Please Don't Regress Quantities and Prices

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R1 of Housing Market Interventions and Residential Mobility in the San Francisco Bay Area

This is an R1 of a recent working paper by the Stanford Changing Cities Lab, studying the effects of new market rate construction on displacement, basically asking whether that new apartment complex in your neighborhood results in low-income tenants being kicked out.

To set up the paper, there's been a recent series of papers about the hyper local effects of new housing construction on neighborhoods. At this point, it's pretty well established that restrictions on the supply of housing drive up rent prices and induce displacement on a metro level, but the hyper local effects of new construction are less well understood, in large part because local production of housing is endogenous. Builders tend to want to build where people want to live, which becomes a problem for getting causal estimates of the effects of new housing.

On it's face, it's not actually a ridiculous argument that development could have hyper local effects. Amenities are endogenous, there can be some signaling effect (build it and they will come), and if people have preferences for living with people with similar income levels then yes, you can even have induced demand. All of these could raise local rent prices and displace existing residents, even if the effect over the entire metro area is to reduce rents. The worry would be that new construction, which is often built in low-income neighborhoods because they lack the ability to NIMBY like their richer counterparts, could displace low-income tenants.

This is, in fact, what the authors find. From the summary:

"In sum, we find that market-rate housing production is associated with increased moving—both out of and into neighborhoods—across all income/financial stability status (hereafter SES) levels, except for the highest-SES households, who move out less with more housing production and are relatively more likely to move in than the lowest-SES groups

Extremely low- to low-SES groups experience increases in outmigration of 1-2% in each subsequent year for 4 years when new market-rate construction occurs in their block group, whether there are 100 or 1,000 new units. For example, while in a normal year 10% of households might move out, new construction will mean that 12% move out per year for the next 4 years. In a block group that houses 500 households with 50 moving out in a typical year, new construction will result in 60 households moving out each year after construction, totaling 40 additional displaced households in 4 years."

To come to this conclusion, the authors run a series of linear probability models that

"estimate the probabilities that a mover makes a constrained move as a result of new production."

The authors add the following individual level controls including:

• whether whether the household has a mortgage as a proxy for homeownership,
• whether the household has delinquency on credit accounts as a proxy for financial instability,
• the adult household size,
• the race of household head,
• length of residence,
• number of children,
• number of adults,
• marital status.

And the following neighborhood controls including:

• percent Hispanic,
• percent college-educated in 2000,
• percent foreign-born in 2000,
• poverty rate in 2000,
• percent homeownership in 2000,
• median home value in 2000,
• median gross rent in 2000
• vacancy rate in 2000,
• percent of housing built in the last 20 years based on 2000 US Census data,
• number of subsidized units,
• a city fixed effect,
• a lagged amount of neighborhood churn,

and the variable of interest, which is the log number of new market rate housing units built in the previous year.

Author's Note: Just add a fixed effect!

So the statistical argument goes as follows:

The authors take tenants with similar demographic and in neighborhood characteristics, but whose neighborhoods built different levels of market rate housing and compare the rate at which they displaced.

There are two major problems with this methodology:

1. Change in Quantity Supplied is endogenous.

Neighborhoods with similar demographic characteristics can experience very different demand shocks, even within the same city, and the authors do not observe these demand shocks, only the changes in housing supply. San Francisco's gentrification wave was characterized by an influx of high-income tech workers moving into working class neighborhoods. In San Francisco's case, those neighborhoods tended to be located nearby downtown, where there was access to transit, reasonable rent prices, and night life cultural amenities. We would expect, absent new construction, that the neighborhoods preferred by high-income techies would experience large increases in rent. We would also expect that this increased demand for housing should spur more market rate housing construction than in neighborhoods that didn't experience demand shocks.

However, unless housing demand is perfectly elastic (which it absolutely isn't, in San Francisco of all places), then any increase in demand for housing will drive up rental prices even if there is an accompanying increase in supply, which could lead to some level of displacement, particularly in the short term. Thus, if we regress housing construction on displacement we will almost always find that increased construction is associated with displacement because a positive shock to housing demand causes both a supply increase and a rent increase. This is true even in a world where new housing construction lowers local rent levels!

The question the researchers should be asking is whether a neighborhood that built more housing would have had less displacement than if it had built less. edit: whether a household would have experienced a higher probability of displacement had their neighborhood built more housing compared to less. This is a similar question to the one asked by Kate Pennington, which is coincidentally also about San Francisco (she looks at prices rather than displacement). She uses fires as a source of exogenous shocks to the supply of housing to figure out whether increases in market rate housing construction lead to increases in rent, with the argument being that fires are random and make development easier (by reducing the costs of tearing down the existing structure). She finds that fact market rate construction reduces rent prices.

Asquith, Mast, and Reed (2021) are another good example of how the authors should have conducted their study. They use a series of difference in difference models based on idiosyncratic variation in timing of individual construction projects to estimate the effect of new construction on rent prices.

2) No consideration for spillover effects

This is a smaller problem than the first one, but still worth noting. The authors make no attempt to model the spillover effects of new housing. Explicitly, their model says that the effects of new housing production stop at the boundary of the Census Block Group. For a trivial example, consider an apartment complex built on a corner bordering another Census Block. The model says that this apartment complex has an affect on displacement down the block, but not across the street, which seems incorrect. Mathematically, it's likely that this pushes their results towards zero (if you think market rate construction displaces tenants, then it should also do that in nearby neighborhoods, which will tend to be demographically similar and will not have built as much housing).

In summary, everything other than the regressions in this paper is great. The data work is wonderful, and these are some of the highest quality measurements of what displacement looks like (where people move to and from). Quantifying residential churn is also a very important project, in and of itself. But please don't reg p q, r.