Econometric Risk Adjustment, Endogeneity, and Extrapolation Bias

In econometric risk-adjustment exercises, models estimated with one or more included endogenous explanatory variables ("risk adjusters") will generally result in biased predictions of outcomes of interest, e.g. unconditional mean healthcare expenditures. This paper shows that a first-order contributor to this prediction bias is the difference between the distribution of explanatory variables in the estimation sample and the prediction sample -- a form of "extrapolation bias." In the linear model context, a difference in the means of the respective joint marginal distributions of observed covariates suffices to produce bias when endogenous explanatory variables are used in estimation. If these means do not differ, then the "endogeneity-related" extrapolation bias disappears although a form of "standard" extrapolation bias may persist. These results are extended to some of the nonlinear models in common use in this literature with some provisionally-similar conclusions. In general the bias problem will be most acute where risk adjustment is most useful, i.e. when estimated risk-adjustment models are applied in populations whose characteristics differ from those from which the estimation data are drawn.

Marginal Effects in Multivariate Probit and Kindred Discrete and Count Outcome Models, with Applications in Health Economics

Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often the main target of applied microeconometric analysis. In the specific context of probit models such estimation is straightforward in univariate models, and Greene, 1996, 1998, has extended these results to cover the case of quadrant probability marginal effects in bivariate probit models. The purpose of this paper is to extend these results to the general multivariate probit context for arbitrary orthant probabilities and to demonstrate the applicability of such extensions in contexts of interest in health economics applications. The baseline results are extended to models that condition on subvectors of y, to count data structures that derive from the probability structure of y, to multivariate ordered probit data structures, and to multinomial probit models whose marginal effects turn out to be a special case of those of the multivariate probit model. Simulations reveal that analytical formulae versus fully numerical derivatives result in a reduction in computational time as well as an increase in accuracy.

Live Long, Live Well: Quantifying the Health of Heterogenous Populations

Various health-, quality-, and disability-adjusted life year or life expectancy (HALY, QALY, DALY; HALE, QALE, DALE) measures have become gold standards for defining outcomes in technology evaluation, population health monitoring, and other evaluative efforts. As such, it is critical that the analytical framework within which these measures are used for descriptive and evaluative purposes be theoretically consistent and statistically rigorous. For instance, widely-accepted definitions of cost-effectiveness ratios and other technology evaluation criteria that are based on expectations of the respective cost and outcome measures must as such be defined in terms of expected HALYs or QALYs. Similarly, measures like HALEs or QALEs used for population health monitoring are typically concerned with population expectations of such measures (or their corresponding totals). This paper demonstrates that estimation of such expectations necessarily requires consideration of the population variation in and covariation between quality and longevity. From the perspective of several different environments characterizing such heterogeneity, quantification or estimation of measures like QUALs are recondidered. An empirical example of the central issues is provided by means of an analysis of the Years of Healthy Life (YHL) measure drawn from the U.S. National Health Interview Survey.

Marginal Effects in Multivariate Probit and Kindred Discrete and Count Outcome Models

Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often the main target of applied microeconometric analysis. In the specific context of probit models, estimation of partial effects involving outcome probabilities will often be of interest. Such estimation is straightforward in univariate models, and Greene, 1996, 1998, has extended these results to cover the case of quadrant probability marginal effects in bivariate probit models. The first purpose of this paper is to extend these results to encompass the general !"!# multivariate probit (MVP) context for arbitrary orthant probabilities. It is suggested that such partial effects are broadly useful in situations wherein multivariate outcomes are of concern. The paper derives the general result on orthant probability partial effects, which contains Greene's bivariate result as a special case. These results are then extended to models that condition on subvectors of y, to count data structures that derive from the probability structure of y, to multivariate ordered probit data structures, and to the multinomial probit model whose marginal effects turn out to be a special case of those of the multivariate probit model. Numerical simulations suggest that use of the analytical formulae versus fully numericalmultivariate probit, multinomial probit, marginal effects, orthant probability partial effects, count data

Employment, Unemployment, and Problem Drinking

The misuse of alcoholic beverages ('problem drinking') has been demonstrated to result in enormous economic costs; most of these costs have been shown to be reduced productivity in the labor market. The purpose of this paper is to present sound structural estimates of the relationship between various measures of problem drinking and of employment and unemployment. The sample of approximately 15,000 observations is drawn from the 1988 Alcohol Survey of the National Health Interview Survey, the first dataset that enables nationally- representative estimates of alcohol abuse and dependence consistent with generally accepted medical criteria. The structural estimates of the effects of problem drinking on employment and labor market participation are obtained using methods proposed by Amemiya and by Heckman and MaCurdy. For our sample of males ages 25 to 59, we find that using the instrumental variable approach suggests that the negative impact of problem drinking on employment is even greater than that estimated using the OLS approach. Interestingly, the IV estimates on the samples of females change the sign from a positive impact of problem drinking on employment to a negative impact. Thus although the conclusions drawn from raw data comparisons and OLS regressions differ by gender, the IV estimates are very similar for men and women. For women, the unobserved heterogeneity masks the negative impact of problem drinking on employment when using OLS estimation methods.

Health, Income, and Risk Aversion: Assessing Some Welfare Costs of Alcoholism and Poor Health

The economic costs of adverse health outcomes have typically been evaluated in a context of risk neutrality, an approach that ignores the potential welfare importance of individuals' risk preferences. This paper presents a framework that unifies the research in health capital and earnings with that on risk preferences in the presence of stochastic outcomes. The model is implemented to obtain estimates of the economic damages due both to general health problems as well as to one specific health problem that is of considerable interest from society's perspective: alcoholism. Our empirical findings, based on data from the Epidemiologic Catchment Area survey, indicate that failure to recognize the possibility of risk averse preferences leads to a potentially serious underestimation of the magnitudes of the 'costs' of alcoholism and poor health. In particular, it is shown that while alcoholism problems have negative impacts on the conditional mean of income (consistent with most of the existing literature), they also have positive impacts on the conditional variance of income. Our conclusions are to some degree provisional because our estimates of conditional variances are necessarily biased to the extent that unobserved heterogeneity is an important determinant of the moment structure of income in our sample.

Multivariate Fractional Regression Estimation of Econometric Share Models

This paper describes and applies econometric strategies for estimating regression models of economic share data outcomes where the shares may take boundary values (zero and one) with nontrivial probability. The main focus of the paper is on the conditional mean structures of such data. The paper proposes an extension of the fractional regression methodology proposed by Papke and Wooldridge, 1996, 2008, in univariate cross-sectional and panel contexts. The paper discusses the stochastic aspects of share definition and measurement, and summarizes important features of the existing literature on econometric strategies for share model estimation. The paper then goes on to discuss the univariate fractional regression estimation strategies proposed by Papke and Wooldridge and to extend the fractional regression approach to estimation of and inference about regression models describing the multivariate share data. Some issues involving outcome aggregation/ disaggregation are considered, as is a full likelihood estimation approach based on Dirichlet-multinomial models. The paper demonstrates the workings of these various empirical strategies by estimating models of financial asset portfolio shares using data from the 2001, 2004, and 2007 U.S. Surveys of Consumer Finances.

Interaction Effects and Difference-in-Difference Estimation in Loglinear Models

In applied econometric work, analysts are concerned often with estimation of and inferences about interaction effects, e.g. 'Does the magnitude of the effect of z1 on y depend on z2? ' This paper develops tests for and proper interpretation of various forms of interaction effects in one prominent class of regression models loglinear models for which the nature of estimated interaction effects has not always been given due attention. The results obtained here have a direct bearing on the interpretation of so-called difference-in-difference estimates when these are obtained using loglinear models. An empirical example of the impacts of health insurance and chronic illness on prescription drug utilization underscores the importance of these issues in practical settings.

Much Ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Economics

In health economics applications involving outcomes (y) and covariates (x), it is often the case that the central inferential problems of interest involve E[y|x] and its associated partial effects or elasticities. Many such outcomes have two fundamental statistical properties: yò0; and the outcome y=0 is observed with sufficient frequency that the zeros cannot be ignored econometrically. Common approaches to estimation in such instances include Tobit, selection, and two-part models. This paper (1) describes circumstances where the standard two-part model with homoskedastic retransformation will fail to provide consistent inferences about important policy parameters; and (2) demonstrates some alternative approaches that are likely to prove helpful in applications.