Spatial Nonstationarity and Spurious Regression: the Case with a Row-normalized Spatial Weights Matrix

This paper investigates the spurious regression in the spatial setting where the regressant and regressors may be generated from possible nonstationary spatial autoregressive processes. Under the near unit root specification with a row-normalized spatial weights matrix, it is shown that the possible spurious regression phenomena in the spatial setting are relatively weaker than those in the nonstationary time series scenario. The regression estimates might or might not converge to 0. The divergence might occur only when the regressant has a near unit root much closer to unity than that of the regressor. For the t and F statistics, there could be over-rejection of the null of uncorrelatedness under certain situations, but they do not diverge. However, the coefficient of determination R-2 converges to 0, which provides strong evidence of the spurious regression even when t and F statistics are large. Simulation results about different statistics are in line with the theoretical results we derive in this paper.