Akaike information criterion in choosing the optimal k-nearest neighbours of the spatial weight matrix

We use the Akaike information criterion (AIC) to assess the quality of non-nested spatial econometric models with a different number of nearest neighbours (knn) included in the spatial weight matrix W. This is of particular importance in two cases: when estimating the model on geolocated point data without explicit guidance on the optimal value of knn; and when dealing with different spatial patterns and a unique W generalizes diverse spatial structures. By minimizing AIC for a set of competing models, one can find the optimal knn that guarantees the best fit. We show through simulation and empirical analysis that AIC is a non-linear function of knn and reaches its minimum for a given knn. We provide practical evidence that misspecified W may result in a 20% bias of model parameters.