A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model

We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square (0, 1)2. The asymptotic distribution is a ratio of two infinite linear combinations of χ-square vari-ables. The formula involves eigenvalues of an integral operator associated with the function approached by the spatial matrices. Under the conditions imposed identifica-tion conditions for the maximum likelihood method and methods of moments fail. A remedial iterative procedure using the OLS estimator is proposed