Panel Data Sample Selection Model: an Application to Employee Choice of Health Plan Type and Medical Cost Estimation

This paper utilizes a nonparametric panel data sample selection model to correct selection bias in the analysis of longitudinal medical claims data. Selection bias in the health economics data is a common problem and many health economists have used Heckman type selection models in cross-sectional analyses. Since longitudinal data structure is common in health economics data, especially medical claims data, the correction of selection bias in the longitudinal sense is especially valuable for health economics related researches. The complicated modeling and extensive computer programming needs, however, resulted to only a few health economics researches in this direction. This paper suggests a relatively simple estimation framework to correct sample selection bias in longitudinal data. An example of health care utilization of PPO type plan holders in an employee pool is also provided as follows: in the first step, a random effect panel data probit model was used to estimate each employee’s choice between HMO type plans and PPO type plans; in the second step, a nonparametric fixed effect panel data selection model, using the estimates from the first step, was used to estimate the medical expenditures of PPO plan holders (similar to Kyriazidou, Econometrica 1997). Since the second step estimation can be expressed as a weighted least squares regression, this framework is simple to use, but among others, this nonparametric framework is robust from any parametric misspecification and free from a controversial health econometric problem called retransformation in two part model (Manning, Journal of Health Economics 1998; Mullahy, Journal of Health Economics 1998; Ai and Norton, Journal of Health Economics 2000). There are some interesting results from this example, but among others, the selection bias influenced significantly on the Age effect of medical expenditures. Since there were more young employees in the HMO plan holders, the Age effect of PPO plan holders was almost doubled after considering for selection bias