Summary Points

  • Regulatory restrictions on land use (of which zoning is one example) exert their effect of home prices through lowering elasticity of housing supply.
  • That is, in a restrictive regime, fewer houses will be produced for a given size of demand shock than in a less restrictive regime, and more of the demand shock will be reflected in price increases instead.
  • None of the City of Charlottesville’s consultants has tried to estimate Charlottesville’s supply elasticity compared to other cities (or outright).
  • We undertook to calculate supply elasticity of housing in all US counties, using three different approaches.
  • We find that in two specifications, Charlottesville has one of the highest elasticities of any county in the US. In the final specification, it has a slightly above-average elasticity.
  • Elasticity analysis is yet another piece of evidence casting doubt on the claim of a zoning-mediated crisis of housing affordability in Charlottesville.

In previous research, we have looked directly at Charlottesville’s zoning restrictiveness, both de facto and de jure. We found little evidence of an unusually restrictive regime. However, it is possible that subtleties of the regime eluded our analysis or that the regulatory barriers exist outside the confines of zoning. One way to check this is to look at the output of the regime. Is housing production in Charlottesville responsive to demand shocks?

In response to a positive demand shock, a housing market will see some combination of price increase and supply response. An elastic housing market will see a greater supply response and a smaller price increase. The elasticity does not relate only to zoning; it measures all the factors that might influence how much supply responds to shifts in demand. Of course, it is not so easy to directly measure “demand” (supply is easily measured in the housing market). Therefore, researchers use various statistical techniques to try to estimate elasticity. We adopted three different approaches to measuring elasticity and applied them to all counties in the US. We then ranked the counties on each of these measures. To make a long story short, Charlottesville shows up as having anywhere from a slightly above-average supply elasticity to one of the highest elasticities in the country.

Due to the technical nature of the estimation procedures, we won’t go that deeply into each one, instead providing a layman’s description. If any reader is interested in learning more, he or she can reach out to us at our email. The first approach is adapted from Orlando and Redfern (2018). We use a technique called sign-restricted stuctural vector autoregression on county-level time-series data of real estate prices (we used Zillow’s ZHVI and FHFA’s HPI, ultimately settling on using the former), unit construction (Census BPS), and vacancy (ACS). The SVAR allows us first to “identify” demand shocks. We then calculate an impulse-response function for prices and unit construction to a demand shock. The elasticity is defined as the ratio of the sensitivity (from the impulse-response function) of unit construction vs prices. Each county is modeled separately. Orlando and Redfern only did their calculations for a few MSAs. Our elasticity estimates for the counties in those MSAs generally agreed with their county-level estimates. Below, you can see the results for Charlottesville compared with several other counties across the USA. We included counties that one would have expected to have low elasticities and a few that one would expect to have very high elasticities. We find that our metric placed these counties as expected, which raises our confidence in he metric. Charlottesville shows up as one of the most elastic counties in the sample.

Charlottesville elasticity among highest

Our next approach was adapted from research published by the Norges Bank (Norway’s Central Bank) in 2019, by Aastveit, Albuquerque and Anundsen. The analytical approach here is to use panel data on housing prices, unit construction and vacancies to determine the impact of an increase in housing prices on supply. Again, the idea is that an upward move in prices represents a measure of demand shift, and the more elastic the market, the bigger the supply response (with a lag). We use a panel regression approach with housing permits as the dependent variable and the change in house price (lagged one year) and the vacancy rate (also lagged one year) as independent variables, plus a county fixed effect. Clearly, there is a potential for endogeneity bias given there is some reverse causality from construction to housing prices. We used change in median income (lagged one year) as an instrument for housing prices to try to deal with this. We found, however, that the results didn’t change much from using housing price change directly vs the instrumental variables approach. We excluded counties with less than 25,000 population due to data quality issues (since, unlike with the SVAR approach, the analysis is across counties, bad data from small counties can compromise the whole analysis). The county-level elasticity is given by that county’s fixed effect. Again, we find that Charlotteville does not show up as an “inelastic” county. We used the same set of counties for comparison and, as before, show percentiles.

Another approach, similar result

Our final approach is loosely adapted from Saiz (2008). Saiz tries to model elasticity slightly differently. Rather than trying to identify a demand shock or look at sensitivity to housing price changes, he postulates that elasticity is best looked at as the response of home construction to the level of profitability of building. To that end, he looks not at changes in home prices, but rather home price levels relative to factors that might affect construction costs, and to what degree a high level of prices brings forth unit additions. One tricky aspect of this analysis is the question of whether land prices ought to be a control variable or not. Since we think that proponents of upzoning would argue that land prices are conditioned on zoning, we did not control for raw land price. Our own view is that topographical characteristics and density have a stronger effect on land prices than zoning. However, by leaving out a land-price control, we err on the side of making places with high land prices look less elastic, even when zoning might not be the cause. We again take a panel regression approach at the county level. We use construction permits as the dependent variable; independent variables are the level of home prices (lagged one year), the vacancy rate (lagged one year — the idea being that there is less incentive to build in the face of high vacancy), and the level of BLS-measured construction sector wages (a measure of cost of construction). We use a random-effects model, and the county-level random effect is the measure of elasticity. Charlottesville does not look quite as extraordinarily elastic on this metric, but it remains well above the median.

Charlottesville a little less elastic in this model, but still well above median

So, in summary, we have three different approaches to calculating housing supply elasticity, and in all of them Charlottesville shows up as relatively elastic. Our easlier research looked at Charlottesville’s regulations directly and found little evidence of restrictiveness. The present analysis looks at results (housing unit additions and prices) and finds in those outputs no trace of an extremely restrictive regime.

As a final check, we tried to model the “production gap” (if any) of Charlottesville and to compare that result to the “production gap” of other counties. In this effort, we were inspired by the methodology of the pro-upzoning organization Up For Growth. This group publishes an estimate of the “housing production gap” by MSA. The basic idea of their methodology is to compare the growth in households to the growth in housing units for an MSA. But we know that households and housing units tend to stay in line with each other (they are cointegrated series) because if housing units are in short supply, people will “double up” or combine households/have roommates. Therefore, both we and UFG try to calculate a measure of “suppressed households” and add this to actual households. We do this using Census Data to find households that contain unrelated adults or multigenerational household composition. We assume that in zero-housing-gap state of the world, these “combined” households would “de-combine.” If anything, this will exaggerate the housing gap at any given point in time. Some people like having roommates. Some multigenerational households exist for reasons of care-giving or preference. Hence we are looking at the change in notional households over time relative to the change in housing units. On the housing unit side, we identify housing units held over for seasonal use or short-term rental and subtract them from the available stock. Starting from a base year (we tried it with both 2009 and 2014 as the base year), we compared the increase in “notional households” with the increase in “available housing units.” If “notional housing unit growth” exceeds “available housing unit growth” by (for example) 1%, that amounts to a 1% housing gap. Essentially, we are controlling for “initial conditions” vis a vis the existence of county-specific features that would lead to more households of “unrelated adults” or mulitgenerational households. We assume that counties that had no growth in “notional households” or vacancy rates above 10% have no housing gap. We think this is a useful check on our elasticity analysis. High elasticity markets should not show large housing production gaps. Low elasticity markets should show gaps. This is generally what we see. We do see a housing gap in some more elastic counties, but we believe that in some of these cases, there was ongoing relatively high vacancy and the “housing production gap” was just a measure of those vacancies being absorbed. In other cases, we think the deviations from elasticities reveals another phenomenon we have talked about elsewhere — that housing affordability is a coin with two sides, and the ignored reverse is income distribution. Some high-elasticity places produce fewer housing units than “notional household growth” would suggest because many of those households earn far less than what it takes to produce a new housing unit. Demand is not just about the number of notional households, but rather the number of notional households with sufficient economic resources to pay something near the marginal cost of production of a housing unit. We can see, though, that at least as regards Charlottesville, there does not appear to be a housing production gap.

Negative gap means insufficient housing production

We think it is pertinent that Up For Growth‘s own analysis shows that the Charlottesville MSA does not have a housing gap.

Narrative is not a substitute for numbers. That Charlottesville’s Comp Plan is so disconnected from the city’s true situation might have something to do with the city’s decision to hire a firm that boasts of “telling the stories of the built environment” rather than to engage additional support to conduct data-driven, scientific analysis of the housing market. We have long given up hope that the city has the capacity to do the right kinds of analysis or even to properly identify and evaluate advisors who can. Instead, we have reluctantly undertaken to do some of this analysis ourselves. We now wonder if it is too much to ask for the city even to consider facts and analysis in its zoning rewrite, or if our through-the-looking-glass City Council has decided to operate on a prescription-first-diagnosis-later basis.