Essays on misspecified models

[摘要] This thesis identifies the asymptotic properties of generalized empirical likelihood estimators when moment conditions are not correctly specified. Classical generalized empirical likelihood estimators rely on the correct moment conditions, however, those conditions are mostly generated from economic theory and some of them are not testable. Hence, it is needed to understand the property of the estimators and test statistics when moments are misspecified and provide robust estimators and test statistics when moment conditions are misspecified.Chapter 1, ”Robust Inference for Instrumental Variable Models with Locally Non-exogenous Instruments”, highlights that conventional tests often fail to give accurate inferences when exogeneity conditions are mildly violated in instrumental variable models. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics un- der the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. We prove that under the null hypothesis, this adjusted score-type test statistic converges to a central chi-squared distribution and thus is not adversely affected by local non-exogeneity. Furthermore, the Monte Carlo simulations confirm that our newly proposed test has considerable size improvement over the conventional ones, while their power is not very different.Chapter 2, ”Mis-specification-Robust Bootstrap for Empirical Likelihood Estimators ”, proposes an adapted bootstrap testing procedure for empirical likelihood estimators. This method extends the bootstrap method in Lee (2014) by using the empirical likelihood weights, which could improve the efficiency if the moment condition model is correctly specified. This proposed bootstrap method is also robust to model misspecification as shown in Lee (2014). The first-order asymptotic validity of the proposed procedure is shown, and multiple Monte Carlo Studies are conducted to support the theoretical findings.Chapter 3, ”Higher Order MSE Comparisons of Generalized Empirical Likelihood Estimators”, calculates the higher order asymptotic mean square errors (MSE) of generalized empirical likelihood (GEL) estimators on a simple linear model. It is well known from Newey and Smith (2004) that the Empirical likelihood (EL) estimator has the smallest higher-order asymptotic bias among the GEL estimators; however, in this paper we find that the EL estimator no longer has this property for the criteria of MSE. We propose a data-driven method to achieve the least asymptotic higher-order MSE in the GEL family.

[关键词] Generalized Emperical Likelihood, Moment Conditions