essays in public finance and industrial organization a dissertation ...

CHAPTER 2. HEALTH PLAN CHOICE 78
an idiosyncratic preference εhj, and household health risk. Our measure of household
health risk is aggregated from the individual level. For each individual i, we decom-
pose health risk into the observable risk score ri and additional privately known health
factors µi. The µis capture information about health status that may affect choice
behavior, but is not subject to risk adjustment. Equivalently, we can interpret µi as
measurement error in the risk score. We assume that each µi is an i.i.d. draw from a
normal distribution with mean zero and variance σ 2 µ, and that the idiosyncratic tastes
εhj are i.i.d. type I extreme value random variables (i.e. logit errors).
We handle heterogeneity in household size and composition by assuming that,
apart from the treatment of health risk, each household behaves as if it had a rep-
resentative member with characteristics equal to the average of those of household
members. 13 We parameterize household risk using two variables: the average risk
of household members (i.e. the average of the ri + µi) and an indicator of whether
the household includes a high risk member. We define high risk as being above 2.25,
which corresponds to the 90% percentile of the observed risk score distribution. The
other household characteristics in the model are the averages of age and the male
indicator among covered household members as well as imputed household income. 14
In addition to the employee contribution, plan characteristics φj include a dummy
variable for plan (the network HMO and PPO and the integrated HMO and POS),
the relevant coinsurance rate and deductible for the given employee, and an indicator
of non-standard drug coverage. 15 To be consistent with our approach to household
h, letρh be the nominal contribution and τh the household’s marginal tax rate. The tax adjusted
contribution is ph =(1− τh)ρh.
13 We experimented with estimating different weights for household members, and also with restricting
the sample to individual enrollees. Neither has much effect on our results. The Appendix
includes individual enrollee estimates.
14 We impute taxable income for each household in our sample by estimating a model of household
income as a function of worker age, sex, family structure, firm size and industry using data from the
Current Population Survey for 2004 and 2005 on workers with employer-sponsored health insurance
in the corresponding state. We then use the model to impute household income for each employee in
our data incorporating random draws from the posterior distributions of the regression coefficients
and the standard deviation of the residuals. Based on these predictions, we use Taxsim to calculate
marginal tax rates based on federal, state, and FICA taxes making some assumptions on the correlation
of coverage tier with filing status and number of dependents. The average taxable family
income and marginal tax rate for workers in our sample are about $73,00 and 41%, respectively.
15 While the prescription drug coverage for each plan is complicated, comprised of both formulate