Dissertations, Theses, and Capstone Projects

Date of Degree


Document Type


Degree Name





Wim P. Vijverberg

Subject Categories

Economics | Economic Theory


Bayesian econometrics,, Heteroskedasticity, Robust estimators,, Spatial econometrics, GMM Estimtion, MLE, Spatial Dependence, Foreign direct investment


This dissertation consists of four essays on the estimation methods and applications of spatial econometrics models. In the first essay, we consider a spatial econometric model containing spatial lags in the dependent variable and the disturbance terms with an unknown form of heteroskedasticity in the innovations. We first prove that the maximum likelihood estimator (MLE) is generally inconsistent when heteroskedasticity is not taken into account in the estimation. We show that the necessary condition for consistency of the MLE depends on the specification of the spatial weight matrices. Then, we extend the robust generalized method of moment (GMM) estimation approach in Lin and Lee (2010) for the spatial models allowing for a spatial lag not only in the dependent variable but also in the disturbance term. We show the consistency of the robust GMM estimator and determine its asymptotic distribution. Finally, through a comprehensive Monte Carlo simulation, we compare the finite sample properties of the robust GMM estimator with other estimators proposed in the literature.

In the second essay, the finite sample properties of heteroskedasticity robust estimators suggested for the spatial autoregressive models are compared through simulation studies. Most of the estimators suggested for the estimation of spatial autoregressive models are inconsistent in the presence of an unknown form of heteroskedasticy. The estimators formulated from the GMM and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to an unknown form of heterokedasticity. In this essay, the finite sample properties of the robust GMM estimators and the Bayesian estimators based on MCMC approach are compared for the spatial autoregressive models. To this end, a comprehensive Monte Carlo simulation is designed for the spatial models containing a spatial lag in the dependent variable and/or disturbance term. In the second part of the study, two empirical applications are provided to show how heteroskedasticity robust estimators are performing in applied research.

In the third essay, we investigate the properties of spatial autoregressive models that have a spatial moving average process in the disturbance term. The spatial moving average process introduces a different interaction structure among observations. In the first part of this essay, we describe the transmission and the effect of shocks under a spatial moving average process. In the second part, we investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. We show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. We also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. We provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters.

In the fourth essay, we analyze the effect of foreign direct investment (FDI) on economic activity through a spatially augmented Solow growth model that takes technological interdependence into account. The technological interdependence manifests itself through spatial externalities which allow technology level of a country to depend on technology levels of its neighbors. Based on this modified growth model, we derive regression specifications and study the impact of FDI on economic growth. The spatial autocorrelation, often cited in the empirical growth literature, is properly accounted for through these new specifications. Estimations are carried out with the tools from spatial econometrics. Our findings indicate that FDI inflows have a significant positive effect on the growth rate of host countries.