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UBC Theses and Dissertations

Essays in econometrics Kojevnikov, Denis

Abstract

Chapter 2, co-authored with Vadim Marmer and Kyungchul Song, considers a general form of network dependence, where dependence between two sets of random variables becomes weaker as their network distance increases. We show that such network dependence cannot be viewed as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This work applies Doukhan and Louhichi (1999)’s notion of weak dependence to networks by measuring the strength of dependence using the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on graphs and conditional dependency graphs, it is most useful when dependence arises through a functional-causal system of equations. The main results of this chapter include a law of large numbers and a central limit theorem for network dependent processes. Chapter 3 focuses on the bootstrap for network dependent processes studied in Chapter 2. Such processes are distinct from other forms of random fields that are commonly used in the statistics and econometrics literature so that the existing bootstrap methods cannot be applied directly. I propose a block-based method and a modification of the dependent wild 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 model and provide the bootstrap alternatives to the network heteroskedasticity-autocorrelation consistent variance estimator obtained in Chapter 2. Finally, Chapter 4, co-authored with Kyungchul Song, presents a large Bayesian game with multiple information groups and develops a bootstrap inference method that does not require a common prior assumption and allows each player to form beliefs differently from other players. By drawing on the intuition of Kalai (2004), this work introduces the notion of a 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 and propose a bootstrap inference procedure for the structural parameters of the game.

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