Rebecca Diamond, on the market from Harvard, presented this interesting paper on inequality here on Friday. As is well-known, wage inequality increased enormously from the 1970s until today, with the divergence fairly well split between higher wages at top incomes and higher incomes to higher educated workers. There was simultaneously a great amount of locational sorting: the percentage of a city’s population which is college educated ranges from 15% in the Bakersfield MSA to around 45% in Boston, San Francisco and Washington, DC. Those cities that have attracted the highly educated have also seen huge increases in rent and housing prices. So perhaps the increase in wage inequality is overstated: these lawyers and high-flying tech employees are getting paid a ton, but also living in places where a 2,000 square foot house costs a million dollars.
Diamond notes that this logic is not complete. New York City has become much more expensive, yes, but it’s crime rate has gone way down, the streets are cleaner, the number of restaurants per capita has boomed, and the presence of highly educated neighbors and coworkers is good for your own productivity in the standard urban spillover models. It may be that wage inequality is underestimated using wage alone if better amenities in cities with lots of educated workers more than compensates for the higher rents.
How to sort this out? If you read this blog, you know the answer: data alone cannot tell you. What we need is a theory of high and low education workers’ location choice and a theory of wage determination. One such theory lets you do the following. First, find a way to identify exogenous changes in labor demand for some industry in cities, which ceteris parabis will increase the wages of workers employed in that industry. Second, note that workers can choose where to work, and that in equilibrium they must receive the same utility from all cities where they could be employed. Every city has a housing supply whose elasticity differs; cities with less land available for development because of water or mountains, and cities with stricter building regulations, have less elastic housing supply. Third, the amenities of a city are endogenous to who lives there; cities with more high education workers tend to have less crime, better symphonies, more restaurants, etc., which may be valued differently by high and low education workers.
Estimating the equilibrium distribution of high and low skill workers takes care. Using an idea from a 1991 paper by Bartik, Diamond notes that some shocks hit industries nationally. For instance, a shock may hit oil production, or hit the semiconductor industry. The first shock would increase low skill labor demand in Houston or Tulsa, and the second would increase high skill labor demand in San Jose and Boston. This tells us what happens to the labor demand curve. As always, to identify the intersection of demand and supply, we also need to identify changes in labor supply. Here, different housing supply elasticity helps us. A labor demand shock in a city with elastic housing supply will cause a lot of workers to move there (since rents won’t skyrocket), with fewer workers moving if housing supply is inelastic.
Estimating the full BLP-style model shows that, in fact, we are underestimating the change in well-being inequality between high and low education workers. The model suggests, no surprise, that both types of workers prefer higher wages, lower rents, and better amenities. However, the elasticity of college worker labor supply to amenities is much higher than that of less educated workers. This means that highly educated workers are more willing to accept lower after-rent wages for a city with better amenities than a less educated worker. Also, the only way to rationalize the city choices of highly educated workers over the time examined is with endogenous amenities; if well-being depends only on wages and rents, then highly educated workers would only have moved where they ended moving if they didn’t care at all about housing prices. Looking at smaller slices of the data, immigrant workers are much more sensitive to wages: they spend less of their income on housing, and hence care much more about wages when deciding where to live. In terms of spillovers, a 1% increase in the ratio of college educated workers to other workers increases college worker productivity by a half percentage point, and less educated worker productivity by about .2 percentage points.
Backing out the implies value of amenity in each MSA, the MSAs with the best amenities for both high and low education workers include places like Los Angeles and Boston; the least desirable for both types include high-crime Rust Belt cities. Inferred productivity by worker type is very different, however. While both types of workers appear to agree on which cities have the best and worst amenities, the productivity of high skill workers is highest in places like San Jose, San Francisco and New York, whereas productivity for low skill workers is particularly high in San Bernardino, Detroit and Las Vegas. The differential changes in productivity across cities led to re-sorting of different types of workers, which led to differential changes in amenities across cities. The observed pattern of location choices by different types of workers is consistent with a greater increase in well-being between high and low education workers, even taking into account changes in housing costs, than that implied by wage alone!
The data requirements and econometric skill involved in this model is considerable, but it should allow a lot of other interesting questions in urban policy to be answered. I asked Rebecca whether she looked at the welfare impacts of housing supply restrictions. Many cities that have experienced shocks to high education labor demand are also cities with very restrictive housing policies: LA, San Francisco, Boston, DC. In the counterfactual world where DC allowed higher density building, with the same labor demand shocks we actually observed, what would have happened to wages? Or inequality? She told me she is working on a similar idea, but that the welfare impacts are actually nontrivial. More elastic housing supply will cause more workers to move to high productivity cities, which is good. On the other hand, there are spillovers: housing supply restrictions form a fence that makes a city undesirable to low education workers, and all types of workers appear to both prefer highly educated workers and the amenities they bring. Weighing the differential impact of these two effects is an interesting next step.
November 2012 working paper (No IDEAS version). Fittingly on the week James Buchanan died, Diamond also has an interesting paper on rent extraction by government workers on her website. Roughly, government workers like to pay themselves higher salaries. If they raise taxes, private sector workers move away. But when some workers move out, the remaining population gets higher wages and pays lower rents as long as labor demand slopes down and housing supply slopes up. If housing supply is very inelastic, then higher taxes lead to workers leaving lead to a large decrease in housing costs, which stops the outflow of migration. So if extractive governments are trading off higher taxes against a lower population after the increase, they will ceteris parabis have higher taxes when housing supply is less elastic. And indeed this is true in the data. Interesting!
A Fine Theorem 