Essays on Econometrics
This dissertation consists of four main chapters that study network social interaction models and panel models with grouped heterogeneity. Chapter 1 and Chapter 2 are representative work finished during my early exploration of economics. Chapter 3 and Chapter 4 are completed during the last two years of my Ph.D. studies.
Chapter 1 studies a network social interaction model with heterogeneous links. I show that the endogenous and exogenous social interaction effects as well as the strength of network links are identified under some mild conditions. I adopt the nonlinear least squares method to estimate the unknown parameters using data of a single network. I also investigate the finite sample performance of the estimation method through Monte Carlo simulations and apply the model to analyze an online social network.
Chapter 2 studies social interactions model with both in-group and out-group effects. The in-group effect follows the standard setup in the literature, while the out-group effect is introduced by assuming the economic outcome also depends on its out-group average value. I present a network game with limited information of outside groups that rationalizes the econometric model. I show that both effects are identified under a set of mild regularity conditions. I propose to estimate the model using the two-stage least squares (2SLS) method and establish the asymptotic normality of the estimators. The finite sample performance of the estimators are investigated through Monte Carlo simulations.
Chapter 3 studies a semiparametric panel quantile regression model with grouped heterogeneity. The model can capture both time-variant and time-invariant effects of explanatory variables when group-specific heterogeneity directly affects the coefficients. A series-based estimation method is developed to estimate the parameters of interest and the group memberships. I investigate the asymptotic properties of the estimators and propose an information criterion to estimate the number of groups. The finite sample performance of the estimation method and the information criterion are investigated through Monte Carlo simulations. I apply the model to study the effect of foreign direct investment (FDI) on economic growth. My empirical findings show that FDI has large and significant heterogeneous effects on economic growth, especially for low-income countries, and such effect diminishes as the GDP per capita increases. None of these findings have been documented in previous literature.
In Chapter 4 (joint with Hualei Shang), we study a nonparametric additive panel regression model with grouped heterogeneity. The model is a valuable extension to the heterogeneous panel model studied in Su et al. (2016). We propose to estimate the nonparametric components using a sieve-approximation-based C-Lasso method. We establish the asymptotic properties of the estimator and show that they enjoy the so-called oracle property. Besides, we present the decision rule for group classification and establish its consistency. A BIC-type information criterion is developed to determine the group pattern of each nonparametric component. We investigate the finite sample performance of the estimation method and the information criterion through Monte Carlo simulations. Results show that both work very well. Finally, we apply the model to study the demand for cigarettes in the United States using panel data of 46 states from 1963 to 1992.