Jesus Mur (p), Marcos Herrera, Manuel Ruiz

Esteban Fernandez-Vazquez

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Ian Gordon, Vassilis Monastiriotis (p)

Jesus Mur

In most economics applications of spatial econometric techniques, the approximations employed for the distance discounting process (i.e., the weights matrices used) are too crude and too “discrete” – often being chosen out of a limited set of alternatives (contiguity- or distanced-based neighbourliness). Less often these approximations are more directly informed by theory (e.g., based on gravity, distance decay, or networks). In both cases, however, they are taken to be largely exogenously determined and not driven by information available in the data. In this paper we develop a flexible functional form that allows for different, both continuous and discrete, distance decay processes; and we propose an estimating technique that allows the parameters of the function (form: binary or continuous; and shape: steep or flat) to be directly identified by the data. Our proposed technique also allows for more complex functional relationships that take into account issues of accessibility (allowing for different degrees of row-standardisation) and permit non-distance based linkages (e.g., relating to densities or flows).

In this paper we demonstrate this technique. We parameterise a generic weights matrix on the basis of a flexible gravity-type function and estimate it with the use of an iterative non-linear least squares procedure. We use simulated data constructed on the basis of various alternative pre-defined matrices, commonly used in the literature, and test the performance of our technique by comparing the estimated matrices against the ‘true’ (pre-defined) ones. We show that our technique is able to reproduce sufficiently well a broad range of pre-defined neighbourliness structures, thus removing the need to search for ‘the correct W’ through examining alternative options one at a time. We then apply our technique on real data from local areas in England and show that our derived estimates of W are substantively different from those W-approximations commonly used in applied spatial econometrics; and that or estimated W produces a more accurate estimation of the impact of spatial determinants on local outcomes.

Esteban Fernandez-Vazquez (p), Rosa Bernardini-Papalia

Vassilis Monastiriotis

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