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Title:Essays on testing spatial models
Author(s):Leiluo, Yufan
Director of Research:Bera, Anil Kumar
Doctoral Committee Chair(s):Bera, Anil Kumar
Doctoral Committee Member(s):Shao, Xiaofeng; Lee, JiHyung; Chung, Eun Yi
Department / Program:Economics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Spatial model
Robust LM tests
Rao's score tests
Abstract:This thesis mainly develops robust Rao’s score tests (Lagrange multiplier (LM) tests) for different types of spatial models. The models studied in this thesis include a spatial dynamic panel data (SDPD) model and a nonlinear SAR (NSAR) model. The proposed test is aiming to solve model selection problems. Chapter 1,"Robust LM tests for spatial dynamic panel data models", introduces robustLM tests for the SDPD model that includes a contemporaneous spatial lag, a time lag and a spatial-time lag. The maximum likelihood estimator for the estimation of SDPD models can have asymptotic bias because of individual and time fixed effects. Bias arises since the limiting distributions of the score functions derived from the corresponding concentrated log-likelihood functions are not centered on zero. First, we show how the score functions should be adjusted to avoid the effect of asymptotic bias on the standard LM test statistics. Second, we further adjust score functions such that the resulting LM test statistics are valid when there is local parametric misspecification in the alternative model. Our robust LM test statistics can be used to test the presence of the contemporaneous spatial lag, time lag and spatial-time lag in an SDPD model. In a Monte Carlo study, we demonstrate that our suggested test statistics have good finite sample size and power properties. We also illustrate implementation of these tests in an application on public capital productivity in 48 contiguous US states. Chapter 2, "Robust LM Tests for Spatial Dynamic Panel Data Models under both Parametric and Distributional Misspecifications", studies the same SDPD model. The proposed tests in this chapter is further robustified to the non-normal distribution of error terms. Another estimation approach of the model is also discussed in this chapter. The performance of the suggested test is shown in a Monte Carlo study and empirical applications with the same data as in Chapter 1. Chapter 3, "Nested and Non-nested Tests of Nonlinear Spatial Autoregressive Model", proposes a nonlinear spatial autoregressive (NSAR) model. The added nonlinearity is introduced through the Box-Cox (BC) transformation. This model encompasses the linear and log linear form with BC parameter being 1 and 0, respectively. First, we derive various combinations of LM tests for testing linear or log linear functional form and the presence of spatial correlation, in their original [Rao (1948)] and robust forms [Bera and Yoon (1993)], assuming normality. We explore the formulation of these tests after estimating the model using generalized method of moments (GMM) [Bera et al. (2010)], instead of by maximum likelihood estimator (MLE) or quasi MLE (QMLE). Our proposed tests can be viewed as the conditional variance counterpart of specification tests suggested for the spatial conditional mean as in Anselin et al. (1996) and Bera et al. (2019). We also develop non-nested tests for linear vs. log linear forms and vice-versa for selecting one of the models which may be of practical interest. The finite sample performance of the proposed tests is investigated by an extensive Monte Carlo simulation study. The usefulness of our suggested test procedures is illustrated by a substantive empirical application.
Issue Date:2020-09-02
Rights Information:Copyright 2020 Yufan Leiluo
Date Available in IDEALS:2021-03-05
Date Deposited:2020-12

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