health insurance and the demand for medical care: evidence ...hmlien/social...

Health Insurance and the Demand for MedicalCare: Evidence from a Randomized Experiment

Willard G. Manning et al. (1987)

June 1, 2007


Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment

Introdution and literature

I Medicare costs have grown about 4% per year in real terms in1940’s-1980’s.

I A prominent explanation: generated demand for medicalservice and health insurance. But no literature has shown that.

I Coinsurance elasticity:I If insurance was treated as endogenous variable (selection

issuea): the coinsurance elasticity is not significant (Newhouseand Phelps (1976)).

I If insurance was treated as exogenous variable: The coinsuranceelasticity is significant. (the elasticity is around -0.1 to -2.1) ⇒Mainly in natural experiments research.



Introdution and literature

Several objectives of HIE (Rand Health Insurance Experiment):

I Uncertainty about how demand responds to insurance-inducedchanges in price.

I Learn the behavior of poor individuals’ insurance throughpublic program.

I Learn if insurance elasticity differed for various medical service.

I Quantify how the change in the consumption of medical servicemight affect health.

I Determine whether any reduced use of service affect healthstatus. (HMO system)



Data and the design of the HIE

I Data: The HIE enrolled families in six cities, betweenNovember 1974 and February 1977.

I Two service system:I Prepaid system (ex. HMO)– separate group.I Free-for-service (FFS)– the main focus of this paper.

I Plans of FFS insurance:I Different coinsurance rate, ex. 0, 25, 50, or 95 percent.I Each plan has upper limit on annual out-of-pocket (MDE)

expense, ex maximum of $1000.

I Select families to these insurance randomly.

I Subsidy to the experiment family: (1) Lump sum subsidy to allfamilies, (2) Unanticipate increase in the lump sum payment to40% families.



Sample

I Sample: Random sample of each city’s nonaged population,but excluding some groups.

I Dependent variables: The use of medical service (ruling outoutpatient psychotherapy and dental services)

I Independent Variables:I Insurance plan variables:

1 The free plan;2 25% coinsurance rate;3 50% coinsurance rate;4 95% coinsurance rate;5 Individual deductible – 95% coinsurance rate for outpatient

service, and free for inpatient care (has upper limit)

I Other covariates: Age, sex, race, family income, health status,family size and city.



Statistical Methods

I Three characteristics of distribution of medica expenses:I A large proportion use no medical services.I Medical expense is Highly skewed.I Distribution is different between outpatient use and inpatient

use.

I Method: ANOVA and the four-equation model.



The four-equation model

1 The 1st equation: A probit equation to estimate the probabilityof receiving any medical service.

2 The 2nd equation: A probit equation to estimate theprobability of having at least one inpatient stay (given somemedical use).

3 The 3rd equation: A linear for log(expense) of outpatient-onlyusers.

4 The 4th equation: A linear for log(expense) of both inpatientand outpatient users.



Main effects in ANOVA (Table 2)

Clearly show that the use of medical services responds to thechanges in the coinsurance rate.

I The expense (and visit number) on the free plan are higherthan those on the plan with the higher coinsurance rate.

I The largest decrease in the use of outpatient service occursbetween the free and 25% plans.

I There are no significant differences among the family-pay plan(20, 50 and 95 percent) in the inpatient service. ⇒ due to theeffect of the upper limit on out-of-pocket expenses ($1000).

I Total expenditures on the plan of Individual deductible aresignificant less than the free plan.



Main effects in the four-equation model (Table 3)

I The pattern is similar to table 2.

I Outpatient-only cost sharing (Individual deductible plan)reduces total expenditures relative to free care, largely byreducing the likelihood of any use.



Main effects across income groups (Table 4)

I Likelihood of any use: Significant increase with income, withlarge increase for the family-pay plans.

I Likelihood of one or more admissions (for inpatient stay):insignificant decrease with income (due to the upper limit).

I Expenses: U-shaped response with income.



Main effects across age groups (Table 5)

I Children are less responsive for inpatient care.

I Adults have significant lower use of inpatient services on thefamily-pay plans than on the free plan.

I For other subgroups, for example, health status (healthy v.s.sickly), there is no evidence to show the differential response tohealth insurance coverage between these two subgroups.



Other results

I Health status outcome: Patients with The relatively prevalentchronic problems (high blood pressure, myopia) have specificgains in use of free FFS rather in use plans with cost sharing.

I HMO results (table 7):I Same rate of using service among the plans.I The participants with one or more hospital admissions differs

with plans.



Conclusions

1 The coinsurance elasticity (demand for medical care): around-0.1 to -0.2.

I Estimating a pure coinsurance elasticity (table 8)I Using indirect utility function:-0.18I Similar calculation to the literature (table 9): -0.10 to -0.21

range.

2 The change of insurance can only explain only a small part ofthe increase in health expenditures.(table 10)



Conclusions

3 Welfare loss moving from 95 percent plan (with a $1000 MDE)to the free care plan is $37 to $60 billion.(It may be overstatedby ignoring externalities)

4 Reject the hypothesis that increased coverage of outpatientservices, holding constant the coverage of inpatient service, willreduce expenditure.⇒ As table3 shows, expenditure on theindividual deductive plan (costly outpatient) is 20 % less thanon the free plan(free outpatient)



Appendix: Two-part model

I Two-part model(2PM):1st part: pr(y > 0|x) is binary probability model2nd part: (ln(y)|y > 0, x) = xβ + εLet y denote health expense; x denotes coinsurance rate and othercovariates.

I The purpose of 2PM is to use there two equations to retransformate theE(y|x) ⇒.

E(y|x) = pr(y > 0|x) · E(y|y > 0, x) + 0

= p̂(x) + E[exp(xβ̂) + ε]

I Properties of y:

(1) y >= 0(2) y = 0 is observed sufficiently frequently and can’t be ignored.(3) Distribution of y is skewed.



Appendix: Two-part model (cont.)

I Error term (ε) issue: Smearing estimator (Duan (1983))

Let smearing estimator φ =P

exp(ε̂i)ni

= E(exp(ε̂i)), where ni is the

number of y > 0 and ε̂i = ln(y)− xβ̂

I Expected expenditure for y > 0

E(y|y > 0, x) = E(exp(xβ̂ + ε̂))

= exp(xβ̂) · E(exp(ε̂))

= exp(xβ̂) · φ

I Expected expenditure

E(y|x) = p̂(y > 0|x) · exp(xβ̂) · φ



Appendix: Four-part model (HIE project)

Denote the expense of inpatient: yi; expense of outpatient: yo; totalexpense: y.

I Equation (1): Use probit model to estimate the probability of having anymedical service ⇒ p̂i = φ(xβ̂1)

I Equation (2): Use probit model to estimate the probability for a medicaluser to have any inpatient use ⇒ π̂i = φ(xβ̂2)

I Equation (3) – outpatient expense:⇒ ln(yo) = xβ3 + εo

⇒ Retransformate to get the estimated outpatient expense.⇒ E(yo|yo > 0, x) = exp(xβ̂3) · φ̂3

I Equation (4) – inpatient expense:⇒ ln(yi) = xβ4 + εi

⇒ E(yi|yi > 0, x) = exp(xβ̂4) · φ̂4



Appendix: Four-part model (HIE project)

According to Equation (1) – (4):

I The expected total expense is:

E(y|x) = P (y > 0, x) · E(y|y > 0, x) + 0 · E(y|y = 0, x)

= P (y > 0, x) ·[(1− π)E(yo|yo > 0, x)

+ πE(yi|yi > 0, x)]+ 0

⇒ E(y|x) = p̂[(1− π̂)exp(xiβ̂3)φ̂3 + π̂exp(xiβ̂4)φ̂4]As reported in pp. 257 in the paper.



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