Essays on misspecified models

Zuo, Bing

Permalink

https://hdl.handle.net/2142/101162 Copy

Description

Title

Essays on misspecified models

Author(s)

Zuo, Bing

Issue Date

2018-04-15

Director of Research (if dissertation) or Advisor (if thesis)

Bera, Anil

Doctoral Committee Chair(s)

Bera, Anil

Committee Member(s)

• Shao, Xiaofeng
• Lee, JiHyung
• Chung, Eun Yi

Department of Study

Economics

Discipline

Economics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Generalized Emperical Likelihood, Moment Conditions

Abstract

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.

Graduation Semester

2018-05

Type of Resource

text

Permalink

http://hdl.handle.net/2142/101162

Copyright and License Information

Copyright 2018 Bing Zuo

Owning Collections