Quick computation of spatial autoregressive estimators

Spatial estimators usually require the manipulation of n(2) relations among n observations and use operations such as determinants, eigenvalues, and inverses whose operation counts grow at a rate proportional to n(3). This paper provides ways to quickly compute estimates when the dependent variable follows a spatial autoregressive process, which by appropriate specification of the independent variables can subsume the case when the errors follow a spatial autoregressive process. Since only nearby observations fend to affect a given observation, most observations have no effect and hence the spatial weight matrix becomes sparse. By exploiting sparsity and rearranging computations, one can compute estimates at low cost. As a demonstration of the efficacy of these techniques, the paper provides a Monte Carlo study whereby 3,107 observation regressions require only 0.1 seconds each when using Matlab on a 200 Mhz Pentium Pro personal computer. In addition, the paper illustrates these techniques by examining voting behavior across U.S. counties in the 1980 presidential election.