Panel Spatial Autoregression with an Unknown Transformation of the Weight Matrix

Abstract We introduce nonlinearities in analyzing spatial panel data by allowing for an unknown matrix analytic transformation of the spatial weights matrix. The proposed model can be estimated using only O ( n ) parameters which is a vast reduction in parameters when compared to $$O(n^2)$$ parameters as seen in the literature for spatial weight matrix estimation. Analyzing the quasi-maximum likelihood estimator, we show consistency and asymptotic normality. In simulations, this estimator can accurately estimate the transformed spatial weights matrix. The procedure is applied to the estimation of unemployment in New Hampshire with county based spatial dependence.