Tuesday, February 13, 2007

Bergstrom, Rubinfeld and Shapiro, Econometrica 1982

"Micro-Based Estimates of Demand Functions for Local School Expenditures"

This paper uses the same Michigan survey data we saw in the Gramlich and Rubinfeld paper, but this one focuses on school expenditures and features a econometric technique to estimate a continuous demand function from a three category survey response.

The dependent variable in most of the Gramlich and Rubinfeld paper was per capita government spending, which had been backed out of survey responses where people were presented with the amount their municipality spent and asked to provide how much more or less they would like the municipality to spend. Here, respondents are asked what they think education spending should be: "more," "less," or "the same." The econometric move the authors are hawking here appears to be an MLE approach to converting this categorical answer into something continuous. It looks to me like they assume that individuals in different municipalities have the same tastes (conditional on their individual characteristics), and they use the variation in the actual spending across municipalities to identify the width of their indifference band. In other words, the width of the indifference band is another parameter in the likelihood model (along with coefficients on individual characteristics, which determine the expected value of the underlying continuous demand for public goods).

The alternative would have been to estimate ordered probit or something like that, but this would not have made full use of the fact that actual expenditures vary across municipalities. The authors want to get a demand function out of this data, and this is how they'll get it.

Gramlich and Rubinfeld, JPE 1982

"Micro Estimates of Public Spending Demand Functions and Tests of the Tiebout and Median-Voter Hypotheses"

In contrast to earlier studies (like Bergstrom and Goodman 1973), Gramlich and Rubinfeld attempt to estimate demand for public spending with a survey. They asked 2001 Michigan households to look at the current profile of spending in their county and assess whether they were happy with this level or would like more or less (in percentage points). What they found is that people were pretty happy with what they had: 2/3 of respondents in urban areas and 3/5 in rural areas asked for no change in spending. These are reasonable and fairly interesting results. As the authors point out, the fairly uniform apparent demand for public goods from citizens within communities stands in contrast to observed differences in the provision of public goods across communities.

The obvious interpretation, in my view, is that people have a cognitive bias in favor of the status quo. Here's the experiment they should have run alongside this survey: give some people the wrong data (expenditure levels that actually are not accurate) and ask them to say what changes they would like to see. I expect that about the same proportion would say this level of spending was right, and about the same would say it was too low or too high. Of course, this does not get at the whole issue -- what we'd really like to do is change the actual level of services people get and see what they think of those altered services, but this is of course not possible. At any rate, lab results in psychology and behavioral economics have confirmed that this sort of bias is rampant. [citation needed] I think any economics paper written today would have to at least mention this possibility.

Gramlich and Rubinfeld do not mention this possibility, and spend the paper instead considering three alternative explanations, one of which I find to be pretty ridiculous and the other two plausible and probably as important as cognitive biases. The first explanation they consider is that the rich actually do want a lot more public goods than the poor do, but they appear to be as satisfied with the status quo as the poor because they actually consume a larger proportion of public goods than do the poor. Public spending, in other words, is "pro-rich." The authors trot out some evidence from other studies (none of which I've seen) arguing that spending on schools and other public services within cities is skewed toward the rich. I can't evaluate these studies but I can say that this did not match what I thought; in fact I thought spending across districts was actually skewed toward poor schools in many cases (although in most states rich districts are able to spend more than poor districts), and that lawsuits would prevent there from being very much of a distinction in spending within districts. Certainly quality varies highly (was my prior) but not spending. Anyway, I find this argument to be the kind of thing that doesn't make sense unless you're thinking about marginal rates of substitution between public and private goods, and something so basic that doesn't make sense unless you have the same stock economic model in mind is probably not right.

The second and more plausible explanation is that people have already done a lot of sorting, and they like what they get because they chose to live there. I really can't argue with this explanation, and I can't think of any particularly good way to test it. The experiment of giving people inaccurate spending profiles and asking how they would change it would only address part of the issue. The third explanation, also plausible, is that we are in or near political equilibrium, and that people are satisfied because their political system has provided the median preferred level of public goods.

My sense was that the paper establishes that some combination of cognitive bias, sorting, and democracy have left people pretty happy with their public goods expenditures, but we don't really know much beyond that.

Monday, February 12, 2007

Romer and Rosenthal, JPE 1979

"The Elusive Median Voter"

Romer and Rosenthal's main point is that empirical evidence of the median voter theorem is not as solid as people think (or thought, in 1979). Existing studies (like that of Bergstrom and Goodman 1973) had demonstrated that expenditures across political units were correlated with characteristics of the median voter, particularly his income and tax price. But this would be the finding even under plausible alternatives to the median voter theorem.

Their critique centers on two problems they see in existing literature on the median voter theorem:

  • the multiple fallacy: It is not clear from existing studies whether the median voter gets what he wants or some multiple of what he wants.
  • the fractile fallacy: It is not clear if the median is the pivotal voter or a voter at some other place in the distribution is the median voter.
Romer and Rosenthal present one alternative to the median voter model that demonstrates how it could be the case that the median is decisive but gets a multiple of what he wants. In a bureaucratic threat model, the bureaucracy is able to force the electorate to choose between a status quo and an alternative. The bureaucracy may be able to maintain the status quo by presenting an alternative that is sufficiently unsatisfying to the median voter. A more straightforward example could be that there are competing parties that do not converge on the median voter for some reason (the literature has provided a number of them, such as directional voting or the need to be generate turnout by providing distinct alternatives), such that the median is pivotal but he again effectively chooses between two somewhat dissatisfying alternatives.
These are useful criticisms. Of note are the mentions in the paper to survey-based research that does a better job than Bergstrom and Goodman at estimating individual demand functions for public goods. Still missing it seems are natural experiment-based approaches to estimating the responsiveness of policy to the median voter, such as Lott and Kenny's work on the effect of female suffrage on social spending.

Sunday, February 11, 2007

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.

Opening Salvo

My plan for this blog is to write up mini-reviews of social science papers (primarily in political science and economics). I anticipate my focus to be on empirical strategies.