Updating weighting matrices by Cross-Entropy

The classical approach to estimate spatial models lays on the choiceof a spatial weights matrix that reflects the interactions among locations. The ruleused to define this matrix is supposed to be the most similar to the «true» spatialrelationships, but for the researcher is difficult to elucidate when the choice of thismatrix is right and when is wrong. This key step in the process of estimating spatialmodels is a somewhat arbitrary choice, as Anselin (2002) pointed out, and itcan be seen as one of their main methodological problems. This note proposes notimposing the elements of the spatial matrix but estimating them by cross entropy(CE) econometrics. Since the spatial weight matrices are often row-standardized,each one of their rows can be approached as probability distributions. EntropyEconometrics (EE) techniques are a useful tool for recovering unknown probabilitydistributions and its application allows the estimation of the elements of thespatial weights matrix instead of the imposition by researcher. Hence, the spatiallag matrix is not a matter of choice for researcher but of empirical estimation byCE. We compare classical with CE estimators by means of Monte Carlo simulationsin several scenarios on the true spatial effect. The results show that CrossEntropy estimates outperform the classical estimates, especially when the specificationof the weights matrix is not similar to the true one. This result points to CEas a helpful technique to reduce the degree of arbitrariness imposed in the estimationof spatial models.