Three Essays on Spatial Econometrics: Specification, Estimation and Model selection for Spatial Models

My dissertation consists of three essays on spatial econometrics.;The first essay, "Model Selection Using J-test for the Spatial Autoregressive Model vs. the Matrix Exponential Spatial Model", studies the non-nested model selection problem between the spatial Autoregressive (SAR) model and the matrix exponential spatial specification (MESS) model .We use the 2SLS and GMM methods to implement the J-test procedure and derive several test statistics under the GMM framework. We also extend the J-test procedure to the setting when error terms in the model are with unknown heteroskedasticity. Monte Carlo results suggest with strong spatial dependence the J-test statistics have good power to distinguish the SAR and MESS models.;In Essay Two, "Bayesian Estimation and Model Selection for Spatial Durbin Error Model with Finite Distributed Lags", we consider the Bayesian MCMC estimation of the model with a smoothness prior. The corresponding Bayesian model selection procedure for the SDEM model, the SAR model and the MESS model are studied and expressions of the marginal likelihood of the three models are derived. Simulation results suggest that the Bayesian estimates of high order spatial distributed lag coefficients are more precise than the maximum likelihood estimates. When the data is generated with a general declining pattern or a uni-modal pattern of spatial externalities, the SDEM model can better capture the pattern than the SAR and MESS models in most cases. We apply the estimation and model selection procedure to study the effect of right to work (RTW) laws on manufacturing employment.;My job market paper, "Bayesian Estimation of a Spatial Autoregressive Model with an Unobserved Endogenous Spatial Weight Matrix and Unobserved Factors", examines the specification and estimation of the SAR model with new features. Motivated by the spillover effects of state medicaid spending on welfare programs, we combine all these new features together for the first time in the SAR model. Specifically, we focus on two ways of defining neighborliness (a source of unobserved spatial weight matrix W): one based on geographical distance and the other on "economic" distance. In this particular application, endogeneity of W comes from the correlation of economic distance and the disturbances in the SAR equation. Unobserved factors are introduced to control for common shocks to all states. For the estimation of the model, the Bayesian MCMC method is employed, which is also supported by simulation results. We find that a dollar increase in a state's neighbors' Medicaid related spending will increase its own Medicaid related spending by about 52 cents. Both geographical and economic distances are shown to have significant effects on the interaction strength of state Medicaid related spending. Our results suggest that in the context of Medicaid spending, welfare motivated move and yardstick competition are both sources of strategic interactions among state governments.