Estimating the Effects of Covariates on Health Expenditures, Issue 7942
National Bureau of Economic Research, 2000 - Analysis of covariance - 60 pages
This paper addresses estimation of an outcome characterized by mass at zero, significant skewness, and heteroscedasticity. Unlike other approaches suggested recently that require retransformations or arbitrary assumptions about error distributions, our estimation strategy uses sequences of conditional probability functions, similar to those used in discrete time hazard rate analyses, to construct a discrete approximation to the density function of the outcome of interest conditional on exogenous explanatory variables. Once the conditional density function has been constructed, we can examine expectations of arbitrary functions of the outcome of interest and evaluate how these expectations vary with observed exogenous covariates. This removes a researcher's reliance on strong and often untested maintained assumptions. We demonstrate the features and precision of the conditional density estimation method through Monte Carlo experiments and an application to health expenditures using the RAND Health Insurance Experiment data. Overall, we find that the approximate conditional density estimator that we propose provides accurate and precise estimates of derivatives of expected outcomes for a wide range of types of explanatory variables. We find that two-part smearing models often used by health economists do not perform well. Our results, both in Monte Carlo experiments and in our real application, also indicate that simple one-part OLS models of level health expenditures can provide more accurate estimates than commonly used two-part models with smearing, provided one uses enough expansion terms in the one-part model to fit the data well
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1st order OLS 2-part Derivative Evaluation 4th order CDE 4th order OLS A2 for measures age2 Appendix Table A2 approximation average derivatives calculate CDE model coinsurance rate conditional density estimation conditional probability dependent variable Derivative Evaluation point discrete distribution function effects Equal Weights Evaluation point Truth expected value explanatory variables fcth interval Glenn Hubbard hazard function hazard rate Health Economics health expenditures Health Insurance Experiment iid normal errors Levels 1st order Levels 4th order logarithmic logit model Logs 4th order Mixture model Monte Carlo experiments NMES Non-white number of intervals number of observations OLS estimator OLS Levels 1st OLS Levels 4th OLS Logs 4th order 4th order order OLS Levels order OLS Logs order polynomials order variables outcome of interest parentheses point Truth OLS positive expenditures Rand Health Insurance random variable regression retransformation RHIE sample Standard deviations standard errors Truth OLS Levels two-part model unobserved heterogeneity Variance Wald test