Hypothesis testing for spatial SARAR Tobit models and high dimensional data and their applications

Lu, Chang

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https://hdl.handle.net/2142/116066 Copy

Description

Title

Hypothesis testing for spatial SARAR Tobit models and high dimensional data and their applications

Author(s)

Lu, Chang

Issue Date

2022-07-11

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

• Bera, Anil K.
• Shao, Xiaofeng
• Hewings, Geoffrey J.D.

Doctoral Committee Chair(s)

Bera, Anil K.

Committee Member(s)

Lee, JiHyung

Department of Study

Economics

Discipline

Economics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• spatial autoregressive Tobit model, robust LM test
• spatial autocorrelation model, spatial Durbin model, crime, house prices, hedonic analysis
• wild bootstrap, high dimension, studentization, overidentification testing, spatial sign.

Abstract

The spatial autoregressive (SAR) model is one of the most important models in spatial econometrics to describe the connection between dependent and independent variables by taking account of spatial dependence. The emphasis on SAR models has become more prominent in not only practical econometrics, but also theoretical econometrics. While the traditional SAR model has been extensively researched in the literature, researchers in the field of spatial analysis are becoming increasingly interested in spatial models with limited dependent variables (LDV). The model specification problem and applications for both the SAR model and the SAR model with LDV are investigated in this dissertation. Chapter 1 proposes the modified Lagrange multiplier (LM) tests for one of the SAR models with LDV, SAR Tobit models with SAR disturbances (SARAR Tobit model). There are two types of models considered in this chapter. One is the latent SARAR Tobit model, and the other one is the simultaneous SARAR Tobit model. The difference of these two types of SARAR Tobit model is whether a certain area's data is affected by the actual data of its neighbors or by the latent data of its neighbors. This chapter includes score functions, two information matrices, and proofs of asymptotic distributions for the suggested test statistics. The finite sample size and power are also investigated through a Monte Carlo simulation study. Our simulated results show that these proposed tests have good finite sample properties both in terms of size and power, even in the presence of misspecification. Chapter 2 examines the geographical distribution of crime in the city of Chicago census tracts and its effects on house values using the SAR model. The results show the spillover effects of crime among census tracts in Chicago and the effect of crime on the local real estate market. We consider two kinds of spatial models: one is the SAR model, and the other one is the spatial Durbin model (SDM). We demonstrate the impact of crime on the local region as well as the large impact of neighborhood area crime on home values using data from 801 census tracts in the city of Chicago. Besides, in our results, theft and burglary have positive but insignificant effects on housing prices, which means they are associated with higher-income neighborhoods, while violent crimes tend to be found in lower-income neighborhood areas. This means that, contrary to the conventional thought that crime always has a negative effect on property prices, our analysis shows that the effects of different types of crimes can have various and complex effects on housing prices. In addition to the SAR model and its application, this dissertation also investigates the hypothesis testing problem in a high-dimensional data setting. High-dimensional data means the dimension of the data can grow with sample size, or even larger than the sample size. When the dimension of data is larger than the sample size, the traditional Hotelling's $T^2$ test cannot be used since the inverse of the sample covariance does not exist. Chapter 3 studies the consistency of the wild bootstrap for the U-statistic in the inference of high-dimensional means. Both unstudentized and studentized U-statistics are investigated and the consistency of wild bootstrap is obtained under mild conditions, allowing for the dimension d growing at the faster rate than sample size n. The results are applied to three problems in statistics and econometrics: overidentification test with growing number of instrumental variables, spatial sign-based mean test and sphericity hypothesis test for the covariance matrix. Overall, this dissertation discusses hypothesis testing for SAR models with LDV and high-dimensional data, as well as certain applications. The findings of this dissertation contribute to a better understanding of the use of robust LM tests in the SARAR Tobit model and the application of unstudentized and studentized U-statistics in the mean zero testing under high-dimensional settings, as well as the possibilities of future research.

Graduation Semester

2022-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Chang Lu

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