Bergstrom and Goodman, AER 1973

“Private Demands for Public Goods”

This paper tries to use the median voter theorem to estimate the parameters of an individual demand function for public goods. The authors rely heavily on the median voter theorem as an assumption, and in fact spend very little time justifying its use or using their own results to assess its plausibility. They specify a functional form for individual demand for public goods, they postulate that observed levels of municipal spending reflect the preferences of the median voter, and then they use the parameters of their fitted model to draw inferences about individual demand for public goods, most notably that consumers seem to view these goods as essentially private. In general my impression is that they are asking too much of this data. The functional form and choice of control variables both seem likely to have a large impact on their estimated parameters, and there is a lot of leeway in choosing both (and no sensitivity tests demonstrating how their estimates change with reasonable modifications to their model). Their structural model approach is audacious but ultimately fails to convince me that I should pay a lot of attention to their estimates, particularly their estimate of the publicness of public goods. (They combine two imprecisely estimated parameters into a single crowding parameter to find that most public goods are in fact private, in the sense that there are no advantages to sharing them on a larger scale in the range of municipalities they consider.)

If we step back from their more rococo modeling endeavors, there are interesting data and correlations to be found here. At a minimum, the authors have provided evidence that policy responds to citizen preferences by showing that expenditures are higher where the median voter has a relatively smaller share of the bill. This is what we would expect from a representative democracy.

True, there are certainly omitted variables involved that make it hard to know whether even this is true. Cities where the median voter pays a lower amount of taxes are different in ways that almost certainly are not properly modeled by their controls. Cities where the median pays a lower proportion of property tax bill may have more inequality (think of what happens to your proportion of property tax revenues when Bill Gates builds a 100 million dollar house next door), and this might lead to more expenditures because the rich have power in the government and get what they want. (This would be a polity in which the median voter theorem does not apply.) The median homeowner’s effective tax price would also be lower in a city with a lot of commercial and industrial development, and again municipal expenditures could be higher here because such places have more crime, or because the industrial interests have captured the government and want the government to provide public goods that benefit them such as transportation infrastructure, security, or beautification.

I interpret this paper as part of an empirical project to confirm that democratic government is
giving us the policies we want it to (kind of the empirical companion to Downs, but engaging in the tradition of assumption-laden structural estimation that produces estimates that are a little hard to believe.