P Deb, PK. Trivedi/Journal of Health Economics 21(2002)601-625 The rhie data are most suitable for our work in spite of the fact that they are considerably older than other nationally representative surveys like the National Medical Expenditure Survey of 1987, the National Health Interview Survey of 1994 or the Medical Expenditure Panel Survey of 1997. First, the rhie dataset is the only one in which individuals were randomized into insurance plans, thus making insurance choice exogenous. Endogeneity of insurance choice is a major problem in non-experimental data; even in cases where suitable instruments exist, they are typically weak thus making statistical corrections fo endogeneity unreliable. Second, RAND researchers gave careful consideration to issues of attrition bias and other sources of"sample contamination"which affect some social experiments(Newhouse et al., 1993, chapter 2; Heckman and Smith, 1995) In the following section of the paper, we formally present the competing models used in this paper and discuss model comparison, selection, and evaluation strategies. The data are described in Section 3. Empirical results are reported in Section 4, and we conclude in 2. Econometric models We develop models for counts of outpatient visits using the LCM and TPM frameworks Both are derived from the negative binomial model (NBM) for count data, so we begin by describing that model 2.. NBM Let yi be a count dependent variable that takes values 0, 1, 2,... The density function for the NBM is given by f(yi|6)= T((y λ+v)(x;+v where ro is the gamma function, i exp(x B)and the precision parameter(vi)is specified as vi=(1/ a)aj. The parameter a >0 is an overdispersion parameter and k is an arbitrary constant. In this specification, the conditional mean is given by E(ylx)=入i nd the variance by Voil ri)=Ai+aii The parameter k is usually held fixed in empirical work. The NBl model is obtained by specifying k= I while the NB2 is obtained by setting k=0 2.2. TPM We choose a nB density to construct the TPM because we wish to focus on the differences between a statistical structure that distinguishes infrequent and frequent users(LCM)from604 P. Deb, P.K. Trivedi / Journal of Health Economics 21 (2002) 601–625 The RHIE data are most suitable for our work in spite of the fact that they are considerably older than other nationally representative surveys like the National Medical Expenditure Survey of 1987, the National Health Interview Survey of 1994 or the Medical Expenditure Panel Survey of 1997. First, the RHIE dataset is the only one in which individuals were randomized into insurance plans, thus making insurance choice exogenous. Endogeneity of insurance choice is a major problem in non-experimental data; even in cases where suitable instruments exist, they are typically weak thus making statistical corrections for endogeneity unreliable. Second, RAND researchers gave careful consideration to issues of attrition bias and other sources of “sample contamination” which affect some social experiments (Newhouse et al., 1993, chapter 2; Heckman and Smith, 1995). In the following section of the paper, we formally present the competing models used in this paper and discuss model comparison, selection, and evaluation strategies. The data are described in Section 3. Empirical results are reported in Section 4, and we conclude in Section 5. 2. Econometric models We develop models for counts of outpatient visits using the LCM and TPM frameworks. Both are derived from the negative binomial model (NBM) for count data, so we begin by describing that model. 2.1. NBM Let yi be a count dependent variable that takes values 0, 1, 2,... The density function for the NBM is given by f (yi|θ) = Γ (yi + ψi) Γ (ψi)Γ (yi + 1)
ψi λi + ψi ψi
λi λi + ψi yi (2.1) where Γ (·) is the gamma function, λi = exp(x iβ) and the precision parameter (ψ−1 i ) is specified as ψi = (1/α)λk i . The parameter α > 0 is an overdispersion parameter and k is an arbitrary constant. In this specification, the conditional mean is given by E(yi|xi) = λi (2.2) and the variance by V(yi|xi) = λi + αλ2−k i . (2.3) The parameter k is usually held fixed in empirical work. The NB1 model is obtained by specifying k = 1 while the NB2 is obtained by setting k = 0. 2.2. TPM We choose a NB density to construct the TPM because we wish to focus on the differences between a statistical structure that distinguishes infrequent and frequent users (LCM) from