This dissertation consists of three chapters that study the identification and estimation of structural economic models. Chapter 1, “Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments” studies the nonparametric identification and estimation of the marginal effect of an endogenous variable X on the outcome variable Y , given a potentially mismeasured instrument variable W∗, without assuming linearity or separability of the functions governing the relationship between observables and unobservables. In order to address the challenges arising from the co-existence of measurement error and nonseparability, I first employ the deconvolution technique from the measurement error literature to identify the joint distribution of Y,X,W∗ using two error-laden measurements of W∗. I then recover the structural derivative of the function of interest and the “Local Average Response” (LAR) from the joint distribution via the “unobserved instrument” approach in Matzkin (2016). I also propose nonparametric estimators for these parameters and derive their uniform rates of convergence. Monte Carlo exercises show evidence that the estimators I propose have goodfinite sample performance.

Chapter 2, “Two-step Estimation of Network Formation Models with Unobserved Heterogeneities and Strategic Interactions”, characterizes the network formation process as a static game of incomplete information, where the latent payoff of forming a link between two individuals depends on the structure of the network, as well as private information on agents’ attributes. I allow agents’ private unobserved attributes to be correlated with observed attributes through individual fixed effects. Using data from a single large network, I propose a two-step estimator for the model primitives. In the first step, I estimate agents’ equilibrium beliefs of other people’s choice probabilities. In the second step, I plug in the first-step estimator to the conditional choice probability expression and estimate the model parameters and the unobserved individual fixed effects together using Joint MLE. Assuming that the observed attributes are discrete, I showed that the first step estimator is uniformly consistent with rate N−1/4, where N is the total number of linking proposals. I also show that the second-step estimator converges asymptotically to a normal distribution at the same rate.

Chapter 3, “Identification and Estimation in Differentiated Products Markets Where Firms Affect Consumers’ Attention” studies the nonparametric identification and estimation of a demand and supply system where firms affect consumers’ consideration sets via costly marketing inputs, when market-level data is available. On the demand side, I characterize preferences and considerations nonparametrically, allowing rich heterogeneities and correlations between them. On the supply side, I characterize firms’ optimal choices by a set of first-order conditions without specifying the form of the oligopoly model. The demand and supply sides form a simultaneous system of equations in the spirit of Berry and Haile (2014). I then show the identification of the system using the method proposed by Matzkin (2015). Moreover, using the variations of exclusive regressors entering preferences and considerations respectively, I separately identify features of the utility functions and the attention functions. Based on the constructive identification results, I propose nonparametric estimators of the demand, utility, and attention functions and show their asymptotic properties.

This dissertation is divided into three chapters. In Chapter 1, I propose a nonparametric estimator for the bidders' utility function and the density of private values in a first-price sealed-bid auction model. Specifically, I study a setting with risk-averse bidders within the independent private value paradigm. I adopt a fully nonparametric approach by not placing any restrictions on the shape of the bidders' utility function beyond strict monotonicity, concavity, and differentiability. In contrast to previous literature, I characterize such utility function and the density of private values by a minimizer of a certain functional. I estimate this minimizer, which is a smooth real-valued function, in two steps by the method of sieves. Then, the estimators for the bidders' utility function and the density of private values are smooth functionals of the estimator for the minimizer. The estimator for the utility function is uniformly consistent and shape-preserving, while the estimator for the density is uniformly consistent and asymptotically normal.

Chapter 2, which is a joint paper with I. Obara, studies a model of repeated Bertrand competition among asymmetric firms that produce a homogeneous product. The discounting rates and marginal costs may vary across firms. We identify the critical level of discount factor such that a collusive outcome can be sustained if and only if the average discount factor within the lowest cost firms is above the critical level. We also characterize the set of all efficient collusive equilibria when firms differ only in their discounting rates. Due to differential discounting, impatient firms gain a larger share of the market at an earlier stage of the game and patient firms gain a larger share at a later stage in efficient equilibrium. Although there are many efficient collusive equilibria, our model provides a unique prediction in the long run in the sense that every efficient collusive equilibrium converges to the unique efficient stationary collusive equilibrium within finite time.

Chapter 3 develops a weighted average derivative estimator for &beta in the context E(y|x^c,x^d) = G(x^c|&beta,x^d), where x^c and x^d are continuous and discrete random vectors, respectively, and G is an unknown function. A distinguishing feature of the proposed estimator is the use of kernel smoothing for the discrete covariates. Under standard regularity conditions, such an estimator is root-N-consistent, asymptotically normal, and non-iterative.

This dissertation consists of three main chapters that study social interactions in networks. In Chapter 1, I study a market with many-to-many contracts when the number of market participants increases. Many-to-many contracts allow a seller to trade with multiple buyers and a buyer to trade with multiple sellers. I focus on investigating the identification of payoff parameters through data observed from equilibrium matches in a large many-to-many matching market. In many-to-many matching markets, several issues have to be addressed: bias would arise since the outcomes are only observed when links are formed between two agents, and the maximum number of relationships an agent can enter into would possibly affect the set of stable outcomes. I show that under certain conditions, the number of firms (workers) that are willing to be matched to a specific worker (firm) grows at a rate regardless of the capacity of both sides. Furthermore, I show a correspondence between the stable matching outcomes in a many-to-many matching framework and that in a one-to-one matching framework.

In Chapter 2, I conduct a structural econometric analysis of the diffusion process with players who observe their neighbors and make decisions based on their neighbors' decisions. I study the identification and estimation of diffusion processes in social and economic networks. Compared to the classic econometric diffusion literature that assumes a continuous population with a stochastic network structure, I provide a new econometric framework to analyze diffusion processes in fixed networks where Bayesian players observe their close neighbors. I demonstrate the existence of the equilibrium of the model and characterize the unique symmetric equilibrium. Based on these theoretical findings, I propose a consistent and tractable two-step estimator for payoff parameters using feasible data from a single large network. I evaluate the finite sample performance using Monte Carlo simulations.

Chapter 3 applies the network diffusion model to data on the participation of a microfinance program in Indian villages to describe the impact of neighbors on individual decisions. Our model allows us to study the various network effect across different types of agents who care about their neighbors' opinions. It depends on unknown equilibrium beliefs, which specify agents' expectations about their neighbors' decisions. Using participation data from 43 villages, each including about 200 villagers, I estimate these equilibrium beliefs and the network effects.

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.

I study how to measure consumer welfare changes from demand in online markets. Specifically, I find formulas for calculating exact compensating variation and equivalent variation as a function of a known demand relation. Consumers are assumed to shop for a single, discrete good. To capture online shopping behavior, I also assume consumers have limited product knowledge. That is, I assume search is costly and consumers thus optimally shop only a subcollection of all available products; I call this consumer-specific subcollection of products a ``consideration set.'' In this framework, I determine formulas to measure consumer welfare changes from price changes and from changes in search result listings. I use simulations and shopping data from an online travel agency to support my analysis.

This dissertation consists of three essays divided into chapters. In chapter 1, I analyze the identification of a simultaneous binary response model without nonadditive unobservable random terms, and suggest an estimation method. In particular, the derivatives of structural equations are identified and estimated. The identification relies on a special regressor, which enters the underlying structural equation linearly. All other exogenous variables held constant, variation on this special regressor generates variation on the structural equation which determines the latent endogenous variable in a known way, so we can recover the conditional distribution of the structural equations. The estimator can be constructed using a least-squares method, after replacing the elements of a matrix with kernel density and density derivative estimates. The estimator is shown to be consistent and asymptotically normal.

In chapter 2, I examine the determinants smartphone adoption among the elderly in South Korea. The advent of smartphones has caused a dramatic change in access to information and media, leading to a super-connected world of real-time services. Meanwhile, the constant dissemination of new technologies makes the digital divide multi-layered. In particular, older persons fall far behind the overall population in the access and use of new devices. To understand the technological environment following the introduction of smartphones and other smart mobile devices, I examine individual, household, and regional factors that can influence the preferences of the elderly with regard to obtaining a smartphone. I find that smartphone ownership among the elderly is mainly determined by personal rather than family characteristics. Also, I find that the area where a person lives has a significant effect on the probability of their owning a smartphone.

In chapter 3, I analyze the evolution of preferences for brands in digital camera market. A consumer considers the value of a brand, as well as product characteristics when deciding which product to buy. One way to capture this effect is to use brand-specific dummy variables. However, including brand-specific dummy variables does not fully account for the variation of the unit sales of compact digital cameras, since the preference for digital camera brands evolves over time. Assuming that the brand preference is affected by the advertising expenditure of each brand and the reputation among consumers, I suggest a method to capture the time-varying brand preference under the specification of BLP model.

In Chapter 1, I extend the techniques in Li and Vuong (1998), Schennach (2004a), and Bonhomme and Robin (2010) to identify nonparametric distributions of unobserved variables in a system of linear equations with more unobserved variables than outcome variables and with subsets of statistically dependent unobserved variables. I construct estimators of the distributions of unobserved variables and derive their uniform convergence rates. In Chapter 2, I develop a method for identification and estimation of coefficients in a linear regression model with measurement error in all the variables. The method is extended to identification in a system of linear equations in which only some of the coefficients on the unobserved variables are known. The estimator uses an assumption that is testable in the data and is in the class of Extremum estimators. The asymptotic distribution of the estimator is derived. In Chapter 3, I identify the nonparametric joint distribution of random coefficients in a linear panel data regression model. The distributions of the coefficients can depend on covariates, coefficients can be statistically dependent or equal in distribution, and there can be more coefficients than the fixed number of time periods. I construct estimators from the identification proofs. In finite sample simulations all the estimators have tight confidence bands around their theoretical counterparts.

In this dissertation we describe conditions for nonparametric identification and methods for estimating dynamic simultaneous equation models. These models have two distinct sources of endogeneity: lagged dependent variables that are related to autocorrelated unobservable variables and endogeneity through a simultaneous equations structure. Until now, nonparametric estimation has been limited to models with either one or the other. In the first chapter we show that the structural functions in such models are identified with panel data under assumptions commonly made in nonparametric econometrics. We do so by borrowing intuition from existing literature on dynamic panel models. In the second chapter of the dissertation we describe conditions needed for consistent and asymptotically normal nonparametric estimation of dynamic simultaneous equations models. In the third chapter we nonparametrically estimate dynamic demand functions for airline travel using recent data.

This dissertation consists of three chapters that study econometrics questions and their applications to education. Chapter 1 studies a nonparametric two-sided many-to-one matching model, where many agents on one side match one institution on the other side. Classical examples include student-college matching and firm-worker matching. In this paper, I study nonparametric identification and estimation of many-to-one matching with non-transferable utility. The existing literature either assumes that the matching algorithm and reported preferences are observed or that preferences are homogeneous. This paper assumes heterogeneous preferences on the two sides and only requires data on who matches with whom in a single large market. Under mild restrictions, I prove that both the utility functions of the students and colleges and the joint distribution of unobserved heterogeneity from the two sides are nonparametrically identified. Based on my constructive identification results, I propose nonparametric and semiparametric estimators of the model and establish their consistency and asymptotic normality. The semiparametric estimator converges at a root-n rate.

Chapter 2 analyzes the U.S. college admissions under a many-to-one matching framework. In recovering the parameters of the utility functions, I am able to demonstrate substantial welfare consequences for different groups of students, relative to a centralized matching mechanism. In estimating the model using data from High School Longitudinal Study of 2009 (HSLS:09) and the Integrated Postsecondary Education Data System (IPEDS), I show that the students who experience the largest losses are first-generation college students and low-ability students. This potential loss among these groups provides an opportunity for policy interventions to lead to substantial gains in welfare.

Chapter 3 (joint with Kathleen McGarry) studies the three generations of changing gender patterns of schooling in China. The phenomenon of son preference in China and throughout much of Asia has been well documented. However, changing economic conditions, such as increases in educational attainment and employment opportunities for women and the rise in the prevalence of one child families, have likely changed the incentives for parents to invest in daughters. In this paper, we take advantage of data spanning three generations of Chinese families to examine the evolution of educational attainment for boys and girls and importantly the relative levels of schooling of each gender. We also use variation in the timing of compulsory schooling laws and the implementation of the one child policy to assess the effect of these policy measures on the relative educational levels. We find a substantial narrowing of the gap between the schooling of boys and girls, so much so that girls now have more schooling on average than boys. In addition, public policy initiatives had a larger effect in rural than urban areas.