Tham khảo tài liệu 'handbook of empirical economics and finance _5', tài chính - ngân hàng, tài chính doanh nghiệp phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Recent Developments in Cross Section and Panel Count Models 105 Latent Factor Models An alternative to the above moment-based approaches is a pseudo-FIML approach of Deb and Trivedi 2006a who consider models with count outcome and endogenous treatment dummies. The model is used to study the impact of health insurance status on utilization of care. Endogeneity in these models arises from the presence of common latent factors that impact both the choice of treatments a interpreted as treatment variables and the intensity of utilization interpreted as an outcome variable . The specification is consistent with selection on unobserved latent heterogeneity. In this model the endogenous variables in the count outcome equations are categorical but the approach can be extended to the case of continuous variables. The model includes a set of J dichotomous treatment variables that correspond to insurance plan dummies. These are endogenously determined by mixed multinomial logit structure MMNL Pr dilZi li A . 1 E k 1 exp zý klik where dj is observed treatment dummies dj di1 di2 . diJ j 0 1 2 . J zi is exogenous covariates li li 1 li2 . liJ and lij are latent or unobserved factors. The expected outcome equation for the counted outcomes is E y l di Xi li exp x 3 J 1 y jdij J 1 X jlij where xi is a set of exogenous covariates. When the factor loading parameter Xj 0 treatment and outcome are positively correlated through unobserved characteristics . there is positive selection. Deb and Trivedi 2006a assume that the distribution of yi is negative binomial n A A py r ộ T y 1 Pi ộ Pi where Pj E yi l di xi li exp x. 3 ljX and Ộ 1 a a 0 is the overdispersion parameter. The parameters in the MMNL are only identified up to a scale. Hence a scale normalization for the latent factors is required accordingly they set 8 j 1 for each j. Although the model is identified through nonlinearity when zi xi they include some variables in zi that are not .
