  Stimulated by the Boston house price data, in this paper, we propose a
semiparametric spatial dynamic model, which extends the ordinary spatial
autoregressive models to accommodate the effects of some covariates associated
with the house price. A profile likelihood based estimation procedure is
proposed. The asymptotic normality of the proposed estimators are derived. We
also investigate how to identify the parametric/nonparametric components in the
proposed semiparametric model. We show how many unknown parameters an unknown
bivariate function amounts to, and propose an AIC/BIC of nonparametric version
for model selection. Simulation studies are conducted to examine the
performance of the proposed methods. The simulation results show our methods
work very well. We finally apply the proposed methods to analyze the Boston
house price data, which leads to some interesting findings.
