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 Title: Unobserved heterogeneity in economic models: testing and estimation Author(s): Gu, Jiaying Director of Research: Koenker, Roger W. Doctoral Committee Chair(s): Koenker, Roger W. Doctoral Committee Member(s): Bera, Anil; Chung, Eun Yi; Hirano, Keisuke; Shao, Xiaofeng; Zhao, Dave Department / Program: Economics Discipline: Economics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Unobserved Heterogeneity Estimation and Inference Abstract: This dissertation consists three chapters with a central theme on unobserved heterogeneity in economic models. The first two chapters discuss tests for parameter homogeneity against general alternatives. In the first chapter, I propose a unified framework for score tests of parameter homogeneity based on Neyman's $C(\alpha)$ approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with respect to the heterogeneity parameter is identically zero, and consequently the conventional Fisher information about the parameter is zero. Nevertheless, local asymptotic optimality of the $C(\alpha)$ tests can be established via LeCam's differentiability in quadratic mean and the limit experiment approach. The new framework reveals that certain regularity conditions commonly employed in earlier developments are unnecessary, i.e. the symmetry or third moment condition imposed on the heterogeneity distribution. Additionally, the limit experiment for the multi-dimensional case suggests modifications on existing tests for slope heterogeneity in cross sectional and panel data models that lead to power improvement. The second chapter focuses on the likelihood ratio test for the same class of testing problems. The test statistic is based on estimation of general (nonparametric) mixture models using the Kiefer and Wolfowitz (1956) maximum likelihood method. Recent developments in convex optimization are shown to dramatically improve upon earlier EM methods for computation of these estimators, and new results on the large sample behavior of likelihood ratios involving such estimators yield a tractable form of asymptotic inference. The computation efficiency also allows the use of a bootstrap method to determine critical values that are shown to work better than the asymptotic critical values in finite samples and consistency of the bootstrap procedure is formally proved. We compare performance of the likelihood ratio test with that of the $C(\alpha)$ test proposed in the first chapter and identify circumstances in which each is preferred. The last chapter discusses estimation method for models with unobserved heterogeneity. In particular, the empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The methods are first illustrated with some simulation examples and then with an application to models of income dynamics. Using PSID data we estimate a simple dynamic model of earnings that incorporates bivariate heterogeneity in intercept and variance of the innovation process. Profile likelihood is employed to estimate an AR(1) parameter controlling the persistence of the innovations. We find that persistence is relatively modest when we permit heterogeneity in variances. Evidence of negative dependence between individual intercepts and variances is revealed by the nonparametric estimation of the mixing distribution, and has important consequences for forecasting future income trajectories. Issue Date: 2015-07-13 Type: Thesis URI: http://hdl.handle.net/2142/88183 Rights Information: Copyright 2015 Jiaying Gu Date Available in IDEALS: 2015-09-29 Date Deposited: August 201
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