curves describe

the relationship between expected number of visits and expected revenue per visit in each payment

model.13

The alternative payment models provide an incentive for physicians to expand their practices, as

long as physician supply is upward sloping in revenue. A physician attains more revenue per visit

from a patient if she is in an enhanced fee-for-service model or a capitation model, regardless of the

utilization of the patient.14 Physicians have a further incentive to decrease per-patient utilization in

order to expand the number of patients in the panel. These incentives are a feature of the alternative

13. In this analysis, I hold patient utilization fixed when comparing the payment models. Section A.1.5 describes howexpected number of visits and expected revenue is estimated.

14. An upward sloping supply curve cannot be assumed. Physicians may have backwards-bending supply curves ormay be unmotivated by financial incentive.

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payment models – the policymakers hoped they would increase access to care.

The alternative payment models also changed the incentive to differentially select patients.

Physicians in the alternative payment models are paid partially on a per-patient basis. These

capitation payments are risk adjusted on sex and five-year age bins. In the capitation payment

models, capitation payments make up the majority of physician revenue. Therefore, there is a large

incentive for physicians to select patients with low expected utilization, conditional on sex and age.

This can be seen graphically in Figure 1.4b. The slope of expected revenue per visit with respect to

expected utilization is particularly steep for the capitation payment model.

The details of the payment models imply that incentives for selection along other dimensions

exist. The access bonus structure of the capitation model provides an incentive for physicians

to select patients who are less likely to visit other physicians. The enhanced fee structure of the

enhanced fee-for-service model provides an incentive for physicians to select patients who are likely

to attain services that have higher margins. I account for these incentives in the model.

Figure 1.4: Alternative Payment Models

(a) Alternative Payment Models Over Time (b) Incentives For Selection and Expansion

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Selection into Alternative Payment Models

Physicians select into alternative payment models based on their characteristics and potential

revenue gains. Table 1.1 shows summary statistics of physicians in each payment model. Enhanced

fee-for-services physicians look roughly similar to fee-for-service physicians, with the exception

that they have more patients. Capitation physicians are younger, more likely to be female, have

older patients, and have more patients. Importantly, capitation physicians have patients who are

particularly profitable in a capitation payment model. This suggests either that physicians select

into capitation models based on the makeup of their patient panel, or that they select patients in

response to incentives that are built into the capitation model.

Table 1.1: Payment Model Selection Dataset Summary Statistics

Payment Model Capitation EFFS FFS

Number of Physician-Years (N) 3,750 1,389 712Age (mean (sd)) 49.30 (10.59) 51.00 (11.05) 50.65 (13.15)Male (%) 2496 (66.6) 1053 (75.8) 506 (71.1)Total Patients (mean (sd)) 816.86 (422.46) 1390.64 (749.27) 853.75 (575.53)Percent Patients over 50 (mean (sd)) 0.51 (0.13) 0.43 (0.13) 0.42 (0.17)Percent Female Patients (mean (sd)) 0.56 (0.09) 0.55 (0.08) 0.55 (0.10)Percent Pats W. Comorbids (mean (sd)) 0.25 (0.07) 0.24 (0.07) 0.23 (0.10)FFS Revenue per visit (mean (sd)) 29.54 (1.09) 28.99 (0.84) 29.34 (1.01)EFFS Revenue per visit (mean (sd)) 36.44 (1.65) 35.70 (1.22) 36.15 (1.49)CAP Revenue per visit (mean (sd)) 44.39 (4.82) 41.57 (3.33) 42.43 (4.26)Area Type (%)

Rural 1773 (47.3) 277 (19.9) 271 (38.1)Semiurban 1219 (32.5) 240 (17.3) 159 (22.3)

Urban 758 (20.2) 872 (62.8) 282 (39.6)Pay Model Last Year (%)

CAP 3001 (80.0) * *EFFS 153 (4.1) 1074 (77.3) *

FFS 596 (15.9) * *(>90)

Note: Statistics are calculated at the physician-year observation level. The sample used to create thistable is the sample used to estimate unobserved taste for revenue. It includes physicians in NorthernOntario from 2004-2015. ∗Excluded due to small bin sizes.

23

1.4.2 Data

The primary dataset used in this analysis is a panel of patient-physician matches at a yearly fre-

quency from 2004-2014. Data with information on patient characteristics, physician characteristics,

and location characteristics are also used in the analysis. These data were compiled from several

administrative datasets at the Institute of Clinical and Evaluative Sciences. In this subsection, I

describe the datasets used in the main analysis and present summary statistics. Section A.1 provides

more detail on how the datasets were constructed.

Patient Characteristics

Patient characteristics and patient-physician matches were collected from Ontario Health Insur-

ance Plan (OHIP) billings data. These data contain a record of every billable service provided to

patients in Ontario. From these data, I collect patient-level information on characteristics, comor-

bidities, and expected utilization. I also infer the number of patients who do not attain care from

census data.

The main analysis requires patient characteristics at the time that they make their choice of

physician. For characteristics that do not change over a year, these are taken to be the most common

value within the year. Location, however, may change in the year and is endogenous to the timing

of choice. I define the location of a patient to be the location they had when attaining services from

their matched physician in that year.15

Patient comorbidities are defined using the ICD-9 Royal College of Surgeons’ Charlson Co-

morbidity Mapping developed by Brusselaers and Lagergren (2017), with adjustments for the

small differences between the Ontario Health Insurance Plan diagnosis codes and ICD-9 codes.

Section A.1.2 provides details on how comorbidities are constructed.

Expected revenue and expected visits are estimated using risk-adjustment methodology (Kautter

et al. (2014)). Section A.1.5 details this estimation procedure.

I estimate the expected number of visits a patient will make to their physician conditional on

15. Precisely, the location is the most common location associated with billings with their chosen physician.

24

their comorbidities and characteristics. Expected visits are estimated assuming a patient has a

fee-for-service physician. For each patient, three estimated revenues are computed: one for each

payment model. Expected revenue is estimated as the expected revenue a physician would attain

from the patient, assuming that the patient’s utilization remains at fee-for-service levels.

Patients who do not attain any services are not observed in the data. I infer the number of these

patients from patient data in adjacent years and census data. First, patients who are absent from the

data in one year but attain services in adjacent years are added as patients who did not attain care.

Second, census data is used to infer the remaining unobserved patients. Census data provide counts

(up to the nearest 5 persons) of the number of persons for each location-age-sex category in the

years 2001, 2006, 2011, and 2016. For non-census years, I assume that the count is the weighted

average of the two closest census years. I subtract the number of patients in each location-age-sex

category that we observe in the data from the corresponding census counts to infer the number of

patients who did not attain care.

Patient types are discrete bins of patients based on characteristics. Characteristics that define

patient types are: age in 15-year bins, sex, location, whether the patient has a comorbidity, and

whether the patient is above or below a cutoff of expected revenue in a fee-for-service payment

model. I use the median expected revenue in the age, sex, location, comorbidity bin as the cutoff.

Table 1.5a presents the patient characteristics summary statistics. 20% of patients have a

comorbidity. 33% do not attain care in a given year. Patients provide more revenue for physicians in

the alternative payment models than in the fee-for-service system. There are 37,873 discrete patient

types, with an average of 230.2 patients in each type.

Physician Characteristics

Physician characteristics were collected from two datasets. The Corporate Provider Database

provides physician characteristics, including physician sex, age, specialty, group affiliations, and

locations. Physician payment models are from the Client Agency Program Enrolment dataset.

Physician choices are made at the “potential panel space” level 𝑞. For each potential panel

25

space, physicians choose a patient type or choose to leave the panel space open. The total number

of potential panel spaces, 𝑚𝑎𝑗, is unobserved in the data. I assume that the total number of potential

panel spaces for each physician is the maximum number of patients they have over all years. Lastly,

I calculate the number of potential panel spaces in market 𝑡, 𝑚 𝑗 𝑡 , by subtracting the number of

patients outside of market 𝑡 who match with the physician from 𝑚𝑎𝑗.

Physicians who match with less than 300 patients and physicians who are not comprehensive care

primary care physician are excluded from the sample. Table 1.5b provides physician characteristics

summary statistics of physicians in the sample. These summary statistics are broken out by

geographical market in Table A.8. Physicians have 1,170 patients and 4,894 visits per year on

average. Physicians who are in the sample for the entire 11-year panel make up most physician-year

observations.

Figure 1.5: Patient and Physician Summary Statistics

(a) Patient Summary Statistics

Summary Statistics

N 8,718,090N Types 37,873Male (%) 48.9Age (%)

0-14 16.115-34 23.535-49 20.550-64 22.0

65+ 17.9Has Comorbidity(mean (sd)) 0.20 (0.40)Revenue (mean (sd))

Capitation 175.41 (81.99)EFFS 147.50 (64.49)

FFS 119.63 (54.67)Area Type (%)

Rural 3,020,672 (34.6)Semiurban 2,482,297 (28.5)

Urban 3,215,121 (36.9)Unmatched (mean (sd)) 0.33 (0.47)

Unit: Patient-Year; Panel: 2004-2014

(b) Physician Summary Statistics

Summary Statistics

N 5,374Male (%) 70.1Age (mean (sd)) 49.82 (11.01)N Years in sample 10.31 (1.86)N Patients 1,169.51 (700.86)Unfilled Capacity 0.16 (0.16)Group Status (%)

Independent 15.8Multiple groups 10.3

One Group 73.9Payment Model (%)

CAP 62.8EFFS 24.6

FFS 12.6Area Type (%)

Rural 40.2Semiurban 27.7

Urban 32.2Visits (mean (sd)) 4,893.79 (3,175.55)Offers Walkins (%) 29.6

Unit: Physician-Year; Panel: 2004-2014

26

Matches and Drivetime

I define patient-physician matches using data on physician visits. Specifically, in each year,

a patient is matched to the physician with whom they have the most visits. A visit is defined

using billings data (detailed in Section 1.6.1). In the case of a tie, a patient matches with the

physician with whom their visits had the highest value.16 This selects physicians who provided

more comprehensive visits.17 This simple definition of a match was adopted to allow for a longer

panel and for sake of simplicity. When a more complex algorithm was used to determine matches,

results were similar.

The distance between a patient and physician is estimated as the population-weighted drive time

between their locations. Locations are known up to the census subdivision, which are municipalities.

Population-weighted average drive times between census subdivisions are derived using census

population data and the Bing Maps Distance Matrix API. Each census subdivision was split

into Canadian Census Dissemination Areas (DA). A dissemination area is the smallest standard

geographic area for Canada. Dissemination areas are loosely uniform in terms of population

(400-700 persons). Statistics Canada has calculated the representative point (latitude/longitude) of

population for each DA. I calculate the drive time between all DA representative points in a market.

The average drivetime between two census subdivisions is calculated as the population-weighted

average drivetime between all combination of DAs.

Match pattern summary statistics presented in Table 1.2 reflect preferences of patients and

physicians. The average drive time between patients and physicians is 17 minutes. The percent

of patients who attain care scale with urbanity, age, and number of comorbidities. Evidence of

homophily also exists: female patients are more likely to match with female doctors than male

patients.

16. Physicians who are more than 150 km away from a patient are excluded from the set of possible physicians tomatch with. Visits to those physicians are likely during temporary residence.

17. Visit value is the service fee associated with the visit fee codes, not the amount paid to the doctor. This insuresthat physicians in fee-for-service payment models are not selected at higher frequency.

27

Table 1.2: Matching Summary Statistics

Summary Statistics

Match ProbabilitiesN 8,718,090Rurality (N (% unmatched))

Urban 3,215,121 (26.50)Semi-Urban 2,482,297 (35.59)

Rural 3,020,672 (37.85)Age (N (% unmatched))

0-14 1,404,284 (43.90)15-34 2,045,868 (37.00)35-50 1,787,272 (34.44)51-64 1,916,392 (27.57)

65+ 1,564,274 (20.51)Comorbidities (N (% unmatched))

Without 7,007,826 (36.40)With 1,710,264 (19.19)

Match CharacteristicsMinutes Drive Time (mean (sd)) 17.23 (17.17)Female Physician (% of matches)

All Patients 24.57Female Patients 28.94

Unit: Patient-Year; Panel: 2004-2014

Geographic Markets

Geographic markets are defined to ensure that there is limited interaction between physicians

and patients outside of a geographic market. Population centers in Northern Ontario are fairly

isolated. Five primary care markets with little inter-market matching are defined. These markets

are the Kenora, Thunder Bay, Timmins, North Bay, and Sudbury regions. Figure 1.6 presents the

regions. The Kenora, Thunder Bay, and Timmins regions are the most isolated, while the Sudbury

and North Bay regions are less isolated. Table 1.3 describes how isolated each market is. Column 3

provides the share of matches that are between patients or physicians outside of the market.

28

Figure 1.6: Markets

Note: Some census subdivisions are removed from the sample due to data issues.Figure A.1 describes the reasons each were removed. The maps in the remainder ofthis chapter correspond to the shaded region. The Ottawa market is used in somespecifications to test the out-of-sample fit of the model. This map is built using 2006CSD geographies. Geographical boundaries will differ slightly from year to year.

Table 1.3: Matchings Within/Across Markets

% Connections

Market Name N CSDs In Market In Sample

Kenora 18 100.00 100.00Thunder Bay 19 99.84 99.98Timmins 35 99.22 99.85Sudbury 38 95.79 99.67North Bay/Parry Sound 40 94.04 97.42Ottawa 67 96.77 99.36

29

1.5 Specification

I specify the model to account for the primary determinants of matching patterns and to allow

for tractable estimation. In the matching model, patient and physician preferences are flexibly

specified as parametric functions of characteristics. Extreme value type I taste error terms and the

Rationing-by-Waiting equilibrium concept provide an explicit formula for match probabilities.

Lastly, I specify a discrete choice model where physicians select payment models. Estimates

from this model are used to account for unobserved heterogeneity in physician matching preferences.

1.5.1 Matching Model

Patient Preferences Over Physicians

The latent utility that patient 𝑖 derives from matching with physician 𝑗 in market 𝑡 depends on a

mean utility term, 𝛿𝜷\ 𝑗𝑡

, and an extreme value type I taste shock. The mean utility can be categorized

into three terms. First, patients derive utility from attaining medical care. Second, a patient of

type \ has additional preferences for physician 𝑗 , depending on 𝑗’s characteristics. Third, patients

experience a disutility of traveling to physicians who are further away.

𝑢𝑖\ 𝑗 𝑡 =

Value of Attaining Care︷︸︸︷𝜷𝑢1 + 𝒙′\𝑡𝜷

𝑢2 +

Net Match Value︷︸︸︷𝒙′\ 𝑗𝑡𝜷

𝑢3 −

Cost of Travel︷︸︸︷𝒇𝒅 (𝑑\ 𝑗𝑡)′𝜷𝑢4︸︷︷︸

𝛿𝜷\ 𝑗𝑡

+𝜖𝑖\ 𝑗 𝑡 (1.6)

In the main specification, the variables that determine the value of attaining care, 𝒙\𝑡 , include an

estimate of the expected number of visits a type \ patient will make and categorical descriptions

of the patient type: 15-year age bins, sex, and whether the patients have comorbidities. Some

interactions between patient characteristics are also included. The net match value variables, 𝒙\ 𝑗𝑡 ,

include variables that describe physician 𝑗 , such as payment model, gender, and whether she offers

walk-in visits. Additionally, 𝒙\ 𝑗𝑡 includes interactions between physician 𝑗’s characteristics and

patient type \’s characteristics. Namely, these are interactions between: physician payment model

and the number of expected visits; patient and physician gender. The cost of distance is specified

30

as a quadratic function of distance, interacted with the population density of the patient’s census

division.

Physician Preferences Over Patients

Physician 𝑗’s mean utility for type \ patients in market 𝑡, 𝛾𝜷\ 𝑗𝑡

, consists of three terms. The first

term is the revenue a physician expects to attain from a type \ patient. Second, the physician attains

utility for treating a type \ patient. This non-revenue match value is a combination of the cost and

the altruistic psychic benefit to the physician of supplying services to the patient. These cannot be

separately identified. Third, physicians suffer a opportunity cost associated with adding a patient to

their panel. Last, an additive random taste shock at the patient type-physician panel space-market

level is assumed to have an extreme value type I distribution.

𝑣\ 𝑗𝑞𝑡 =

Revenue︷︸︸︷[𝛽𝑣1 + 𝛽

𝑣2𝛼 𝑗 ]𝑅\ 𝑗𝑡 +

Net Match Value︷︸︸︷𝛽𝑣3𝑉\𝑡 + 𝒚′\𝑡𝜷

𝑣4 −

Value of Leaving Space Open︷︸︸︷[𝛽𝑣5 + 𝒚′𝑗 𝑡𝜷

𝑣6]︸︷︷︸

𝛾𝜷\ 𝑗𝑡

+[\ 𝑗𝑞𝑡 (1.7)

Expected revenue 𝑅\ 𝑗𝑡 corresponds to the revenue of physician 𝑗’s payment model.18 Recall

that expected revenue is the revenue assuming fee-for-service utilization levels. That is, physicians

select patients based on the revenue levels they would receive from those patients in the absence of

practice style changes that are made in response to the alternative payment models.

Physicians vary in their responsiveness to revenue, 𝛽𝑣1 + 𝛽𝑣2𝛼 𝑗 . This heterogeneity is specified as

an unobserved taste for revenue, 𝛼 𝑗 . Accounting for this heterogeneity is important for two reasons.

First, the coefficient on revenue is identified by variation in revenue across physician payment

models. Physicians who choose the alternative payment models, however, are more likely to have

high taste for revenue, generating a selection effect. Second, this selection effect also impacts the

counterfactual analysis of the alternative payment model reforms. For accurate predictions of how a

physician will select patients in a different payment model, I must account for physician selection

18. Note that expected revenue (visits) of a type \ patient is the average expected revenue (visits) of all patients in thepatient type 𝑅\ 𝑗𝑡 = �̄�𝑖 \ 𝑗𝑡 (𝑉\𝑡 = �̄�𝑖 \𝑡 ).

31

into their current payment model.

The variables that enter the net match value term are the expected utilization (in visits) of a type

\ patient, 𝑉\𝑡 , and patient characteristics, 𝒚\𝑡 . The included patient characteristics are: 15-year age

bins, sex, and whether the patient has a comorbidity. The value of leaving a space open depends on

physician characteristics that change over time, 𝒚 𝑗 𝑡 , including age, payment model, and years in

practice.

Additional variables are included in 𝒚 𝑗 𝑡 that account for potential systematic error in the

estimation of physician panel capacity 𝑚 𝑗 𝑡 . Since panel capacity is estimated as the maximum over

all years, physicians who exist for less years in the panel are likely have less open panel spaces. To

account for this, I include the proportion of years that the physician is in the sample as a variable in

𝒚 𝑗 𝑡 .

Equilibrium

Matchings are assumed to be generated by a Rationing-by-Waiting equilibrium (Equations

1.1, 1.2, 1.3, 1.4, and 1.5). Under the preference specifications above, the Rationing-by-Waiting

equilibrium conditions for market 𝑡 can be written as explicit functions.

Market Clearing:

`𝜷∅ 𝑗 𝑡 +

∑\ `

𝜷\ 𝑗𝑡

= 𝑚 𝑗 𝑡 ∀ 𝑗

`𝜷\∅𝑡 +

∑𝑗 `

𝜷\ 𝑗𝑡

= 𝑛\𝑡 ∀\

`𝜷\ 𝑗𝑡

= 𝑛\𝑡𝑒𝑥𝑝(𝛿𝜷

\ 𝑗𝑡−𝜏𝑢

\ 𝑗𝑡)

1+∑ 𝑗 ′ 𝑒𝑥𝑝(𝛿𝜷\ 𝑗𝑡

−𝜏𝑢\ 𝑗𝑡

)= 𝑚 𝑗 𝑡

𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

−𝜏𝑣\ 𝑗𝑡

)

1+∑\ ′ 𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡


)∀\∀ 𝑗

One-Sided Effort: 𝑚𝑖𝑛{𝜏𝑢\ 𝑗𝑡 , 𝜏𝑣\ 𝑗𝑡} = 0 ∀\∀ 𝑗

Recall the interpretation of these equilibrium conditions. The market clearing conditions state

that supply must equal demand. Given effort costs, 𝜏𝑢\ 𝑗𝑡, 𝜏𝑣\ 𝑗𝑡

, and preferences 𝜷, physician 𝑗 chooses

to match with `𝜷\ 𝑗𝑡

type \ patients and `𝜷\ 𝑗𝑡

type \ patients choose to match with physician 𝑗 . The

32

last part of the equilibrium concept is the the one-sided effort condition. This is a constrained

efficiency condition that guarantees that either type \ patients expend effort to match with physician

𝑗 or physician 𝑗 expends effort to match with type \ patients.

Under this specification, the equilibrium efforts 𝜏𝑢\ 𝑗𝑡, 𝜏𝑣\ 𝑗𝑡

can be eliminated. The odds ratio

between the number of patients of type \ who match physician 𝑗 and the outside option shares for

patient \ and physician 𝑗 are constructed from the equilibrium conditions.

`𝜷\ 𝑗𝑡

`𝜷\∅𝑡

= 𝑒𝑥𝑝(𝛿𝜷\ 𝑗𝑡

− 𝜏𝑢\ 𝑗𝑡)

`𝜷\ 𝑗𝑡

`𝜷∅ 𝑗 𝑡

= 𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

− 𝜏𝑣\ 𝑗𝑡)

Solving for the equilibrium effort costs and plugging them into the One-Sided Effort condition

implies that

0 = 𝑚𝑖𝑛

{𝛿𝜷\ 𝑗𝑡

− 𝑙𝑜𝑔(`𝜷\ 𝑗𝑡

`𝜷∅ 𝑗 𝑡

) , 𝛾𝜷\ 𝑗𝑡

− 𝑙𝑜𝑔(`𝜷\ 𝑗𝑡

`𝜷∅ 𝑗 𝑡

)}

Lastly, taking the monotonic transformation `\ 𝑗𝑡𝑒𝑥𝑝(·) to both sides provides the matching condi-

tion provided by Galichon and Hsieh (2019):

`𝜷\ 𝑗𝑡

= 𝑚𝑖𝑛

{`𝜷\∅𝑡𝑒𝑥𝑝(𝛿

𝜷\ 𝑗𝑡

) , `𝜷∅ 𝑗 𝑡𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

)}

The Rationing-by-Waiting Equilibrium conditions thus simplify to:

∑︁𝑗

`𝜷\ 𝑗𝑡

+ `𝜷\∅𝑡 = 𝑛\𝑡 ∀\ (1.8)∑︁

\

`𝜷\ 𝑗𝑡

+ `𝜷∅ 𝑗 𝑡 = 𝑚 𝑗 𝑡 ∀ 𝑗 (1.9)

`𝜷\ 𝑗𝑡

= 𝑚𝑖𝑛


𝜷\ 𝑗𝑡


)}∀\∀ 𝑗 (1.10)

These equilibrium conditions show the logic of the rationing-by-waiting equilibrium. The

number of matches between patient type \ and physician 𝑗 is driven by the preferences of the side

33

of the market that is not expending effort to match.

1.5.2 Payment Model Selection

As previously discussed, accounting for physician unobserved taste for revenue 𝛼 𝑗 is important.

I use additional identifying information from physicians’ payment model choices to estimate the

unobserved taste for revenue. Physicians with high taste for revenues are likely to choose the

payment model that provides them the most revenues. A model of how physicians choose payment

models is specified as follows.

Physician Preferences over Payment Models

Physician 𝑗 in market 𝑡 derives utility in payment model 𝑠 from the matching market outcomes

and the fixed costs of operating the payment model. Fixed costs include pecuniary and psychic

costs, such as the distaste a physician may have for operating in an unfamiliar model.

𝑤 𝑗 𝑠𝑡 =

Matching Value︷︸︸︷𝜙1Y(𝑣\ 𝑗𝑞𝑡 , 𝑠) −

Fixed/Switching Costs︷︸︸︷𝜙3𝑠𝑚 𝑗 𝑡 − 𝝓′

4𝑠𝒛𝐹𝐶𝑗𝑡 − 𝝓′

5𝑠𝒄 𝑗 𝑦−1 + 𝜙𝑠 +a𝑠 𝑗𝑡 (1.11)

The value of a matching is the physician’s expectation of per-patient latent utility attained from

the matching market Y(𝑣\ 𝑗𝑞𝑡 , 𝑠). This expectation depends on the payment model chosen, 𝑠. Fixed

and switching costs include the physician’s panel capacity 𝑚 𝑗 𝑡 , physician-time varying variables,

𝒛𝐹𝐶𝑗𝑡

, indicators for lagged payment model 𝒄 𝑗 𝑦−1, and payment model fixed effects, 𝜙𝑠. Note that the

subscript 𝑡 denotes a market, which are defined by year and geographic market. The subscript 𝑦

denotes only year.

The physician-specific characteristics in 𝒛𝐹𝐶𝑗𝑡

are: age, squared age, sex, and indicators for

rurality. Additionally, the average characteristics of physicians who are within a 30 minute drive

from physician 𝑗 are also included in 𝒛𝐹𝐶𝑗𝑡

. To belong to an alternative payment model, physicians

must generally join as a group of 3 physicians or more (see Table A.6). Therefore, if nearby

34

physicians have a distaste for payment model 𝑠, it will be more difficult to do so. The average age

and number of patients of close physicians are used.

Myopic Choice Assumption

I assume that physicians are myopic when determining their expectation of the per-patient

latent utility they would attain from the matching market in the sense that they are not looking

forward at how their payment model choice will change the matching market equilibrium. Further, I

assume that physicians make payment model choices before, not jointly with, the matching market

equilibrium. These assumptions translate to simplifications in the payment model selection model.

Specifically, physicians expect to keep the same patients irrespective of the payment model they

choose. Loosening this assumption is difficult for both conceptual and computational reasons. For

example, it is not clear whether a unique equilibrium exists in a game where physicians first choose

a payment model, then compete in a matching market.

Under the myopia assumption, Y(𝑣\ 𝑗𝑞𝑡 , 𝑠) is equal to the expected average utility that physician

𝑗 choosing payment model 𝑠 attains from a patient on her panel.

Y(𝑣\ 𝑗𝑞𝑡 , 𝑠) = 𝐸 [𝑣\ 𝑗𝑞𝑡 |𝑐 𝑗 𝑦 = 𝑠] = 𝛾𝑒 +1𝑚 𝑗 𝑡

∑︁\

`\ 𝑗𝑡𝛾𝜷\ 𝑗 𝑠𝑡

where 𝛾𝑒 is Euler’s constant and 𝛾𝜷\ 𝑗 𝑠𝑡

is the mean utility of physician 𝑗 matching with a type \

patient in market 𝑡 while in payment model 𝑠. `\ 𝑗𝑡 is the observed matching in the data. I normalize

such that choosing fee-for-service provides zero mean latent utility.


Matching Value︷︸︸︷𝜙1ΔY(𝑣\ 𝑗𝑞𝑡 , 𝑠) −

Fixed/Switching Costs︷︸︸︷𝜙3𝑠𝑚 𝑗 − 𝝓′


5𝑠𝒄 𝑗 𝑦−1 + 𝜙𝑠 +a𝑠 𝑗𝑡 𝑠 ∈ {Capitation,EFFS}(1.12)

𝑤 𝑗 𝑠𝑡 = a𝑠 𝑗𝑡 𝑠 = FFS

where ΔY(𝑣\ 𝑗𝑞𝑡 , 𝑠) = Y(𝑣\ 𝑗𝑞𝑡 , 𝑠) − Y(𝑣\ 𝑗𝑞𝑡 , FFS) is the difference between the per-patient latent

35

utility that physician 𝑗 attains in payment model 𝑠 and in the fee-for-service payment model.

Since only revenue and the value of leaving a panel space open vary by payment model in

physician preferences over patients, the difference in the per-patient latent utility can be written

simply.

ΔY(𝑣\ 𝑗𝑞𝑡 , 𝑠) = [𝛽𝑣1 + 𝛽𝑣2𝛼 𝑗 ]Δ𝑠𝑅\ 𝑗𝑡 + Δ𝑠𝒚

′𝑗 𝑡𝜷

𝑣6

where Δ𝑠𝑅 𝑗 𝑠𝑡 =1𝑚 𝑗𝑡

∑\ `\ 𝑗𝑡 [𝑅\ 𝑗 𝑠𝑡 − 𝑅\ 𝑗𝐹𝐹𝑆𝑡] is the difference in average revenues between

payment model 𝑠 and FFS for physician 𝑗 . Δ𝑠𝒚′𝑗 𝑡

is the difference in physician characteristics

between payment model 𝑠 and FFS. This becomes a constant for each payment model. Thus,

physician latent utility can be simplified.


Matching Value︷︸︸︷[𝜙1 + 𝛼 𝑗 ]Δ𝑠𝑅 𝑗 𝑠𝑡 −

Fixed/Switching Costs︷︸︸︷𝜙3𝑠𝑚 𝑗 − 𝝓′


5𝑠𝒄 𝑗 𝑡−1 + 𝜙𝑠︸︷︷︸𝑊 𝑗𝑠𝑡 (�̃�,𝜖𝑅𝑗 )

+a𝑠 𝑗𝑡 (1.13)

where 𝜙1 = 𝜙1𝛽𝑣1, 𝜙3𝑠 = 𝜙3𝑠, 𝝓4𝑠 = 𝝓4𝑠, 𝝓5𝑠 = 𝝓5𝑠, and 𝜙𝑠 = 𝜙𝑠 + Δ𝑠𝒚

′𝑗 𝑡𝜷𝑣6

Lastly, I allow unobserved taste for revenue to depend on physician observables 𝒛𝑅𝑗𝑡

and an

error term 𝜖𝑅𝑗

, which will be estimated. The vector 𝒛𝑅𝑗𝑡

includes physician variables that may affect

sensitivity to revenue. These include age, squared age, and sex.

𝛼 𝑗 = 𝝓2𝒛𝑅𝑗𝑡 + 𝜖𝑅𝑗

1.6 Estimation

Preferences are estimated in two stages. First, the unobserved physician taste for revenue 𝛼 𝑗 is

estimated using data on observed payment model choices. In the second stage, patient and physician

preferences are jointly estimated using matching data. I present the estimation procedure in reverse

order.

36

1.6.1 Estimation of Matching Preferences

I estimate preferences using a nested fixed point maximum likelihood method. The likelihood

function of the matching model can be written as a simple function of matching data and predicted

matchings.

L𝑡 (𝜷) = 2∑︁𝑗

∑︁\

`\ 𝑗𝑡 𝑙𝑜𝑔(`𝜷\ 𝑗𝑡) +∑︁\

`\∅𝑡 𝑙𝑜𝑔(`𝜷\∅𝑡) +∑︁𝑗

`∅ 𝑗 𝑡 𝑙𝑜𝑔(`𝜷∅ 𝑗 𝑡)

where `𝜷\ 𝑗𝑡

is the number of patients of type \ who match with physician 𝑗 in the predicted

Rationing-by-Waiting equilibrium when preferences are defined by 𝜷. For brevity I use the notation

`𝜷\ 𝑗𝑡

= `\ 𝑗𝑡 (𝜷), `𝜷\∅𝑡 = `\∅𝑡 (𝜷), and `𝜷∅ 𝑗 𝑡 = `\∅𝑡 (𝜷).19

I predict matchings under the parametric specification laid out in Section 1.5. Thus, we can

reformulate the estimation problem as:

max𝜷

2∑︁𝑡

∑︁𝑗

∑︁\

`\ 𝑗𝑡 𝑙𝑜𝑔(`𝜷\ 𝑗𝑡) +∑︁𝑡

∑︁\

`\∅𝑡 𝑙𝑜𝑔(`𝜷\∅𝑡) +∑︁𝑡

∑︁𝑗


𝑠.𝑡.∑︁𝑗

`𝜷\ 𝑗𝑡

+ `𝜷\∅𝑡 = 𝑛\𝑡 ∀\∀𝑡∑︁

\

`𝜷\ 𝑗𝑡

+ `𝜷∅ 𝑗 𝑡 = 𝑚 𝑗 𝑡 ∀ 𝑗∀𝑡

`𝜷\ 𝑗𝑡

= 𝑚𝑖𝑛


𝜷\ 𝑗𝑡


)}∀\∀ 𝑗∀𝑡

Nested Fixed Point Algorithm

The nested fixed point algorithm uses a non-linear optimization algorithm over 𝜷 in an outer

loop to maximize the likelihood. At each step of this outer loop, the predicted matching 𝝁𝜷 must

be calculated. To calculate 𝝁𝜷, the solution to the Rationing-by-Waiting Equilibrium system of

equations is found. This solution is found using an inner iterative loop that converges to a fixed

19. The likelihood has an intuitive interpretation. Maximizing the likelihood is equivalent to minimizing the Kullback–Leibler divergence from the predicted matching `𝜷𝑡 to the matching observed in the data `𝑡 . The likelihood approachis therefore similar to the minimum distance approaches used in the existing literature (Hitsch, Hortaçsu, and Ariely(2010), Boyd et al. (2013), Vissing (2017), Agarwal (2015), and Matveyev (2013)). In both, a predicted matching isdetermined by an assumed equilibrium concept and parameterized preferences. Parameters are chosen to minimize adistance between the predicted matching and the matching observed in the data.

37

point.

Inner Loop

Given a parameter value 𝜷, the inner loop solves the non-linear set of equations for 𝝁𝜷:

`𝜷\∅𝑡 +

∑︁𝑗

`𝜷\ 𝑗𝑡

= 𝑛\𝑡 ∀\∀𝑡

`𝜷∅ 𝑗 𝑡 +

∑︁\

`𝜷\ 𝑗𝑡

= 𝑚 𝑗 𝑡 ∀ 𝑗∀𝑡

`𝜷\ 𝑗𝑡

= 𝑚𝑖𝑛

{`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡, `

𝜷∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

}∀\∀ 𝑗∀𝑡

Where 𝑎𝜷\ 𝑗𝑡

= 𝑒𝑥𝑝(𝛿𝜷\ 𝑗𝑡

) and 𝑏𝜷\ 𝑗𝑡

= 𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

). Given the parameter vector 𝜷, 𝒂𝜷 and 𝒃𝜷 are

known. Therefore, they are calculated at the beginning of each inner loop step and are treated as

data thereafter.

This system of equations does not have a simple closed form solution due to non-linearities.

I solve the system numerically using an iterative procedure similar to the iterative proportional

fitting procedure used elsewhere in the empirical matching literature (Galichon and Salanie (2010)).

Starting at an initial value of `(0)∅ 𝑗 𝑡 ∀ 𝑗 , 𝑡, I iteratively solve the following two sets of equations until

convergence. 20

`𝜷\∅𝑡 +

∑︁𝑗

(1{`\∅𝑡𝑎

𝜷\ 𝑗𝑡< `

(𝑘−1)∅ 𝑗 𝑡 𝑏

𝜷\ 𝑗𝑡

}`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡

+ 1{`\∅𝑡𝑎

𝜷\ 𝑗𝑡> `

(𝑘−1)∅ 𝑗 𝑡 𝑏

𝜷\ 𝑗𝑡

}`𝜷∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

)= 𝑛\𝑡∀\∀𝑡

(1.14)

`𝜷∅ 𝑗 𝑡 +

∑︁\

(1{`(𝑘)\∅𝑡𝑎

𝜷\ 𝑗𝑡< `∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

}`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡

+ 1{`(𝑘)\∅𝑡𝑎

𝜷\ 𝑗𝑡> `∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

}`𝜷∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

)= 𝑄 𝑗∀ 𝑗∀𝑡 (1.15)

20. An alternative iterative procedure was also used to test for consistency of results. This procedure involved iteratingon the matrix form of the system. At each step, the procedure updated 𝑅 (𝑘) , then 𝝁 (𝑘)

∅ = [𝑅 (𝑘) ]−1𝒗. This procedurereturned identical results but was less efficient.

38

Outer Loop

In the outer loop, I maximize the likelihood function.

max𝜷

2∑︁𝑡

∑︁𝑗

∑︁\

`\ 𝑗𝑡 𝑙𝑜𝑔(`𝜷\ 𝑗𝑡) +∑︁𝑡

∑︁\

`\∅𝑡 𝑙𝑜𝑔(`𝜷\∅𝑡) +∑︁𝑡

∑︁𝑗


using a quasi-newton non-linear optimization algorithm. To aid the algorithm, I derive the gradient

of the likelihood. Section A.6.1 presents those derivations.

1.6.2 Estimation of Unobserved Taste for Revenue

I estimate the physician choice of payment model using an L2 (Ridge) regularized maximum

likelihood model. Recall that the object of interest in this exercise is the unobserved taste for

revenue, 𝛼 𝑗 , which is a function of observable characteristics and an error term 𝜖𝑅𝑗

.

The regularized maximum likelihood method penalizes the squared magnitude of 𝜖𝑅𝑗

according

to a smoothing parameter _. Additionally, I assume that the idiosyncratic taste shock, a𝑠 𝑗𝑡 , is

distributed Extreme Value type I. Thus, the regularized log likelihood problem has the form

max𝝓,𝝐𝑹

∑︁𝑗

∑︁𝑡

∑︁𝑠

𝑐 𝑗 𝑠𝑡 𝑝 𝑗 𝑠𝑡 (�̃�, 𝜖𝑅𝑗 ) −_

2

∑︁𝑗

(𝜖𝑅𝑗 )2

𝑝 𝑗 𝑠𝑡 (�̃�, 𝜖𝑅𝑗 ) = 𝑙𝑜𝑔(

𝑒𝑥𝑝(𝑊 𝑗 𝑠𝑡 (�̃�, 𝜖𝑅𝑗 ))∑𝑠′ 𝑒𝑥𝑝(𝑊 𝑗 𝑠′𝑡 (�̃�, 𝜖𝑅𝑗 ))

)Recall that𝑊 𝑗 𝑠𝑡 (�̃�, 𝜖𝑅𝑗 ) is the mean utility of physician 𝑗 choosing payment model 𝑠 in market

𝑡. Thus, 𝑝 𝑗 𝑠𝑡 (�̃�, 𝜖𝑅𝑗 ) is the probability that physician 𝑗 chooses payment model 𝑠 in market 𝑡. The

smoothing parameter, _, is chosen by cross-validation. I use a 12-fold cross validation technique

and the log loss classification metric. Folds are created to accommodate the panel structure of the

dataset. Each fold is a collection of randomly sampled observations. No fold includes more than

one observation from the same physician. The _ is chosen by the one-standard error rule. The one

standard error rule accounts for error in the log loss function (Hastie, Tibshirani, and Friedman

(2009)). That is, define 𝐿𝐿 (_) as the log loss produced in cross validation using smoothing

39

parameter _. The _∗ is chosen by the rule

_𝑚𝑖𝑛 = 𝑎𝑟𝑔𝑚𝑖𝑛_∈Λ𝐿𝐿 (_)

_∗ = 𝑚𝑖𝑛_∈Λ𝐿𝐿 (_)

𝑠.𝑡. 𝐿𝐿 (_) > 𝐿𝐿(_𝑚𝑖𝑛) + 𝑆𝐸 (_𝑚𝑖𝑛)

where 𝑆𝐸 (_𝑚𝑖𝑛) is the estimated standard error of the log loss function at the minimizing

smoothing parameter. This is estimated using the variation of log loss among folds. Λ is a grid of

values. I use a grid of 200 points spread from .001 to .5.

The intuition behind this methodology is simple. This is a high dimension problem. There are

5,851 observations and 905 parameters. 879 of these parameters are random effects 𝜖𝑅𝑗. Thus, to

avoid overfitting, the size of the random effects must be penalized.

Intuitively, the argument is that the estimators of the random effect 𝜖𝑅𝑗

suffer from the incidental

parameters problem. However, it is reasonable to assume that physicians with similar observables

will have similar revenue sensitivities. From a Bayesian perspective, I put a prior on the difference

between the revenue sensitivity of each physician and the mean revenue sensitivity of physicians

with identical characteristics. Specifically, the prior has the form 𝜖𝑅𝑗∼ 𝑁 (0, 1

_).

Alternatives

Due to the high dimensional nature of this model, 𝜖𝑅𝑗

are not point identified. Theoretically, the

distribution of 𝜖𝑅𝑗

could be identified (Revelt and Train (2000)). However, due to the computational

complexity of the empirical matching model, integrating the matching predictions over the distri-

bution of 𝜖𝑅𝑗

is infeasible. Determining more efficient methods to predict Rationing-by-Waiting

matchings with random coefficients is a potential avenue for further research.

40

1.6.3 Identification

Most importantly, identification rests on the assumption that patient preferences depend on

distance, while physician preferences do not. This exclusion restriction allows the model to

separately identify patient and physician preferences. Under this assumption, patients who are

close to a physician are likely to have to wait for that physician. This implies that among those

patients who are close, match probabilities should reflect the choice probabilities of physicians. With

physician preferences identified, patient preferences are then identified by the match probabilities

conditional on physician preferences. Other exclusion restrictions may help in identification.

Namely, revenue enters only into physician preferences. Revenue, however, is less predictive of

matchings than distance.

Identification of preferences relies on three key features of the primary care market in Northern

Ontario. First, the market is a many-to-one market. This is necessary for non-parametric identifi-

cation of both the idiosyncratic taste shock distribution and preferences. Without a many-to-one

market, any set of match probabilities could be explained by multiple taste shock distributions,

therefore generating a reliance on the extreme value type I assumption for identification (Agarwal

(2013)). Second, I observe multiple markets – both over years and geography. Additionally, even

within a year and geographic market, the data structure is similar to many overlapping markets, as

patients rarely match with physicians who are located more than 45 minutes away. This provides

useful variation in the distribution of patient and physician types. Even in one-to-one settings, many

markets can aid in identification (Hsieh (2012)).

1.7 Results: Patient and Physician Preferences

1.7.1 Physician Choice of Payment Model

Table 1.4 shows the results of the payment model choice model. The top panel presents the

parameters that enter the unobserved taste for revenue 𝛼 𝑗 . The bottom panel presents the fixed and

switching cost parameters.

41

Fixed and switching cost parameters largely follow similar patterns to previous work by Rudoler,

Deber, Barnsley, et al. (2015), who estimate payment model selection via mixed logit and allow for

rich heterogeneity in physician panel characteristics. Conditional on revenue, characteristics that

predict a higher probability of switching into an enhanced fee-for-service model are female, middle

aged, larger patient panels and urban. Characteristics that predict a higher probability of switching

to the capitation system are female, middle aged, rural, and smaller panel sizes.

42

Table 1.4: Physician Choice of Payment Model Estimates

All Payment Models

Estimate (Std. Dev.)Parameter

RevenueParameters in 𝛼 𝑗Constant 7.449***

(2.322)Num. of Patients 6.573***

(2.436)Female -0.061

(2.237)Penalty_ 0.071Payment Model: EFFS CapitationParameter Estimate (Std. Dev.) Estimate (Std. Dev.)

Fixed/Switching CostPhysician CharacteristicsConstant -1.828 -5.706***

(1.581) (1.633)Age 6.463 5.600

(4.566) (5.014)Age2 -8.769* -11.422**

(4.557) (5.143)Num. of Patients -0.402 -2.039***

(0.362) (0.639)Semiurban -0.244 0.667*

(0.366) (0.370)Rural -0.361 0.340

(0.487) (0.523)Female -0.076 -0.007

(0.378) (0.669)Nearby PhysiciansNum. of Physicians -0.101 -0.528

(0.653) (0.669)Average Age -2.198 7.620***

(2.451) (1.800)Lagged IndicatorsEFFS 6.445*** 4.544***

(0.594) (0.602)Capitation 1.023** 5.318***

(0.436) (0.359)

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

43

There is substantial estimated unobserved taste for revenue. A penalty parameter of 0.071 is

generated by the cross validation exercise – translating to a 3.75 hyperparameter standard deviation

of the prior distribution of 𝜖𝑅𝑗

. Figure 1.7 shows the estimated distribution of unobserved taste for

revenue. The average estimated 𝛼 𝑗 is 13.75. Physicians who choose the capitation model are more

likely to have high taste for revenue, while those in the fee-for-service model have a low taste for

revenue.

Figure 1.7: Distribution of �̂� 𝑗

1.7.2 Empirical Matching Model Estimates

The results of the empirical matching model are presented in Table 1.5 and Table 1.6. Individual

parameter magnitudes are difficult to interpret. The signs of the estimates are generally intuitive.

As expected, I estimate that patients with more expected visits and female patients have higher

preferences for attaining care. The estimates suggest that patients with more expected visits are more

likely to prefer physicians in alternative payment models (non-fee-for-service models), perhaps due

to the increased continuity of care these models provide. Evidence of homophily in sex is similarly

44

strong.

Physician preferences over patients are positively associated with revenue and expected number

of visits. However, conditional on expected revenue and visits, the estimates suggest that physicians

prefer male patients, younger patients, and patients without comorbidities. This could be explained

by unobserved health that is observed by the physician but not the econometrician. For example, a

young patient with high number of expected visits may have a serious unobserved health condition

that physicians are particularly motivated to treat.

1.7.3 Exposition of Preferences

The estimated model suggests that physician preferences over patients are fairly responsive to

expected utilization (visits) and are only mildly responsive to revenue. Figure 1.8 illustrates these

findings. To do so, I construct an illustrative physician who is 50 years old, female, in a capitation

payment model, and does not offer walk-in visits. For panel (a), I separate all patients in 2014 into

50 bins according to their expected number of visits. The figure shows the percent of patients in

each bin who do not attain care, the probability that a patient chooses no care over choosing to

go to the illustrative physician, and the probability that the illustrative physician would reject a

patient. Panel (b) presents the results of the same procedure when conducted for expected capitation

revenue.

Panel (a) suggests that physician preferences contribute to the low rates of attaining care among

patients with low expected utilization. Both the probability of rejection and the patient’s probability

of attaining no care are downward sloping in expected utilization. Physicians discriminate in favor

of patients with higher expected utilization. This suggests that physicians may be giving priority to

patients with more need for healthcare.21 However, there is no evidence from the matching model

to separate this story from one where physicians prefer higher utilization due to cost efficiencies.

On the other hand, while the share of patients who attain care is decreasing in expected capitation

revenue, the correlations do not suggest that physician responsiveness to revenue is driving those

21. Such preferential treatment is welfare improving under reasonable assumptions (Gravelle and Siciliani (2008)).

45

Table 1.5: Patient Preferences

Parameter Estimate (Std. Dev.) Parameter Estimate (Std. Dev.)

Care Value Net Match ValueConstant -1.012*** EFFS -0.124***

(0.008) (0.002)Expected Utilization (5 visits) 1.240*** CAP -0.307***

(0.013) 0.002)Comorbidity -0.085*** Female doctor -0.857***

(0.005) (0.003)Female 0.301*** Female doctor × Female 0.861***

(0.006) (0.004)Under 14 0.045*** Offers Walk-in Visits -0.017***

(0.005) (0.002)35-49 -0.066***

(0.004) Travel Cost50-64 -0.143*** Drivetime (hours) 6.295***

(0.009) (0.006)Over 65 -0.352*** ... × log(Pop Density ( 𝑝𝑜𝑝5𝑘𝑚2 )) 0.430***

(0.013) (0.003)Over 50 × Expected Utiliz. 0.230*** Drivetime2 -0.971***

(0.012) (0.002)Female × Expected Utiliz. -0.351*** ... × log(Pop Density) -0.079***

(0.006) (0.001)

Included: Market Fixed EffectsNote: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

46

Table 1.6: Physician Preferences

Parameter Estimate (Std. Dev.)

RevenueRevenue ($100) 0.102***

(0.004)𝛼 𝑗 (𝑆𝑡𝑑.𝐷𝑒𝑣.) × Revenue($100) 0.042***

(0.001)Net Match ValueExpected Utilization (5 visits) 3.335***

(0.008)Comorbidity -2.196***

(0.004)Female -0.310***

(0.002)Under 14 -0.206***

(0.003)35 to 49 -0.761***

(0.003)50 to 64 -1.213***

(0.003)Over 65 -2.317***

(0.007)Value of Leaving Panel Space OpenConstant 2.199***

(0.005)EFFS -0.551***

(0.003)CAP -0.595***

(0.003)Years in Practice 0.117***

(0.0003)Adjustments for �̂� 𝑗𝑡

Proportion of years in sample -0.034***(0.004)

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

47

matching patterns. Other patient characteristics, such as age, exhibit similar patterns (see Appendix

Figure A.4).

This does not, however, imply that physicians are unresponsive to revenue on the margin, as

matching patterns are a function of both demand and supply. To further explore the notion of how

responsive physicians are to revenue, I calculate the elasticity of the number of type \ patients that

physician 𝑗 chooses with respect to revenue. The average elasticity, weighted by observed matches,

is 0.14. The relatively low elasticity is consistent with the existing quasi-experimental literature,

which finds little effect of revenue on selection by physicians in Ontario (Kantarevic and Kralj

(2014)).

Figure 1.8: Preference Exposition

(a) Expected Number of Visits (b) Expected Capitation Revenue

1.7.4 Model Fit

The model predicts the data reasonably. Figure 1.9 compares the model’s predictions to the data.

The figure in panel (a) shows the density of the predicted share of patients without care compared to

the share without care in the data. Most of the density falls along the 45-degree line, suggesting a

reasonable fit. However, there is substantial density off of the 45-degree line. Panel (b) presents the

relationship between the predicted and observed shares without care across three important cuts of

the data. The table shows that the model underpredicts the outside option share in urban areas and

48

overpredicts in rural areas.

Unobserved heterogeneity in a patient’s latent utility of attaining no care may cause the predicted

share to differ from its empirical counterpart. For example, patients may experience shocks to their

health which necessitate that they attain care that cannot be accounted for by the extreme value type

1 taste shock. Such unobserved heterogeneity could cause physician demand to be inelastic at both

high levels of access and low levels of access. Unobserved heterogeneity could be easily added to

the empirical specification, but at high computational costs. An avenue for future research is to

determine an efficient methodology to implement unobserved heterogeneity in patient preferences.

Figure 1.9: Model Fit

(a) Comparison of Model to Data: Density (b) Comparison of Model to Data: Across Cuts

% Without Care

Subset N Data Model

Area TypeRural 237,388 49.688 44.876

Semiurban 198,356 58.847 63.661Urban 274,538 69.029 73.999

Age0-34 271,910 50.351 52.036

35-64 295,418 61.552 64.72165+ 142,954 73.761 72.242

ComorbiditiesNo 572,588 55.809 58.099Yes 137,694 75.990 75.015

1.8 Patterns And Determinants of Access to Care

I use the estimated model to study the distribution of access to care and what determinants

contribute most to access loss. Before turning to these results, I define access to care and access

loss precisely.

49

1.8.1 Measures of Access to Care

I define access to care 𝐴\𝑡 for type \ patients under choice conditions (J , 𝜏𝑢) as the share of

patients who would have attained care under full access choice conditions that attain care under

conditions (J , 𝜏𝑢). Choice conditions include the set of all physicians in the patient’s choice set,

J , and a vector of effort costs to match with each physician, 𝜏𝑢. The choice set J describes the

characteristics and distances of each physician that the patient may match with.22

𝐴\𝑡 =P\𝑡(𝜷,𝜏𝑢

\𝑡,J\𝑡)

P\𝑡(𝜷,𝜏𝑢,𝐹𝐴,J 𝐹𝐴)

P\𝑡(𝜷,𝜏𝑢\ ,J ) = 1 −[1/

∑︁𝑗∈{J𝑡 ,∅}

𝑒𝑥𝑝(𝛿\ 𝑗𝑡 (𝛽) − 𝜏𝑢\ 𝑗𝑡 (𝛽))]

The probability that a patient attains care, P\𝑡(𝜷,𝜏𝑢,J ), depends on preferences 𝜷, effort costs

𝜏𝑢, and the choice set J . (𝜏𝑢\𝑡,J\𝑡) defines the choice conditions of the estimated matching model in

market 𝑡. (𝜏𝑢,𝐹𝐴,J 𝐹𝐴) defines the full access choice conditions. In rare cases where the numerator

exceeds the denominator, I set access to equal 1.

Access for a set of patient types, Θ̄, under the conditions (J , 𝜏𝑢) is defined as the average

access faced by patients within that set.

𝐴Θ̄𝑡 =1∑

\∈Θ̄ 𝑛\𝑡

∑︁\∈Θ̄

𝑛\𝑡𝐴\𝑡

22. I define a second measure of access to care as the share of patient surplus attained in a full access counterfactualthat is attained in the present equilibrium.

𝐴2\𝑡 =

logsum\𝑡 (𝜷,𝝉𝑢\

,J\𝑡 )logsum\𝑡 (𝜷,0,J\ 𝐹 𝐴)

logsum\𝑡 (𝛽,𝝉\ ,J ) = 𝑙𝑜𝑔(∑︁

𝑗∈{J,∅}𝑒𝑥𝑝(𝛿\ 𝑗𝑡 (𝛽) − 𝜏𝑢\ 𝑗𝑡 )

Results are qualitatively similar when this alternative measure is used. However, since there is no normalizingcoefficient in patient preferences, it is difficult to interpret comparisons of magnitudes of this measure of access acrosspatient types. Section A.4 presents results for this measure, and others.

50

This measure of access depends on how full access is defined. I assume that patients would have

full access if they lived in Sudbury and every physician was willing to accept them. Sudbury is the

largest city in my sample, with a population of 165,000 in 2014. Thus, in the main specification,

I define the full access choice conditions to consist of the choice set of patients in Sudbury

(J 𝐹𝐴 = J 𝑆𝑢𝑑𝑏𝑢𝑟𝑦) and an effort cost vector of zero (𝜏𝑢,𝐹𝐴 = 0).

For ease of exposition, I define access loss, 𝐴𝐿Θ̄𝑡 , as the share of potential access that is not

attained in the present equilibrium.

ALΘ̄𝑡 = 1 − 𝐴Θ̄𝑡

1.8.2 Patterns in Access to Care

Access loss is large and unequally distributed. I find that access loss by patients in Northern

Ontario in 2014 is 27%. Figure 1.10 summarizes these results. For more detailed statistics, refer to

Table A.9.

Figure 1.10: Distribution of Access in 2014


51

Age and Comorbidities

Access loss is lower for older patients and patients with comorbidities. Access loss for pa-

tients without comorbidities and aged 0-34 is 36%. This compares to 18% for 65+ patients with

comorbidities.

As discussed above, physicians discriminate in favor of patients with greater expected utilization.

This discrimination decreases the effort that sicker and older patients must expend to attain care. In

turn, this increases the effort that healthier and younger patients must expend. I find that patients

without comorbidities face an average effort cost that is 9% higher than the average effort cost of

patients with comorbidities. This discrimination results in lower access loss for sicker and older

patients and higher access loss for healthier and younger patients.

Within the subset of patients who have comorbidities, older patients do not always have greater

access to care than younger patients. This also derives from physician discrimination. Conditional on

having comorbidities, younger patients still have high expected utilization. Additionally, physicians

discriminate in favor of younger patients, all else equal.

Geography

Access loss is higher in more rural areas. Access loss is 44% in rural areas and 26% in

semiurban areas, which are non-metropolitan agglomerations with a population of 10,000 or more.

In comparison, urban areas have low levels of access loss at 13%. Pockets of extremely low access

to care exist, where I estimate that access loss is over 90%. In such areas, the nearest primary care

physician can be further than 60 km away.

1.8.3 Determinants of Access Loss

I decompose access loss for each patient type into potential determinants. I conduct two

decompositions of access loss. First, access loss is decomposed into the amount of access lost

due to capacity constraints and the amount of access lost due to an insufficient choice set. Second,

access loss is decomposed into four aspects of the physician supply: the distribution of physician

52

characteristics among existing physicians, the geographic distribution of physicians, the aggregate

supply of physicians, and remaining access loss.

Decomposition One: Effort Costs and Insufficient Choice Sets

Access loss is decomposed into the amount of access lost due to capacity constraints and the

amount of access lost due to an insufficient choice set. The impact of capacity constraints on access

loss can be interpreted as the access loss caused by patients expending effort to attain care. Since

physicians are capacity constrained, patients must expend effort to match with a physician. The

impact of capacity constraints on access loss is calculated as the difference in access loss between

the present equilibrium and a counterfactual equilibrium with no effort.

The remaining access loss is explained by the difference between the full access choice set and

the current choice set. For patients living in Sudbury, this effect will be zero by construction. For

others, it is the difference in access between their current choice set and the choice set in Sudbury,

assuming that all physicians are accepting patients.

𝐴𝐿\𝑡 =P\𝑡(𝜷,0,J 𝐹𝐴) − P\𝑡(𝜷,0,J𝑡)

P\𝑡(𝜷,0,J 𝐹𝐴)︸︷︷︸Choice Set

+ P\𝑡(𝜷,0,J𝑡) − P\𝑡(𝜷,𝝉\𝑡 ,J𝑡)P\𝑡(𝜷,0,J 𝐹𝐴)︸︷︷︸

Capacity

Figure 1.11 summarizes the results of this decomposition. Table A.9 provides more information.

Physician capacity constraints contribute an average access loss of 14 percentage points. Deter-

minants of access loss differ by patient type. Rural access loss is primarily driven by choice sets

(33pp), rather than capacity constraints (11pp). Although patients must expend effort to match with

physicians, the distance they must travel to the nearest doctor is a larger contributor to low access to

care. In urban and semiurban areas, capacity constraints are the main drivers of access loss.

53

Figure 1.11: Share of Access Loss Attributed to Physician Capacities


These results indicate that policy remedies should be calibrated to specific populations. Where

capacity constraints are a main contributor, policies should aim to increase capacity. Either expand-

ing the capacity of existing physicians or encouraging the entry of new physicians would suffice.

When poor choice conditions is the primary determinant of access to care, policies should target

entry of new physicians to areas with especially low access.

Decomposition Two: Physician Supply

In a second decomposition, I study how different aspects of physician supply across Northern

Ontario contribute to access loss. To do so, I iteratively estimate counterfactual equilibria where

one aspect of physician supply is changed at a time. First, I randomly redistribute physician charac-

teristics, holding physician locations steady. Access loss for type \ patients in this counterfactual is

labeled 𝐴𝐿char\𝑡

. Second, I randomly distribute physicians to make the ex-ante physician to popu-

lation ratio equal across locations.23 For this counterfactual, access loss is labeled 𝐴𝐿ppr\𝑡

. Third,

23. The probability that a physician is assigned a location is proportional to the population of the location. If aphysician is assigned to a location, the probability of the next physician being assigned that location decreases as if its

54

I add physicians such that there is one physician per 1000 patients in all locations.24 The access

loss that remains is labeled 𝐴𝐿agg\𝑡

. For each counterfactual, I average access loss over 10 simulated

equilibria.

I use the estimated counterfactuals to decompose access loss in 2014 into four determinants. First,

I estimate the impact of the distribution of physician characteristics on access loss by comparing

access loss in the 2014 equilibrium to access loss in the counterfactual where characteristics are

redistributed. The contribution of the distribution of physician locations to access loss is similarly

defined as the difference between access loss in the counterfactual with redistributed physician

characteristics and the counterfactual with redistributed physician locations. Lastly, the aggregate

number of physicians in 2014 was lower than a target of 1 physician per 1000 patients. I estimate

the impact that the low aggregate number of physicians (relative to the target) has on access loss by

comparing access loss in the counterfactual where physicians were redistributed to access loss in

the counterfactual with the target physician to patient ratio.

𝐴𝐿\𝑡 = 𝐴𝐿\𝑡 − 𝐴𝐿char\𝑡︸︷︷︸

Distribution of characteristics

+ 𝐴𝐿char\𝑡 − 𝐴𝐿ppr

\𝑡︸︷︷︸Distribution of locations

+ 𝐴𝐿ppr\𝑡

− 𝐴𝐿agg\𝑡︸︷︷︸

Aggregate # of physicians

+ 𝐴𝐿agg\𝑡︸︷︷︸

Remainder

Figure 1.12 presents the results of this decomposition. The contribution of each determinant

of access loss, as outlined above, is presented in the dark bars. The light bars show total access

loss, 𝐴𝐿\𝑡 . Table A.9 provides more detail. I find that the distribution of physician characteristics

worsens access loss for rural patients and mitigates access loss for urban patients, mainly because

of larger physician capacities in urban areas. In contrast, the distribution of physicians increases

access loss for urban patients and decreases access loss for rural patients. Indeed, the physician

to population ratio is larger in rural areas than urban areas. The aggregate number of physicians

contributes to access loss of all patients. However, young and healthy patients are the most affected.

population decreased by 1000.24. An additional physician is assigned with probability 𝑅

1000 where R is the remainder after population is divided by1000. Physicians are randomly sampled from the existing pool of physicians.

55

When supply is insufficient, physicians are at capacity and discriminate against patients with low

expected utilization.

Distribution of Physician Characteristics

Physicians are heterogeneous in capacities, payment models, and other characteristics. This

affects the spatial distribution of access loss. I find that younger and more urban patients benefit

from the distribution of physician characteristics. The likely cause of this phenomenon is that

physicians in urban areas have larger capacities than physicians in rural areas (mean panel size is

1,329 in urban areas; 1,246 in semi-urban, and 818 in rural areas). Interestingly, while the positive

impact on urban patients is substantial, the negative impact on rural patients is small. In many

rural areas, there are few potential patients. In these areas, physicians with large capacities would

not be able to attract enough patients to hit their capacity constraints. Thus, adding high-capacity

physicians to rural areas would not significantly increase access. For this reason, the distribution of

physician characteristics decreases access loss across the entire population by 2.22pp.

Distribution of Physician Locations

I find that the 2014 distribution of physician locations benefits rural patients. This result is

unsurprising given the observed physician to population ratios. In the main sample, there are 0.96

physicians per 1000 patients in rural areas, 0.81 in semiurban areas, and 0.73 in urban areas. The

effect of the physician location distribution is essentially zero-sum. While the distribution benefits

rural patients, it increases urban and semiurban access loss. In sum, the distribution of physician

locations decreases access loss across the entire population by 0.47pp.

Aggregate Supply of Physicians

I estimate that 16pp of access loss across the entire population can be attributed to the low

aggregate number of physicians in Northern Ontario (relative to a target of 1 physician per 1000

patients). Young patients are affected most by low supply. When physicians are working at capacity,

56

these patients are unable to attain care due to physician discrimination. If supply is expanded,

physicians are no longer at capacity and therefore accept all patients.

Remainder

After accounting for the distribution of physicians and the aggregate supply of physicians, some

access loss remains. This remaining access loss is due to low levels of physician variety in sparsely

populated areas. Even with a sufficient number of physicians, rural patients are restricted to choose

among the few physicians who are close to them. Those physicians may have low capacity, or they

may not produce high match value with the patients. This remaining access loss is fairly large in

rural areas but is close to zero in urban areas.

57

Figure 1.12: Access Loss Attributed to Characteristics of Physician Supply

(a) Physician Characteristics Distribution (b) Physician Location Distribution

(c) Aggregate Supply (d) Remainder

58

1.9 Conclusion

This chapter studies access to care as an equilibrium output of a matching market between

patients and physicians. In the model, the market is cleared by a non-price mechanism: the effort it

takes for a patient (physician) to match with a physician (patient). Patient and physician preferences

are estimated using data from the Northern Ontario primary care market. Using the estimated

preferences, I study the distribution and determinants of access to care.

I find that access to care is low and unevenly distributed across types of patients. Further, I

find that the determinants of low access to care differ for different patient types. In rural areas,

low access to care is mostly driven by the high travel costs that patients must pay to attain care.

In urban areas, low access to care is driven by physician capacities. Since physicians do not have

enough capacity to accept all patients, patients compete to attain a limited supply of care. Physician

preferences over patients determine which patients attain care and which do not. I estimate that

physicians prefer to treat patients with greater expected utilization. Thus, younger and healthier

patients experience lower access to care than their counterparts.

The determinants of access to care have policy implications. Many policies aim to increase

access to care by providing incentives to physicians. These policies include grants to physicians

who locate in low access areas, and payment incentives to accept more patients. If the primary

determinant of access to care in an area is a sparsity of physicians, then location grant incentives

could be highly effective at increasing access, whereas incentives for physicians to increase capacity

would be ineffective. These policy implications are studied in detail in Chapter 2 of this dissertation.

I conclude by identifying important avenues for future work. This chapter is the first to my

knowledge to measure access to care as an output of an equilibrium model. It does so under a

purely positive framework. Using the estimated model, I am able to discuss the distribution and

determinants of a well-defined measure of access to care. However, I am unable to make judgments

about the value of access to care for different types of patients. For such normative statements to

be made, I must determine the relative value to society of an additional unit of access for different

59

types of patients.

Once a normative framework is established, the applications of the model expand. The model

could then be used to design optimal policy and regulation. For example, the welfare implications of

the decentralized market design could be compared to alternative centralized mechanisms. Further

afield, a model of access to care in equilibrium could inform the value to society of different network

adequacy rules for insurance in the United States. These questions are beyond the scope of this

chapter. Yet, they are of primary importance for policymakers seeking to increase access to care

and for the patients who would benefit.

60

Chapter 2: Increasing Access to Care Through Policy: A Case Study of

Northern Ontario, Canada

Nathaniel Mark1

2.1 Introduction

Increasing access to medical care is a priority for Canadian health policymakers and patients.

57% of Canadians state that either “Wait times” or “Availability/Accessibility” is the “most important

health care issue facing Canada today.” This compares to 8% who report that it is “the high cost

of care” and 4% who report “the quality of care” (Samuelson-Kiraly et al. (2020)). Accordingly,

federal and provincial governments devote many resources to policies that aim to increase access to

care. 2

In this paper, I assess the impact of two such policies on access to care in the empirical setting

of the primary care market of Northern Ontario. The first policy is a grant program, the Northern

and Rural Recruitment and Retention (NRRR) grant, that provides up to $117,600 to physicians

who locate in designated low-access areas. Second, I study a reform to the primary care physician

payment system. Before 2001, primary care physicians were paid on a fee-for-service basis. The

reforms introduced alternative payment models that used capitation payments, quality bonuses, and

other incentives. The alternative payment models were designed to increase access by incentivizing

1. This study made use of de-identified data from the ICES Data Repository, which is managed by the Institutefor Clinical Evaluative Sciences with support from its funders and partners: Canada’s Strategy for Patient-OrientedResearch (SPOR), the Ontario SPOR Support Unit, the Canadian Institutes of Health Research and the Government ofOntario. The opinions, results and conclusions reported are those of the authors. No endorsement by ICES or any of itsfunders or partners is intended or should be inferred. Parts of this material are based on data and information compiledand provided by CIHI. However, the analyses, conclusions, opinions and statements expressed herein are those of theauthor, and not necessarily those of CIHI.

2. In Northern Ontario alone, Pong (2008) finds that the provincial government introduced new programs to reducephysician shortages at a rate of two per year in the 1990s and early 2000s.

61

physicians to accept additional patients.

To assess the policies’ impact on access to care, I estimate a model of the market for primary

care. I also define of measure of access as an outcome of the market in equilibrium. Then, I use the

estimated model to simulate equilibria under counterfactual policy regimes. For each counterfactual,

the model predicts the probability that each patient receives care and a measure of their level of

access to care. The measure of access used is the probability of attaining care divided by the

probability of attaining care in a full access environment. The measure can be interpreted as the

probability of attaining care in the current equilibrium for those who would attain care if they had

full access to care.

My findings suggest that both policies are successful at increasing access to care. I estimate that

the Northern and Rural Recruitment and Retention grant increases access to care by between 0.1

and 3.1 percentage points. This translates to an increase in the percent of Northern Ontarians who

see a primary care physician by between 0.1 and 2.4 percentage points. To attain these estimates, I

conduct counterfactual simulations where the NRRR grants are removed. I use estimates of primary

care physician own-wage elasticities from the literature to determine the number of physicians who

leave each area in the absence of the grant (Kulka and McWeeny (2018) and Hurley (1991)).

Due to limitations in the data, I am unable to conduct a cost-benefit analysis of the Northern

and Rural Recruitment and Retention grant. However, I show evidence that the grant is potentially

justified. In high population areas, I estimate that physicians can attain high revenues after entry

by stealing patients from incumbent physicians. Thus, an entry into these locations does not

significantly increase access to care. In low access, low population areas, an entrant physician may

attract few patients but increase access significantly. Therefore, providing financial incentives for

physicians to locate in low access areas may be justified, as it incentivizes physicians to locate in

areas where the government would attain greater “access for buck”.

I find that the physician payment reforms increase access to care by 5.4 percentage points

(pp). Both reduced form analyses and estimated physician preferences show that physicians accept

more patients when they are in an alternative payment model. This explains most of the impact

62

of the alternative payment models on access. In line with the existing literature, physicians are

relatively unresponsive to revenue when they are selecting patients (Rudoler, Laporte, et al. (2015)

and Kantarevic and Kralj (2014)).

Importantly, the two policies have heterogeneous impacts on patients. As expected, the Northern

and Rural Recruitment and Retention grant primarily benefits rural patients, who have lower baseline

access. Within an area type, the effect of the grant on access is similar for different types of patients.

In contrast, the payment reforms increased access for urban patients more than rural patients. For

urban patients, low access to care was primarily caused by physicians being unwilling to accept

them. The payment systems loosened these constraints by inducing physicians to accept more

patients.

Related Literature

This research contributes to the literature on how policy affects access to care. Its primary

innovation is methodological. An intuitive definition of access to care is the ability for a patient

to attain care if they want it. Such an object is an outcome of a market for medical care. That is,

patients demand care from physicians, and physicians supply care. When demand exceeds supply,

rationing generates low access. As a result, assessing the efficacy of policy at increasing access to

care is challenging. Indeed, simply measuring access is difficult, as it is a function of unobserved

supply and demand. Instead, previous literature has relied on proxies for access to care, such as

the patient to physician ratio. Further, physician responses to policy interact in the market. For

example, if a physician is induced to enter into a market by a policy, they may crowd out incumbent

physician supply. This complicates policy assessment based on individual physician observables.

In this paper, I account for these challenges by estimating a model of the primary care market and

using this model to conduct counterfactual analyses.

The literature on the efficacy of location incentives for physicians is well-established. Since

Hurley (1991), several policies have been studied using discrete choice modeling techniques. In

these models, physicians choose locations according to their preferences over amenities, salaries,

63

incentives, and other factors.3 Analyses vary in model and data complexity. A recent burst in

research activity on loan repayment and scholarship programs in the United States has advanced

the literature. These papers account for the endogeneity of salaries and other factors by using

instruments and/or by modeling the market for physician supply (Kulka and McWeeny (2018)

and Falcettoni (2018)). The number of physicians in each region or the physician to population

ratio are the most common outcomes studied in these papers. While these outcomes are important

contributors to patient access, other factors impact access as well.4 Thus, I advance the literature by

assessing the impact of an incentive policy on a measure of access to care. Further, I am able to

assess how the policy affects different types of patients.

Lastly, this paper contributes to the literature on the effect of physician payment models on

access to care. Much of this literature focuses on the impact of payment models on physician

productivity (Kantarevic, Kralj, and Weinkauf (2011)) and patient selection (Alexander; Rudoler

et al.; Kantarevic and Kralj). Due to the wide range of policies studied world-wide, results have

been mixed. Within studies of the Ontario payment reforms, Kantarevic, Kralj, and Weinkauf

(2011) find that physicians who switch to an enhanced fee-for-service model increase the number of

patients they accept. Rudoler et al. (2016) finds no selection of patients based on risk (expected

utilization). Unlike these reduced form studies, I am able to account for the equilibrium effects of

the payment models. Encouragingly, my results largely confirm the reduced form conclusions.

A related subject is the effect of insurance reimbursement rates in the United States on access

3. Hurley (1991) use a nested multinomial logit model to study physician choices over specialty and community sizein the United States based on average lifetime income. Bolduc, Fortin, and Fournier (1996) study incentive policies inQuebec using a spatially correlated multinomial probit model. They find that Quebec’s incentive policies increased theprobability of young physicians locating in remote regions by 53%. Holmes (2005) focuses on a scholarship program,the National Health Service Corps, finding that removing the program would “ decrease the supply of physicians inmedically underserved communities by roughly 10%.” Chou and Lo Sasso (2009) focus on the effect of malpracticepremiums on physician location within New York state, while Nunes, Francisco, and Sanches (2015) study locationchoice in Brazil. Zhou (2017) studies dynamic physician choices of location, facility and hours of patient care inNorth Carolina. A consistent finding by Zhou (2017), Kulka and McWeeny (2018), and Falcettoni (2018) is thatloan repayment policies are much less cost effective than direct financial incentives such as the Northern and RuralRecruitment and Retention grant.

4. Patient and physician characteristics in a market affect access. For example, if an area has a particularly youngpopulation, access will be higher ceteris paribus. The geographic distrbution of patients and physician also affect access.For instance, a suburb with a low physician to population ratio may have high access due its proximity to physicians inthe city. See Pong (2002) for a good discussion of these issues.

64

to physician services (Shen and Zuckerman (2005), Chen (2014), Alexander and Schnell (2018),

and Benson (2018)). The literature has found that physicians are responsive to reimbursement

rates when choosing to accept patients. In a recent paper, Alexander and Schnell (2018) exploit a

quasi-exogenous shift in Medicaid reimbursement rates caused by the Affordable Care Act. They

find a large effect: they estimate an elasticity of physician willingness to accept “adult Medicaid

patients with respect to reimbursement” of 0.83. Further, they do not find evidence that the increased

Medicaid reimbursements negatively impacted the probability that physicians accepted privately

insured patients. This suggests that physicians “accommodate more patients when payments

increase.” Consistent with these findings, I estimate that physicians substantially increase the

number of patients they treat when they switch into an alternative payment system that provides

higher reimbursements per patient. However, I find that physicians are only modestly sensitive to

financial incentives when choosing between patients in the matching market (I estimate an average

elasticity of physician willingness to match with a patient with respect to expected revenue of 0.12).5

This suggests that physicians may have strong responses to financial incentives when choosing

policies such as which insurance to accept, but are less responsive to financial incentives when

selecting between patients conditional on a policy being chosen.

The remainder of this chapter is structured as follows: First, I describe the empirical setting

and the empirical model of the primary care market in Northern Ontario. These topics are covered

in greater depth in Chapter One of this dissertation. Second, I assess the Northern and Rural

Recruitment and Retention grant. Third, I present an assessment of the physician payment reforms.

Within each assessment, I outline the details of the policies, discuss assessment methodologies,

and present results. Last, I conclude by comparing the effects of the policies on access to care and

interpreting the results.

5. Both of these findings are consistent with the existing reduced form literature (Kantarevic, Kralj, and Weinkauf(2011) and Rudoler et al. (2016)).

65

2.2 An Empirical Model of the Primary Care Market in Northern Ontario, Canada

To assess the impact of policies on access to care, I estimate access in counterfactual policy

regimes using an estimated model of the market for primary care in Northern Ontario, Canada.

The model and estimation procedure are detailed in Chapter One of this dissertation. This section

presents an overview of the empirical setting and the estimated model.

2.2.1 The empirical setting

The primary care market of Northern Ontario was chosen as the empirical setting because

its institutional details allow for an empirical matching model to be estimated under reasonable

assumptions. Specifically, the market is modeled as a non-transferable utility, decentralized, many-

to-one empirical matching market. Additionally, the Ontario government has implemented policies

to increase access to care which are similar to policies that exist in many other markets. Thus, the

primary care market of Northern Ontario provides a useful setting to study the effect of policy on

access to care.

The assumptions needed to estimate a non-transferable utility, decentralized, many-to-one

matching market are reasonable in this empirical setting. First, there are no financial or in-kind

transfers from patients to physicians. Primary Health Care in Ontario is a single payer, private

practice system. The Ontario Health Insurance Plan (OHIP) pays for all diagnostic and physician

services that are deemed necessary care. There are zero user fees for these services. Thus, the

payment a physician attains for supplying care to a patient is exogenous to the matching process.

Further, it is illegal for a physician to sell access to care in Ontario. “Boutique” clinics that bend

these rules do not exist in Northern Ontario (Mehra (2008, 2017)).6

Second, there is no centralized entity that matches patients and physicians. A government-funded

program, Health Care Connect (HCC), was created in 2009 to aid patients in finding a physician who

is accepting patients. Many family physicians prefer not to use HCC, and participation is entirely

voluntary. The effectiveness of the program is limited in Northern Ontario. The CBC reported

6. Boutique clinics do exist in Southern Ontario, particularly in the Golden Horseshoe region.

66

in 2017 that “just eight percent of new registrants to Health Care Connect received referrals to

physicians through the service last year” in Northwestern Ontario. The program gives preference to

patients who are “classed as complex of vulnerable.” Even among this population, only 15 percent

of patients received referrals (Kitching (2017)). For this reason, many practitioners advise patients

to look for doctors in other ways (Breton et al. (2018) and Graham (2018)).

Lastly, primary care markets in Northern Ontario are well-defined. Private primary care clinics

do not exist in Northern Ontario (Mehra (2008, 2017)). Primary care in Ontario is provided almost

exclusively by family physicians. And, importantly, population centers in Northern Ontario are

isolated. Therefore, geographic markets can be defined to ensure that there is limited interaction

between physicians and patients outside of a geographic market.

The two policies that are studied in this paper are representative of similar policies in many

settings. Many regions and countries provide grants similar to the NRRR to physicians who locate

in low-access areas. These include Australia (Yong et al. (2018)), the United Kingdom (Rimmer

(2019)), Peru (Huicho et al. (2012)), France, and Germany (Hassenteufel et al. (2020)). The

United States does not have a location grant program. Instead, the federal government issues loan

repayments and scholarships to health professionals who practice in low access areas through the

National Health Services Corps (Heisler (2018)). Payment models vary across country and region,

and discussion of payment model reform is ubiquitous among health policymakers. Fee-for-service,

capitation, and enhanced fee-for-service models are used in other settings (Luca, Paul, Organization,

et al. (2019)).

2.2.2 Model specification

I specify the model of the market for primary care as a matching model between patients and

physicians. Patients have preferences over physicians and physicians have preferences over patients.

Matchings are generated by the Rationing-by-Waiting Equilibrium (Galichon and Hsieh (2019)). In

this subsection, I briefly outline the model and specification. Chapter One, Section Five presents the

model in detail.

67

Patient Preferences Over Physicians

Patients have preferences over physicians that depend on patient-physician characteristics. The

latent utility that patient 𝑖 derives from matching with physician 𝑗 in market 𝑡 depends on a mean

utility term, 𝛿𝜷\ 𝑗𝑡

, and an extreme value type I taste shock. The mean utility can be categorized into

three terms. First, patients derive utility from attaining medical care. Second, a patient of type \ has

additional preferences for physician 𝑗 , depending on 𝑗’s characteristics. Third, patients experience

a disutility of traveling to physicians who are distant.

𝑢𝑖\ 𝑗 𝑡 =

Value of Attaining Care︷︸︸︷𝜷𝑢1 + 𝒙′\𝑡𝜷

𝑢2 +

Net Match Value︷︸︸︷𝒙′\ 𝑗𝑡𝜷

𝑢3 −

Cost of Travel︷︸︸︷𝒇𝒅 (𝑑\ 𝑗𝑡)′𝜷𝑢4︸︷︷︸

𝛿𝜷\ 𝑗𝑡

+𝜖𝑖\ 𝑗 𝑡 (2.1)

In the main specification, the variables that determine the value of attaining care, 𝒙\𝑡 , include an

estimate of the expected number of visits a type \ patient will make and categorical descriptions

of the patient type: 15-year age bins, sex, and whether the patients have comorbidities. Some

interactions between patient characteristics are also included. The net match value variables, 𝒙\ 𝑗𝑡 ,

include variables that describe physician 𝑗 , such as payment model, gender, and whether she offers

walk-in visits. Additionally, 𝒙\ 𝑗𝑡 includes interactions between physician 𝑗’s characteristics and

patient type \’s characteristics. Namely, these are interactions between: physician payment model

and the number of expected visits; patient and physician gender. The cost of distance is specified

as a quadratic function of distance, interacted with the population density of the patient’s census

division.

Physician Preferences Over Patients

Additionally, physicians have preferences over patients. Physician 𝑗’s mean utility for type \

patients in market 𝑡, 𝛾𝜷\ 𝑗𝑡

, consists of three terms. The first term is the revenue a physician expects

to attain from a type \ patient. I allow physicians to be heterogeneous in their taste for revenue.

Second, the physician attains utility for treating a type \ patient. This non-revenue match value is

68

a combination of the cost and the altruistic psychic benefit to the physician of supplying services

to the patient. These cannot be separately identified. Third, physicians suffer an opportunity cost

associated with adding a patient to their panel. Last, an additive random taste shock at the patient

type-physician panel space-market level is assumed to be distributed extreme value type I.

𝑣\ 𝑗𝑞𝑡 =

Revenue︷︸︸︷[𝛽𝑣1 + 𝛽

𝑣2𝛼 𝑗 ]𝑅\ 𝑗𝑡 +

Net Match Value︷︸︸︷𝛽𝑣3𝑉\𝑡 + 𝒚′\𝑡𝜷

𝑣4 −

Value of Leaving Space Open︷︸︸︷[𝛽𝑣5 + 𝒚′𝑗 𝑡𝜷

𝑣6]︸︷︷︸

𝛾𝜷\ 𝑗𝑡

+[\ 𝑗𝑞𝑡 (2.2)

The variables that enter the net match value term are the expected utilization (in visits) of a type

\ patient, 𝑉\𝑡 , and patient characteristics, 𝒚\𝑡 . The included patient characteristics are: 15-year age

bins, sex, and whether the patient has a comorbidity. The value of leaving a space open depends on

physician characteristics that change over time, 𝒚 𝑗 𝑡 , including age, payment model, and years in

practice.

Additional variables are included in 𝒚 𝑗 𝑡 that account for potential systematic error in the

estimation of physician panel capacity 𝑚 𝑗 𝑡 . Since panel capacity is estimated as the maximum over

all years, physicians who exist for less years in the panel are likely have less open panel spaces. To

account for this, I include the proportion of years that the physician is in the sample as a variable in

𝒚 𝑗 𝑡 .

The random coefficient on revenue, 𝛼 𝑗 , is specified as a linear function of observable physician

characteristics, 𝒛𝑅𝑗𝑡, including gender and size of practice, and an unobserved physician-specific

parameter, 𝜖𝑅𝑗

:

𝛼 𝑗 = 𝝓2𝒛𝑅𝑗𝑡 + 𝜖𝑅𝑗

Equilibrium

Matchings are assumed to be generated by a Rationing-by-Waiting equilibrium (Galichon and

Hsieh (2019)). In market 𝑡, type \ patients face a cost (in utils) of effort to match with physician

𝑗 , 𝜏𝑢\ 𝑗𝑡

. Similarly, physician 𝑗 faces a cost of effort to match with patients of type \, 𝜏𝑣\ 𝑗𝑡

. In

equilibrium, effort costs adjust such that demand equals supply for each (\, 𝑗) pair. Further, only

69

one side of the market exerts effort at one time. That is, if 𝜏𝑢\ 𝑗> 0, then 𝜏𝑣

\ 𝑗= 0 and vice versa.

Thus, the equilibrium conditions are:

Market Clearing:

`𝜷∅ 𝑗 𝑡 +

∑\ `

𝜷\ 𝑗𝑡

= 𝑚 𝑗 𝑡 ∀ 𝑗

`𝜷\∅𝑡 +

∑𝑗 `

𝜷\ 𝑗𝑡

= 𝑛\𝑡 ∀\

`𝜷\ 𝑗𝑡

= 𝑛\𝑡𝑒𝑥𝑝(𝛿𝜷

\ 𝑗𝑡−𝜏𝑢

\ 𝑗𝑡)

1+∑ 𝑗 ′ 𝑒𝑥𝑝(𝛿𝜷\ 𝑗𝑡

−𝜏𝑢\ 𝑗𝑡

)= 𝑚 𝑗 𝑡

𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡


)

1+∑\ ′ 𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡


)∀\∀ 𝑗

One-Sided Effort: 𝑚𝑖𝑛{𝜏𝑢\ 𝑗𝑡 , 𝜏𝑣\ 𝑗𝑡} = 0 ∀\∀ 𝑗

2.2.3 Estimation and Key Model Results

I estimate the matching model using a nested fixed point maximum likelihood method. The

results of the empirical matching model are presented in detail in Chapter One. Table 2.1 highlights

the most important results. In this table, I describe preferences in the context of an illustrative

patient choosing between an illustrative physician and no physician and the context of an illustrative

physician choosing to accept an illustrative patient or accept no patient. I define an illustrative

patient as a 50-64 year old male without comorbidities who is expected to visit his physician 5

times and provide a capitation revenue of $175.21. I define an illustrative physician as a 50 year

old female who works in a capitation system and does not offer walk-ins. The illustrative patient is

located 5 minutes away from the illustrative physician.

Both a patient’s expected utilization of physician services and the drivetime to the physician

impact patient preferences. The illustrative patient’s elasticity of the probability of choosing the

illustrative physician with respect to their expected number of visits is 0.64. The elasticity with

respect to drivetime is -0.51.7

7. The illustrative patient’s elasticity of the probability of choosing the illustrative physician with respect to acharacteristic 𝑥 is:

𝜖 𝑥\̃ 𝑗𝑡

=1

1 + 𝑒𝑥𝑝(𝛿𝜷\̃ 𝑗𝑡

)

𝜕𝛿𝜷

\̃ 𝑗𝑡

𝜕𝑥 \̃ 𝑗𝑥 \̃ 𝑗

70

Interestingly, I also find evidence of homophily among men. A male illustrative patient is more

likely to choose a male illustrative physician over the outside option than the female illustrative

physician. The same relationship is not apparent for female patients.

Physician preferences over patients are primarily driven by expected patient utilization. That is,

I estimate that physicians are more likely to accept patients who are more likely to attain greater

amounts of care. Importantly, this finding is conditional on the revenue that the physician expects

to attain from the patient. One potential interpretation for this finding is that physicians behave

altruistically and prefer to treat patients with greater need for care. However, decreasing average

costs of supplying a visit to a given patient is an alternative explanation. For example, if there

are high administrative costs for on-boarding patients, physicians may prefer to treat patients with

higher expected utilization.

I estimate that physician preferences over patients are only weakly determined by the revenue.

Specifically, the elasticity of the illustrative physician’s probability of accepting the illustrative

patient (over the outside option) with respect to the expected revenue that the patient would supply

to the doctor is 0.12. This suggests that physicians do not select their patients primarily to maximize

revenue. This finding is consistent with the previous literature on patient selection in Ontario

(Rudoler, Laporte, et al. (2015), Kantarevic and Kralj (2014), and Rudoler et al. (2016)).

Lastly, ceteris paribus, a physician’s probability of accepting patients depends on their payment

system. If the illustrative physician is in a fee-for-service payment system, she is less likely to

accept the illustrative patient than if she is in an alternative payment system. Potentially, this is a

response to design aspects of the alternative payment models which incentivize physicians to accept

more patients. These includes bonuses for signing up for new patients and higher average payments

for treating patients. These incentives are explained in more detail in Section 2.3. This finding

\̃ denotes the illustrative patient and 𝑗 denotes the illustrative physician. The illustrative physician’s elasticity of theprobability of accepting the illustrative patient with respect to a characteristic 𝑦 is:

𝜖𝑦

\̃ 𝑗𝑡=

1

1 + 𝑒𝑥𝑝(𝛾𝜷\̃ 𝑗𝑡

)

𝜕𝛾𝜷

\̃ 𝑗𝑡

𝜕𝑦 \̃ 𝑗𝑦 \̃ 𝑗

71

suggests that physicians are perhaps responsive to financial incentives along the margin of choosing

the number of patients to accept, whereas the low acceptance probability elasticity with respect to

revenue suggests that physicians are not responsive to financial incentives when selecting among

patients.

Table 2.1: Estimated Preferences

(a) Illustrative Patient Preferences

Elasticity of choice probability...with respect to utilization: 0.64with respect to drivetime: -0.51

Probability of choosing physician if the...patient is male and physician is male: 23.96%patient is male and physician is female: 11.80%patient is female and physician is male: 25.75%patient is female and physician is female: 25.83%

(b) Illustrative Physician Preferences

Elasticity of acceptance probability...with respect to revenue: 0.12with respect to utilization: 1.28

Probability of accepting if the...physician is in a capitation system: 34.16%physician is in an EFFS system: 33.19%physician is in a FFS system: 22.26%

2.2.4 A Measure of Access to Care

To assess the impact of policy on access to care, I define a measure of access to care for a

hypothetical counterfactual environment. Access to care is defined as the ratio of the probability of

matching with a physician in the counterfactual environment and the probability of matching with a

physician in a full access environment.

Access\𝑡 =Probability of matching with a physician in counterfactual environmentProbability of matching with a physician in a full access environment

This measure of access to care reflects an intuitive definition of access to care: “the ability for a

patient to attain care if they want it.” The probability that a patient would attain care in a full access

environment reflects whether a patient is likely to want to attain care. In the main specification, I

define the full access environment as the hypothetical choice environment faced by a patient who

lives in the largest city in Northern Ontario (Sudbury) and to whom all physicians are willing to

72

accept.

Further, I am able to easily compute this measure of access to care for each patient type using

the estimated matching model. Thus, I am not only able to assess the impact of policy on average

access to care. I am able to explore the heterogeneous effects that policy have on different types of

patients.

2.3 Policy One: Practice Location Incentives

The Ontario government has several policies that are designed to incentivize primary care

physicians to locate in rural and Northern areas. The longest-standing and largest incentive policy is

the Northern and Rural Recruitment and Retention (NRRR) grant. This program was established in

1969 and provides grants to primary care physicians who practice in an “underserved” area.8 Grants

are valued at $40,000 to $117,600 and paid out over the first four years of practice. The grants

are paid in installments: 40% in the first year that a physician practices in the location, 15% in the

second and third years, and 30% in the fourth year of practice (Ministry of Health and Long-Term

Care (2017)).9

The value of the grant depends on the severity of access issues in the chosen location, as

measured by the Rurality Index for Ontario (RIO). For a physician to be eligible for the grant, they

must locate in a census subdivision with a Rurality Index for Ontario score of 40 or larger. Most

census subdivisions in Northern Ontario are eligible location (129 of 143 in the 2014 sample). The

cities of Thunder Bay, Sudbury, and Timmins are among the ineligible locations (see Figure 2.1).

8. Previously, the policy was named the Underserved Area Program.9. The Ontario Ministry of Health and Long Term Care (MOHLTC) established the Rurality Index for Ontario to

determine census subdivision eligibility for the NRRR grant in 2009. Before 2009, a political process determinedwhether an area attain shortage area designation. This process led to many designated shortage census subdivisions andmany that were located in the relatively densely populated South (Whaley (2020)). The Rurality Index for Ontario isa reasonable measure of access to care, unlike many common measures for access to care (see Appendix B.1). TheNRRR grant value is determined by a piece-wise function of the Rurality Index for Ontario:

NRRR grant =

0 𝑅𝐼𝑂 < 072, 0000 + 200𝑅𝐼𝑂 40 ≤ 𝑅𝐼𝑂 < 507, 600 + 1480𝑅𝐼𝑂 50 ≤ 𝑅𝐼𝑂 < 7097, 6000 + 200𝑅𝐼𝑂 70 ≤ 𝑅𝐼𝑂

73

The Rurality Index for Ontario is a weighted average of population, population density, and

distance to the nearest physician (Kralj (2009)). Similar policies use different measures to distribute

funds. For example, the National Health Service Corps in the United States uses a measure of

access that is a weighted average of physician to population ratio (25 weight), a measure of poverty,

an infant health index, and travel time to nearest doctor (15weight each)

Figure 2.1: RIO Map

2.3.1 Previous Literature

The existing literature finds that physician grant incentives impact physician location choices

and the distribution of physician supply, but the magnitude of these impacts are small. In pioneering

work, Bolduc, Fortin, and Fournier (1996) finds that Quebec’s incentive policies increased the

probability of young physicians locating in remote regions by 53.3%. Similarly, Holmes (2005)

finds that removing the US’ flagship incentive program, the National Health Service Corps (NHSC),

would “decrease the supply of physicians in medically underserved communities by roughly 10%."

74

A related literature examines how physician location choices are affected by income (Hurley (1991)

and Nunes, Francisco, and Sanches (2015)) and malpractice premiums (Chou and Lo Sasso (2009)).

In more recent work, Kulka and McWeeny (2018) and Falcettoni (2018) advanced the literature

by accounting for the endogeneity of salaries. Both study the impact of medical school loan

repayment schemes and changes in income on physician supply. Kulka and McWeeny (2018) use

a difference-in-differences approach that exploits the staggered introduction of loan repayment

schemes in different states. They estimate that loan repayment programs cause an increase of three

physicians per rural county – a small effect. Then, they estimate a static discrete choice model to

study the responsiveness of physicians to income. They estimate a median own-wage elasticity

of supply of 1.91, concluding that income bonuses are much more effective than loan repayments

in increasing physician supply. They note that this result is similar to previous work in the field,

where “Hurley (1991) finds an average income elasticity of supply of 1.05, and Bolduc, Fortin, and

Fournier (1996) report an average income elasticity of 1.11.” I use these own-wage elasticities to

benchmark my counterfactuals which analyze the effect of the NRRR grant.

Falcettoni (2018) uses different modeling techniques but comes to similar conclusions. She uses

a spatial equilibrium model where physicians choose locations based on heterogeneous preferences

over salary, amenities, Physicians are heterogeneous both according to demographics, but also

specialty and a quality ranking. She finds that physicians are responsive to financial incentives,

but only mildly. For example, she finds that a $7,500 one-time salary bonus in rural areas would

increase the supply of primary care physicians in those areas by 0.2%.10 Loan forgiveness programs

are estimated to increase primary care physician supply by 0.7%. Thus, as in Kulka and McWeeny

(2018), income mechanisms were found to be more effective than loan forgiveness programs.

10. Assuming an average annual primary care physician salary is $213,270 in the United States in 2019 (BLS), thisroughly translates to very small rural physician supply elasticity with respect to an income bonus of 0.057. This estimatecannot be directly compared to that of Kulka and McWeeny (2018), but serves to show that the literature has yet tosettle the question of whether income is an effective tool to incentivize physician location choice.

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2.3.2 Policy Counterfactual

To assess the efficacy of the NRRR grant in increasing access to care, I simulate counterfactual

equilibria where the NRRR grants are removed. In the absence of the grant, the number of physicians

decreases in areas where the grant applies. To determine the magnitude of this decrease, I adopt

the own-wage elasticities estimated by Hurley (1991) and Kulka and McWeeny (2018) for the

primary care market in the United States. These estimated elasticities, along with several simplifying

assumptions, provide a back-of-the-envelope prediction of the physician supply response to the

NRRR grants.

Specifically, I first assume that cross-wage elasticities are equal to zero among locations within

Northern Ontario. That is, all physicians who are induced to enter a location by the NRRR

grant incentive are implicitly assumed to be transitioning from either unemployment or from a

location outside of Northern Ontario. This is a strong assumption, as physician location choices are

influenced by preferences over regions. Thus, estimates of the policy effect should be interpreted as

upper bounds.11

The benchmark income I use is $207,600 per year. This is the mean net income of family

physicians in 2009/2010 derived from public payments data and survey data on overhead costs by

Petch et al. I make two separate assumptions on how income is affected by the NRRR grant and I

report results for both assumptions. In the first case, I assume that the relevant income increase is

the average yearly NRRR grant value over the four years that the physician receives the grant. In

the second case, I assume that the present value of all future income is the pertinent statistic. Thus,

I estimate the present value of the NRRR grant to physicians. Then, I derive the percent increase in

the present value of income. To do so, I assume a 30-year stream of income and a 5% discount rate.

A $100,000 4-year NRRR grant would increase the first measure of income by 12% and the second

by 3%.

To estimate the effect of the NRRR grant on access to care, I simulate a counterfactual equilib-

11. A further reason for this interpretation: Falcettoni (2018) estimates a much lower responsiveness of supply toincome than Hurley (1991) or Kulka and McWeeny (2018).

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rium where the NRRR grant is removed. Physician supply is lower in the absence of the grant. To

determine the number of physicians to remove from each census subdivision, I define the probability

that a physician 𝑗 would leave their location, 𝑃 𝑗 𝑙 , as the own-wage elasticity of supply, 𝜖 , multiplied

by the percent increase in income caused by the grant, %Δ𝑌 𝑗 . I then remove each physician with

probability 𝑃 𝑗 𝑙 . To account for randomness in the process of removing physicians, I simulate 20

equilibria and report averages over these simulations.

Depending on the specification used, I estimate that the NRRR grant induces 6 to 43 additional

physicians to practice in Northern Ontario. These physicians increase access to care by between

0.10 and 3.05 percentage points. The largest effect is estimated when Kulka and McWeeny (2018)’s

own-wage elasticity estimate and the average yearly grant income change measure are used. These

translate to a 0.08 to 2.43 percentage point increase in the number of Northern Ontarians who attain

primary care. The sensitivity of the results to specification assumptions suggest that further research

is needed to establish the efficacy of location grant policies.

While the magnitudes of results are sensitive to specification, the relative effect of the NRRR

grant on different types of patients remains consistent across specifications. As expected, rural

patients attain the greatest benefit. In the specification with the largest effects, rural access increases

by 7.74 percentage points, semiurban access increases by 1.88pp, and urban access by 0.05pp. Table

2.2 details these results.12

The grants increase access the most for patient who have low access. In three of four specifi-

cations, patients with access between 30% and 40% attain the greatest percentage point increases

in access to care. For the specification with the largest effect, access for these patients increases

by 6.70 percentage points. This compares to 4.75pp for patients with access between 60 and 70%.

Table B.1 provides the increase in access for all groups of patients.13 Differences in access gains

between patients who have comorbidities and those who do not are small, as are differences in gains

between ages (see Table B.2 and Figure B.2).

12. Semiurban areas are non-metropolitan agglomerations with a population of 10,000 or more. Urban areas aremetropolitan.

13. In the specification with elasticity = 1.05 and the present value income is used, patients with 50-60% access attainthe greatest increases.

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Table 2.2: NRRR Grant Counterfactual Results (Access Gain)

Income Type: Average Present Value

Elasticity: 𝜖 = 1.05 𝜖 = 1.91 𝜖 = 1.05 𝜖 = 1.91

Access Gain (pp)Rural 3.42 7.74 0.25 0.77Semirural 0.94 1.88 0.05 0.42Urban 0.03 0.05 0.00 0.01Total 1.38 3.05 0.10 0.37

% W/ Doctor GainRural 2.65 6.00 0.21 0.62Semirural 0.84 1.67 0.04 0.37Urban 0.03 0.04 0.00 0.00Total 1.10 2.43 0.08 0.31

New Physicians 24.40 42.80 5.65 10.40

2.3.3 Gains in Access to Care

Assessing the welfare implications of the NRRR grant is beyond the scope of this paper. I do

not observe the cost of the NRRR grant to the government. Additionally, I am not able to identify

the welfare gains associated to patient access. However, I am able to provide evidence in support

of the policy’s justification: I show that the NRRR grant is designed to incentivize physicians to

locate in areas that provide greater increases in access per government dollar spent. Physicians that

enter locations that are ineligible for the NRRR grant often increase access insignificantly while

still attaining high revenues. In contrast, physicians that enter locations with large NRRR grant

incentives would have a larger impact on access.

When physicians enter a low access area, they are generally rewarded with high revenues.

In those areas, demand is high and competition is low. In contrast, entry into high access areas

generates low revenue. This relationship improves access under mild conditions. Physicians are

attracted to areas where they can attain high revenues, thus attracting physicians to low access areas.

However, this relationship breaks down due to the business stealing effect. That is, in areas with

high access to care and high population density, physicians can attain high revenues at entry by

78

stealing patients from incumbent physicians rather than attracting new patients who previously did

not receive care. This effect works through the effort mechanism. After entry, incumbent physicians

must expend more effort to attract patients. In response, individual physician supply decreases. The

population is large enough, however, that the entrant physician can still attain high revenues. This

may result in higher entry into high access urban areas than what is socially desirable (assuming

access is a social objective). This suggests that there is scope for entry incentives to increase social

welfare.

To show this, I simulate the impact of an illustrative physician entering into each census

subdivision on access to care. Additionally, I estimate the revenue (in 2004 dollars) that the

illustrative physician would attain if she entered in each census subdivision in 2014. As in previous

analyses, the illustrative physician in is a 50 year old female physician in the capitation payment

model who does not offer walk in visits and has a capacity of 1000 patients. Figure B.3 illustrates

the phenomenon. The black curve represents the relationship between the NRRR grant level and the

ratio of the increase in access due to an entry and the revenue the entrant physician attains. Using

the right-hand side axis, the red curve represents the value of the NRRR grant size.14

14. The line represents the local polynomial regression mean of the ratio of access gained from entry and revenueattained upon entry onto the Rurality Index For Ontario at the census subdivision observation level. The accompanyingscatter plot, Figure B.3, is in the appendix.

79

Figure 2.2: Entry and Access

2.4 Policy Two: Physician Payment Reforms

Traditionally, Canadian primary care physicians are paid according to a fee-for-service payment

model. Policymakers have long recognized that the fee-for-service model incentivizes physicians

to provide services, not higher quality care or better patient outcomes (Lavis, Pasic, and Wilson

(2013)). This may lead to over-provision of services and high costs. Additionally, fee-for-service

may contribute to low access to care. If there are per-patient costs associated with on-boarding

patients or keeping patient records, physicians are incentivized to provide additional services to

their existing patients, rather than accept new patients.

With these considerations in mind, the Ontario provincial government introduced several

alternative payment models (APMs) between 2002 and 2006.15 These include both capitation

15. Before 2001, the vast majority of primary care physicians participated in the fee-for-service payment model.However, there were exceptions. Two early programs, the Health Service Organization (HSO) model and the CommunityHealth Center (CHC) model, were introduced in 1973 to nudge the system from its reliance on the fee-for-servicemodel. The HSO model consisted of capitated payments and a patient rostering program. The program was small,there being only 63 HSO physician clinics in 2001. The CHC model, introduced in 1982, was specifically designed forlow-access areas. CHC clinics are run by communities, and physicians in CHCs are salaried. In 2001, there were 56CHCs (139 salaried physicians). The CHC model was restricted to underserved communities. HSOs and CHCs in 2001served 4.7% of the population of Ontario. Additionally, five pilot projects called Primary Care Networks were launchedin 1998 to evaluate a capitation and enhanced fee for service programs (Aggarwal and Williams (2019), Hutchison,Abelson, and Lavis (2001), and Lavis, Pasic, and Wilson (2013)).

80

payment models and enhanced fee-for-service models. The government hoped that these payment

models would increase access, control costs, and increase quality of care (Hutchison, Abelson, and

Lavis (2001)). To assuage physician opposition to reform, the payment models were voluntary –

physicians could choose to participate in any of the models for which they qualified. Additionally,

the fee-for-service model remained as an option. To induce physicians to participate, the alternative

payment models were designed to be financially attractive (Aggarwal and Williams (2019)).

I assess the effect of the primary care payment reforms on access to care in Ontario. The

alternative payment models affect access to care through physician incentives. First, alternative

payment models incentivize physicians to increase the number patients they accept. Revenue per

patient is higher in the alternative models than in the fee-for-service model. Physicians are therefore

incentivized to increase the size of their patient panels either by working longer hours or changing

practice styles, thereby increasing access.

Second, alternative payment models incentivize physician to select patients on characteristics.

Enhanced fee-for service physicians are incentivized to select patients who attain “in-basket”

services, while capitation provides incentives to select physicians with low demand for services.

The selection incentives for capitation physicians are large. Capitation payments are only risk

adjusted by age in 5-year bins and sex. By changing physician’s preferences over patients, the

alternative payment models affect the distribution of access across patient types.

The estimated physician preferences imply that access is affected by the alternative payment

models, primarily through the first incentive. Physicians are substantially more likely to accept

patients when they are in an alternative payment model. I estimate that the log odds of a physician

leaving a panel space open decreases by 0.60 in the capitation model and by 0.55 in the enhanced

fee-for-service model, relative to the fee-for-service model. In contrast, physician selection of

patients based on potential revenue is modest. I find an elasticity of physician willingness to accept

with a patient of 0.12.16

16. The average elasticity of physician willingness to match with a patient is calculated in the following way: First,for each physician 𝑗 and patient type \, I estimate the elasticity of physician 𝑗 choosing a patient of type \ with respectto the revenue a physician attains from patient type \, assuming that the physician faces a choice between the type \patient and the outside option of no patient.

81

Reduced form exercises confirm these patterns. Using a two-way fixed effect model with

physician-year level panel data, I estimate that physicians in an alternative payment model increase

the number of patients on their roster relative to when they are in the fee-for-service model. The

magnitudes of these estimates (6.6% increase in capitation and 16.0% in enhanced fee-for-service)

are significant. Additionally, fixed effect model results suggest that physicians have mildly different

matching patterns in capitation models than in fee-for-service and enhanced fee-for-service models,

perhaps due to physician selection of patients on expected revenue.

These findings are in line with the existing literature. This literature focuses on comparing

physician behavior before and after physicians switch to the alternative payment models. Kantarevic,

Kralj, and Weinkauf (2011) find that physicians who switch to an enhanced fee-for-service model

increase the number of patients they accept. Rudoler et al. (2016) do not find evidence that

physicians deferentially select patients based on risk or comorbidities when practicing in the

capitation system.17

Neither the previous literature nor the above reduced form work accounts for equilibrium effects.

For example, when an individual physician changes to an alternative payment model, they may

increase the number of patients that they accept. However, other physicians may respond by

decreasing their own panel sizes. Therefore, to determine the effect of the alternative payment

model on the whole market, I estimate a counterfactual equilibrium where the alternative payment

models are never introduced. Counterfactual equilibrium outcomes are then compared with the

𝜖𝑅𝑗 \𝑡 =1

1 + 𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

)[𝛽𝑣1 + 𝛽𝑣2𝛼 𝑗 ]𝑅\ 𝑗𝑡

Second, I average these elasticities over all physician-patient type combinations. I weight the average by number ofpatients in each type: ∑︁

𝑡

1|J𝑡 |

∑︁𝑗∈J𝑡

1∑\ ∈Θ𝑡

𝑛\𝑡

∑︁\ ∈Θ𝑡

𝑛\𝑡𝜖𝑅𝑗 \𝑡

17. In an early analysis, Devlin and Sarma (2008) find the surprising result that physicians with high number of visitsper week were attracted to the alternative payment models, but decreased the number of visits per week after adoptingthe new payment model. These trends may be due to changing physician patient pools or to changing practices. Indeed,anecdotally, physicians who practice in the capitation system focus on longer, more comprehensive visits. In contrast,fee-for-service physicians are more likely to request multiple visits for multiple problems from their patients (Stewart(2018)).

82

current equilibrium outcomes. In the remainder of this section, I first detail the payment reforms.

Then, I present the reduced form evidence. Last, I show the results of the counterfactual exercises.

2.4.1 Details of the Policy

Before the primary care payment reforms in 2002-2006, almost all primary care physicians

in Ontario were paid by a fee-for-service payment model. Following the payment model reforms,

there are five main payment models available for physicians to choose. Table A.6 shows the main

characteristics of each model.18 Except for the CCM model, the alternative payment models require

physicians to work in a group of 3 or more physicians. However, “physicians practicing in groups

do not need to be co-located or share the same electronic medical record” (Kiran et al. (2018)).

For the purposes of assessing the impact of the alternative payment models, I group the models

into three categories: fee-for-service, enhanced fee-for-service, and capitation. In the empirical

specification, I assume that physicians in a capitation model are paid under the FHG model and that

physicians in an enhanced fee-for-service plan are paid under the FHO model.

Table 2.3: Characteristics of Payment Models

Payment % Revenue % Physicians MinimumModel Type Introduced from fees in 2015 Group Size

FFS FFS 1966 98 14 1FHN Capitation 2002 27 2 3FHG EFFS 2003 81 27 3CCM EFFS 2005 84 4 1FHO Capitation 2006 21 53 3

In the fee-for-service model, physicians receive a prespecified fee for each service provided, as

specified in a Schedule of Benefits and Fees. Rostered patients, who are formally signed up as a

patient, and unrostered patients are treated identically under the FFS model.

In addition to the fee-for service fees, the enhanced fee-for-service payment models provide

additional compensation for rostered patients. Enhanced fee-for-service physicians are paid fees

18. Source: Rudoler, Deber, Barnsley, et al. (2015), Hurley et al. (2013), author’s calculations.

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that are 10% or 15% higher than the fee-for-service fee for certain services provided to rostered

patients. Further, the physician receives small monthly capitation payments for rostered patients

and bonuses for hitting quality of care goals. For example, a physician can attain $1,100 if more

than 75% of their senior patients receive an influenza vaccine by March 31. The revenue function

for this model can be written out as follows: 19

𝑅𝐹𝐻𝐺𝑗 (X𝑅,N𝑅,N0) =∑︁𝑠

𝑝𝑠𝑁0𝑠 +∑︁𝑠

(1 + 1

101{𝑠 ∈ 𝐵𝐹𝐻𝐺}

)𝑝𝑠𝑁𝑅𝑠 +𝑄𝐵(N𝑅,X𝑅) + 𝐶𝐶𝐶 (X𝑅)

Where X𝑅 represent the ages and sexes of the physician’s rostered patients, N𝑅,N0 are the fees

attained by rostered and unrostered patients respectively, and 𝑝𝑠 is the fee associated with service 𝑠.

𝑄𝐵(N𝑅,X𝑅) are quality bonuses and 𝐶𝐶𝐶 (X𝑅) are the “comprehensive care” capitation payments.

𝐵𝐹𝐻𝐺 is the set of services for which FHG physicians get an enhanced payment for their rostered

patients.

Capitation payment models provide yearly and monthly payments for each patient on a physi-

cian’s roster, regardless of the services provided to the patient. These capitation payments are

risk-adjusted according to a patient’s sex and age in five-year bins. Additionally, physicians in

capitation payment models receive the same quality of care bonuses as the enhanced fee-for-service

physicians.

The designers of the capitation payment model were concerned about physician incentives in the

capitation model, and designed the model accordingly. For rostered patients, physicians receive only

10% (until October 2010, then 15% (Zhang and Sweetman (2018))) of the OSBF fees for services in

a basket of services. These payments are called “shadow fees,” and exist to encourage physicians to

report all services provided. To disincentivize physicians from rostering patients who do not actually

go to their practice (and go elsewhere), the capitation payment models have an “Access Bonus”

19. The less popular enhanced fee-for-service model, CCM, does not have the higher associated fees. The revenuefunction for this model is:

𝑅𝐶𝐶𝑀𝑗 (X𝑅,N𝑅,N0) =∑︁𝑠

𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠) +𝑄𝐵(N𝑅,X𝑅) + 𝐶𝐶𝐶 (X𝑅)

84

structure: A physician group is provided an access bonus of 18.59% of all capitation payments. If

rostered patients receive services from physicians outside of the group, the cost of those services

are deducted from the access bonus (Glazier et al. (2019)). Lastly, to disincentivize physicians from

cherry-picking which patients to roster and which to treat on a fee-for-service basis, payments for

services provided to non-rostered patients are capped at $40,000. The capitation physician revenue

equation is below.20

𝑅𝐹𝐻𝑂𝑗 (X𝑅,N𝑅,N−𝑔( 𝑗)𝑅

,N0) =∑︁𝑠

1{𝑠 ∉ 𝐵𝐹𝐻𝑂}𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠)

+ 110

∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑂}𝑝𝑠𝑁𝑅𝑠 + 𝑚𝑎𝑥{∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑂}𝑝𝑠𝑁0𝑠, $40, 000}

+𝐶𝑎𝑝(X𝑅) + 𝑚𝑎𝑥{.1895𝐶𝑎𝑝(X𝑅) −∑︁

𝑝𝑠N−𝑔( 𝑗)𝑅𝑠

, 0} +𝑄𝐵(N𝑅,X𝑅) + 𝐶𝐶𝐶 (X𝑅)

Where 𝐶𝑎𝑝(X𝑅) are capitation payments and N−𝑔( 𝑗)𝑅𝑠

are the services provided to physician 𝑗’s

rostered patients by physicians who are not in 𝑗’s medical group. 𝐵𝐹𝐻𝑂 are the set of capitated

services.21

Alternative payment models increase the incentive for physicians to add patients and increase

the incentive for patient selection. The models paid physicians more to treat a patient. I estimate

that the revenue a capitation physician would attain from treating the average patient is 47% higher

than what a fee-for-service physician would attain, holding patient utilization fixed. An enhanced

fee-for-service physician would attain 23% higher revenue. These differences increased the total

payments made by the Ontario government to family physicians by 58% between 2003/2004 and

2009/2010 in inflation-adjusted dollars (Henry et al. (2012)).

Additionally, the alternative payments models introduced incentives for physicians to cherry

pick patients. Capitation payments are risk-adjusted only by age and sex. Thus, physicians in

20. The smaller capitation system, FHG, has a different basket of goods and a different access bonus percentage.Otherwise, the models are very similar.

21. Unless otherwise specified, this information was gathered from billings guides: Ministry of Health and Long-TermCare (2007a, 2007b, 2014, 2011) and OMA (2015).

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the alternative payment models, particularly in the capitation models, can attain large payments

with very little costs if they attract patients who did not attain many services. Chapter 1, Section 4

provides a more detailed discussion of these incentives.

2.4.2 Reduced Form Evidence

Before turning to the counterfactual analyses, I conduct reduce form exercises to analyze whether

physicians respond to payment incentives. Specifically, I exploit quasi-experimental variation in

the data caused by the staggered switching of physicians between payment models to estimate the

impact of the alternative payment models on physician outcomes. I use a two-way fixed effects

regression methodology to account for physician- and year- specific effects. I study physician-level

outcomes, such as the total number of patients the physician matches with (panel size), and the

characteristics of patients in the physician’s panel.

This analysis uses a physician-year level dataset of physician characteristics and physician-

patient matches. The dataset includes comprehensive care primary care physicians in Ontario from

2004 to 2014 with more than 300 patients. I restrict the sample further to only physicians who stay

in the same location throughout the entire sample. The final sample includes 633 physicians and

4,496 physician-years.

The regression is specified as a two-way fixed effects model:

𝑊 𝑗 𝑦 = 𝛼 𝑗 + _𝑦 + 𝛽′𝒄 𝑗 𝑦 + 𝜖 𝑗 𝑦

where 𝑊 𝑗 𝑦 is an outcome variable of physician 𝑗 in year 𝑦. 𝒄 𝑗 𝑦 is a vector of indicators for

physician 𝑗’s payment model.

Table 2.4 contains the key results. Physicians who switch from fee-for-service to an alternative

payment model are predicted to increase the number of patients on their roster. I estimate that

physicians increase their panel size by 6.6% in capitation and 16.0% in enhanced fee-for-service

models relative to when they are in the fee-for-service model.

Additionally, the results suggest that physicians have mildly different matching patterns in

the alternative payment models. Alternative payment models are associated with older and sicker

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patient panels. Further, I find a positive and significant association between capitation and a panel of

patients who provide more revenue and have greater expected utilization on average. These results

do not provide evidence as to whether physicians select patients on the revenue that they would

provide, conditional on age and gender, but they do suggest that physician-patient matching patterns

are affected by the payment models.

Without placing more structure on this analysis, the results are difficult to interpret. In addition

to physician responses to incentives, there are several alternative explanations for an increase in

physician panel sizes and changing patient-physician matching patterns. First, patient preferences

may be heterogeneous over alternative payment models. Second, panel sizes and matching patterns

are an outcome of the market for primary care in equilibrium. If physician choice of payment

model is also endogenous to market conditions, this complicates the interpretation of parameters.

I account for these complications in the estimated model of the market for primary care. Patient

preferences over alternative payment models are estimated. Endogenous physician selection into

payment models is modeled.

Further, neither the previous literature nor the above reduced form work accounts for equilibrium

effects. For example, when an individual physician changes to an alternative payment model, they

may increase the number of patients that they accept. However, other physicians may respond by

decreasing their own panel sizes. Therefore, to determine the effect of the alternative payment

model on the market as a whole, I conduct a counterfactual analysis using the estimated model of

the market for primary care.

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Table 2.4: Regression Results

(a) Panel Observables

Dependent variable:

Share of patients in panel

𝑙𝑜𝑔(𝑚 𝑗 𝑡 − ` 𝑗∅) Over 50 Female Has Comorbidity

Capitation 0.066∗∗∗ 0.041∗∗∗ −0.001 0.020∗∗∗

(0.021) (0.004) (0.002) (0.003)

EFFS 0.160∗∗∗ 0.007∗ −0.0003 0.012∗∗∗

(0.021) (0.004) (0.002) (0.003)

Mean of Dep. Var: 6.788 0.472 0.557 0.243Observations 4,492 4,492 4,492 4,492R2 0.883 0.933 0.961 0.865Adjusted R2 0.863 0.922 0.955 0.842Residual Std. Error 0.205 0.041 0.020 0.030

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

(b) Expected Revenue and Visits

Dependent variable:

Average of patients in panel

Cap. Revenue EFFS Revenue FFS Revenue Visits

Capitation 2.364∗∗∗ 1.714∗∗∗ 1.370∗∗∗ 0.057∗∗∗

(0.660) (0.541) (0.459) (0.017)

EFFS −0.644 −0.253 −0.218 −0.003(0.651) (0.533) (0.453) (0.017)

Mean of Dep. Var: 181.808 156.123 126.916 4.323Observations 4,492 4,492 4,492 4,492R2 0.863 0.876 0.880 0.882Adjusted R2 0.840 0.855 0.860 0.862Residual Std. Error 6.409 5.248 4.458 0.165

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

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2.4.3 Policy Impacts on Access

Using the estimated model of the market for primary care, I estimate the impact of the alternative

payment models on the primary care market in 2014 by simulating a counterfactual where all

physicians are forced into the fee-for-service payment model. I keep patient preferences over

physicians stable. I find that the alternative payment model increased access by 5.39 percentage

points (pp) across the entire population.

As shown in Figure 2.3, the alternative payment models have heterogeneous effects on different

types of patients I find that the alternative payment models increase urban and semiurban access

(6.46pp, 5.66pp) more than rural area access (3.84pp). As discussed in Chapter One, low access in

urban areas is primarily driven by capacity constraints, whereas low access in rural areas is driven

by a geographic sparsity of physicians. Therefore, a policy that primarily increases the number of

patients that each physician accepts will favor urban access. However, it should be noted that this

analysis does not consider changes in entry and exit. Alternative payment models could change

entry and exit decisions in rural areas by changing the distribution of practice profitability across

locations. Additionally, I find that the policy had a greater impact on the access of healthier and

younger patients, though these trends are less clear.

The alternative payment models primarily increase access to care by increasing physician

propensity to accept patients. To determine the magnitude of this effect, I estimate an intermediate

counterfactual where the expected revenue of patients 𝑅\ 𝑗𝑡 is not adjusted from their fee-for-

service levels. The latent utility a physician attains from leaving a panel space open, however, is

adjusted to reflect the physician’s participation in an alternative payment model. I find that access

to care increases by 5.08pp in the intermediate counterfactual relative to the all fee-for-service

counterfactual. Selection of patients accounts for the remaining 0.30pp of the access gains. However,

selection of patients does affect patients heterogeneously. Notably, physician selection of patients

on revenue disproportionately increases access for older patients and patients with comorbidities.

For the patients aged 0-34, I estimate that physician selection of patients on revenue decrease access,

though this is counteracted by the increase in physician propensity to accept patients. Appendix

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Table B.4 details these results.

Figure 2.3: Effect of Payment Reforms on Access to Care (By Patient Type)


2.5 Discussion and Conclusion

In this chapter, I used an estimated model of the market for primary care in Northern Ontario

to assess the impact of two policies on access to care. The first policy, the Northern and Rural

Recruitment and Retention (NRRR) grant, provides financial incentives to physicians to locate

in designated low-access areas. The second policy is a physician payment system reform that

introduced alternative payment models, including capitation and enhanced fee-for-service payment

models. My findings suggest that both increase access to care. I estimate that the NRRR grant

increases access to care by between 0.10 and 3.05 percentage points, depending on the counterfactual

specification. I find that the physician payment reforms increase access to care by 5.39 percentage

points (pp).

The policies have a heterogeneous effect on access for different types of patients. The NRRR

grant primarily increases access for rural patients. In these areas, low access is primarily driven by

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a geographic sparsity of physicians (see Chapter 1 of this dissertation). Thus, a policy that induces

physician entry in those area is effective at increasing access.

In contrast, the alternative payment models increase access for patients in urban areas more than

patients in rural areas. The alternative payment models primarily increase access by increasing the

number of patients that each physician is willing to accept. In urban areas, low access is primarily

driven by congestion – demand exceeds supply, making it difficult to attain care for some patients.

Thus, each physician increasing supply is effective at decreasing access to care. In rural areas,

where access is driven by geographic sparsity of physicians, these effects are more limited.

Since the NRRR is comparatively more effective at increasing access for rural patients (relative

to total impact), it is also more effective at increasing access for those with the lowest levels of

access. Figure 2.4 compares how the two policies affect the distribution of access. Panel A plots the

distribution of access in the counterfactual where the alternative payment models are removed and

the distribution of access in the current equilibrium. Panel B plots the distribution of access in the

counterfactual where the NRRR grants are removed and the distribution of access in the current

equilibrium.22 The effect of the NRRR grant is noticeably concentrated at low levels of access.

These findings suggest that location-incentive grants such as the NRRR can be particularly

effective at increasing access for patients with very low levels of access. However, these findings

were sensitive to specification assumptions. Under some specifications, I estimate that the NRRR

grant has an insignificant effect on access. To attain a clearer picture of how the NRRR grant affects

access, a model of physician entry and exit must be married with a model of the market for primary

care. This is beyond the scope of this paper.

This paper contributes to the literature by assessing how policies impact a well-defined measure

of access. Further, by using an estimated model of the market for primary care, it accounts for the

equilibrium effects of these policies. However, in this paper, I am unable to make judgments about

which policies are best. For such normative statements to be made, I must determine the relative

value to society of an additional unit of access for different types of patients. Additionally, I must

22. I use the counterfactual specification where the own-wage elasticity is 1.91 and the income change is calculatedusing the averaging method.

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attain data on the costs of each policy. Once a normative framework is established, these methods

can be used to answer important questions. Indeed, the methods could potentially be used to design

the optimal location grant incentives or the optimal payment model.

Figure 2.4: Effect of Policies on the Distribution of Access in Northern Ontario

(a) Alternative Payment Models (b) Northern and Rural Recruitment and Retention

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Chapter 3: Market Segmentation and Competition in Health Insurance

Nathaniel Mark, Michael Dickstein, and Kate Ho

3.1 Introduction

Households in the US obtain health insurance from a splintered set of payers. In 2017, for

example, 56% of the population obtained coverage through an employer, 16% purchased a plan

individually, 17% obtained coverage through Medicare, 19% through Medicaid, and 5% through

military health care. Roughly 9% lacked coverage.1 The heterogeneity in coverage sources in the

US contrasts with the insurance market design in other developed countries. Single payer public

insurance systems operate in the UK, Canada, Australia, Sweden and Norway. In Germany, France,

and Israel, households receive coverage through large health plans, often private and non-profit, that

compete with each other to cover patients of a range of ages and employment statuses (Tikkanen

et al. (2020)).

We explore how the segmented system in the US affects the degree of adverse selection in

each insurance market pool, the level of insurance premiums, and ultimately consumer surplus.

We focus on the division between coverage that households select through small employers vs.

coverage obtained on the individual market through direct purchase from insurance marketplaces

or brokers. These two markets offer an ideal laboratory to study the effect of segmentation. They

comprise roughly the same number of households: in the US in 2016, 15 million households

received coverage in the small group market and 12.5 million households purchased individual

market plans (The Kaiser Family Foundation (2017)). Importantly, following the implementation of

the Affordable Care Act (ACA) in 2014, plan designs in the two markets are also standardized in the

1. These shares sum to over 120%, as households often receive coverage from two or three sources simultaneouslyor sequentially in a year (U.S. Census Bureau (2018)).

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same way: plans fall into metal tiers by actuarial value, for example, and must cover the same set

of essential health benefits. In both markets, insurers cannot use underwriting to reject applicants

based on past health conditions and can only set premiums by age, family size, and smoking status.

There is, however, scope for welfare effects from changes to the pooling between the two

markets. First, small group insurance choice is mediated by employers and brokers, who typically

choose one or two plans to offer to eligible employees. The plan choice itself may appeal to

particular employees and not others, may act as a recruiting tool for the employer, or may be skewed

by a broker’s incentives to recommend costly plans that pay higher fees. Second, households

insured in the small group market do not face the full cost of premiums, both because of employer

subsidies and because insurance is a tax-advantaged employee benefit; in the individual market,

households typically use post-tax dollars for premiums and only qualify for premium subsidies

based on low income. Third, the distribution of household characteristics–including family size,

income, underlying health states, risk aversion, and the propensity for moral hazard–may differ

between the small group and individual insurance market pools. Thus, the effect of combining the

two populations on both plan choice and pricing will ultimately depend upon the preferences of

each group and their underlying expected costs of coverage.

We examine the effect of market segmentation in the context of Oregon’s small group and

individual insurance market. The individual exchange in Oregon supports a relatively large number

of insurance carriers compared to other states: there were 10 carriers and 140 plans in 2015,

implying the potential for substantial competition between carriers. In Oregon, small employers use

brokers as intermediaries and typically offer a small number of plans to their employees, similar to

national statistics (Agency for Healthcare Research and Quality (2016)). Our data from the Oregon

Health Authority covers plan characteristics, including premiums; household enrollment status by

year and market segment; and comprehensive medical claims. We focus on the small group and

individual insurance markets, although we observe transitions to other types of private insurance as

well.

To study the effects of insurance pooling, we begin by examining plan choice, premiums,

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mark-ups, and health spending in Oregon’s small group and individual insurance markets. From the

raw data, we observe that small group enrollees have relatively low spending by household type.

However, we find their raw premiums are higher; even after accounting for their tax savings, small

group enrollees face premiums that are larger or at best roughly comparable to individual market

premiums in the years 2014-2016. Higher carrier markups in the small group market explain the

differences.

When comparing plan choice, we find important differences in the two populations. Despite

Oregon’s strict requirement that carriers entering the individual exchanges must offer plans in the

bronze, silver, and gold coverage tiers, the most generous (gold) tier is highly adversely selected,

with high enrollee spending leading to high premiums and low market share for these plans (Cutler

and Reber (1998)). Only 13% of insured households choose gold plans, with an average spending

of $961 per month. The equilibrium outcome is quite different in the small group market, where the

presence of intermediaries and the use of insurance benefits as a recruitment device may shield such

plans from adverse selection. In the small group market, gold plans—and even the highest coverage

platinum plans—have much lower average spending and higher market shares than in the individual

market. Here, gold plans account for 25% of the market. The average enrollee spends $586 per

month.

These summary statistics illustrate a potential value from pooling risks in the small group and

individual insurance markets and setting common premiums, an institutional design already present

in some early mover states, including Massachusetts, Vermont, and the District of Columbia (Hall

and McCue (2018)). Combining the two markets may be beneficial to individual market enrollees,

stabilizing the risk pool and reducing the premiums charged by high-coverage plans, without much

loss to small group enrollees. However, the impact of such a policy on market outcomes—including

plan offerings, take-up, and pricing—depends not only on empirical objects, such as the relative

health levels in the two groups, but also on the risk preferences of subscribers, the tendency for

moral hazard, household preferences for certain insurers, and the equilibrium pricing decisions of

insurers in response to competition in the individual market.

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To measure these preferences, we use our Oregon data to estimate a model of households’ plan

choices and subsequent utilization (Einav et al. (2013)). The model also quantifies the degree

of moral hazard in response to plan generosity. Combining this measurement with a model of

competition and price-setting among insurers that follows Azevedo and Gottlieb (2017), we predict

the effect of pooling the small group and individual markets.

Importantly, we allow the preferences of households in the current small group and individual

insurance markets to differ; assuming the two groups have the same preferences ex ante would limit

the scope for our welfare analysis and might produce misleading predictions. However, estimating

preferences in the small group market is difficult because of the role of employers and brokers in

the plan choice. Our rich all-payers claims data provides a solution. In particular, we can identify

small group households forced to switch out of their plan when their employer canceled group

coverage. We study the subset of these “forced switchers” who do not regain coverage through

other employers or through public insurance. Thus, we estimate plan choice and spending using our

model and two distinct populations. First, we apply our model to data on current individual market

enrollees and a pool of uninsured households. Second, we estimate the preferences of our forced

switcher group as a proxy for the entire small group’s preferences in the individual market. We

justify this approach by showing that the forced switchers’ characteristics appear balanced when

compared to the small group as a whole. We find that the preferences are largely similar in the two

markets, conditional on observables.

Applying our model estimates, our primary counterfactual analyses are motivated by a regulatory

change in June 2019. Prior to the rule change, employers could set up Health Reimbursement Ar-

rangements (HRAs), contributing pre-tax dollars to an employee account from which the employee

could be reimbursed for medical expenses incurred through their group health plan (Keith (2019)).

As of January 2020, small employers can now offer an individual coverage HRA (HRA-IIHIC

or ICHRA). Under this arrangement, employers provide pre-tax dollars for an employee to pay

premiums for individual insurance. In effect, small employers shift the choice of coverage to

employees in the individual market while still providing the same tax benefits available in the small

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group market.2 A second motivation for our counterfactuals is the ongoing trend away from small

group insurance enrollment, which may increase with the economic downturn resulting from the

COVID-19 pandemic.3 Bartik et al. (2020), in survey analyses, report small businesses reduced

their active employment by 39% between January 2020 and April 2020.

Accordingly, we estimate two counterfactuals. In the first, we simulate market outcomes in a

scenario in which the small group market shuts down and small group employees must purchase

insurance on the individual market. Those with sufficiently low income have access to the same

premium and cost-sharing subsidies (if they choose silver plans) as other individual market enrollees.

We find that removing small group employer coverage does not significantly change outcomes in the

individual market. While small group employees have lower expected non-discretionary spending

than individual market subscribers, low spending households opt for uninsurance when moved into

the individual market. Thus, the distribution of costs among households choosing insurance remains

similar, as do average premiums. Across all coverage levels, premiums remain fairly constant. For

households who are currently in the individual market, we estimate that average consumer surplus

decreases by $2 per month per household and the share of households who go uninsured remains

constant.

In our second counterfactual, we simulate an extension of the HRA-IIHIC regulation where we

force small group employers to participate in the HRA-IIHIC program. In this setting, small group

households enter into the individual market with tax benefits and employer contributions but they

lose access to premium and cost-sharing subsidies in silver plans. In this setting, we assume that tax

benefits and employer contributions are made as a fixed percent of premium costs. We find that

adverse selection is mitigated. In this counterfactual, average gold premiums fall from $898 per

month to $526. However, since small group households no longer benefit from premium subsidies,

low spending small group households are less likely to purchase silver plans, driving up silver plan

premiums in the individual market. In total, consumer surplus for households who are currently

2. In June 2019, the federal government projected 800,000 employers would offer employees coverage using ICHRAaccounts, for a total enrollment of 11 million households following full implementation of the policy.

3. Even prior to the pandemic, the share of small employers offering group coverage fell almost six percentagepoints from 2011 to 2015 (Corlette et al. (2017)).

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in the individual market again remains relatively unchanged. In both counterfactuals, employer

and government spending decrease, suggesting that merging the two markets would be a revenue

positive policy.

To assess the impact of these market designs on small group employee welfare, we adopt a

simple model of plan choice in the small group market where employers choose health plans for

their employees to minimize costs. Using this model’s predicted plan choices and our estimated

small group preferences from the “forced switchers" sample, we estimate consumer surplus in

the small group market. In both merged-market counterfactuals, we find that consumer surplus

falls substantially for small group households with high expected non-discretionary spending, but

increases for households with low expected spending.4 In shifting to the individual market, high

spending households lose access to a larger choice set that include platinum plans. Lastly, we

predict that small group market households face lower premiums for bronze and silver plans on

average in the counterfactual simulations, but larger premiums for gold plans. These results suggest

that integrating the two markets may be beneficial for some small group households but detrimental

to others.

Previous literature.

Our analysis relates to several literatures in the economics of health insurance markets. A

growing set of papers studies plan choice and the optimal menu design for employer-sponsored

insurance, including issues of selection on moral hazard, adverse selection, and risk preferences

(Einav et al. (2013), Ho and Lee (2020), and Marone and Sabety (2020)). Our contribution is to

study the welfare consequences of different plan offerings and pooling outside a single employer’s

choice of plans. Without the employer acting as a type of central planner in setting premiums for

its chosen plan designs, we model equilibrium premium-setting as insurers compete in an (albeit

regulated) private market.

A relatively smaller literature considers the characteristics of small group insurance, including

4. These findings are sensitive to modeling assumptions and thus should be interpreted with caution.

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the allocative efficiency of plan designs and pricing and the extent of re-classification risk in

the market(Bundorf, Levin, and Mahoney (2012) and Fleitas, Gowrisankaran, and Sasso (2018)).

Abraham, Royalty, and Drake (2019) compare the small group premiums reported in national

data against individual premiums. Our contribution is to invoke the specific pricing regulations in

Oregon’s small group market after the implementation of the ACA to show markups in the small

group market and then consider the potential remedy of market pooling.

Finally, our work also connects to a literature identifying the consequences of market design

in individual insurance, including the design of subsidies (Tebaldi (2017), Jaffe and Shepard

(2020), and Polyakova and Ryan (2019)), risk adjustment (Geruso, Layton, and Prinz (2019) and

Einav, Finkelstein, and Tebaldi (2019)), participation penalties (Diamond et al. (2020)), and re-

classification risk (Handel, Hendel, and Whinston (2015) and Atal et al. (2020)). Our contribution

is again to focus on the effect of pooling in a managed competition insurance setting.

The rest of the paper proceeds as follows: in Section 2, we detail the market structure and

regulations of the individual and small group health insurance markets in Oregon. Then, we

introduce our data in Section 3 and discuss the differences between the small group and individual

markets as observed in these data in Section 4. Section 5 presents the model of supply and demand

in the individual market and Section 6 describes how we take this model to data. In Section 7, we

discuss our results. Section 8 concludes.

3.2 Institutional Detail and Setting

Both the individual market and the small group market faced new regulations following the

implementation of the Affordable Care Act (ACA) in 2014. In this section we summarize the key

features of these two markets in Oregon that are relevant for our analysis. We provide further details

in Appendix C.1.

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3.2.1 Individual Insurance Market

Households seeking to purchase insurance coverage in the individual market have two options.

First, they can search and select a health plan through a marketplace created under the ACA.

Enrollees in Oregon use the federal Healthcare.gov online platform, in an arrangement known as a

“state-based exchange on the federal platform”.5 Through this portal, Oregon residents can shop

for health plans whose prices and cost-sharing levels may be subsidized to reflect their financial

circumstances. Households with incomes between 100% and 400% of the federal poverty line

(FPL) see plans with reduced premiums, and those between 100% and 250% also see reduced

out-of-pocket costs, reflecting a schedule of government subsidy payments.6 Only households above

400% of the FPL face the full plan premiums and out-of-pocket costs determined by insurance

carriers operating in their geographic market. Between 2015 and 2020, Oregon’s marketplace

enrolled between 112,000 and 156,000 annually (The Kaiser Family Foundation (2020b)).7

Households that are eligible for subsidies must purchase through the marketplace to receive

them. Other households, however, may purchase individual coverage through an agent outside

the marketplace channel. Some off-marketplace plans are “grandfathered”, meaning they were

initially purchased prior to March 23, 2010 and renewed in future years; grandfathered plans need

not adhere to the benefit design requirements of the ACA. The remaining off-marketplace plans

are ACA-compliant. They may be identical to plans offered on the marketplace or unique to the

channel.

Partly due to decreasing enrollment in grandfathered plans, the share of individual insurance

enrollment directly via agents in Oregon fell from a high of 66% in 2014 to a low of 18% in 2018,

mirroring similar reductions at the national level.8 When we later consider demand for individual

5. In 2011, Oregon’s legislature voted to establish a state-based marketplace for individual insurance enrollment,later named Cover Oregon. Facing difficulties with its technology, the state abandoned Cover Oregon and adopted thefederal platform for the 2015 plan year (Ornstein (2014)).

6. Households with incomes at or below 133% of FPL, as well as those meeting several other criteria, are eligiblefor Medicaid, the state-federal means-tested government insurance program.

7. Annual enrollment from 2015 through 2020 in the federal and state-based marketplaces has averaged between 11and 12 million households, peaking in 2016 at 12.7 million. Roughly 85% of these enrollees received federal premiumsubsidies to purchase coverage (Fehr, Cox, and Levitt (2019)).

8. Nationwide, the share of off-marketplace enrollment fell from 47% in 2014 to 16% in 2018 (The Kaiser Family

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insurance, we omit those households purchasing grandfathered plans but do include households

purchasing ACA-compliant plans through brokers. We define the choice set of off-marketplace

purchases differently from the on-marketplace plans by using the observed menus in our data.

Importantly, off-marketplace enrollees in our setting must pay unsubsidized premiums.9

Plans offered in the individual market face regulation of both premiums and the level of coverage.

Since the implementation of the ACA in 2014, insurers in all states must ‘guarantee issue’ all plans

to all consumers.10 Premiums may vary only with family size, state-defined geographic regions,

tobacco use, and age (following a standard age curve, with a ratio of 3 to 1 from the oldest to

youngest enrollee). We exploit the formulaic variation in premiums by age in later analyses. Plans

must cover a set of ten essential health benefit categories, including outpatient services, emergency

room visits, pregnancy and maternity visits, mental health care, and prescription drugs. All offered

plans fall into metal tiers classified by their actuarial value, defined as the percentage of health

costs the plan is expected to cover. The plan tiers are Bronze, Silver, Gold and Platinum, with

actuarial values of 60%, 70%, 80% and 90%, respectively. Oregon requires that all insurers

entering the marketplace must offer a bronze, silver, and gold plan; carriers offering plans outside

the marketplace must offer at least one bronze and one silver plan.11 Partly as a result of these

requirements, consumers in the individual market often can choose plans from a large menu. For

example, a buyer in the Portland area in 2015 would have a choice of 31 bronze plans, 40 silver

plans, and 24 gold plans, offered by 8 unique carriers (SERFF).

Households that are eligible for cost-sharing subsidies must purchase a silver plan in order to

receive these reduced out-of-pocket costs. These subsidies change the standard silver plan design to

a more generous actuarial value of between 73% and 94% for consumers with incomes on 100% to

Foundation (2020b)).9. We consider off-marketplace demand separately because outside the marketplace, agents may have incentives to

recommend some particular carriers over others. Some agents work internally at a carrier, but many are independent,appointed by multiple participating insurance carriers to enroll households. In Oregon, independent agents must showall plans to all consumers, but agents typically only receive commissions from carriers that appoint them.

10. ‘Grandfathered’ plans—that is, plans that existed before March 2010 and currently in effect—are not subject tothese regulations.

11. This is more stringent than the federal requirements, which state that insurers must sell at least one gold andone silver plan in the marketplace in each geographic market they enter. Oregon also requires insurers to offer a“standardized” plan in each metal tier (Blumberg et al. (2013)).

101

250% of the FPL, with the lowest incomes receiving the higher actuarial values. As noted below,

this subsidy structure has meaningful implications for household enrollment decisions, and hence

the costs and premiums of plans in different tiers.

3.2.2 Small group insurance market

Small employers, defined in Oregon as firms with up to 50 full-time employees, have the option

of offering health insurance coverage for their employees. In 2015, approximately 47% of firms with

3-9 workers and 68% of firms with 10-49 workers offered coverage to employees; approximately

76% of eligible workers took up this coverage (Claxton et al. (2015)). After the implementation of

the ACA, the small group market faces many of the same plan design restrictions as the individual

market. Plans must cover the same essential health benefits, must be structured according to the

same metal tiers, and must be ‘guarantee issued’; the insurer cannot set premiums based on the

health status or pre-existing conditions of the employees in the small group. The small group and

individual markets differ in the purchasing channel and the pricing rules. We discuss each feature in

turn.

While the ACA intended states to offer a marketplace for small group employers to shop for

plans (known as the Small Business Health Options program or SHOP), Oregon did not have a

working small group marketplace during the span of our data.12 Instead, small employers purchase

plans through an insurance broker that typically receives a fee per enrollee from the insurance

carrier. 13 Not surprisingly, the broker purchasing channel generates a much smaller choice set than

that available in the individual market, although one that may have been tailored by the employer to

meet employee preferences. A typical small group offers one to two broker-recommended plans to

its employees, often from the same carrier (Agency for Healthcare Research and Quality (2016)).

12. Oregon small businesses cannot use the federal SHOP enrollment platform because Oregon requires communityrating in the small group market with no age-based variation in premiums (Cite).

13. Brokers typically receive a per month per enrollee commission, plus occasional sign-on bonuses. One carrier inOregon, for example, offered a $14.27 per enrollee per month payment for groups with fewer than 26 enrollees and$11.25 for plans with 26 - 49 enrollees. Bonuses equaled $100 for a 1-9 enrollee group, $200 for a 10-25 enrolleegroup, and $400 for 26 -49 enrollee group (Providence Health Plan (2011)). The average small group per-enrolleeper-month fee in Oregon in 2016 was $19.70 (The Kaiser Family Foundation (2020a)).

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The presence of intermediaries may also shield insurance carriers from premium competition; we

show later that the markups of plans offered by small employers are often meaningfully higher than

those available for comparable plans in the individual market.

After choosing a menu of plans to offer, employers contract with the relevant carrier(s) and

pay premiums on behalf of the group. Employees pay their share of the group premium from their

pre-tax earnings—that is, all premiums for insurance obtained through an employer are federal

and state tax exempt, regardless of whether the employer or the employee pays. This creates a tax

wedge relative to the individual market, where households typically pay for insurance with post-tax

dollars.14 There is also premium variation relative to the individual market because small group

market insurers are required to use ‘tiered composite’ community rating, described in detail in the

Appendix, which creates a cross-subsidy within the employer pool between older and younger

enrollees and between employees covering only themselves and those covering families. Finally,

employers typically subsidize the cost of employee premiums, covering as much as two thirds of

the premium cost (Claxton et al. (2015)).15

In the analysis below, we use household enrollment and claims data for individual market

enrollees to estimate the preferences and health needs of consumers in the individual market,

and also model health plan premium setting under the assumption that this market is plausibly

perfectly competitive (or at least, that carriers’ small markups can be estimated and held fixed

in counterfactual simulations). We do not attempt to model the process by which consumers are

assigned to plans in the small group market, nor the price setting process there. Instead we use a

sample of “forced switchers”, whose preferences we can estimate based on choices made after their

small group plans were discontinued by their employers and they switched to the individual market.

Under reasonable assumptions, these estimates can be used to infer small group preferences more

14. Premiums in the individual market are part of itemized deductions, but subject to limitations: only medicalexpenses exceeding 7.5% of adjusted gross income are deductible.

15. Small businesses with fewer than 25 employees are eligible for tax credits of up to 50% of premium costs if theysatisfy a number of qualifications, including: they must buy a plan certified for SHOP, average employee pay must beless than $50,000, and the employer must cover at least 50% of the premium (Oregon Health Insurance Marketplace(2020)).

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broadly and hence to conduct our counterfactual simulations.

3.3 Data

We use data from three sources. First, to analyze both plan enrollment and claims, we collect data

from the Oregon Health Authority’s All Payer All Claims (APAC) dataset. Second, for information

on plan design and premium levels, we match our plan level claims data to plan characteristics

reported in the National Association of Insurance Commissioners’ SERFF database for Oregon.

Third, we collect Medical Loss Ratio (MLR) reports from the Centers for Medicare and Medicaid

Services for the insurance carriers operating in the small group and individual insurance markets in

Oregon. We describe each data source and their uses in turn.

Claims and Enrollment Data

From Oregon’s APAC data, we collect private insurance claims and enrollment information for

all small group and individual insurance plans purchased from 2010-2016 (although our analyses

focus on the post-ACA period 2014-16). Our claims data cover out of pocket costs and costs to the

insurer for inpatient, outpatient, and pharmaceutical claims for each covered enrollee (including

spouses and dependents). The data also contain household insurance plan enrollment and informa-

tion on the insurer, metal tier, coverage period, and in some cases, premiums for plans chosen by

households. Focusing on the period around the introduction of the Affordable Care Act, in years

2014 to 2016, the data include 512,373 unique Oregon households in the individual market and

383,137 small group and individual insurance markets.16

We use the claims data, together with the Johns Hopkins ACG (Adjusted Clinical Groups)

Case-Mix System software, to construct a measure of predicted health spending for each household

in each year. The ACG software predicts expected medical expenditure of each enrollee based on

diagnostics and demographics data.17 The results are then normalized to an ACG score, where a

16. Households who choose plans from fringe insurers or are missing key demographic characteristics are excludedfrom these counts. Appendix C.2 details our data construction procedures.

17. We use the ACG software’s “concurrent” risk measure. This measure uses diagnostics and demographics to predict

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score of 1 corresponds to average expenditure in a reference population.

Plan Characteristics

We obtain additional information on plan design and premium levels by matching the claims

data to public data contained in the National Association of Insurance Commissioners’ SERFF

database for Oregon. Each year, insurers operating in Oregon’s individual and small group markets

file details of their plan offerings via SERFF. These filings allow us to characterize the generosity

of each plan chosen in Oregon’s APAC data, including the levels of deductibles, copayments, and

the gross premium levels set for each plan. To simplify the model of household plan choice, we

bin similar plans together to create constructed plans. In the model, households choose among

constructed plans, defined by a combination of insurer, rating area, metal tier, and whether a plan is

a managed care plan.18 Constructed plan actuarial value is defined by the metal tier; premium is

defined as the average premium of plans in the constructed plan. Hereafter, we refer to constructed

plans simply as plans.

We derive a measure of household income using a combination of APAC and SERFF datasets.

The APAC dataset includes reliable information on premiums paid by each household for one

insurer on the on-exchange individual insurance market. When paired with household demographics

and plan (charged) premiums from the SERFF database, these data identify the exact subsidy

provided to the household and hence its income. We use this subsample to estimate a predictive

model of income that we apply to the entire sample. The resulting measure of income is used to

derive premium subsidies and tax rates for all households in the individual and small group markets.

Appendix C.2 describes the APAC data, and our data cleaning procedures, in further detail.

expected medical expenditure in the same year. An alternative measure that uses lagged diagnostics and demographicswas infeasible in this setting due to high rates of consumer churn in the individual market.

18. We define managed care plans as an EPO or an HMO plan.

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Insurer Costs

Lastly, we collect Medical Loss Ratio (MLR) reports from the Centers for Medicare and

Medicaid Services for the insurance carriers operating in the small group and individual insurance

markets in Oregon. The reports contain details on state-wide enrollment and costs, including health

spending and broker fees, that insurers incur in each business line in which they operate. We

exploit these observed measures of administrative cost in later analyses of insurer pricing. We

also use the national enrollment and revenue information for each carrier that operates in Oregon

to create measures of insurance participation, enrollment, revenues and costs in states outside the

Oregon market. These are useful instruments for the premium-setting regressions described in

Section 3.6.3.19

Table 3.1 summarizes the demographics, costs, and plan choices of households enrolled in

non-grandfathered plans in both our small group and individual market samples.20 On average,

households in the small group market are younger, healthier (as measured by household ACG

score), and more urban than households in the individual market. Additionally, small group market

households have lower medical spending (both a higher probability of zero spending, and a lower

mean conditional on positive spending) than individual market households. This relationship is

particularly apparent among households who choose Gold plans, consistent with adverse selection

into this tier in the individual market. An individual market household in a Gold tier plan that

has positive spending costs their insurer $961 per month on average, and their probability of zero

spending is only 13%, compared to $586 and 25% in the small group market. Further, as shown

in Figure 3.1, only 14% of individual market households enroll in gold plans compared to 36%

of small group market households. The descriptive analyses below explore these comparisons in

further detail.

19. These data are summarized in Table 6.20. This table omits households with grandfathered plans that do not adhere to the benefit design requirements of the

Affordable Care Act. We also omit households with certain missing variables .

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3.4 Descriptive Analyses

3.4.1 Comparing the Small Group and Individual Markets

Before describing our model, we highlight the differences between the small group and individ-

ual market—in terms of underlying premiums, spending and the degree of adverse selection—in our

raw data. The empirical state of these markets in Oregon will underlie our model estimates and help

illustrate the likely consequences of pooling small group enrollees with individual market enrollees.

Comparing costs.

Figure 3.2 depicts the distribution of observed total medical spending by household, for house-

holds enrolled in small group and individual market insurance, in 2015 (top panel) and 2016. We

control for moral hazard effects by considering plans of the same actuarial value in the two markets.

The panel on the left depicts the distribution of spending for enrollees in silver plans, while that on

the right considers gold plans. Within each metal tier, we see a larger share of small group enrollees

spend $0 over the course of the year, and conditional on positive spending, the small group spending

distribution appears more concentrated at lower levels of spending. Consistent with selection of

relatively high-spending households into higher-coverage plans, the distribution of spending in the

gold tier is shifted to the right relative to the silver tier, in both years and both market segments. All

these findings are consistent with the mean and median spending levels reported in Table 3.1.

Comparing Premiums.

Given the observed differential in spending, we examine whether the premiums faced by

enrollees also differ between the small group and individual markets. The comparison in Oregon

is not as simple as comparing the age-based premiums for a given household size and plan tier:

because of the tiered composite pricing in the small group market, the composition of the small

group pool matters for any household’s effective premium.

To illustrate the premium differential, we focus on a standardized enrollee who is single, 40

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years old, and too wealthy to receive government premium or cost-sharing subsidies in the individual

market. We use the individual market premiums reported directly in the SERFF plan database.

Figure 3.5 provides an initial comparison of premiums charged by carriers across the two markets.

It depicts the distribution of base premiums—the premium for our standardized enrollee purchasing

insurance alone, averaged across different plans as marketed on the exchange—in gold and silver

tiers in the years 2014-2016. Base premiums are higher for small group plans in 2014-2015 despite

their lower medical claims costs, consistent with more intense price competition in the individual

market. Individual plan premiums increase in 2016, leading the difference to be statistically

insignificant in that year.

However, a more useful comparison between markets would adjust for differences in demo-

graphics across small group pools and also account for the tax wedge and employer contribution

towards premiums. Figure 3.6 makes these adjustments. We adjust the premium for (a) the typical

composition of a small group pool in Oregon in terms of age and family size, (b) adjust to post-tax

dollars to account for the tax advantage in small group premiums, and (c) adjust for any employer

subsidy of premiums. We account for the composite rating by drawing simulated groups from the

distribution of small groups in Oregon, replacing one member of the group with our standardized

enrollee. We take an average of the single employee premium across all simulated groups. To

adjust for taxes, we multiply the premium by 1 − 𝜏, where 𝜏 is the average tax rate for a single adult

making the median annual income in Oregon. Finally, we assume an employer subsidy rate of 50%,

the minimum required for eligibility for the small business tax credit described in Section C.1.2.

Figure 3.6 Panel A.i. presents the distribution of small group premiums for our standardized

enrollee, adjusted only for typical group composition, compared to the distribution of individual

market premiums. As in Figure 3.5, despite their lower average costs, small group enrollees have

higher listed premiums. Panels A.ii. and A.iii. adjust for the tax wedge and the 50% employer

subsidy respectively. Even with tax savings, small group enrollees typically pay higher premiums in

2014 and 2015; in 2016, the increase in individual market premiums makes them slightly higher on

average. Only when we account for employer subsidies do small group plan premiums fall below

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individual market levels. In Figure 3.6 Panel B, we show what percentage subsidy an employer

would have to provide to make the employee indifferent between a typical small group plan and

a typical individual market plan. In 2014 and 2015, this subsidy rate is on the order of 15%. For

consumers eligible for premium subsidies in the individual market, the small group subsidy rate

would have to be even higher to make the premiums comparable.

Insurer Mark-ups over Health Costs.

Given our measurement of both costs and premiums by plan, we can also compute a plan-specific

insurer mark-up of premiums over cost. For this analysis in the small group market, we use the full

premium paid to small group plans independent of employee tax savings or employer subsidies,

since the full premium flows to the insurer as revenue.

In Figure 3.4 we plot the distribution of mark-ups as a share of premium revenue by year in the

small group and individual market. Panel A shows that for silver plans, the median small group

plan in 2014 had a roughly 50% mark-up as a share of premiums. This median mark-up fell over

time, but remained above zero in all years of our data. In 2014 and 2015, even the 25th percentile

plan ended the plan year with a positive mark-up.21 Unsurprisingly, in the individual market where

premiums are lower, we see much lower mark-ups as a share of premiums. The median firm had

negative markups in all three years, while even the 75th percentile firm’s markups were negative

in 2014 and 2015. We observe this pattern across a range of plan types. Panel B of Figure 3.4

focuses on gold plans. Again, small group plans achieve positive markups while the markups of

plans in the individual market are zero or negative. We use this evidence from the data to motivate

our assumption of perfect competition in the individual market.

21. Our mark-up calculation does not include administrative costs and other taxes and fees that may be deductedwhen calculating the carrier’s medical loss ratio (MLR) across all plans the carrier offers in a state and insurance marketsegment in a year. We collect these administrative costs for our supply analysis in later years.

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3.4.2 Potential Consequences of Market Pooling

The institutional details and summary statistics discussed above suggest several possible con-

sequences of eliminating market segmentation. First, note that small group enrollees are both

lower-spending than individual market enrollees on average, and partially shielded from plan premi-

ums by the tax wedge and the employer contribution.22 Thus we can view complete market pooling

as bringing a population of relatively low-cost consumers with a low exposure to premiums onto the

individual exchange. If the high market share of the small group gold tier reflects a preference for

coverage, many of these new customers may continue to choose gold plans, reducing these plans’

costs and premiums and potentially prompting more individual-market enrollees to move up to a

gold plan. This could effectively address the gold tier adverse selection problem discussed above.

The costs of silver and bronze plans, in turn, may fall as relatively sick enrollees move up to the next

metal tier; hence reducing their premiums and reducing the percent uninsured. Further, there may

be little cost to small group enrollees, since the benefit of entering a more competitive marketplace

(with lower plan markups) may more than offset the loss from being pooled with a higher-spending

consumer group.23

However, there is a different possible outcome of market pooling that is less beneficial to

consumers. If the popularity of gold plans in the small group market is due to employers providing

generous coverage—perhaps as a recruitment device—rather than fully reflecting employee risk

preferences and health needs, then employees moving to the individual market may choose lower-

coverage plans when given the option. In that case, the market share of gold plans may remain low,

and their premiums very high. Further, in the absence of employers prompting employees to enroll,

many small group employees may choose to forego insurance on the individual market entirely,

which could further destabilize the market. In that case the existing subsidy structure that stabilizes

22. While the tax treatment is a true benefit to employees, the employer contribution is not: it is likely to be passedthrough in reduced wages. Our primary simulations will hold employer premium contributions fixed, and implicitlyassume that wages are therefore unaffected.

23. The perfect competition model rules out some welfare costs of market pooling. For example, under oligopoly,individual market plans might increase their markups when small group enrollees paying pre-tax dollars entered themarket, generating a further welfare loss.

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silver plans may remain necessary to sustain the market share of that tier, and small group enrollees

may pay higher premiums, for lower coverage plans, than in the current equilibrium.

Further, note that the current policy does not require—it only permits—small employers to

move their employees into the individual market. If only a selected sample of small groups choose

to stop offering coverage, the equilibrium outcome may depend critically on the characteristics of

that sample. For example, if employers with relatively sick employees drop out, this will shift up

the individual market cost curve and may lead to market unraveling of some or all metal tiers with

negative consequences for enrollees.

Distinguishing between these possible outcomes requires a model that captures the preferences

and underlying characteristics of individuals in both the individual and the small group markets.

Underlying health care needs are clearly important; so are the extent of moral hazard (i.e., price

responsiveness at the point of care) and risk aversion in the two populations, since these will affect

plan choices and subsequent medical spending, costs, and equilibrium premiums. In the following

section we outline the model we use to estimate these objects and describe the estimation method in

detail.

3.5 Model

We build a model that features a household’s choice of plan and subsequent health spending in

the individual market, as well as insurers’ choices of premium levels. We use the multiplicative

moral hazard model from Einav et al. (2013); this accounts for selection based on measures of

sickness that are not priced into premiums and that affect costs (adverse selection) and a spending

response to insurance (moral hazard). We model insurer pricing in the individual market following

the framework for insurance plan competition from Azevedo and Gottlieb (2017).

3.5.1 Consumer Demand and Spending

At the beginning of each year, a household engages in the following sequential choice model:

in Stage 1, the household—internalizing the needs and preferences of its members—chooses an

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insurance plan from a set of offered plans.24 In Stage 2, conditional on plan choice and the

realization of health care status, the household chooses the amount of medical care to consume.

Following the notation and structure of Einav et al. (2013), a household is characterized by three

objects: (𝐹_,𝑡 (·), 𝜔, 𝜓) (where, for clarity, we omit household-specific subscripts). 𝐹_,𝑡 (·) represents

the household’s expectation over its uncertain health status _ ≥ 0 in period 𝑡. The value of _ in a

given period is realized after a household chooses its plan, and a higher value of _ corresponds to a

household with greater health care needs. The second object, 𝜔, represents the household’s price

sensitivity for medical care and can be interpreted as the household’s level of moral hazard. Lastly,

𝜓 represents the household’s coefficient of absolute risk aversion.

We present this model in reverse order, beginning with Stage 2. We use the multiplicative moral

hazard specification because it predicts higher moral hazard spending for sicker individuals, which

seems natural and which Ho and Lee (2020) find to be more consistent with the variation in their

employer sample.

Stage 2: Medical Care Utilization

At the beginning of Stage 2 in each period (year) 𝑡, a household is enrolled in an insurance plan

𝑗 , and realizes health _. The household then chooses its level of medical spending 𝑚 ≥ 0 for that

period to maximize its utility given by:

𝑢 𝑗 ,𝑡 (𝑚;_, 𝜔) = (𝑚 − _) − 12𝜔_

(𝑚 − _)2 + [𝑦𝑡 − 𝑐𝑂𝑂𝑃𝑗,𝑡 (𝑚) − 𝑝 𝑗 ,𝑡] + 𝑔(𝑋 𝑗 ,𝑡 , 𝜖 𝑗 ,𝑡) . (3.1)

In (3.1), 𝑦𝑡 is annual income, 𝑐𝑂𝑂𝑃𝑗,𝑡

(𝑚) are out-of-pocket (OOP) payments made by the household

for its medical spending, and 𝑝 𝑗 ,𝑡 is the annual plan premium. We specify 𝑐𝑂𝑂𝑃𝑗,𝑡

(𝑚) as (1−𝑥 𝑗 ,𝑡) ×𝑚,

where 𝑥 𝑗 ,𝑡 is the % of spending that the insurer pays in period 𝑡 under plan 𝑗—i.e., the plan’s

actuarial value. The final term is a function of other variables that can affect household utility.

24. In reality, most consumers choose their household’s insurance plan for the subsequent calendar year during an“open enrollment period,” typically occurring in the fall of each year. For ease of exposition, we will refer the planchoice decision as if it occurs “at the beginning” of each (calendar) year.

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The household’s medical spending, denoted 𝑚∗𝑗 ,𝑡

, must satisfy the following first-order condition

from (3.1):

𝑚∗𝑗 ,𝑡 = _ + 𝜔_𝑥 𝑗 ,𝑡 . (3.2)

The second term in this expression implies that the amount of additional medical spending due to

cost-sharing is increasing in the “moral hazard” parameter 𝜔 and also in household “sickness” _. A

zero value of _ will result in zero spending, even under full insurance.

Stage 1: Insurance Plan Choice

In Stage 1, each household realizes its 𝜖 𝑗 ,𝑡 and chooses an insurance plan from a choice set of

plans J𝑡 to maximize its expected utility for the current year. The household anticipates that its

health needs follow 𝐹_,𝑡 and its health spending will be governed by optimal Stage-2 behavior. We

assume the household has constant absolute risk aversion (CARA) preferences over Stage-2 utilities

given optimal medical spending, denoted 𝑢∗𝑗 ,𝑡(_, 𝜔) ≡ 𝑢 𝑗 ,𝑡 (𝑚∗

𝑗 ,𝑡(_);_, 𝜔). Given these assumptions,

the expected utility that a household anticipates receiving from plan 𝑗 at the beginning of period 𝑡 is

given by

𝑣 𝑗 ,𝑡 (𝐹_,𝑡 , 𝜔, 𝜓) = −∫

𝑒𝑥𝑝(−𝜓 × 𝑢∗𝑗 ,𝑡 (_, 𝜔))𝑑𝐹_,𝑡 (_) , (3.3)

where 𝜓 is the household’s coefficient of absolute risk aversion and the household’s optimal choice

of plan is 𝑗∗ = arg max 𝑗∈J𝑡 𝑣 𝑗 ,𝑡 (·).

3.5.2 Insurance Supply

To model insurer pricing and equilibrium supply in the individual market, we follow the

assumption of perfect competition in Azevedo and Gottlieb (2017), who adopt the Einav et al.

model with additive moral hazard as an example.25 Insurance carriers in the individual market are

assumed to choose their premiums, plan-by-plan, to equal average costs (including both claims and

25. Their goal, and ours, is to write down a tractable model that allows them to predict new market equilibria undercounterfactual scenarios, using consistent utility and cost specifications. They show that under the additive moral hazardmodel, if _ ∼ 𝑁 (𝑀\ , 𝑆

2\), then the utility and cost equations can be written analytically in terms of the parameters of

the model.

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administrative costs), where expected claims costs for a household characterized by (_, 𝜔) are:

𝑐 𝑗 ,𝑡 =

∫(𝑥 𝑗 ,𝑡_ + 𝜔𝑥2

𝑗 ,𝑡_)𝑑𝐹_,𝑡 (_).

3.6 Empirical Model

We transform the model of insurance demand and insurer supply into a two stage empirical

model for estimation. We begin by detailing the data samples used for estimation and then provide

information on estimation.

3.6.1 Data Samples

We estimate our model using our detailed data on households and plans in the individual and

small group health insurance markets in Oregon. To estimate preferences of households in the

individual market, we use a dataset of household characteristics and plan choices of households in

the individual market and uninsured households. We construct a dataset of small group households

who are forced into the individual market that we use to estimate small group market household

preferences. Lastly, we use both claims and administrative cost data to estimate insurer pricing

equations.

Individual Market Sample

To estimate preferences of households in the individual market, we construct a dataset of all

households who purchase individual market insurance and all uninsured households. Households

who purchase individual market insurance are directly observed in the APAC data. The U.S. Census

ACS 1-year dataset provides the size of the uninsured population for each rating area, year, and age.

We infer additional characteristics of the uninsured population using a detailed survey of uninsured

households in California, the California Health Interview Survey. Appendix C.2.5 details this

procedure. Table 3.9 compares the uninsured population to the insured individual market population.

On average, insured households are older, have larger incomes, and are more likely to be single

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than uninsured households.

Switcher Sample

Our counterfactual simulations require reasonable estimates of the preferences and attributes of

current small group households. We do not estimate a full model of plan and utilization choices in the

small group market; this would require many assumptions, particularly because we do not observe

employer identifiers (only group identifiers). Further, we prefer to avoid making assumptions

regarding the role of employer, rather than employee, preferences in determining market shares

in this market. Instead we consider the sample of small group enrollees whose plans were closed

during the time period of our data. We can track these households as they choose plans in the

individual market (or other markets; we exclude those moving to the large group market or aging

into Medicare), and hence can plausibly estimate their preferences conditional on observables. We

compute the outside option share for these forced switchers under the assumption that households

formerly enrolled in small group insurance who do not appear in our group or individual insurance

plans in Oregon lack insurance for the year and are therefore choosing the outside option. Appendix

C.2.2 describes how we identify our forced switcher population.

The sample of forced switchers differs from the larger small group market population on some

dimensions. Table 3.8 compares the characteristics of the two populations in the year before the

forced switchers leave the small group market.26 On average, the forced switchers are older and

more likely to purchase coverage that includes dependents. Accordingly, they have higher medical

spending than the full small group population. We use the model to estimate switcher preferences

conditional on observables, and assume that these estimates are valid for the broader small group

population.

26. The small group market sample used for this comparison consists of households in non-grandfathered plans. Inthe counterfactual analysis, we also use households in small group grandfathered plans.

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3.6.2 Joint likelihood of plan choice and health spending

We next define the likelihood of observing (a) the plan choices of households and (b) the health

care spending of subscribers to each plan 𝑗 , accounting for moral hazard potentially risk averse

enrollees. We estimate the parameters of this joint likelihood using maximum likelihood estimation.

Equations for Estimation

We begin by making a distributional assumption regarding _ that is motivated by the spending

distribution depicted in Figure 3.2. If _ ∼ 𝑒𝑥𝑝(𝛼), plugging optimal medical spending into the

utility equation ((3.4)) and accounting explicitly for variation in the underlying parameters and

variables across households 𝑖 yields

𝑢∗𝑖, 𝑗 ,𝑚,𝑡 =12𝑥2𝑖, 𝑗 ,𝑡𝜔𝑖_𝑖 − (1 − 𝑥𝑖, 𝑗 ,𝑡)_𝑖 + 𝑦𝑖,𝑡 − 𝑝𝑖, 𝑗 ,𝑚,𝑡 + 𝑔(𝑋 𝑗 ,𝑚,𝑡 , 𝜖𝑖, 𝑗 ,𝑚,𝑡)

where 𝑚 indexes markets (rating areas) and 𝑡 years. Suppressing (𝑚, 𝑡) subscripts for notational

simplicity, the expected utility over the distribution of _ is:

𝑣𝑖, 𝑗 (𝐹_,𝑖, 𝜔𝑖, 𝜓𝑖) = −∫

𝑒𝑥𝑝(−𝜓𝑖𝑢∗𝑖, 𝑗 )𝑑𝐹_,𝑖 (_).

Noting that our distributional assumption implies 𝐸 (_) = 1/𝛼 and applying the order-preserving

monotonic transformation − 1𝜓𝑖𝑙𝑛(−𝑣𝑖, 𝑗 ), we write the expected utility as 27:

𝑈𝑖, 𝑗 ≈ −𝑝𝑖, 𝑗 +𝑥𝑖, 𝑗

𝛼𝑖 − 𝜓𝑖+

𝑥2𝑖, 𝑗𝜔𝑖

2(𝛼𝑖 − 𝜓𝑖)+ 𝑔(𝑋 𝑗 , 𝜖𝑖, 𝑗 )

𝑈𝑖,0 = 𝑔0(𝜖𝑖,0).

We specify 𝑔(𝑋 𝑗 , 𝜖𝑖, 𝑗 ) = (𝛽0𝑋 𝑗 + 𝜖𝑖, 𝑗 )/(𝛼𝑖 − 𝜓𝑖) so that sicker or more risk averse consumers put

more weight on plan characteristics like carrier identity, in the same way that they put more weight

27. This also requires us to recognize that when 𝐴𝑥 + 𝐵𝑥2 is close to zero, we can approximate 𝑙𝑛(1 + 𝐴𝑥 + 𝐵𝑥2) ≈𝐴𝑥 + 𝐵𝑥2. Details are provided in Appendix C.3

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on coverage. Making an analogous assumption for the outside option, we find:

𝑈𝑖, 𝑗 = −𝑝𝑖, 𝑗 +𝑥𝑖, 𝑗

𝛼𝑖 − 𝜓𝑖+


2(𝛼𝑖 − 𝜓𝑖)+𝛽0𝑋 𝑗 + 𝜖𝑖, 𝑗𝛼𝑖 − 𝜓𝑖

(3.4)

𝑈𝑖,0 =𝜖𝑖,0

𝛼𝑖 − 𝜓𝑖

From this expression, we see three components to utility that derive from the financial terms of

insurance plans: disutility from premium; utility from covered nondiscretionary spending (𝑥 𝑗/𝛼𝑖);

and utility from spending due to moral hazard. Non-financial characteristics like carrier name

may also matter. In addition, risk coverage also generates utility: both spending-related terms are

adjusted upwards because we divide by 𝛼𝑖 − 𝜓𝑖 in place of simply 𝛼𝑖.

Finally, the expected cost to the insurer of enrolling a consumer of type 𝑖 is:

𝑐𝑖, 𝑗 =

∫(𝑥𝑖, 𝑗_𝑖 + 𝜔𝑖𝑥2

𝑖, 𝑗_𝑖)𝑑𝐹_,𝑖 (_)

𝑐𝑖, 𝑗 =𝑥𝑖, 𝑗

𝛼𝑖+𝜔𝑖𝑥

2𝑖, 𝑗

𝛼𝑖

which approaches zero when 𝛼𝑖 is large. The insurer is assumed to be risk-neutral. As in the model

with additive moral hazard discussed in Azevedo and Gottlieb (2017), the insurer pays the full cost

of spending due to moral hazard while consumer utility reflects only half of that spending (adjusted

up due to risk coverage).

Demand Estimation: Plan Choice and Health Spending

Plan choice.

Taking equation (3.4) as a starting point and multiplying through by 𝛼𝑖 − 𝜓𝑖 > 0, we have:

𝑢𝑖, 𝑗 = 𝑥𝑖, 𝑗 +12𝜔𝑖𝑥

2𝑖, 𝑗 − (𝛼𝑖 − 𝜓𝑖)𝑝𝑖, 𝑗 + 𝛽0𝑋 𝑗 + 𝜖𝑖, 𝑗 . (3.5)

𝑢𝑖,1 = 𝜖𝑖,1

117

where 𝑖 denotes households, 𝑗 health plans, and we have suppressed the indices (𝑚, 𝑡) denoting

geographic markets (rating areas) and time periods. We assume 𝜖𝑖, 𝑗 follows a Gumbel or type I

extreme value distribution. The probability that an enrollee 𝑖 chooses plan 𝑗 then takes the standard

logit form:

𝑠𝑖, 𝑗 = 𝑃𝑟 (𝑑𝑖, 𝑗 = 1) =𝑒𝑥𝑝(𝑉𝑖, 𝑗 )∑𝐽𝑘=1 𝑒𝑥𝑝(𝑉𝑖,𝑘 )

(3.6)

where 𝑉𝑖, 𝑗 = 𝑥 𝑗 + 12𝜔𝑖𝑥

2𝑗− (𝛼𝑖 − 𝜓𝑖)𝑝 𝑗 + 𝛽0𝑋 𝑗 , and 𝑑𝑖, 𝑗 = 1 when household 𝑖 chooses plan 𝑗 . Here,

plan choice 𝑗 = 1 represents the outside good of no insurance. Thus, 𝑉𝑖,1 = 0 since both the actuarial

value and premium equal zero when the ‘plan’ represents a lack of insurance, and other components

of the utility equation are normalized relative to the outside option.

Accounting for Health spending.

Based on our model above with multiplicative moral hazard and with our particular parame-

terization, we can write the expected level of health spending by the insurer with the following

form:

𝑐𝑖, 𝑗 = (𝑥𝑖, 𝑗 + 𝜔𝑖𝑥2𝑖, 𝑗 )_𝑖

where again we have omitted subscripts (𝑚, 𝑡).

We further assume that all enrollees have some positive health care spending, and the insurer

bears some cost of enrolling even healthy consumers, but that there is a spending cutoff 𝑐 such that,

for 0 ≤ 𝑐𝑖 ≤ 𝑐, “hassle costs” of submitting claims may lead the enrollee or insurer not to submit a

claim. That is, we interpret zero spending observations as implying “small but positive” health care

spending by the enrollee, with an associated small cost to the insurer. We therefore employ a fixed

cutoff, 𝑐, and treat all observed costs before that threshold as censored.28

Given our assumption that _𝑖 follows an exponential distribution with parameter 𝛼𝑖, we can

write:

28. In robustness analyses, we vary the cutoff to test the effect on our coefficients of interest. We also design alikelihood routine to recover the threshold. See Appendix C.5.

118

𝑓 (𝑐𝑖, 𝑗 |𝑥𝑖, 𝑗 , 𝜔𝑖, 𝛼𝑖) =

1 𝑥𝑖, 𝑗 = 0, 𝑐𝑖, 𝑗 = 0

0 𝑥𝑖, 𝑗 = 0, 𝑐𝑖, 𝑗 ≠ 0

1 − 𝑒𝑥𝑝(−𝛼𝑖

(𝑐

𝑥𝑖, 𝑗+𝜔𝑖𝑥2𝑖, 𝑗

))𝑥𝑖, 𝑗 ≠ 0, 𝑐𝑖, 𝑗 ≤ 𝑐

𝛼𝑖𝑥𝑖, 𝑗+𝜔𝑖𝑥2

𝑖, 𝑗

𝑒𝑥𝑝

(−𝑐𝑖, 𝑗 𝛼𝑖

𝑥𝑖, 𝑗+𝜔𝑖𝑥2𝑖, 𝑗

)𝑥𝑖, 𝑗 ≠ 0, 𝑐𝑖, 𝑗 > 𝑐

The joint likelihood of the household’s plan choice and its health spending is:

L(\) =𝑁∏𝑖=1

𝐽∏𝑗=1

𝑓 (𝑑𝑖, 𝑗 , 𝑐𝑖, 𝑗 |·, \)𝑑𝑖, 𝑗 =𝑁∏𝑖=1

𝐽∏𝑗=1

𝑃(𝑑𝑖, 𝑗 = 1|·, \)𝑑𝑖, 𝑗 𝑓 (𝑐𝑖, 𝑗 |·, \)𝑑𝑖, 𝑗 (3.7)

where 𝑗 = 1 is the outside option, 𝑃(𝑑𝑖, 𝑗 = 1|·, \) is the probability that patient 𝑖 chooses plan 𝑗 , and

𝑓 (𝑐𝑖, 𝑗 |·, \) is the likelihood of patient 𝑖 in plan 𝑗 having cost 𝑐𝑖, 𝑗 . A derivation of the log-likelihood

used for estimation is provided in Appendix C.3.

We further parameterize 𝛼𝑖, 𝜔𝑖, 𝜓𝑖 as functions of household and/or plan level observables. 𝛼𝑖

contains observables relevant for nondiscretionary spending: the sum of the ACG scores in the

household; an indicator for a family member having a top-quartile ACG score; and indicators

for household head aged over 50 and for households with dependents. We assume 𝜔𝑖 and 𝜓𝑖 are

constant across households in our sample. We account for any steering effect of subsidies, offered

to eligible enrollees if they purchase silver plans, on plan choices by including in 𝑋 𝑗 an interaction

between an indicator for silver plans and an indicator that equals 1 if the household’s purchase is

subsidized either through premium subsidies or cost-sharing subsidies.29

The assumption of perfect competition, if taken literally, implies no role for an unobserved

quality term in the utility equation. However, we recognize that this is an approximation to reality:

plans in the individual market may in fact be differentiated in ways that consumers value, and

premiums may (at least somewhat) respond to this unobserved heterogeneity. Following prior

29. The household’s premium and their coverage 𝑥𝑖, 𝑗 are both adjusted to account for subsidies. Allowing the subsidyto affect their preference for silver plans, in an additively separable way, accounts for any additional steering to silverplans from the subsidy structure that is not captured by premium and out-of-pocket cost reductions.

119

literature (Polyakova and Ryan (2019), Tebaldi (2017), and Tebaldi, Torgovitsky, and Yang (2019)),

we address this issue by using the fact that insurers in the individual market are not permitted to

vary premiums freely across consumers. Within each rating area, premiums for a given plan vary

only by age, family size and (through subsidies) across income levels, and this variation is based

on pre-specified statutory formulae that do not vary by carrier or plan. That is, the institutional

features of this market permit us to address premium endogeneity concerns by including carrier

fixed effects to control for unobserved quality differences across carriers in each year and rating

area. Remaining variation within tier stems from variation in the age composition and size of each

observed household.30

3.6.3 Premium setting

We calculate the total premium revenue collected by the insurer for plan 𝑗 , denoted 𝑅 𝑗 , as the

share-weighted average premium charged to enrollees across markets served by the plan. First label

plan 𝑗’s normalized premium, for a single 40 year old enrollee (suppressing 𝑚 and 𝑡 subscripts as

before), as 𝑝 𝑗 ; this will be useful for our counterfactual simulations below. To find the premium

paid by household 𝑖, we multiply this normalized premium by the rating factors 𝛾𝑘,𝑖 assigned to

all individuals 𝑘 covered in household 𝑖. Under the ACA, Oregon fixes the value of these weights

according to a published age curve; we apply these published weights in our calculation.31 We sum

these weighted premiums to the plan level, multiplying the premium each household faces by the

predicted probability it chooses plan 𝑗 , 𝑠𝑖, 𝑗 . In our notation, revenue then equals:

𝑅 𝑗 =

𝑁𝑡∑︁𝑖∈{𝑡}

𝑠𝑖, 𝑗 ∗ 𝑝𝑖, 𝑗 =𝑁𝑡∑︁𝑖∈{𝑡}

𝑝 𝑗 ∗ 𝑠𝑖, 𝑗𝐾𝑖∑︁𝑘∈𝑖

𝛾𝑘,𝑖 (3.8)

Then, under the assumption of perfect competition, we can estimate the costs of each plan (the

30. Given that our utility model already controls directly for plan tier actuarial values, we did not also add plan tierfixed effects. As a robustness check, we run an additional specification in which we control for carrier, year and ratingarea fixed effects. The qualitative results remain unchanged.

31. The federal default standard age curve under the ACA normalizes premium weights to equal one for householdmembers aged 21-24. The weights vary from as low as .765 for children under 14 to a maximum of 3 for enrollees aged64 and older.

120

extent to which claims costs are borne by the plan rather than addressed by risk adjustment; and

the magnitude of administrative costs) by finding the vector of parameters that equate the insurer’s

revenue with its total health and administrative costs. We assume the insurer sets premiums to break

even on each plan it offers, summing expected costs across individuals and geographic markets in a

given time period.32 Thus total premium revenues for plan 𝑗 equal its total costs:

𝑅 𝑗 =

𝑁∑︁𝑖∈{𝑡}∀𝑚

(𝑠𝑖, 𝑗 ∗ 𝛽4, 𝑗 ^𝑖, 𝑗𝑐𝑖, 𝑗

)+ 𝛽5 ∗ 𝐴 𝑗 + [ 𝑗 (3.9)

where 𝑠𝑖, 𝑗 is the probability that household 𝑖 chooses plan 𝑗 and 𝑐𝑖, 𝑗 is the expected medical claims

cost of household 𝑖 in plan 𝑗 .33 The observed variable ^𝑖, 𝑗 =𝑥𝑜𝑗

𝑥𝑖, 𝑗, where 𝑥𝑜

𝑗is the actuarial value of

the plan without any cost-sharing subsidies, accounts for the fact that the insurer’s realized costs do

not include the cost-sharing subsidies that entered the model of consumer choice. We assume the

federal government commits to reimbursing insurers for those subsidies. In particular, low-income

households who choose silver plans have a higher expected actuarial value of the plan than other

consumers; this higher actuarial value is accounted for in 𝑥 since it impacts consumer choices

of plan and subsequent utilization. The carrier expects this subsidy to be reimbursed and should

therefore choose premiums based on a lower effective actuarial value.

The parameter vector 𝛽4, specific to an insurance carrier and metal tier, adds flexibility to adjust

observed costs for the risk adjustment rules that allow the insurance carrier to themselves insure

against some fraction of the health spending risk. Second, 𝛽4 could also capture a markup over

variable costs, as in Bundorf, Levin, and Mahoney (2012): we would interpret a value greater than

one as such a markup for that carrier and plan type. We hold this value fixed in our counterfactual

simulations.

32. Our assumption that carriers break even plan by plan is consistent with the approach of Azevedo and Gottlieb(2017).

33. Given that spending follows an exponential distribution and given our first-stage estimates, we can write 𝑐 𝑗 ,𝑡 as:

𝑐𝑖, 𝑗 = 𝐸 [𝑐𝑖, 𝑗 |�̂�𝑖 , 𝜔𝑖] =𝑥𝑖, 𝑗 + 𝜔𝑖𝑥2

𝑖, 𝑗

�̂�𝑖. (3.10)

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The second term in the premium-setting equation reflects plan-level fixed costs. 𝐴 𝑗 includes

observable inputs into each carrier’s (plan-level) administrative costs. We approximate these

administrative costs in two ways. First, we use carrier x time period indicators to reflect common

per-plan or per-plan-region administrative costs incurred by the carrier in each plan year. Second,

as a robustness test, we include observed prior-year administrative cost variables from MLR data

to capture the plan-level administrative costs. The primary measure used is the carrier’s total

per-enrollee monthly administrative cost, which is the sum of taxes and fees; wellness activities;

and general administrative expenses. We allocate these costs to the plan level based on plan

enrollment by geographic market. Finally, [ 𝑗 is an element of the carrier’s administrative costs that

the econometrician does not observe.34

We begin by estimating equation (3.9) via ordinary least squares, using 2015-16 data since

carriers may not have reached an equilibrium in 2014. We then adopt a two-stage least squares

approach to address the possibility that [ 𝑗 may be correlated with the predicted market share and

claims variables.35 We use two sets of instruments 𝑍 𝑗 that are assumed to be correlated with 𝑠𝑖, 𝑗 and

𝑐𝑖, 𝑗 but mean independent of [ 𝑗 : 𝐸 [[ 𝑗 |𝑍 𝑗 ] = 0. The first set of instruments act as demand shifters.

These include the number of plans offered to households in the same market and the fraction of

households in the market who are subsidized. We also use lagged values of these two instruments.

The second set of instruments affect insurer costs through economies of scale. These include the

total number of subscribers of the carrier’s plans in other states and the total number of subscribers

of the carrier’s plans in the individual market in other states. Lastly, we employ year fixed effects to

account for time-varying administrative costs.

34. In our counterfactual analysis, we describe a fixed point algorithm to find the equilibrium 𝑝 𝑗 ,𝑚 under which allinsurers break even given enrollment shares 𝑠𝑖, 𝑗 ,𝑚, which are a function of 𝑝 𝑗 ,𝑚. In that analysis, we simplify notationby defining 𝐷 𝑗 ,𝑚 =

∑𝑁𝑚

𝑖∈{𝑚} 𝑠𝑖, 𝑗 ,𝑚∑𝐾𝑖

𝑘∈𝑖 𝛾𝑘,𝑖 so that market-specific revenue, for example, equals 𝑅 𝑗 ,𝑚 = 𝑝 𝑗 ,𝑚 ∗ 𝐷 𝑗 ,𝑚.35. For example, the instruments address the potential for unobserved quality variation within a plan—e.g. across

enrollee types—that is not correlated with premiums because of the institutional restrictions on premium setting alreadydescribed, and therefore does not bias the premium coefficient, but that does affect shares and is correlated with [. Notethat these issues do not apply to the claims equation because spending is determined only by actuarial value of the plan(𝑥 𝑗 ) and consumer attributes (_, 𝜔, 𝜓), and selection on these attributes is modeled fully rather than being unobserved.

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3.7 Results and Counterfactuals

3.7.1 Demand Estimates

Table 3.4 reports quantities of interest that are derived from our parameter estimates, for both

individual market and switcher populations, under two assumptions regarding the cost cutoff c. The

underlying parameter estimates are reported in Table 3.3. In general, they are less intuitive and

more difficult to discuss, with the exception of the estimated preference for silver plans among

subsidy-eligible consumers. This coefficient is large and positive. It is particularly large in the

switcher specification, implying that the group of forced switchers—who were newly eligible for

subsidies on moving to the individual market—were strongly influenced to choose the silver plans

in which they could receive those subsidies. We will return to this in the counterfactual analysis

below.

The top panel of Table 3.4 provides estimates for households’ expected non-discretionary

medical spending 𝐸 (_𝑖) that are implied by the estimated parameters of 𝛼𝑖. We report 𝐸 (_𝑖) by

family size and age using the median ACG score within the individual market for all households.

Unsurprisingly, when we condition on demographics and ACG score, there is no clear ranking of

expected health needs across the two samples. Enrollees with no dependents have essentially the

same expected non-discretionary spending: e.g. $1330-$1360 per year for those aged under 50.

For those with dependents, switchers have somewhat higher expected non-discretionary spending

($2300 per year for those under 50) than enrollees on the individual market ($1800 per year),

consistent with their somewhat larger family sizes (Table 1). However, these statistics ignore

differences in the distributions of ACG scores, age (under- versus over-50) and household type

(with- versus without-dependents) across the samples. Table 3.5 translates the estimated parameters

into the implied expected non-discretionary spending (𝐸 (_𝑖)) separately for the individual and small

group markets, accounting for these issues (and extrapolating the switcher preferences to apply to

the whole small group market). Predicted non-discretionary spending is still higher in the small

group market for enrollees with dependents, but the much higher proportion of young (under-50)

123

enrollees with no dependents generates a lower overall 𝐸 (_𝑖) than in the individual market ($3990

compared to $4850 per year on average). We note this contributor to the difference in medical

claims costs between the two markets; we will condition on it in our counterfactual simulations.

The second and third panels of Table 3.4 provide estimates of moral hazard and risk aversion

parameters. Moral hazard is higher for the sample of switchers than it is in the individual market.

Under our preferred assumption for c (a value of 20), we predict that moving switchers from

zero insurance to full insurance would increase medical spending by 24%. For individual market

enrollees, the increase would be 17%. Finally, the estimated CARA coefficient is 0.086 for the

individual market and 0.077 for the sample of switchers. Following Einav et al. (2013), this implies

that a household would be indifferent between receiving nothing and a 50-50 gamble in which

it earns $100 or loses $92.10 (for the individual market) or $92.80 (for switchers). That is, the

individual market households and switchers have essentially the same risk aversion. Our estimated

magnitudes for both moral hazard and risk aversion are in line with estimates in the previous

literature (Einav et al. (2013), Marone and Sabety (2020), and Ho and Lee (2020)).

What do these estimates imply for our counterfactual analyses? The two groups of enrollees are

quite similar on most dimensions. While the higher moral hazard parameter for the small group

market may imply a stronger preference for high-coverage plans than in the individual market

(Einav et al. (2013))—and the lower non-discretionary spending of small group enrollees should

also be helpful—it is not clear that the differences are large enough to address the gold tier’s adverse

selection problems when the markets are pooled. The new equilibrium will depend partly on the

extent to which claims costs are passed through to plan premiums; we move to these estimates

next.36

36. Note that the substantial preference for silver plans among switchers who are eligible for subsidies will be “turnedoff” in the counterfactuals where we allow tax exemptions and employer subsidies to persist (since federal subsidieswill not be available in that case).

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3.7.2 Cost Estimates

The estimates from the premium setting equation are set out in Table 3.6. Columns 1 and 2

summarize the OLS regression of predicted plan premium revenues on predicted medical claims

costs, with and without payer-year fixed effects. In Column 3 we instrument for predicted claims

costs using the number of plans in the market and the fraction of households in the market who are

subsidized. In all four columns, the estimated coefficient on claims costs is between 0.80 and 0.83

and highly statistically significant. That is, approximately 80% of claims costs are passed through

to premiums (and 𝛽4 captures some additional risk adjustment that is not reflected in ^𝑖, 𝑗 ).

Column 4 replaces the payer-year fixed effects with measures of lagged plan administrative

costs and year fixed effects, and instruments for both predicted claims costs and administrative

costs. The coefficient on claims falls to 0.63 and the coefficient on administrative costs is 1.30; both

are statistically significant. We view this as a useful sanity check on our other estimates, but since

we do not observe administrative costs for every carrier in the data, we use column (3) as the main

specification for counterfactuals.

3.7.3 Counterfactual Simulations

We apply our insurance demand estimates, both for current enrollees in individual insurance

and our observed population of small group enrollees forced out of employer coverage, to quantify

consumer surplus and the level of premiums under two alternative market designs. For each

counterfactual scenario, we collect the population of small group enrollees in Oregon in the year

2016 and allow these households to choose individual coverage.

First, we simulate market outcomes under a scenario where small group employer coverage

is removed. Employees of small group employers must purchase insurance on the individual

market, where they are eligible for ACA premium subsidies. For this population, premiums are no

longer tax-exempt and employers do not contribute to premium costs. Second, we approximate

an extension to the June 2019 regulation allowing health reimbursement arrangements paired with

individual market coverage (HRA-IIHIC). In this extension, small group employers may no longer

125

offer a group insurance option. In choosing a plan on the individual market or going uninsured,

small group employees benefit from the same tax advantages and premium subsidies that their

employer offered when sponsoring coverage on their behalf.

To model these counterfactuals, we need an algorithm that will allow us to find new equilibrium

premiums under the changes in enrollee population–both in terms of their sickness levels and plan

choice preferences. Under our assumption of a perfectly competitive individual insurance market,

Azevedo and Gottlieb (2017) provide an algorithm to compute this equilibrium. We describe the

algorithm in detail in Appendix Section C.6. In brief, we assume consumers have the same choice

of carriers, metal tiers, and plan types as in the observed market. Following Azevedo and Gottlieb

(2017), we augment our pool of households with a mass of ‘behavioral consumers’ who incur zero

covered health costs and choose each available contract with equal probability; the inclusion of

these behavioral types ensures that all contracts are traded. We then apply a fixed point algorithm in

which, in each iteration, consumers choose contracts according to their preferences taking prices as

given. Prices are adjusted up for unprofitable contracts and down for profitable contracts until an

equilibrium is reached. If any contract (tier) is priced so that no non-behavioral consumers enroll in

it, we interpret the outcome as unravelling.

We use four outcome measures to compare our counterfactual equilibrium to the simulated

equilibrium before we add the small group population to the pool: the share uninsured; the share in

each metal tier; the level of gross premiums; and average consumer surplus.

Consumer surplus.

Going back to the notation from Section 5 and defining (as in Einav et al. (2013)) the certainty

equivalent of plan 𝑗 as 𝑒 𝑗 such that −𝑒𝑥𝑝(−𝜓𝑒 𝑗 ) = 𝑣 𝑗 , we can show that for individuals of type 𝑖

(integrating over the distribution of _):

𝑒𝑖, 𝑗 =1

𝛼𝑖 − 𝜓𝑖

[𝑥𝑖, 𝑗 +


2− (𝛼𝑖 − 𝜓𝑖)𝑝𝑖, 𝑗 + 𝛽0𝑋 𝑗 + 𝜖𝑖, 𝑗

](3.11)

126

so that, for individuals of type 𝑖, ex ante CS (before their 𝜖 shock is realized in Stage 1) is:

𝐶𝑆𝑖 = 𝐸𝜖 (𝑚𝑎𝑥 𝑗𝑒𝑖, 𝑗 ) =1

𝛼𝑖 − 𝜓𝑖𝑙𝑜𝑔

𝐽∑︁𝑗=1𝑒𝑥𝑝

(𝑥𝑖, 𝑗 +


2− (𝛼𝑖 − 𝜓𝑖)𝑝𝑖, 𝑗 + 𝛽0𝑋𝑖, 𝑗

)(3.12)

where each individual chooses from 𝐽 plans in the individual market and premium is predicted as

described in Section 6.2.

In the small group market, we assume a simple model of plan choice to derive consumer surplus.

In the model, employers choose a health plans for their employees to minimize wage and health

benefit cost. Wage costs fall according to the certainty equivalent value of the health plan to the

employee. Employers have complete information about their employee’s preferences over insurance

plans, including individual 𝜖 shocks. Employers can choose a separate plan for each of their

employees, must offer a plan to each employee. To match observed plan choices, we also assume

that employees do not have an outside option.37 Under these assumptions, the post-tax ex ante

surplus attained by the employer from household 𝑖’s health insurance is:38

𝐶𝑆𝑖 =1

(𝛼𝑖 − 𝜓𝑖)𝑙𝑜𝑔

( 𝐽∑︁𝑗=1𝑉𝑖, 𝑗 − (1 − 𝜏𝑖) (𝛼𝑖 − 𝜓𝑖)

a𝑖

1 − a𝑖𝑝𝑖, 𝑗

)where a𝑖 is the share of premiums paid by the employer. Appendix C.7 describes alternative models

of plan choice in the small group market and presents measures of consumer surplus for each. Our

estimates are sensitive to which model of plan choice we use. Also, small group consumer surplus

estimates are derived from observed premiums, whereas counterfactual consumer surplus estimates

are derived from simulated premiums. Thus, estimates of small group consumer surplus should be

interpreted with caution. For this reason, we omit small group consumer surplus estimates from the

main counterfactual result tables. Estimates are instead reported in Appendix Table C.2.

37. Households may not choose the outside option because of default bias or social and employer pressure. Thoughstrong, this assumption is needed to marry observed plan choices with the model’s predictions.

38. Note that employers are able to extract all consumer surplus from employees in this model.

127

Simulated Market Outcomes in the Current Market.

Before turning to our alternative market design counterfactuals, we simulate market outcomes

for the individual market under current conditions. Column (1) of Table 3.12 presents these in-

sample predictions. We find that adverse selection has severely impacted the market for gold tier

plans. On average, simulated premiums of gold plans (normalized to a single 40-year old premium)

are $878 per month. Only 7% of households purchase these plans.

Average consumer surplus in the individual market is large – $1,575 per month for the set

of households for which the measure is defined. However, consumer surplus is driven by high

spending households. When conditioning on the 6% of households with the highest expected

non-discretionary spending, average consumer surplus drops to $272.39

The Impact of Removing Small Group Employer Coverage.

We find that removing small group employer coverage essentially leaves the individual mar-

ket unchanged, while providing savings to the government and employers. Despite lower non-

discretionary spending among small group employees, small group preferences are such that low

spending small group households choose uninsurance over insurance. Thus, only higher spending

households enter into the individual market pool.

In this counterfactual scenario, the prices of gold plans remain high – increasing to $927 on

average. Accordingly, the share of households choosing gold plans changes little. Table 3.12

shows that other market outcomes also experience only small changes. For bronze plans, average

premiums decrease by $6 per month for a 40-year old single household and the premiums of silver

plans increase by approximately $13. The share of households who choose uninsurance remains

constant. These changes generate an average surplus loss of $2 per month per household.

For households who shift from employer coverage to the individual market, the new market

design offers both benefits and costs. These households lose large tax subsidies and employer

39. Consumer surplus is defined for the set of households where 𝛼 > 𝜓. The 6% of households with the highestexpected non-discretionary spending, 𝛼 > 𝜓 + 0.05.

128

contributions (as a percent of premiums) on premium payments. Further, households with large

willingness to pay for insurance both lose access to platinum metal tier plans (which we assume

remain in a death spiral in the counterfactual simulations) and enter into a market which suffers

from adverse selection. On the other hand, small group market households gain ACA premium

subsidies and face insurance premiums that are not subject to the large markups that exist in the

small group market.

For this population, we find that premiums for bronze and silver plans are lower in the merged

market than observed premiums in the small group market with employer coverage (a decrease of

$69 and $85 per month respectively). However, premiums for gold plans are larger in the merged

market by $588. Since gold tier premiums do not stabilize, adverse selection effects outweigh the

gains from removing these plan’s premium markups.

Decreased markups are unable to counteract the loss of tax subsidies, employer contributions,

and a stable market for platinum plans in determining plan choices. Plan coverage for small group

households decreases significantly, with 64% opting to attain no coverage and only 1% choosing

a gold plan. This contrasts with observed plan choices in the small group market, where 39% of

households have gold or platinum coverage.

Average consumer surplus decreases by $38 for small group market households. This effect is

driven by households with high expected non-discretionary spending who lose access to platinum

plans and face higher gold tier premiums. Indeed, when excluding the top 4% of households

by expected non-discretionary spending (with 𝛼 ≤ 𝜓 + 0.05), average consumer increases by a

substantial $123. As noted previously, these estimates should be interpreted with caution.

Government expenditures on insurance coverage for small group employees is significantly

lower in the merged counterfactual market than under current market conditions. Under employer

coverage, premiums are tax-exempt. Thus, we measure government expenditures at the household

level as the household’s average tax rate times the observed premium of their chosen plan. In the

individual market, government expenditures for a household are expected premium subsidies. We

find that government expenditures for small group employees decrease from $130 per month per

129

household under employer coverage to $51 in the merged market. This finding is driven by small

group market households shifting to unemployment. When conditioning on households who attain

coverage, government expenditures are higher in the merged market ($140). That is, the average

premium subsidies provided to households who entered into the individual market are $10 greater

than the tax benefits provided to those households when they had attained insurance on the small

group market.

Employers, on the other hand, benefit immensely from the removal of group coverage. Under

the assumption that employers contribute 50% of premium costs, we estimate that small employers

spend an average of $211 per employee per month on health coverage. In the counterfactual

scenario, this drops to $0. In total, removing small employer group coverage and forcing small

group employees onto the individual market would yield approximately 318 million dollars in yearly

savings for small employers in this sample.

The Impact of An Extension of the HRA-IIHIC

By allowing small group employees to purchase insurance on the individual market with tax-

exempt and employer-subsidized premiums, we introduce a population to the individual market

who are less price sensitive and have lower spending on average than the existing individual market

population. By merging the two markets in this way, the adverse selection problem among gold

tier plans in the individual market is somewhat mitigated. 8% of small group employee households

choose gold tier plans in the merged market. Accordingly, for individual market households, the

average normalized prices for gold plans drop from $898 per month to $526 and the share of

households choosing those plans increases by 1.6pp.40

However, while small group employee households are less price sensitive than individual market

households, they do not attain subsidies or cost sharing supplements. Without these additional

benefits, the households who choose silver plans are higher spending.41 Thus causing average

40. Table 3.13 details the counterfactual results.41. In our demand model, we estimate that households have a particular preference for subsidized silver plans.

For small group households, this preference was estimated to be especially large (see Table 3.3). We turn off thesepreferences for small group market households in this counterfactual.

130

normalized monthly premiums for silver plans rise by $65 and for the share of individual market

households choosing silver plans to fall by 3%.

Despite this, merging the two markets remains mildly beneficial for individual market households

on average, but these benefits are primarily attained by households with high non-discretionary

spending. We find that average consumer surplus increases by $1.3 per month all households and

decreases by $3.8 for the bottom 94% of non-discretionary spenders.42

For small group employees, average normalized premiums fall in bronze and silver metal

tiers (by $56 and $65) but increase in gold metal tiers (by $1.136), as adverse selection remains

in the merged market. Further, these households lose access to platinum plans. As in the first

counterfactual scenario, consumer surplus decreases for all households, but increases for those with

less expected non-discretionary spending.43

Lastly, both government expenditure and employer spending decrease substantially. Here, the

formula for government expenditures and employer spending are the same under the current market

design and the extended HRA-IIHIC scenario. Still, both government expenditures and employer

spending decrease to 13 of their previous levels. Much of these savings are caused by small group

households shifting to uninsurance. Conditional on purchasing insurance, spending levels are

similar in the two markets.44

3.8 Conclusion

This paper set out to assess the impact of market segmentation on outcomes in US health

insurance markets. We focus on an ideal laboratory to study the effect of segmentation: the division

between individual market coverage through insurance marketplaces or brokers vs. employer

coverage through the small group market. Using a detailed data set of plan choices, health diagnoses,

42. Again, by all households we mean the households for whom consumer surplus is measurable (𝛼 > 𝜓). The top6% of non-discretionary spenders are those with 𝛼 > 𝜓 + 0.5.

43. Comparing the first and second counterfactual scenario, we note that the premiums faced by small group employeesin the second are lower than those in the first. However, consumer surplus is much lower. This is caused by the removalof preferences for subsidized silver plans.

44. Government spending: $3 higher per month per household; employer spending: $2 lower per month perhouseholds.

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and health spending that allows for tracking subscribers across insurance plans and markets, we are

able to estimate preferences for both individual market and small group market households. We

then use these estimated preferences, along with premium setting equations, to simulate market

outcomes in counterfactuals where we integrate the markets.

Our findings are mixed in their support of market integration. We find that removing the small

group coverage and shifting small group employees to the individual market would shift many small

group employees to uninsurance, without improving market conditions in the individual market.

Employer and government savings, however, would be large. In a second counterfactual scenario,

we find that an extension of the HRA-IIHIC rule, where employers contribute a percentage of

their employee’s premiums for plans purchased on the individual market, would mitigate severe

adverse selection in the individual market. Our findings suggest that even this alternative policy is

detrimental to high spending small group households, who face higher premiums for gold plans and

are constrained to a smaller set of insurance options. Thus, the effects of integration on households

is likely to be heterogeneous.

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3.9 Figures and tables

Individual Small Group

0.2

.4.6

.81

2014 2015 2016

0.2

.4.6

.81

2014 2015 2016

Bronze Silver Gold

Figure 3.1: Market sharesNote: This figure denotes the market shares of plans offered in the individual and small group insurance markets inyears 2014-2016. Panel A depicts shares by metal tier; we sum the shares across all payers and plan types in a metaltier, for a particular year and market segment. Panel B depicts shares by payer in each year and market segment. Weomit payer names due to data confidentiality. In each panel, the figure at left depicts shares for the individual marketand the figure at right depicts shares in the small-group market.

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Panel A: 2015Silver Gold

0.1

.2.3

frac

tion

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)

0.1

.2.3

frac

tion

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)


Panel B: 2016Silver Gold

0.1

.2.3

frac

tion

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)

0.1

.2.3

frac

tion

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)


Figure 3.2: Distribution of monthly medical costsNote: This figure depicts the distribution of monthly medical cost across households. Panel A and B show the distributions for the years 2015 and2016, respectively. In each panel, the left graph reflects the costs of subscribers who purchased a Silver plan while the right graph reflects the costsof subscribers who purchased a Gold plan. For each histogram, a bar depicts the fraction of households who fall into that range of costs acrossthe sample. The bars on the far left depict the fraction of households with zero monthly medical cost. The bars on the far right depict the fractionof households with more than $1,000 of monthly medical cost. Interior bins have equal width of $50 and start from $1. The lighter bars reflecthouseholds who choose plans in the Individual market while the darker bars bars reflect households in the Small Group market.

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0.0

02

.00

4.0

06

den

sity

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)

0.0

02

.00

4.0

06

den

sity

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)



0.0

02

.00

4.0

06

den

sity

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)

0.0

02

.00

4.0

06

den

sity

0 100 200 300 400 500 600 700 800 900 1000monthly cost ($)


Figure 3.3: Kernel density of medical costsNote: This figure depicts the density of monthly medical cost across households. All plots exclude households with zero cost and those with morethan $1,000 of monthly cost. Panel A and B show the density for the year 2015 and 2016 respectively. For each panel, the left graph is of subscriberswho purchased a Silver plan and the right graph is of subscribers who purchased a Gold plan. The lighter curve reflect households who choose plansin the Individual market while the darker curve bars reflect households in the Small Group market.

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Panel A: Silver Panel B: Gold

0.5

11.5

22.5

tota

l p

rem

ium

s /

med

ical

co

sts

2014 2015 2016

0.5

11.5

22.5

tota

l p

rem

ium

s /

med

ical

co

sts

2014 2015 2016


Figure 3.4: Medical markup (total premiums over medical costs)Note: This figure depicts the distribution of medical markups across our constructed plans. The figures on the left and right show the distributions forSilver and Gold plans, respectively. For each panel, from left to right, each sub-panel is for the year 2014, 2015, and 2016, respectively. For eachsub-panel, the box on the left is of plans in the Individual market and the box on the right is of plans in the Small-Group market. The medical markupis calculated as the ratio of a plan’s total premium revenue divided by the total medical cost the plan pays on behalf of its subscribers.

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Panel A: Silver Panel B: Gold

150

250

350

450

550

bas

e m

on

thly

pre

miu

m (

$)

2014 2015 2016

150

250

350

450

550

bas

e m

on

thly

pre

miu

m (

$)

2014 2015 2016


Figure 3.5: Base monthly premiumNote: This figure depicts the distribution of base premiums across constructed plans. The figures on the left and right show the distributions for Silverand Gold plans respectively. For each panel, from left to right, each sub-panel is for the year 2014, 2015, and 2016 respectively. For each sub-panel,the box on the left is of plans in the Individual market and the box on the right is of plans in the Small-Group market. The base premium is calculatedas the plan bin’s average for a non-smoking single 40-year-old person, where the average is taken across different plans as marketed on the Exchange.

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Panel A: Comparison of subsidy schemes

i.Tiered-composite pricing ii. Premium tax-subsidy iii. Employer contribution

0

2,000

4,000

6,000

8,000

2014 2015 2016

0

2,000

4,000

6,000

8,000

2014 2015 2016

0

2,000

4,000

6,000

8,000

2014 2015 2016


Panel B: Subsidy size in order for indifference between Individual and Small Group plans

i. Single-member HH ii. HH with spouse and two dependents

−.4

−.2

0

.2

.4

2014 2015 2016

−.4

−.2

0

.2

.4

2014 2015 2016

Figure 3.6: Distribution of subsidiesNote: This figure depicts the distribution of differential subsidies for constructed plans between the Individual and Small Group markets.Panel A depicts comparisons of annual premiums across different subsidy scheme for different constructed plans. For each constructed plan availablein the Small Group market, we identify an identical constructed plan in the Individual market which has the same base premium. We then simulatefor each plan the average premium that a 40-year-old single subscriber would pay in the Individual market vs. the Small Group market under differentpricing schemes. The plot on the left assumes that the only difference in pricing schemes is in the tiered-composite pricing system in the Small-GroupMarket. The plot in the middle assumes the presence of tiered-composite pricing system as well as the premium tax subsidy in the small-groupmarket. The plot on the right assumes the presence of the tiered-composite pricing system, the premium tax-subsidy, as well as the employer’sminimum premium contribution allowable in order to earn the Small Business Health Care Tax Credit (which is 50% of premium).Panel B plots the necessary employer subsidy rates for an employee to be indifferent between the tax-subsidized tier-compositely-priced small-grouppremium and the equivalent individual market plan’s premium. The figure on the left depicts that for a 40-year-old single subscriber. The figure onthe right depicts that for a household that includes a spouse and two dependents.

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0.1

.2.3

.4

fracti

on

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

HH−sum risk

0.1

.2.3

.4

fracti

on

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

HH−sum risk



0.1

.2.3

.4

fracti

on

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

HH−sum risk

0.1

.2.3

.4

fracti

on

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

HH−sum risk


Figure 3.7: HH-sum risk scoreNote: This figure depicts the distribution of household-sums of risk scores across households. Panel A and B show the distributions for the year 2015and 2016 respectively. For each panel, the left graph is of subscribers who purchased a Silver plan and the right graph is of subscribers who purchaseda Gold plan. For each histogram, each bar depicts the fraction of households in the according bin across the sample. Bins have equal width of 0.25and start from 0. Orange bars only include households in the Individual market and navy bars only include households in the Small Group market.

139

10

12

14

16

18

Nu

mb

er

of

en

rolle

es (

mill

ion

s)

2013 2014 2015 2016 2017 2018Year


Figure 3.8: Number of enrolleesNote: This figure depicts the number of annual enrollees across years in the Affordable Care Act marketplaces from 2013 to 2018. The orange seriesdepicts the number of enrollees in the Individual market and the navy series depicts that in the Small Group market. Figures are obtained from theKaiser Family Foundation’s website (https://www.kff.org/health-reform/state-indicator/marketplace-enrollment/).

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Individual Market Small-Group MarketVariable Mean S.D. Median Mean S.D. MedianSingle-membered 0.70 0.75Married, no dependent 0.14 0.08Not married, with dependent(s) 0.07 0.07Married, with dependent(s) 0.09 0.10Number of dependents 1.93 1.09 2.00 2.21 1.25 2.00Sum of ACGs within the HH 1.39 2.44 0.62 1.25 2.21 0.60Income (as ratios of the FPL) 3.11 0.63 2.88 3.20 0.28 3.16Age 46.96 11.75 48.00 42.62 11.28 42.00Over-50 0.42 0.28Living in rating areas 1, 2, or 3 0.69 0.78Number of unique subscribers 354,245 218,863Number of subscriber-years 512,373 383,137

Table 3.1: Summary statistics on demographics variablesNote: This table presents summary statistics on the population of households in Oregon choosing insurance plans in both the individual and smallgroup markets in years 2014-2016. In both markets, we omit households who choose grandfathered plans, platinum plans, or plans that are notobserved in the SERFF data. We compute the sum of risk score for members of a household, where we predict each member’s risk using the JohnsHopkins’ ACG software. Number of dependents is calculated with the subset of households who have dependents. Rating areas 1-3 include theurban areas of Portland, Eugene, and Salem, respectively. Rating areas 4-7 include largely rural areas of the state. There are 16,966 households withPlatinum plans in the small group subset.

141

Variable Mean S.D. Median Mean S.D. MedianSpending = 0 0.29 0.32

Bronze plans 0.45 0.43Unsubsidized Silver plans 0.27 0.34

Subsidized Silver plans 0.24Gold plans 0.13 0.25

Monthly spending 5.93 14.33 1.28 5.24 12.93 1.27(cond. on > 0, in $100s)

Bronze plans 3.87 11.84 0.70 4.59 12.71 0.93Unsubsidized Silver plans 4.35 11.15 1.13 4.89 12.62 1.16

Subsidized Silver plans 6.09 14.59 1.38Gold plans 9.61 17.78 2.87 5.86 13.32 1.58

Monthly HH premiums (in $100s) 3.75 2.38 2.87 4.26 2.64 3.16Bronze plans 3.13 2.13 2.25 3.29 1.98 2.51

Unsubsidized Silver plans 3.57 1.94 2.80 4.03 2.40 2.96Subsidized Silver plans 3.75 2.21 2.86

Gold plans 5.29 3.06 4.17 4.97 3.00 3.55Market shares

Bronze plans 0.30 0.15Unsubsidized Silver plans 0.12 0.50

Subsidized Silver plans 0.44 0Gold plans 0.14 0.36

Number of insurers activein rating areas 1-3 (mean) 7.0 8.0in rating areas 4-7 (mean) 6.5 7.3

Number of unique subscribers 311,617 73,540Number of subscriber-years 438,003 105,864

Table 3.2: Summary statistics on insurance variabelsNote: This table presents summary statistics on the population of households in Oregon choosing insurance plans in both the individual andsmall group markets in years 2014-2016. In both markets, we omit households who choose grandfathered plans, platinum plans, or plans that arenot observed in the SERFF data. Our monthly spending variable includes all medical costs covered under the insurance plan but omits patientout-of-pocket expenses. Household premiums in the individual market reflect gross premiums by plan, apart from the subsidized silver plan premiums,which reflect the weighted average subsidized premiums across all households eligible for premium subsidies. Small group premiums reflect thegross premiums paid by the employer per household; the household’s tax subsidy or employer subsidy are not included in the statistics shown.

142

Main Switchers(1) (2) (1) (2)

𝛼

Low-risk [0/1] -0.230 -0.259 -0.014 -0.038(0.002) (0.002) (0.025) (0.025)

Household-sum risk score -0.491 -0.468 -0.476 -0.461(0.000) (0.000) (0.005) (0.005)

Dependents [0/1] -0.295 -0.285 -0.565 -0.556(0.001) (0.001) (0.016) (0.016)

Over-50 [0/1] -0.675 -0.664 -0.567 -0.555(0.001) (0.001) (0.012) (0.012)

𝜔

Constant -1.787 -1.287 -1.446 -1.124(0.007) (0.005) (0.079) (0.062)

𝜓

Constant -2.452 -2.355 -2.563 -2.473(0.010) (0.009) (0.106) (0.098)

𝛽0Payer fixed-effects X X X X

Subsidized silver plan [0/1] 0.888 0.886 2.899 2.900(0.003) (0.003) (0.037) (0.037)

𝑐 $20 $50 $20 $50𝑁 938,541 17,448

Number of insured HHs 438,003 3,786

Table 3.3: Main parameter estimates

Note: This table reports the maximum likelihood estimates from the demand specification in Equation 3.7. Columns under “Main” contain estimatesfrom the population of individual market subscribers in the years 2014-2016. Columns under “Switchers” contain estimates from the sample oftracked households that we observe switching away from the small group market after years 2014 and 2015. As described in Section XX, we definethe switcher population as households belonging to small groups that exited the insurance market in the prior year. For each sample, we run twospecifications, defined by the cost-censoring threshold 𝑐: in (1) 𝑐 = $20 and in (2) 𝑐 = 50. Low risk [0/1] is an indicator equal to one if a household’srisk score is below the 30th percentile of the distribution of risk scores. We define the household risk score as the sum of risk scores for insuredmembers in the household, where we predict risk using the Johns Hopkins’ ACG software. Dependents [0/1] is an indicator equal to one if there is adependent in the household. Over-50 [0/1] is an indicator equal to one if the primary subscriber is older than age 50. Payer fixed-effects includeindicators for the seven major payers. Subsidized silver plan [0/1] is an indicator equal to one if the relevant insurance plan is a Silver plan and thehousehold’s purchase is subsidized either through premium subsidies or cost-sharing subsidies.

143

Household type Main Switchers(1) (2) (1) (2)

E[_𝑖]No dependent, under-50 1.356 1.337 1.343 1.331

(0.000) (0.000) (0.004) (0.004)With dependent(s), under-50 1.821 1.777 2.363 2.320

(0.002) (0.002) (0.039) (0.039)No dependent, over-50 2.661 2.596 2.367 2.319

(0.003) (0.003) (0.029) (0.029)With dependent(s), over-50 3.575 3.452 4.165 4.042

(0.007) (0.007) (0.094) (0.092)𝜔𝑖

Constant 0.167 0.276 0.236 0.325(0.001) (0.001) (0.019) (0.020)

𝜓𝑖Constant 0.086 0.095 0.077 0.084

(0.001) (0.001) (0.008) (0.008)loss interpretation

Constant 0.921 0.913 0.928 0.922(0.001) (0.001) (0.007) (0.007)

Table 3.4: Derived parameter estimates

Note: This table reports the derived choice parameters implied by the maximum likelihood estimates in Table 2. Columns under “Main” denoteestimates from the population of individual market subscribers in the years 2014, 2015, and 2016. Columns under “Switchers” denotes estimatesfrom the sample of tracked households that we observe switching away from the small group market after years 2014 and 2015. As described inSection XX, we define the switcher population as households belonging to small groups that exited the insurance market in the prior year. For eachsample, we run two specifications, defined by the cost-censoring threshold 𝑐: in (1) 𝑐 = $20 and in (2) 𝑐 = 50. We report the expected health state,𝐸 [_𝑖 ], based on our exponential distributional assumption and our estimate of the parameters underlying 𝛼𝑖 , the rate parameter of the exponentialdistribution. We compute 𝐸 [_𝑖 ] using the median risk score within the individual market (0.62) for all example households. 𝜔𝑖 is the multiplicativemoral hazard parameter. 𝜓𝑖 is the CARA risk aversion parameter. We also report risk aversion using the loss interpretation: we compare the utility of(a) a 50/50 gamble between losing X dollars and gaining $100 with (b) the certainty equivalent utility of 0. We report X in the table in $100s ofdollars.

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Individual Small-GroupHousehold type Mean S.D. Share Mean S.D. Share

E[_𝑖] Overall 4.85 13.55 3.99 11.76No dependent, under-50 2.14 7.77 0.44 1.72 5.85 0.61

With dependent(s), under-50 5.32 13.20 0.11 7.61 16.02 0.13No dependent, over-50 6.90 16.51 0.40 5.94 14.76 0.22

With dependent(s), over-50 12.22 21.76 0.04 17.05 25.36 0.04𝑁 438,003 105,864

Table 3.5: Derived parameters across markets

Note: This table describes the distribution of 𝐸 [_𝑖 ] as implied by the maximum likelihood estimates in Table 3.3 separately for the individual andsmall group markets. The ‘overall’ rows reports the expected underlying health costs across the full sample, using household level covariates in ourspecification of the parameters of the exponential distribution for _𝑖 . In the subsequent rows, we break down the sample by household type andcompute 𝐸 [_𝑖 ] within type. We also report the share of the sample that each household type represents.

145

(1) (2) (3) (4)Medical costs 0.828 0.830 0.801 0.625

(0.032) (0.034) (0.024) (0.062)Administrative costs (t-1) 1.299

(0.393)Year FEs XPayer-Year FEs X X𝑁 233 231 231 1861𝑠𝑡-stage F-stat 18.112 6.058𝑅2 0.978 0.983 0.982 0.974

Table 3.6: Premium setting equation

Note: This table contains the estimates of our premium setting model across payer-metal tier insurance offerings. A market is defined as a calendaryear and rating area combination. The model’s predicted total monthly premiums and costs are in 100s of dollars. Column 1 presents an ordinaryleast squares (OLS) regression of premium on cost. Column 2 presents an OLS regression of premium on cost and includes payer-year fixed effects.Column 3 presents a two-staged least squares (2SLS) regression where the instrumented variable is a plan’s predicted cost and the instruments are thenumber of plans in the same market and the fraction of households in the market who are subsidized and includes payer-year fixed effects. Column 4presents a 2SLS where the instrumented variables are a plan’s predicted cost as well as its predicted administrative costs from the previous year andthe instruments are the number of plans in the same market, the fraction of households in the market who are subsidized, those two variables for thesame plan in the previous year, the total number of subscribers of the carrier’s plans in other states, the total number of subscribers of the carrier’splans in the Individual market in other states, and includes year fixed effects. For details on the construction of a plan’s predicted administrative costs,please see Table 5.

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Variable Mean S.D. MedianPer-enrollee monthly admin costs in the individual market ($)

Total 71.53 28.24 62.86Taxes and fees 21.23 25.64 11.96Wellness activities 4.14 2.99 3.64General administrative expenses 46.17 16.22 42.85

Number of annual subscribers in OregonIndividual market 25,931 31,702 16,778Small-group market 21,883 13,197 19,812Large-group market 84,770 92,063 42,990Other markets 40,772 68,557 6,543

Number of states where the payer is active 7.5 14.8 2

Table 3.7: Administrative costs

Note: This table displays the various measures of insurers’ administrative cost employed. All cost measures are computed across the publiclyavailable CMS Medical Loss Ratios forms for years 2014, 2015, and 2016. The primary measure employed in Table 4 is of the total per-enrolleemonthly administrative cost, which is the sum of the following three cost categories. Taxes and fees refer to Section 3 of the CMS form and includefederal and state taxes deductible from premiums, community benefit expenditures, contribution to the Federal Transition Reinsurance Program, andvarious other regulatory fees. Wellness activities refer to Section 4 of the CMS form and include activities to improve and promote health outcomesand prevent hospital readmission as well as expenses related to Health Information Technology. General administrative expenses refer to Section 5 ofthe CMS form and include direct sales salaries and benefits, agents and broker fees, and all other non-medical general and administrative expenses.The number of annual subscribers in Oregon refers to the size of a carrier’s subscriber pool across different business lines. Finally, we present thenumber of states where the average payer is active and files a report with CMS.

147

Switchers Small-Group MarketDemographic variable Mean S.D. Mean S.D.Single-membered 0.77 0.76Married, no dependent 0.02 0.07Not married, with dependent(s) 0.19 0.07Married, with dependent(s) 0.02 0.10Number of dependents (conditional on > 0) 2.16 1.36 2.28 1.33Sum of risk scores within the HH 1.85 2.76 1.21 2.15Income (as ratios of the FPL) 3.23 0.65 3.13 0.26Age 48.96 10.60 42.20 11.04Over-50 0.53 0.26Living in rating areas 1, 2, or 3 0.72 0.77Insurance variable Mean S.D. Mean S.D.Spending = 0 0.19 0.32Monthly spending (cond. on > 0, in $100s) 6.45 14.32 5.24 12.93Market shares

Bronze plans 0.24 0.15Silver plans 0.52 0.50Gold plans 0.24 0.36

Number of subscriber-year observations 3,786 105,864

Table 3.8: Demographics of the switchers

148

Uninsured Households Insured HouseholdsDemographic variable Mean S.D. Mean S.D.Single-membered 0.48 0.70Married, no dependent 0.19 0.15Not married, with dependent(s) 0.15 0.06Married, with dependent(s) 0.18 0.09Number of dependents (conditional on > 0) 2.03 1.45 1.91 1.10Sum of risk scores within the HH 1.72 2.49 1.45 2.50Income (as ratios of the FPL) 2.82 0.70 3.07 0.63Age 37.93 12.88 46.96 11.82Over-50 0.21 0.45Living in rating areas 1, 2, or 3 0.70 0.69Number of subscriber-year observations 500,538 438,003

Table 3.9: Demographics of the uninsured

149

(1) (2) (3)Silver plans 2.129 2.122 2.126

(0.035) (0.036) (0.036)Gold plans 6.152 6.077 6.108

(0.074) (0.074) (0.074)Year 2015 -0.058 0.058 0.052

(0.047) (0.050) (0.050)Year 2016 -0.282 0.172 0.110

(0.045) (0.053) (0.053)Family size 1.255 1.251 1.248

(0.021) (0.021) (0.021)Age 0.089 0.087 0.084

(0.002) (0.002) (0.002)Income -0.214 -0.233 -0.218

(0.029) (0.031) (0.031)Number of months enrolled 0.182 0.181 0.179

(0.005) (0.005) (0.005)Constant -4.873

(0.117)Carrier FEs � �

Rating Area FEs �

𝑁 438,003 438,003 438,003𝑅2 0.047 0.048 0.049

Table 3.10: Cost regressionNote: This table contains the estimates of ordinary least squares (OLS) models of subscribers’ monthly medical costs (in $100s) on various variables.All specifications include indicators for whether the plan purchased was a Silver or Gold plan (Bronze plans omitted), in year 2015 or 2016 (2014omitted), family size i.e. the number of people in the household on the insurance plan, the primary subscriber’s age, the household’s predicted incomeas a ratio over the federal poverty line, and the number of months that the subscriber was enrolled in that year. Column 1 includes a constant, column2 includes carrier fixed-effects, and column 3 includes both carrier fixed-effects and rating area fixed-effects.

150

Year Metal Market Number of observations Mean cost S.D.

2015Silver

Individual 84,584 457.95 1,273.30Small Group 14,949 337.86 1,071.66

GoldIndividual 19,436 888.47 1,721.37

Small Group 12,377 484.08 1,244.96

2016Silver

Individual 92,547 410.26 1,198.00Small Group 26,840 329.20 1,072.99

GoldIndividual 23,210 781.53 1,637.90

Small Group 13,621 469.23 1,260.13

Table 3.11: Cost distribution

151

Individual Market Small Group Market

Subsample Full

Variable Pre Post Change Pre Post Change Post

Consumer Surplus (𝛼 > 𝜓) 15.749 15.73 -0.019 N/A 17.467 N/A 20.048P(𝛼 > 𝜓) 0.927 0.927 0 0.944 0.944 0 0.946Cons. Sur. (𝛼 − 𝜓 > 0.05) 2.719 2.701 -0.019 N/A 2.130 N/A 2.142P(𝛼 − 𝜓 > 0.05) 0.867 0.867 0 0.906 0.906 0 0.908𝐸 [_𝑖] 5.938 5.938 0 4.627 4.627 0 4.52Moral Hazard Spending 0.271 0.27 -0.001 0.484 0.266 -0.218 0.262Share Uninsured 0.49 0.494 0.003 0 0.638 0.638 0.639Share Bronze 0.141 0.145 0.004 0.141 0.048 -0.093 0.048Share Silver 0.304 0.297 -0.007 0.486 0.299 -0.187 0.298Share Gold 0.065 0.065 0 0.247 0.015 -0.232 0.015Ave (Base) Bronze Prem 1.828 1.77 -0.058 2.509 1.815 -0.694 1.808Ave (Base) Silver Prem 2.093 2.219 0.126 3.123 2.272 -0.851 2.269Ave (Base) Gold Prem 8.975 9.27 0.295 3.924 9.799 5.875 9.824Government Spending 0.85 0.845 -0.004 1.304 0.508 -0.796 0.508Employer Spending NA NA NA 2.106 0 -2.106 0N 178115 178115 0 55073 55073 0 125487

Table 3.12: Counterfactual: Employees have premium subsidies

Note: This table shows the effects of merging the individual and the small group markets in 2016, assuming that small group households receivepremium subsidies in the individual market. All reported numbers are averages over households. In the small group market, changes between thepost-merge counterfactual and the pre-merge counterfactual are reported for the subset of households who choose a non-grandfathered plan that existsin our SERFF data. In this subsample, 7,894 households choose Platinum plans. To account for outliers, consumer surplus is reported for two sets ofhouseholds. 𝐸 [_𝑖 ] is a windsorized average across households at $8,937 per month. Moral hazard spending is the difference between expectedspending and expected spending if 𝜔𝑖 = 0. The Average (Base) premiums are a measure of age-adjusted premiums faced by households. To calculatethese base premiums, we first calculate the average premium faced by each household in each metal tier. Then, we account for the household’spremium subsidies and age to compute a premium that would be faced by a 40-year old without subsidies. Last, we average over households to attainthe Average base premium. In the pre-merged small group market subsample, Average Base Premiums are the age-adjusted average of premiumspaid by households who chose plans in that metal tier. Similarly, other variables in the pre-merged small group market are calculated based on theobserved plan choices of those households, rather than simulated plan choices. In the pre-merged small group market, employer spending is equal to50% of the premiums paid for households in coverage. Government spending is equal to the expected premium subsidies (

∑𝑗 𝑠𝑖 𝑗𝑚𝑡 𝑝𝑖 𝑗𝑚𝑡 𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡 )

if the household receives premium subsidies and is equal to the expected tax revenue lost by the government (∑

𝑗 𝑠𝑖 𝑗𝑚𝑡 𝑝𝑖 𝑗𝑚𝑡 𝜏𝑖𝑚𝑡 ) if the householdreceives tax subsidies.

152

Individual Market Small Group Market

Subsample Full

Variable Pre Post Change Pre Post Change Post

Consumer Surplus (𝛼 > 𝜓) 15.749 15.763 0.013 N/A 6.287 N/A 7.709P(𝛼 > 𝜓) 0.927 0.927 0 0.944 0.944 0 0.946Cons. Sur. (𝛼 − 𝜓 > 0.05) 2.719 2.681 -0.038 N/A 1.009 N/A 1.015P(𝛼 − 𝜓 > 0.05) 0.867 0.867 0 0.906 0.906 0 0.908𝐸 [_𝑖] 5.938 5.938 0 4.627 4.627 0 4.52Moral Hazard Spending 0.271 0.264 -0.007 0.484 0.17 -0.313 0.168Share Uninsured 0.49 0.506 0.015 0 0.718 0.718 0.717Share Bronze 0.141 0.14 -0.001 0.141 0.096 -0.045 0.096Share Silver 0.304 0.274 -0.03 0.486 0.11 -0.376 0.11Share Gold 0.065 0.081 0.016 0.247 0.076 -0.172 0.076Ave (Base) Bronze Prem 1.828 1.887 0.059 2.509 1.952 -0.557 1.947Ave (Base) Silver Prem 2.093 2.449 0.356 3.123 2.476 -0.647 2.473Ave (Base) Gold Prem 8.975 5.261 -3.714 3.924 5.059 1.136 4.997Government Spending 0.85 0.799 -0.05 1.304 0.373 -0.931 0.375Employer Spending NA NA NA 2.106 0.59 -1.515 0.591N 178115 178115 0 55073 55073 0 125487

Table 3.13: Counterfactual: Employees have tax and employer subsidies

Note: This table shows the effects of merging the individual and the small group markets in 2016, assuming that employers share 50% of premiumcosts for plans purchased in the merged market by small group households. Further, we assume that small group households pay premiums withtax-exempt funds. All reported numbers are averages over households. In the small group market, changes between the post-merge counterfactualand the pre-merge counterfactual are reported for the subset of households who choose a non-grandfathered plan that exists in our SERFF data. Inthis subsample, 7,894 households choose Platinum plans. To account for outliers, consumer surplus is reported for two sets of households. 𝐸 [_𝑖 ] isa windsorized average across households at $8,937 per month. Moral hazard spending is the difference between expected spending and expectedspending if 𝜔𝑖 = 0. The Average (Base) premiums are a measure of age-adjusted premiums faced by households. To calculate these base premiums,we first calculate the average premium faced by each household in each metal tier. Then, we account for the household’s premium subsidies and ageto compute a premium that would be faced by a 40-year old without subsidies. Last, we average over households to attain the Average base premium.In the pre-merged small group market subsample, Average Base Premiums are the age-adjusted average of premiums paid by households who choseplans in that metal tier. Similarly, other variables in the pre-merged small group market are calculated based on the observed plan choices of thosehouseholds, rather than simulated plan choices. Employer spending is equal to 50% of the premiums paid for households in coverage. Governmentspending is equal to the expected premium subsidies (

∑𝑗 𝑠𝑖 𝑗𝑚𝑡 𝑝𝑖 𝑗𝑚𝑡 𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡 ) if the household receives premium subsidies and is equal to the

expected tax revenue lost by the government (∑

𝑗 𝑠𝑖 𝑗𝑚𝑡 𝑝𝑖 𝑗𝑚𝑡 𝜏𝑖𝑚𝑡 ) if the household receives tax subsidies.

153

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Appendix A: Appendix For Chapter One

A.1 Dataset Construction

This section details the construction of the main analysis dataset.

A.1.1 Sample Subset

Geographical

I geographically restrict the dataset to fit my empirical exercise. First, I remove all patients and

physicians who do not reside in Ontario. Second, I remove all patients and physicians in census

subdivisions that are affiliated with First Nations of Indian bands, as defined by Statistics Canada.

These areas have data limitations and may not fully appear in the billings data. I also remove all

patients and physicians in census subdivisions that are larger than 5000 square kilometers or have

populations that are lower than the reporting threshold (generally 40). These census subdivisions

tend to be in frontier areas with extremely low population densities and have alternative healthcare

environments. In each individual year, the sample is restricted further to those with population data

in that year. All these resulting CSDs had patients choosing physicians in them in every year.

One last census subdivision is removed from the sample: Unorganized Mainland Manitoulin

(351091). This census subdivision was annexed by neighboring Killarney in 2006. It had a

population of 5 and had 9 (mostly seasonally inhabited) dwellings in the 2006 census. This census

subdivision was removed because it did not appear in the census population data in 2006.

Lastly, I restrict the census subdivisions to those in one of five markets in Northern Ontario.

These markets are detailed in Section 1.4.2.

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Figure A.1: Eligible Census Subdivisions

Physicians

I restrict the physician dataset to comprehensive care primary care physicians with more than

300 patients. Schultz and Glazier (2017) define a comprehensive care physician as a primary care

physician who saw patients more than 43 days per year, “more than half of their services were for

core primary care and their services fell into at least 7 of 22 activity areas.” I expand this definition

to any physician who ever fell into this category and did not change their practice locations. This

limits the influence of coding differences in different years and different payment models on the set

of included physicians.

Years

The original data span the years 2003-2015. The final sample includes only data from 2004

- 2014. 2003 and 2015 are excluded to allow lag and lead years to be used to construct patient

characteristics and outside option shares.

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A.1.2 Comorbidities

Patient comorbidities are defined using the ICD-9 Royal College of Surgeons’ Charlson Comorbidity

Mapping (Brusselaers and Lagergren (2017)), with adjustments for the differences between the

Ontario Health Insurance Plan (OHIP) diagnoses codes in the billings data and ICD-9 codes.

Table A.1 presents the differences between the ICD-9 codes and the OHIP diagnosis codes used in

the comorbidity mapping. The primary difference is the omission of several ICD-9 codes from the

set of possible OHIP diagnosis codes. Only one ICD-9 code was excluded because of a difference

in definition (ICD-9 725). In the ICD-9 codebook, code 725 is Polymyalgia Rheumatica. In the

OHIP diagnosis codebook, code 725 is Lumbar Disc Disease (degenerative) (ICES (2020)).

Comorbidities are defined for a patient based on their previous year’s claims. If they have a

diagnosis code associated a comorbidity in year 𝑡 − 1, they are labeled as having that comorbidity in

year 𝑡.

Table A.1: Charlson Comorbidity Codes

Comorbidity Code ICD-9 Diagnosis Codes OHIP Diagnosis CodesMyocardial Infraction MI 410, 412 410, 412Congestive Heart Failure CHF 402, 425, 428, 429 402, 428, 429Peripheral Vascular Dis. PVD 440-447, 785E, V43D 440, 441, 443, 446, 447Cerebrovascular Dis. CD 362C, 430-438 432, 435, 436, 437Dementia Dem 290, 294 290Chronic Pulmonary Dis. CPD 416, 490-496, 500-505, 506D 491-494, 496, 501, 502Rheumatic Disease Rhe 710-714, 725 710-712, 714Liver Disease LD 070, 456A-456C, 571-573 070, 571, 573Diabetes Mellitus DM 250 250Renal Disease Ren 403-404, 580-586, 588, V420, V451 403, 580, 581, 584, 585Metastatic Tumors MT 196-199 196-199Malignancy Mal 140-172, 174-195, 200-208 140-172, 174-195, 200-208

A.1.3 Patient Characteristics

Age, sex, and location (census subdivision) are provided at the billing-level. Therefore, there

is some variation in age, sex, and location for the same patient in each year. Simply, I define a

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patient’s age and sex in a year to be the age and sex that are associated with the largest number of

billings in that year. If the patient is not present in the data in year t, they are assigned age and sex

from year t+1 data. If they are not present in year t or year t+1 data, they are assigned age and sex

from year t-1 data.

The census subdivision (CSD) of a patient is determined by a lengthier process. First, missing

CSDs, non-Ontario CSDs, and CSDs that are more than 150km from the patient’s doctor are

removed as possibilities, unless they are the only CSDs that are observed in the data in year t and

year t+1. After these removals, if there is a unique CSD observed in the data, then that CSD is used.

If there are still multiple CSDs that exist in that year, the CSD that is most associated with the next

year is used. A CSD is most associated with the next year if: 1) it is the unique CSD of the patient

in the next year; 2) it has the most billings the next year. Lastly, if no billings appear next year, then

the CSD is assigned to the CSD with the most billings this year. In 2015, when there is no next year,

the most associated CSD this year is used. If no billings exist in year t, then the CSD with the most

associated claims in year t+1 is used as the CSD for this year. If no billings exist in year t or year

t+1, then the CSD with the most associated claims in year t-1 is used.

Five CSDs in the billings data did not exist in the census data due to changes in geographies

over time. Three of these CSDs (3554012, 3554016, 3554018) were consolidated into a the new

CSD of Temiskaming Shores in 2006. Two others (3554046, 3554048) were consolidated into a

new CSD of Charlton and Dack. The coding of these CSDs were changed to reflect the consolidated

CSDs.

I use the Canadian Census’ Statistical Area Classification (SAC) as a proxy for rurality. CSDs

with an SAC equal to 1 are labeled urban. CSDs with an SAC equal to 2 or 3 are labeled semi-urban.

Semi-urban are non-metropolitan population agglomerations with more than 10,000 residents.

Rural areas are CSDs with an SAC above 3. See Statistics Canada (2011) for detailed definitions.

Figure A.2 is a map of SAC in the geographical sample.

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Figure A.2: Rurality (SAC)

A.1.4 Physician Characteristics

Most physician characteristics are directly observed in the Corporate Provider Database or

the ICES Physician Database. These variables include age, sex, specialty, practice type (special-

ist/CCPCP). Other variables are provided at the group level in the Corporate Provider Database

and the Client Agency Program Enrolment Database. These include the location of the physician’s

office and payment model.

Some physicians are members of multiple groups. The distance/drive time between a physician

and a patient is defined as the minimum distance/drive time between any of the physician’s group

locations and the patient. For the purposes of defining the physician’s market, the physician’s

primary CSD is defined as the group location that is closest (in sum of squared distances) to the

physician’s patients.1

To determine whether a physician’s payment model is fee-for-service, enhanced fee-for-service,

or capitation, group payment model data from the Corporate Provider Dataset and revenue de-

1. For physicians who are not in a group, the office location is assumed to be equal to the maincsd variable from theICES Provider Database, which is based on patient postcodes.

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scription data from the ICES Provider Database are used. 98.19% of physician group-years are in

one of five payment models: CCM, FHG, FHN, FHO, and traditional fee-for-service. CCM and

FHG payment models are labeled “enhanced Fee for Service” models and FHN and FHO payment

models are labeled “capitation” models.

Most comprehensive care primary care physicians had only one payment model category each

year (952,99 out of 107,724 physician-years for all of Ontario 2003-2015). However, the remaining

physicians have multiple payment models in one year because they switch payment models halfway

through the year or are in multiple groups. I must assign a unique payment model to each physician

to estimate the model. To do so, I determine the main payment model for each physician by a

series of tie-breaking rules. First, I break ties between fee-for-service and an alternative payment

model in favor of the alternative payment model. Participation in an alternative payment model is

an investment and in some cases comes with explicit patient minimums (e.g. 2,400 enrolled patients

per group in the FHN model). Fee for service work, on the other hand, may be temporary work

for another physician group or for a hospital. Second. I break ties between two payment models if

only one remains as a payment model for that physician in the next year. In this case, physicians

were likely to have switched payment models in the middle of the year. Physician and patients were

likely to make choices knowing that this change was occurring. Third, if there are still multiple

payment model, I label all physicians who make less than 50% of their revenue off of fee for service

billings as being in a capitation model. I label physicians who make more that 50% of their revenue

from fee for service billing as being in an enhanced fee for service model. I use this same rule to

assign a physician when they are in a payment model that is not fee-for-service, CCM, FHG, FHN,

or FHO.

Table A.2 shows the number of physician payment models that are determined by each step.

The first three steps appear to have been appropriate. Physicians are allocated to the enhanced

fee-for-service payment model at a higher rate when they attain the majority of their revenue from

fee-for-service payments.

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Table A.2: CCPCP Payment Model Data Cleaning

% with most revenue coming from FFS paymentsStep # Determined FFS EFFS CAPUnique 95,299 92.05% 98.30% 3.73%First Step 2,563 N/A 98.85% 1.97%Second Step 2,337 N/A 71.43% 40.96%Third Step 7,525 N/A 100% 0%

A.1.5 Expected Revenue and Expected Number of Visits

I estimate expected number of visits and expected revenue using a risk adjustment-like method-

ology. Expected number of visits, 𝑉𝑖 is the expected number of visits that patient 𝑖 would make to

their physician, if their physician was in a fee-for-service payment model. Expected revenue, 𝑅𝑖𝑠, is

estimated separately for each payment model. Expected revenue is the revenue in 2004/2005 dollars

that a physician in payment model 𝑠 ∈ {Capitation, EFFS, FFS} would expect to attain from patient

𝑖, assuming that patient attained care as if their physicians was in a fee-for-service model.

Care acquisition behavior is held constant in these estimations to remove a confounding factor

in the identification of physician response to revenue. That is, physicians may change their practice

styles to increase revenue after they adopt an alternative payment model, thus introducing variation

into the revenue attained by a physician. This variation is correlated with an unobserved physician

ability to change practice styles. My measure of expected revenue avoids this issue by holding

patient utilization constant across the revenue calculations.

The following methodology is used to estimate expected revenue and expected number of

visits. First, a dataset is constructed at the patient-year observation level. The dataset includes

comorbidities, characteristics, number of visits, and the revenues the patient would provide for their

physician in each of the three main payment models. Second, the dataset is restricted to a sample

of patients with doctors in the fee-for-service model and who are similar to the sample used in the

estimation of the empirical matching model. Third, regressions of revenues and visits onto patient

comorbidities and characteristics are estimated. Fourth, predictions of revenues and visits are made

for all patients in the main sample. The remainder of this section presents more detail on each of

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these steps.

Previous literature has shown that the alternative payment models increased the incomes of

physicians significantly. Gray et al. (2015) find a 25% increase in incomes after a move from

fee-for-service to capitation and a 12% increase after a move from fee-for-service to enhanced

fee-for-service using a diff-in-diff strategy with survey data. This result is confirmed by estimates

of per-patient revenue. I estimate that the average patient in Northern Ontario in 2015 would

provide 46.63% more revenue in the capitation model and 23.30% more revenue in the enhanced

fee-for-service model than in they would in the fee-for-service model, holding utilization fixed.

Fixed and marginal costs may be larger in the alternative payment models.

Dataset Construction

Patient comorbidities and characteristics are defined as in the matching model sample. Number

of visits are the number of claims with a visit feecode. 83 feecodes are associated with a visit. 74 of

these are the visit fee codes used by Buckley et al. (2014b). This list can be found in the appendices

of the working paper version of this paper (Buckley et al. (2011)). Nine additional feecodes were

added to their list: P004, A002, A261, A268, K130, K131, K132, K267, K267, and K269. These

feecodes were not in use during the time frame of the Buckley et al. (2011) sample.

Fee-for-service revenue is the sum of fees for services attained by the patient’s matched physician.

Each feecode is associated with a fee specified by the Ontario Ministry of Health’s Schedule of

Benefits and Fees (SBF). For each service a patient attains, I use the fee level specified by the SBF,

rather than the physician paid variable. Thus, if physicians supply services under a non-fee-for-

service payment model, the correct fee sum will still be tabulated.

Enhanced fee-for-service revenue is equal to the fee-for-service revenue, a comprehensive care

capitation (CCC) payment, and an additional 10% bonus for fees associated with the comprehensive

care premium eligible (CCPE) basket of services. The CCC payment is a monthly payment.

However, I assume each patient is rostered for a full year. The base annual CCC payment used

is $17.04 (Ministry of Health and Long-Term Care (2007a)). The CCC fee is adjusted according

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to age and sex, as specified below. Services that are in the CCPE basket are defined as the set of

eligible fees for the FHG that existed in 2014 (33 fees) (OMA (2015)). 13 services were added

to the FHG CCPE basket from 2007 to 2014 (Ministry of Health and Long-Term Care (2007a)).

However, only 6.71% of the estimated comprehensive care premium revenue in 2004 is from those

13 services. In future work, variation in the size of the CCPE basket will be taken into account.

Capitation revenue is equal to the SBF fees associated with services outside of the capitation

service basket (CSB) that are provided by the patient’s matched physician, a comprehensive care

capitation (CCC) payment, a capitation rate (CR) payment, an Access Bonus, and Shadow fees. See

Section A.2 for a clearer exposition of how capitation physicians are paid. The CCC payments are

equivalent to the payments in the enhanced fee-for-service model. The base capitation rate payment

used is $126.04 (Ministry of Health and Long-Term Care (2007b)). The access bonus is estimated

as the difference between .1895 times the CR payment and the sum of the SBF fees associated with

physicians who are not the patient’s matched physician. Lastly, shadow fees are estimated as 110of

the SBF fees of services inside the CSB.

The CSB used is the 2014 FHO basket. This basket consists of 157 fee codes (Ministry of Health

and Long-Term Care (2014)). In 2007, the FHO basket consisted of 137 fee codes. Differences

between these baskets are insignificant. Services associated with the 2014 basket but not with the

2007 basket are associated with .000037% of the estimated SBF fee payment totals for in-basket

CSB services.

Physicians in the enhanced fee-for-service and capitation models also receive bonuses for

quality of care (see Section A.2 for details). However, these bonus payments are not included in the

calculation of expected revenue. Bonuses are computed based on the percent of rostered patients

who receive specific services. Therefore, the additional expected revenue a new patient would

provide along this dimension is difficult to estimate, as it would be a function of the behavior of

other rostered patients. Further, these bonuses contribute less than 2% of enhanced fee-for-service

physician revenue (Henry et al. (2012)).2

2. This source only provides aggregate bonus payments for capitation physicians, which include quality bonuses andaccess bonuses. Quality bonus revenue for capitation physicians is likely to be similar.

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I restrict the sample to mirror the empirical matching sample and to minimize the effect of

selection into payment models. The data used are at the physician-year observation level. The sample

is restricted to patients in the geographical area of the 5 markets used to estimate the empirical

matching model. The sample is further restricted to patients who are matched to physicians with

more than 300 patients. Lastly, the sample is restricted to patients with a fee-for-service physician

in 2004 and 2005.

Before regressions are estimated, I winsorize revenues at the 0.5th and 99.5th percentiles and

visits from above at the 99.5th percentile.

Table A.3 provides summary statistics of the dataset used in the regression analysis.

Table A.3: Revenue and Visit Estimation Data Summary Statistics

Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max

CD 310,186 0.011 0.105 0 0 0 1CHF 310,186 0.030 0.172 0 0 0 1CPD 310,186 0.069 0.254 0 0 0 1Dem 310,186 0.008 0.090 0 0 0 1DM 310,186 0.065 0.246 0 0 0 1LD 310,186 0.005 0.071 0 0 0 1Mal 310,186 0.031 0.172 0 0 0 1MI 310,186 0.044 0.205 0 0 0 1MT 310,186 0.002 0.048 0 0 0 1PVD 310,186 0.015 0.123 0 0 0 1Ren 310,186 0.007 0.080 0 0 0 1Rhe 310,186 0.014 0.119 0 0 0 1Has Comorbidity 310,186 0.228 0.419 0 0 0 1Income 310,186 35.240 6.084 16.763 30.929 37.098 61.089Female 310,186 0.538 0.499 0 0 1 1FFS (Winsorized) 310,186 123.743 138.103 8.500 33.530 153.250 1,003.895EFFS (Win.) 310,186 152.257 148.306 8.500 56.511 188.877 1,062.889Capitation (Win.) 310,186 177.072 114.509 −168.026 110.682 234.343 827.820Visits (Win.) 310,186 4.226 4.629 1 1 5 31

Regression

I regress revenues and visits on comorbidity indicators, median income of a patient’s census

subdivision, age, sex, and interactions. Table A.3 shows regression results.

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Table A.4: Revenue and Visits Estimation Regression Results

Dependent variable:

Cap. Revenue EFFS Rev FFS Rev Visits

(1) (2) (3) (4)

CD 23.254∗∗∗ 67.885∗∗∗ 65.790∗∗∗ 2.155∗∗∗

(1.453) (2.370) (2.247) (0.074)CHF 4.779∗∗∗ 50.114∗∗∗ 47.788∗∗∗ 1.590∗∗∗

(0.935) (1.526) (1.446) (0.048)CPD 2.230∗∗∗ 57.613∗∗∗ 54.718∗∗∗ 1.561∗∗∗

(0.838) (1.368) (1.297) (0.043)Dem 106.596∗∗∗ 153.600∗∗∗ 161.666∗∗∗ 5.702∗∗∗

(2.802) (4.573) (4.335) (0.143)DM 4.533∗∗∗ 45.396∗∗∗ 42.088∗∗∗ 1.158∗∗∗

(0.810) (1.321) (1.252) (0.041)LD 5.052∗∗ 53.084∗∗∗ 50.250∗∗∗ 1.014∗∗∗

(2.110) (3.443) (3.264) (0.107)Mal 7.787∗∗∗ 35.864∗∗∗ 34.067∗∗∗ 0.805∗∗∗

(0.995) (1.623) (1.539) (0.051)MI 9.793∗∗∗ 48.161∗∗∗ 44.881∗∗∗ 1.454∗∗∗

(0.862) (1.407) (1.334) (0.044)MT 3.066 54.067∗∗∗ 52.299∗∗∗ 0.780∗∗∗

(3.057) (4.988) (4.728) (0.155)PVD 1.724 34.355∗∗∗ 31.955∗∗∗ 0.981∗∗∗

(1.242) (2.027) (1.922) (0.063)Ren 7.359∗∗∗ 40.459∗∗∗ 39.369∗∗∗ 1.090∗∗∗

(1.840) (3.002) (2.846) (0.094)Rhe −3.964∗∗∗ 46.100∗∗∗ 43.163∗∗∗ 1.664∗∗∗

(1.325) (2.162) (2.050) (0.067)Income(k) −0.996∗∗∗ 4.100∗∗∗ 3.894∗∗∗ 0.138∗∗∗

(0.169) (0.276) (0.261) (0.009)Income(𝑘)2 0.010∗∗∗ −0.052∗∗∗ −0.050∗∗∗ −0.002∗∗∗

(0.002) (0.003) (0.003) (0.0001)hasclaims −3.412∗∗∗ 32.740∗∗∗ 29.811∗∗∗ 1.331∗∗∗

(0.371) (0.606) (0.574) (0.019)sac2 15.442∗∗∗ 20.146∗∗∗ 18.895∗∗∗ 0.428∗∗∗

(0.464) (0.757) (0.717) (0.024)sac3 0.385 8.348∗∗∗ 7.716∗∗∗ 0.193∗∗∗

(0.680) (1.110) (1.052) (0.035)sac4 8.651∗∗∗ 7.109∗∗∗ 6.385∗∗∗ 0.198∗∗∗

(1.030) (1.680) (1.593) (0.052)sac5 1.540∗∗∗ 16.960∗∗∗ 16.347∗∗∗ 0.482∗∗∗

(0.431) (0.703) (0.666) (0.022)sac6 −4.494∗∗∗ −15.773∗∗∗ −13.570∗∗∗ −0.743∗∗∗

(0.456) (0.745) (0.706) (0.023)sac7 0.935 −17.492∗∗∗ −15.287∗∗∗ −0.760∗∗∗

(1.172) (1.913) (1.814) (0.060)

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Table A.5: Revenue and Visits Estimation Regression Results (Continued)

Dependent variable:

Cap. Revenue EFFS Rev FFS Rev Visits

(1) (2) (3) (4)

age15-34 −20.291∗∗∗ −3.034∗∗ 0.148 −0.341∗∗∗

(0.741) (1.210) (1.147) (0.038)age35-49 33.400∗∗∗ 30.136∗∗∗ 26.029∗∗∗ 0.455∗∗∗

(0.747) (1.219) (1.156) (0.038)age50-64 89.846∗∗∗ 54.544∗∗∗ 43.344∗∗∗ 1.061∗∗∗

(0.786) (1.283) (1.216) (0.040)age65+ 200.775∗∗∗ 100.260∗∗∗ 76.303∗∗∗ 2.455∗∗∗

(0.963) (1.571) (1.489) (0.049)age0-14:female 0.067 −0.345 −0.238 0.010

(0.801) (1.307) (1.239) (0.041)age15-34:female 78.223∗∗∗ 36.178∗∗∗ 26.223∗∗∗ 0.746∗∗∗

(0.638) (1.041) (0.987) (0.032)age35-49:female 65.518∗∗∗ 26.736∗∗∗ 18.295∗∗∗ 0.635∗∗∗

(0.670) (1.093) (1.036) (0.034)age50-64:female 52.065∗∗∗ 22.524∗∗∗ 15.506∗∗∗ 0.568∗∗∗

(0.753) (1.229) (1.165) (0.038)age65+:female 19.747∗∗∗ 18.539∗∗∗ 15.602∗∗∗ 0.588∗∗∗

(1.012) (1.651) (1.565) (0.051)Dem:female 32.384∗∗∗ 40.598∗∗∗ 44.217∗∗∗ 1.697∗∗∗

(3.483) (5.684) (5.389) (0.177)age0-14:hascomorbid:sexM −15.450∗∗∗ −51.398∗∗∗ −48.969∗∗∗ −1.408∗∗∗

(1.866) (3.045) (2.887) (0.095)age15-34:hascomorbid:sexM −14.557∗∗∗ −39.266∗∗∗ −37.534∗∗∗ −1.011∗∗∗

(1.839) (3.001) (2.845) (0.094)age35-49:hascomorbid:sexM −9.659∗∗∗ −7.101∗∗∗ −7.524∗∗∗ 0.053

(1.433) (2.338) (2.216) (0.073)age50-64:hascomorbid:sexM −6.715∗∗∗ −6.913∗∗∗ −7.479∗∗∗ 0.121∗∗

(1.188) (1.939) (1.838) (0.060)age65+:hascomorbid:sexM −1.159 −1.152 −1.448 0.372∗∗∗

(1.297) (2.117) (2.007) (0.066)age0-14:hascomorbid:sexF −19.134∗∗∗ −53.077∗∗∗ −50.505∗∗∗ −1.495∗∗∗

(2.056) (3.356) (3.181) (0.105)age15-34:hascomorbid:sexF −21.029∗∗∗ −27.861∗∗∗ −27.193∗∗∗ −0.433∗∗∗

(1.524) (2.486) (2.357) (0.078)age35-49:hascomorbid:sexF −16.166∗∗∗ 0.026 −1.052 0.490∗∗∗

(1.319) (2.152) (2.041) (0.067)age50-64:hascomorbid:sexF −11.762∗∗∗ −3.755∗ −4.521∗∗ 0.225∗∗∗

(1.179) (1.924) (1.824) (0.060)age65+:hascomorbid:sexF 2.827∗∗ 4.852∗∗ 4.948∗∗∗ 0.446∗∗∗

(1.195) (1.949) (1.848) (0.061)Constant 114.265∗∗∗ −18.189∗∗∗ −29.473∗∗∗ −0.797∗∗∗

(3.441) (5.614) (5.322) (0.175)

Mean of Dependent Var 177.072 152.257 123.743 4.226Observations 310,186 310,186 310,186 310,186R2 0.500 0.206 0.177 0.208Adjusted R2 0.500 0.206 0.177 0.208Residual Std. Error (df = 310144) 80.988 132.152 125.281 4.120F Statistic (df = 41; 310144) 7,560.055∗∗∗ 1,963.633∗∗∗ 1,628.893∗∗∗ 1,984.634∗∗∗

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

176

A.2 Details of the Physician Payment Models

There are five main payment models available for physicians to choose between 2003 and 2015.

These are fee-for-service (FFS), Family Health Group (FHG), Comprehensive Care Model (CCM),

Family Health Organization (FHO), and Family Health Network (FHN). The FHG and CCM models

are enhanced fee for service models. The FHO and FHN are capitation models. Table A.6 describes

the main attributes of these models.3

Table A.6: Characteristics of Payment Models

Payment % Revenue % Physicians MinimumModel Type Introduced from fees in 2015 Group Size

FFS FFS 1966 98 14 1FHN Capitation 2002 27 2 3FHG EFFS 2003 81 27 3CCM EFFS 2005 84 4 1FHO Capitation 2006 21 53 3

Under the fee-for-service model, physician 𝑗’s revenue is simple. The physician receives the sum

of fees for services they provide as specified in the OHIP Schedule of Benefits and Fees (OSBF).

Rostered patients and unrostered patients are treated identically under the FFS model. For clarity,

the FFS revenue function is:

𝑅𝐹𝐹𝑆𝑗 (X𝑅,N𝑅,N0) =∑︁𝑠

𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠)

where X𝑅 are the ages and sexes of rostered patients, 𝑁𝑅𝑠 are the number of services of type 𝑠 from

rostered patients, 𝑁0𝑠 are the number of services of type 𝑠 from non-rostered patients, and 𝑝𝑠 is the

OSBF fee for service 𝑠.

Under both enhanced fee-for-service models, EFFS physicians receive bonuses for hitting

certain quality goals and small monthly payments based on their rostered patient’s characteristics.

These capitation payments are called “Comprehensive Care Capitation” payments. CCM physician

𝑗’s revenue is:

3. Source: Rudoler, Deber, Barnsley, et al. (2015), Hurley et al. (2013), author’s calculations.

177

𝑅𝐶𝐶𝑀𝑗 (X𝑅,N𝑅,N0) =∑︁𝑠

𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠) +𝑄𝐵(N𝑅,X𝑅) + 𝐶𝐶𝐶 (X𝑅)

Where 𝑄𝐵(·) is the function from rostered patient age, patient sex, and services provided to quality

bonus and𝐶𝐶𝐶 (·) is the function from rostered patient age and sex to comprehensive care capitation

payments. In the FHG model, there are additional payments for a specific basket of services. This

basket of services, 𝐵𝐹𝐻𝐺 , is a set of services for which FHG physicians get an enhanced payment

for their rostered patients. The enhanced payment is an additional 10% bonus for services in the

basket. FHG physician 𝑗’s revenue can thus be written:

𝑅𝐹𝐻𝐺𝑗 (X𝑅,N𝑅,N0) =∑︁𝑠

𝑝𝑠𝑁0𝑠 +∑︁𝑠

(1 + 1

101{𝑠 ∈ 𝐵𝐹𝐻𝐺}

)𝑝𝑠𝑁𝑅𝑠 +𝑄𝐵(N𝑅,X𝑅) + 𝐶𝐶𝐶 (X𝑅)

Most physicians who chose an EFFS model chose the FHG model

The capitation models are structured differently than the EFFS and FFS models. For rostered

patients, physicians receive only 10% (until October 2010, then 15% (Zhang and Sweetman (2018)))

of the OSBF fees for services in a basket of services, 𝐵𝐹𝐻𝑂and 𝐵𝐹𝐻𝑁 . These payments are called

“shadow fees,” and exist to encourage physicians to report all services provided. Instead, physicians

receive most of their revenue from yearly capitation payments that are a function of the age and

sex of their rostered patients. Services provided to non-rostered patients and services outside of

the basket are still paid for on a fee-for-service basis. There are some restrictions placed on these

payments: payments for services provided to non-rostered patients cannot exceed $40,000. A certain

percent of capitation fees called the “Access Bonus” is decreased dollar for dollar for every service

a rostered patient receives from physicians outside of the physician group they are rostered with.

Note that a patient is rostered to a physician, not a group. Lastly, physicians in the capitation models

receive the same quality bonus and comprehensive care capitation payments as their enhanced

fee-for-service colleagues.

FHO Physician 𝑗’s revenue is:

𝑅𝐹𝐻𝑂𝑗 (X𝑅,N𝑅,N−𝑔( 𝑗)𝑅

,N0) =∑︁𝑠

1{𝑠 ∉ 𝐵𝐹𝐻𝑂}𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠)

+ 110

∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑂}𝑝𝑠𝑁𝑅𝑠 + 𝑚𝑎𝑥{∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑂}𝑝𝑠𝑁0𝑠, $40, 000}

178

+𝐶𝑎𝑝𝑂 (X𝑅) + 𝑚𝑎𝑥{.1895𝐶𝑎𝑝𝑂 (X𝑅) −∑︁



FHN Physician 𝑗’s revenue is:

𝑅𝐹𝐻𝑁𝑗 (X𝑅,N𝑅,N−𝑔( 𝑗)𝑅

,N0) =∑︁𝑠

1{𝑠 ∉ 𝐵𝐹𝐻𝑁 }𝑝𝑠 (𝑁0𝑠 + 𝑁𝑅𝑠)

+ 110

∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑁 }𝑝𝑠𝑁𝑅𝑠 + 𝑚𝑎𝑥{∑︁𝑠

1{𝑠 ∈ 𝐵𝐹𝐻𝑁 }𝑝𝑠𝑁0𝑠, $40, 000}

+𝐶𝑎𝑝𝑁 (X𝑅) + 𝑚𝑎𝑥{.2065𝐶𝑎𝑝𝑁 (X𝑅) −∑︁



Where 𝐶𝑎𝑝(·) is the function from rostered patient age and sex to capitation payments and N−𝑔( 𝑗)𝑅𝑠

are the services provided to physician 𝑗’s rostered patients by other physicians who are not in 𝑗’s

medical group.4

A.3 Figures and Tables

Figure A.3: Heterogeneity in Physician Outputs

(a) Number of Patients (b) Number of Visits

4. Unless otherwise specified, this information was gathered from billings guides: Ministry of Health and Long-TermCare (2007a, 2007b, 2014, 2011) and OMA (2015).

179

Table A.7: Patient Characteristics Summary Statistics

All Markets 1 2 3 4 5

N 8,718,090 639,273 1,641,845 1,181,480 3,237,340 2,018,152Year (mean (sd)) 2008.99 (3.16) 2008.95 (3.17) 2008.96 (3.17) 2008.95 (3.16) 2009.01 (3.16) 2009.02 (3.16)Male (%) 4,263,135 (48.9) 311,914 (48.8) 801,872 (48.8) 583,408 (49.4) 1,574,031 (48.6) 991,910 (49.1)Age (%)

0-14 1,404,284 (16.1) 119,738 (18.7) 267,075 (16.3) 197,803 (16.7) 512,524 (15.8) 307,144 (15.2)15-34 2,045,868 (23.5) 152,477 (23.9) 406,312 (24.7) 276,717 (23.4) 758,775(23.4) 451,587 (22.4)35-49 1,787,272 (20.5) 131,529 (20.6) 342,605 (20.9) 249,566 (21.1) 660,784 (20.4) 402,788 (20.0)50-64 1,916,392 (22.0) 133,097 (20.8) 354,227 (21.6) 261,262 (22.1) 709,409 (21.9) 458,397 (22.7)

65+ 1,564,274 (17.9) 102,432 (16.0) 271,626 (16.5) 196,132 (16.6) 595,848 (18.4) 398,236 (19.7)Has Comorbidity (mean (sd)) 0.20 (0.40) 0.15 (0.36) 0.19 (0.40) 0.18 (0.39) 0.21 (0.41) 0.20 (0.40)Revenue (mean (sd))

Capitation 175.41 (81.99) 163.77 (79.75) 169.01 (80.99) 168.58 (79.99) 177.90 (82.39) 184.29 (82.84)EFFS 147.50 (64.49) 126.55 (60.53) 141.81 (63.52) 137.28 (63.56) 151.98 (63.91) 157.58 (65.19)

FFS 119.63 (54.67) 101.04 (50.94) 114.47 (53.90) 110.59 (53.91) 123.49 (54.01) 128.83 (55.31)Visits (mean (sd)) 4.07 (1.98) 3.28 (1.86) 3.94 (1.96) 3.68 (1.95) 4.25 (1.93) 4.37 (2.00)Area Type (%)

rural 3,020,672 (34.6) 459,452 (71.9) 256,917 (15.6) 694,848 (58.8) 403,100 (12.5) 1,206,355 (59.8)semiurban 2,482,297 (28.5) 179,821 (28.1) 0 (0.0) 486,632 (41.2) 1,004,047 (31.0) 811,797 (40.2)

urban 3,215,121 (36.9) 0 (0.0) 1,384,928 (84.4) 0 (0.0) 1,830,193 (56.5) 0 (0.0)Unmatched (mean (sd)) 0.33 (0.18) 0.42 (0.19) 0.31 (0.15) 0.45 (0.21) 0.30 (0.16) 0.30 (0.16)

180

Table A.8: Physician Characteristics Summary Statistics

All Markets 1 2 3 4 5

N 5,374 467 970 652 1,896 1,389Male (%) 3766 (70.1) 302 (64.7) 644 (66.4) 498 (76.4) 1314 (69.3) 1008 (72.6)Age (mean (sd)) 49.82 (11.01) 49.10 (10.54) 49.31 (12.12) 47.82 (10.53) 50.75 (11.47) 50.07 (9.71)N Years (of 11)) 10.31 (1.86) 10.40 (1.67) 10.21 (2.06) 10.28 (1.83) 10.22 (2.03) 10.51 (1.51)N Patients 1,169.51 (700.86) 717.08 (228.72) 1,230.90 (769.40) 946.56 (537.59) 1,396.05 (818.19) 1,074.16 (497.05)Unfilled Capacity 0.16 (0.16) 0.17 (0.14) 0.15 (0.14) 0.15 (0.15) 0.18 (0.18) 0.15 (0.14)Group Status (%)

Independent 850 (15.8) * (<20) *(<30) *(<30) 314 (16.6) 180 (13.0)Multiple groups 554 (10.3) * (<20) *(<30) *(<30) 155 (8.2) 211 (15.2)

One Group 3,970 (73.9) 375 (80.3) 713 (73.5) 457 (70.1) 1,427 (75.3) 998 (71.9)Payment Model (%)

Capitation 3,369 (62.8) 343 (73.4) 461 (47.7) 458 (70.2) 1,120 (59.1) 987 (71.3)EFFS 1,321 (24.6) *(<30) 352 (36.4) *(<30) 528 (27.8) 245 (17.7)

FFS 677 (12.6) *(<30) 154 (15.9) *(<30) 248 (13.1) 153 (11.0)Consultations (mean (sd)) 23.89 (89.71) 28.15 (68.92) 9.85 (35.70) 42.01 (126.97) 20.64 (70.50) 28.11 (120.99)Visits (mean (sd)) 4,893.79 (3,175.55) 3,562.98 (1,623.85) 4,821.09 (3,223.74) 4,362.14 (2,429.72) 5,451.92 (3,761.73) 4,879.71 (2,765.68)Consultations 24.92 (97.38) 38.24 (81.28) 8.88 (36.15) 45.16 (136.24) 20.09 (73.93) 28.76 (130.13)FTE (mean (sd)) 0.96 (0.35) 0.84 (0.26) 0.92 (0.39) 0.92 (0.28) 1.00 (0.38) 0.99 (0.30)Offers Walkins (%) 1,589 (29.6) 58 (12.4) 361 (37.2) 168 (25.8) 572 (30.2) 430 (31.0)Area Type (%)

Rural 2,159 (40.2) 369 (79.0) 232 (23.9) 375 (57.5) 274 (14.5) 909 (65.4)Semiurban 1,487 (27.7) 98 (21.0) 0 (0.0) 277 (42.5) 632 (33.3) 480 (34.6)

Urban 1,728 (32.2) 0 (0.0) 738 (76.1) 0 (0.0) 990 (52.2) 0 (0.0)*Excluded due to small bin sizes.

181

Table A.9: Decomposition of Access Loss

Patient Characteristics Decomposition One Decomposition Two

Has Access Char Loc. AggArea Type Age Comorbid N # Types Loss Capacities Dist Dist Supply Remainder

Rural 0-34 No 81,557 521 51.098 15.253 4.640 -6.456 24.481 28.432Semiurban 0-34 No 72,930 72 36.308 30.160 6.049 2.194 25.722 2.342Urban 0-34 No 102,500 36 23.542 21.453 -1.448 4.188 20.226 0.577Rural 0-34 Yes 3,859 430 34.722 0.951 -1.922 -5.099 17.316 24.427Semiurban 0-34 Yes 3,855 82 4.054 0.074 -0.613 1.781 1.409 1.477Urban 0-34 Yes 7,209 47 2.824 0.933 0.418 0.438 1.533 0.434Rural 35-6 No 83,785 713 46.177 11.193 2.611 -5.362 21.840 27.088Semiurban 35-6 No 66,459 103 20.583 14.505 3.158 1.991 12.994 2.440Urban 35-6 No 91,189 63 8.553 6.546 -0.878 1.599 7.160 0.671Rural 35-6 Yes 16,875 521 34.059 5.865 0.523 -4.950 17.756 20.730Semiurban 35-6 Yes 14,767 61 17.178 13.760 5.752 0.517 9.354 1.556Urban 35-6 Yes 22,343 41 6.918 5.621 -0.461 1.890 5.078 0.411Rural 65+ No 28,018 302 38.880 7.551 0.938 -4.919 19.328 23.534Semiurban 65+ No 20,396 30 18.693 13.173 6.075 0.436 9.511 2.671Urban 65+ No 25,754 18 5.327 3.962 0.566 1.687 2.656 0.418Rural 65+ Yes 23,294 243 29.506 8.911 2.698 -4.775 16.418 15.165Semiurban 65+ Yes 19,949 30 21.147 18.623 12.067 -1.228 8.903 1.404Urban 65+ Yes 25,543 18 4.611 3.879 0.339 1.548 2.501 0.223

All Patients 710,282 3,331 27.078 13.854 2.215 -0.469 15.986 9.346

182

Figure A.4: Preferences: Age

A.4 Alternative Full Access Counterfactual Definitions

In the main specification, I define the full access environment as the choice environment that a

patient would face in the city of Sudbury under the counterfactual assumption that all physicians are

accepting all patients. This full access definition is subjective. Other definitions could be used. In

this section, I present measures of access to care using the main specification and two alternative

definitions of a full access environment. Additionally, I present measures of an alternative definition

of access to care: the share of patient surplus that would be attained in the full access environment

that is attained in the current equilibrium.

In a second full access environment definition, each patient chooses from 10 randomly selected

physicians who are placed 0 kilometers from the patient. Additionally, each of these 10 physicians

are always willing to accept the patient. This is equivalent to making all physician capacities infinite,

shifting 10 to the same location as the patient, and shifting all other physicians to infinite distance

from the patient.

In a third full access environment definition, I add physicians to the market until there is 1

physician per 1000 patients. Physicians are randomly sampled from the set of existing physicians.

The reported results for each full access definition are the average over 10 simulated counterfactuals.

I define a second measure of access to care as the share of patient surplus attained in a full

183

access counterfactual that is attained in the present equilibrium.

Access\𝑡 =logsum\𝑡(𝜷,𝝉𝑢

\,J\𝑡)

logsum\𝑡(𝜷,𝜏𝑢,𝐹𝐴,J\𝐹𝐴)

logsum\𝑡(𝛽,𝝉\ ,J ) = 𝑙𝑜𝑔(∑︁

𝑗∈{J ,∅}𝑒𝑥𝑝(𝛿\ 𝑗𝑡 (𝛽) − 𝜏𝑢\ 𝑗𝑡)

where as before, individual patient surplus, logsum\𝑡(𝛽,𝝉\ ,J ), depends on preferences 𝜷, effort

costs 𝜏𝑢, and the choice set J . (𝜏𝑢\𝑡,J\𝑡) defines the choice conditions of the estimated matching

model in market 𝑡. (𝜏𝑢,𝐹𝐴,J 𝐹𝐴) defines the full access choice conditions.

Table A.10 compares the different estimates of access loss for different patient types. Quali-

tatively, the results are similar for the first two full access environment definitions. The third full

access environment definition produces significantly lower estimates of access for rural patients.

Even in the choice environment where there is one physician per 1000 patients, rural patients still

do not have a large variety of physicians in their choice set.

184

Table A.10: Average Access Loss Under Full Access Alternatives

Patient Characteristics Ratio of Choice Probability Ratio of Patient Surplus

Area Type Age Comorbidities N # Types % W/o Doctor Sudbury Ten Doctors One Per 1000 Sudbury Ten Doctors One Per 1000

Rural 0-34 No 81,557 521 62.244 51.098 54.906 30.437 65.491 70.703 37.208Semiurban 0-34 No 72,930 72 53.381 36.308 37.465 37.822 50.999 52.530 55.100Urban 0-34 No 102,500 36 39.291 23.542 21.205 30.009 39.687 33.702 52.372Rural 0-34 Yes 3,859 430 45.063 34.722 40.476 16.386 48.714 58.399 22.540Semiurban 0-34 Yes 3,855 82 37.951 4.054 5.537 7.744 6.204 9.176 18.900Urban 0-34 Yes 7,209 47 25.399 2.824 0.654 6.814 7.205 1.035 21.380Rural 35-64 No 83,785 713 52.822 46.177 49.526 26.125 62.405 67.505 33.392Semiurban 35-64 No 66,459 103 42.498 20.583 21.660 23.074 32.501 34.124 40.589Urban 35-64 No 91,189 63 31.222 8.553 5.990 13.381 17.196 9.819 32.241Rural 35-64 Yes 16,875 521 31.775 34.059 37.057 17.894 54.159 59.933 26.608Semiurban 35-64 Yes 14,767 61 23.282 17.178 17.618 18.828 34.496 35.355 41.294Urban 35-64 Yes 22,343 41 17.048 6.918 5.722 10.896 18.219 12.892 32.677Rural 65+ No 28,018 302 37.901 38.880 41.879 21.022 57.544 62.799 29.204Semiurban 65+ No 20,396 30 26.736 18.693 18.583 20.507 34.597 33.909 42.597Urban 65+ No 25,754 18 23.371 5.327 4.381 10.649 14.671 10.086 32.585Rural 65+ Yes 23,294 243 28.737 29.506 31.169 17.484 53.735 57.724 28.820Semiurban 65+ Yes 19,949 30 20.552 21.147 21.155 22.087 43.976 44.232 49.793urban 65+ Yes 25,543 18 18.107 4.611 3.485 7.069 15.373 8.539 28.584

All Patients 710,282 3,331 40.279 27.078 27.618 23.279 41.388 40.993 39.253

185

A.5 A Simple Proof of Stability

A matching is stable if

1. No patient prefers to be unmatched than be matched with their current physician.

2. No physician would rather have an empty space than have that space be filled with one of

their current patients.

3. No patient and physician would both prefer to match with each other than keep their current

matches.

Each of these conditions are met in the Rationing-by-Waiting equilibrium.

Condition One

If a patient 𝑖 matches with physician 𝑗 then 𝑢𝑖\ 𝑗 𝑡 − 𝜏𝑢\ 𝑗𝑡 > 𝑢𝑖\∅𝑡 . The one sided waiting condition

implies that 𝜏𝑢\ 𝑗𝑡

≥ 0. Therefore when patient 𝑖 matches with physician 𝑗 , they prefer 𝑗 to ∅:

𝑢𝑖\ 𝑗 𝑡 > 𝑢𝑖\∅𝑡 .

Condition Two

A symmetric argument applies to condition 2. If physician 𝑗 in panel space 𝑞 matches with

patient type \ then 𝑣\ 𝑗𝑞𝑡 − 𝜏𝑣\ 𝑗𝑡 > 𝑣\ 𝑗𝑞∅𝑡 . The one sided waiting condition implies that 𝜏𝑣\ 𝑗𝑡

≥ 0.

Therefore, 𝑣\ 𝑗𝑞𝑡 > 𝑣\ 𝑗𝑞∅𝑡 .

Condition Three

Patient 𝑖 matches with physician 𝑗 ′ if 𝑢𝑖\ 𝑗 ′𝑡 − 𝜏𝑢\ 𝑗 ′𝑡 > 𝑢𝑖\ 𝑗 𝑡 − 𝜏𝑢\ 𝑗𝑡

for all 𝑗 ≠ 𝑗 ′. Physician 𝑗 in

panel space 𝑞 matches with patient type \′ if 𝑣\ ′ 𝑗𝑞𝑡 −𝜏𝑣\ ′ 𝑗 𝑡 > 𝑣\ 𝑗𝑞𝑡 −𝜏𝑣\ 𝑗𝑡

for all \ ≠ \′. The one-sided

waiting condition requires that 𝜏𝑢\ 𝑗𝑡

= 0 or 𝜏𝑣\ 𝑗𝑡

= 0. Therefore, either

𝑢𝑖\ 𝑗 ′𝑡 − 𝜏𝑢\ 𝑗 ′𝑡 > 𝑢𝑖\ 𝑗 𝑡

186

or

𝑣\ ′ 𝑗𝑞𝑡 − 𝜏𝑣\ ′ 𝑗 𝑡 > 𝑣\ 𝑗𝑞𝑡

Further, as both 𝜏𝑢\ 𝑗 ′𝑡 ≥ 0 and 𝜏𝑣

\ ′ 𝑗 𝑡 ≥ 0, one of the following two conditions hold.

𝑢𝑖\ 𝑗 ′𝑡 > 𝑢𝑖\ 𝑗 𝑡

𝑣\ ′ 𝑗𝑞𝑡 > 𝑣\ 𝑗𝑞𝑡

Thus, if patient 𝑖 matches with physician 𝑞′ and physician space 𝑞 matches with a patient of

type \′, then either patient 𝑖 prefers physician 𝑗 ′ to 𝑗 or physician 𝑗 prefers patient type \′to patient

type \ for panel space 𝑞.

A.6 Gradient and Standard Errors

A.6.1 Gradient

I calculate the gradient to aid the algorithm.

In order to do so, I rewrite the inner loop system in matrix form. I introduce the variable

𝑊𝜷\ 𝑗𝑡

= 1{`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡

< `𝜷∅ 𝑗 𝑡𝑏

𝜷\ 𝑗𝑡

}. This variable describes which side of the market is driving

matching patterns for each patient type-physician pair. The likelihood function can be written in

terms of𝑊 𝜷\ 𝑗𝑡

and the predicted outside option shares only.

L̃(𝜷) = 2∑︁𝑡

∑︁𝑗

∑︁\

`\ 𝑗𝑡

(𝑊

𝜷\ 𝑗𝑡𝑙𝑜𝑔(`𝜷

\∅𝑡𝑒𝑥𝑝(𝛿𝜷\ 𝑗𝑡

)) + (1 −𝑊 𝜷\ 𝑗𝑡

)𝑙𝑜𝑔(`𝜷∅ 𝑗 𝑡𝑒𝑥𝑝(𝛾𝜷\ 𝑗𝑡

)))

+∑︁𝑡

∑︁\

`\∅𝑡 𝑙𝑜𝑔(`𝜷\∅𝑡) +∑︁𝑡

∑︁𝑗


187

Now, take a parameter element that is in the patient utility function: 𝛽 ∈ 𝜷𝑢. The derivative of

the likelihood function with respect to that parameter is:

𝜕L̃(𝜷)𝜕𝛽

= 2∑︁𝑡

∑︁𝑗

∑︁\

`\ 𝑗𝑡𝑊𝜷\ 𝑗𝑡

𝜕𝛿𝜷\ 𝑗𝑡

𝜕𝛽

+∑︁𝑡

∑︁\

1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡𝜕𝛽

(`\∅𝑡 + 2

∑︁𝑗

𝑊𝜷\ 𝑗𝑡`\ 𝑗𝑡

)+

∑︁𝑡

∑︁𝑗

1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡𝜕𝛽

(`∅ 𝑗 𝑡 + 2

∑︁\

(1 −𝑊 𝜷\ 𝑗𝑡

)`\ 𝑗𝑡)

Similarly, if the parameter is in the physician utility function (𝛽 ∈ 𝜷𝑣), then

𝜕L̃(𝜷)𝜕𝛽

= 2∑︁𝑡

∑︁𝑗

∑︁\

`\ 𝑗𝑡 (1 −𝑊 𝜷\ 𝑗𝑡

)𝜕𝛾

𝜷\ 𝑗𝑡

𝜕𝛽

+∑︁𝑡

∑︁\

1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡𝜕𝛽

(`\∅𝑡 + 2

∑︁𝑗


)+

∑︁𝑡

∑︁𝑗

1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡𝜕𝛽

(`∅ 𝑗 𝑡 + 2

∑︁\

(1 −𝑊 𝜷\ 𝑗𝑡

)`\ 𝑗𝑡)

The derivatives have two phrases. The first phrase is the direct effect of the change in preferences

on the choices made. The second is the indirect effect of changing preferences on the matching equi-

librium. The direct effect can be easily computed, as mean preferences are linear in 𝛽. Computing

the indirect effect involves finding the derivatives of the predicted outside options `𝜷\∅𝑡 and `𝜷∅ 𝑗 𝑡 .

To find the derivatives of the outside options with respect to 𝛽, I rewrite the equilibrium

conditions in terms of𝑊 𝜷\ 𝑗𝑡

.

`𝜷\∅𝑡 +

∑︁𝑗

(𝑊

𝜷\ 𝑗𝑡`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡

+ (1 −𝑊 𝜷\ 𝑗𝑡

)`𝜷∅ 𝑗 𝑡𝑏𝜷\ 𝑗𝑡

)= 𝑛\𝑡∀\∀𝑡

`𝜷∅ 𝑗 𝑡 +

∑︁\

(𝑊

𝜷\ 𝑗𝑡`𝜷\∅𝑡𝑎

𝜷\ 𝑗𝑡

+ (1 −𝑊 𝜷\ 𝑗𝑡

)`𝜷∅ 𝑗 𝑡𝑏𝜷\ 𝑗𝑡

)= 𝑄 𝑗∀ 𝑗∀𝑡

This can be written in matrix form:

188

𝑅𝜷𝝁𝜷∅ = 𝒗

𝝁𝜷∅ =

`𝜷1∅𝑡

`𝜷2∅𝑡...

`𝜷∅1𝑡

`𝜷∅2𝑡...

, 𝒗 =

𝑛1𝑡

𝑛2𝑡...

𝑄1𝑡

𝑄2𝑡...

𝑅𝜷 =

1 + ∑𝑗𝑊

𝜷1 𝑗𝑡𝑎

𝜷1 𝑗𝑡 0 . . . (1 −𝑊𝜷

11𝑡 )𝑏𝜷11𝑡 (1 −𝑊𝜷

12𝑡 )𝑏𝜷12𝑡 . . .

0 1 + ∑𝑗𝑊

𝜷2 𝑗𝑡𝑎

𝜷2 𝑗𝑡 . . . (1 −𝑊𝜷

21𝑡 )𝑏𝜷21𝑡 (1 −𝑊𝜷

22𝑡 )𝑏𝜷22𝑡 . . .

......

. . ....

.... . .

𝑊𝜷11𝑡𝑎

𝜷11𝑡 𝑊

𝜷21𝑡𝑎

𝜷21𝑡 . . .

∑\ 1 + (1 −𝑊𝜷

\1𝑡 )𝑏𝜷\1𝑡 0 . . .

𝑊𝜷12𝑡𝑎

𝜷12𝑡 𝑊

𝜷22𝑡𝑎

𝜷22𝑡 . . . 0

∑\ 1 + (1 −𝑊𝜷

\2𝑡 )𝑏𝜷\2𝑡 . . .

......

. . ....

.... . .

The derivative of𝑊 𝜷\ 𝑗𝑡

with respect to any 𝛽 ∈ 𝜷 is zero with probability one, due to the existence

of continuous characteristics in the utility specifications.

Recall that the equilibrium conditions can be written in matrix form.

𝑅𝜷𝝁𝜷∅ = 𝒗

In this notation, I need to find the object𝜕𝝁𝜷

∅𝜕𝜷 . I apply the implicit function theorem to derive

this object:

Define the function 𝐹 (𝜷, 𝝁) = 𝑅𝜷𝝁𝜷∅ − 𝒗.

The implicit function theorem implies that

189

𝜕𝝁

𝜕𝜷= −𝐽−1

𝐹,`

𝜕𝐹 (𝜷, 𝝁)𝜕𝜷

𝜕𝝁

𝜕𝜷= −𝑅(𝜷)−1 𝜕𝑅(𝜷)

𝜕𝜷𝝁

A.6.2 Standard Errors

There are three alternatives for the estimation of standard errors for parameter estimates in the

main matching model. I present the methodology to calculate each in this section. Currently, the

reported standard errors are the outer product of gradients standard errors.

Outer Product of Gradients

In the main specification, the outer product of gradients estimator of the variance matrix is:

Φ̂( �̂�) =[∑︁

𝑡

(2∑︁𝑗

∑︁\

`\ 𝑗𝑡 �̂�\ 𝑗𝑡 �̂�′\ 𝑗𝑡 +

∑︁\

`\∅𝑡 �̂�\∅𝑡 �̂�′\∅𝑡 +

∑︁𝑗

`∅ 𝑗 𝑡 �̂�∅ 𝑗 𝑡 �̂�′∅ 𝑗 𝑡

)]−1

where

�̂�\ 𝑗𝑡 =𝜕𝑙𝑛(`𝜷

\ 𝑗𝑡)

𝜕𝜷=

(𝑊

𝜷\ 𝑗𝑡

(1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡

𝜕𝜷+𝜕𝛿

𝜷\ 𝑗𝑡

𝜕𝜷

)+ (1 −𝑊 𝜷

\ 𝑗𝑡)(

1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡

𝜕𝜷+𝜕𝛾

𝜷\ 𝑗𝑡

𝜕𝜷

))

�̂�\∅𝑡 =𝜕𝑙𝑛(`𝜷

\∅𝑡)𝜕𝜷

=1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡

𝜕𝜷

�̂�∅ 𝑗 𝑡 =𝜕𝑙𝑛(`𝜷∅ 𝑗 𝑡)𝜕𝜷

=1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡

𝜕𝜷

All objects have previously been derived in A.6.1.

190

Empirical Hessian

The estimated Hessian matrix of the log likelihood could also be used:

�̄� ( �̂�) =[∑︁

𝑡

(2∑︁𝑗

∑︁\

`\ 𝑗𝑡

𝜕2𝑙𝑛(`𝜷\ 𝑗𝑡

)𝜕𝜷𝜕𝜷′

+∑︁\

`\∅𝑡𝜕2𝑙𝑛(`𝜷

\∅𝑡)𝜕𝜷𝜕𝜷′

+∑︁𝑗

`∅ 𝑗 𝑡𝜕2𝑙𝑛(`𝜷∅ 𝑗 𝑡)𝜕𝜷𝜕𝜷′

)]−1

For ease of exposition, I show the matrix-by-scaler derivations of the second derivatives. Take

(𝛽0, 𝛽1) ∈ 𝜷,

𝜕2𝑙𝑛(`𝜷\ 𝑗𝑡

)𝜕𝛽0𝜕𝛽1

=

(𝑊

𝜷\ 𝑗𝑡

(1`𝜷\ ∅𝑡

𝜕2`𝜷\ ∅𝑡

𝜕𝛽0𝜕𝛽1−

(1`𝜷\ ∅𝑡

)2𝜕`

𝜷\ ∅𝑡

𝜕𝛽0

𝜕`𝜷\ ∅𝑡

𝜕𝛽1

)+ (1 −𝑊𝜷

\ 𝑗𝑡)(

1`𝜷∅ 𝑗𝑡

𝜕2`𝜷∅ 𝑗𝑡

𝜕𝛽0𝜕𝛽1−

(1`𝜷∅ 𝑗𝑡

)2𝜕`

𝜷∅ 𝑗𝑡

𝜕𝛽0

𝜕`𝜷∅ 𝑗𝑡

𝜕𝛽1

))

𝜕2𝑙𝑛(`𝜷\∅𝑡)

𝜕𝛽0𝜕𝛽1=

1`𝜷\∅𝑡

𝜕2`𝜷\∅𝑡

𝜕𝛽0𝜕𝛽1−

(1`𝜷\∅𝑡

)2𝜕`

𝜷\∅𝑡

𝜕𝛽0

𝜕`𝜷\∅𝑡

𝜕𝛽1

𝜕2𝑙𝑛(`𝜷∅ 𝑗 𝑡)𝜕𝛽0𝜕𝛽1

=1`𝜷∅ 𝑗 𝑡

𝜕2`𝜷∅ 𝑗 𝑡

𝜕𝛽0𝜕𝛽1−

(1`𝜷∅ 𝑗 𝑡

)2𝜕`

𝜷∅ 𝑗 𝑡

𝜕𝛽0

𝜕`𝜷∅ 𝑗 𝑡

𝜕𝛽1

Therefore, the 𝑖, 𝑗 𝑡ℎ element of the matrix �̄� (𝜷) can be written as follows:

ℎ̄(𝛽𝑖, 𝛽 𝑗 ) =∑︁𝑡

(2∑︁𝑗

∑︁\

`\ 𝑗𝑡

[𝑊

𝜷\ 𝑗𝑡

(1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡

𝜕𝜷

)+ (1 −𝑊 𝜷

\ 𝑗𝑡)(

1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡

𝜕𝜷

)]+

∑︁\

`\∅𝑡1`𝜷\∅𝑡

𝜕`𝜷\∅𝑡

𝜕𝜷+

∑︁𝑗

`∅ 𝑗 𝑡1`𝜷∅ 𝑗 𝑡

𝜕`𝜷∅ 𝑗 𝑡

𝜕𝜷

)

ℎ̄(𝛽𝑖 , 𝛽 𝑗 ) =∑︁𝑡

(∑︁\

(`\ ∅𝑡 + 2

∑︁𝑗


) (1`𝜷\ ∅𝑡

𝜕`𝜷\ ∅𝑡𝜕𝜷

)+

∑︁𝑗

(`∅ 𝑗𝑡 + 2

∑︁𝑗

(1 −𝑊𝜷\ 𝑗𝑡

)`\ 𝑗𝑡

) (1`𝜷∅ 𝑗𝑡

𝜕`𝜷∅ 𝑗𝑡

𝜕𝜷

))

All objects have previously been derived except for the second derivatives. Recall that the derivative

191

of 𝝁𝜷∅ with respect to 𝛽0was found to be:

𝜕𝝁𝜷∅

𝜕𝛽0= −[𝑅𝜷]−1 𝜕𝑅

𝜷

𝜕𝛽0𝝁𝜷∅

where

𝝁𝜷∅ =

`𝜷1∅𝑡

`𝜷2∅𝑡...

`𝜷∅1𝑡

`𝜷∅2𝑡...

𝑅𝜷 =

1 + ∑𝑗𝑊

𝜷1 𝑗𝑡𝑎

𝜷1 𝑗𝑡 0 . . . (1 −𝑊𝜷

11𝑡 )𝑏𝜷11𝑡 (1 −𝑊𝜷

12𝑡 )𝑏𝜷12𝑡 . . .

0 1 + ∑𝑗𝑊

𝜷2 𝑗𝑡𝑎

𝜷2 𝑗𝑡 . . . (1 −𝑊𝜷

21𝑡 )𝑏𝜷21𝑡 (1 −𝑊𝜷

22𝑡 )𝑏𝜷22𝑡 . . .

......

. . ....

.... . .

𝑊𝜷11𝑡𝑎

𝜷11𝑡 𝑊

𝜷21𝑡𝑎

𝜷21𝑡 . . .

∑\ 1 + (1 −𝑊𝜷

\1𝑡 )𝑏𝜷\1𝑡 0 . . .

𝑊𝜷12𝑡𝑎

𝜷12𝑡 𝑊

𝜷22𝑡𝑎

𝜷22𝑡 . . . 0

∑\ 1 + (1 −𝑊𝜷

\2𝑡 )𝑏𝜷\2𝑡 . . .

......

. . ....

.... . .

Taking the second derivative:

𝜕2𝝁𝜷∅

𝜕𝛽0𝜕𝛽1= [𝑅𝜷]−1

(𝜕𝑅𝜷

𝜕𝛽1[𝑅𝜷]−1 𝜕𝑅

𝜷

𝜕𝛽0𝝁𝜷∅ − 𝜕2𝑅𝜷

𝜕𝛽0𝜕𝛽1𝝁𝜷∅ − 𝜕𝑅𝜷

𝜕𝛽0

𝜕𝝁𝜷∅

𝜕𝛽1

)

Sandwich Estimator

Given these derivations, the sandwich estimator of the variance matrix has the following form.

�̂�𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ =1∑

𝑡

( ∑𝑛\𝑡 +

∑𝑄 𝑗 𝑡 +

∑𝑛\𝑡𝑄 𝑗 𝑡

) �̄� ( �̂�)−1Φ̂( �̂�)�̄� ( �̂�)−1

192

Appendix B: Appendix For Chapter Two

B.1 Rurality Index for Ontario and Access

In this section, I assess how well the Rurality Index for Ontario measures access to care. To

do so, I compare the index to the measure of access to care which is derived from the estimated

model at the census subdivision observation level (see figure B.1). I find that the Rurality Index for

Ontario performs reasonably well. The two measures have a correlation coefficient of 0.448.

This compares favorably to common measures that are used to distribute funding elsewhere.

For example, in the United States, the flagship program to incentivize physicians to practice in

“shortage areas”, the National Health Service Corps, uses a formula that relies heavily on the

population to physician ratio to distribute funds. I find that physician to population ratios, when

calculated at the census subdivision level, perform poorly at predicting access to care (Correlation:

-0.252). Physician to population ratios do not account for heterogeneity in physician capacity or the

proximity of physicians outside of the census subdivision boundaries.

193

Figure B.1: Relationship Between Estimated Access to Care and Common Measures

(a) Physician to Population Ratio (b) Rural Index For Ontario

B.2 Other Incentive Programs

In addition to the UAP/NRRR, the Ontario Ministry of Health provides a grant program named

the Northern Physician Retention Initiative grants. This program is a straightforward flat payment

of $7,000 per year for any physician that has been practicing in the North for more than 4 years. The

North, as defined by the program is neither a subset nor a superset of those locations that qualify for

the UAP/NRRR grant.1

Salary-based payment models for physicians who practice in the far North have existed since

1996 in two programs: Community Sponsored Contracts (CSCs) and Northern Group Funding

Plans (NGFPs). In 2004, these payment plans were consolidated into one new program: the Rural

and Northern Physician Group Agreement (RNPGA). In this program, physicians are given a lump

base salary that depends on the RIO of the community they serve (Buckley et al. (2011)). This base

1. The North is defined as the districts of Algoma, Cochrane, Kenora, Manitoulin, Muskoka, Nipissing, Parry Sound,Rainy River, Sudbury, Thunder Bay and Timiskaming. Note that this includes the cities of Sudbury and Thunder Baywhich are not eligible for UAP/NRRR grants.

194

salary starts at $60,000 and increases according to the following function:

RNPGA Base Salary =

0 𝑅𝐼𝑂 < 45

12, 000(−4 + b 15𝑅𝐼𝑂c) 45 ≤ 𝑅𝐼𝑂

Lastly, in 2001, Ontario established the Northern Ontario School of Medicine (NOSM). This

medical school is the first in the province’s North. Ontario has five more established medical

schools, all in cities in the South: Queen’s (Kingston), University of Ottawa (Ottawa), University of

Toronto (Toronto), McMaster (Hamilton), and Western (London). The main premise for the NOSM

was to train physicians that would be more likely to practice in Northern Ontario after graduation.

It’s curriculum is focused on rural and Northern health and includes clerkships in rural areas. The

school began graduating students in 2009.

B.3 Figures and Tables

Table B.1: NRRR Effect on Patient Access (By Base Access Level)

Access Gained from NRRR


Base AccessDecile N # Types Access 𝜖 = 1.05 𝜖 = 1.91 𝜖 = 1.05 𝜖 = 1.91

(0,0.1] 8,558 151 7.177 0.447 0.834 0.029 0.114(0.1,0.2] 16,985 218 15.021 1.030 1.552 0.055 0.155(0.2,0.3] 15,052 208 25.981 2.104 4.072 0.058 0.469(0.3,0.4] 34,351 377 35.614 3.059 6.596 0.097 0.688(0.4,0.5] 47,831 361 45.545 2.330 5.105 0.117 0.652(0.5,0.6] 75,469 417 54.766 2.184 5.141 0.170 0.628(0.6,0.7] 75,006 454 65.326 2.220 4.750 0.164 0.650(0.7,0.8] 116,739 494 74.460 1.677 3.763 0.132 0.494(0.8,0.9] 95,579 349 85.269 1.383 3.132 0.134 0.362(0.9,1] 224,712 302 97.061 0.233 0.513 0.014 0.045Total 710,282 3,331 72.922 1.381 3.046 0.095 0.372

195

Table B.2: Effect of NRRR on Access to Care (By Patient Type)



Area Type Age Comorbidity N # Types Access 𝜖 = 1.05 𝜖 = 1.91 𝜖 = 1.05 𝜖 = 1.91

Rural 0-34 No 78,645 465 49.323 3.566 7.848 0.267 0.804Semiurban 0-34 No 75,842 128 62.688 0.971 1.897 0.056 0.392Urban 0-34 No 102,500 36 76.458 0.051 0.089 0.005 0.010Rural 0-34 Yes 3,736 388 66.047 2.666 6.325 0.122 0.483Semiurban 0-34 Yes 3,978 124 94.275 0.142 0.355 0.004 0.080Urban 0-34 Yes 7,209 47 97.176 0.003 0.008 0.001 0.001Rural 35-64 No 79,771 619 54.475 3.454 7.827 0.248 0.773Semiurban 35-64 No 70,473 197 77.221 0.808 1.661 0.034 0.388Urban 35-64 No 91,189 63 91.447 0.016 0.033 0.002 0.004Rural 35-64 Yes 15,991 464 66.727 3.151 7.401 0.190 0.640Semiurban 35-64 Yes 15,651 118 81.065 0.970 1.938 0.041 0.457Urban 35-64 Yes 22,343 41 93.082 0.028 0.038 0.001 0.004Rural 65+ No 26,612 272 62.003 3.169 7.529 0.253 0.759Semiurban 65+ No 21,802 60 78.926 1.162 2.349 0.047 0.574Urban 65+ No 25,754 18 94.673 0.022 0.029 0.001 0.003Rural 65+ Yes 22,223 215 70.951 3.399 7.813 0.281 0.827Semiurban 65+ Yes 21,020 58 77.944 1.181 2.276 0.054 0.467Urban 65+ Yes 25,543 18 95.389 0.023 0.027 0.001 0.002

All Patients 710,282 3,331 72.922 1.381 3.046 0.095 0.372

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Table B.3: Effect of NRRR on Percent of Patients With Care (By Patient Type)



Area Type Age Comorbidity N # Types Access 𝜖 = 1.05 𝜖 = 1.91 𝜖 = 1.05 𝜖 = 1.91

Rural 0-34 No 78,645 465 36.896 2.585 5.676 0.215 0.609Semiurban 0-34 No 75,842 128 51.092 0.806 1.572 0.047 0.324Urban 0-34 No 102,500 36 61.009 0.039 0.070 0.004 0.008Rural 0-34 Yes 3,736 388 49.797 2.010 4.682 0.104 0.380Semiurban 0-34 Yes 3,978 124 80.997 0.152 0.364 0.005 0.079Urban 0-34 Yes 7,209 47 84.711 0.003 0.008 0.001 0.001Rural 35-64 No 79,771 619 43.037 2.644 5.988 0.207 0.612Semiurban 35-64 No 70,473 197 65.402 0.737 1.508 0.031 0.349Urban 35-64 No 91,189 63 78.357 0.016 0.031 0.002 0.004Rural 35-64 Yes 15,991 464 57.045 2.651 6.226 0.171 0.552Semiurban 35-64 Yes 15,651 118 73.450 0.898 1.795 0.038 0.422Urban 35-64 Yes 22,343 41 83.717 0.024 0.033 0.001 0.003Rural 65+ No 26,612 272 51.768 2.623 6.180 0.223 0.641Semiurban 65+ No 21,802 60 70.129 1.084 2.191 0.044 0.530Urban 65+ No 25,754 18 83.203 0.021 0.027 0.001 0.002Rural 65+ Yes 22,223 215 64.907 3.072 7.042 0.262 0.751Semiurban 65+ Yes 21,020 58 73.392 1.127 2.170 0.052 0.446Urban 65+ Yes 25,543 18 89.761 0.021 0.025 0.001 0.002

All Patients 710,282 3,331 61.378 1.104 2.425 0.081 0.308

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Figure B.2: Effect of NRRR on Access to Care (By Patient Type)


Figure B.3: Entry and Access Scatterplot

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Table B.4: Effect of Alternative Payment Models on Access to Care (By Patient Type)

Patient Characteristics Current Effect of APMs on Access

Area Type Age Comorbid N # Types Access Loss Total Selection Capacity

Rural 0-34 No 78,645 465 49.323 3.785 -0.033 3.818Semiurban 0-34 No 75,842 128 62.688 4.919 -0.750 5.669Urban 0-34 No 102,500 36 76.458 10.324 -0.076 10.401Rural 0-34 Yes 3,736 388 66.047 0.695 -0.048 0.743Semiurban 0-34 Yes 3,978 124 94.275 0.371 -0.046 0.417Urban 0-34 Yes 7,209 47 97.176 0.209 -0.094 0.303Rural 35-64 No 79,771 619 54.475 4.063 0.413 3.650Semiurban 35-64 No 70,473 197 77.221 5.444 0.884 4.560Urban 35-64 No 91,189 63 91.447 3.898 0.127 3.771Rural 35-64 Yes 15,991 464 66.727 3.006 -0.105 3.111Semiurban 35-64 Yes 15,651 118 81.065 4.379 -0.931 5.310Urban 35-64 Yes 22,343 41 93.082 5.337 0.139 5.198Rural 65+ No 26,612 272 62.003 3.681 0.928 2.754Semiurban 65+ No 21,802 60 78.926 9.433 3.374 6.058Urban 65+ No 25,754 18 94.673 5.432 1.644 3.788Rural 65+ Yes 22,223 215 70.951 4.515 0.536 3.978Semiurban 65+ Yes 21,020 58 77.944 7.122 0.965 6.158Urban 65+ Yes 25,543 18 95.389 3.853 0.661 3.192

All Patients 710,282 3,331 72.922 5.386 0.303 5.083

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Appendix C: Appendix For Chapter Three

C.1 Institutional Details

This appendix section provides more detail on the institutional setting.

C.1.1 Individual Market

Pricing constraints. In 2012, prior to the implementation of ACA regulations, only six states

required insurers to issue individual insurance to any applicant and only seven states used a form of

community rating to prohibit premium setting based on health status (The Kaiser Family Foundation

(2012)). Oregon had neither rule in place. In the state, insurance carriers could reject most

categories of applicants based on their risk and health status.1 Carriers could also price based on

health status, though not as freely as in some states. Along with 10 other states and the District

of Columbia, Oregon applied rate bands in the individual market prior to the ACA, prohibiting

insurance companies from charging premiums beyond a specified share of the average premium in

the market (The Kaiser Family Foundation (2012)).

The implementation of the ACA in 2014 harmonized formerly divergent state-based regulation of

the individual market. Now, insurers in all states must ’guarantee issue’ all plans to all consumers.2

In setting rates, carriers may only vary premiums with family size, state-defined geographic regions,

tobacco use, and age. Further, premiums may only vary by age following a standard age curve,

with a ratio of 3 to 1 from the oldest to youngest enrollee. We exploit the formulaic variation in

premiums by age in later analyses.

1. Some households who could show continuous coverage under an existing insurance plan received a guarantee ofindividual insurance enrollment in Oregon prior to the ACA. Under federal statute, for example, individuals leavinggroup coverage of at least 18 months duration could not be turned down for individual coverage provided they enrolledwithin 63 days of losing group coverage.

2. ’Grandfathered’ plans–that is, plans that existed before the ACA and currently in effect–were not subject to thesenew regulations.

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Plan design. Plans offered in the individual market after the ACA are also subject to regulation

on both covered benefits and patient out-of-pocket costs. Under the ACA, all plans must cover a

set of ten essential health benefit categories, including outpatient services, emergency room visits,

pregnancy and maternity visits, mental health care, and prescription drugs. All plans offered fall

into metal tiers classified by their actuarial value, the percentage of health costs the plan is expected

to cover. The plan tiers are Bronze, Silver, Gold and Platinum, with actuarial values of 60%, 70%,

80% and 90%, respectively.

Oregon added additional regulation in the marketplace beyond the federal requirements on two

dimensions: required tier offerings and plan standardization (Blumberg et al. (2013)). First, while

the federal regulations require insurers to sell at least one gold and one silver plan in the marketplace

in each geographic market they enter, Oregon requires that all insurers entering the marketplace

must offer a bronze, silver, and gold plan. If an insurer chooses to offer individual plans outside

the marketplace, it must offer at least one bronze and one silver plan. Second, Oregon requires

insurers to offer a standardized plan in each of the required metal tiers. The standardized plan

features a specific cost-sharing and benefit design; under the broader federal regulations, insurers

have flexibility to design plan copayments, deductibles, and other benefits within a metal tier so

long as it achieves the specified actuarial value for the tier.

Households eligible for cost-sharing subsidies must purchase a silver plan in order to receive

them. These subsidies shift the standard silver plan design to a more generous actuarial value of

between 73% and 94% for consumers with incomes on 100% to 250% of the FPL, with the lowest

incomes receiving the higher actuarial values.

C.1.2 Small group insurance market

Small employers, defined as firms with up to 50 full-time employees, have the option of offering

health insurance coverage for their employees. In 2015, approximately 1 in 4 full-time employees

worked for a small employer. The share of these employees covered by employer-provided insurance

equaled 35% for workers at firms with 3-24 workers and 49% for firms between 25 and 50 workers.

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These rates combine both the likelihood of firms’ offering coverage to classes of employees and

employees taking up that coverage. 47% of firms with 3-9 workers and 68% of firms with 10-49

workers offered coverage to at least some of their workers. Within the set of small firms that offer

insurance, approximately 76% of eligible workers take-up coverage (Claxton et al. (2015)).

The small group market is subject to many of the same plan design restrictions as the individual

market. Plans must cover the same essential health benefits, must be structured according to the

same metal tiers, and must be "guarantee issued", meaning the insurer cannot set premiums based

on the health status or pre-existing conditions of the employees in the small group. The small group

and individual markets differ in the purchasing channel and the pricing rules. We discuss each

feature in turn.

Purchasing channel As in the individual market, the ACA intended states to offer a marketplace

for small group employers to shop for plans, known as the Small Business Health Options program

or SHOP. During the span of our data, from 2014 through 2016 Oregon never had a working SHOP

marketplace; all small groups purchase coverage through agents.3 Employees in a small group face

two levels of agency: the employer and the insurance broker.4 A typical small group offers one to

two broker-recommended plans to its employees, often from the same carrier (cite Katie Button or

national statistics). By contrast, consumers shopping in the individual market face a much larger

choice set. For example, a buyer in the Portland area in 2015 would have a choice of 31 bronze

plans, 40 silver plans, and 24 gold plans, offered by 8 unique carriers (SERFF). We show later that

the prices of plans offered by the employer are often meaningfully higher than those available for

similar plans in the individual market.

After choosing which plans to offer, employers contract with the relevant carrier(s) and pay

premiums on behalf of the group. Employees pay their share of the group premium from their

3. Oregon small businesses cannot use the federal SHOP enrollment platform because Oregon requires communityrating in the small group market with no age-based variation in premiums (Cite).

4. Brokers typically receive a per month per enrollee commission, plus occasional sign-on bonuses. One carrier inOregon, for example, offered a $14.27 per enrollee per month payment for groups with fewer than 26 enrollees and$11.25 for plans with 26 - 49 enrollees. Bonuses equaled $100 for a 1-9 enrollee group, $200 for a 10-25 enrolleegroup, and $400 for 26 -49 enrollee group (Providence Health Plan (2011)). The average small group per enrollee permonth fee in Oregon in 2016 was $19.70 (The Kaiser Family Foundation (2020a)).

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pre-tax earnings–that is, all premiums for insurance obtained through an employer are federal and

state tax exempt, regardless of whether the employer or the employee pays. This creates a tax

wedge relative to the individual market, where households typically pay for insurance with post-tax

dollars.5 Employers also typically subsidize the cost of employee premiums, covering as much as

two thirds of the premium cost (Claxton et al. (2015)).6 We later explore the implications of this tax

wedge and employer subsidy for small group pricing.

Premium setting. Oregon requires insurers in the small group market to use a form of community

rating known as ‘tiered composite’ rating. Employees at a firm do not face premiums proportional

to their family size or the ages of members of their family. Instead, these ages and family sizes

contribute to a group level premium cost which is then divided into four premium prices, based on

the household size: (a) employee only, (b) employee and spouse, (c) employee and children, and (d)

employee, spouse, and children.

To determine these four premium levels, the employer creates a list of all households who would

be covered in the plan, including the family size and the ages of each household member.7 With this

list, and for a chosen plan design (e.g. a silver managed care plan), the insurer applies its baseline

plan-specific premium to each employee and dependent according to the individual’s age. Summing

all of these premiums generates the total payment the employer owes the insurer for coverage under

the chosen plan.

To determine the four premiums that households will face (before any employer subsidy), the

insurer needs two measures. The first is the total age-based premiums in the group. The second is a

sum of ‘rating factors’, determined at the state level, which are specific to a household. The rating

factor equals 1 for employee-only, 2 for employee and spouse, 1.85 for employee and children, and

5. Premiums in the individual market are part of itemized deductions, but subject to limitations: only medicalexpenses exceeding 7.5% of adjusted gross income are deductible.

6. Small businesses with fewer than 25 employees are also eligible for tax credits of up to 50% of premium costs ifthey satisfy a number of qualifications, including: they must buy a plan certified for SHOP, average employee pay mustbe less than $50,000, and the employer must cover at least 50% of the premium (Oregon Health Insurance Marketplace(2020)).

7. The prices also vary geographically based on the location of the employer. If an employer has multiple locationsthat span more than one pricing region in the state, employees may face different premiums by location.

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2.85 for employee, spouse, and children. The rating factors do not vary with the number of children.

With these measures, the insurer calculates the average employee premium by dividing the total

age-based premiums by the total rating factors. The four actual employer premium levels equal

this average employee premium multiplied by the respective rating factor for each household size

category.

This tiered composite system creates a cross-subsidy within the employer pool between older

and younger enrollees and between employees covering only themselves and those covering families.

The extent of the subsidy depends on how well the fixed rating factors match the differential in

premium costs the families contribute to the small group pool. We discuss the implications of this

pooling later when comparing the typical premiums different household sizes face in the individual

vs. small group markets.

C.2 Dataset Construction

C.2.1 Household Dataset Creation

Our primary dataset is the 2014 – 2016 Oregon Health Authority All Payer All Claims (APAC).

These data include all medical claims, drug claims, and insurance plan enrollment records for

commercially insured individuals in the state of Oregon. The medical and drug claim data include

financial variables, diagnoses, and dates of claims. The insurance plan enrollment records are at

the individual – month level and include details of both medical and drug insurance plans. Before

2016, reporting of all claims and enrollment records were mandatory by law for all commercial

insurers. An exemption was created in 2016 for self-insured employer records. This exemption

does not affect our research, as it does not apply to the individual or small group insurance market.

The sample we use in the analysis is a subset of the APAC. The original insurance plan

enrollment data included approximately 50 million observations per year (49,952,770, 48,957,463,

and 38,364,318 in 2014, 2015, and 2016 respectively). Only unique medical plan observations are

kept (leaving 27,882,303, 27,037,082, and 20,034,911 observations). Next, the data are collapsed to

the individual – year observation level from the individual – month observation level (2,160,301,

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2,035,972, 1,643,776).

The individual - year observation level dataset is further restricted to reflect the specifics of our

analysis. We restrict the data to non-fringe carriers. We define a non-fringe carrier as a carrier with

more than 5% of individuals in any of the years in the individual market or small group market.

These cutoffs are selected to avoid including a payer with unreliable claims data. Eight carriers

qualify as non-fringe. This removes approximately 22% of individuals from the entire sample

(1,583,235, 1,494,126, and 1,477,922 observations remain in the sample), but only 3.3% and 2.1%

of the individuals in the individual and small group markets. We further restrict the dataset to only

individuals in the individual and small group markets (506,356, 466,320, 494,539). Lastly the

dataset is collapsed to the household – year observation level from the individual – year observation

level. After these changes, the sample includes 312,122 households in 2014, 294,745 households in

2015, and 320,273 households in 2016.

C.2.2 Switcher Dataset Creation

To estimate the preferences of small group market households, we use a sample of small group

households whose plans were closed during the time period of our data. We then track these

households as they choose plans in the individual market, and hence can plausibly estimate their

preferences, conditional on observables. Our APAC data are distinctively advantageous for this

exercise, as they include an identifier that allows us to track individuals across plans, markets, and

years. We exploit this feature of the data to determine which plans are closed, which households

move to the individual market in the following year, and what plans they choose in the individual

market.

We identify households whose plans were closed by tracking the members of employer-health

plans in the following year. We define an employer-plan as a closed plan if 80% or more of its

members are either uninsured or in a plan in the individual market in the following year. Our results

are robust to different cutoffs (see Figure C.1). We identify 7,328 closed employer-plans. These

plans had a total of 18,621 enrollees.

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Figure C.1: Percent of Switchers to Ind. Market/Uninsurance

Note: This figure shows the distribution of the fraction of subscribers in a group who switched to either the individualmarket or uninsurance among groups that are discontinued. We define a group as discontinued in year t if its contractnumber appears in year t-1 but not in year t. Subscribers are untracked if they do not appear in individual, small group,or large group coverage in year t and are not aged over 65.

Table C.1 describes the destinations of these enrollees in the year after their plan closed. 3,907

choose plans in the individual market. 530 attain coverage in other markets, including group

coverage or Medicare coverage (medicare coverage is assumed if the enrollee turns 65). 14,092

enrollees do not attain coverage in any of the above markets. These enrollees are uninsured, on

Medicaid, have moved out of Oregon, or are untracked for some other reason. We assume that these

enrollees choose the outside option of uninsurance. We then estimate preferences of households

with individual market coverage and uninsured households using their plan choices in the individual

market. In counterfactuals, we use these preferences to simulate the choices of small group market

households over plans in the individual market.

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Small Group Individual Group/ Untracked TotalMetal Tier Metal Tier Total Medicare(year 𝑡 − 1) Bronze Silver Gold Grand. Unknown

Bronze 89 86 17 0 1 193 20 542 758Silver 61 184 43 1 0 289 52 1148 1495Gold 37 126 98 0 0 261 21 892 1186Platinum 12 39 45 0 0 96 6 391 494Grandfathered 744 1558 735 11 2 3055 420 11038 14592Unknown 3 9 1 0 0 13 1 81 96Total 946 2002 939 12 3 3907 530 14092 18621

Table C.1: 2014-16 real forced-out small group transitions

Note: This is a transition table for enrollees whose plans where closed in 2014 or 2015. The metal tier is given inyear 𝑡 − 1 (in the small group; 2014 or 2015) and in year 𝑡 (2015 or 2016) if the enrollee transitions to the individualmarket. “Group” comprises enrollees who are tracked to a plan in the small group, medium group, or large groupmarkets. “Medicare” comprises enrollees who were aged 64 in year 𝑡 − 1. “Untracked” comprises people who wereuntracked in year 𝑡.

C.2.3 Household Demographic Variable Construction

Household characteristics, costs, and plan choices are collected from the claims data and the

insurance plan enrollment data.

Age

An individual’s year of birth is defined as the most common year of birth observed in their

claims over years 2010 – 2016. Age is computed assuming that all individuals are born on December

31 of their year of birth. For individuals without claims, age needs to be inferred. If the individual

is a dependent, missing ages are replaced with (in order of precedence): the mean age of other

dependents in the household, the mean age of other dependents in their contract, the mean age of

other dependents in their constructed plan, and the mean age of other dependents in their market

and payer. If the individual is an adult (subscriber of spouse), missing ages are replaced with (in

order of precedence): the mean age of their spouse, the mean age of other adults in their contract,

the mean age of other adults in their constructed plan, and the mean age of other dependents in their

market and payer.

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Rating Area

Rating areas are sets of counties. We assign rating areas to individuals using zipcodes from

claims data and city names from the plan enrollment data.

First, we assume that all members of a household live in the same location. We assign the mode

of zipcodes observed in a household to every member of that household. We also assign the mode

of city names in a household to every member of that household. Second, we assign rating areas in

the following order:

An individual’s rating area is assumed to be the rating area where their city is located. We

allow the individual’s city name to approximately match with the city name in an external dataset

according to the minimal optimal string alignment distance with a maximum distance of 1. The

external database of city names and their rating areas was partially manually creating and partially

attained from publicly available census datasets. Some individuals are not assigned a rating area

based on their city name due to missing city names or incorrectly spelled city names. These

individuals are assigned the rating area that is associated with their zipcode. If the zipcode falls

within two rating areas, the rating area with the largest share of zipcode population is chosen. The

data used in this process is the HUD-USPS zipcode-county crosswalk using the 2010 census data.

Employer-Health Plan Identifier

For the small group market, we construct an employer-health plan identifier. For most insurance

carriers, this identifier corresponds with a variable in the data named contract number. For two

carriers, there are multiple health plans associated with each contract number. For these carriers, we

set the employer-health plan identifier equal to a contract number-health plan index.

Income

We estimate income for all households in the individual and small group markets using a

predictive model of income. The predictive model of income is estimated using a subset of

households where we can reliably measure income. Income for this subset of households is

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determined by comparing the premiums paid by the household to the unsubsidized premium of

their chosen plan. Incomes for subsidized households can be backed out from the premium subsidy

formula.

Our APAC data include a measure of premiums paid by households and include a plan indicator.

By matching this data with the SERFF dataset by plan indicator, we are able to attain the listed

(per-subsidy) premium for each household’s chosen plan. However, neither of these variables are

consistently populated. Further, the premiums paid data are not checked for accuracy by the data

vendor and must be used with caution. We test for premium data accuracy by comparing premiums

to the listed premiums in the SERFF data for households in the off-exchange individual market.

There are no premium subsidies in the off-exchange individual market. Thus, if accurate, premiums

paid should equal the listed premiums in this market.

We find that one payer has both accurate premium data and consistently populated plan indica-

tors.8 Using the sample of this payer in the individual on-exchange market, we are able to recover a

reliable measure of income for 73,473 households. We recover income in the following way. First,

we can translate the normalized listed baseline premium to the gross pre-subsidy premiums for the

plan j purchased by household i, 𝑝𝑖 𝑗𝑚𝑡 , using regulated age-rating factors in effect in Oregon in our

sample period. We label these factors 𝛾𝑘,𝑖 for household member 𝑘 in household 𝑖. Additionally,

we observe the premium paid by household i for plan j, 𝑝𝑠𝑖 𝑗𝑚𝑡

, which is a function of the gross

pre-subsidy premium and the premium subsidy attained by household i for plan j.

𝑝𝑖 𝑗𝑚𝑡 = 𝑝 𝑗𝑚𝑡

𝐾𝑖∑︁𝑘∈𝑖

𝛾𝑘𝑖

𝑝𝑠𝑖 𝑗𝑚𝑡 = 𝑝𝑖 𝑗𝑚𝑡 ∗ (1 − 𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡)

8. Of households in this payer with no dependents in the January 2016 off-exchange individual market, 97% ofreported premiums paid are within 25$ of the listed premium. On average, the difference between the two premiummeasures is $6.39.

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Thus, we can recover the subsidies attained by household i when purchasing plan j:

𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡 = 1 −𝑝𝑠𝑖 𝑗𝑚𝑡

𝑝𝑖 𝑗𝑚𝑡

The subsidy level is a function of the premium of the second cheapest silver plan offered to

household i, 𝑝𝑠𝑐𝑠𝑖𝑚𝑡

, the relevant federal poverty level for household i, 𝐹𝑃𝐿𝑖𝑚𝑡 , and household i’s

income as a percent share of the federal poverty level, 𝑦𝑖𝑚𝑡 . By regulation, subsidies are set such

that post-subsidy price of the second cheapest silver plan is capped at 𝑓 𝑃𝐶𝑅𝑚𝑡 (𝑦𝑖𝑚𝑡) percent of income

, where 𝑓 𝑃𝐶𝑅𝑚𝑡 (·) is a known function. Specifically:

𝑠𝑢𝑏𝑠𝑖 = 𝑚𝑎𝑥

{𝑝𝑠𝑐𝑠𝑖𝑚𝑡 −

112𝑦𝑖𝑚𝑡𝐹𝑃𝐿𝑖𝑚𝑡 𝑓

𝑃𝐶𝑅𝑚𝑡 (𝑦𝑖𝑚𝑡), 0

}Income is the only unknown in this equation. Thus, when subsidies are larger than 0, 𝑦𝑖𝑚𝑡 can

be recovered by inverting the equation. When subsidies are equal to 0, the minimum 𝑦𝑖𝑚𝑡 that

could explain the data can be recovered by setting 𝑠𝑢𝑏𝑠𝑖 = 0 and inverting the equation. For most

households, this minimum is 𝑦𝑖𝑚𝑡 = 4, the eligibility limit.

Using the recovered incomes, we estimate a predictive Tobit model of income. In the model,

incomes 𝑦𝑖𝑚𝑡 follow a normal distribution, conditional on household characteristics 𝑥𝑖𝑚𝑡 :

𝑦𝑖𝑚𝑡 = 𝛽′𝑥𝑖𝑚𝑡 + 𝑢𝑖𝑚𝑡

𝑢𝑖𝑚𝑡 ∼ 𝑁 (0, 𝜎2)(C.1)

However, the econometrician observes a truncated version of income:

𝑦∗𝑖𝑚𝑡 = 𝑚𝑖𝑛{𝑦𝑖𝑚𝑡 , 4}

The model parameters 𝛽, 𝜎2 are estimating via maximum likelihood. Household characteristics

used include marital status, number of dependents, age, year, whether the household is insured for

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all 12 months of the year, and the 10th and 50th income percentile of the household’s zipcode.9

Interactions between these characteristics are also included.

The estimated model is used to predict the income of households in both the individual and

small group markets. Using the estimated income of each household, we determine the household’s

federal and state marginal tax rates using the NBER’s Internet TAXSIM version 27. Marital status

and number of dependents are also taken into account when estimating marginal tax rates. We

assume that married households file taxes jointly and that households have zero tax deductions.

C.2.4 Household Plan Choice Variable Construction

Metal Tier

Metal tiers and health plans are not consistently reported by all insurance carriers in the

enrollment data. When they are missing, we estimate the metal tier of a household’s chosen plan

using their contract number, premiums, zipodes, and external data on the number of subscribers

in each metal tier and year by insurer and zipcode from the Oregon Department of Financial

Regulation.

First, we set an household’s metal tier to equal the metal tier of their health plan. Second, we

use the metal tier reported by the insurer. Third, in the individual market, we set all remaining

household’s metal tiers to equal the mode of assigned metal tiers in their contract, if the household

is in a contract that is likely to have consistent metal tiers for all of its members. We define these

contracts as those in carrier-markets where more than 95% of households have the metal tier that is

most common in their contract. For data from most insurance carriers, these three steps generate

numbers that match with external counts of metal tiers from the Oregon Department of Financial

Regulation. For these carriers, all other households are assumed to be in grandfathered plans.

In the individual market, two insurance carriers (payer 19 and payer 77) have many unlabeled

metal tiers. In the small group market, two insurance carriers (payer 19 and payer 37) have many

unlabeled metal tiers. We use claims data and data from the Oregon Department of Financial

9. When zipcode is unknown, city is used.

211

Regulation (DFR) to label metal tiers for these carriers.

For the two carriers whose metal tier counts did not match up with the external data in the

individual market, the reason is apparent: 82% of observations from these carriers are missing both

metal tier and plan ID. This is a much larger percent than are grandfathered according to DFR data.

In both on- and off-exchange, we can label plan metal tiers for a small subset of plans using

outside information. For one carrier (payer 77), the contract number is specific to a plan. Therefore,

we assume that households are in a grandfathered plan if their contract existed before 2014, as those

plans must legally be grandfathered. For another carrier in one year, DFR counts match for all metal

tiers except for silver. Therefore, we assume that all remaining households are in a silver plan in

that carrier in that year.

In the remaining un-labelled off-exchange individual market, we use observed premiums to

determine the metal tier of households. In the off-exchange individual market, there are no subsidies

and no employer contributions, so the out-of-pocket premium we observe corresponds with the

premium set by the insurance carrier. If a household’s observed premium can only come for one

metal tier, then we assume that is the household’s metal tier. In some cases, there are multiple metal

tiers that could explain an observed premium (e.g. an expensive bronze plan and a cheap silver

plan) or there are no metal tiers that could explain an observed premium (due to measurement error

in premiums). In these cases, we assume that a household’s metal tier is the tier whose minimum

premium is closest to the household’s observed premium. In the on-exchange market, we can still

use observed premiums to label households in gold metal plans. If an observed premium is larger

than the maximum silver premium available to them, then we assume that they are in a gold metal

plan. However, premium subsidies remove the ability to label plans using observed premiums.

For the remaining households, we randomly assign either bronze or silver such that the metal tier

coverage is matched at each zipcode-year-insurer level.

In the small group market, we use copayment and coinsurance levels observed from the claims

data to label unobserved metal tiers. Copayment and coinsurance levels are good measures for

212

metal tier in the small group market, since there are no cost-sharing reductions. 10 Additionally, we

label all contract numbers that existed before 2014 as grandfathered plans.

We estimate group copayment as the most common subscriber copayment that is greater than $0

and lower than $75 (this is the range of PCP copayments in these years) in the group. We estimate

group coinsurance as the most common subscriber coinsurance rate in the group.11 Then, we label

metal tiers if the group copayment is uniquely in one metal tier’s range of primary care physician

visit copayments. If metal is still missing, it is assigned if the group coinsurance rate is unique in

one metal tier’s range of primary care physician coinsurance rates. If the group copayment and

coinsurance rates do not uniquely identify the metal tier, then the metal is associated with the metal

tier with the closest median copayment level. If a group does not have any copayment observations

but does have coinsurance observations, then the metal is associated with the metal tier with the

closest median coinsurance rate. Lastly, if a group in a certain year still does not have an associated

metal tier, then we assign the most assigned metal tier from other years.

C.2.5 Uninsured Population

Uninsured households are not observed in our data. We use the American Community Survey

(ACS) to infer the number of uninsured households by county and age and we use the California

Health Interview Survey (CHIS) to determine the likely characteristics of uninsured households.

The ACS includes estimates of the uninsured populations by age, sex, and geography groups. The

CHIS provides measures of the joint distribution of characteristics of the California uninsured

population.

10. Other potential identifiers of metal tier, such as out of pocket premiums, observed actuarial values, or deductiblelevels, are difficult to use. That is, employers contribute towards premiums, making out-of-pocket premiums difficult touse to identify metal tiers. Group sizes tend to be small (less than 50 subscribers). Therefore, estimates of actuarialvalue and deductibles are inaccurate at the group level.

11. Subscriber copayments are the two most common copayments, rounded to the nearest dollar, among all claimsassociated with that subscriber. Subscriber coinsurance rates are the two most common coinsurance payments, roundedto neared percentage point, among all claims associated with that subscriber.

213

Data

To infer the size of the uninsured population, we use the 2014-2016 American Community

Survey 1-year Estimates Health Insurance Coverage Status by Sex by Age datasets from the U.S.

Census Bureau. These data include estimates of the number of civilian noninstitutionalized persons

in each age and sex group that report “No health insurance” and “With health insurance.” The

estimates are available at the county level if county populations are above 65,000. Estimates are

also available at the Public Use Microdata Area (PUMA) level. Counties with populations below

65,000 are proper subsets of PUMAs.

We chose to use the mixture of 1-year county level and 1-year PUMA level data over using only

5-year county data. Using 5-year county data offers improved precision of estimates, especially for

small counties. However, the 5-year ACS relies on a moving average of 5 years of survey results.

Therefore, its estimates are biased upwards by higher uninsurance rates in pre-2014 years.

To infer the characteristics of the uninsured population, we use the 2014-2016 California Health

Interview Survey. The survey provides data on the joint distribution of family size and type, income,

urbanicity, and health conditions for uninsured households. Unlike the ACS, the CHIS observations

are at the household level. We believe that the empirical distribution of characteristics observed in

the CHIS is similar to the distribution of characteristics in Oregon. In 2016, California and Oregon

had similar uninsurance rates (7% and 6%, respectively). This similarity remains in cross sections

of the income distribution. Within the subset of incomes below 200% of the Federal Poverty Line,

California had a non-elderly uninsurance rate of 13%. Oregon had a non-elderly uninsurance rate of

11% (The Kaiser Family Foundation (2017)).

Procedure

Using the ACS, we estimate the uninsured populations in each age group and rating area. Since

rating areas are a collection of counties, we conduct these estimates at the county level and aggregate

to the rating area. If a county is small in population, the ACS does not include county-level data.

For these counties, we infer county age group uninsured populations using PUMA-level ACS data.

214

Specifically, a small county’s uninsured population for an age group is calculated as the percent of

the PUMA population that is in that county multiplied by the uninsured population in the PUMA

for the age group. Out of 36 counties, 21 had populations below 65,000 and had to be estimated.12

We use the CHIS to map the number of individuals who are uninsured to the number of

households who are uninsured. For each year, age group, and rating area, we estimate the expected

number of adults in a household using the CHIS data. The number of uninsured households is

estimated by dividing the number of uninsured individuals by the expected number of adults in a

household.

Then, characteristics are distributed to the uninsured households. First, uninsured households

are distributed to bins according to populations according to the empirical joint distribution of

characteristics from the CHIS, conditional on metropolitan area status of the rating area, year, and

age group. Bins are defined by income (< 1.73 FPL, ≥ 1.73 FPL), marital status, and whether the

household survey respondent has health conditions.13

Lastly, specific values of characteristics for each uninsured household are drawn randomly from

the insured population of households in the same bin. Here, we assume that the distributions of

characteristics are similar between the insured and uninsured populations once we condition on

metropolitan area status, age, income, marital status, and health conditions.

C.3 Estimation Details

C.3.1 Further details on deriving equations for estimation

As noted in Section 3.6.2, the assumption that _ ∼ 𝑒𝑥𝑝(𝛼) implies

12. For greater accuracy, we use population data from the American Community Survey 5-year estimates.13. Health statuses used are Asthma, Diabetes, High Blood Pressure Status, Heart Disease Status. A rating area is

defined as metropolitan if most of its counties are designated metropolitan counties by the U.S. Census Bureau. Theseare rating areas 1, 2, 3, and 7. The ACS reports 0 uninsurance in some metropolitan area-year-age-income-maritalstatus-family status-health status groups. We found this to be unreasonable and replaced those uninsurance estimateswith: first, the average of uninsurance rates across other years in the same bin, holding everything else stable (139);second, if the first method is unavailable, the average of other uninsurance rates across other metropolitan status, holdingeverything else stable (114).

215

𝑢∗𝑗 ,𝑡 =12𝑥2𝜔_ − (1 − 𝑥)_ + 𝑦𝑡 − 𝑝𝑡, 𝑗 + 𝑔(𝑋 𝑗 ,𝑡 , 𝜖)

Now the expected utility over the distribution of _ is:

𝑣 𝑗 ,𝑡 (𝐹_,𝑡 , 𝜔, 𝜓) = −∫

𝑒𝑥𝑝(−𝜓𝑢∗𝑗 ,𝑡)𝑑𝐹_,𝑡 (_).

If _ ∼ 𝑒𝑥𝑝(𝛼) so that 𝐸 (_) = 1/𝛼, we can apply the properties of the exponential distribution

along with the monotonic transformation − 1𝜓𝑙𝑛(−𝑣 𝑗 ,𝑡) to find the order preserving utility function14:

𝑈 𝑗 ,𝑡 = 𝑦𝑡 − 𝑝𝑡, 𝑗 +1𝜓𝑙𝑛

[𝛼 − 𝜓(1 − 𝑥) + 𝜓 12𝑥

2𝜔

𝛼

]+ 𝑔(𝑋 𝑗 ,𝑡 , 𝜖)

.

Comparing this utility to the utility from the outside option

𝑈0,𝑡 = 𝑦𝑡 +1𝜓𝑙𝑛

[𝛼 − 𝜓𝛼

]+ 𝑔0(𝜖0,𝑡),

we obtain the utility of the inside goods relative to the (non-stochastic component of the) outside

option as

𝑈 𝑗 ,𝑡 = −𝑝𝑡, 𝑗 +1𝜓𝑙𝑛

[1 + 𝜓𝑥

𝛼 − 𝜓 + 𝜓2( 𝑥2𝜔

𝛼 − 𝜓) ]

+ 𝑔(𝑋 𝑗 ,𝑡 , 𝜖)

and

𝑈0,𝑡 = 𝑔0(𝜖0,𝑡).

Recognizing that when 𝐴𝑥 + 𝐵𝑥2 is close to zero, we can approximate 𝑙𝑛(1 + 𝐴𝑥 + 𝐵𝑥2) ≈

𝐴𝑥 + 𝐵𝑥2., we write our utility expression as:

𝑈 𝑗 ,𝑡 ≈ −𝑝𝑡, 𝑗 +𝑥

𝛼 − 𝜓 + 𝑥2𝜔

2(𝛼 − 𝜓) + 𝑔(𝑋 𝑗 ,𝑡 , 𝜖).

14. Marone (2020) describes this step as “estimating demand in certainty equivalent units”. In our setting, when𝑋 ∼ 𝑒𝑥𝑝(𝛼), 𝑘𝑋 ∼ 𝑒𝑥𝑝(𝛼/𝑘). Further, 𝑒𝑥𝑝(𝑘𝑋) ∼ 𝑃𝑎𝑟𝑒𝑡𝑜(1, 𝛼/𝑘) so that

∫𝑒𝑥𝑝(𝑘𝑋)𝑑𝑓𝑋 = 𝐸 (𝑒𝑥𝑝(𝑘𝑋)) = 𝛼

𝛼−𝑘provided 𝛼 > 𝑘 .

216

We specify 𝑔(𝑋 𝑗 ,𝑡 , 𝜖) = (𝛽0𝑋 𝑗 ,𝑡 + 𝜖 𝑗 ,𝑡)/(𝛼 − 𝜓) so that sicker or more risk aversion consumers

put more weight on plan characteristics like carrier identity, in the same way that they put more

weight on coverage. Making an analogous assumption for the outside option, we find:

𝑈 𝑗 ,𝑡 ≈ −𝑝𝑡, 𝑗 +𝑥

𝛼 − 𝜓 + 𝑥2𝜔

2(𝛼 − 𝜓) +𝛽0𝑋 𝑗 ,𝑡 + 𝜖 𝑗 ,𝑡𝛼 − 𝜓 (C.2)

𝑈0,𝑡 =𝜖0,𝑡

𝛼 − 𝜓

C.3.2 Likelihood derivation

Section 3.6.2 provides a joint likelihood for the household’s plan choice and its health spending

that can be rewritten as

L(\) =𝑁∏𝑖=1

{ (1∑𝐽

𝑘=1 𝑒𝑥𝑝(𝑉𝑖,𝑘 )

)𝑑𝑖,1 𝐽∏𝑗=2

[ (𝑒𝑥𝑝(𝑉𝑖, 𝑗 )∑𝐽𝑘=1 𝑒𝑥𝑝(𝑉𝑖,𝑘 )

) (1 − 𝑒𝑥𝑝

(−𝛼𝑖𝑐

𝑥 𝑗 + 𝜔𝑖𝑥2𝑗

) )1{𝑐𝑖 𝑗≤𝑐}

∗[(

𝛼𝑖


)𝑒𝑥𝑝

(−𝑐𝑖, 𝑗 ∗

𝛼𝑖


)]1{𝑐𝑖 𝑗>𝑐} ]𝑑𝑖, 𝑗} (C.3)

With this notation, we write the log-likelihood:

𝐿 (\) =𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖, 𝑗 𝑙𝑛

(𝑒𝑥𝑝(𝑉𝑖, 𝑗 )∑𝐽𝑘=1 𝑒𝑥𝑝(𝑉𝑖,𝑘 )

)+ 𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 ≤ 𝑐}𝑙𝑛

(1 − 𝑒𝑥𝑝

(−𝛼𝑖𝑐


))+𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 > 𝑐}

[𝑙𝑛

(𝛼𝑖


)− 𝑐𝑖, 𝑗 ∗

(𝛼𝑖


)](C.4)

217

Given the exponential distribution, we need to constrain 𝛼𝑖𝑥 𝑗+𝜔𝑖𝑥2

𝑗

> 0 as well. The score function of

our log likelihood is:

𝜕𝐿 (\)𝜕\

=

𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖, 𝑗

[𝜕𝑉𝑖, 𝑗

𝜕\− 1∑𝐽


𝐽∑︁𝑘=1

𝑒𝑥𝑝(𝑉𝑖,𝑘 )𝜕𝑉𝑖,𝑘

𝜕\

]+

𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 ≤ 𝑐}

©«

−𝑒𝑥𝑝(

−𝛼𝑖𝑐𝑥 𝑗+𝜔𝑖𝑥2

𝑗

)1 − 𝑒𝑥𝑝

(−𝛼𝑖𝑐

𝑥 𝑗+𝜔𝑖𝑥2𝑗

) ª®®®®¬((

−𝑐𝑥 𝑗 + 𝜔𝑖𝑥2

𝑗

)𝜕𝛼𝑖

𝜕\+

(𝛼𝑖𝑐𝑥

2𝑗

(𝑥 𝑗 + 𝜔𝑖𝑥2𝑗)2

)𝜕𝜔𝑖

𝜕\

)+

𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 > 𝑐}[𝜕𝛼𝑖

𝜕\

1𝛼𝑖

− 𝜕𝜔𝑖

𝜕\

𝑥2𝑗


−𝑐𝑖, 𝑗


(𝜕𝛼𝑖

𝜕\−

𝛼𝑖𝑥2𝑗


𝜕𝜔𝑖

𝜕\

)](C.5)

C.3.3 Specification

We further parameterize 𝛼𝑖, 𝜔𝑖, 𝜓𝑖 as a function of household and/or plan level observables:15

𝑙𝑛(𝛼𝑖) = 𝑊1,𝑖𝛽1

𝑙𝑛(𝜔𝑖) = 𝑊2,𝑖𝛽2

𝑙𝑛(𝜓𝑖) = 𝑊3,𝑖𝛽3

(C.6)

We simplify notation by defining the following vector16:

15. Here, 𝛽1 is 𝐾1 x 1, 𝛽2 is 𝐾2 x 1, 𝛽3 is 𝐾3 x 1. 𝑥 𝑗 is a scalar.16. We could also allow 𝑥 𝑗 , the subscriber’s expectation of the actuarial value of plan 𝑗 , to be different from our

measurement of actuarial value, call it 𝑥𝑜𝑗. In this case, we determine 𝑥𝑜

𝑗based on plan 𝑗’s metal tier and the household’s

eligibility for cost-sharing subsidies (which affect consumer choices and hence both enrollment and spending outcomes).Note that we will add back these subsidies, which are reimbursed by the regulator, to insurance carrier revenues in Step2 when we model premium setting. Recall that in October 2017, the federal government ceased payment of cost-sharingsubsidies to insurers. Our study period includes only years in which insurers were paid/promised cost-sharing subsidypayments. We can allow two alternative specifications of 𝑥 𝑗 : 𝑥 𝑗 = 𝛿 ∗ 𝑥𝑜𝑗 and 𝑥 𝑗 = 𝑥𝑜𝑗 ∗ (𝛿1 + 𝛿2 ∗ 𝐼{𝐻𝑀𝑂}) to accountfor different effective actuarial values for a plan in the same metal tier but with a more restricted plan network.

218

\ =

©«

𝛽0

𝛽1

𝛽2

𝛽3

ª®®®®®®®®¬Under this specification, the score function has the form

𝜕𝐿 (\)𝜕\

=

𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖, 𝑗

[𝜕𝑉𝑖, 𝑗

𝜕\− 1∑𝐽


𝐽∑︁𝑘=1

𝑒𝑥𝑝(𝑉𝑖,𝑘 )𝜕𝑉𝑖,𝑘

𝜕\

]+

𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 ≤ 𝑐}

©«

−𝑒𝑥𝑝(

−𝛼𝑖𝑐𝑥 𝑗+𝜔𝑖𝑥2

𝑗

)1 − 𝑒𝑥𝑝

(−𝛼𝑖𝑐


) ª®®®®¬©«(

−𝛼𝑖𝑐𝑥 𝑗 + 𝜔𝑖𝑥2

𝑗

) ©«

0

𝑊1,𝑖

0

0

ª®®®®®®®®¬+

(𝜔𝑖𝛼𝑖𝑐𝑥

2𝑗

(𝑥 𝑗 + 𝜔𝑖𝑥2𝑗)2

) ©«

0

0

𝑊2,𝑖

0

ª®®®®®®®®¬

ª®®®®®®®®¬

+

𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 > 𝑐}

©«

0

𝑊1,𝑖

0

0

ª®®®®®®®®¬−

𝑥2𝑗


©«

0

0

𝑊2,𝑖

0

ª®®®®®®®®¬−

𝛼𝑖𝑐𝑖, 𝑗


©«

©«

0

𝑊1,𝑖

0

0

ª®®®®®®®®¬−

𝜔𝑖𝑥2𝑗


©«

0

0

𝑊2,𝑖

0

ª®®®®®®®®¬

ª®®®®®®®®¬

(C.7)

where

𝜕𝑉𝑖,𝑘

𝜕\=

©«

𝑋𝑘

−𝑒𝑥𝑝(𝑊1,𝑖𝛽1)𝑝𝑖,𝑘 ·𝑊1,𝑖

12𝑒𝑥𝑝(𝑊2,𝑖𝛽2)𝑥2

𝑘·𝑊2,𝑖

𝑒𝑥𝑝(𝑊3,𝑖𝛽3)𝑝𝑖,𝑘 ·𝑊3,𝑖

ª®®®®®®®®¬(C.8)

219

C.4 Consumer surplus calculation

In Section 3.7.3 in the main text, we define the certainty equivalent utility, 𝑒𝑖 𝑗 𝑡 , for household 𝑖,

plan choice 𝑗 , and year 𝑡. Here we provide more details of its derivation. To simplify notation, we

suppress market 𝑚 subscripts in our description.

As in Einav et al. (2013), we define 𝑒𝑖 𝑗 𝑡 such that −𝑒𝑥𝑝(−𝜓𝑖𝑒𝑖 𝑗 𝑡) = 𝑣𝑖 𝑗 𝑡 . Thus, 𝑒𝑖 𝑗 𝑡 =

− 1𝜓𝑖𝑙𝑜𝑔(−𝑣𝑖 𝑗 𝑡). Here, 𝑣𝑖 𝑗 𝑡 is the expected utility of choice 𝑗 . In Section 3.5.1, we derived a

form for 𝑣𝑖 𝑗 𝑡 by combining our chosen functional form for utility with the assumption that the

household’s underlying health care need, _𝑖, follows an exponential distribution:

𝑣𝑖 𝑗 𝑡 (𝐹_,𝑡 , 𝜔𝑖, 𝜓𝑖) = −∫

𝑒𝑥𝑝(−𝜓𝑖 × 𝑢∗𝑖 𝑗 𝑡)𝑑𝐹_,𝑡 (_) (C.9)

= −𝑒𝑥𝑝[−𝜓𝑖 (𝑦𝑡 − 𝑝 𝑗 𝑡 + 𝑔(𝑋 𝑗 𝑡 , 𝜖))

] (𝛼𝑖

𝛼𝑖 + 𝜓𝑖 ( 12𝑥

2𝑗 𝑡𝜔𝑖 − (1 − 𝑥 𝑗 𝑡))

)(C.10)

where 𝜓𝑖 is the household’s coefficient of absolute risk aversion. Substituting 𝑣𝑖 𝑗 𝑡 into our definition

of 𝑒𝑖 𝑗 𝑡 , we find:

𝑒𝑖 𝑗 𝑡 = − 1𝜓𝑖𝑙𝑜𝑔

[𝑒𝑥𝑝

(−𝜓𝑖

[𝑦𝑡 − 𝑝 𝑗 𝑡 + 𝑔(𝑋 𝑗 𝑡 , 𝜖)

] ) (𝛼𝑖

𝛼𝑖 + 𝜓𝑖2 𝑥

2𝑗 𝑡𝜔𝑖 − 𝜓𝑖 (1 − 𝑥 𝑗 𝑡)

)](C.11)

= 𝑦𝑡 − 𝑝 𝑗 𝑡 + 𝑔(𝑋 𝑗 𝑡 , 𝜖) +1𝜓𝑖𝑙𝑜𝑔

(𝛼𝑖 + 𝜓𝑖

2 𝑥2𝑗 𝑡𝜔𝑖 − 𝜓𝑖 (1 − 𝑥 𝑗 𝑡)𝛼𝑖

)(C.12)

Similarly, the certainty equivalent utility for the outside option under the same approach equals:

𝑒𝑖0𝑡 = 𝑦𝑡 + 𝑔(𝑋0𝑡 , 𝜖) +1𝜓𝑖𝑙𝑜𝑔

(𝛼𝑖 − 𝜓𝑖𝛼𝑖

)(C.13)

We then normalize 𝑒𝑖 𝑗 𝑡 by the deterministic component of the certainty equivalent utility for

the outside option. Again, recognizing that when 𝐴𝑥 + 𝐵𝑥2 is close to zero, we can approximate

220

𝑙𝑛(1 + 𝐴𝑥 + 𝐵𝑥2) ≈ 𝐴𝑥 + 𝐵𝑥2, we find:

𝑒𝑖 𝑗 𝑡 ≈ −𝑝 𝑗 𝑡 +𝜔𝑖

2(𝛼𝑖 − 𝜓𝑖)𝑥2𝑗 𝑡 +

1𝛼𝑖 − 𝜓𝑖

𝑥 𝑗 𝑡 +𝛽0𝑋 𝑗 𝑡

𝛼𝑖 − 𝜓𝑖+ 1𝛼𝑖 − 𝜓𝑖

𝜖 𝑗 𝑡 (C.14)

𝑒𝑖0𝑡 =𝜖0𝑡

𝛼𝑖 − 𝜓𝑖(C.15)

We want to compute consumer surplus for each household 𝑖. In notation:

𝐶𝑆𝑖𝑡 = 𝐸𝜖

[max𝑗𝑒𝑖 𝑗 𝑡

](C.16)

We substitute our expression for the certainty equivalent utility into 𝐶𝑆𝑖𝑡 . Multiplying and dividing

by 𝛼𝑖 − 𝜓𝑖, we find:

𝐶𝑆𝑖𝑡 = 𝐸𝜖

[max𝑗𝑒𝑖 𝑗 𝑡

](C.17)

= 𝐸𝜖

[1

𝛼𝑖 − 𝜓𝑖max𝑗(𝛼𝑖 − 𝜓𝑖) ∗ 𝑒𝑖 𝑗 𝑡

](C.18)

=1

𝛼𝑖 − 𝜓𝑖𝐸𝜖

[max𝑗(𝛼𝑖 − 𝜓𝑖) ∗ 𝑒𝑖 𝑗 𝑡

](C.19)

=1


©«𝐽∑︁𝑗=0

[𝑒𝑥𝑝

(−(𝛼𝑖 − 𝜓𝑖)𝑝 𝑗 𝑡 +

𝜔𝑖

2𝑥2𝑗 𝑡 + 𝑥 𝑗 𝑡 + 𝛽0𝑥 𝑗 𝑡

)]ª®¬ (C.20)

C.5 Cost Censor

In the main specification, the spending cutoff is fixed. As a robustness exercise, we allow the

data to recover the cutoff 𝑐. Insurers may not submit a claim when a cost draw falls below the cost

cutoff 𝑐. The probability that an insurer does not submit a claim when cost is below the cutoff is

𝐺 (𝑐 |𝑥 𝑗 ,𝜔𝑖) = 𝑃(𝑐𝑖, 𝑗 = 0|𝑥 𝑗 ,𝜔𝑖,𝑐𝑖, 𝑗 ≤ 𝑐). Thus, the density of a cost observation is:

221

𝑓 (𝑐𝑖, 𝑗 |𝑥 𝑗 , 𝜔𝑖, 𝛼𝑖) =

1 𝑥 𝑗 = 0, 𝑐𝑖, 𝑗 = 0

0 𝑥 𝑗 = 0, 𝑐𝑖, 𝑗 ≠ 0[1 − 𝑒𝑥𝑝(− 𝛼𝑖𝑐


)]𝐺 (𝑐 |𝑥 𝑗 ,𝜔𝑖) 𝑥 𝑗 ≠ 0, 𝑐𝑖, 𝑗 = 0

𝛼𝑖𝑥 𝑗+𝜔𝑖𝑥2

𝑗

𝑒𝑥𝑝

(−𝑐𝑖, 𝑗 𝛼𝑖


)𝑥 𝑗 ≠ 0, 𝑐𝑖, 𝑗 ≠ 0

The probability that costs are not submitted, given a cost below the cutoff, 𝐺 (𝑐 |𝑥 𝑗 ,𝜔𝑖), is an

unknown object. We estimate this object.

We assume that the probability of not submitting a claim is independent of moral hazard. The

object is estimated non-parametrically, conditioning on only on actuarial value: �̂� (𝑐 |𝑥).

For each potential actuarial value, we estimate �̂� (𝑐 |𝑥) non-parametrically using Gaussian kernel

methods. First, we define the number of cost observations associated with the actuarial value and

the number of cost observations associated with the actuarial value for which insurers did not submit

a claim.

𝑁𝑥 =

𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖 𝑗1{𝑥 𝑗 = 𝑥}

𝑁0𝑥 =

𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖 𝑗1{𝑐𝑖 = 0, 𝑥 𝑗 = 𝑥}

Second, the empirical probability and cumulative distributions of non-zero cost observations

below the cutoff are estimated.

�̂� (𝑧 |𝑥 𝑗 = 𝑥) =1

𝑁𝑥 − 𝑁0𝑥

𝑀∑︁𝑚=1

𝐾 ( 𝑐𝑚 − 𝑧ℎ

)

𝑓 (𝑧 |𝑥 𝑗 = 𝑥) =1

(𝑁𝑥 − 𝑁0𝑥 )ℎ

𝑀∑︁𝑚=1

𝑘 ( 𝑐𝑚 − 𝑧ℎ

)

The probability that claims are not submitted can be recovered from these objects.

222

�̂� (𝑐 |𝑥 𝑗 ) =𝑁0𝑥

𝑁0𝑥 + (𝑁𝑥 − 𝑁0

𝑥 )�̂� (𝑐 |𝑥 𝑗 )

�̂�(𝑐 |𝑥 𝑗 ) =𝜕�̂� (𝑐 |𝑥 𝑗 )

𝜕𝑐=

−𝑁0𝑥 (𝑁𝑥 − 𝑁0

𝑥 ) 𝑓 (𝑐 |𝑥 𝑗 )[𝑁0

𝑥 + (𝑁𝑥 − 𝑁0𝑥 )�̂� (𝑐 |𝑥 𝑗 )]2

The log likelihood has the form:

𝐿 (\, 𝑐) =𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖, 𝑗 𝑙𝑛

(𝑒𝑥𝑝(𝑉𝑖, 𝑗 )∑𝐽𝑘=1 𝑒𝑥𝑝(𝑉𝑖,𝑘 )

)+𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 = 0}

[𝑙𝑛(1 − 𝑒𝑥𝑝(−

𝛼𝑖𝑐


)) + 𝑙𝑛(�̂� (𝑐 |𝑥 𝑗 )

)]+𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 ≠ 0}

[𝑙𝑛

(𝛼𝑖


)− 𝑐𝑖, 𝑗 ∗

(𝛼𝑖


)]The gradient of this likelihood with respect to \ remains unchanged from the specification where

𝑐 is assumed. The derivative of the likelihood with respect to 𝑐 is:

𝜕𝐿 (\, 𝑐)𝜕𝑐

=

𝑁∑︁𝑖=1

𝐽∑︁𝑗=1

𝑑𝑖, 𝑗1{ 𝑗 ≠ 1}1{𝑐𝑖, 𝑗 = 0}

𝛼𝑖


𝑒𝑥𝑝(− 𝛼𝑖𝑐


)

1 − 𝑒𝑥𝑝(− 𝛼𝑖𝑐


)+�̂�(𝑐 |𝑥 𝑗 )�̂� (𝑐 |𝑥 𝑗 )

To estimate \ and 𝑐, we use a penalized maximum likelihood approach. A standard maximum

likelihood approach would overfit the data by setting 𝑐 very high. That is, a high enough 𝑐 ensures

that the likelihood of observed any cost 𝑐𝑖, 𝑗 is 1. To avoid overfitting, we penalize the magnitude of

𝑐, maximizing the penalized likelihood function:

𝑃𝐿 (\, 𝑐) = 𝐿 (\, 𝑐) −Ψ

[𝑙𝑜𝑔(𝑐𝜎

√2𝜋) +

(𝑙𝑜𝑔(𝑐) − `)2

2𝜎2

]

Where the penalization parameter Ψ, and hyperparameters `, 𝜎2 are specified before estimation.

223

This method can be derived from the assumption that 𝑐 has a log normal prior distribution.

𝑐 ∼ 𝑙𝑜𝑔𝑛𝑜𝑟𝑚𝑎𝑙 (`, 𝜎2)

Then, the likelihood of observing the data and 𝑐 under the assumed prior is equal to the penalized

likelihood function:

𝑃𝐿 (\, 𝑐) = 𝑙𝑜𝑔(𝑃(observe data|\, 𝑐)) +Ψ𝑙𝑜𝑔(𝑃(observe 𝑐 |`, 𝜎2)

𝑃𝐿 (\, 𝑐) = 𝐿 (\, 𝑐) −Ψ

[𝑙𝑜𝑔(𝑐) +

(𝑙𝑜𝑔(𝑐) − `)2

2𝜎2

]

C.6 Counterfactual algorithm

In this appendix section, we provide more detail on the algorithm we use to compute our

counterfactual equilibrium. The approach mirrors that of Azevedo and Gottlieb (2017) for a

competitive insurance market. We adjust the algorithm for the specific regulatory environment in

Oregon and for our specification of expected utility.

We begin by collecting the parameters from both our supply and demand side estimation. From

our maximum likelihood routine, which relies on both household plan choices and observed health

care spending to identify the parameters of demand, we collect \:

\ =

©«

𝛽0

𝛽1

𝛽2

𝛽3

ª®®®®®®®®¬

224

where the derived parameters of utility depend on \ under our specification:

𝑙𝑛(𝛼𝑖) = 𝑊1,𝑖𝛽1

𝑙𝑛(𝜔𝑖) = 𝑊2,𝑖𝛽2

𝑙𝑛(𝜓𝑖) = 𝑊3,𝑖𝛽3

(C.21)

Here, 𝛽0 is the parameter vector multiplying the plan-specific indicator variables in the utility

specification.

We also collect (𝛽4, 𝛽5), the parameters of our supply-side price-setting equation, Equation 3.9,

where under perfect competition insurance carriers set total premium revenue equal to the sum of

the portion of health care costs the insurer bears and the insurer’s allocated administrative costs for

operating the plan:

𝑅 𝑗𝑚𝑡 =

𝑁𝑚𝑡∑︁𝑖∈{𝑚,𝑡}

(�̂�𝑖 𝑗𝑚𝑡 ∗ 𝛽4^𝑖 𝑗𝑐𝑖 𝑗𝑚𝑡

)+ 𝛽5𝐴 𝑗𝑚𝑡 (C.22)

In the equilibrium search, our goal is to find 𝑝 𝑗𝑚𝑡 , the plan-market-year baseline premium the insurer

sets to equate revenue and costs in equilibrium for all plans and markets. We can translate the

normalized baseline premium to (a) gross premiums for household i, 𝑝𝑖 𝑗𝑚𝑡 , and (b) net (subsidized)

premiums for household i, 𝑝𝑠𝑖 𝑗𝑚𝑡

, using regulated age-rating factors in effect in Oregon in our sample

period. We label these factors 𝛾𝑘,𝑖 for household member 𝑘 in household 𝑖:17

𝑝𝑖 𝑗𝑚𝑡 = 𝑝 𝑗𝑚𝑡

𝐾𝑖∑︁𝑘∈𝑖

𝛾𝑘𝑖

𝑝𝑠𝑖 𝑗𝑚𝑡 = 𝑝𝑖 𝑗𝑚𝑡 ∗ (1 − 𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡)

(C.23)

We simplify the premium subsidy formula for the purpose of searching for counterfactual

premiums. In the true formula, premium subsidies depend both on household income relative

to regulated thresholds and the premium for the second cheapest silver plan offered in a market

and year. To simplify our equilibrium search while still capturing the key feature of premium

17. We re-normalize the regulated 𝛾𝑘𝑖 to equal one for a 40 year-old adult. In the federal regulated age-rating schedule,the normalization of premium rating factors equals 1 for 21-24 year-old adults.

225

subsidies – that subsidized buyers face lower overall prices for silver plans and therefore exhibit

more inelastic demand relative to a world without subsidies – we compute the subsidized share

of premiums a household faces in the observed data and market. We fix this share, 𝑠𝑢𝑏𝑠𝑖 𝑗𝑚𝑡 by

household under counterfactual prices. Under this method, we capture the differential elasticity of

subsidized consumers but still allow a degree of price-sharing to constrain insurers from raising

price. We omit the specific demand shift for an insurer that sets its premium to rank as the second

cheapest silver plan.

C.6.1 Steps in the equilibrium search

With these components, our algorithm proceeds as follows:

1. Compute each household’s expected utility for plan 𝑗 given the 𝑙th guess at the household’s

effective premium, 𝑝𝑙,𝑠𝑖 𝑗𝑚𝑡

:18

�̂�𝑖 𝑗𝑚𝑡 = 𝑥 𝑗 𝑡 +12�̂�𝑖𝑥

2𝑗 𝑡 − (�̂�𝑖 − �̂�𝑖)𝑝𝑙,𝑠𝑖 𝑗𝑚𝑡 + 𝛽0𝑍 𝑗𝑚𝑡

2. Compute predicted shares, 𝑠𝑖 𝑗𝑚𝑡 :

𝑠𝑖 𝑗𝑚𝑡 =𝑒𝑥𝑝(�̂�𝑖 𝑗𝑚𝑡)∑𝐽𝑚𝑡𝑘=0 𝑒𝑥𝑝(�̂�𝑖𝑘𝑚𝑡)

where 𝑘 = 0 represents the outside good, with �̂�𝑖0𝑚𝑡 = 0. Here 𝐽𝑚𝑡 equals the number of

insurance options in market 𝑚 in year 𝑡.

3. Compute expected costs for household 𝑖 under plan 𝑗 :

𝑐𝑖 𝑗𝑚𝑡 = 𝐸 [𝑐𝑖 𝑗𝑚𝑡 |�̂�𝑖, �̂�𝑖] =𝑥 𝑗 𝑡 + �̂�𝑖𝑥2

𝑗 𝑡

�̂�𝑖

18. In the notation below, we leave off an 𝑖 subscript from 𝑥 𝑗𝑡 , the actuarial value of plan 𝑗 at 𝑡. In our implementation,we allow 𝑥 𝑗𝑡 to vary by household for those low income households eligible for cost sharing subsidies.

226

4. Compute total costs to the insurer, the right-hand side of the price-setting equation:

𝑅 𝑗𝑚𝑡 =

𝑁𝑚𝑡∑︁𝑖∈{𝑚,𝑡}


)+ 𝛽5𝐴 𝑗𝑚𝑡

We can also compute the left-hand side of the pricing equation using prices:

𝑅 𝑗𝑚𝑡 = 𝑝𝑙𝑗𝑚𝑡

𝑁𝑚𝑡∑︁𝑖∈(𝑚,𝑡)

(𝑠𝑖 𝑗𝑚𝑡

(𝐾𝑖∑︁𝑘∈𝑖

𝛾𝑘𝑖

))

Thus, to find the next guess at the normalized premium vector, 𝑝𝑙+1𝑗𝑚𝑡

, we can combine the two

sides of the equation as:

𝑝𝑙+1𝑗𝑚𝑡 =

∑𝑁𝑚𝑡𝑖∈{𝑚,𝑡}


)+ 𝛽5𝐴 𝑗𝑚𝑡∑𝑁𝑚𝑡

𝑖∈(𝑚,𝑡)

(𝑠𝑖 𝑗𝑚𝑡

(∑𝐾𝑖𝑘∈𝑖 𝛾𝑘𝑖

))5. We test for convergence by comparing the plan-specific price vector 𝑝𝑙+1

𝑗𝑚𝑡from the (𝑙 + 1)st

iteration against the 𝑙th iteration across all plans. We compute the mean across plans 𝑗 =

1, ...𝐽𝑚𝑡 in all markets 𝑚 and 𝑡, which total 𝐽 possible plans:

1𝐽

𝐽∑︁∀( 𝑗 ,𝑚,𝑡)

(𝑝𝑙+1𝑗𝑚𝑡

− 𝑝𝑙𝑗𝑚𝑡

𝑝𝑙𝑗𝑚𝑡

)

If the mean percentage difference in prices (excluding the outside good) is less than .001,

we stop the search algorithm and define the equilibrium price vector, 𝑝𝑒𝑞𝑙 , of length 𝐽. An

entry in 𝑝𝑒𝑞𝑙 is equal to 𝑝𝑒𝑞𝑙𝑗𝑚𝑡

= 𝑝𝑙+1𝑗𝑚𝑡

. If our condition on the mean percentage difference in

premiums is not satisfied, we return to Step 1, using 𝑝𝑙+1𝑗𝑚𝑡

in place of 𝑝𝑙𝑗𝑚𝑡

.

C.6.2 Counterfactual sample

For each counterfactual scenario we examine, we define the set of households able to choose

a plan in the individual insurance market (i.e. all households in the data who purchase either an

227

individual market or small group plan). In addition to this sample, which varies for each economic

question we define, we also add a group of households we label “behavioral types,” as in Azevedo

and Gottlieb (2017). In each market-year pair (𝑚, 𝑡), we add a total number of additional behavior

types equal to 1% of households in (𝑚, 𝑡). These households incur no health care costs and choose

each of the 𝐽𝑚𝑡 plans in the market-year with equal probability: 𝑠𝑏𝑒ℎ𝑎𝑣𝑖 𝑗𝑚𝑡

= 1/𝐽𝑚𝑡 . We also assume

there is no additional administrative cost to serve these households; that is, 𝐴 𝑗𝑚𝑡 remains unchanged.

Following Azevedo and Gottlieb (2017), we must include behavioral types in the counterfactual

sample to guarantee existence of the equilibrium.

C.7 Consumer Surplus in the Small Group Market

We do not estimate a model of how employers and households choose insurance plans in the

small group market.19 Instead, we predict consumer surplus under three potential models for plan

choice in the small group market. We determine small group market household preferences over

plans using their observable characteristics and the switchers’ parameter estimates from Table 3.3

(estimated for the subset of households who were forced to switch from the small group market). In

this section, we discuss each model of plan choice and present measures of consumer surplus for

each.

No Choice

We assume that employers choose exactly one plan for each household. The household is then

forced to purchase that plan. Further, employers do not have information on the individual 𝜖 shock.

In this setting, ex ante consumer surplus (before the individual shock is realized in Stage 1) for a

household 𝑖 forced to choose plan 𝑗 is

19. Such a model would be complicated. Small employers choose a set of plans for their employees to choose from.They choose these plans with the help of a broker, who often has incentives to steer employers to a certain insurer’splans. Employers also share the cost of premiums with their employees. Our data do not include information on brokersor premium sharing.

228

𝐶𝑆𝑖 =1

𝛼𝑖 − 𝜓𝑖(𝑉𝑖, 𝑗 + 𝛾𝐸𝑀) (C.24)

where household 𝑖 attains mean latent utility 𝑉𝑖, 𝑗 from plan 𝑗 coverage and 𝛾𝐸𝑀 is the Euler –

Mascheroni constant. In this case, we estimate consumer surplus using observed plan characteristics

of chosen plans from the SERFF data.

Patient Choice

We assume that employees can choose from the full set of possible plans offered in the small

group market (or the outside option of no insurance in more specifications). They do so after their

𝜖 shock is realized. In this setting, the equation for ex ante consumer surplus is equivalent to the

individual market consumer surplus equation.

𝐶𝑆𝑖 =1


𝐽∑︁𝑗=1𝑒𝑥𝑝

(𝑥𝑖, 𝑗 +


2− (𝛼𝑖 − 𝜓𝑖)𝑝𝑖, 𝑗 + 𝛽0𝑋𝑖, 𝑗

)(C.25)

If employers did not share premium costs with their employees, this consumer surplus measure

could also be supported by a model where employers chose a plan for their employees but were able

to extract the consumer surplus by decreasing wages. In this case, minimizing wage costs would

yield equivalent plan choices to maximizing household latent utility over plans. This is discussed in

greater depth in the third plan choice model.

This setting has the advantage that it compares directly with the consumer surplus measure in

the merged market. The choice set is similar in size to the individual market, though it includes

platinum plans in addition to bronze, silver, and gold plans. However, the disadvantage is that,

under this assumption, predicted plan choices do not fit the observed data.

Employer Choice

Lastly, we assume that employers choose plans for their employees. We use a simple model

of employer plan choice. Employers choose a health insurance plan for each of their employees

229

to minimize cost. We assume that employers must provide compensation to each employee, �̄�𝑖.

Compensation can be in the form of wages, 𝑤𝑖, or the certainty equivalent value of the health

insurance plan 𝑗 that is chosen for the employee, 𝑒𝑖, 𝑗 . Wages are taxed at the employee’s marginal

income tax, 𝜏𝑖, while health insurance is not. Additionally, employers must pay a share of the

health insurance premium, a𝑖. Lastly, employers have complete information about their employee’s

preferences over insurance plans, including individual 𝜖 shocks. The cost of employing individual 𝑖

when plan 𝑗 is chosen is:

𝑐𝑒𝑖, 𝑗 = �̄�𝑖 −1

1 − 𝜏𝑖𝑒𝑖, 𝑗 +

a𝑖


Employers choose plans to minimize costs. From employing individual 𝑖, ex ante employer savings

(before the individual 𝜖 shock is realized in Stage 1) is:

𝐸𝑆𝑖 = 𝐸𝜖 (�̄�𝑖 − 𝑚𝑖𝑛 𝑗𝑐𝑒𝑖, 𝑗 ) =1

(𝛼𝑖 − 𝜓𝑖) (1 − 𝜏𝑖)𝑙𝑜𝑔

( 𝐽∑︁𝑗=1𝑉𝑖, 𝑗 − (1 − 𝜏𝑖) (𝛼𝑖 − 𝜓𝑖)

a𝑖


)Employer savings are in pre-tax dollars. To make this measure comparable to consumer surplus

in the individual market, we transform the measure into post-tax dollars: (1 − 𝜏𝑖)𝐸𝑆𝑖. We report

post-tax employer savings instead of consumer surplus. All consumer surplus is extracted by the

employer. If the employer extracted no consumer surplus, then the employer would choose the

cheapest plan.

C.7.1 Measures

The analysis uses households in the small group market in 2015 and 2016. There are 383,156

household-year observations in the years 2014-2016. There are 262,612 subscribers who choose

plans that are not in the SERFF data or are not in our insurer sample. These are grandfathered,

catastrophic, or fringe plans. This leaves 120544 subscribers. Note that this differs from the number

of observations in Table 3.2 because it includes households who chose platinum plans. After

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subsetting to the years 2015-2016, this leaves 91,776 households.

We restrict the choice set to plans that have more than 1% market share. Plans with less than 1%

market share are unlikely to be shown to employers by brokers. We ignore the intricacies of plan

pricing in the small group market.20 That is, We assume that the premium a household faces for

plan 𝑗 are equal to the normalized listed baseline premium 𝑝 𝑗𝑚𝑡 , adjusted by the household’s rating

factors 𝛾𝑘𝑖, tax rate 𝜏𝑖, and employer contribution share a𝑖:

𝑝𝑖 𝑗𝑚𝑡 = (1 − a𝑖) (1 − 𝜏𝑖)𝑝 𝑗𝑚𝑡𝐾𝑖∑︁𝑘∈𝑖

𝛾𝑘𝑖

No Outside Option Outside Option

Household Employer Household EmployerVariable No Choice Choice Choice Choice Choice

Consumer Surplus (𝛼 > 𝜓) -30.142 19.468 17.842 22.955 21.954P(𝛼 > 𝜓) 0.944 0.944 0.944 0.944 0.944(Consumer Surplus (𝛼 + 𝜓 > 0.1) -6.694 2.431 0.903 3.539 2.638P(𝛼 + 𝜓 > 0.1) 0.873 0.873 0.873 0.873 0.873Moral Hazard Spending 0.484 0.502 0.499 0.388 0.362Share Uninsured 0 0 0 0.309 0.309Share Bronze 0.141 0.074 0.089 0.027 0.023Share Silver 0.487 0.389 0.411 0.285 0.253Share Gold 0.247 0.422 0.399 0.292 0.231Share Platinum 0.124 0.115 0.101 0.087 0.068Choice Set Size 1 18.15 18.15 19.15 19.15N 55066 55066 55066 55066 55066

Table C.2: Consumer Surplus Estimates

Table C.2 presents the consumer surplus estimates for the small group market using the three

alternative assumptions. It also reports other predictions of small group market choice models,

including the predicted coverage levels. Using the first model of plan choice, we find negative

consumer surplus. Healthy households in this setting are forced to purchase insurance when they

20. In future work, we hope to incorporate the differences in pricing in the small group and individual markets.

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would prefer to be uninsured.

Consumer surplus is substantial in the household choice models. In the specification where

the outside option is available, average consumer surplus is $3,204 per month among households

with 𝛼 > 𝜓. This high number is driven by outliers. When we restrict the sample to households

with 𝛼 − 𝜓 > .1, average consumer surplus drops to $632. As expected, predicted plan choices do

not match observed plan choices (compare to the No Choice column). Both the model where the

outside option is excluded and the model where employers are choosing plans bring predicted plan

choices closer to observed plan choices. Estimated consumer surplus is smaller in both of these

alternative models.

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three essays on access and welfare in health care and

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