The Spatial Connectivity Matrix

Alternative specifications of the spatial connectivity matrix (W) are typically non-nested. A non-nested test procedure based on the encompassing principle is suggested to test rival hypotheses about W. An empirical illustration is presented using spatial cross-section data for house prices in Greater Tel Aviv in which W is based on contiguity and inverse distance. The spatial ARCH model is introduced (SpARCH) in which the variances of residual disturbances are spatially autocorrelated. Whereas ARCH models explain how volatility is transmitted over time, SpARCH models explain how volatility is transmitted across space. An empirical illustration of SpARCH is provided for house price in Greater Tel Aviv. In cross-section data, W has to be specified exogenously. In long spatial panel data where T is greater than N, W may be estimated. We discuss the identification problem in estimating the elements of W. Since in general they are under-identified, a restriction is proposed under which the identification problem is solved, and estimates of W are consistent. This solution is compared to recent proposals to estimate W. An empirical illustration is presented using spatial panel data for house prices in Israel.