UBC Theses and Dissertations

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UBC Theses and Dissertations

Essays on econometrics Yu, Zhengfei


This thesis studies two topics in Econometric models, multiple equilibria and weak instruments. Chapter 1 is an introduction. Chapter 2 considers nonparametric structural equations which may have multiple solutions for the endogenous variables. The main finding is that multiple equilibria would reveal itself in the form of jump(s) in the density function of the endogenous variables. When there is a unique equilibrium, the density function of endogenous variables will be continuous, while when there are multiple equilibria, the density will have a jump at some point, under reasonable conditions. Our test statistic is based on maximizing local jumps over the support of endogenous variables and the critical value is computed via a Gaussian multiplier bootstrap. Chapter 3 shows that in games with incomplete information, even when the payoff functions and the latent distributions are all smooth, the observed conditional choice probabilities may have a jump with respect to continuous covariates. This chapter provides a theoretical analysis on the relationship between the equilibrium behaviour of the game and the presence of a jump in the conditional choice probabilities. Such jump(s) matters in empirical research for two reasons. Statistically, it affects the estimation of the conditional choice probabilities. Economically, whether the conditional choice probabilities have a jump or not reveals information about the equilibrium behaviour of the game. Our findings are robust to correlated private information and unobserved heterogeneity independent of covariates. Chapter 4 considers efficient inference for the coefficient of the endogenous variable in linear regression models with weak instrumental variables (Weak-IV). We focus on the power of tests for the alternative hypotheses that are determined by arbitrarily large deviations from the null. We derive the power envelope for such alternatives in the Weak-IV scenario. Then we compare the power properties of popular Weak-IV robust tests, focusing on the Anderson-Rubin (AR) and Conditional Likelihood Ratio (CLR) tests. We find that their relative performance depends on the degree of endogeniety in the model. In addition, we propose a Conditional Lagrange Multiplier (CLM) test. We also extend our analysis to heteroskedastic models.

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