Essays on Estimation and Inference for Spatial Economic Models

This dissertation consists of two essays on the estimation and inference for spatial economic models. The first essay discusses the estimation for a simultaneous system of spatial autoregressive equations with random effects in panel data setting. I suggest an error component three-stage least squares (EC3SLS) estimator for the model. The second essay focuses on the estimation and inference for a threshold spatial autoregressive model for cross sections. I propose a spatial two-stage least square (S2SLS) estimator for the model and prove the consistency of the threshold parameter estimator. The first essay derives a 3SLS estimator for a simultaneous system of spatial autoregressive equations with random effects which can therefore handle endogeneity, spatial lag dependence, heterogeneity as well as cross equation correlation. This is done by utilizing the Kelejian and Prucha (1998) and Lee (2003) type instruments from the cross-section spatial autoregressive literature and marrying them to the error components 3SLS estimator derived by Baltagi (1981) for a system of simultaneous panel data equations. The Monte Carlo experiments indicate that, for the single equation spatial error components 2SLS estimators, there is a slight gain in efficiency when Lee (2003) type rather than Kelejian and Prucha (1998) instruments are used. However, there is not much difference in efficiency between these instruments for spatial error components 3SLS estimators. The second essay extends the threshold model to the spatial framework. This allows different spatial lag coefficients for different regimes (subsamples), while the sample splitting point is unknown. We suggest a spatial two-stage least squares (S2SLS) estimator for the threshold and slope parameters based on Kelejian and Prucha (1998) type instruments. We also prove the consistency of the threshold parameter estimator. A Monte Carlo study is provided to examine the finite sample properties. Our results show that the performance of our estimator improves as the sample size increases and as the difference between the spatial parameters of the two subsamples increases