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Chapter 2, co-authored with Vadim Marmer and Kyungchul Song, considers a general formof network dependence, where dependence between two sets of random variables becomesweaker as their network distance increases. We show that such network dependence cannotbe viewed as a random field on a lattice in a Euclidean space with a fixed dimension whenthe maximum clique increases in size as the network grows. This work applies Doukhanand Louhichi (1999)’s notion of weak dependence to networks by measuring the strength ofdependence using the covariance between nonlinearly transformed random variables. Whilethis approach covers examples such as strong mixing random fields on graphs and conditionaldependency graphs, it is most useful when dependence arises through a functional-causalsystem of equations. The main results of this chapter include a law of large numbers and acentral limit theorem for network dependent processes.Chapter 3 focuses on the bootstrap for network dependent processes studied in Chapter2. Such processes are distinct from other forms of random fields that are commonly usedin the statistics and econometrics literature so that the existing bootstrap methods cannotbe applied directly. I propose a block-based method and a modification of the dependentwild bootstrap for constructing confidence sets for the mean of a network dependent process.In addition, I establish the consistency of these methods for the smooth function modeland provide the bootstrap alternatives to the network heteroskedasticity-autocorrelationconsistent variance estimator obtained in Chapter 2.Finally, Chapter 4, co-authored with Kyungchul Song, presents a large Bayesian gamewith multiple information groups and develops a bootstrap inference method that does notrequire a common prior assumption and allows each player to form beliefs differently fromother players. By drawing on the intuition of Kalai (2004), this work introduces the notion ofa hindsight regret, which measures a player’s ex post value of other players’ type information,and obtains its belief-free bound. Using this bound, we derive testable implications andpropose a bootstrap inference procedure for the structural parameters of the game.
Chapter 1 develops an empirical two-sided matching model with endogenous pre-investment. The model can be used to measure the impact of frictions in labour markets using a single cross-section of matched employer-employee data. The observed matching of workers to firms is the outcome of a discrete, two-sided matching process where firms with heterogeneous preferences over education sequentially choose workers according to an index correlated with worker preferences over firms. The distribution of education arises in equilibrium from a Bayesian game: workers, knowing the distribution of worker and firm types, invest in education prior to the matching process. I propose an inference procedure combining discrete choice methods with simulation. Counterfactual analysis using Canadian data shows that changes in matching frictions can lead to economically significant equilibrium changes in both inequality and the probability of investing in higher education. These effects are more pronounced when worker and firm attributes are complements in the match surplus function.In many economic settings, agents behave similarly because they share information with one another. Information-sharing relations among agents can be modeled as a network, and the strategic interactions among them as a game on a network. Chapter 2, coauthored with Kyungchul Song and Nathan Canen, develops a tractable empirical model of social interactions where each agent - without seeing the full information network - shares information with their neighbors and best responds to the other players based on simple beliefs about their strategies. We provide conditions on the information networks and beliefs of agents such that their best responses exhibit economically intuitive features and desirable external validity relative to equilibrium models of social interaction. Moreover, the setup admits asymptotic inference without requiring that the researcher observes all the players in the game, nor that the they know precisely the sampling process. Chapter 3 discusses how discrete distributions of unobserved heterogeneity can be identified using information on sample attrition. Although attrition is often seen as a source of selection problems, we argue that it can also be used to solve selection problems - even in the absence of covariates or panel data.
Chapter 1 studies the identification of a preemption game where the timing decisions are expressed as mixed hitting time (MHT). It considers a preemption game with private information, where agents choose optimal time to invest, with payoffs driven by Geometric Brownian Motion. The game delivers the optimal timing of investment based on a threshold rule that depends on both the observed covariates and the unobserved heterogeneity. The timing decision rules specify durations before the irreversible investment as the first time the Geometric Brownian Motion hits a heterogeneous threshold, which fits the MHT framework. As a result, identification strategies for MHT can be used for a first stage identification analysis of the model primitives. Estimation results are performed in a Monte Carlo simulation study.Chapter 2 studies the identification of a real options game similar to chapter 1, but with complete information. Because of the multiple equilibria problems associated with the complete information game, the point identification is only achieved for a duopoly case. This simple complete information game delivers two possible different kinds of equilibria, and we can separate the parameter space of unobserved investment cost accordingly for different equilibria. We also show the non-identification result for a three-player case in appendix B.4.Chapter 3 studies the estimation of a varying coefficient model without a complete data set. We use a nearest-matching method to combine two incomplete samples to get a complete data set. We demonstrate that the simple local linear estimator of the varying coefficient model using the combined sample is inconsistent and in general the convergence rate is slower than the parametric rate to its probability limit. We propose the bias-corrected estimator and investigate the asymptotic properties. In particular, the bias-corrected estimator attains the parametric convergence rate if the number of matching variables is one. Monte Carlo simulation results are consistent with our findings.