Identification and Estimation in Semiparametric Social Interaction Models

This dissertation investigates semiparametric social interaction models. The goal is to identify and estimate the endogenous social interactions using a flexible semiparametric model to control for confounding factors. The rationale for considering nonparametric controls is that, if the groups or networks are not randomly assigned, or if the contextual effects are heterogeneous, identifying the endogenous social interaction effect is difficult without adequate controls. This thesis contains two chapters. Chapter 1 first studies the identification of the endogenous social interaction effect in the semiparametric models. The identification is attained by using the instrumental variable (IV) approach after partialling out the nonparametric controls. To estimate the endogenous social interaction effect, I propose a semiparametric two-step generalized method of moments (GMM) estimator with the optimal weight matrix clustered at the group or network level. This chapter focuses on the semiparametric estimators that use the first step series method. The primitive regularity conditions are provided for the consistency and asymptotic normality of the semiparametric series GMM estimators. In Chapter 2, I apply more flexible machine learning methods in the first step nonparametric estimation to detect severe nonlinearities and higher-order interactions, including LASSO, Random Forest, and Neural Nets. %The asymptotic properties of the semiparametric machine learning estimators are proved given high level conditions. Monte Carlo simulations are conducted to investigate the finite sample performance of semiparametric estimators using different first-step Machine Learning methods. The results suggest that no estimation method dominates across all the Data Generating Processes (DGPs) considered. It is also reflected in the simulation results that the debiased estimators using first step post-LASSO or Neural Nets methods are more reliable and performs relatively well across the settings considered. For this reason, these two debiased estimators are recommended for use in empirical studies