Spatial Structures and Spatial Spillovers: A GME Approach

Spatial econometrics is a subdiscipline that have gained a huge popularity in the last twenty years, not only in theoretical econometrics but in empirical studies as well. Basically, spatial econometric methods measure spatial interaction and incorporate spatial structure into regression analysis. The specification of a matrix of spatial weights W plays a crucial role in the estimation of spatial models. The elements of this matrix measure the spatial relationships between two geographical locations i and j, and they are specified exogenously to the model. Several alternatives for W have been proposed in the literature, although binary matrices based on contiguity among locations or distance matrices are the most commons choices. One shortcoming of using this type of matrices for the spatial models is the impossibility of estimating "heterogeneous" spatial spillovers: the typical objective is the estimation of a parameter that measures the average spatial effect of the set of locations analysed. Roughly speaking, this is given by "ill-posed" econometric models where the number of (spatial) parameters to estimate is too large. In this paper, we explore the use of generalized maximum entropy econometrics (GME) to estimate spatial structures. This technique is very attractive in situations where one has to deal with estimation of "ill-posed" or "ill-conditioned" models. We compare by means of Monte Carlo simulations "classical" ML estimators with GME estimators in several situations with different availability of information.