Essays on Spatial Econometrics

A bias-adjusted estimator for small samples and a hybrid estimator, which combines the guaranteed invertibility of the MLE with original non-hybridised estimators, are introduced in Chapter 2. Their performance is extensively compared with that of the Maximum Gaussian Likelihood and several Instrumental Variable-type estimators in the context of the spatial error model (SEM). We show that the bias-adjusted estimator is effective across various sample sizes and the hybridised forms of the estimators outperform even the best of the IV methods across a majority of the cases examined. Chapter 3 introduces a sub-model for spatial weights and estimates a variable weight matrix for the mixed regressive, spatial autoregressive (MR-SAR) model by maximum Gaussian likelihood. We establish the identifiability of the weight parameter, the consistency and the asymptotic normality of the QMLE under appropriate conditions that extend those given by Lee (2004a). Finite properties of our estimator are investigated in a Monte Carlo study and we show that it outperforms other competing estimators in many cases considered. Its applicability is illustrated in Chapter 4, where the estimator using two types of sub-models for the spatial weights is applied to the cross-sectional data set used in Ertur and Koch (2007) in the framework of the MR-SAR model to study the impact of saving, population growth and interdependence among countries on growth. It is shown that our QML estimator is able to capture positive spatial spillovers of growth among countries and provide significant estimates of other parameters of the model including the parameter defining the spatial weights.