Book Description
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.
