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.

The dissertation consists of three chapters. The first chapter studies the identification and estimation of binary choices with hidden information diffusion. It investigates the hidden information diffusion and consumer preferences for a new product, where only informed individuals who have acquired product information can make adoption decisions. Due to unobserved information acquisition/diffusion, we cannot distinguish informed but unwilling-to-adopt individuals from uninformed ones. In addition to a random utility model, we introduce a binary threshold crossing model to characterize information diffusion: an individual becomes informed if the exposure to the information, which depends on the fraction of already informed neighbors and personal attributes, exceeds some idiosyncratic threshold. We show the identification of diffusion and utility parameters through two subsets of observations: (i) adoption behaviors of seeds (first-informed individuals) over time; (ii) adoption behaviors of seeds' neighbors at time two. We estimate diffusion and utility parameters using the subset of observations that yields the identification. With regularity conditions, we establish consistency and asymptotic normality of the estimator.

The second chapter applies the econometric framework developed in the first chapter to the diffusion of a microfinance program in rural India. We study the parametric estimation and have two major findings. First, communication with informed neighbors is crucial in acquiring the information. Second, the participation rate of neighbors has a non-monotone impact on the household's incentive to participate. We conduct a counterfactual analysis based on model estimates and evaluate the performance of many seeding strategies. The results suggest the benefits of exploiting available information in selecting seeds.

The third chapter studies the nonparametric identification in generalized separable models. It provides new sufficient conditions for nonparametrically identifying structural models with generalized additive or multiplicative separability. The conditions generalize the normalizations used in the literature, such as differentiability of link and component functions, functional form normalization, and large support of an explanatory variable. We show that when a generalized separable model has two component functions, the identification only requires three location normalizations and weak support conditions. The new results can be applied to various influential econometric models after transformation.

The dissertation consists of three chapters on different econometric topics. The first chapter studies jackknife bias reduction for simulated maximum likelihood estimator of discrete choice models. We propose to reduce asymptotic biases of simulated maximum likelihood estimators (SMLE) by using a jackknife method similar to Dhaene and Jochmans (2015), which was originally proposed to reduce bias in nonlinear panel models. Lee (1995) investigates the asymptotic bias of the SMLE, and derives the analytical formula of higher order bias due to simulation. However, implementation of Lee (1995)’s method requires analytical characterization of the higher order bias, which may not be convenient for practice. Because the jackknife method does not require an explicit characterization of the bias, it may be a practically attractive alternative to Lee (1995)’s estimator. The second chapter studies estimation of average treatment effects for massively unbalanced binary outcomes. The maximum likelihood estimator (MLE) of the average treatment effects (ATE) in the logit model for binary outcomes may have a significant second order bias if the event has a low probability. The analysis of rare events is relevant for economics because some of the big data sets are collected from online sources where the number of events (such as “ clicks” and “ purchases”) is much smaller than the number of nonevents. The literature about rare events (King and Zeng, 2001; Chen and Giles, 2012; Rilstone, 1996; Wang, 2020) does not shed light on the finite sample behavior of logit MLE and ATE if events are rare. In this chapter, we also derive the second order bias of the logit ATE estimator and propose bias-corrected estimators of the ATE. We also propose a variation on the logit model with parameters that are elasticities. Finally, we propose a computational trick that avoids numerical instability in the case of estimation for rare events. The third chapter studies a Vuong test (Vuong, 1989) for panel data models with fixed effects. This chapter generalizes the Vuong test to nonlinear panel models where the dimension of incidental parameters grows with the sample size. The incidental parameters (Neyman and Scott, 1948) that affect the unbiasedness of the parameters of interest are also important for panel data models as they capture unobserved heterogeneity. The discrepancy in incidental parameters plays an important role in model selection; for example, as noted by MacKinnon et al. (2020), there is a vast literature on the cluster-robust inference that assumes the structure of the clusters is correctly specified, which is often violated. In the presence of incidental parameters, we cannot easily apply the classical Vuong test to select a panel data model. This chapter proposes a new model selection test for panel data models by extending the classical Vuong test, which selects from two parametric likelihood models based on their Kullback–Leibler information criterion (KLIC). This chapter proposes three different test statistics for researchers who need to deal with all possible relationships between candidate models: overlapping models, nested models, and strictly nonnested models. These three model relationships are classified according to the structure of low-dimensional parameter of interest and high-dimensional incidental parameters. We allow for disagreements about incidental parameters and obtain specification tests based on a modified likelihood function.