Updating weighting matrices by Cross-Entropy
The classical approach to estimate spatial models lays on the choice of a spatial weights matrix that reflects the interactions among locations. The rule used to define this matrix is supposed to be the most similar to the «true» spatial relationships, but for the researcher is difficult to elucidate when the choice of this matrix is right and when is wrong. This key step in the process of estimating spatial models is a somewhat arbitrary choice, as Anselin (2002) pointed out, and it can be seen as one of their main methodological problems. This note proposes not imposing 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. Entropy Econometrics (EE) techniques are a useful tool for recovering unknown probability distributions and its application allows the estimation of the elements of the spatial weights matrix instead of the imposition by researcher. Hence, the spatial lag matrix is not a matter of choice for researcher but of empirical estimation by CE. We compare classical with CE estimators by means of Monte Carlo simulations in several scenarios on the true spatial effect. The results show that Cross Entropy estimates outperform the classical estimates, especially when the specification of the weights matrix is not similar to the true one. This result points to CE as a helpful technique to reduce the degree of arbitrariness imposed in the estimation of spatial models.
Check other articles from the issue Monográfico 2011 'Contributions to spatial econometrics' or from other issues.