P. Deb, PK Trivedi/Journal of Health Economics 21(2002)601-625 We hypothesize that the underlying unobserved heterogeneity which splits the population into latent classes is based on an individual's latent long-term health status. Proxy variables such as self-perceived heal th status and chronic health conditions may not fully capture population heterogeneity from this source. Consequently, in the case of two latent sub- populations, a distinction may be made between the "healthy"and the "ill groups, whose demands for medical care are characterized by low mean and high mean, respectively From a statistical point of view, the TPM is also a finite mixture with a degenerate component. It combines zeros from a binomial density with the positives from a zero- truncated density. The LCM is more flexible because it permits mixing with respect to both zeros and positives. While the TPM and LCM are clearly related, they are not nested Hence it is not a priori clear which model would perform better empirically. In a study of medical care demand by the elderly (Deb and Trivedi, 1997)find that the LCM is superior to the TPM. In other empirical work Cameron and Trivedi(1998), it is shown that the TPM describes the number of recreational trips taken by individuals better than the lCm A careful comparison of the LCM and TPM is useful from a policy perspective. The TPM has been used extensively to estimate demand responses to prices, income and changes in insurance status. The results have been used to propose changes in health insurance design. Statistics of interest in many such policy exercises are non-linear functions of the underlying parameters of the conditional mean function. Therefore, consistent estimation of the conditional mean function does not ensure consistent estimates of the statisties of interest for policy exercises, see Mullahy(1998)for a detailed discussion. Estimating a model that fits the empirical distribution adequately does, on the other hand, ensure that such statistics will be estimated consistently. Moreover, if in fact the TPM is dominated by the lCm, the accumulated evidence in favor of the TPM, interpreted as evidence in favor of a principal-agent framework, is ambiguous. Policies based on the principal-agent framework might, therefore, have unintended consequences Finally, both the TP and the lCM require that the investigator specifies the probability distribution of the data. Although this is a potential source of misspecification in both cases, its impact is smaller in the case of the LCM. This is because LCM is more flexible and can serve as a better approximation to any true, but unknown, probability density (laird, 1978, Heckman and Singer, 1984). Its growing popularity is reflected in an increase in the number of regression-based applications in econometrics. Recent applications include Heckman et al. (1990), Gritz(1993), Wedel et al. (1993), Deb and Trivedi (1997), geweke and Keane (1997), Morduch and Stern(1997), and Wang et al. (1998) We use data from the RAND Health Insurance Experiment(RHIE). The RHIe is one of the largest social experiments ever completed, generating over 400 research studies by members of the RANd group(Newhouse et al., 1993). It is widely regarded as the basis of the most reliable estimates of price sensitivity of demand for medical services. For example, Burtless(1995, p. 82) has stated: "The Health Insurance Experiment improved our knowledge about the price sensitivity of demand for medical services in a way that no non-experimental study has been able to match". Therefore, the public-use data from the RHIE provide a suitable test-bed for our proposed investigations We examine two measures of counts of utilization. The covariates are among those commonly used in studies of health care demandP. Deb, P.K. Trivedi / Journal of Health Economics 21 (2002) 601–625 603 We hypothesize that the underlying unobserved heterogeneity which splits the population into latent classes is based on an individual’s latent long-term health status. Proxy variables such as self-perceived health status and chronic health conditions may not fully capture population heterogeneity from this source. Consequently, in the case of two latent sub￾populations, a distinction may be made between the “healthy” and the “ill” groups, whose demands for medical care are characterized by low mean and high mean, respectively. From a statistical point of view, the TPM is also a finite mixture with a degenerate component. It combines zeros from a binomial density with the positives from a zero￾truncated density. The LCM is more flexible because it permits mixing with respect to both zeros and positives. While the TPM and LCM are clearly related, they are not nested. Hence it is not a priori clear which model would perform better empirically. In a study of medical care demand by the elderly (Deb and Trivedi, 1997) find that the LCM is superior to the TPM. In other empirical work Cameron and Trivedi (1998), it is shown that the TPM describes the number of recreational trips taken by individuals better than the LCM. A careful comparison of the LCM and TPM is useful from a policy perspective. The TPM has been used extensively to estimate demand responses to prices, income and changes in insurance status. The results have been used to propose changes in health insurance design. Statistics of interest in many such policy exercises are non-linear functions of the underlying parameters of the conditional mean function. Therefore, consistent estimation of the conditional mean function does not ensure consistent estimates of the statistics of interest for policy exercises; see Mullahy (1998) for a detailed discussion. Estimating a model that fits the empirical distribution adequately does, on the other hand, ensure that such statistics will be estimated consistently. Moreover, if in fact the TPM is dominated by the LCM, the accumulated evidence in favor of the TPM, interpreted as evidence in favor of a principal-agent framework, is ambiguous. Policies based on the principal-agent framework might, therefore, have unintended consequences. Finally, both the TPM and the LCM require that the investigator specifies the probability distribution of the data. Although this is a potential source of misspecification in both cases, its impact is smaller in the case of the LCM. This is because LCM is more flexible and can serve as a better approximation to any true, but unknown, probability density (Laird, 1978; Heckman and Singer, 1984). Its growing popularity is reflected in an increase in the number of regression-based applications in econometrics. Recent applications include Heckman et al. (1990), Gritz (1993), Wedel et al. (1993), Deb and Trivedi (1997), Geweke and Keane (1997), Morduch and Stern (1997), and Wang et al. (1998). We use data from the RAND Health Insurance Experiment (RHIE). The RHIE is one of the largest social experiments ever completed, generating over 400 research studies by members of the RAND group (Newhouse et al., 1993). It is widely regarded as the basis of the most reliable estimates of price sensitivity of demand for medical services. For example, Burtless (1995, p. 82) has stated: “The Health Insurance Experiment improved our knowledge about the price sensitivity of demand for medical services in a way that no non-experimental study has been able to match”. Therefore, the public-use data from the RHIE provide a suitable test-bed for our proposed investigations. We examine two measures of counts of utilization. The covariates are among those commonly used in studies of health care demand