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.

Generalized Modeling Approaches to Risk Adjustment of Skewed Outcomes Data

There are two broad classes of models used to address the econometric problems caused by skewness in data commonly encountered in health care applications: (1) transformation to deal with skewness (e.g., OLS on ln(y)); and (2) alternative weighting approaches based on exponential conditional models (ECM) and generalized linear model (GLM) approaches. In this paper, we encompass these two classes of models using the three parameter generalized gamma (GGM) distribution, which includes several of the standard alternatives as special cases OLS with a normal error, OLS for the log normal, the standard gamma and exponential with a log link, and the Weibull. Using simulation methods, we find the tests of identifying distributions to be robust. The GGM also provides a potentially more robust alternative estimator to the standard alternatives. An example using inpatient expenditures is also analyzed.

The selection of an appropriate count data model for modelling health insurance and health care demand: Case of Indonesia

This is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.We apply several estimators to Indonesian household data to estimate the relationship between health insurance and the number of outpatient visits to public and private providers. Once endogeneity of insurance is taken into account, there is a 63 percent increase in the average number of public visits by the beneficiaries of mandatory insurance for civil servants. Individuals' decisions to make first contact with private providers is affected by private insurance membership. However, insurance status does not make any difference for the number of future outpatient visits

Parametric modelling of cost data: some simulation evidence

Recently, commentators have suggested that the distributional form of cost data should be explicitly modelled to gain efficiency in estimating the population mean. We perform a series of simulation experiments to evaluate the usual sample mean and the mean estimator of a lognormal distribution, in the context of both theoretical distributions and three large empirical datasets. The sample mean is always unbiased, but is somewhat less efficient when the population distribution is truly lognormal. However the lognormal estimator can perform appallingly when the true distribution is not lognormal. In practical situations, where the true distribution is unknown, the sample mean generally remains the estimator of choice, especially when limited sample size prohibits detailed modelling of the cost data distribution

Thomism and mathematical physics

Montréal Trigonix inc. 201