1. Introduction
This paper studies the effects of remote work on housing affordability and inflation. We argue that the longrun impacts of remote work on housing affordability are likely to be different than the shortrun changes because housing supply is more elastic in the longrun and heterogeneous across space. We consider two ways that remote work changes housing demand. First, demand shifts away from the central business districts of large cities, where housing is inelastically supplied. Because relative demand increases in areas with inelastic housing supply, housing costs fall on average in the long run. Second, remote work increases the demand for space. This force raises the cost of housing in both the short and long run, but with smaller longrun effects because housing supply is more elastic.
Understanding the longrun effects is important in part because the shortrun effects of remote work have been so large. Real rents in the United States rose by eight percent and real house prices rose by over twenty percent from 2020 to 2022, and these changes have been heterogeneous across space. A growing body of literature has argued that many of these shortrun changes are due to remote work.1 If the longrun effects are different than the shortrun effects, as we argue, this means that there are still substantial changes to come for housing markets.
We study the net effect of these forces using a model of the U.S. housing market designed to capture housing demand in the short and longrun, as well as differences in short and longrun housing supply elasticity. Building on Howard and Liebersohn (2021), households have demand for a quantity of housing and demand for living in a location, in this case, a county. Locations have a sitespecific longrun housing supply elasticity. We derive formulas for rent and population changes in each location as a function of shocks to housing demand and the demand to live in each location, given supply elasticities and the two demand elasticities.
We use this model to calculate the longrun effects of remote work in two steps. We first invert the model to calculate the housing demand shocks and location demand shocks caused by remote work using observed rent and population changes from 2020–2022. Backing out the shocks requires assumptions about housing demand elasticity which we take from the literature. Importantly, we assume that the housing supply is inelastic in the short run. To confirm that our location demand shocks are indeed related to remote work, we validate that the shocks for each county are correlated to local remote work measures from Dingel and Neiman (2020).
In the second step, we consider a longrun version of the same model where housing is supplied with a longrun elasticity specific to each region. We then consider the housing and location demand shocks from the first step and ask what effect these shocks would have on aggregate rents in the long run. We show in the model that there are two forces that govern house prices and derive simple formulas for them. The first force is the effect of the changing demand for where people want to live, which we call the location demand channel. We calculate the magnitude of the location demand channel by feeding in the location demand shocks from the first step, assuming that the housing supply elasticity in each region equals its longrun historical levels. Under our preferred calibration, the shift in location demand to more elastic areas will cause a 0.3 percentage point decline in rents in the long run.2
In addition to changing where people wanted to live, remote work raised demand for housing in general which caused rents to rise. We call this second force the housing demand channel. Similar to the location demand channel, we calculate the size of the housing demand channel by feeding the implied housing demand shocks into formulas derived from the longrun version of the model. The estimates shows that the longrun effects of greater housing demand on rents are less than onehalf of the shortrun effects. The precise amount of the housing demand shock is somewhat uncertain, because housing demand rose from 2020–2022 for reasons other than remote work.3 Under the conservative assumption that the entire increase in demand for housing quantity was due to remote work, we estimate that the longrun impact of the housing demand channel is a 1.8 percentage point increase in rents. Since the shortrun effect is even larger, this implies a decline of about 5.2 percentage points from the shortrun to the longrun.
The net effect of remote work on housing costs is the sum of the effects coming from housing demand and location demand. Taken together, the longrun effect on real rents will be about onefifth of the short run effect on average. We also show that the net effects of remote work vary across space. For the five most expensive U.S. cities, the net effect of remote work will be a fall in housing costs.
Our results also have implications for the housing component of the consumer price index (CPI). Because the CPI is a measure developed for urban consumers, the rental component of CPI is calculated for 87 urban areas, not the entire country (Bureau of Labor Statistics, 2013). These urban areas experienced a relative decline in location demand versus the rest of the country, so both the short and the longrun effects of remote work on CPIrents are more negative than the effects on the average rent. We calculate the effect on the housing component of CPI by considering the model’s implications for the areas that are measured for CPIrents, finding that the effect of location demand on CPI counties is about −1 percentage points.
The housing demand channel is an example of the Le Chatelier (1884) principle in that the longrun housing supply is more elastic than the shortrun, leading to smaller effects on prices in the longrun. The location demand channel has a bigger impact because the average housing supply becomes more elastic when people choose to demand housing in places that are more elastic. For this channel, the distinction is not about the short versus the longrun, but rather the location that people are choosing.
Two stylized facts motivate the model assumptions and structure. The first stylized fact is that real rents grew by 8 percent, with most of the change occurring over a sixmonth period in mid2021. The rise in real rents appears in a variety of data sets and was a major driver of inflation over the same time period. The second stylized fact is that populations and rents grew in areas where housing supply has historically been more elastic. Looking within urban areas, populations fell and rents grew by less in center cities, as compared to the suburban and exurban ring surrounding them. Rents and populations also grew less in the surrounding countryside, leading to what Ramani and Bloom (2021) call the “Donut Effect.” The fact that demand fell in supplyinelastic areas, and rose in supplyelastic areas, motivates us to study the longrun effects of regional demand changes on rental affordability.
Throughout, we compare the effects of remote work to a counterfactual where location and housing demand did not change. This means that our estimates are conservative relative to a counterfactual where location demand continued to shift towards inelastic places, as it had done in the previous two decades (Howard and Liebersohn, 2021).
In the later part of the paper, we expand our model to include a notion of house prices as the present discounted value of rents. We find that crosssectional regressions of shortrun house price changes on shortrun rent changes give similar coefficients in both the model and the data, lending credibility to the longrun predictions of our model.
The structure of the model allows us to easily calculate the longrun effects of remote work under a variety of possible scenarios: first, we consider alternative assumptions about the effects of remote work on housing demand, and second, we consider different assumptions about the future of remote work. Since the location demand channel scales linearly with the size of the shock, an increase in remote work will raise the location demand channel proportionally to our baseline estimate. Finally, we consider alternate assumptions about how remote work might affect where people decide to move.
1.1. Literature review
Prior to the COVID19 pandemic, only a few papers considered the implications of remote work. Blinder (2005) emphasized the potential tradability of service jobs through improved telecommunications. Ozimek (2019) argued that occupational tradability predicted domestic remote work and not job loss. Dingel and Neiman (2020) extended this research by calculating the remote work potential for jobs across cities, introducing occupational remoteability scores that are widely used today.4
The rise of remote work during the pandemic sparked increased research interest, particularly regarding its impact on the housing market. Within cities, remote work shifted housing demand from highdensity, highcost areas to lowerdensity, lowercost locations (Davis, Ghent, Gregory, 2023, Ramani, Bloom, 2021, Gupta, Mittal, Peeters, Van Nieuwerburgh, 2021, Brueckner, Kahn, Lin, 2021). Remote work also shifted housing demand across cities, moving demand from high productivity, high cost, high density places towards lower productivity, lower cost, lower density places (Davis, Ghent, Gregory, 2023, Ozimek, Althoff, Eckert, Ganapati, Walsh, 2022, Liu, Su, 2021, Brueckner, Kahn, Lin, 2021). Remote work also increased the overall demand for housing in the shortrun (Davis, Ghent, Gregory, 2023, Mondragon, Wieland, 2022, Ozimek, Carlson).
We build on this research by considering the longrun implications of remote work for aggregate housing costs using a spatial equilibrium model. While existing literature has predominantly focused on crosssectional demand changes during the pandemic, our contribution lies in studying the aggregate longterm effects of remote work on housing affordability. To understand these implications, we propose a model of the aggregate housing market that incorporates the interaction of local markets through migration.5 Our results show that the effects of remote work can be quite different in the long run as compared to the short run.
Another line of research uses quantitative spatial equilibrium models to investigate remote work. These models incorporate rich features such as spatial spillovers and a model of production. In contrast, our moreparsimonious model highlights the particular mechanism we have in mind and allows us to solve for sufficient statistics related to those mechanisms. Davis et al. (2023) examine the productivity effects of remote work and highlight adoption externalities that contribute to its rapid increase. Like ours, their model considers the effects of remote work in the shortrun and the longrun, where the longrun difference is that housing supply is allowed to adjust.6 While they consider many outcomes that we do not, their results on rents are qualitatively similar to ours: an increase in rents in the shortrun, which is moderated in the longrun by the adjustment of housing supply.7 Compared to their paper, our paper models each county individually instead of considering only two residential locations, allowing us to calculate counterfactuals for specific geographies.8 Furthermore, we base our calibration on the shortrun rent changes, allowing us to match the shortrun exactly and only using the model to calculate the longrun.9 Finally, our paper has a closed form solution for longrun rent changes which we think is helpful for understanding the economics of the effects of remote work on housing markets, in particular the decomposition of the aggregate effect into location demand and housing demand.
Delventhal and Parkhomenko (2020) and Delventhal et al. (2022) estimate the welfare, price and mobility effects of the rise of work. Both papers feature endogenous agglomeration externalities and congestion costs, and Delventhal and Parkhomenko (2020) models the underlying reasons for increased remote work, distinguishing technological from preferencebased reasons. Both papers are focused on the longrun, but they find one similar result to ours, which could be interpreted as a difference between the short and longrun: when floor space is not allowed to adjust to the remote work shock in their model, residential rents are higher.10 Given the focus of their paper on the reasons for greater remote work and the impressive quantitative features that shed light on its implications for income and welfare, it is not possible to decompose this exercise into a location demand or housing demand channels as we do here.
2. Data
We create a panel of migration, real rents, house prices, and other covariates at the county level. We use countylevel data because we want to capture changes in demand in relatively narrow areas: for example, we hope to measure differences between suburbs and center cities. We face a tradeoff between granular geographic and data coverage because geographic units narrower than counties tend to have sparse data coverage. For example, ZIP codelevel rent data does not cover the entire country, and imputing it from higher geographic levels would lead to inaccuracy. We chose counties as the constrainedbest mix of narrow geographies and data availability.
In Howard and Liebersohn (2021), we use longrun housing supply elasticity from Saiz (2010); however, the Saiz (2010) elasticities are disadvantaged in that they only include MSAs and miss rich geographic variation within MSAs. Instead, we use the census tractlevel elasticities in BaumSnow and Han (2022), which we aggregate to the county level by taking the populationweighted average across tracts.11 We use their preferred measure, the quadratic finitemixturemodel elasticities of housing square footage.
The elasticities in BaumSnow and Han (2022) are only available in certain areas, meaning that some rural areas are missing from the elasticity measure. Our model requires elasticities for the entire country, so we impute them by assuming that they are equal to the 95th percentile of elasticity in the data, which is about one. Housing supply elasticity is closely related to population density, and this value is roughly what we would expect based on the population density of rural areas in the data. Appendix Figure A1 shows that the missing locations are at roughly the 5th percentile of population density.12
In the crosssection, movements in rents and house prices during this time are highly correlated.We focus on rents for the quantitative exercises, so as not to worry about changes in interest rates or expectations that may have affected home prices. At the same time, we believe our results can be useful for thinking about house prices in the longrun.
Data on both prices and rents comes from Zillow: for prices, we use the Zillow Home Value Index (ZHVI) at the county level, and for rents, we use the Zillow Observed Rent Index (ZORI) which is provided to us by Zillow at the county level. The ZORI is the average of the middle quintile of rents in each location, created using a repeatsales methodology similar to Ambrose et al. (2015). It is then reweighted to be representative of the entire housing market with weights calculated using property characteristics from the American Housing Survey. Finally, it is seasonally adjusted and smoothed using a threemonth moving average.13
The ZORI has several advantages over other rent indexes. One advantage is that it is representative of the entire housing market, not just the multifamily market like data from CoreLogic and other sources. Compared to CPIrents it is available at a more granular level and for a larger number of locations, and it is more highfrequency and less smoothed. We do expect the ZORI to closely match CPIrents over longtime horizons when we consider the locations used to calculate CPI. To understand the implications of our results for CPI, we will consider the effect on those locations explicitly.
The ZORI includes rents for areas that include most of the U.S. population but it is still missing for many rural places; we infer what is happening in these places using price data. To extrapolate rents for these locations, we run a crosssectional regression of rent changes on price changes and take the fitted values wherever the ZORI is missing. Appendix Figure A2 shows rent changes and inferred rent changes for places with and without ZORI data. In general, places with missing rents data tend to have low population, and since our results are populationweighted, this procedure is unlikely to matter that much.
Population changes come from Census and post office change of address requests. The post office data is the result of a Freedom of Information Act request from Ramani and Bloom (2021), and we clean the data in the same way as Ramani and Bloom (2021). Specifically, we measure gross address changes in each ZIP code as the gross number of individual moves plus the gross number of households multiplied by 2.5. Net moves are the difference between gross moves in and gross moves out. We aggregate moves at the ZIP level to the county level using a correspondence file from the Missouri Census Data Center. Finally, we adjust the population growth rate in all regions by a constant, to reflect the fact that the post office changes capture more outmigration than inmigration, and that the overall population grew slightly during this time period. We pick the constant to match the aggregate population growth as estimated by the Census Bureau.
We validate the use of the post office data by comparing it to a subtimeperiod in which we can compare it to estimates from the U.S. Census. We do this in Appendix B.
Data on remote work comes from Kolko (2020). This measure builds on the workfromhome propensity measure developed by Dingel and Neiman (2020) and is aggregated to the county level using employment shares from U.S. census data.
We measure natural amenities using the natural amenities scale from the United States Department of Agriculture Economic Research Service (2019). The scale combines six climate, topography, and water measures and is available at the county level. The highestamenity places are coastal areas with warm winters, and the lowestamenity places are flat, landlocked locations with extreme weather.
All nominal variables are deflated by CPI.
3. Stylized facts
This section reviews stylized facts about the time series and crosssection of the U.S. housing market from 2020 to 2022. These facts are the main aggregate and regional patterns that our model is intended to interpret. They will also be a natural benchmark for comparison to the longrun changes we discuss in Section 6.
3.1. Rent and population changes
The first fact we document is the increase in real housing costs coinciding with the rise of remote work. Fig. 1 shows real rents and real house prices indexed to January 2020. Real rents rose by about eight percentage points, with most of the change concentrated in early 2021. Real house prices rose by about twentyfive percentage points. The fact that rents and house prices rose at about the same time suggests a role for an underlying shock affecting both markets.
Fig. 1. Panel A of shows the ZORI (Zillow Observed Rent Index) indexed to January 2020 dollars. Panel B shows the ZHVI (Zillow Home Value Index) indexed to January 2020 dollars.
Based on the timing of rent and price changes, we think that changes during the COVID19 pandemic increased demand for housing. Possible reasons include both rising demand for space due to remote work and an increased rate of household formation. We think that remote work increases demand for home offices (Behrens, Kichko, Thisse, Stanton, Tiwari) and raises the value of living space if people spend more time there. For these reasons, we think that remote work played an important role in raising housing demand.
The second fact we document is changes in where people demanded housing. Demand shifted away from highdensity, high price areas (like city centers) and towards lowerdensity, lower price areas, such as suburbs and rural areas. Fig. 2 provides evidence using price and population data. Panel (a) is a binned scatter plot of countylevel population changes from 2019 to 2021 against county population density. Panel (b) is a binned scatter plot of countylevel real rent changes against population density. Panels (c) and (d) show population and rent changes respectively graphed against average rent levels from Zillow.14
Fig. 2. This figure shows binned scatter plots. Panels show the relationship between rent/population changes and population density (Panels A and B) and between rent/population changes and ex ante prices (Panels C and D). Plot created with 20 bins, which are weighted by 2019 county population.
Panels (a) and (b) provide evidence that housing demand shifted from dense central business districts (CBDs) to relatively suburban and rural areas. These figures are consistent with the evidence in several recent papers showing shifting demand away from citycenters.15 Population changes are Ushaped; populations fell the most in the densest and most expensive counties, but rose the most in areas with densities and rents near the middle of the distribution. This confirms the “donut” pattern documented in Ramani and Bloom (2021). As with the time series rise in rents, we might expect changes to housing demand to come either from the rise in remote work or from temporary pandemicrelated factors. We find no evidence for a reversal in the location of housing demand, suggesting that temporary pandemic factors were not the main driver.
Panels (c) and (d) of Fig. 2 show that the relative rise in demand for lowdensity areas also led to a rise in demand for cheaper areas. Rents rose by less in the highestprice, most dense areas. Rent data is not available in the lowestdensity areas so the Ushaped pattern is not as pronounced in panels (c) and (d). The association between demand for low density and lowcost areas is not surprising, because rural areas tend to have lower rents. If living near a central city is no longer desirable, the places people move to will be cheaper. In addition, if remote work increases demand for space, we would expect them to move to areas where space is cheaper. What is more surprising is that rents rose even in places where they were cheap prepandemic (these places also have a high housing supply elasticity).
3.2. Discussion
The time series and crosssectional changes shown in Figs. 1 and 2 point to changes in housing demand during the pandemic. The patterns in these figures motivate a model which can capture different types of demand shocks coming from the rise of remote work: first, a shock to demand for location (i.e., location outside city center), and second, a shock to housing demand, since people want bigger houses or want to form new households.
Previous papers have already documented many of the same facts, such as the shift in demand from central cities to lowerdensity suburban areas. Our goal is to interpret changes in rents and populations through a structural model that allows us to make predictions for the longrun effects of housing supply elasticity. To model these shocks, we build on the longrun housing market model developed in Howard and Liebersohn (2021).
The model in Howard and Liebersohn (2021) interprets changes in rents, populations, and housing quantities using housing demand shocks, location demand shocks, and housing supply shocks. To capture the shortrun dynamics of the housing market from 2020–2022, we modify this model by setting the housing supply elasticity to zero in the short run. Assuming that housing supply is inelastic in the short run captures a key fact of the pandemic: housing prices rose everywhere, even in places where it used to be very easy to build. We think that inelastic shortrun housing supply is a good approximation because the rise in rents—even in rural areas—suggests that the housing supply could not accommodate demand changes right away. Permitting can take years even in relatively flexible housing markets, and evidence from Glaeser and Gyourko (2006) shows that the construction sector generally responds to demand shocks with long lags. Supply chain disruptions during the pandemic may also have made construction delays worse than otherwise.
The first step in our analysis is to back out the shocks to location and housing demand using the structure of our model. The result is a locationspecific housing demand and location demand shock implied by changes in rents and populations. In the long run, we think that housing supply is somewhat elastic. To simulate the longrun effects of remote work, we consider the same shocks in a model where supply elasticities are their prepandemic longrun values. With the same location and housing demand shocks in the longrun version of model, we can calculate the net effects on real rents.
One approach taken in the literature has been to run reducedform regressions of changes in housing costs (or population) on regional characteristics. Reducedform regressions are insufficient if we want to make counterfactual statements or understand the longrun effects of new construction. One reason is that the longrun depends differently on the different demand shocks which reducedform estimates cannot distinguish. For example, remote work increases the demand for housing and lowers the attractiveness of living in the CBD of major metros. Both of these forces will cause people to move to more rural areas where housing costs are lower. In the long run, this movement will decrease rents because housing is more elastic in cheaper, more rural areas. In addition, rents will fall as supply is able to respond since supply everywhere is more elastic in the long than the shortrun.
We abstract away from the ultimate sources of location and housing demand shocks, some of which have been considered in the previous literature (Davis, Ghent, Gregory, 2023, Delventhal, Parkhomenko). The approach allows for a model that is rich enough to capture the key housing market changes that occurred during the pandemic, while also providing intuitive formulas for the longrun effects of remote work that we can derive analytically. At the same time, the model is flexible enough to discuss how results might be different under different assumptions about the future of remote work, or with different assumptions about the elasticity of housing demand.
4. Model and calibration
In this section, we modify the model from Howard and Liebersohn (2021) to include both a short and a longrun component. The shortrun version of the model assumes the housing supply is inelastic everywhere whereas the longrun version allows for locationspecific housing supply elasticities. We show how to use the shortrun model to decompose the data into “shocks” to housing demand and location demand, assuming that the housing supply elasticity is zero everywhere. Then, using the longrun version of the model, we derive formulas for the effect of the shocks on housing costs in the longrun.
This section lays out the framework to tell us how to interpret the shortrun data and calculate the longrun equilibrium effects. In later sections, we will use this framework, along with observed data from 2020–2022, to estimate the longrun effects of the housing market shocks of recent years.
4.1. Model
We consider a model of I discrete locations, indexed by i, over three time periods, T=0,1,2, where T=0 is the prepandemic period, roughly early 2020, T=1 is the shortrun, roughly early 2022, and T=2 is the longrun. A mass L of people, indexed by j, choose a location and a housing quantity at time T=0. Housing is produced and supplied according to a longrun housing supply curve. A fraction of people adjust their location and housing quantity at T=1, but the quantity of housing is held fixed. In the longrun at T=2, everyone adjusts and housing is built along the original housing supply curve. For most of our analysis, we consider the logdifferences between T=0 and T=1, which we call shortrun changes, or T=0 and T=2, which we think of as longrun changes. We typically suppress the T notation for simplicity.
Individuals choose location based on a location specific utility—which incorporates wages and amenities—and the rent. They also receive a matchspecific utility shock, which we assume is distributed as an i.i.d. Gumbel as is standard in the literature.16
Uij=v(ui,ri)+ζijwhere ui is a cityspecific term that accounts for wages and amenities, and ri is the rent. v(·,·) is decreasing in ri, and we assume that its elasticity is −1.17Percapita housing demand is then given by(1)hi=h(xi,ri)where xi is a housing demand shifter, such as wages or the demand for remote workspace.18We assume h(·,·) is decreasing in ri with a constant elasticity λ.In periods T=0 and T=2, housing production is described by Hi=Zi1σi+1Xiσiσi+1, where Zi is local land and Xi is the tradable good whose price is normalized to one. This defines a supply curve:(2)
logHi=σilogri+constantiCrucially, housing supply elasticity depends on i.19Local housing markets clear, so the total amount of housing is the per capita housing times the population.(3)Hi=LihiEveryone must live in a city:(4)L=∑iLiwhere L is the total population of the country.Because of the extreme value distribution, the population of a city at time T=0 or time T=2 is:Li=Lv(ui,ri)μ∑kv(uk,rk)μwhere 1/μ is the scale parameter of the Gumbel distribution. The summation in the denominator is over all cities in the economy. Taking the log of the previous equation,(5)
logLi=μlogv(ui,ri)−u˜where u˜ is defined as log∑kv(uk,rk)μ. Importantly u˜ is an endogenous object, but it does not depend on i.Eqs. (1)–(5) define the equilibrium at time T=0. For time T=1 and T=2, we consider deviations from that equilibrium.First consider T=2, i.e. the long run. We take a loglinearized approximation of the indirect utility around the steadystate, as in Howard and Liebersohn (2021):(6)
dloghi=−λdlogri+ϵi(7)
dlogHi=σidlogri+ξi(8)
dlogLi=−μdlogri+ηi−du˜(9)
dlogHi=dlogLi+dloghi(10)
dlogL=∑iLidlogLi=EdlogLiwhere the expectation is initialpopulationweighted. ηi is a shock in location demand, ϵi is a shock to housing demand, and ξi is a local shock to housing supply. λ is the housing demand elasticity and μ is the location demand elasticity.20 We assume both elasticities are constant across cities. These five equations are a housing demand (per capita) curve, a housing supply curve, a location demand curve, a housing market clearing condition, and a population addingup constraint. Note that the addingup constraint is a loglinear approximation.21With these equations, then for any set of shocks ϵi, ηi, and ζi, we can calculate the log change in rents, housing quantities, and populations.The shortterm, T=1, has a similar structure, but with a couple of key differences. We assume that shortterm housing supply is fixed, and we allow only a fraction ϕ of people to adjust the size or quantity of their housing in response to the shocks.22 The 1−ϕ fraction of people that cannot adjust stay in the same location and consume the same amount of housing as they did at T=0. The housing market clearing condition, and the population addingup constraint are the same as in the longrun. The equations for T=1 are:(11)
1ϕdloghi=−λdlogri+ϵi(12)dlogHi=0(13)
1ϕdlogLi=−μdlogri+ηi−du˜(14)
dlogHi=dlogLi+dloghi(15)
dlogL=∑iLidlogLi=EdlogLiIn contrast to the longrun equations, we will use these equations, along with data on population changes and rent changes to infer what the shocks ϵi and ηi−du˜ are in the shortrun. We go into more detail in the following subsections.
4.1.1. Calculating shocks from the shortrun model
Using Eqs. (11)–(14), we can use the shortrun model to identify the shocks to housing demand and location demand (up to a constant):(16)
ϵi=−1ϕdlogLi+λdlogri(17)
ηi=1ϕdlogLi+μdlogri+du˜This is done by solving the system of linear equations for ϵi and ηi, so that it can be expressed in terms of observed moments of the data: the change in population and rents.
4.1.2. Longrun effect of housing demand shocks
If those same shocks persist into the longrun, we can estimate their effect on the longrun rents using a version of the model where the σis are set to their longrun values. Define the Housing Demand Channel to be the difference in average rents at T=2, Edlogri, between an equilibrium with the ϵi shocks and an equilibrium where the ϵi shocks are all set to 0.23 Then, for the housing demand shocks ϵ, their longrun effect on aggregate rents is:(18)
HousingDemandChannel=Eϵiλ+μ+σiEλ+σiλ+μ+σi(19)
=−1ϕEdlogLiλ+μ+σiEλ+σiλ+μ+σi+λEdlogriλ+μ+σiEλ+σiλ+μ+σiwhere Eq. (19) comes from plugging Eq. (16) into Eq. (18). Note that if μ=0, then (18) simplifies to E[ϵi/(λ+σi)], and if μ→∞, then (18) simplifies to E[ϵi]/(λ+σ¯) where σ¯ is the average of σi, weighted by population.Intuitively, the housing demand channel is larger when the shocks to housing demand, ϵ’s, are larger and smaller when housing demand or supply is more elastic. This effect does not depend on how mobile people are across locations if the demand shocks are uncorrelated to the housing supply elasticities. To note, if population growth is zero and μ→∞, then the longrun effect of housing demand is the initial rent increase times λλ+σ¯. This is the ratio of the sum of the supply and demand elasticities in the short and longrun, which often shows up in applications of the Le Chatelier (1884) principle.Similarly, define the Location Demand Channel to be the change in T=2 rents for a particular set of ηi shocks as compared to all the ηi shocks being set to 0.24 This is given by:(20)
LocationDemandChannel=1Eλ+σiλ+μ+σiCov(1μ+λ+σi,ηi)(21)
=1ϕ1Eλ+σiλ+μ+σiCov(1μ+λ+σi,dlogLi)−1Eλ+σiλ+μ+σiCov(λ+σiμ+λ+σi,dlogri)
The location demand channel depends on the covariance of the location demand shocks with an expression that depends on the local housing supply elasticity.25 If the location demand shocks are larger in places with higher elasticities, that will have a negative effect on average rents.
Note that as μ→∞, Eq. (21) simplifies to
−Cov(σi,dlogri)/(σ¯+λ). And if μ=0, then the location demand channel simplifies to
Cov((λ+σi)−1,dlogLi)/ϕ. This is because when μ is large, the location demand shocks are reflected in the rent changes of a place, whereas when μ is small, the population changes are the primary way to measure location demand shocks. In either case, if people want to move to more housingsupplyelastic places, that causes overall housing costs to fall.
4.2. Calibration of model parameters
In the next section we will use the formulas from the model to back out the location demand shocks ηi and housing demand shocks ϵi. The formulas used to calculate the shocks depend on housing demand elasticities. Here, we discuss the sources of these and other parameters, their interpretation, and the range of estimates that we think are reasonable.4.2.1. Location demand elasticity μThe parameter μ governs how sensitive people are to the price in a particular location. A large value of μ decreases agents’ locationspecific preference and results in a more elastic location demand. At one extreme, μ=0 would imply that households’ location demand is perfectly price inelastic. In this scenario, changes to location demand are reflected in population changes only. At the other extreme, μ→∞ implies that households are perfectly elastic to price changes. Previous papers in the tradition of Rosen (1979) and Roback (1982) make this assumption implicitly by equalizing utility across space. When μ→∞, shocks to location demand are reflected in the crosssection of real rent changes.The literature proposes a variety of values for μ, nearly all above one and many as high as infinity.26 We use μ=1.07, following Hsieh and Moretti (2019) and Parkhomenko (2020).27 We will show that ultimately the estimates depend very little on the particular value of μ that we choose for the calibration.
Table 1. Main Results.
Empty Cell(1)(2)(3)(4)(5)(6)RegionShort Run TotalShort Run Location DemandShort Run Housing DemandLong Run TotalLong Run Location DemandLong Run Housing Demand
μ=1.07
National .07 0 .07 .015
−.003
.018 CPI Cities .056
−.012
.068 .009
−.01
.018 Expensive Metros .012
−.06
.072
−.013−.035
.022
μ=100
National .07 0 .07 .013
−.003
.016 CPI Cities .056
−.014
.07
−.001−.017
.016 Expensive Metros .012
−.058
.07
−.044−.06
.016
BaumSnow & Han Elasticity
National .07 0 .07 .037
−.003
.041 CPI Cities .056
−.012
.068 .025
−.014
.039 Expensive Metros .012
−.06
.072
−.007−.05
.043
Location Demand Projected Onto Remote Work Measure
National  0  
−.001
 CPI Cities 
−.007
 
−.004
 Expensive Metros 
−.057
 
−.032

Notes: This table shows the main results, as well as alternative calibrations for the model. The numbers represent the percentage point change in rents relative to February 2020. λ is the housing demand elasticity, how much demand for housing demand declines as a function of costs. ϕ is the share of households who want to migrate who are actually able to migrate in the short run. μ is the location demand elasticity, how sensitive people are to prices in each location. The benchmark calibration uses λ=2/3 and ϕ=0.5. The first two sections show calibrations for μ=1.07 (as in Hsieh and Moretti 2019 and Parkhomenko 2020) and μ=100 (as in Howard and Liebersohn 2021), respectively. The third section shows BaumSnow and Han (2022) Elasticity with μ=1.07. The fourth section uses a projection of η onto the remote work measure with μ=1.07. CPI cities include all Metropolitan Statistical Areas which are used to calculate CPI. Expensive metros are the counties in the New York, San Francisco, San Diego, Seattle, and Boston Metropolitan Statistical Areas. Within each category, the average is taken by 2019 population.4.2.2. Housing demand elasticity λThe housing demand elasticity tells us how much housing demand declines as a function of housing costs. At one extreme of the literature, λ=1 corresponds to CobbDouglas demand, so households spend a constant portion of their income on housing in each city, regardless of the price. At the other extreme, λ=0 would imply unit housing demand, so housing quantities do not change with price.We use λ=23 as our benchmark value, based on an estimate from Albouy et al. (2016). We discuss how important the value of λ is in this setting in Section 6.2.4.2.3. Mobile share of households ϕThe parameter ϕ governs the fraction of households that are allowed to adjust their housing in the short run. If ϕ=1, all households adjust their housing and location based on their demand shocks and the rent changes. If ϕ is small, the model will interpret the same data as coming from a larger underlying shock but where fewer households are allowed to move. In this case, the longrun effects of the shock may be larger than the shortrun.We think ϕ is the hardest parameter to calibrate because there is little evidence about it. We view different values of ϕ as making different predictions about the future of remote work. Ozimek (2022) provides survey evidence from November 2021 that four times as many households plan to move because of remote work as were able to. If all these households end up switching to working remotely and that none did between November and February, it will imply that ϕ=14. Therefore, as our benchmark we take ϕ=12, which we consider conservative relative to the survey results. We also consider other values of ϕ as a way to explore the range of possible effects that remote work might have. Overall, we think that ϕ between 14 and 1 may be possible.284.2.4. Housing supply elasticities σiThe parameter σi, which varies by location, governs the longrun housing supply elasticities of each individual county. As discussed in Section 2, we base our calibration on BaumSnow and Han (2022), which estimates 10year elasticities at the Censustract level. We aggregate them up to countylevel by taking the average elasticity within a county, weighted by the quantity of housing.However, for a slowly depreciating asset like housing, 10year elasticities are not the same as longrun steadystate elasticities, which we require for the model. Consider the following housing production function, in which housing depreciates at rate δ and σi governs the shortrun investment elasticity:29
Hit=(1−δ)Hit−1+Zipitσiwhere pit is the price of housing, which (in the longrun steadystate of some models) is proportional to rents. In this case, the longrun elasticity of housing supply—the quantity we are interested in—is σi. However, what would be measured as a tenyear elasticity is (1−(1−δ)10)σi.30
So, for our baseline calibration, we use
σi=σBaumSnowandHan(2022)11−(1−δ)10We calibrate δ=0.03636, based on the depreciation rate in the U.S. tax code, but which is also similar to estimates in Glaeser and Gyourko (2005).31 Doing the arithmetic, this means we multiply the elasticities from BaumSnow and Han (2022) by 3.23. However, so that readers can understand the implications of this assumption, we also present our results using the unadjusted BaumSnow and Han (2022) elasticities throughout the paper, which are qualitatively similar to our main results.
5. Effect of remote work on housing demand
With the calibrated parameters we could, in principle, use Eqs. (19) and (21) in order to estimate the size of the housing demand channel and the location demand channel without estimating any shocks; however, we think it is helpful to first describe the estimated housing demand shocks, ϵi, and the location demand shocks, ηi, and then estimate the magnitudes of the channel to better understand the intuition behind the two channels. We do this in this section.
5.1. Demand shock estimates
Location demand shocks ηi Equation (17) shows that location demand shocks are equal to a linear combination of rent changes and population changes. To estimate the relative location demand shock for a given county, we need data on both the rent change and the population change.
Anticipating the way that we will use them, we know that the important statistic will be the covariance of the location demand shocks with a function of the local housing supply elasticity, and therefore the relationship between rent or population changes and local supply elasticities will matter.
μ→∞, local rent changes are equivalent to location demand shocks. For smaller values of , population changes matter as well. The relationship between population changes and housing supply elasticity is shown in Panel (b). Again, there is a positive relationship between population changes and housing supply elasticity.
Fig. 3. Binned scatter plot the relationship between real rent changes and housing supply elasticity (Panel A) and between population changes and housing supply elasticity (Panel B). Plot created with 20 bins and weights by 2019 county population. Source: Authors’ calculations using data from Zillow and USPS.
Each location’s location demand shock is a linear combination of the rent changes and population changes in Panels (a) and (b). For higher values of μ—the elasticity of population to rents—the location demand shock will be more similar to the rent changes. Importantly, for any parameter combination, location demand is increasing more in areas that are more housingsupply elastic.Housing demand ϵi Like for location demand, housing demand can also be calculated based on observed rent and population changes. Equation (19) tells us that we should care about the average values of the housing demand shocks. This focus is different than location demand shocks, where we anticipated being interested in the crosssectional variation.The rise in real rents from February 2020 to February 2022 was about 8 percentage points and U.S. population growth was 0.5 percentage points. Assuming λ=23 and ϕ=12, this implies an average housing demand shock (i.e. ϵ) of.043 (Eq. (16)). This means that in partial equilibrium—i.e. if housing costs had stayed the same—people would have consumed an average of 4.3 percent more housing because of the ϵ shocks.
5.2. Relation to remote work measures
We now take a brief digression to discuss the relation of the estimates of location demand—the ηi’s—to observable measures of remote work. A reader that is impatient to find out the magnitudes of the location demand channel and the housing demand channel may wish to skip to Section 6, and come back to this discussion later.
Up to this point, we estimated the location demand shocks and the housing demand shocks without regard to their origins. Given that one of the major changes in the economy during this time was the rise of remote work, we want to investigate how related the estimated shocks—particularly the location demand shocks—are to remote work variables. One reason to suspect that they are closely related is the findings of previous papers such as Gupta et al. (2021) and Ramani and Bloom (2021). In this section, we show additional evidence that location demand rose in areas we would expect, using proxies for remote work developed in the literature.
Specifically, we show that the ηi’s we estimate are located where remote work is possible. To do this, we project the rent and population changes on several observable measures related to remote work, including both vulnerability to remote work in each county itself as well as in nearby counties (to account for spillovers).
Our main measure is the remote work feasibility measure developed by Dingel and Neiman (2020), which calculates the feasibility of remote work by profession. We aggregate it to the county level to measure the remote work vulnerability of each region. Because demand for remote work spills over across counties, we include variables measuring the remote work share in neighboring counties at various distances. We also include measures of relative housing costs because workers tend to move towards relatively cheap areas in their vicinity. Finally, to account for the fact that households moved to areas with nicer amenities, we interact house prices with a natural amenities measure from the USDA.
We project the components of location demand (i.e., population changes and rent changes) onto remote work variables by running the following regression:(22)
yi=β1WFHi+β2ai+β3log(pi)+β4ailog(pi)+∑{d}[β5dWFHid+β6dpxid+β7dWFHidpxid]+ϵiwhere WFHi is the remote work vulnerability in location i, ai is the level of amenities, pi is the house price, and yi is the population or rent growth from February 2020 to February 2022. We include lowerorder terms in addition to interaction terms. For a given distance d, WFHid is the average remote work vulnerability for counties within d miles and pxid is the log house price minus the populationweighted average log house price of counties within d miles. To nonparametrically estimate the effects of remote work, we allow the effects to vary at different distances by estimating Eq. (22) with
d=25,50,100,250,500 miles. The main reason we consider these spatial patterns is because we think people are likely to commute to nearby locations (Monte et al., 2018). With remote work, those commutes may be less frequent and allow people to live at a fairly large distance to their job.32Estimates show that location demand is very much related to remote work. When we estimate specification (22) using the location demand shock, we calculate an R2 of 0.37 and an Fstatistic of 84.33 The WFH variation explains less than half of the change location demand, but given the relative coarseness of the measure, we think this is quite high. We also reject at the 1 percent level that the changes are unrelated to WFH.
Fig. 4 shows that the projection capture a lot of the variation in location demand.34 The top panel is a map of the United States showing the real rent change at the county level. The bottom panel is a projection of the real rent change onto the remote work shock, estimated in Eq. (22). The maps look qualitatively very similar, the main difference being that the projection is somewhat smoothed out. This makes sense given that rents are noisy and that our measures will not capture everything that is desirable to remote workers.
Fig. 4. This figure shows location demand shocks and location demand projected onto remote work shocks. Panel A is a choropleth map showing the location demand at the county level. Panel B shows the location demand shock projected onto remote work measures estimated using Eq. (22). The colors are on the same scale in both maps.
Eq. (22) is able to capture many of the features that may be associated with remote work. As can be seen in the figure, there are smaller rent predicted rent increases in New York, Los Angeles, and San Francisco, with large increases in the counties surrounding them. There are significant increases in the South, particularly Florida, and in California, which are high amenity regions.
We can do a similar exercise using housing demand shocks to see if remote work variables are highly correlated to that. We run the same regression, but instead use the estimated ϵ’s from the model. Under our preferred specification, the R2 is actually fairly small, around 0.06. More fundamentally, while the projection of location demand shocks are helpful to estimate the longrun effects of remote work, the formulas for the longrun effects of housing demand rely on the average housing demand shock, not the crosssection. This regression does not help us understand the average without stronger assumptions.
6. Longrun effects of remote work
Having discussed the demand shocks in the previous section, we are now ready to estimate the magnitudes of the housing demand and location demand channels in the longrun.
6.1. Benchmark estimates
Given the location and housing demand shocks from the previous section, we can estimate the location demand channel and the housing demand channel using Eqs. (18) and (20).
These results can be found in Table 1. In our preferred calibration for the entire country (the first row),35 the longrun location demand channel is −.003 logpoints and the longrun housing demand channel is.018 logpoints. The total effect is.015 logpoints, meaning that the same housing and location demand channels that we measured in the shortrun through the lens of our model will increase rents in the longrun by 1.5 percentage points. For comparison, these same effects had a 7 percentagepoint impact in the short run, so the longterm impact is only about 20 percent as large as the shortrun impact.36
In the next row, we show the same rent changes but for counties in which CPI is measured, which may be of interest since housing costs make up a large share of the consumption basket in CPI. The short and longrun housing demand channels are quantitatively similar, but there is a more negative location demand channel in both the shortrun and the longrun, as these counties experienced negative location demand shocks compared to the rest of the country. In particular, this brings the longrun total to be less than.01 logpoints.
Finally, we also show the same numbers, but for just the five most expensive metropolitan statistical areas in our data: New York, San Francisco, San Diego, Seattle, and Boston. Again, the housing demand channels are comparable to the national average, but the location demand channels are much more negative, meaning the longrun total effect is actually a.013 logpoint decrease in rents. Of course, there was a much smaller shortrun impact as well, with only a total effect of 0.12 logpoints. This highlights the crosssectional heterogeneity of the impact of remote work, with much different effects on average than in specific highcost cities.
The model can be solved for longrun rent and population changes in every county. While we show the results for the expensive metros in Table 1, a reader may be interested in other specific areas. For that reason, we have included maps of the crosssection of effects that can be found in Appendix D.
6.2. Alternative parameterizations
We also present two alternative parameterizations in Table 1 for comparison. In the first, we use a much higher elasticity of population to rents, μ=100. This approaches the Rosen (1979)Roback (1982) benchmark of utility equalization everywhere. The results are quantitatively similar for the entire country, with a difference of only.002 log points for the longrun housing demand channel and no different for the longrun location demand channel.However, when we focus on CPI cities or Expensive Metros, the location demand channel is more negative—almost twice as large. This leads to a longrun total effect on CPI cities of around 0, and a longrun total effect on expensive metros of −0.044 logpoints. The reason for this difference is that these areas had the largest negative location demand shocks, so they must be offset by relative rent declines—even in the longrun—when utility is equalized everywhere. When μ is much smaller, as in our benchmark, then people moving into the city, as the housing supply grows, means that the marginal agent can still be indifferent between the two cities with smaller rent adjustments.The similarity in results for different values of μ is perhaps surprising, given that it does not hold generally, as in Howard and Liebersohn (2021); therefore, it is worth discussing why that is the case. If μ→∞, then people are very sensitive to rents, so local rents will adjust to offset location demand changes and the outside option, du˜. The formula for the location demand channel is given by:(23)
LocationDemandChannel=−Cov(ηi,σi)σ¯+λ=−Cov(dlogri,σi)σ¯+λOn the other hand, if μ=0, people do not move at all in response to rents, and therefore all movements will be governed simply by the location demand shock. In this case, the formula is given by:(24)
LocationDemandChannel=1ϕCov(ηi,1σi+λ)=1ϕCov(dlogLi,1σi+λ)In the data, the quantity in Eqs. (23) and (24) are both small in magnitude and negative.37 Intuitively, this occurs because the patterns of rent changes and population changes are similar in the data. Inelastic places saw a relative decline in rents and in populations. While it is a coincidence that the magnitudes end up being essentially the same regardless of μ, it would be expected that the sign would be negative based on easily observe aspects of the data.The fact that μ does not greatly affect the housing demand channel is less surprising. The measurement of demand shocks using the shortrun data does not depend on μ, and the longrun effects of demand shocks are given by: E[ϵiσi+λ] or Eϵiσ¯+λ when μ is 0 or ∞ respectively. These would differ only if the demand shocks and the housing supply elasticity are correlated, and in the data, the demand shocks are positive everywhere, not just in inelastic regions.Finally, we wish to note that the effect on rents and populations in individual cities are different as we change the calibration of μ. It is only the average effect that is insensitive to its parameterization.
We also show the calibration with lower housing supply elasticities, by using the unadjusted BaumSnow and Han (2022) elasticities instead of the ones we adjusted for housing depreciation. Mechanically, the shortrun results are the same as the benchmark, since the housing supply elasticity does not matter. In the longrun, the location demand effects are comparable, but the housing demand effects are much larger; this is because there was a large increase in housing demand. If supply is constrained to react less, then the price will rise by more. The overall effect is a.037 logpoints, which is a bit larger than the baseline estimates, but still much smaller than the shortrun effect.38
Besides the two alternative calibrations in Table 1, we also show different parameter combinations of ϕ and λ in Fig. 5. We start by reiterating our result regarding μ. Even though there is very little agreement on the population elasticities to rent in the literature, the effects are not very different for extreme values of μ=1.07 or μ→∞ (here we show μ=100, but this is visually indistinguishable from larger values of μ).
Fig. 5. This figure shows the longrun average effects of housing demand and location demand on house prices. The two figures sidebyside consider different and extreme values of the location demand elasticity,
Next, we discuss the sensitivity to λ. When λ=0, the size of house that people choose is completely inelastic to rent, and when λ=1, then it has unit elasticity. λ=1 is the most common parameterization in the literature, but largely due to tractability. When it is estimated as in Albouy et al. (2016), the estimates are usually smaller than 1. Our preferred estimate is λ=2/3. While the effects are a bit smaller for λ=.5 and a bit larger for λ=1, the results do not change much.39Finally, we show results for different values of ϕ. Changing the value of ϕ from 12 to 1 has only a minor negative effect on the longrun effects. When we get to smaller values of ϕ, like 0.25, the effects become a bit smaller but are still qualitatively similar to our preferred estimates.
Overall, we view our estimates as relatively robust to different parameterizations.40
6.3. Location demand channel projected onto remote work variables
In the previous section, we showed that observed location demand shocks were related to variables we expected to be related to remote work. If we wish to consider only the effects of the location demand shocks that project onto these variables, we can revisit the analysis by using those shocks instead.
To carry out this analysis, we use the predicted values of location demand shocks from the previous section, rather than the observed location demand shocks from the data. Plugging in the numbers, the longrun effects of remote work are −.001 logpoints from location demand. Numbers for CPI Cities and Expensive Metros can be found at the bottom of Table 1. This is about 40 percent of the size of the location demand channel that we calculated assuming all relative rent changes are the result of remote work.
We cannot do the same for housing demand shocks. The reason for this is that a crosssectional regression only identifies the relative housing demand shocks correlated to remote work variables. This is fine for location demand shocks, since relative location demand shocks are what matters, but the formula for housing demand shocks depends on the average, which we cannot identify off of crosssectional regressions.
6.4. Comparison to house prices
To this point in the paper, we have only considered the effect of the remote work shock on rents and populations. However, a reader might reasonably be interested in how the remote work shock affected house prices for two reasons: first, because house prices are inherently interesting; and second, because it might serve as a robustness check for the model.
The model we presented in Section 4 did not include house prices and because of its simplicity, there is no obvious way to solve for house prices. In order to make progress on this point, we write down a discretetime dynamic model that features house prices. Importantly, this new model nests the previous model, in the sense that period 0 and period 1 are the same, and the steadystate of the new model is the same as period 2 in the previous model.
The key features of the model that were not present in the simpler model from Section 4 are: (1) house prices are the present discounted value of rents; (2) housing depreciates each period and is replenished through housing investment that depends on house prices; (3) housing investment is subject to a timetobuild constraint; and (4) people reoptimize their housing consumption and location with a certain probability each period. Details can be found in Appendix C. Compared to models such as Favilukis et al. (2023), our model is relatively simple. For example, the agents in our model do not make forwardlooking tenure choices. The main reason for variation in the pricetorent ratio is changes in the interest rate, which is an important margin we hope to capture; however, this means that we do not capture much of the location variation in the pricetorent ratio as confirmed by our empirical estimates.
Because the dynamic model nests the two time periods from the simple model as the initial shock and the longrun steadystate, the main “new” aspect of the dynamic model is that it is able to solve for the transition dynamics of rents, housing quantities, and populations. Solving for the transition dynamics of rents is particularly important because it allows us to calculate house prices as the present discounted value of rents. Since solving for house prices was the goal of the model, this is a crucial step.41
In the longrun steadystate of our model, house price and rent changes converge to the same values locally. If county A had an x logpoint increase in rents, then county A’s house prices also increased by x logpoints. Hence, all the results we had previously shown for the longrun effects of remote work on rents would also apply as the longrun effects on house prices.
More interesting are some of the results regarding shortrun house prices. While the model is not simple enough to solve in closed form for house prices, it is still easily linearizable, and we use Dynare (Adjemian et al., 2011) to solve for the shortrun impact on house prices, which we can compare to the data. Since we use rents and not house prices to estimate the location and housing demand shocks, comparing the data and model predictions can serve as a check of the validity of the model, or show us what features might be missing from the model that are important for house prices in particular.
To analyze the effects on house prices, we regress the shortrun changes in house prices on the shortrun changes in rents. We can do this using both the model and the data, since the shortrun changes in rents are the same in both the model and the data.
R2 is above 0.99. This means that places that had larger increases in rents also had a higher increase in modelimplied house prices, although the effect was not quite oneforone. This coefficient being less than one is because people have strong idiosyncratic preferences over location, and so as more people move to the places that had rent increases in the long run, the relative rent changes need to be less big to make the marginal person indifferent. We can confirm this intuition by considering an alternative calibration where and we see a coefficient on house prices of almost exactly 1.
Table 2. House Price Results.
μ=100 instead of in the baseline simulation. Column (5) assumes that in addition to the housing demand and location demand shocks in our baseline model, that the economy is also hit with an interest rate shock, in which rates fall. Column (6) assumes that instead of our being the elasticities measured by BaumSnow and Han (2022) times 3.23 as discussed in Section 4.2, that the are the BaumSnow and Han (2022) elasticities without any adjustment. All regressions are weighted by 2019 populations. Robust standard errors in parentheses.
 p<0.05,**p<0.01,***p<0.001
How does this compare to the data? In column (1), we run the same regression of house prices on rents (excluding the counties for which we infer rents from house prices). We get a coefficient that is quite high, 0.845, which is a bit larger than our baseline specification, but still less than 1.
One concern with the regression in column (1) is measurement error.42 If there is classical measurement error, we can correct the regression coefficient using instrumental variables, where the instrument is another estimate of rent changes that is uncorrelated to the measurement error of Zillow. We use an estimate of the rent changes from Costar as our instrument. The Fstatistic on the firststage regression is above 300. The point estimate of the two stage least squares regression, shown in column (2), is almost exactly 1, although with wide standard errors.
We also consider an alternative calibration of the model in column (6), using the unadjusted (BaumSnow and Han, 2022) housing supply elasticities. Here, the coefficient is larger than in our baseline model, near the OLS, but still below 1.
Given that the across all four columns (1)–(4) and (6), there is a very high coefficient less than 1 when regressing house prices on rents, we think the model is generally consistent with the data with regards to the crosssectional predictions regarding house prices.
However, there is another major difference between the data and the baseline model, which is that house prices in the data increased by a significant amount compared to house prices in the model. To see this, compare the average house price change in columns (2) and (3). While the regression is limited by the number of counties for which we observe rent, the average house price change at the bottom of the table is for a consistent sample of counties. In the data, house prices rose by nearly 20 percent, while the model has only a small increase.
The model predicts shortrun house prices should rise less than shortrun rents because longrun rents rise less than shortrun rents, and house prices depend on both shortrun and longrun rents; therefore, the data strongly suggests our dynamic model is missing something.43 A natural candidate for what the model might be missing is a change in the interest rate. In column (5), we add an interest rate shock to the model which is described in Appendix C. With the interest rate shock, the crosssectional predictions of the model do not change much—the regression coefficient is still about threequarters, and the R2 is still close to 1—but the constant term is much closer to the one in the data. Admittedly, we impose a larger interest rate shock than is observed in the data, but our main point is that the constant term may react to changes in credit markets, of which there were many between February 2020 and February 2022; therefore, the different constant terms should not be taken as a rejection of the model.
6.5. Crosssectional effects on population
Our model also has implications for which regions will gain and lose population in the longrun. In the longrun, housing supply adjusts to changes in location demand, which increases the equilibrium population in places where housing supply increases. We show the longrun effects on populations, by bins of housing supply elasticity in Fig. 6. The figure shows the average population growth in response to the location and housing demand shocks, for counties binned by housing supply elasticity. The most inelastic counties lost population in the shortrun, and are predicted to lose even more population in the longrun. The most elastic counties gained population in the shortrun, and those effects are also expected to be larger in the longrun.
Fig. 6. A binned scatter plot of the short and longrun population changes due to housing and location demand shocks, by housing supply elasticity.
Under other parameterizations, the population predictions may be more or less extreme. Intuitively, when μ→∞, people are more mobile in response to rent changes, and there should be more longrun population movements. Similarly, when housing supply is less elastic (i.e. when we use the unadjusted (BaumSnow and Han, 2022) elasticities), then there will be less longterm population movement since the housing supply will adjust less.
We can also calculate how the house price or the housing supply elasticity of the average American will change in both the short and the longrun. In 2019, the average American lived in a county that had a 0.688 supply elasticity (using the (BaumSnow and Han, 2022) measure), had a Zillow home value index of $309,987, and had a population density of 1659 people per square mile. The shortrun effect of population changes was to change those numbers to 0.690, $308,129, and 1597 people per square mile, respectively. But the longrun effect of these shocks is that people will move to places that had 0.695 elasticity, $303,772 Zillow home value index, and 1480 people per square mile in 2019.44 The longrun effect on population movements is that the average American lives in a county that is 1.0 percent more elastic, 2.0 percent cheaper, and 10.2 percent less dense in 2019. This is in addition to the fact that we expect housing costs to increase by 1.5 percentage points on net, and that outmigrants will affect the density of the densest places.
6.6. Scenarios for the future of remote work
To this point, our assumption has been that the modelimplied shocks to housing demand and location demand were fully realized and permanent, and we have used the lens of the model to extrapolate what the longterm effects of those shocks were. As with any predictive exercise, a reader may disagree on the expected future path of the housing and location demand shocks. Our model is tractable enough that it is relatively straightforward to map different assumptions about the future of remote work onto the predictions.
In this section, we consider a few different ones: first, we ask what happens if the housing demand shocks are more temporary because they were actually due to factors other than remote work; and second, we ask what happens if remote work continues to evolve and the shocks are larger in the longrun. Finally, we ask what happens if remote work not only becomes more important, but also is no longer tied at all to office location, and there is an even bigger shift to highamenity lowrent places. All of the results are presented in Table 3.
Table 3. Alternative Scenarios.
Empty Cell(1)(2)(3)RegionTotalLocation Demand ChannelHousing Demand Channel
Baseline
National .015
−.003
.018 CPI Cities .009
−.01
.018 Expensive Metros
−.013−.035
.022
60% Housing Demand
National .008
−.003
.011 CPI Cities .001
−.01
.011 Expensive Metros
−.022−.035
.013
700% Location Demand
National
−.001−.019
.018 CPI Cities
−.049−.068
.018 Expensive Metros
−.224−.246
.022
200% Amenities
National .014
−.003
.018 CPI Cities .006
−.012
.018 Expensive Metros
−.02−.042
.022
Notes: Estimates correspond to alternative scenarios considered in Section 6. See text for details.
6.6.1. How much of housing demand is remote work?
While Section 5.2 argues that the majority of the location demand channel is driven by observable variables that relate to remote work, we cannot make a similar argument regarding the housing demand channel. The reason for this is that the location demand channel relies on the crosssection of location demand shocks, so only the relative exposure to remote work matters, which is what we can identify in a regression. In contrast, calculating the size of the housing demand shocks requires taking a stand on their absolute size, which we cannot do without auxiliary assumptions.
It makes sense to consider the longrun if the housing demand changes that we have observed over the last few years are due to temporary factors,such as expansionary fiscal policy that has spurred spending on durable goods.
If none of the housing demand shocks are due to remote work, then the longrun effect of remote work is simply the location demand channel, a 0.003 logpoint decrease in rents. The linearity of our model helps calculate intermediate values as well. If x percent of the housing demand shocks are due to remote work, then the total effect will be 0.015 times x percent. If you think only 20 percent is due to remote work, you would believe that the net effect is 20 percent times 0.015, plus the location demand channel, for a net effect very close to zero. If you think that 60 percent of the increase in recent house prices is due to remote work (as in Mondragon and Wieland, 2022), you would think the net effect is 0.009, plus the location demand channel, for a net effect of 0.006.
6.6.2. Expansion of remote work
Our location demand channel also scales linearly with the size of the shock. If we wish to consider a world in which the relative location demand shocks increase by a factor of 7, we can do that. In this case, we simply multiply the location demand channel by 7, yielding a location demand channel of 0.019, which would make the net effect basically zero. In this scenario, the location demand effect for CPI rents and aggregate rents is also multiplied by a factor of 7.
6.6.3. Greater flexibility of location demand
When projecting the changes in rents onto remote work variables, it is clear that highamenity, lowrent places saw increases in location demand in the shortterm. One possible counterfactual is to consider that if remote work becomes even easier, people will move even further from their jobs and into highamenity places—especially those highamenity and lowrent places.
Regression (22) showed that higheramenity places (and particularly higheramenity places with lower house prices) had larger location demand shocks. If we take those coefficients to be causal and double the impact of the amenities by doubling those coefficients while leaving everything else the same, then we can recalculate the longrun effects using those new shocks. The location demand channel becomes more negative modestly, with slightly larger effects for CPI cities and Expensive Metros. This can be seen in the last panel of Table 3.
7. Conclusion
In this paper, we compare the short and longrun effects of remote work, using a simple model of housing markets within the United States. We show that even though remote work has increased rents in the shortrun, they are likely to decline going forward and in the longrun may end up lower than prepandemic.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.