Inference in Unilateral Spatial Econometric Models

In spatial econometric models dependence between observations may extend in all directions. The bilateral structure of the process complicates the analysis of asymptotic properties of estimators, making it necessary to resort to high-level assumptions guaranteeing that certain convergences hold. Estimators may then in general be shown to be consistent and asymptotically normal. Under some relatively mild conditions the existence of a unilateral autoregressive approximation to a spatial series may be established. By restricting attention to the class of unilateral spatial autoregressive processes, the asymptotic analysis simplifies. The stationarity condition for unilateral spatial autoregressive processes is well known. The paper studies inference in spatial econometric models when data are assumed to be generated by a two-dimensional unilateral stationary spatial autoregressive process of finite order. The estimator of the autoregressive parameter is shown to be consistent and asymptotically normal. Some simulation results to examine the finite sample properties of the estimator show that it is nearly unbiased, except at the boundary of the parameter space. In the nonstationary case the estimator is inconsistent and diverges. In the estimation of spatial econometric models, the parameter space is usually restricted to the stationary region. An estimate of the spatial autoregressive parameter close to one in absolute value is then an indication of nonstationarity. In many cases the weights matrix is unknown. We find that underspecifying the weights matrix results in an underestimated spatial autoregressive parameter and overspecifying the weights matrix results in an overestimated spatial autoregressive parameter. Depending on the choice of the weights matrix, a very different picture of the magnitude of spatial autocorrelation in the data may be obtained. An empirical application to house prices in the county of Stockholm, Sweden, is included as an illustration of the findings.