R23 | Macro Paper Warehouse

An Equilibrium Analysis of the Effects of Neighborhood-Based Interventions on Children

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. How should governments design neighborhood-based policies to improve long-run outcomes for children, once one accounts for general equilibrium (GE) forces—endogenous rents, neighborhood quality, wages, and distortionary taxation—that small-scale experimental studies cannot identify?

Model. The paper embeds neighborhood effects into a quantitative, heterogeneous-agent overlapping-generations (OLG) model with endogenous location choice and child skill development. The economy has three building blocks: (1) a dynastic life-cycle structure in which parents choose a neighborhood (from two options: a disadvantaged n=1 and an advantaged n=2) and allocate time to child development, with child skills produced by a nested CES aggregator combining parental time and neighborhood quality (proxied by per-capita income in the tract); (2) a GE Aiyagari incomplete-markets framework with endogenous labor supply, wage uncertainty, and progressive labor taxation; and (3) a government that finances housing vouchers or place-based wage subsidies by adjusting the labor income tax parameter, with all additional net expenses fully offset by tax revenue. Housing supply is upward-sloping (elasticity 1.75, from Saiz 2010), so rents are endogenous.

Data and calibration. The model is estimated by simulated method of moments to match U.S. data from the 2000s, drawing on the PSID, NLSY, ATUS, the 2012–2016 ACS, and the Opportunity Atlas (Chetty et al. 2018). Neighborhoods are mapped to Census tracts divided into bottom-10-percent and top-90-percent median household income groups within each commuting zone. Key targeted moments include the income gap between neighborhoods (108 percent higher mean individual income in n=2), the 30 percent higher incomes for children from low-income families raised in the better neighborhood, and a 32 percent gap in weekly parental time with children across neighborhoods.

Validation. Before policy counterfactuals, the calibrated model is validated against two bodies of reduced-form evidence. First, a simulated small-scale, single-generation, partial-equilibrium voucher experiment generates 23 percent higher income for children—close to the 31 percent MTO experimental estimate from Chetty et al. (2016), with the difference largely explained by a smaller poverty-rate contrast (18 vs. 22 percentage points) in the simulation. Second, a simulated 20 percent place-based wage subsidy generates 17–21 percent earnings gains for adult residents of n=1, consistent with Busso et al.’s (2013) quasi-experimental EZ estimates of 17–24 percent.

Main findings — housing vouchers. The welfare-maximizing voucher program features a 100 percent subsidy rate, targets households with children and wages below the 80th percentile (fourth quintile), and is financed by progressive labor taxes. In the long-run steady state this policy raises 12.5 percent more children in the advantaged neighborhood, increases labor productivity by 1.1 percent, reduces income inequality (variance of log after-tax lifetime earnings) by 6.3 percent—comparable in magnitude to the Sweden–U.S. after-tax inequality gap—and raises upward mobility by 27.7 percent (roughly half its standard deviation across U.S. Census tracts). The average marginal tax rate must increase by 15.7 percent to fund the program. Despite this, long-run welfare rises by 3.4 percent in consumption equivalence units. A decomposition shows that intergenerational dynamics add 11.5 percentage points to welfare (relative to a short-run, single-generation scenario), while taxation subtracts 10.2 percentage points, and rent plus neighborhood-quality effects together subtract only 1.4 percentage points—leaving the net long-run GE gain similar to the short-run partial-equilibrium gain of 3.5 percent. Crucially, non-targeting children generates welfare losses of 5.0 percent, confirming that restriction to households with children is essential.

Main findings — place-based wage subsidies. A 12 percent wage subsidy to workers in the disadvantaged neighborhood yields the highest steady-state welfare gain of 0.7 percent. This is approximately one-fifth of the gain achievable with the optimal voucher. The subsidy induces substantial resorting toward n=1, reducing the share of children in n=2 by 6.7 percent while raising neighborhood quality in n=1 by 19.7 percent. Income inequality falls by 8.7 percent and upward mobility rises by 20.4 percent. However, in a short-run partial-equilibrium setup, the wage subsidy has a negative welfare effect of −1.0 percent because it draws parents (and their children) into the disadvantaged area; the positive net effect only emerges through long-run intergenerational channels (+2.5 percentage points) and equilibrium neighborhood-quality adjustments.

Political economy. Because voucher gains are concentrated among young cohorts (those aged 16–43 at introduction), only 33 percent of incumbent adults would rationally vote for the housing voucher program. In contrast, the place-based wage subsidy provides positive average welfare gains for all age cohorts alive at introduction, yielding estimated majority support from over 63 percent of adults. This creates a fundamental political economy tradeoff: the policy with the larger long-run social gains lacks majority democratic support, while the policy with broader support delivers smaller long-run gains.

In depth

Q1. What are the two market frictions that justify government intervention in the model?

A1: The first friction is the absence of intergenerational borrowing markets: parents cannot borrow against their child’s future income, which limits the parent’s willingness to pay the higher rent in n=2 to give their child a developmental advantage. Housing vouchers act as a tax-financed substitute for this missing contract by paying the rent premium and recovering the cost through taxes on the high-earning adults the children become. The second friction is a neighborhood externality: individuals do not internalize the effect of their own income on the neighborhood quality experienced by neighbors’ children. Place-based wage subsidies partially correct this externality by subsidizing work in the disadvantaged area, raising local income per capita and thereby improving the neighborhood quality index for all children resident there.

Q2. How is neighborhood quality defined and modeled, and why is this specification chosen?

A2: Neighborhood quality sn is defined as total income per capita (the sum of labor and capital income) for all residents of neighborhood n, including non-workers. This specification is intended to capture multiple mechanisms: school quality (which depends on local tax bases), role-model effects from productive adults, and social organization effects through adult supervision of children. The formulation includes retired and non-working residents, which means the arrival of children mechanically reduces neighborhood quality per capita in the model, partially capturing a crowding channel. Formally, the neighborhood spillover function takes the power form f(sn) = A * sn^ζ, where ζ governs the elasticity of child development to neighborhood quality.

Q3. How does the paper validate the model’s key mechanism — the neighborhood effect on children?

A3: The validation mimics the MTO RCT within the calibrated model: the government provides a 100 percent rent voucher usable only in n=2 to households in n=1 with incomes below the 10th percentile, holding prices and neighborhood qualities fixed (as in a small-scale experiment). The model generates 25 percent voucher take-up and a 23 percent increase in children’s income in their late 20s. This compares to the experimental MTO estimate of approximately 31 percent. The paper attributes most of the gap to the smaller poverty-rate contrast in the simulation (18 percentage points) relative to MTO (22 percentage points), and shows that plotting the simulated result against the site-specific MTO estimates in a scatterplot of child income gains against neighborhood poverty reductions places the model prediction on the fitted line through the experimental data.

Q4. What is the quantitative role of long-run intergenerational dynamics in the voucher program, relative to other GE channels?

A4: The decomposition in Table 5 isolates four GE channels. Starting from a short-run partial-equilibrium welfare gain of 3.5 percent (for the children of a single treated generation), allowing the economy to operate for the long run while holding prices and taxes fixed raises welfare to 15.0 percent — an increase of 11.5 percentage points — because improved skills in one generation create higher-skilled, higher-income parents who invest more in the next generation. Introducing housing market price adjustments (rents rise by 3.9 percent in n=2) reduces welfare by only 0.6 percentage points. Allowing neighborhood quality to adjust (quality in n=2 falls by 4 percent as lower-income families move in) reduces welfare by an additional 0.8 percentage points. Adding full taxation to balance the government budget reduces welfare by 10.2 percentage points, from 13.6 to 3.4 percent. The four channels nearly cancel, leaving the long-run GE steady-state gain close to the short-run single-generation gain.

Q5. Why does the optimal voucher program require targeting to families with children, and what happens without this restriction?

A5: When the voucher is extended to all households regardless of children (Column 6 of Table 4), nearly 82.6 percent of the population receives a subsidy, pushing almost everyone to n=2. Rents in n=2 rise by 5.3 percent. To finance this much broader program, the average marginal tax rate must increase by 44 percent, far exceeding the 15.7 percent required for the children-targeted program. The large tax increase suppresses labor supply and income, which reduces neighborhood quality in n=2 by 11.6 percent. The net effect is a welfare loss of 5.0 percent. The intuition is that the benefit of the voucher program flows primarily through child skill development, so subsidizing adults without children is fiscally expensive without producing the intergenerational gains that justify the cost.

Q6. What drives the difference in long-run welfare gains between vouchers (3.4 percent) and place-based wage subsidies (0.7 percent)?

A6: The primary channel is labor productivity. The optimal voucher program raises labor productivity by 1.1 percent by increasing the average neighborhood quality to which children are exposed by 1.2 percent. The wage subsidy raises productivity by only 0.2 percent because it induces resorting toward the disadvantaged neighborhood, meaning children’s average neighborhood quality actually decreases by 0.2 percent despite large improvements in n=1’s quality (up 19.7 percent), since fewer children reside in n=1 after the subsidy draws their parents there. Inequality reduction is not the source of the gap: the wage subsidy actually reduces inequality more (8.7–8.9 percent) than the voucher (6.3 percent), but this inequality effect does not translate into larger aggregate welfare because productivity effects dominate.

Q7. How does the wage subsidy produce positive long-run welfare when it generates negative welfare in the short run?

A7: In the short run, the wage subsidy draws parents into the disadvantaged neighborhood to exploit higher wages, which reduces the share of children in the advantaged neighborhood n=2 and lowers children’s late-life productivity (welfare of −1.0 percent for treated children in the single-generation scenario). Two long-run channels flip the sign. First, the subsidy is permanent, so children themselves receive it as adults, providing a direct wage income benefit. Second, the sustained presence of higher-income workers in n=1 raises neighborhood quality there durably (by 19.7 percent at the steady state), which benefits the children who reside in n=1. Together these intergenerational effects add 2.5 percentage points to welfare, while taxation costs reduce it by only 1.4 percentage points, yielding a net gain of 0.7 percent.

Q8. What determines the political economy divide between the two policies?

A8: For the housing voucher, welfare gains are concentrated among younger incumbent adults (ages 16–43), particularly those who are about to have or already have children, while older adults tend to lose because they face higher taxes without benefiting from improved neighborhood quality for their (now independent) children. This concentration implies only 33 percent of incumbent adults would support the voucher under the model’s welfare metric. For the place-based wage subsidy, average welfare gains are positive for every age cohort alive at introduction (though larger for younger cohorts), because the wage subsidy raises incomes for workers in n=1 immediately and benefits from equilibrium rent declines in n=1 that allow all residents to benefit. Over 63 percent of adults would support the wage subsidy. The paper notes that if the government could borrow to initially finance the voucher program and pay for it later (as in Daruich 2020 for early childhood programs), majority support for the voucher could potentially be achieved.

Q9. How sensitive are the welfare results to the key calibrated parameters?

A9: The sensitivity analysis (Table 9, following Andrews et al. 2017) shows that individual parameters would need to change substantially to overturn the conclusion that vouchers generate larger steady-state welfare gains than wage subsidies. For example, the altruism parameter β̃ would need to increase by 22 percent to eliminate the voucher welfare gain, which would require average parental transfers to rise to 198 percent of income — far from the empirical target of 125.4 percent. Using the more conservative tract-level housing supply elasticity from Baum-Snow and Han (2021) of 0.3–0.4 (about 80 percent below the baseline Saiz 2010 estimate of 1.75) would reduce the voucher welfare gain from 3.37 to approximately 2.57 percent, not reversing the qualitative conclusion. The parameters with the largest influence on welfare gains are the labor disutility parameter µ and the altruism parameter β̃; the housing supply elasticity matters more for the voucher than the wage subsidy because easier housing supply accommodates growth in n=2 without displacement under the voucher.

Q10. What does the transition path of the voucher program look like, and why do welfare gains initially dip before recovering?

A10: When the voucher is unexpectedly introduced, the first newborn cohort gains approximately 4 percent welfare, but gains for subsequent cohorts initially dip to around 3 percent before stabilizing at 3.4 percent by the 20th post-introduction cohort. The dip occurs because moving costs slow resorting: immediately after introduction, rents in n=2 begin rising and neighborhood quality there begins falling as low-income families move in, but the capital stock adjustment (which would counteract these effects by raising GDP) lags the resorting. The rebound comes as capital accumulates in n=2 over time and as intergenerational productivity gains build through successive cohorts of better-skilled parents. Labor productivity jumps noticeably for the first cohort born to parents who received the voucher (approximately 28 years after introduction) and again for the first cohort born to grandparents who received it, visibly demonstrating the intergenerational mechanism. In contrast, the wage subsidy’s welfare gains are approximately constant at 0.7 percent across all cohorts because the key channels (neighborhood quality improvement in n=1 and wage gains) materialize rapidly and remain stable throughout the transition.

Key Concepts

Neighborhood quality (sn): In this paper, neighborhood quality is not school quality or amenities in a generic sense but is explicitly defined as total income per capita — the sum of labor income and capital income — for all residents of neighborhood n, including non-workers. This endogenous measure rises when higher-income or more productive residents move in and falls when lower-income residents or additional children arrive.

Intergenerational borrowing constraint: The inability of parents to borrow against their child’s future income, modeled as a non-negativity constraint on the monetary transfer from parent to child (transfer ≥ 0). This is the paper’s first key market friction: without it, a poor parent who moved to a better neighborhood would smooth consumption across generations by having the high-earning child compensate the parent. The constraint prevents this, reducing parental investment below the socially efficient level.

Consumption equivalence (veil of ignorance): The welfare metric used throughout the policy analysis. It is defined as the percentage change in consumption that would make a newborn individual indifferent between the pre-policy and post-policy steady states, computed before knowing their position in the skill or income distribution. This is the paper’s measure of long-run steady-state welfare.

Parental investment aggregator (CES): A nested constant-elasticity-of-substitution function that determines how parental time τ and neighborhood quality sn combine to form the effective investment input I into child skill development: I = Ā[αI f(sn)^γ + (1 − αI)τ^γ]^(1/γ). The elasticity parameter 1/(1 − γ), estimated at 0.41, governs the degree of complementarity between time and neighborhood quality; a lower elasticity (γ = −1.43) implies the two inputs are complements, so parents with children in better neighborhoods also spend more time with them.

Place-based wage subsidy: A neighborhood-specific wage premium (denoted w̃s) paid to all workers who both live and work in the disadvantaged neighborhood n=1, raising their effective wage to w1 = (1 + w̃s)w2. This policy targets the neighborhood externality by increasing the income of residents in n=1, which raises neighborhood quality and provides an incentive for higher-skilled workers to relocate to (or remain in) the disadvantaged area.

Upward mobility: Measured in this paper as the probability that a child born to parents in the bottom 20 percent of the income distribution reaches the top 20 percent of the income distribution during the working stage of their own life. This is distinct from mean income rank measures; it specifically tracks cross-quintile transitions in the model’s stationary distribution.

Equilibrium decomposition: A simulation-based method in which GE channels are progressively activated. Starting from a short-run, partial-equilibrium, single-generation baseline (analogous to an RCT), the authors sequentially allow: (i) long-run intergenerational dynamics while holding prices fixed; (ii) housing market price adjustments; (iii) neighborhood quality adjustments; (iv) tax and production-price adjustments. Each step’s change in outcomes identifies the quantitative contribution of that specific channel.

Homeownership, Polarization, and Inequality

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks why job polarization and income inequality are higher in large U.S. cities, and proposes a novel housing-market mechanism that operates independently of — but interacts with — the skill-biased technical change (SBTC) explanations dominant in the existing literature.

The core argument is that large cities have experienced faster growth in house prices relative to both wages (price-wage ratio) and rents (price-rent ratio) since 1980. This excess price growth has priced middle-income households out of homeownership in expensive cities. Because low-income households cannot afford to own anywhere and high-income households can afford to own everywhere, it is specifically middle-income (middle-skilled) households whose location choice becomes entangled with their tenure choice. These households increasingly sort toward smaller, more affordable cities where they can purchase a home. This selective out-migration hollows out the middle of the income distribution in large cities, producing greater employment polarization and income inequality there.

Empirically, the paper uses Census and ACS data from 1980 to 2019 covering 465 commuting zones (CZs). Polarization is measured following Autor and Dorn (2013) by assigning 3-digit occupations to income percentiles fixed at 1980 levels; inequality is measured by the Gini coefficient and variance of log annual wages. Housing costs are captured by hedonic price and rent indices and three derived ratios. OLS and IV results (instrumented using the interaction of land unavailability and long-run changes in real interest rates) show that doubling of prices is associated with a 1 percentage point decline in the middle-skilled employment share; doubling of the price-rent ratio is associated with an 11.3 percentage point decline; doubling of the price-wage ratio with a 5.3 percentage point decline. Inequality follows the same pattern: doubling prices raises 100x the variance of log wages by 2.3 points; doubling the price-rent ratio raises it by 11.7 points; doubling the price-wage ratio by 7.7 points.

The migration mechanism is documented using 2001–2019 CPS ASEC data, which — uniquely among available sources — reports reasons for moving. A doubling of the price index, price-wage ratio, or price-rent ratio in the origin state relative to the destination raises the probability that a middle-income (2nd–4th quintile) household moves for housing-related reasons by approximately 5–10 percentage points in absolute terms, implying a 50–80% relative increase compared with low- or high-income households making a housing-related move.

The theoretical framework extends the standard spatial equilibrium (Rosen-Roback) model with two additions: skill heterogeneity and housing tenure choice. Households face a minimum house size constraint and a payment-to-income (PTI) constraint (calibrated at lambda = 0.308). These constraints create distinct skill thresholds for homeownership that vary by city; the interaction between location and tenure choices applies only to middle-skilled households who can afford ownership in cheap but not expensive cities.

In the quantitative model, calibrated separately for 1980 and 2019 with two locations (top 30 CZs vs. the rest), counterfactual experiments show that holding price-wage ratios at their 1980 levels reduces the excess polarization gap between large and small CZs by 93% and the excess inequality gap by 40%. Holding price-rent ratios constant reduces the polarization gap by 96% and the inequality gap by 27%. By contrast, shutting down SBTC entirely reduces the polarization gap by only 54% and the inequality gap by 73%. These results establish that while SBTC is an important driver, its effect on polarization and inequality is substantially amplified by faster house price growth in large cities; without the housing affordability channel, the effect of SBTC on disproportionate polarization would be 63–81% smaller and on the inequality gap 18–36% smaller.

Q: What is the paper’s central research question? A: The paper asks why job polarization and income inequality are systematically higher in large U.S. cities than in small ones. Prior literature attributed this to skill-biased technical change, external labor demand shocks, or IT-driven displacement of routine jobs; this paper proposes a complementary, housing-market-based explanation that does not rely on features of the production technology.

Q: What is the core mechanism linking house prices to polarization? A: When price-wage and price-rent ratios are higher in large cities, middle-income households face binding minimum-size and payment-to-income constraints that prevent them from owning a home there but not in cheaper cities. Because homeownership carries financial advantages, these households sort toward smaller, more affordable cities. Low-income households cannot afford ownership anywhere and high-income households can afford it anywhere, so only the middle group’s location choice is distorted by tenure considerations. This selective out-migration hollows out the middle of the income distribution in expensive large cities.

Q: What empirical patterns in CZ-level data motivate the paper? A: Doubling CZ size is associated with a 1.9 percentage point greater fall in the middle-skilled employment share and a 2.7 point higher growth in 100x the variance of log wages from 1980 to 2019. Larger CZs also experienced 3.4% higher price growth, 3.1% higher price-wage ratio growth, and a 10% greater increase in price-rent ratios. These associations persist after controlling for initial CZ size and other characteristics.

Q: What do the OLS and IV results show about house prices and polarization? A: A doubling of house prices is associated with a 1 percentage point decline in the middle-skilled share; a doubling of the price-rent ratio with an 11.3 percentage point decline; and a doubling of the price-wage ratio with a 5.3 percentage point decline. IV results using the interaction of land unavailability and the change in real interest rates as an instrument confirm the negative relationship remains statistically significant, suggesting a causal interpretation is plausible.

Q: What do the OLS and IV results show about house prices and income inequality? A: A doubling of prices is associated with a 2.3 point increase in 100x the variance of log wages; a doubling of the price-rent ratio with an 11.7 point increase; and a doubling of the price-wage ratio with a 7.7 point increase. IV results suggest a causal relationship between price growth and income inequality at the CZ level.

Q: What evidence does the paper provide for the migration mechanism? A: Using 2001–2019 CPS ASEC data (which reports stated reasons for moving, unlike the ACS), the paper estimates logit regressions of interstate migration for housing-related reasons. A doubling of the price index in the origin state relative to the destination raises the probability of a housing-related move for middle-income (2nd–4th quintile) households by 5–6 percentage points; a doubling of the price-wage ratio raises it by 6–7 percentage points; and a doubling of the price-rent ratio raises it by 7–10 percentage points. These effects imply a 50–80% relative increase in housing-related migration probability for the middle quintiles compared with the bottom or top quintile. Housing-related movers constitute over 12% of all interstate migrants in the sample.

Q: What is the key finding about homeownership rates? A: There is no statistically significant relationship between the change in homeownership rates and the growth in prices, price-rent, or price-wage ratios from 1980 to 2019. This is consistent with the model’s mechanism, in which middle-income households who cannot afford ownership in large cities move away rather than simply switching to renting there — so aggregate local ownership rates need not fall.

Q: How does the theoretical model generate the polarization result? A: The model extends the Rosen-Roback spatial equilibrium framework with skill heterogeneity and housing tenure choice. Two skill thresholds — one for minimum-size-constrained ownership and one for unconstrained ownership — interact with the price-wage and price-rent ratios of each city. Proposition 1 proves that a city with higher price-wage and price-rent ratios will have a lower middle-skilled share, because middle-skilled workers (those who can afford to own in cheap but not expensive cities) are drawn to cheaper locations. Proposition 2 shows that in a world with only renters or only owners, skill shares would be identical across cities regardless of price differences — the polarization result requires heterogeneity in tenure choice.

Q: What does the no-SBTC counterfactual show? A: Holding the parameters governing local returns to skills at their 1980 levels (shutting down skill-biased technical change) reduces the difference in the decline in the middle-skilled share between large and small CZs by 54% and the gap in the increase in the variance of log wages by 73%. This is broadly consistent with prior literature attributing the bulk of disproportionate polarization and inequality in big cities to SBTC.

Q: What do the constant price-ratio counterfactuals show? A: When price-wage ratios are held at 1980 levels (but SBTC is allowed to operate), the excess polarization gap between large and small CZs falls by 93% and the excess inequality gap by 40%. When price-rent ratios are held at 1980 levels, the polarization gap falls by 96% and the inequality gap by 27%. When both are held constant simultaneously, the polarization gap falls by 89% and the inequality gap by 27%. These results show that the effect of SBTC on polarization would be 63–81% smaller in the absence of the housing affordability amplification channel.

Q: Who are the largest losers from rising price-wage ratios in large cities? A: The counterfactual welfare analysis identifies middle-skilled workers with skill levels between approximately 0.29 and 0.80 as the primary losers. In the counterfactual with fixed price-wage ratios, workers with skills from 0.29 to 0.57 who previously could not afford ownership in large cities are now able to own there, and those with skills from 0.57 to 0.80 spend a smaller share of income on housing. This group either lost homeownership opportunities or was induced to move to less productive CZs by the actual price growth that occurred.

Q: How is the quantitative model calibrated and structured? A: The model is calibrated separately for 1980 and 2019 as two stationary spatial equilibria. It features two locations (the top 30 CZs, which account for 49.3% of employment, and the remaining CZs). Key parameters include a Frechet elasticity of 6.1, an agglomeration externality of 0.04, a PTI constraint of 0.308, and an annual discount factor of 0.96. Land shares differ between large and small CZs (0.3965 vs. 0.2239). The model finds that the price-rent ratio was relatively stable in large cities but fell in small ones, while the price-wage ratio increased much more in large CZs — both indicators point to purchasing a home becoming relatively more expensive in large CZs.

Q: What are the paper’s policy implications? A: Zoning reforms and other policies that increase housing supply in large, unaffordable cities could produce a more efficient spatial allocation of labor, greater aggregate productivity, and more economically diverse — less polarized and less unequal — cities, while also reducing the wealth gap between owners and renters. Policies that promote homeownership by reducing the cost of owning without raising housing supply may reduce local polarization and inequality but could lower aggregate output and do not necessarily increase homeownership rates.

Q: How does this paper relate to existing explanations for city-level polarization? A: The paper’s housing-market mechanism is explicitly complementary to SBTC-based explanations (Baum-Snow, Freedman, and Pavan, 2018; Cerina et al., 2023), external demand shock explanations (Davis, Mengus, and Michalski, 2020), and IT-displacement explanations (Eeckhout, Hedtrich, and Pinheiro, 2024). The paper’s key added contribution is that even if SBTC were the primary driver of disproportionate polarization, its measured effect would be substantially smaller in the absence of faster house price growth in large cities — the housing market amplifies rather than replaces the technology channel.

Job polarization (city-level): The hollowing out of middle-income employment shares in a commuting zone, measured as the change in the share of workers in occupations assigned to the 21st–80th income percentile (using the 1980 occupation-to-percentile mapping fixed over time). In this paper, polarization is greater in cities where price-wage and price-rent ratios grew faster, attributed to selective out-migration of middle-skilled households.

Price-wage ratio: The ratio of hedonic house prices to median annual wages in a commuting zone, constructed from Census and ACS data. A higher price-wage ratio tightens the payment-to-income constraint on potential homebuyers and is the primary driver of the skill threshold for homeownership in the model.

Price-rent ratio: The ratio of hedonic house prices to rents in a commuting zone. In the model, a higher price-rent ratio reduces the financial advantage of owning over renting, raising the skill threshold at which ownership becomes optimal. The paper treats price-rent and price-wage ratios as distinct channels that both independently amplify polarization.

Housing tenure choice: The household decision to own or rent, modeled as a discrete choice made at the start of life that interacts with location choice. Ownership requires satisfying both a minimum house size constraint and a payment-to-income (PTI) constraint (lambda = 0.308). The interaction between tenure and location choices is the paper’s key model innovation; it exists only for middle-skilled workers whose income is sufficient for ownership in cheap but not expensive cities.

Skill threshold for homeownership (s*_i): The minimum skill level at which a worker in city i chooses to own rather than rent, defined by Lemma 2. This threshold is decreasing in local labor productivity and increasing in price-wage and price-rent ratios. Workers with skill below s*_i in all cities always rent; those with skill above s*_i in all cities always own; those in between face city-dependent tenure choice that distorts their location decision.

Skill-biased technical change (SBTC): In the paper’s quantitative model, SBTC is represented by faster growth in the skill dispersion parameter (alpha_it) in large CZs, reflecting differential productivity growth concentrated at the top of the skill distribution. The paper finds SBTC accounts for 54% of the polarization gap and 73% of the inequality gap in its counterfactual, but argues its effect is amplified 4–5x by the housing affordability channel.

Payment-to-income (PTI) constraint: The constraint that a homebuyer cannot spend more than a fraction lambda (calibrated at 0.308) of annual labor earnings on the annual housing payment (user cost times price times quantity). This constraint, together with the minimum house size, determines the income threshold for ownership and makes location and tenure choices interdependent for middle-skilled workers.

Spatial Implications of Telecommuting

Mon, 01 Jan 0001 00:00:00 +0000

Delventhal and Parkhomenko build a quantitative spatial model of the United States to study how the rise of telecommuting reshapes the distribution of residents, jobs, and housing costs across and within cities. The model divides the continental U.S. into 4,502 locations (defined as intersections of Census PUMAs and counties) and allows each worker to choose any residence-job pair. Workers differ by education (college vs. non-college) and occupation type (telecommutable vs. non-telecommutable). Telecommutable workers can split labor time between on-site and remote work; their remote-work intensity responds endogenously to relative remote productivity, a work-from-home aversion parameter, home floorspace costs, and commute time.

The model is calibrated to pre-2020 U.S. data (2012–2016 ACS, 2018 SIPP, 2017 NHTS). Key calibrated facts include: 33.6% of workers have telecommutable jobs (40.6% of non-college, 72.7% of college workers); remote work is nearly as productive as on-site work (relative productivity 0.99–1.00); elasticities of substitution between work modes range from 3.48 to 5.05; and work-from-home aversion parameters range from 2.48 to 3.35, indicating large non-pecuniary barriers especially for non-college workers in non-tradable sectors.

The counterfactual simulates a permanent increase in remote work driven by an 8–10% rise in remote productivity and a fall in work-from-home aversion, guided by Barrero, Bloom, and Davis (2021) survey evidence. Results show net reallocation of jobs and residences equivalent to nearly 5% of the population.

Main spatial findings exhibit a non-monotonic pattern. Telecommutable residents move away from dense, high-cost locations toward sparser areas with lower housing costs and better amenities. Non-telecommutable residents partially counteract this by centralizing — moving toward denser areas as housing costs fall near job centers. Non-tradable jobs follow telecommuters outward. Tradable jobs move in both directions: some firms relocate to low-density areas with newly accessible remote worker pools; others expand in the largest, most productive city centers as office space costs fall and the catchment area of workers widens.

In aggregate: the average worker lives 47% farther (in commuting time) from their workplace but spends 25% less time commuting, because average remote-work frequency rises by 1.1 days per week. The share of workers living in one commuting zone and working in another increases from 24.6% to 34%. Average income falls marginally by 1%, masking large gains for telecommutable workers and losses for non-telecommutable workers. Average floorspace prices fall by 2%; non-tradable prices rise by 2.6%. Overall welfare increases by an average of 12.7%, driven by gains for telecommutable workers, while non-telecommutable workers experience net losses.

The model predicts a partial reversal of the “Great Divergence”: skill sorting falls both within and across commuting zones, residential income inequality across CZs falls, and house price dispersion falls both within and across cities. These predictions are directionally consistent with 2019–2023 data.

Scope conditions: results are for a permanent shock to the full-time U.S. workforce as modeled in 2012–2016; the model does not predict the end of big cities but rather a reallocation at the margin. The model shows that the introduction of telecommuting narrows the parameter range guaranteeing a unique spatial equilibrium, because remote-capable firms can draw from a broader worker catchment area, amplifying agglomeration forces.

Q: What are the four stylized facts about pre-2020 telecommuting that discipline the model? A: Fact 1: telecommutability is higher for college workers and those in tradable industries — 68.8% of college-tradable workers can work from home versus 18.9% of non-college non-tradable workers. Fact 2: among telecommutable workers, uptake is also higher for college-tradable workers (38% actually work from home at least one day per week) than for non-college non-tradable workers (21%). Fact 3: the distribution of remote-work frequency is bimodal — most workers are either fully on-site or fully remote, with the bimodality less pronounced for college-tradable workers where hybrid (1–4 days/week) accounts for over 11% of paid workdays. Fact 4: there is a positive relationship between work-from-home frequency and distance from the job site, consistent with telework reducing effective commuting costs.

Q: How is the counterfactual shock calibrated and what drives it? A: The counterfactual raises remote-work productivity by 8–10% across all worker types and simultaneously reduces work-from-home aversion, guided by Barrero, Bloom, and Davis (2021) survey evidence that 25–30% of paid workdays will be remote post-pandemic, compared to about 8% in 2018. The authors consider both a technology shock (productivity increase) and a preference shock (aversion decrease) as mechanisms, consistent with their view that multiple hypotheses about the COVID-19 telework shock are plausible and non-exclusive.

Q: How do residents reallocate in response to the rise in telecommuting? A: Net reallocation of residents equivalent to nearly 5% of the population occurs. Telecommutable residents decentralize — moving to less dense areas with lower housing costs and better amenities — because the cost of choosing a residence far from work falls. Non-telecommutable residents partially centralize, moving toward denser locations in larger metro areas, because housing costs fall in locations with short commutes, making them more affordable.

Q: How do jobs reallocate? A: Non-tradable jobs follow the decentralization of residents (their source of demand) monotonically to less dense locations. Tradable jobs move in both directions: some firms relocate to low-density areas that can now access a larger pool of remote workers at lower real estate costs; others expand operations in the highest-productivity city centers, benefiting from both an expanded catchment of remote workers and a decline in the high cost of office space.

Q: What are the aggregate commuting implications? A: The average worker lives 47% farther in commuting time from their workplace in the counterfactual, yet spends 25% less time commuting, because average remote-work frequency increases by 1.1 days per week. The share of workers living in one commuting zone and working in another rises from 24.6% to 34%, which the authors note may call into question current administrative definitions of commuting zones and have major impacts on travel patterns.

Q: What are the welfare and income effects? A: Overall welfare increases by an average of 12.7%, but this masks very unequal distribution: telecommutable workers experience large gains while non-telecommutable workers suffer losses. Average worker income falls marginally by 1%, reflecting sizable gains for remote-capable workers offset by losses for those who cannot telecommute. Average floorspace prices fall by 2%, while non-tradable goods prices rise by 2.6%.

Q: What does the model predict for the “Great Divergence”? A: The model predicts a significant re-convergence across multiple dimensions: skill sorting falls both within and across commuting zones, residential wage inequality across CZs falls, and house price dispersion falls both within and across cities. The authors find that commuting zones with higher college shares in 2019 experienced slower growth in college shares 2019–2023, and that there is a negative correlation between average wages by CZ in 2019 and wage growth 2019–2023 — both consistent with model predictions.

Q: How does the model validate against post-2019 data? A: The authors show that their counterfactual results are positively correlated with observed changes in population, jobs, and housing rents since 2019. Within-city price variance has already converged in 2019–2023 data, consistent with model predictions. CZ-level patterns of skill concentration and wage growth also move in the direction the model predicts.

Q: Is the COVID-19 shock better described as a technology shock or a preference shock? A: The authors test both. To replicate observed changes in remote-work frequency using only a productivity shock requires a 55–99% jump in remote productivity, which yields implausibly large wage gains for remote-capable workers of 47–82%. The preference-based scenario yields results more consistent with observed data, supporting the view that a preference shock — changes in norms, attitudes, and institutional policies — is the primary driver.

Q: What happens to real estate prices when supply and amenities are held fixed? A: When real estate supply, productivity, and amenities are all held fixed, residential prices jump by 16% and commercial prices fall by 16%. The authors note this mimics the bifurcated shift in real estate values observed during the pandemic years, suggesting that supply responses and amenity adjustments are important for dampening the price effects in the full model.

Q: How does the model handle the uniqueness of spatial equilibrium, and how does telecommuting affect it? A: In a standard quantitative spatial model, agglomeration forces are dampened by the finite pool of workers willing to commute daily to a productive location. When telecommuting is introduced, productive locations can draw workers from a much broader catchment area, amplifying agglomeration forces and narrowing the range of parameter values for which a unique equilibrium is guaranteed. The authors establish conditions under which uniqueness is preserved.

Q: What are the model’s three main advantages over more stylized spatial models of remote work? A: First, by including 4,502 locations, the model can predict how far telecommuters will move from their jobs — a key variable for real estate markets and commuting patterns. Second, it can represent changes in the distribution of workers across different work-from-home frequencies, which is crucial as hybrid work has emerged as the dominant post-pandemic arrangement. Third, it predicts how the location of jobs (not just residents) changes, which has important implications for city centers.

Q: What is the overall welfare conclusion regarding non-telecommutable workers and income inequality? A: Non-telecommutable workers suffer welfare losses from the rise of remote work, even as overall average welfare rises by 12.7%. The overall income inequality — as opposed to spatial wage dispersion — does not fall. The authors note this means the spatial re-convergence does not translate into a broader reduction in income inequality, which they flag as an important limitation for policy.

Telecommutability: the ability of a worker’s occupation to be performed from home, measured using Dingel and Neiman (2020) occupational classifications; varies by education and industry, with 68.8% of college-tradable workers telecommutable versus 18.9% of non-college non-tradable workers.

Work-from-home aversion (ς): a preference parameter representing tastes, norms, and institutional policies that create non-pecuniary barriers to remote work; calibrated to range from 2.48 to 3.35 across worker types, higher for non-college workers in non-tradable sectors.

Hybrid work: an arrangement in which a telecommutable worker splits paid workdays between on-site and remote work (1–4 days per week from home); the model’s bimodal distribution of work-from-home frequency replicates the empirical observation that most workers are either fully on-site or fully remote, with hybrid most prevalent among college-tradable workers.

Catchment area: the pool of workers from which a firm can practically hire, which widens under telecommuting because workers no longer need to commute daily; this widening amplifies agglomeration forces and narrows the parameter range guaranteeing a unique spatial equilibrium.

Great Divergence: the multi-decade trend (documented in Moretti 2012 and related work) of spatially concentrating talent, income, and housing costs in a small number of large, high-skill cities; the paper predicts a partial reversal — “Great Re-Convergence” — driven by the rise of telecommuting.

Productive externalities (agglomeration): local productivity in the model depends on employment density; remote workers participate in these externalities only partially (parameter ψ ∈ [0,1]), so the shift to remote work can reduce agglomeration benefits in city centers.

Source text origin: the paper’s own classification of the text on which a summary is based (full PDF, open-access HTML, or abstract-only); the paper’s CLAUDE.md rules mandate that abstract-only summaries are blocked.

The Dynamics of Internal Migration: A New Fact and its Implications

Mon, 01 Jan 0001 00:00:00 +0000

Howard and Shao document a new empirical regularity in U.S. internal migration: the t-year interstate migration rate — defined as the share of people living in a different state than they did t years ago — is approximately proportional to the square root of t. The fact is established using the Gies Consumer and Small Business Credit Panel (GCCP), a 15-year panel (2004–2018) covering approximately 1 percent of all Americans with a credit report, and is corroborated in the Panel Survey of Income Dynamics (PSID, 1969–1997), where the square root pattern holds out to a 25-year horizon. The fact is not an artifact of averaging across origins, destinations, cohorts, or age groups: most of the distribution across these cuts is concentrated close to the square root line. It holds for both people under 45 and over 45, and is robust to the choice of time period and inter-state distance.

The standard moving cost model — in which location choice is a Markov process with i.i.d. extreme-value utility shocks and large bilateral moving costs — is shown (Proposition 1) to imply that the t-year migration rate is approximately proportional to t, not sqrt(t), as moving costs tend to infinity. Simulations confirm the linear pattern persists in calibrated versions of the moving cost model even when adding state variables for prior location, home state, or age.

The paper’s main theoretical contribution is the SPACE model (Spatially and Persistently Autocorrelated Epsilons). Rather than imposing moving costs, the SPACE model assumes that person-location match-specific utility is (i) persistent over time, governed by an autocorrelation parameter rho, and (ii) spatially correlated across locations via a generalized extreme-value (cross-nested logit) structure. The model has no moving costs by default. Proposition 3 proves that as rho approaches 1, the ratio of t-year migration to 1-year migration is bounded below by sqrt(t) and above by sqrt(pi/3) * sqrt(t) — a tight bound, since sqrt(pi/3) is approximately 1.023. The calibrated rho-tilde is 0.892, implying a period-to-period autocorrelation of 1 − (1 − rho-tilde)^2 = 0.988.

The SPACE model replicates bilateral one-year migration flows, matches the decreasing hazard rate of migration conditional on duration of stay, reproduces the distribution of lifetime move counts (including the large fraction who never move and the few percent who move four or more times in 14 years), and outperforms the moving cost model at out-of-sample individual location forecasting: by 2018, the moving cost model’s mean Kullback-Leibler divergence reaches approximately 0.12 log-points per observation above the maximum-possible benchmark, versus only 0.014 log-points for the SPACE model.

Key divergences from the moving cost model arise in four areas. First, moving costs need not be large: the SPACE model rationalizes observed low migration without any moving costs, in contrast to Kennan and Walker’s (2011) estimate of average moving costs of $312,146 (2010 dollars), more than six times median household income; when moving costs are added to the SPACE model, they are roughly two orders of magnitude smaller. Second, long-run population elasticities differ sharply: in the SPACE model they remain proportional to bilateral gross migration rates, while in the moving cost model they converge to a static logit proportional to population shares — and population shares and gross migration rates have little empirical correlation, so the long-run elasticities of the two models are essentially uncorrelated across state pairs. Third, adjustment dynamics differ: in the SPACE model a permanent utility shock to Louisiana produces immediate, full population adjustment; in the moving cost model adjustment takes roughly 200 years, with Mississippi overshooting its new steady-state and New York adjusting implausibly slowly. Fourth, welfare inferences are almost reversed: the correlation between log utility changes implied by the two models using U.S. population data is −0.497, with the SPACE model attributing relative utility gains to the South and West and the moving cost model attributing gains to New York and New England.

Q: What is the square root fact, and which datasets confirm it? A: The t-year interstate migration rate scales approximately as sqrt(t). It is documented in the GCCP (2004–2018, ~1% of Americans with credit reports) and verified in the PSID (1969–1997), where the pattern holds out to a 25-year horizon. It is not driven by averaging across subgroups: the distribution of the fact across origin-destination pairs, age groups, cohorts, and starting years is concentrated close to the square root line.

Q: Why does the standard moving cost model fail to match the square root fact? A: In the moving cost model, location choice is a Markov process with i.i.d. extreme-value shocks. Proposition 1 proves that as the common component of moving costs tends to infinity, the t-year migration rate is proportional to t (linear). Because the model requires large moving costs to rationalize low migration rates, the linear prediction is unavoidable. Simulations of calibrated versions — including variants with home bias, prior-location state variables, or age — confirm the relationship remains approximately linear.

Q: What is the SPACE model, and why does it generate a square root? A: The SPACE model replaces moving costs with persistent and spatially correlated person-location match-specific utility. Utility shocks are drawn from a generalized extreme-value (cross-nested logit) distribution that allows spatial correlation, and they are autocorrelated over time with persistence parameter rho. Proposition 3 shows that as rho → 1, the ratio of t-year to 1-year migration is bounded in [sqrt(t), sqrt(pi/3)*sqrt(t)], a tight interval since sqrt(pi/3) ≈ 1.023. The intuition is that when rho is close to 1, the idiosyncratic utility process resembles a random walk, whose standard deviation grows as sqrt(t), causing migration thresholds to be crossed at a sqrt(t) rate.

Q: What is the calibrated persistence parameter, and what does it imply? A: The calibrated rho-tilde is 0.892, close enough to 1 to generate the square root fact in simulations. The implied period-to-period autocorrelation of match-specific utility is 1 − (1 − 0.892)^2 = 0.988. This calibration is achieved by solving for the largest eigenvalue of an I×I matrix of conditional migration rates.

Q: How do the two models compare on individual-level forecasting accuracy? A: Performance is evaluated using mean Kullback-Leibler divergence from the maximum-achievable log likelihood. Both models perform similarly in 2005, but by 2018 the moving cost model’s KL divergence reaches approximately 0.12 log-points per observation, while the SPACE model’s reaches only 0.014 log-points — roughly an order of magnitude better — leaving little room for improvement.

Q: How large are implied moving costs under each model? A: Kennan and Walker (2011) estimate average moving costs of $312,146 in 2010 dollars, exceeding six times the median household income. The baseline SPACE model requires zero moving costs to match observed migration levels. When an augmented SPACE model with both persistence and moving costs is calibrated to match the one-year and ten-year migration rates, the estimated moving costs are approximately two orders of magnitude smaller than those from a moving-cost-only model.

Q: How do short-run population elasticities compare across models? A: In both models, the short-run cross-elasticity of population in state i with respect to utility in state j is approximately proportional to the gross migration rate between them. Corollary 1 formalizes this for the SPACE model: dp_i/du_j = −(1/(1−rho)) * m_{i→j} for i ≠ j. This means that in the short run, both models deliver similar predictions for how populations respond to local shocks.

Q: How do long-run population elasticities differ? A: In the SPACE model, long-run elasticities remain proportional to bilateral gross migration rates — the same relationship as in the short run. In the moving cost model, Proposition 4 shows that the long-run elasticity converges to the static logit: d(log p_i)/d(v_j) = −2*p_j for i ≠ j, depending only on population shares. Since population shares and gross migration rates are empirically uncorrelated, the long-run elasticities of the two models are essentially uncorrelated across state pairs.

Q: What do the models predict about the speed of regional adjustment? A: In the SPACE model, a permanent utility shock to Louisiana causes full, immediate population adjustment in the first period with no further dynamics. In the moving cost model, the same shock generates adjustment lasting roughly 200 years. Mississippi overshoots its long-run steady state in the moving cost model due to high bilateral migration with Louisiana, while New York adjusts especially slowly due to low bilateral migration — a pattern the authors describe as potentially counterintuitive.

Q: How do the models handle events involving rapid population change, such as Hurricane Katrina? A: The SPACE model accommodates fast adjustments by assuming rapid utility changes, consistent with the observed sharp decline in Louisiana’s population share followed by a small rebound. The moving cost model requires implausible utility assumptions to match these dynamics: it implies that Louisiana utility two years after Katrina was higher than before the hurricane.

Q: What do the two models infer about which U.S. states have gained or lost relative utility over time? A: Using exact-hat algebra applied to observed U.S. population changes, the SPACE model infers that the South and West have the largest relative utility gains, while New England and the Rust Belt have the largest relative declines. The moving cost model produces nearly the opposite inference: New York and New England show relative utility gains, while the South and West show declines. The correlation between the log utility changes implied by the two models is −0.497.

Q: Why do the authors argue that spatially and temporally correlated utility is realistic, not merely a mathematical convenience? A: Surveys (Jia et al., 2023) show that people primarily cite family and employment considerations as reasons for interstate moves — both are persistent and geographically concentrated. Proximity to family is spatially correlated: if state i is close to one’s family, nearby states are also relatively close. Job opportunities in specific industries or skills are geographically clustered. Natural amenities and regional cultures are spatially correlated as well. The authors argue it is harder to defend the i.i.d. assumption of the moving cost model than the SPACE model’s correlated structure.

Q: What is the distinction between moving costs and persistent match-specific utility? A: A moving cost is a one-time irreversible cost paid upon leaving a location. Persistent match-specific utility implies that the utility change from moving is ongoing, partially reversible upon return, and decays with time away from the original location. The authors argue that many factors labeled “moving costs” in the literature — such as distance from friends or amenities — are more accurately characterized as persistent and partially reversible utility losses, a distinction previous models could not draw.

Q: Does the SPACE model replicate the gravity equation for bilateral migration? A: Yes. Proposition 2 shows that migration from i to j in the SPACE model is given by m_{i→j} = (1 − rho) * p_i * p_j * (1 + tau_ij), where tau_ij captures spatial correlation. This resembles a gravity equation: more spatially correlated location pairs have higher bilateral migration, and higher persistence (higher rho) implies lower overall migration levels.

Q: Can the SPACE model be embedded in broader quantitative spatial models? A: Yes. The SPACE model admits closed-form solutions for state populations and bilateral migration flows, is compatible with exact-hat algebra for dynamic counterfactuals, and supports computationally feasible individual-level simulations. Appendix E embeds the SPACE model in a housing model with durable local housing production and shows that slow population adjustment can emerge from housing durability rather than slow migration per se, providing an alternative explanation for regional divergence persistence.

SPACE model: A model of internal migration featuring Spatially and Persistently Autocorrelated Epsilons — person-location match-specific utility that is both autocorrelated over time (with persistence parameter rho) and spatially correlated across locations via a generalized extreme-value (cross-nested logit) distribution. The model contains no moving costs by default.

Square root fact: The empirical regularity that the t-year interstate migration rate (share of people living in a different state than t years ago) is approximately proportional to sqrt(t). Documented in GCCP data (2004–2018) and PSID (1969–1997) up to a 25-year horizon.

Moving cost model: The standard dynamic discrete-choice model of migration in which an agent living in state i chooses location j to maximize u_j − delta_ij + epsilon_j + beta*E[V’], where delta_ij is a bilateral one-time irreversible moving cost and epsilon_j is i.i.d. extreme-value. Low migration rates are rationalized by large moving costs (e.g., $312,146 average in Kennan and Walker 2011).

Persistence parameter (rho): In the SPACE model, rho governs the autocorrelation of match-specific utility over time. The calibrated value is rho-tilde = 0.892, implying period-to-period autocorrelation of 0.988. As rho → 1, the model generates a square root relationship between the t-year migration rate and t.

Population cross-elasticity: The elasticity of population in state i with respect to utility in state j. In both models it is proportional to gross bilateral migration in the short run. In the long run, the SPACE model retains this proportionality to migration rates, while the moving cost model converges to a static logit proportional to population shares.

Exact-hat algebra: A solution method for computing counterfactual equilibria in terms of ratios of new to old values (hats), without requiring knowledge of levels. The SPACE model admits simple exact-hat formulas for population changes; the moving cost model’s exact-hat algebra additionally requires tracking past population changes.

Kullback-Leibler divergence (in this context): The mean divergence between a model’s predicted distribution over future locations and the empirical distribution, used as a measure of forecasting accuracy. By 2018, the SPACE model achieves KL divergence of 0.014 log-points per observation versus approximately 0.12 for the moving cost model.

The Power of Proximity to Coworkers

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies how physical proximity to coworkers affects on-the-job training and productivity, using software engineers at a Fortune 500 online retailer observed from 2019 to 2024. The authors exploit two quasi-experimental shocks to proximity: the office closures of 2020, which eliminated proximity differentials that previously existed across team types, and the firm’s subsequent return-to-office (RTO) mandates in 2022 and 2023, which restored proximity for co-located teams while leaving geographically-distributed teams apart. The core identification strategy is a difference-in-differences design comparing engineers whose teams were co-located in a single headquarters building to those whose teams were split across two buildings a ten-minute walk apart — a distinction that became immaterial once offices closed.

The central finding is that sitting near teammates substantially increases the digital feedback engineers receive on their code. Before the office closures, engineers on co-located teams received 23.9% (1.92 comments per program) more code review feedback than engineers on multi-building teams. Once offices closed, this advantage narrowed by 18.3% (1.47 comments per program, p-value = 0.0026). The lost comments were disproportionately those predicted by a machine-learning classifier to be helpful, actionable, well-reasoned, and impactful, with high-quality comments declining by 21–23% — exceeding the overall volume decline. Face-to-face and digital communication are complements, not substitutes: proximate engineers drew on a wider pool of reviewers and asked 48.4% more follow-up questions, a differential that vanished once offices closed.

Proximity’s effects are highly heterogeneous. Gains in feedback are concentrated among less-tenured, younger, and female engineers — those with the most to learn. Junior engineers on co-located teams lost 2.03 more comments per program upon office closure than junior engineers already on distributed teams (p-value = 0.001); young engineers lost 2.47 more comments (p-value = 0.0001). Female engineers lost 38.9% more comments than their distributed female counterparts (p-value < 0.0001), partly because women stop asking as many people for feedback when they cannot do so in person.

Proximity improves code quality for inexperienced engineers. Around the second RTO (three days per week), engineers on co-located teams became 2.2 percentage points less likely to add files subsequently deleted — a measure of churn — and 1.4 pp less likely to introduce bugs, relative to distributed teams (p-values of 0.041 and 0.022 respectively). These gains were roughly twice as large for less-tenured and younger engineers. The benefits persist: engineers who spent more pre-closure time on co-located teams continued to write higher-quality code during the fully remote period.

However, mentorship is costly for those who provide it. Senior engineers on co-located teams wrote 0.76 fewer programs per month in the main codebase before closures (p-value = 0.0005), a gap that closed when offices did and widened again during the second RTO. The firm faces a fundamental tradeoff: proximity accelerates junior engineers’ human capital development while reducing experienced engineers’ immediate coding output.

These dynamics shape hiring. The firm shifted toward hiring older, more experienced engineers during closures — buying talent it could no longer build in-house — and back toward younger hires once offices reopened. Nationally, young college graduates in remotable occupations (classified per Dingel and Neiman, 2020) experienced a 0.88 pp increase in unemployment between 2017–2019 and 2022–2024, while older graduates saw a marginal decline of 0.11 pp. A triple-difference estimate finds a 0.65 pp greater increase in young workers’ unemployment in remotable versus non-remotable occupations (p-value = 0.029), a pattern that predates generative AI diffusion and is robust to controlling for AI exposure. Back-of-the-envelope, remote work accounts for an estimated 64% of the total unemployment increase among young college graduates over this period.

The paper also documents that proximity is fragile: a ten-minute walk between two buildings reduces feedback as much as being multiple states away, and even a single distant teammate imposes negative externalities on those who remain co-located, reducing their feedback by 1.71 comments per program (p-value = 0.095) via a “one Zoom, all Zoom” norm.

Q: What is the main identification strategy for the office-closure analysis, and what is the key parallel-trends evidence?

A: The authors compare engineers on co-located teams (all members in one headquarters building) to those on multi-building teams (split across two buildings a ten-minute walk apart), before and after the March 2020 office closures. Co-located teams lost more proximity when offices closed, while multi-building teams experienced a smaller shock, enabling a difference-in-differences design. Pre-closure trends in feedback are parallel across the two team types (Figure I), supporting the identifying assumption. Standard errors are clustered by team, the unit of treatment assignment.

Q: How large is the effect of proximity on total code review feedback, and how is it broken down by feedback source?

A: Before closure, co-located engineers received 23.9% (1.92 comments per program) more feedback than multi-building engineers. The DiD estimate indicates that losing proximity reduced feedback by 18.3% (1.47 comments per program, p-value = 0.0026, Column 3 of Table II). This decline stems entirely from reduced feedback from teammates; there is no detectable effect on feedback from engineers on other teams — a placebo check that supports the identification strategy and rules out explanations based on differential project complexity.

Q: How does proximity affect the quality — not just the quantity — of code review comments?

A: Using a gradient-boosted decision tree trained on 5,377 human-labeled comments, the authors predict comment quality across all 174,014 comments. Losing proximity reduced comments predicted to be helpful, well-reasoned, actionable, and likely to change the code by 21–23% — exceeding the 18.3% overall volume decline. The residual comments were lower quality: 2.9 pp fewer were helpful (p-value = 0.039), 1.7 pp fewer explained their reasoning (p-value = 0.094), and 1.9 pp fewer were likely to change the code (p-value = 0.072).

Q: What mechanisms drive the complementarity between face-to-face interaction and digital feedback?

A: Proximity increases feedback on both the extensive and intensive margins. On the extensive margin, co-located engineers draw on a wider pool of reviewers, returning less frequently to the same commenter. On the intensive margin, losing proximity reduces follow-up questions by 48.4% (0.12 questions per program, p-value = 0.0083), accounting for roughly half of the total feedback decline. The other half comes from reduced initial reviewer feedback. References to other communication channels (e.g., Slack) within code reviews also decline when proximity is lost, confirming that face-to-face and digital communication are complements.

Q: How small a physical barrier is sufficient to reduce feedback substantially?

A: A ten-minute walk between two buildings on the same headquarters campus reduces feedback by as much as being multiple states away — both groups receive significantly less feedback than engineers whose entire team sits in the same building (Figure Ib). This finding aligns with research on academics showing that different floors or buildings reduce coauthorship, and extends it to daily teammates sharing projects.

Q: What are the externality effects of a single distant teammate?

A: Through the firm’s implicit “one Zoom, all Zoom” norm, even one teammate in a different location shifts all team meetings to video calls. Engineers in the same building exchange 14.5% less feedback when even one teammate is in another building versus when all teammates are co-located (p-value = 0.037). When a new hire transforms a co-located team into a multi-building one, feedback between the original co-located teammates drops by 1.71 comments per program (p-value = 0.095); adding a new co-located hire produces no such decline.

Q: How does the effect of proximity on feedback differ by engineer tenure, age, and gender?

A: Less-tenured engineers on co-located teams lost 2.03 more comments per program upon closure than less-tenured engineers on distributed teams (p-value = 0.001). Young engineers (under 29) on co-located teams lost 2.47 more comments per program than young distributed engineers (p-value = 0.0001). Female engineers on co-located teams lost 38.9% (3.71) more comments than female engineers on distributed teams (p-value < 0.0001), partly because women draw feedback from 14.7% fewer people when proximity is lost (p-value = 0.0078), compared to a negligible 2.6% decline for men. The extra feedback women receive in person is of higher quality, not rude or condescending.

Q: How is the effect of proximity on code quality identified using the RTO design, and what are the magnitudes?

A: The RTO design compares engineers on co-located (same-city) teams to geographically-distributed teams across three periods: full closure, first RTO (two days per week), and second RTO (three days per week). The authors predict γ_closed ≈ 0 (office assignment irrelevant when closed) and γ_2nd_RTO > γ_1st_RTO (more in-office days means more proximity). Both predictions are confirmed. During the second RTO, co-located engineers were 2.2 pp less likely to add files later deleted (p-value = 0.041) and 1.4 pp less likely to introduce bugs (p-value = 0.022), with effects roughly twice as large for less-tenured and younger engineers.

Q: Does the benefit of co-location on code quality persist after remote work resumes?

A: Yes. After all engineers returned to remote work, those who had been on co-located teams pre-closure were 2.37 pp less likely to write disposable code (p-value = 0.013) and 3.09 pp less likely to introduce bugs (p-value = 0.0012). Code quality improves monotonically with the number of pre-closure months spent on co-located teams (Figure A.5). These gaps persist when including current team fixed effects, meaning within the same post-closure team, the previously co-located engineer writes higher-quality code.

Q: What is the cost of mentorship for senior engineers, and how does it manifest in coding output?

A: Senior engineers on co-located teams wrote 0.76 fewer programs per month in the main codebase when offices were open (p-value = 0.0005). Once offices closed, this gap disappeared, and senior engineers who lost proximity to their teammates saw a relative increase in output of 0.58 programs per month (p-value = 0.0014). During the second RTO, engineers with more than sixteen months of tenure on co-located teams wrote fewer programs, while no significant difference emerged for less-tenured engineers. Overall, the DiD estimate indicates losing proximity to teammates increases immediate output by 0.48 programs per month (p-value = 0.0002).

Q: How does the firm’s hiring age distribution respond to changes in proximity?

A: When offices were closed, the firm shifted toward hiring older engineers: the share of hires under age 29 fell from over half pre-closure to less than a third during the closure. After the RTOs, the firm shifted back toward younger hires. Geographic variation reinforces this: headquarters-campus hires were 7–10 years younger than those hired into distributed roles when offices were open; this gap narrowed substantially during closures when everyone was far from teammates.

Q: Does proximity affect which engineers are poached by other firms?

A: Yes. During the office closures, 1.2% of co-located engineers were poached per month, compared to 0.9% of multi-building engineers of similar tenure, age, and engineering group (p-value = 0.044). By the end of the closure period, nearly a quarter of co-located engineers had been poached versus a sixth of multi-building engineers. There is a dose response: more pre-closure time on co-located teams predicts higher poaching rates. The effect is concentrated among younger and female engineers, consistent with their feedback building more transferable general human capital. Tenure does not moderate the poaching effect, consistent with less-tenured engineers’ feedback being more firm-specific.

Q: What does national unemployment data show about the scarring effects of remote work on young workers?

A: Between 2017–2019 and 2022–2024, young college graduates (under 29) in remotable occupations experienced a 0.88 pp increase in unemployment (p-value < 0.00001), while older graduates in the same occupations saw a marginal decline of 0.11 pp (p-value = 0.053). A triple-difference regression finds a 0.65 pp greater increase in young workers’ unemployment in remotable versus non-remotable occupations (p-value = 0.029). Back-of-the-envelope, scaling this estimate by the 61% share of young graduates in remotable jobs predicts a 0.4 pp increase in young college graduates’ overall unemployment — equal to 64% of the realized 0.63 pp increase.

Q: Is the unemployment increase among young workers in remotable jobs driven by generative AI rather than remote work?

A: The authors argue against AI as the primary driver on two grounds. First, the uptick in young workers’ unemployment in remotable occupations predates the rapid diffusion of generative AI. Second, the differential increase is not concentrated among occupations with the highest AI task exposure. The triple-difference estimate is robust to controlling for occupational AI exposure using the Eisfeldt, Schubert and Zhang (2023) index. The authors acknowledge that AI may become more important as it diffuses further.

Q: How do young workers’ own office attendance decisions reflect the value of proximity?

A: At the partner firm, engineers under 29 were 8.8 pp (37.6%) more likely to come into the office during the RTOs than older engineers when on co-located teams (solid line in Figure VIIa). This difference was roughly halved on geographically-distributed teams (p-value of difference = 0.0085), indicating that the draw is specifically proximity to teammates. Co-located managers raised attendance by 2.6 pp, while co-located teammates raised it by 5.1 pp. Nationally, Stack Overflow survey data show nearly half of engineers under 25 are in the office each day, versus a quarter of older engineers (p-value < 0.00001).

Q: What does the paper imply about why remote work was rare before the pandemic despite workers’ stated preferences for it?

A: The paper offers a resolution: firms may have recognized that the value of the office lies in training for tomorrow and improving the quality — not the quantity — of work today. Remote work boosts immediate output, especially for experienced workers, but it reduces mentorship and long-run skill development. The tradeoff between current and future productivity, and between individual and collective returns to human capital, explains why firms historically resisted remote work even when workers preferred it and short-run output was unaffected.

Q: What are the implications for gender equity in remote work?

A: The findings suggest remote work has ambiguous gender effects. While remote work may help working mothers remain in the workforce, it appears costly for young women’s professional development, which is especially sensitive to physical proximity. Women receive substantially more high-quality feedback when co-located, draw feedback from a wider network in person, and lose disproportionately more feedback when proximity is lost. Young female engineers on co-located teams were also disproportionately poached — suggesting their human capital gains from co-location are more general and transferable.

Code review feedback: The digital comments engineers exchange when reviewing each other’s code before it is merged into the live codebase; the paper’s primary measure of on-the-job training and mentorship investment, distinct from mere volume because the authors also classify comments by helpfulness, reasoning, actionability, and expected impact using supervised machine learning.

Co-located team: A team in which all members are assigned to the same office building; the treatment group in the difference-in-differences designs, distinguished from multi-building teams (split across two headquarters buildings, a ten-minute walk apart) and geographically-distributed teams (members in different cities or permanently remote).

One Zoom, all Zoom norm: The implicit team practice of holding all meetings virtually if any single teammate cannot be physically present; the mechanism by which one distant colleague generates negative externalities for the remaining co-located teammates, reducing their in-person interaction and feedback.

Proximity fragility: The finding that even small physical barriers — a ten-minute walk between buildings — reduce feedback as much as being multiple states away, implying that the relationship between physical distance and mentorship is highly nonlinear near zero.

Churn (disposable code): Files that are added by an engineer but deleted within the subsequent six months, either because the code was poorly structured or because it introduced a feature later abandoned; used as one of two code quality proxies in the RTO analysis (occurring in 15% of programs).

Bugs (immediate reversions): Programs that are immediately and fully reverted after being merged, typically indicating the engineer’s changes precipitated an emergency requiring rollback to an earlier version; used as the more serious of the two code quality proxies (occurring in 3.5% of programs).

Scarring effects: The persistent adverse impact on young workers’ human capital and labor market outcomes from reduced mentorship during the remote work period; manifested both as lower code quality at the individual level and higher unemployment rates nationally among young college graduates in remotable occupations.

Remotable occupation: An occupation classified by Dingel and Neiman (2020) as feasibly performed from home; used to construct the national triple-difference analysis comparing age gaps in unemployment across remotable and non-remotable jobs before and after the pandemic.