Dan Ben Moshe
Hebrew UniversityStochastic Frontier Estimation of Housing Supply
Traditional estimation of housing production costs has been by conditional mean regres-
sion. Given the ubiquity of regulation in housing markets, the resulting estimates embed
unobservable regulatory restrictions. A major concern is endogeneity due to these regulations
and the lack of exogenous variables in this setting. Leaving aside endogeneity bias, regres-
sion estimates will be of limited use in predicting how the housing market might change were
regulation relaxed, or in measuring the degree to which the market is affected by regulation.
One requires, instead, an estimation procedure that separates regulation from other aspects
of cost. Our solution is to estimate the frontier supply of housing, which captures housing
supply under minimal regulation. Our focus is on the cost of building up since in highly urban
environments, housing prices are determined in large part by the costs of building high. We
establish that identification is possible even where price and height are simultaneously deter-
mined in a demand-supply model. We also consider identification under increasing returns,
where we find that these methods estimate the average cost curve, instead of the marginal cost
curve. We consider various estimators, including (a) extreme value theory-based boundary
estimators, (b) stochastic frontier, maximum likelihood estimators, and (c) Bayesian random
effects estimators. We apply these methods to the Israeli housing market from 1998-2017.
We find evidence of economies of scale for buildings less than seven-floors high, flat marginal
costs until around height 17, and increasing marginal costs beyond this, with marginal costs
rising steeply from about height 25. About fifty percent of housing value can be ascribed to
regulatory taxes, which suggests that new housing could have been much less land intensive
than it was. The share of regulatory taxes is higher in more expensive areas. The effects of
measurement error and quality differences on price are small relative to regulatory taxes.