Learning from man or machine: Spatial fixed effects in urban econometrics

Econometric models with spatial fixed effects (FE) require some kind of spatial aggregation. This aggregation may be based on postcode, school district, county or some other spatial subdivision. Common sense would suggest that the less aggregated, the better inasmuch as aggregation over larger areas tends to gloss over systematic spatial variation. On the other hand, low spatial aggregation results in thin data sets and potentially noisy spatial fixed effects. We show, however, how this trade-off can be substantially lessened if we allow for more flexible aggregations. The key insight is that if we aggregate over areas with similar location premiums, we obtain robust location premiums without glossing over too much of the spatial variation. We use machine learning in the form of a genetic algorithm to identify areas with similar location premiums. The best aggregations found by the genetic algorithm outperform a conventional FE by postcode, even with an order of magnitude fewer spatial controls. This opens the door for spatially sparse FEs, if economy in the number of variables is important. The major takeaway, however, is that the genetic algorithm can find spatial aggregations that are both refined and robust, and thus significantly, lessen the trade-off between robust and refined location premium estimates.