Three Essays on the Spatial Autoregressive Model in Spatial Econometrics

The spatial autoregressive model (SAR) is a standard tool to analyze spatial data. It is of great interest in econometrics because it has a game structure and, therefore, can be interpreted as a reaction function: the outcome or behavior of observations at one location is directly affected by those of its neighbors. The corresponding spatial weight matrix is a measure of the relationship between different locations. The associated parameter provides a multiplier for these spillover effects. The conventional SAR model has been well studied in the literature, but little has been done to analyze spatial models with limited dependent variables or with endogenous spatial weight matrices. This dissertation research tries to fill in the gap. It consists of three chapters: the first two chapters consider the SAR models with limited dependent variables, especially the simultaneous SAR Tobit model; the third chapter studies estimation methods of the SAR model with an endogenous spatial weight matrix.Chapter One considers the LM tests of spatial models with limited dependent variables. It focuses on the specification and hypothesis test of SAR models which have a Tobit structure. Some results can also be applied to spatial error models and spatial models with a Probit structure. We derive an extended central limit theorem for statistics of a linear-quadratic form with multivariate random variables. We consider the LM statistics for testing spatial correlation in five spatial models with limited dependent variables and establish their asymptotic distributions. Finite sample behaviors of our tests are compared with some existing tests using the Monte Carlo simulation.Chapter Two focuses on three classical tests, namely, Wald, LM, and LR, of spatial interactions in the simultaneous SAR Tobit model. We derive the asymptotic distributions of those three tests under both the null and the local alternative hypotheses, establish their asymptotic equivalence and local efficiency, and study finite sample properties using the Monte Carlo simulation. The tests are applied to an empirical example involving the school district income tax in Iowa in 2009. Among 361 school districts, 18.3 percent had rates of zero, so it fits the Tobit setting. Testing results indicate the existence of tax competition among neighboring school districts.Chapter Three considers the specification and estimation of the SAR model with an endogenous spatial weight matrix W. Conventional estimation methods rely on the key assumption that W is strictly exogenous, which is likely to be violated in empirical applications. In Chapter Three, we consider two equations: a cross-sectional SAR outcome equation and an equation for entries in W. Endogeneity of W comes from the correlation between error terms in these two equations. We consider estimation methods such as 2SIV, GMM, and MLE for this model with an endogenous spatial weights matrix. We establish the consistency and derive the asymptotic distributions of these estimators. Finite sample properties of these estimators are investigated by the Monte Carlo simulation. Simulation results indicate a strong bias of conventional methods which ignore the endogeneity of W and estimation methods we propose work quite well.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Economics

Grantor dc:publisher

The Ohio State University

Year dc:date

2013

Author dc:creator

• Qu, Xi

Contributors dc:contributor

• Lee, Lung-fei

• Economics
• Regional Studies

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=osu1365455610

OAI identifier oai:identifier

oai:etd.ohiolink.edu:osu1365455610