Put some economics back into spatial econometrics

One of the hot areas for econometric research in recent years has been spatial econometrics. Think of it, at least initially as time series econometrics in a different dimension. One interesting aspect of it is that instead of being single-dimensional like time series, it can be two-dimensional, or even more I guess. This field brings interesting new challenges, and it must be exciting working in this field. However, as too often in econometric theory, research becomes quickly detached from reality, and more specifically from the needs of empiricists. N never goes to infinity, for example.

Luisa Corrado and Bernard Fingleton bring forward another important point. These techniques are used to test economic theories, so one should be able to embed some restrictions from economic theory. It is all nice and sweet when one can find an optimal weighting matrix with the right properties, but it is useless if the found weights cannot be matched with anything one wants to test. The causality goes the wrong way: first determine restrictions from the theory, then use the constraints to find the optimal weighting matrix.

This is not just a theoretical consideration. Spatial lags are crucial in spatial econometrics and are suppose to capture some network effects. But they can also soak up the impact of latent or unobserved variables, as in "regular" econometrics. This can lead to severe miss-specification and biased inference, somethings one is all to familiar with using lags in time series. In fact, one should be downright suspicious of any time-series results that only holds when lagged dependent variables are used. The same must apply to spatial econometrics.