Essays on Semiparametric Binary Models With Endogeneity Applied in Health Economics

This thesis develops an innovative control function estimator for a binary response model that includes a continuous endogenous regressor in the absence of exclusion restrictions. The estimator is designed to handle empirical challenges associated with a binary outcome variable and a continuous endogenous regressor when exclusion restrictions are not feasible. The application of this estimator is to study the causal link between education and health. The empirical results highlight the heterogeneous effect of education on health and healthrelated behaviors. Chapter 1 addresses the endogeneity issue theoretically in a binary model without feasible exclusion restrictions. This chapter introduces parametric and semiparametric control function estimators. The main idea of this approach is to utilize heteroscedasticity to construct a control variable to address the endogeneity issue. This chapter establishes the large sample properties of the proposed estimator. In Monte-Carlo simulations, it performs quite well in finite samples. Chapter 2 applies the model proposed in Chapter 1 to solve the empirical challenge posed by the undesirability of using the commonly employed instrumental variable, compulsory schooling laws, in studying the educational effect on health. Using the Health and Retirement Study (HRS) data, the semiparametric estimation method is employed to estimate the heterogeneous effect of education on health and health behaviors without introducing an instrumental variable for the endogenous variable, education. The empirical results indicate that the effect of education on health varies based on the initial health status of individuals, age, and the level of education attained. These findings provide insights into the mechanisms through which education influences health outcomes and inform targeted interventions to enhance population health.