Adverse Selection: The Dog that Didn’t Bite

July 2010

Abstract

We assess the welfare impact of health status based selection in health insurance plans using detailed panel data on health plan choices and complete health care utilization. Our estimates suggest that adverse selection plays an important role in explaining cost differentials across plans and much of the selection occurs along difficult to contract upon dimensions. The distortionary consequences of the asymmetric information are modest because individuals are very premium inelastic in our data. Our findings show that the presence of significant adverse selection need not cause meaningful welfare loss.

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1. Introduction

The vast majority of under-65 year old Americans, accounting for 160 million enrollees

with an average annual family premium of $12,658 in 2008, obtain health insurance through an

employer.1 Because employers play such a large role in health insurance markets, the welfare of

health insurance outcomes depends in large part upon the ability of employers to offer the

appropriate health plan menu at efficient prices. Given the size of the market, small deviations

from the optimal premium have the potential to generate large welfare losses. Economists have

long been concerned that the presence of adverse selection in health insurance markets makes it

difficult for employers (and market mechanisms more generally) to price these products

optimally.

Cutler and Reber (1998) and Einav, Finkelstein and Cullen (2010) show that the optimal

sorting of enrollees into health plans requires the premium differentials to equal the differential

cost of the marginal enrollee across plans. In most employer-sponsored settings, premiums will

equal (or be a function of) the average cost of the enrollees in the plan and not the cost of

marginal enrollee. Sub-optimally set premiums result in welfare loss as some enrollees fail to

enroll in the plan that yields the highest net surplus. The magnitude of the selection induced

welfare loss depends upon the number of enrollees who sort into the `wrong plan’, which

depends upon the size of the premium distortion and the premium elasticity of enrollees, and the

net loss in welfare that results from enrollees selecting the `wrong’ plan. To accurately estimate

the welfare loss from selection, therefore, requires accurate estimates of the premium distortions,

the elasticity of demand for health plans, as well as the net loss in welfare from the misallocation

of enrollees to plans.

1 Source: Kaiser Family Foundation (http://ehbs.kff.org/pdf/2009/7981.pdf)

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In this paper, we estimate the impact of health plan selection on welfare in the context of

the employee health plan offerings of a large employer.2 We possess detailed information on

both the health insurance choices and the complete health care utilization experience of a large

number of individuals over multiple years. Our data allow us to formulate rich measures of the

employee’s health status that are based upon previous diagnoses. These data provide sufficient

detail to cleanly model the importance of selection in determining the cost differentials across

health plans. It is well known that identifying adverse selection separately from moral hazard can

be challenging (Chiappori and Salanie, 2000). Furthermore, the information available in the

claims data allows us to decompose health plan selection into easily observable (to the employer)

demographic variables and more difficult to observe health status dimensions.

In order to estimate welfare impact of selection, we estimate models of the health plan

demand and costs. To model demand, we construct a model of health insurance choice in which

individuals assess the quality of the health plan, their estimated health status, premiums, and

expected level of expenses when selecting a plan. We exploit the detailed data and formulate

measures of the health status and expected out-of-pocket expenditures that reflect actual enrollee

medical care utilization between different plans.

We estimate utility parameters using an autoregressive, multinomial probit choice model

(Geweke, Keane and Runkle, 1997). The probit model allows for flexibility in the correlation

structure of the choice-specific errors. Our implementation also allows the unobserved choice-

specific error term to be autocorrelated, and the autocorrelation parameter can vary across health

plans. Work by Handel (2010) suggests that persistence in health plan choice is important, and

individuals in our data tend to remain in the same health plan for multiple years. Thus,

2 Here we use the term `selection’ to refer to both adverse and advantageous selection. In our setting, we have multiple plans and thus some plans will experience adverse selection while others will therefore experience advantageous selection.

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incorporating autocorrelated unobserved heterogeneity into the model is likely important. This

model removes many of the unappealing implications (and potential biases) of the literature’s

workhorse empirical model, the iid, multinomial (or nested) logit. Statistical inference is

generated using Bayesian methods (Gelfand and Smith, 1990) as convergence for these types of

models using classical approaches is often problematic. Importantly, Monte Carlos analysis

indicates that in the presence of autocorrelated unobservables, standard static discrete choice

methods generate biased coefficients estimates.

Health expenditure data are censored and skewed and it is well known that accounting for

these features is important for unbiased inference. To estimate the cost side, we estimate the

parameters of a set of health expenditure equations, allowing for individual- and plan-specific

heterogeneity, censored and skewed dependent variable outcomes. In keeping with the spirit of

the choice model estimation, we use a Bayesian framework to generate statistical inference. The

model allows for individual-specific effects and nonlinear plan-specific relationships between

costs and health status. The estimates from the expenditure equations enable us to decompose

cost heterogeneity across plans into differences that are a consequence of selection and

differences that are related to plan design.

The estimates from the choice model indicate that enrollees select into plans based on

both the relatively easy-to-observe demographic variables and the much more difficult–to-

observe health status dimension. That is, much of the information that individuals use to make

health plan choice is private, unlikely to be contractible and is correlated with their expected

cost. The impact of selection on realized average health plan expenditures quite large – upwards

of 50% of the plan cost differentials are driven by selection. Consistent with our Monte Carlos

analysis, in our setting, the use of the cross-sectional multinomial logit choice model leads to

erroneous conclusions over several important dimensions of health plan choice. Unobserved

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heterogeneity in plan preference is extremely persistent and failure to account for this inertia

leads to biased estimates of premium elasticities and other important factors that influence health

plan choice.

Using the demand and cost side estimates, we perform several premium counterfactuals

in order to quantify the impact of selection on welfare. In these simulations we adjust premiums

according to commonly used risk adjustment rules and we also calculate an optimal premium

structure. While there is significant health status based health plan selection in our setting, the

distortionary consequences of asymmetric information are modest. The welfare gain from using

optimal premium structures is minimal and the reason selection does not greatly affect welfare in

our context is straightforward: plan choices are relatively insensitive to large changes in

premiums. Counter to the conclusions of Cutler and Reber (1998) and roughly consistent with

the work of Einav, Finkelstein and Cullen (2010), we find that large distortions in premiums

induced by selection do not meaningfully distort the plan choices of enrollees. Roughly,

individuals sort into the same plans at the optimal premiums and under the premiums we

observed, even though those premiums are very different from the actual premiums in the data.

The remainder of the paper has the following structure. We provide a brief overview of

the relevant literature in Section 2. The data on which the analysis rests is described in Section 3,

and the model is laid out in Section 4. The results of the model estimation are presented in

Section 5, and the results of the employer pricing policy experiments shown in Section 6. Section

7 concludes. Details of the Bayesian inference used to estimate the parameters in the model are

available in appendices from the authors.

2. Background

At least since the work of Rothschild and Stiglitz (1976) economists have known that

adverse selection can have deleterious impacts on health insurance market outcomes. It is

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therefore not surprising that a large literature has arisen measuring health status selection in

health plans.3 The typical research in this line of analysis studies differences in demographic or

cost experience between some form of managed care and a less restrictive health insurance

product (e.g. a preferred provider organization or fee-for-service plan).4 While there are a

number of studies that find no selection, the typical study finds that the more restrictive the

provider network or the more managed the care, the more favorable is the health plan risk

selection. Sicker enrollees have a greater willingness to pay for broad provider access and less

insurer involvement in their care.5, 6

Cutler and Reber (1998) study the health plan choices of Harvard employees after the

implementation of a fixed employer premium contribution policy. They show that under such a

premium setting strategy, the premium differentials between plans is likely to be too high and

result in welfare loss. Specifically, they note that the optimal premium differences between plans

should be based solely upon the cost differential of treating the marginal enrollee. However, in

most settings the premium differentials will reflect the average plan-specific cost differential as

well as the average health status of the enrollees. If sicker enrollees prefer plans that offer a

broader choice of providers and choice is more costly to offer, the premium differentials will be

3 Cutler and Zeckhauser (2000) provide an excellent review of this research. More recent examples of adverse selection in health plans studies are: Atherly, Dowd, Feldman (2004), Barrett and Conlon (2003), Tchernis, et al. (2003), Gray and Selden (2002), Riphahn, Wambach and Million (2002), Feldman and Dowd (2000) and Altman, Cutler and Zeckhauser (2003). 4 There is an important body of work that examines adverse selection in the non-health insurance context. An incomplete list of papers in this literature include Cawley and Philipson (1999), Chiappori and Salanie (2000), Finkelstein and Poterba (2004) and Einov, Finkelstein and Schrimpf (2007). 5 While much of the literature on adverse selection does not have access to information that might be considered ‘private’ when modeling selection, several paper incorporate measures of health status into their analysis. Notably, Strombom, Buchmueller and Feldstein (2002) acquire data on hospitalizations and cancer diagnoses around the time of plan enrollment and include this information as regressors in a choice model. Others researchers use chronic illness indicators or paid claims information to construct health status measures (e.g. Parente, Feldman and Christianson, 2004; Atherly, Dowd and Feldman 2004; Harris, Schultz and Feldman, 2002; Royalty and Solomon, 1999). 6 Parente, Feldman and Christianson (2004) use data from a similar setting to ours, supplemented with an employee survey to examine the profile of those who enroll in a Consumer Directed Health Plan (CDHP). Using a MNL approach, they find the CDHP plan enrolled wealthier employees and the CDHP was not more attractive to the young and healthy.

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too high relative to the optimum. Cutler and Reber estimate the parameters and utility functions

using multinomial logit methods and estimates of costs using other data sources to conclude that

adverse selection resulted in a welfare loss of 4% of gross premiums. However, it is uncommon

for employers to risk adjust premiums (Kennen et al., 2001). Thus, their findings introduce a

puzzle that our paper addresses. If the welfare loss from adverse selection in health insurance is

so large, why do not more employers risk-adjust their premiums?

Cardon and Hendel (2001) use data from the 1987 National Medical Expenditure Survey

aggregating many different heath plans into three choice categories to quantify the influence of

information asymmetries on health plan selection. They estimate a structural model of health

plan choice and health care expenditures.7 Conditioning on an information set that includes age,

gender, geographic location, and race, they find little evidence of adverse selection.

More recently, several researchers have sought to leverage detailed claims data to

measure the welfare loss from adverse selection in employer-sponsored health insurance. Einav,

Finkelstein and Cullen (2010) note that the demand and cost curves can be separately identified

from premium variation alone. This observation along with linearity and premium exogeneity

assumptions makes estimating welfare loss a simple OLS problem. Using cross-sectional data

from a large employer and focusing on two plans, they estimate that the welfare loss from

adverse selection of $9.55 per employee per year. Bundorf, Levin and Mohoney (2008) use data

from a single health insurance broker to analyze the welfare gains from individually risk-

adjusting the out-of-pocket premium to enrollees. The underlying idea is that risk-adjusting the

out-of-pocket premium better sorts enrollees to plans, thereby increasing net surplus. Handel

(2010) uses medical claims data from a large employer to measure health plan switching costs.

He finds that significant switching costs are large and lead to significant inertia in health plan

7 See also, Marquis and Holmer (1996).

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choice. In Handel’s setting the reduction of switching costs leads to welfare loss as it increases

adverse selection which leads to significant premium distortions. Finally, Bajari, et al. (2010) use

a two-step method to semiparametrically isolate moral hazard from adverse selection and find

evidence of both.8

3. Data and Institutional Setting

The data used here are detailed employee health care claims and health plan enrollment

history for a very large, self-insured employer. Linked, but de-identified, enrollment history is

available for 2002-2005 and claims history is available for 2002-2004, with six months of claims

run-out paid in 2005. As the employer is self-insured, all covered medical care rendered to an

employee will have an associated claim included in our data. A claim contains all information

needed to process an insurance payment and thus includes valuable information such as primary

and secondary diagnosis codes, procedure codes and identification of provider. The claim also

contains information on the amount paid by the insurer and by the enrollee. For each enrollee we

aggregate all their health care claims throughout the year to formulate a precise measure of both

the total claims paid for the enrollee’s care, and the share of these expenditures incurred by the

enrollee as out-of-pocket costs for covered medical care.

The employer offers health insurance coverage for individuals, spouses/domestic partners

and families. Employees select their health plan during the open enrollment period in November.

Information about the plan options, benefits and provider network structures are mailed directly

to each employee just prior to open enrollment. Using these documents, it is easy for the enrollee

8 There is a literature on modeling health plan choices for Medicare and employer-based plans that is also relevant to our work. An incomplete list of the papers in this literature includes Feldman, et al. (1989), Dowd and Feldman (1994-1995), Marquis and Holmer (1996), Cutler and Reber (1998), Royalty and Solomon (1999), Buchmueller (2000), Scanlon, et al. (2002), Strombom, Buchmueller and Feldstein (2002), Dowd, Feldman and Coulam (2003) and Atherly, Dowd and Feldman (2004). All rely on the iid, logit family of choice models to estimate the parameters of interest. These papers estimate premium elasticities for health insurance that range from the moderately elastic to the very inelastic.

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to compare out-of-pocket premiums and benefits structures across the plans. The Human

Resources department also sends out several emails reminding employees to select a health plan

during open enrollment. Information about the spouse/domestic partner employment-based

benefits choices are not available – we do not know what the exact choice set is in this case, as

the partner may have insurance benefits at another firm. For this reason our analysis focuses

solely on individuals continuously enrolled in single coverage over the three years. While single

coverage does not equate to single marital status, the approximation likely introduces little error.

In addition, employees outside the metropolitan service area were eliminated from the analysis

sample because they have a different health insurance choice set. This leaves 3,578 employees

for the estimation.9

Employee demographics information is gathered from several sources. Age and gender

are taken directly from the encrypted plan enrollment files. Employee earnings were matched

from a separate accounting file. This demographic information is merged with health plan

enrollment files, along with health status and expenditure data culled from the claims files. Plan

characteristics (provider panel structure, copayments, out-of-pocket limitations, employee

contribution levels) are drawn from the employer’s open enrollment materials.

The employer offered a total of four plans in 2002 through 2005. The employer contracts

with the plans to access their provider network and specifies the benefit design. The plans charge

the employer a fee for accessing their network and processing the claims while the employer

pays the medical care claims net of enrollee out-of-pocket payments. The plans include one

closed-panel health maintenance organization (HMO), two point-of-service (POS) plans, and a

Consumer-Driven Health Plan (CDHP).

9 The relative plan shares of the entire sample before imposing our inclusion restrictions closely match the relative shares of our analysis sample suggesting that our inclusion criteria is not inducing a sample selection bias.

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The HMO is a restricted provider network plan in which enrollees incur modest co-pays

for any within-network utilization, however the plan does not cover any out-of-network medical

care. The organization offered two POS plans with differing provider networks both across and

within the plans. One of the POS plans (POS 1) has three tiers, each with different premium

levels; the tiers corresponding to successively broader provider networks. Tier 2 includes all the

providers in Tier 1 as well as offering enrollees access to additional, potentially higher cost

providers. Likewise, Tier 3 includes all the providers in Tier 2 in addition to other higher-cost

providers.10 The other POS plan (POS 2) has only one option. The POS plans charge higher in-

network co-pays than the HMO but allow out-of-network care (with a higher out-of-network co-

pay). All of these plans had the same out-of-pocket limits of $1,500 and the same prescription

drug carve-out plan.

The CDHP is a recently developed health insurance product that combines a catastrophic

indemnity plan matched with an employer-funded medical spending account. In the CDHP a

single enrollee is given an account of $750 (2003 and 2004) or $600 (2005) to draw upon for

medical care. Once the account is exhausted, the enrollee pays the balance of the $1500

deductible out of pocket. After the enrollee utilizes more than $1,500 of medical care, there is no

additional copayment for in-network health care. Pharmacy coverage is integrated into this plan,

unlike the carve-out in the traditional plans. In sum, there are a total of six health plan choices

available to the employee: HMO, POS 1/tier 1, POS 1/tier 2, POS 1/tier 3, POS 2, CDHP.

Table 1 presents the annualized employee premiums and enrollment shares for the plans

in our data. The premiums vary across plans and time. The organization spends considerable

resources attempting to inform employees of their health plan options, thus enrollees are well

informed of the premiums and benefit differences across the plans when making their plan 10 While the Tiers were advertised as differing in the prices paid to providers, as we discuss in Section 5 we found little cost differential between the tiers in POS 1.

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selections. During the open enrollment period, brochures and emails are distributed to all

employees detailing the premiums and changes in premiums from the previous year, as well as

the plan benefit structures and provider panels. In addition, the detailed plan information is

available on the organization’s human resources web site.

The temporal variation in out-of-pocket premiums is driven by two changes in the

employer’s premium-setting strategy. First, the employer used a defined contribution strategy

and the formula used to construct the premiums changed over time. For 2002-2003 the employee

share for single coverage was set to zero for the base plan. Employee share for other plans was

simply the excess of other plan total premium over base plan total premium. For 2004-2005 the

employee share was set at 10% of the base plan premium. Employee share for other plans was

10% of this base amount plus the excess of other plan total premium over base plan total

premium. These changes were driven by the organization’s drive to push more of the cost of

health care onto employees. The second change was that the employer moved from a strategy of

no risk adjustment in 2002 to one of rudimentary risk adjustment by the end of our data.

Importantly, we have discussed, in great detail, the premium setting strategy with the human

resource personnel and they assured us that the changes in the relative premiums did not reflect

specific changes in the plan characteristics or employee preferences but changes in the premium-

setting strategy of the organization. Thus, to the best of our understanding, time varying

differences in premiums are exogenous.

The most popular plan is the HMO, and it is also the cheapest plan. Another noteworthy

pattern in Table 1 is that while the premiums of the plans shifted considerably, the shares did not.

This pattern suggests that controlling for autocorrelation in enrollee preferences is likely to be

important.

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Measuring Health Status

An important feature of this study is that we are able to use past health care utilization

information to formulate health status measures that are incorporated into the choice model. In

order to construct this measure, we need to map the thousands of ICD-9CM codes (and millions

of potential combinations of codes) into a parsimonious representation of current health status.

We use algorithms developed by the Johns Hopkins University ACG Case-Mix System (v. 6),

developed by the Health Services Research and Development Center.

The ACG Case-Mix System employs a combination of clinical assessments and grouping

of diagnoses and procedures along with extensive regression fitting to take the thousands of ICD-

9CM codes that are embedded in the claims to construct simple measures of health status. The

predictive modeling feature of the ACG software produces a concurrent weight (CW), a

summary measure of the current individual health status and resource utilization. The CW is

constructed so that the national average is 1.0 with higher values denoting poorer health and

likely higher expenditures.

A potential concern with our measure of health status is that it is based on the previous

year’s health care utilization which, in turn, is potentially a function of plan characteristics and

benefit structures. That is, our measure of health status may be an endogenous function of plan

choice. The influence of plan choice in affecting the CW is mitigated by the fact that the CW is

based on diagnosis code history, rather than the health care utilization, per se. Thus, impact of

the plan on CW can only occur through differences in accessing care that affect the diagnoses

recorded in their claims history. To investigate this possibility, we examine the impact of plan

choice on CW for those individuals that switched plans. We regress CW on plan and individual

fixed effects. Since we are controlling for time-invariant, individual differences in CW, if the

plan choice does not affect CW, it suggests (but is not dispositive) that our measure of health

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status is not a function of health plan choice. In this analysis, plan fixed effects are insignificant.

This is true for both each plan individually and for the joint test of their significance. Thus the

evidence we can bring to bear suggests that CW is not a function of plan choice.

Table 2 provides summary statistics of our estimation sample. The organization has a

high percentage of female employees and the average health status (as measured by CW) of the

employees is poorer than the national average. Interestingly, there are important differences in

the mean demographic and health status measures across the plans, however the health status

measures display much greater across-plan variance than the demographic variables. This

suggests that relying solely on demographic variables to measure variation in expected cost may

underestimate the true magnitude of adverse selection.

The simple summary statistics in Table 2 show that health plans differ in both

demographics and in measured health status, and this is prima facie evidence of selection. The

HMO attracts a younger, more male, lower-paid and healthier population than the other plans.

The plan that garners the least favorable selection is the POS 2 plan—the mean age and CW is

significantly higher than the HMO. The CDHP enrolls an older population with a higher salary,

and a higher CW than the HMO but a lower CW than the other plans.

4. Empirical Approach

To measure the welfare consequences of we first must accomplish two tasks: 1) estimate

the expected total health claims and patient out-of-pocket expenditures that individuals would

incur if they were to enroll in any of the available plans; and 2) estimate the parameters of an

indirect utility function. Below we describe our approach to estimating the cost functions and

health plan choice demand parameters.

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Medical Care Cost Model

In order to estimate total health care expenditures and patient out-of-pocket (OOP)

expenses as a function of observable individual and plan characteristics, we face three important

modeling challenges. First, we need to account for unobserved individual heterogeneity. Second,

much of the data is censored at zero. Third, OOP and total claims expenditure are determined

jointly with plan-specific rules placing nonlinear restrictions on the OOP realizations. To account

for these features of the data, we use a two-part, three-equation censored regression model

building upon the work of Cowles, Carlin and Connet (1996). The first equation in the model is

an indicator of whether the patient receives care. The thresholds are stochastic and are a function

of observables, a time-invariant unobservable individual effect and an iid error. Conditional on

the threshold being breached, the other two equations of the model predict total claims

expenditure, denoted Clmit, and total out-of-pocket expenditure, OOPit.

More specifically, the threshold variable is a zero-one indicator of non-zero claims,

and is a function of the latent variable in the following way:

Positive values of claims and out-of-pocket expenditures are observed only when this threshold

is met. Letting the asterisk denote latent values, the observed Clmit is given by

,

and OOPit is modeled by capping OOP expenditures at the plan’s out-of-pocket limit, denoted

, where Ij denotes the set of plan j’s enrollees:

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We allow for individual-specific, unobserved, time-invariant shocks that differ across

equations. The system of latent variables is simply:

,

where are the time-invariant, individual-specific intercepts. In the language of

frequentist econometrics the ’s are similar to random effects. The iid error vector is assumed to

be normally distributed: for . Note that the covariance

matrix, , is plan-specific, as we expect different correlations between the threshold, claims and

OOP expense across the plans.

In order to flexibly model health plan costs, the vector of explanatory variables, ,

includes the demographic and health status variables, and interactions of those variables.

Specifically, includes age, age squared, female indicator, age interacted with female, CW

(health status) and a female indicator interacted with age and CW. We estimate plan-specific

parameters for all of the explanatory variables. In this way, we allow for the possibility that some

plans may be more efficient at treating enrollees with relatively good health status while others

may be more efficient in providing care for sicker enrollees.

Bayesian inference is used to formulate our estimates of the parameters of interest. The

aim in Bayesian estimation is to construct the posterior distribution of the parameters given

assumptions on the prior distribution of the parameters and the data. We simulate the posterior

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distribution of the parameters using Monte Carlo Markov Chain (MCMC) methods. Specifically,

we use the Gibbs sampler (Gelfand and Smith, 1990) and data augmentation techniques (Tanner

and Wong, 1987). Chib (1992) first proposed a Bayesian approach for estimating the tobit

model. The details of the estimation algorithm are described in an appendix available from the

corresponding author.

Our estimates will be unbiased as long as residual, unobserved health status is

uncorrelated with plan choice. We believe this is a reasonable assumption in our setting as we

include in the set of regressors a health status measure based on very detailed information on

prior diagnoses and procedures. The health status measure is based on much of the same

information the enrollee has access to when selecting a health plan.11 While we believe that that

the institutional setting and the quality of our data make it unlikely that, conditional on our

measure of health status, enrollees are cognizant of health status information that affects their

choice of plan, it is clearly still a possibility.12 In order to assess the plausibility of our

assumption, we perform two direct tests for the presence of unobservable health status

information that is correlated with plan choice.

For the first test, we reformulate and generalize our model allowing for linkages between

the cost and health plan choice equations. That is, we allow the plan choice to be endogenous.

Specifically, the error from the choice equation is allowed to impact directly on plan cost

estimates.13 The exclusion restriction that identifies the parameters is that changes in premiums,

conditional on covariates, are not correlated with the cost shocks. This framework is similar to

11 There is a sense in which we have better health status information than the enrollee as we are running their claims histories through a sophisticated algorithm constructed for the purposed of predicting future health care expenditures. 12 In addition, others have argued (and tested) that the type of risk adjustment we employ corrects for unobserved selection bias in an environment where unobservable health status is more likely to bias the results (Shea, et al., 2007). Pietz and Peterson (2007) find that other measures of self-reported health status beyond the diagnostic information in claims do not help predict mortality. 13 In this specification, we cannot include the measures of the variance of OOP expenditures in the plan choice equation.

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Deb, Munkin and Trivedi (2006) and Geweke, Gowrisankaran and Town (2003). Again, the

inference here is generated using Bayesian methods. The posterior distribution of the parameters

on the utility errors meaningfully overlaps zero, implying that plan choice is not correlated with

unobserved health status information.14 Furthermore, the posterior distribution of the plan

coefficients is very similar to the corresponding distribution from our base specification. Again,

this suggests that unobserved choice shocks are not correlated with plan cost. In the analysis we

present below, we retain separate expenditure and choice models to allow the inclusion of an

estimate of the variance of out-of-pocket expenditures as a covariate in the choice model to

explore risk aversion.

In the second direct test, we estimate health care costs, conditional on the costs being

greater than zero using both individual fixed and random effects.15 We compare the parameter

estimates between the random effects and fixed effects models using a standard Hausman-Wu

test. If individuals use time-invariant information about their health status to inform their plan

choice then we should expect the coefficients estimates between the random effects and fixed

effects models to differ. The Hausman-Wu test fails to reject the hypothesis at the 10% level that

the coefficients are different between the models. That is, there is little evidence that our

estimates from the cost equation will be biased due to enrollees using time invariant information

in selecting a plan.16

Once the cost model is estimated, we construct estimates of the expected Clm and OOP

expenses for each individual (in logarithm scale) across all plans including the plan actually

selected by the individual. Because the Gibbs Sampler method results in a sample from the

posterior distribution of the parameters, including the latent expenditure variables, we can use

14 We do not present results from the joint model here but the results are available upon request from the authors. 15 Less than 10% of the enrollee/year observations have zero reported health care claims. 16 Documentation of additional, indirect, tests of endogeneity is available in Carlin and Town (2010).

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this sample to calculate the sample mean and variance of out-of-pocket expenditures for each

individual in each plan, to be included in the choice utility equations.

Health Plan Choice Model

We model health plan choice using a multinomial probit with autocorrelated errors (AR-

MNP). In our model the unobservable components of utility are allowed to be freely correlated

across plans and autocorrelated over time. Most analyses of health plan choice rely upon the iid

logit model or the heteroskedastic but independent nested logit model. Our results suggest that

these assumptions may lead to biased inference. Only 7% of the enrollees switch plans in any

given year, suggesting that plan preferences are likely to be correlated over time; our framework

explicitly accounts for this autocorrelation. We are unaware of any analysis of health plan choice

that allows for both full freedom in cross-plan correlation, and correlation of unobserved

preferences across time.

In selecting their health plan, we assume enrollees observe their health status and

formulate consistent estimates of both the mean and variance of their out-of-pocket expenditures

across all plans. Given these estimates they select the plan that maximizes their utility. Let

be the indirect utility of the person for the plan at time t

. Individuals choose plan j if and only if for all . It is well known

that is not identifiable because level and scale are irrelevant to the maximization problem.

The Jth plan is used to normalize the level of utility so that . The CDHP is used

as the baseline choice because of its distinct plan design. We normalize for scale by setting the

variance of the unobserved preferences for the HMO to 1.

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It is assumed that is linearly related to the characteristics of the individuals and the

choices ( ), so where is the unobservable component of utility. In matrix

form, we have the relationship . The errors are assumed to be normally

distributed: . In a slight modification of Geweke, Keane and Runkle (1997), the

“stickiness” of plan choice across time is captured via an AR(1) relationship in the error terms.

Specifically, , with iid . The variance matrix is a diagonal

matrix, whose diagonal elements are plan-specific variances. The AR(1) coefficient, ,

is a plan-specific parameter, based on the plan individual i is in at time , when the time t plan

election is made. Given the apparent persistence in plan market shares, we anticipate estimated

values of closer to one than to zero.17

Convergence is often elusive when estimating the parameters of a multinomial probit

model using a classical maximum likelihood approach. However, the parameters of this

autoregressive multinomial probit model can be readily estimated using Bayesian methods. As in

the cost model, we specify a diffuse prior distribution for the parameters and simulate the

posterior distribution using the Gibbs sampler and data augmentation techniques for the latent

utilities. An appendix available from the corresponding author describes the likelihood function

and Gibbs algorithm in detail.

The vector includes the following plan invariant variables: age, female indicator, age

interacted with female, and CW (the measure of health status in the year the enrollment election

is made). The parameters on these variables can vary by plan. The vector also includes the

17 It is an open question whether εit captures pure, exogenous preference differences for plans or if captures switching costs that accrue as patients develop relationships with providers. That is, it is an open question whether the errors capture state dependences (e.g switching costs) or correlated heterogeneity. In the results section we provide some evidence that suggests that correlated errors do not capture switching costs.

19

following variables that vary across plan and time: natural log of net salary,

, and the expected value of the natural log of out-of-pocket (OOP)

expenditure, the variance of the natural log of the OOP expenditure, and the office visit

copayment level for the plan.

Our model imposes fewer restrictions than traditionally used multinomial estimation

approaches. Because the elasticity estimates from our AR-MNP model differ from the MNL

estimates, it is instructive to decompose the source of those differences into the importance of

capturing heteroskedasticity and modeling persistence in health plan preferences.

Misspecification of the variance-covariance structure can lead to biased coefficient estimates in

discrete choice estimation, however in many cases that misspecification does not significantly

impact coefficient estimates. That will not be true in our case and thus it is instructive to isolate

the source of the misspecification bias. Specifically, we decompose differences into the

importance of accounting for serial correlation and cross-plan correlation in the residuals. For

comparison purposes we use frequentist methods to estimate a cross-sectional multinomial logit

model and a cross-sectional nested-logit model.18 We also use a Bayesian approach to estimate

an autoregressive, MNP model with a diagonal covariance matrix. The later model is the same

as our base model except the off-diagonals of the variance-covariance matrix are constrained to

zero, which maintains the autoregressive structure but constrains the cross-plan premium

elasticities.

Monte Carlo Analysis

Unlike linear regression framework, failure to account for autocorrelation in the discrete

choice setting can result in large biases in the coefficient estimates of interest. The intuition

18 All cross-sectional models are based on data with one year drawn randomly from the panel for each individual, to eliminate temporal correlation. A cross-sectional multinomial probit model did not converge.

20

underlying this bias is that the coefficients in the discrete choice framework are normalized by

the variance of the error. Static approaches will result in downwardly biased estimates of the

relevant variance and hence biased estimates of parameters of interest.

In this Monte Carlo we generate data on health plan choice for 1,000 individuals over 3

years. The data generating process is constructed to mimic the data we analyze here. We allow

for four plan choices and include covariates that correspond to age, gender, premium and out-of-

pocket co-pays. The realized values of these variables are all randomly generated. Data is

generated using three different auto-regressive parameters: 0, .80, and .95. The premium

elasticity of demand is equal across plans and differs with the AR parameters with the true

elasticity being .6, .4 and .3 for AR parameters of 0, .8 and .95, respectively. We estimate the

parameters using the MNL, multinomial probit, and a multi-period, multinomial probit

approaches. Frequentist methods are used to generate the parameter estimates for the MNL and

the multinomial probit while the Bayesian approach outlined above is used to estimate the multi-

period probit model. In this analysis we focus on the elasticity estimates implied by the estimated

model.

The results show that the static models generate elasticity estimates that are significantly

biased when the true AR parameters is large.19 When the AR parameter is .8, the average bias of

the elasticity estimates from both the MNL and the MNP are upwardly biased by approximately

50%. When the true AR parameter is .95, the average bias from both the static models jumps to

over 100%. Interestingly, the flexibility of the VCV of the MNP model does not help mitigate

the bias. In sum, the results from our simple Monte Carlo exercise suggest that in the presence of

significant persistence in unobserved heterogeneity, discrete choice models will generate large

upward biases in the coefficient estimates.

19 Details of the Monte Carlo estimates are available from the authors upon request.

21

5. Results

Cost Model

The Monte Carlo chains for the cost model converge well after the initial burn-in of 500

iterations.20 Given the space constraints, the cost model contains too many parameters to report

here. However, the posterior distributions for the parameters look sensible. Costs are increasing

in age, female and CW. The model fits the data well and closely replicates the realized

distribution of costs, primarily because the panel data allows the estimation of individual-specific

intercepts. The R2 is 0.56 for claims and 0.68 for out-of-pocket expenses. In Figure 1 we present

the actual and fitted distributions of total expenditures and out-of-pocket costs. The model under-

predicts the number of zeros but otherwise does capture the skewness of both the total cost and

OOP distributions.

The results of the cost model imply that there are significant cost differentials across the

plans. This is not surprising as the plans have different provider networks ranging from a

restrictive HMO network to the open access CDHP plan. The plans also impose different out-of-

pocket payment structures that also can affect marginal utilization. For example, the HMO

generally has constant co-payments for a doctor visit while the CDHP will have very low

effective out-of-pocket expenditures for both low and high utilization, and high out-of-pocket in

the doughnut hole. These differences in plan features likely translate into important differences

in utilization and prices paid to providers which, in turn, lead to plan-specific cost differences.

To quantify the cost differentials we perform the following experiments. We take the

entire sample population and estimate their mean expenditures (the total of expenditures paid

out-of-pocket and by the plan) as if they were all to enroll in each plan. We also take the

20 Details on the convergence of the MCMC chains and estimated parameters are available from the corresponding author.

22

enrollees of each plan and estimate the costs of the enrolling that population in the other plans.

This latter exercise provides a sense of the differential selection into each plan.

Table 3 presents the results of this exercise. These results show that health status based

selection is present in our data and economically important. The realized HMO costs are

predicted to be 11% lower than if they had to treat the entire enrollment. In contrast, the per-

capita costs for the POS 1 are 18% higher, the POS 2 plan is 43% higher and the CDHP plan is

13% higher than if they enrolled the entire population. The significant cost differentials across

the plans imply that the welfare loss from premium distortions are potentially large. It is

important to note that these cost figures are total cost differentials and do not decompose

selection into easily observable, and hence contractible, and non-contractible components.

The results presented in Table 3 also suggest that the relative costs of the plans differ by

health status. For example, the cost differential between the HMO and the POS 1 plans depends

upon the health status of the comparison populations. The cost of the POS 2 plan is 38% higher

than the HMO for those who enrolled in the HMO but is 29% higher for those who enrolled in

the POS 2 plan.

Health Plan Choice Model

The posterior distribution of the parameters for the choice model is presented in Table 4.

The estimation relies heavily on the data augmentation process of sampling the unobserved latent

utilities, thus the convergence of the Monte Carlo process is somewhat slower than in the cost

model, taking 3000-4000 iterations before the variance parameters appear to converge. We used

a 4500 iteration burn-in for our analysis. For comparison purposes, Table 4 also presents the

results of a multinomial logit model, estimated using maximum likelihood methods.

The results of the AR-MNP model indicate: 1) Selection is present both on easily

observed demographics of age and gender and on the more difficult to observe health status

23

dimension; 2) Enrollees are premium inelastic particularly for the HMO and POS 2 plans; 3)

There is significant autocorrelation in the unobservable dimensions of health plan choice and this

autocorrelation is unrelated to health status; and 4) Many of these conclusions would be reversed

if one relied on the estimates of the more traditional approaches to estimating plan choice (e.g.,

MNL model.)21

Our principal focus in this analysis is on the role of selection in health plan choice. Recall

that the coefficient estimates measure the influence of the variables relative to CDHP. The

estimates in Table 4 indicate that the HMO attracts a lower-cost pool than the CDHP (and most

other plans). The HMO enrolls a younger and more male population. Furthermore, the HMO

also attracts an enrollment that has a lower concurrent weight (CW) than the other plans.

The patterns of selection are more complicated for the POS plans. All else equal, relative

to the CDHP, the POS 1 plans attract a younger population, but enrollment in the third cost tier is

more popular with those who have higher CW. Said somewhat differently, on the basis of easily

observed demographics, the POS 1 plan looks to get a better selection than the CDHP, however

examining only the health status measures the POS 1 plan appears to get some measure of

adverse selection. The lesson we take from these estimates is that adverse selection may occur

along multiple dimensions and simple approaches to risk adjustment may be incomplete and

potentially magnify the impact of selection.22

Table 5 presents the distributions of the posterior for the autocorrelation parameters and

the variance-covariance terms from the AR-MNP. As expected, there is significant persistence in

unobserved preferences towards health plans. In Table 5a, the sample means of the posterior

21 While there are important differences in the models, classic measures indicate that the AR-MNP and MNL models have similar fit. An R2 calculation based on the squared differences between 0/1 indicators of plan election and the probability of electing each plan gives a statistic of 0.42 for both models. Not surprisingly, the AR-MNP model R2 jumps to 0.81 when the 2005 enrollment is predicted conditional on the 2004 actual enrollment. This conditional prediction is not relevant to the MNL model. 22 Finkelstein and Poterba (2004) draw a similar conclusion using data from annuities markets.

24

distribution for the autocorrelation parameters are all above 0.50. Interestingly, the errors

associated with the HMO plan have a significantly lower autocorrelation than the non-HMO

plans. The mean of the posterior distribution of the HMO autocorrelation parameter is 0.58 while

the mean of the posterior distribution for the other plans in excess of 0.90.

The variance-covariance terms are presented in the Table 5b, with the implied correlation

coefficients shown in Table 5c. These estimates look quite sensible. Many of the cross health

plan covariances are significantly different from zero, with 4 of the implied correlation

coefficients in excess of 0.20. This finding, in conjunction with the AR(1) estimates,

convincingly rejects the MNL assumption of iid, homoskedastic errors. The error terms from the

POS 1 plans are all positively correlated with the plans which are closest substitutes (Tier 1 /

Tier 2 and Tier 2 / Tier 3). It is also noteworthy that there is a high correlation between the errors

in the HMO and POS 2, suggesting that they are closer substitutes than one might infer given

that they have very different provider networks.

We now turn our attention to the estimates of the premium sensitivity of health plan

enrollees. In Table 4 the parameter estimate on ln(Salaryi - Premiumj) is positive and practically

none of the posterior sample crosses zero. Increases in premiums led to decreases in enrollment.

This is true for both AR-MNP and MNL models. Table 6 quantifies the magnitudes of the

parameter estimates by presenting the own- and cross-premium elasticity estimates from our base

specification.23 For comparison purposes, Table 6 also presents the elasticity estimates from

several other estimation strategies: Classical MNL, classical nested MNL (the nests being the

POS 1 plans and the other plans), and a Bayesian AR-MNP with a diagonal covariance matrix.

Attempts to model a static MNP model had poor convergence and generated small, nonsensical

positive premium elasticities, thus the results are not presented here.

23 We combine all the POS 1 tiers in this elasticity analysis.

25

The implied price elasticities (from the enrollee’s perspective) from our base model are

low and somewhat lower than previous estimates.24 The estimated average enrollee price

elasticity is -.06. An examination of the plan-specific elasticities reveals that the low estimated

average elasticities are driven by a strong enrollee loyalty towards the HMO and POS 2 plans.

The own price elasticities for these plans are approximately -0.01 and -0.07, respectively, while

the plan-specific elasticities for the other plans are approximately -0.10. The plan-perspective

elasticities (not shown) are much larger than the enrollee perspective elasticities ranging from

-0.06 for the HMO to -1.04 for the CDHP. The cross-premium elasticity estimates reveal some

interesting asymmetric substitution patterns. The POS 1 plan is the closest substitute for all the

other plans. The CDHP is the closest substitute to the POS 1 plan.

The MNL model generates much larger price elasticities than those implied by our

primary model. This result is consistent with the Monte Carlo experiment presented in the

previous section. The mean price elasticity across plans and enrollees from this model is -.14

with non-HMO plan elasticities ranging from -.26 to -.36. Our results reject the underlying

assumptions of the MNL model in this population; and, in so far as the importance of persistence

in enrollee unobserved heterogeneity generalizes to other settings, it suggests that the widespread

use of the iid, MNL model may be significantly inflating health plan elasticity estimates.

Estimated elasticities from the nested MNL are approximately half as large as the MNL

suggesting that allowing for simple forms of heteroskedasticity in the plan choice framework

reduces but does not eliminate bias. The implied own-price elasticities estimates from the AR-

MNP models with the constrained variance matrix imply elasticity estimates that are closer to

our primary model than the logit models. In the discrete choice context, the magnitude of the bias

24 For example, Royalty and Solomon (1999) estimate health plan elasticities for Stanford University employees between -.2 and -.3. Using a very different sample of Medicare beneficiaries, Atherly, Dowd, Feldman (2004) and estimate an out-of-pocket premium elasticity for enrollment in Medicare HMOs of -.13.

26

is increasing in the autoregressive parameter, and our estimated AR coefficient is generally quite

large. We have performed Monte Carlo analyses that also find that the coefficient bias is, in fact,

increasing in the AR parameter.

Not surprisingly, the cross-price elasticities from the constrained model differ from our

base specification. The fact that the AR models generate similar own-price elasticities that are

significantly smaller in magnitude than all the static models suggests that the bias in the own

price estimates is a consequence of a failure to account for persistence in unobserved plan choice

preferences.

The estimated cross-price elasticities (and their economic implications) implied by the

MNL and nested MNL models are very different from those implied by the AR-MNP,

highlighting again that the functional form assumptions of these MNL can drive the estimates.

For example, the MNL estimates suggest that the HMO is the closest substitute for all of the

plans because it has the largest share. The AR-MNP estimates imply that the HMO, the only

option with a closed provider panel, is not the closest substitute for any of the other plans.

While not shown in detail here, we further explore the nature of health plan choice by

constructing elasticity of demand estimates by age, gender and health status. There is a literature

that argues that the healthy are more premium sensitive than the sick and these differential

elasticities affect the dynamic stability of health plan premium setting. In general, our results are

not consistent with this view. In the AR-MNP, there are no differences in the elasticities by

gender and modest differences by age. The mean elasticity for the non-HMO plans for enrollees

30 years and younger is -0.12 while for those enrollees who are 45 years of age and older the

corresponding elasticity is -0.09. We also find there are virtually no differences in the elasticities

across health status quartiles. The lowest CW score quartile has an elasticity of -0.10 for the non-

HMO plans while the highest risk quartile has an elasticity of -0.09.

27

Our estimates suggest that unobserved factors affecting enrollees’ plan choice are highly

persistent. There are two classic explanations for this persistence. First, persistence could be a

function of unobserved preference heterogeneity – enrollees have strong preferences for plans

and those preferences do not change over time. Second, persistence could be endogenously

generated via switching costs. Once an individual enrolls in a plan they develop plan-specific

capital and provider-specific relationships that increase the utility of the plan relative to the

alternatives. Handel (2010) finds evidence of large switching costs in his setting.

As noted by Heckman (1981), distinguishing unobserved heterogeneity from switching

costs can be difficult. However, the richness of our data allows us to construct a reasonable,

indirect test of whether the causes of plan “stickiness” differ by health status. The importance of

switching costs should differ by health status – sicker enrollees have more interactions with their

providers and with the health plan and those interactions carry greater health consequences for

sicker enrollees. Thus, if switching costs are important, sicker enrollees should display more

persistence in their health plan choice than their healthier counterparts. The logic underlying this

test is similar to Strombom, Buchmueller and Feldstein (2002) who use a MNL framework and

find that plan enrollees with a previous admission or cancer diagnoses are less likely to switch

plans.

In order to investigate whether enrollees in our data displayed similar patterns in plan

choice we divide the sample into four quartiles based on health status (CW) and allowed the AR

parameters to vary across the quartiles. In this model, the AR(1) coefficients were held constant

across plans.

Table 7 presents the coefficient estimates from this exercise. The results indicate that

there are statistically significant differences between the healthy and the sick in the

autoregressive coefficient, but the magnitudes are not economically important. The implied

28

premium elasticities between the healthiest and sickest cohorts are essentially identical. Our

estimates do not provide much support for the notion that the healthy are more premium

sensitive and experience less health plan inertia than the sick. That, in turn, suggests that

persistence in health plan choice is a consequence of unobserved heterogeneity and not switching

costs.

The results from the cost and health plan choice models suggest that there is 1) health

plan selection based on easily-observed and hard-to-observe differences in health status; and 2)

employees are relatively premium insensitive when selecting a plan. Thus, the importance of

selection on welfare is unclear. Clearly, the presence of differential selection opens up the

possibility that it may result in large premium distortions as suggested by Culter and Reber

(1998). However, the low premium response of enrollees mitigates the impact of these premium

distortions on plan selection and total welfare. To investigate the direction and magnitude of the

welfare consequences requires simulating the impact of alternative premiums setting strategies

on enrollee wellbeing and that is the subject of the next section.

6. Welfare Analysis of Alternative Premium Setting Strategies

The influential Jackson Hole group sought to bring the beneficial effects of market forces

to the health care sector, and one important feature of its managed competition strategy was to

force employees to face the cost differential between different health plans (Enthoven and

Kronick, 1989a and 1989b). However, as noted by Newhouse (1996), Cutler and Reber (1998),

and Cutler and Zeckhauser (2000), unless the premium setting strategy accounts for health status

based selection, managed competition can lead to inefficient premiums. Cutler and Reber (1998)

argue that, in fact, Harvard University’s implementation of this managed competition approach

to premium setting led to significant selection induced welfare loss.

29

In our context, the welfare harm arises because the individuals sort into plans where the

relative (to other plans) cost of their enrollment is greater than the relative utility of that plan. In

order to measure the welfare harm associated with this suboptimal premium setting, we calculate

the impact of alternative premium setting strategies on the compensating variation of employees,

treating the self-insured organization’s health care budget as fixed.25 The optimal set of

premiums would maximize the utility of enrollees given this fixed budget.

As we have estimated the structural indirect utility parameters, it is straightforward to

perform counterfactual premium experiments via simulation. In each of these experiments we

calculate the expected utility from alternative premium strategies and then find the change in

salary for each individual in our data that would make them indifferent between the new

premium vector and the old premium vector.

More formally, letting Pij denote the probability of individual i of selecting plan j, and

letting Wij denote the estimated expected utility of individual i enrolling in plan j conditional on

choosing plan j, we find the compensating variation, CV, such that:

.

Here, Oldprem and Newprem are the base level premium and the new premium in the

experiment, respectively. In the risk adjustment experiments, we use the 2005 data and

employer’s actual 2005 premium level as the comparison point. We explored the welfare impact

25 If the cost differentials between plans are solely a consequence of differential prices paid to providers and not moral hazard then our approach would still capture the welfare loss as the cost differentials still lead to distorted plan choices given those costs.

30

of shifting to four possible premium-setting scenarios.26 The first three of these scenarios are

strategies that are used by employers, with the first two being the most common. The third

strategy is a modestly sophisticated risk adjustment approach that requires the analysis of

previous claims data. The fourth strategy is the optimal strategy modified from Cutler and Reber

(1998). In each of the scenarios below, is the expected average cost of plan j

conditional on the resulting employee premiums (and the characteristics of the plan j’s

enrollees). In addition, in each of the four scenarios, employee premiums were set so that the

average employer contribution remained at $1,726, the actual 2005 average annual employer

contribution.

1. Fixed percent of premium: where is chosen to

meet the target employer contribution. 2. Fixed dollar contribution with no risk adjustment:

where F is set equal to the target employer contribution. 3. Fixed dollar contribution adjusted to the average population risk:

where is the average concurrent weight

across all employees and is the average concurrent weight of plan j enrollees. Here

the nominal F is adjusted so that the actual average employer contribution matches the target.

4. Optimal Premiums: The differential between the premium for plan j and the HMO is set equal to the weighted difference in plan costs across employees, where the weight is the marginal probability of enrollment for each individual:

The HMO premium, on which all other plan premiums are based is then selected so that the average employer contribution matches the target. This is a generalization of the optimal premium setting strategy as characterized by Cutler and Reber (1998), to a setting with more than two plan options in a random utility environment. This is not a first best outcome, but rather, the maximized utility subject to the constraints of a fixed employer contribution and that enrollees face the same premium schedule.

26An obvious strategy to explore is the Nash premium outcome. However, because our estimated plan perspective elasticities are low at the current premiums, the Nash equilibrium would result in equilibrium premiums an order of magnitude larger than our the current premiums and thus seems to be of little practical relevance.

31

The fixed percent of premiums strategy can be viewed as a crude mechanism to risk

adjust premiums as individuals do not fully incur the cost differential of enrolling in high cost

plans. The fixed dollar contribution is a strategy that promotes the efficient allocation of

enrollees across plans; the high cost plans are not subsidized for higher health care risk, and

enrollees join high cost plans if the utility of those plans exceeds the increased cost. The risk

adjusted, fixed dollar premium is the strategy promoted by the early advocates of managed

competition and attempts to maintain the efficiency aspects of the fixed dollar approach while

mitigating the impact of adverse selection. The optimal premium difference between plans is

given by the difference in the marginal cost of the plans for the marginal enrollee. This is the

approach we take in implementing the optimal premium in this experiment.

As mentioned above, by 2005 this employer partially risk adjusted the premiums using an

ad hoc approach. So the baseline premiums should not be viewed as representing a state “no risk

adjustment,” but rather are crudely risk adjusted using an ad hoc risk approach.

The results of this simulation are presented in Table 8. The premiums based on fixed

employer contribution, with and without risk adjustment, are very different from the baseline

premiums levels. The HMO becomes significantly cheaper and the CDHP plan is much more

expensive. All of the premium setting strategies yield welfare improvements. However, despite

the large changes in premiums, the magnitudes of the increases are very modest. The best

performing strategies are the nearly identical third and fourth scenarios, which result in a

compensating variation decrease of approximately $13, or 0.5% of average total health care

expenditures. It is significant that the optimal strategy can be achieved using a fairly simple risk

adjustment methodology when historical health claims data are available.

In order to get a sense of the importance of the underlying model in affecting welfare

conclusions, we also calculate the welfare using the estimates from the Multinomial Logit model.

32

The implied estimated improvement in welfare is significantly higher for the MNL. The welfare

gain from the optimal premium is $275 or 10% of total expenditures – more than 20 times the

estimates from our base model. So not only does it appear that the MNL approach (and its static

cousins) yield biased estimates of the elasticities, it also affects welfare inferences.

Cutler and Reber (1998) find that moving to a fixed contribution setting from one that

subsidized high cost plans at Harvard University increased health status based selection and

results in welfare loss of between 2 to 4 percent of baseline spending. To compare our results to

Cutler and Reber’s, simply difference the compensating variation values of scenarios (2) and (1)

in Table 8. Our results indicate that a change in premium setting strategy such as the one that

occurred at Harvard would actually induce a small welfare gain of $0.84. Our results differ from

Cutler and Reber’s, in part, because of the difference in the estimated premium elasticities.

Cutler and Reber estimate the average out-of-pocket premium elasticity between -0.3 and -0.6 –

a figure that is five to ten times larger than our estimates. The lower the price sensitivity, the

lower the welfare loss due to adverse selection as premium distortions do translate into

distortions in the distribution of enrollees across health plans. Our welfare loss magnitudes are

similar to those in Einav, Finkelstein and Cullen (2010). They estimate the welfare loss from

adverse selection to be $9.55 per year for enrollees in a large multinational firm.

In Table 9 we analyze the distribution of the welfare impact of the different premium

setting strategies across employees. In general, the low salary, healthier and younger employees

see an increase in their welfare from risk-adjusting premiums, while older, sicker employees and

those with higher salaries see a decline in welfare. This finding highlights that employers may be

hesitant to risk-adjust premiums not only because the average welfare gain may be small, but

also because they have other goals besides maximizing total employee welfare subject to an

expenditure constraint. Executives and administrators who make health benefit decisions are

33

likely to be older and better paid and thus would likely be made worse off under a risk

adjustment scheme. In addition, the firm may seek to transfer welfare from the healthy to the sick

and, in our context, risk-adjusting premiums would undermine that goal.

In sum, in our setting, there is significant health status based selection into health plans.

The magnitude of selection can be seen by examining the large differences between the risk-

adjusted premiums and the actual premiums set by the employer. However, the welfare impact of

this selection is small. This finding highlights that most economists’ intuitive reaction that

selection must lead to market distortions is not necessarily correct. The welfare loss will be a

potentially complex function of both the degree of selection, the price elasticity of demand and

the cost-differentials across plans.27

7. Conclusion

Using flexible models of health insurance choice and medical care expenditures that

remove many of the unappealing assumptions of traditional approaches, we estimate the welfare

impact of cost-based health plan selection. Our estimates suggest that adverse selection is present

and economically important – there are significant mean cost differences across plans as a

consequence of differential enrollee health status. Importantly, this selection does not translate

into significant welfare loss induced by pricing distortions and the implementation of risk-

adjusted premiums only improves welfare marginally. This finding highlights the tension

between health insurance competition, cost-based selection and efficiency. Welfare loss due to

selection is low because premium elasticities are low. However, since estimated premium

elasticities are low it suggests that market-based health plan competition will not result in

premiums near marginal cost. The standard prescription to resolve these conflicting incentives

27 Newhouse (1996) points out that increasing competition in health insurance markets can result in larger welfare loss do to selection. Our results are consistent with that observation, as competition should lead to larger premium elasticities and thus larger distortions.

34

induced by health plan competition is to risk-adjust premiums. While this strategy can certainly

solve the selection problem, and in our experiment led to a nearly-optimal premium

configuration, risk adjustment has historically been difficult to implement and is the exception in

employment-based health insurance (Kennen et al., 2001). Our results suggest why this is the

case.

35

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Table 1 Annual premiums and health plan shares 2002-2005

2002 2003 2004 2005

Share

Premium ($)

Share

Premium ($)

Share

Premium ($)

Share

Premium ($)

HMO .622 0.00 .688 0.00 .688 382 .686 408

Tier 1 .077 0.00 .044 21 .040 741 .047 770

Tier 2 .096 242 .082 247 .080 1,064 .072 1,074 POS 1

Tier 3 .073 522 .095 512 .050 1,474 .031 1,721

POS 2 .090 1,346 .060 1,258 .064 1,463 .086 783

CDHP .041 329 .061 194 .074 670 .073 793

Table 2 Demographics and health status by plan (standard deviations in parentheses)

POS

All Enrollees

HMO Tier 1 Tier 2 Tier 3

POS2

CDHP

Age 46.0 (11.4)

44.3 (11.4)

47.5 (9.8)

48.7 (10.2)

48.5 (10.0)

52.1 (10.3)

50.4 (10.5)

Percent Female

62.5 (48.4)

59.2 (49.1)

76.0 (42.7)

71.6 (45.1)

64.2 (48.0)

71.9 (44.9)

63.8 (48.1)

Salary ($) 48,810 (25,127)

45,249 (21,920)

51,489 (25,197)

49,149 (21,950)

53,772 (29,127)

61,283 (32,761)

65,096 (33,757)

Concurrent Weight

1.78 (3.30)

1.47 (2.76)

2.59 (4.42)

2.22 (3.26)

2.41 (2.76)

2.85 (3.96)

2.14 (3.85)

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Table 3 Estimated per enrollee cost of alternative enrollments

Estimated Annual Per-Capita Cost ($) if Enrolled

in Plan HMO POS 1 POS 2 CDHP

HMO 1,727 2,471 2,377 2,928 POS 1 2,323 3,227 3,077 3,898 POS 2 2,929 3,897 3,771 5,026

Currently Enrolled in Plan

CDHP 2,178 2,970 2,956 3,716 All in One Plan 1,941 2,731 2,630 3,289

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Table 4 Posterior means and coefficient point estimates for choice models (standard deviations of posterior in parentheses) [standard errors in brackets]

Parameter Bayesian AR(1)

Probit Classical MNL HMO Intercept 1.7306 *** 5.9475 +++ (0.1405) [0.6413] POS 1, Tier 1 Intercept 0.4449 *** 2.3547 +++ (0.1163) [0.8138] POS 1, Tier 2 Intercept 0.2987 ** 2.6903 +++ (0.1211) [0.7172] POS 1, Tier 3 Intercept 0.2838 *** 2.6077 +++ (0.1128) [0.7722] POS 2 Intercept 0.1782 1.5955 + (0.1235) [0.9356] HMO Age -0.0168 *** -0.0670 +++ (0.0025) [0.0104] POS 1, Tier 1 Age -0.0083 *** -0.0452 +++ (0.0022) [0.0147] POS 1, Tier 2 Age -0.0054 *** -0.0361 +++ (0.0021) [0.0123] POS 1, Tier 3 Age -0.0037 * -0.0309 ++ (0.0020) [0.0129] POS 2 Age 0.0002 -0.0082 (0.0022) [0.0159] HMO Female -0.4624 *** -1.4261 ++ (0.1447) [0.6507] POS 1, Tier 1 Female -0.1887 -0.5932 (0.1216) [0.9150] POS 1, Tier 2 Female -0.1677 -0.9128 (0.1169) [0.8141] POS 1, Tier 3 Female -0.1045 -0.3820 (0.1207) [0.8550] POS 2 Female -0.2095 -0.5777 (0.1388) [0.9895] HMO log(Health Status) -0.0186 *** 0.0269 ++ (0.0073) [0.0125] POS 1, Tier 1 log(Health Status) 0.0063 0.0223 (0.0070) [0.0180] POS 1, Tier 2 log(Health Status) 0.0065 0.0252 (0.0069) [0.0157] POS 1, Tier 3 log(Health Status) 0.0131 ** 0.0073 (0.0069) [0.0165] POS 2 log(Health Status) 0.0138 * 0.0189 (0.0074) [0.0186]

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Table 4, continued Posterior means and coefficient point estimates for choice models (standard deviations of posterior in parentheses) [standard errors in brackets]

Parameter Bayesian AR(1)

Probit Classical MNL HMO Female x Age 0.0079 *** -0.0761 (0.0030) [0.0483] POS 1, Tier 1 Female x Age 0.0051 ** 0.0976 (0.0026) [0.0735] POS 1, Tier 2 Female x Age 0.0049 * 0.1524 ++ (0.0024) [0.0600] POS 1, Tier 3 Female x Age 0.0019 0.1681 ++ (0.0025) [0.0670] POS 2 Female x Age 0.0054 ** 0.1707 ++ (0.0028) [0.0713] log(Salaryi-Premiumj) 1.5253 ** 19.2587 +++ (0.6302) [3.7340] E(logOOP) -0.0242 ** -0.0699 (0.0119) [0.1128] Var(logOOP) -0.0078 0.0454 (0.0064) [0.0601] Office Visit Copay -0.0130 *** -0.0378 +++ (0.0016) [0.0115]

* 90% Bayesian confidence interval excludes zero. + 90% classical confidence interval excludes zero. ** 95% Bayesian confidence interval excludes zero. ++ 95% classical confidence interval excludes zero. *** 99% Bayesian confidence interval excludes zero. +++ 99% classical confidence interval excludes zero.

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Table 5 Estimated parameters of variance matrix

Table 5a – AR(1) parameters AR(1) Model

HMO POS 1, Tier 1 POS 1, Tier 2 POS 1, Tier 3 POS 2 CDHP Rho 0.6065 *** 0.9895 *** 0.9790 *** 0.9551 *** 0.9966 *** 0.9966 *** (0.0271) (0.0094) (0.0149) (0.0232) (0.0033) (0.0033) Tau2 0.0891 *** 0.1100 *** 0.1104 *** 0.0989 *** 0.1193 *** (0.0095) (0.0133) (0.0135) (0.0116) (0.0144)

Table 5b – Across-plan variance/covariance matrix Across-Plan Variance-Covariance Matrix (std dev) HMO POS 1, Tier 1 POS 1, Tier 2 POS 1, Tier 3 POS 2 HMO 1.0000 *** (0.0000) POS 1, Tier 1 0.2188 *** 0.1916 *** (0.0407) (0.0341) POS 1, Tier 2 0.0420 0.0302 * 0.1619 *** (0.0439) (0.0161) (0.0329) POS 1, Tier 3 0.0677 ** 0.0073 0.0650 *** 0.1862 *** (0.0325) (0.0140) (0.0267) (0.0439) POS 2 0.2520 *** 0.0517 *** -0.0150 0.0216 0.2595 *** (0.0414) (0.0194) (0.0180) (0.0188) (0.0499)

Table 5c – Across-plan implied correlation coefficients Implied Across-Plan Correlation Coefficients HMO POS 1, Tier 1 POS 1, Tier 2 POS 1, Tier 3 POS 1, Tier 1 0.4998 POS 1, Tier 2 0.1045 0.1713 POS 1, Tier 3 0.1569 0.0388 0.3744 POS 2 0.4948 0.2318 -0.0732 0.0983

* 90% Bayesian confidence interval excludes zero. ** 95% Bayesian confidence interval excludes zero. *** 99% Bayesian confidence interval excludes zero.

44

Table 6 Own- and Cross-Price Elasticities

AR(1) Multinomial Probit Elasticities: Unconstrained Covariance Matrix (Base Model)

HMO POS 1 POS 2 CDHP HMO -0.007 0.014 0.017 0.012 POS 1 0.017 -0.104 0.048 0.140 POS 2 0.003 0.008 -0.068 0.017 CDHP 0.002 0.018 0.015 -0.103

Multinomial Logit HMO POS 1 POS 2 CDHP HMO -0.054 0.120 0.113 0.124 POS 1 0.078 -0.417 0.095 0.087 POS 2 0.023 0.030 -0.293 0.030 CDHP 0.024 0.026 0.028 -0.306

Nested Logit HMO POS 1 POS 2 CDHP HMO -0.052 0.106 0.095 0.110 POS 1 0.081 -0.344 0.068 0.093 POS 2 0.006 0.006 -0.250 0.008 CDHP 0.032 0.035 0.034 -0.265 AR(1) Multinomial Probit Elasticities: Diagonal

Covariance Matrix HMO POS 1 POS 2 CDHP HMO -0.011 0.030 0.027 0.047 POS 1 0.017 -0.147 0.046 0.134 POS 2 0.004 0.011 -0.106 0.029 CDHP 0.006 0.027 0.025 -0.196

Note: Cell entry i,j, where i indexes row and j column, give the percentage change in market share of i with a 1% increase in the price of j.

45

Table 7 AR(1) coefficients by risk group

AR Coefficient Sample Mean (std dev) of Posterior

Healthiest Quartile 0.8564 *** (0.0189) 2nd Quartile 0.8442 *** (0.0177) 3rd Quartile 0.9226 *** (0.0221) Sickest Quartile 0.9152 *** (0.0190)

*** 99% Bayesian confidence interval excludes zero.

46

Table 8 Employer pricing scenarios – Impact on welfare and claims cost Annual Employee Contribution

Actual % of

Premium

Fixed $, no Risk

Adj

Fixed $, w/ Risk

Adj Optimal Premium

HMO $408.20 $466.18 $112.06 $250.12 $230.36 Tier 1 $769.60 $809.64 $1,470.30 $1,223.04 $1,262.30 Tier 2 $1,073.80 $815.36 $1,491.10 $1,237.60 $1,248.26 POS 1 Tier 3 $1,721.20 $823.42 $1,518.14 $1,150.76 $1,311.96

POS 2 $782.60 $809.38 $1,466.92 $768.30 $899.86 CDHP $793.00 $1,019.20 $2,301.26 $2,015.00 $1,965.60 Compensating Variation -- ($7.68) ($8.52) ($12.74) ($12.81) std dev 13.5 67.4 35.8 41.5

Break-Down of Average Annual Per-Capita Costs 1 a. Employer Contribution $1,726 $1,726 $1,726 $1,726 $1,726 b. Employee Contribution $591 $589 $563 $568 $568 c. Plan Cost (1a+1b) $2,316 $2,314 $2,289 $2,294 $2,294 2. Ave Employee OOP Cost $368 $366 $359 $361 $361 3. Total Claims Cost (1c+2) $2,684 $2,680 $2,648 $2,655 $2,655

47

Table 9 Employer pricing scenarios – Distribution of welfare

Count Ave Age

% Female

Ave cwt

Average Income

Average Compensating

Variation Current Premiums 3578 47.0 62% 1.857 $49,299 --- % of Premium Benefit/Same 2565 49.1 72% 2.408 $51,547 ($14.24) Harmed 1013 41.8 38% 0.461 $43,608 $8.93 Total 3578 47.0 62% 1.857 $49,299 ($7.68) Fixed $, no Risk Adjustment Benefit/Same 1811 38.5 52% 1.147 $44,347 ($61.18) Harmed 1767 55.7 73% 2.584 $54,375 $45.45 Total 3578 47.0 62% 1.857 $49,299 ($8.52) Fixed $, with Risk Adjustment Benefit/Same 2230 41.1 60% 1.452 $45,975 ($33.39) Harmed 1348 56.8 67% 2.527 $54,798 $21.41 Total 3578 47.0 62% 1.857 $49,299 ($12.74) Optimal Premium Benefit/Same 2104 39.8 58% 1.297 $45,507 ($35.95) Harmed 1474 57.4 70% 2.655 $54,712 $20.21 Total 3578 47.0 62% 1.857 $49,299 ($12.81)

48

Figure 1 Comparison of actual and predicted claims and out-of-pocket payments