Semivariogram Estimation And Panel Data Structure In Spatial Models

The equicorrelated structure of individual dependence that is typically specified for the error-components in panel data models does not allow for distance decay effects. Furthermore, the equicorrelation is associated with the time, and not the individual, dimension of the data set. Such a structure is not adequate for estimating spatial patterns in panel data. This study provides theoretical and empirical advances on this topic.New insights are provided on constructing contiguity matrices for spatial models when only the X-Y latitude-longitude coordinates of the centroids from spatial units are available. The spatial weights matrix is computed from the so-called "range" of the two-dimensional semivariogram estimation, that is, the plot of semivariances against the sampling interval. The resulting contiguity matrix is then included in an error-components model for a regressive spatial autoregressive process. The model is estimated in two stages using the sequential estimator suggested by Chamberlain (1982, 1984). To overcome the computational difficulties that beset spatial processes, the data, in the first stage, are treated as T cross-sections whose parameters are estimated by a pseudo maximum likelihood procedure. In the second stage, nonlinear restrictions that combine both weak simultaneity and correlation effects are imposed in the application of the minimum distance method. The presence of a weighting matrix precludes direct and/or linear restrictions on parameters of interest.This framework is applied to a model using a lattice sample on 115 neighboring municipalities from the French network of residential water distribution. The balanced nature of the panel (from 1988:1 to 1993:2 half year period) allows us to consider a fixed spatial weighting scheme over time. Initial estimation results and tests clearly support the proposed approach: household demands display spatial patterns.