*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.

## 3 comments:

That's a bit harsh there... "N never goes to infinity", just like market are not frictionless, people are not expected utility maximizers, people don't choose sequential equilibrium plays, there are more than two assets in the economy, etc. etc.

So? For the empiricist who has to deal with small sample numbers by the econometric theoreticians standards, it still is a serious problem. Getting the latter is a problem, because results may be wrong.

The same applies to the other points you make. The fact that the problem exists elsewhere does not make it disappear here.

N is finite? Yawn...

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