Discrete Choice Models with Endogeneity

Open Access
Xu, Haiqing
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
June 16, 2011
Committee Members:
  • Joirs Pinkse And Sung Jae Jun, Dissertation Advisor
  • Coenraad Arnout P Pinkse, Committee Chair
  • Sung Jae Jun, Committee Chair
  • Herman J Bierens, Committee Member
  • Runze Li, Committee Member
  • Barry William Ickes, Committee Member
  • Bayesian Nash Equilibrium
  • Endogeneity
  • Discrete Choice Model
  • Monotone Strategy
  • Triangular System
CHAPTER 1: Discrete Choice Models With Local Interactions: A Game Theoretical Approach Consider observations from a single equilibrium of a local interaction game in which each player, a firm, has a finite number of actions (discrete choice) and is subject to interactions that are local–for example, the two surrounding neighbors in a ‘linear’ Hotelling model. Asymptotics in this setting is studied by assuming that all the players are located in a single market and that the number of them grows. All observations are potentially dependent on each other because they are interpreted as arising from a single equilibrium of settings where players interact directly or indirectly. Simple assumptions about the structure are made that ensure that the game with a fixed number of players has a unique equilibrium and the equilibrium has a stability property. The formulation of this stability property is new and is the basis for consistency. I introduce an estimation procedure called (sieve) maximum approximated likelihood. This estimator has the same asymptotic properties as the corresponding maximum likelihood estimator, but is easier to compute. CHAPTER 2: Estimation of Bayesian Nash Equilibrium in Static Discrete Games with Correlated Private Signals This paper studies a two by two static game of incomplete information. I allow players' private signals to be correlated, which adds complexity to Bayesian Nash Equilibrium (BNE) solutions of the game. Further, the econometric structure of this model is ‘incomplete’ due to the existence of multiple equilibria (Tamer (2003)). I therefore focus on a nontrivial subset of the support of public information variables (regressors), where a unique Monotone Strategy Bayesian Equilibrium (MSBE) exists. I propose a four–step procedure to estimate the payoff structure. In the first step I estimate a set of parameters containing the underlying parameter of interest. I then obtain a point estimator in the second step and prove its consistency. The third and fourth step estimators are square n-consistent; the fourth step estimation is more efficient. CHAPTER 3: Semiparametric estimation of binary decision games of incomplete information with correlated private signals (with Yuanyuan Wan) This paper studies the identification and estimation of a semiparametric binary decision game of incomplete information. We make no parametric assumptions on the joint distribution of private signals and allow them to be correlated. Focusing on Monotone Strategy Bayesian Equilibrium, we show that the equilibrium strategies can be represented by a binary choice model with an unobserved regressor, of which we find (estimable) upper and lower bounds. We show that the parameters of interest can be point–identified subject to a scale normalization under mild support requirements for the regressors (publicly observed states) and errors (private signals). Following Manski and Tamer (2002), we use the modified maximum score estimator with estimated bounds and show its consistency. CHAPTER 4: Tighter Bounds in Triangular System (with Sung Jae Jun and Joris Pinkse) We study a nonparametric triangular system with (potentially discrete) endogenous regressors and nonseparable errors. Like in other work in this area, the parameter of interest is the structural function evaluated at particular values. We impose a global exclusion and exogeneity condition, in contrast to Chesher (2005), but develop a rank condition which is weaker than Chesher’s. The alternative rank condition can be satisfied for binary endogenous regressors, and it often leads to a tighter identified interval than Chesher (2005)’s minimum length interval. We illustrate the potential of the new rank condition using the Angrist and Krueger (1991) data.