| This thesis introduces two new semiparametric spatial autocovariance models, a semiparametric spatially autoregressive model with exogenous variables (SP-SARX) and a semiparametric spatially autocorrelated errors model (SP-SACE). Small sample properties of the two models are analysed with monte-carlo simulations and the abilities of the models to estimate the spatial autocovariance parameters and the fits of the data are compared to the parametric models. For the SP-SARX model it is found that the estimates of both the spatial parameters and the fits outperform those of the parametric model, while for the SP-SACE model it is found that the estimation of the spatial parameter is about the same as the parametric model while the fits are superior. In addition, the effects of edge-effects, changing degrees of contiguity of the spatial matrix ( W), and alternate definitions of the spatial matrix are found to have significant effects on the estimation of both the spatial autocorrelation parameters as well as the slopes of the parametric spatially autoregressive with exogenous variables (SARX) model. Finally, the two semiparametric models are applied to the estimation of hedonic housing price models for 22 years of cross-sectional data from approximately 80 zipcodes in the Dallas, Texas area. Thirteen models are compared as to their in-sample fits, their out-of-sample prediction, their ability to removed detectable spatial autocorrelation from in-sample residuals, and their ability to meet an industry standard automated valuation model (AVM) criteria for out-of-sample prediction. It is found that even though according to the selected criteria a SP-SARX specification generally best describes the data, nevertheless the inclusion of relative spatial effects in the form of spatial autocorrelation provides very little improvement in out-of-sample prediction ability, and that the primary source of predictive improvement comes from the inclusion of absolute spatial effects in the form of an estimated price surface, and from the inclusion of non-linear or flexible functional forms for the independent variables. It is also noted that a non-parametric specification of absolute spatial effects outperforms a parametric specification. |
