Estimating Who Benefits from Productivity Growth: Local and Distant Effects of City Productivity Growth on Wages, Rents, and Inequality

ECONOMISTS have long considered differences in productivity across countries to be a key source of differences in standard of living. Indeed, increases in consumption and welfare depend centrally on productivity growth in many macroeconomic models (see Solow, 1956), although empirical evidence is mixed on the causal link between productivity and real earnings.¹ There is tremendous variation in productivity growth across cities within the United States, and workers’ migration responses to these productivity differences can change the distribution and magnitude of gains from productivity growth.

In this paper, we examine differences in revenue total factor productivity growth (TFPR) across U.S. metropolitan areas (MSAs) and estimate the magnitude and distribution of effects on workers’ earnings and housing costs. We explore how within-country productivity differences influence workers’ standard of living and the division of economic gains between labor and land, in contrast to more recent focus on the division of economic gains between labor and capital. On a methodological level, we propose a new approach to estimate general equilibrium effects of local shocks.

The incidence of local productivity growth, or who benefits to what degree, is not clear ex ante. City TFPR growth raises local labor demand and therefore is likely to increase earnings for local workers. When city TFPR growth induces substantial in-migration from other cities, however, this may raise housing costs and limit wage gains for local workers who rent their homes. Because housing and other nontradable goods account for the majority of worker consumption, changes in these local costs have potential large consequences for workers’ standard of living (Moretti, 2013; Diamond & Moretti, 2022). Substantial increases in housing costs in increasingly productive cities revive the classical concern of Ricardo, in which landowners capture the gains from productivity growth.

We measure city-level changes in TFPR using data from the U.S. Census of Manufactures. The manufacturing sector experienced gains in TFPR from 1980 to 1990, and we uncover substantial geographic differences in TFPR growth across cities. We use this cross-city heterogeneity in TFPR growth, from 1980 to 1990, to estimate its effects on city employment, earnings, and housing costs using U.S. Census data from 1980 to 2010. We focus on the manufacturing sector because in the period we focus on, the manufacturing sector was at its peak and employed 20 million Americans (Charles, Hurst, & Notowidigdo, 2018), accounting for the majority of employment in the tradable sector.

An important aspect of our analysis is that we do not limit our focus to direct effects of local TFPR growth on earnings and housing costs in that same city. We propose and implement a novel way to estimate indirect effects that local productivity growth has on other cities through worker mobility. Empirically, these general equilibrium effects are quantitatively important for characterizing the magnitude and distribution of who benefits from local productivity growth.

In the first part of the paper, we estimate direct effects of TFPR growth on cities experiencing relatively larger TFPR growth. Because of the potential for local shocks to create spurious associations between TFPR growth and wages or housing costs, our empirical approach uses four instrumental variables to predict changes in city-level TFPR. Our baseline instrumental variable reflects industry-specific changes in nationwide TFPR that have differential effects on cities due to differences in cities’ initial industry concentration. We construct an alternative instrument, based on changes in stock prices by industry, to proxy for unexpected shocks to industry TFPR that may differentially affect cities concentrated in those industries. A third instrument is based on changes in exposure to export markets, since trade exposure affects firm output prices and has been associated with patenting and investment in R&D (Aghion et al., 2020; Autor et al., 2020). A fourth instrument is based on patenting activity within technology classes, which disproportionately increases TFPR in cities that had been patenting more in those technology classes.

The instruments have a similar structure, but the underlying identification assumptions are instrument specific. Importantly, the instruments use different sources of empirical variation: the cities that are predicted to have larger TFPR changes for one of our instruments are different from the cities predicted to have larger TFPR changes for other instruments. In addition, the most influential industries for predicting MSA-level TFPR growth are often different across the instruments (Goldsmith-Pinkham, Sorkin, & Swift, 2020). The alternative instruments yield similar estimates, however, and overidentification tests fail to reject that the estimates are statistically indistinguishable.

We estimate that local TFPR growth increases the earnings of local workers. A 1% increase in city-level manufacturing TFPR from 1980 to 1990 is associated with an average long-run increase of 1.5% in annual earnings from 1980 to 2000. Local employment increases by 4%, driven by in-migration. As a consequence of this in-migration, demand for housing increases. We estimate that a 1% increase in city-level manufacturing TFPR is associated with a 1.5% increase in housing rents and a 2.5% increase in home values.

Who benefits from local TFPR growth then depends in large part on residents’ position in the housing market. For workers who rent their home, much of the increase in earnings is offset by increases in the local cost of living. For workers who had owned their home, the gains are much larger because they come through both higher wages and higher housing values. We calculate impacts on worker purchasing power, which reflects earnings adjusted for cost of living, and find that a 1% increase in local TFPR increases purchasing power of renters and homeowners by 0.6% and 1.6%, respectively.

Who benefits locally from TFPR growth also depends substantially on workers’ level of education. We estimate greater impacts on both nominal earnings and purchasing power for high school graduates than for college graduates. At the same time, increases in local employment are substantially larger for more educated workers. We interpret the larger earnings gains and smaller employment effects experienced by high school graduates as caused by their lower geographical mobility compared to college graduates (Bound & Holzer, 2000; Wozniak, 2010; Malamud & Wozniak, 2012; Notowidigdo, 2020). Since less educated workers are less geographically mobile, their local supply is more inelastic, and so the incidence of local TFPR growth falls more on less educated workers. An important implication is that local TFPR growth compresses local inequality. We estimate that increases in nominal earnings and purchasing power are substantially greater for workers at the 10th percentile and 50th percentile of the income distribution than for workers at the 90th percentile of the income distribution.

In the second part of the paper, we turn to the indirect effects of local TFPR growth on earnings and housing costs in other cities. To see why indirect effects may be important, consider an example in which Houston experiences a positive TFPR shock that raises wages and employment in Houston. As migrants to Houston leave other places, this puts upward pressure on wages and downward pressure on housing costs in those other places (given a downward-sloping labor demand and upward-sloping housing supply). These indirect effects are diffused when a small share of migrants to Houston come from each other place, but the sum of these indirect effects may be quantitatively important alongside the direct effect in Houston.

To estimate indirect effects from worker mobility, for each city hit by a TFPR shock, we use our estimates of the direct employment effects and assumptions on city-to-city migrant flows to estimate employment declines in other cities due to out-migration. We then use data on city-level elasticities of housing supply, along with an assumption on the elasticity of labor demand, to gauge the general magnitude of these indirect effects on housing costs and earnings in other cities.

The typical approach in the literature to estimate general equilibrium effects of localized shocks is to impose a quantitative spatial model, identifying general equilibrium effects by drawing on the structure of the model. An advantage of our approach is that it requires fewer assumptions. A disadvantage is that we do not explore impacts on workers through changes in traded goods prices or impacts on firms and shareholders, which are components of the aggregate impacts of TFPR growth and depend on how much TFPR growth is driven by physical productivity improvements or increases in firm pricing power.

We find indirect effects that are economically substantial and have important implications for understanding who ultimately benefits from local TFPR growth. We estimate that 38% of the combined increase in purchasing power for the average worker occurs outside cities directly affected by local TFPR growth. These indirect effects disproportionately benefit college-educated workers due to their greater geographic mobility, which counterbalances the local decrease in inequality associated with local TFPR growth. Further, these indirect effects disproportionately benefit renters in other cities, who benefit from decreased housing costs.

Overall, when we sum the direct effects and indirect effects from local TFPR growth, we find that the average worker benefited substantially from manufacturing TFPR growth that averaged 5.3% from 1980 to 1990. We estimate that this increase in real TFPR led to economically large increases in purchasing power: on the order of 0.5% to 0.6% per year, between 1980 and 2000, for the average full-time worker.

The summed direct effects and indirect effects are roughly similar for more educated workers and less educated workers, in percentage terms. Less educated workers benefit more from TFPR growth in their city, but more educated workers benefit more from TFPR growth in other cities. Thus, neglecting indirect effects from worker mobility would both understate the gains from local TFPR growth and also yield a biased view of its distributional consequences. These estimates complement the large literature on skill-biased technological change and labor-saving technological change, which explores increases in inequality from productivity growth.²

The gains from TFPR growth are very different, however, depending on workers’ geographical location. The benefits of productivity growth are economically large in cities that benefit from strong direct and indirect effects (e.g., San Jose) and minimal in cities with weak direct and indirect effects (e.g., St. Louis). Thus, on net, the average worker benefits substantially from productivity growth, but these gains depend in large part on where the worker lives. A high-level view of average country-level changes would mask substantial variation in experiences across areas and people.

From a methodological point of view, our results suggest caution for interpreting empirical results that focus exclusively on the local impacts of local shocks. Many studies in economics seek to estimate the effects of economic shocks, such as immigration (Card, 2001) or trade (Autor, Dorn, & Hanson, 2013), by comparing areas that experience large shocks to areas that do not. Our findings indicate that when local shocks generate large migration responses, a substantial portion of the overall effects may be missed when focusing only on the direct effects. Including these indirect effects, even those indirect effects from worker mobility only, can yield qualitatively and quantitatively different conclusions. Our approach, based on migrant flows and certain key elasticities, can be used in other contexts to gauge the magnitude of indirect effects in a reduced-form manner. General equilibrium models can quantify additional indirect effects, such as impacts on prices of traded goods, though at the cost of imposing stronger theoretical assumptions on the structure of the economy.

For 193 metropolitan statistical areas (MSAs), covering 63% of the U.S. population in 1980, we combine data from the Census of Population and the Census of Manufactures.

We measure labor market outcomes and housing market outcomes at the MSA level, aggregating individual-level data and household-level data from the 1980, 1990, and 2000 waves of the Census of Population and the five-year sample from the American Community Survey centered on 2010 (2008–2012). The main outcome variables are average annual earnings, average household gross rent (for renters), average household home value (for owners), and city employment. For all outcomes, we analyze city-level averages and separate city-level averages within education group.³ Appendix table 1 reports average characteristics of the 193 sample cities in 1980 and average changes over time.

We measure average city-level TFPR using confidential plant-level data from the Census of Manufactures (CMF) in 1977, 1987, and 1997. The CMF contains plant-level data on all manufacturing plants’ employment, capital stock, materials, and total value of shipments. We refer to years 1980, 1990, and 2000 with the understanding that these data are measured three years prior.

To estimate average city-level TFPR, in each decade, we adopt an econometric approach that is similar to that used in our previous work based on the same data from the Census of Manufactures (Greenstone, Hornbeck, & Moretti, 2010). We assume each plant uses a Cobb-Douglas technology and, in each year separately, we regress log output on log input expenditures and city fixed effects (weighting by plant output). The estimated 193 city fixed effects, in each decade, reflect average TFPR in that city and decade. In appendix A, we report details of the estimation procedure and its limitations.

Our measure of TFPR is a measure of “revenue productivity,” as is typical in the literature, and therefore productivity growth in our context reflects increased value of plant output given plant input expenditures. This reflects not only physical productivity increases (more quantity produced for a given set of inputs), but also relative increases in output prices (e.g., due to increased demand for firm output). This measure of revenue productivity captures changes in local labor demand, the main focus of our paper, and both sources of variation in TFPR (from prices or physical productivity) have equivalent effects on local labor markets and local housing markets through increases in firm labor demand. Consumers of traded goods are affected differently by increases in physical productivity or increased firm prices, as are firm owners, but we do not analyze these other consequences of productivity growth.

For each city, figure 1 shows average TFPR in 1980 (panel A), in 1990 (panel B), and in changes from 1980 to 1990 (panel C). There is substantial variation in TFPR growth across cities, within broader geographic regions, that we use in the empirical analysis.⁴ Reassuringly, though, there is also persistence in TFPR across areas, with higher productivity places in 1980 remaining higher productivity in 1990 (appendix figure 1). Appendix figure 2A shows that measured local TFPR growth from 1980 to 1990 is largely uncorrelated with measured local TFPR growth from 1990 to 2000. Panels B, C, and D show that local TFPR growth from 1980 to 1990 is weakly positively correlated with local TFPR growth in cities within 100 miles and not correlated with local TFPR growth in cities within 250 miles and 500 miles.

To estimate the direct effects of local TFPR growth, we relate changes in city TFPR to changes in that city’s labor and housing market outcomes (employment, earnings, housing costs). Local TFPR growth increases local labor demand, which increases nominal wages and the cost of housing. The local gains from TFPR growth are then split between workers and landowners: the incidence depends on relative elasticities and which of the two factors (labor or housing) is supplied more elastically. Appendix B presents a simple spatial equilibrium model (Rosen-Roback) that helps interpret how TFPR growth in a city may affect employment, wages, and housing costs in that city and indirectly affect other cities through worker mobility.

These equations reflect reduced-form relationships between city TFPR and city-level outcomes, which we expect to depend on the relative elasticities of local labor supply and housing supply (appendix B). We explore how the estimated impacts of local TFPR growth vary with worker education, as more educated workers are generally more geographically mobile and the more elastic supply of more educated workers may reduce the impact on local earnings of more educated workers and compress local inequality. We also explore how the impacts vary with cities’ elasticity of housing supply (Saiz, 2010).

OLS estimation of equations (1 to 3) is likely to be biased for two categories of reasons. First, estimated changes in TFPR are likely to contain substantial measurement error. TFPR is a residual, measured with error, and the empirical specifications examine changes in TFPR that exacerbate bias from measurement error. Second, changes in city-level TFPR may be influenced by changes in local factors that independently affect employment, local earnings, or housing costs. These biases could be either positive or negative, given changes in productive amenities or consumption amenities.⁶

We instrument for changes in city-level TFPR using four alternative instrumental variables, in isolation or in combination, with the goal of isolating changes in local TFPR that reflect national influences that disproportionately affect cities based on their initial characteristics.

Our baseline instrumental variable uses nationwide changes in TFPR by industry to predict each city’s change in TFPR depending on each city’s initial concentration of industries. For each city, the instrument is defined by summing over all three-digit SIC industries: the city’s 1980 fraction of manufacturing output in an industry (⁠$αi,c,1980$⁠), multiplied by the national change in TFPR for that industry from 1980 to 1990 (⁠$γi,c,1980-1990$⁠), such that $IVcbaseline=∑iαi,c,1980×γi,c,1980-1990$⁠. The national change in TFPR for industry $i$ is indexed by city $c$ because, to avoid mechanical correlation between industry-level changes and city-specific shocks, we omit that particular city and estimate “leave-out” national changes in TFPR by industry across all other cities. For each city, the predicted change in TFPR from 1980 to 1990 then depends on that city’s industries in 1980 and changes in TFPR from 1980 to 1990 for those industries in other parts of the country.

A second instrument uses industry-level stock market returns to capture a variety of factors, including improvements in production technologies and increased demand for firm output, which are associated with increased revenue productivity of particular industries and increased labor demand. These industry-level gains may then benefit most those cities that were initially concentrated in those industries: we calculate industry-specific stock market returns from 1980 to 1990 (⁠$γi,c,1980-1990s$⁠), assigned to cities based on their industry employment shares in 1980 (⁠$αi,c,1980s$⁠), such that $IVcstock=∑iαi,c,1980s×γi,c,1980-1990s$⁠.⁷

One notable feature of this instrument, which may also be useful when applied to other empirical contexts, is that relative changes in stock prices between 1980 and 1990 are arguably unpredictable in 1980. This is in contrast to the baseline instrument and other instruments, which use variation that may be partially predicted at the beginning of the period. Thus, a comparison of estimates based on this instrument with estimates based on the other instruments is informative about how much the estimates based on the other instruments reflect unexpected changes.

The third instrument is based on increased industry exposure to export markets, which may increase TFPR for two reasons. First, increased export demand may translate into higher output prices and therefore higher revenue productivity in cities initially more concentrated in those industries. Second, increased net imports have been found to reduce innovation in U.S. firms (Autor et al., 2020); conversely, increased net exports may have a positive effect (Aghion et al., 2020). We aim to isolate exogenous trade shocks to U.S. industries by measuring increases in exports from other high-income countries. This instrument is calculated as the product of baseline city industry employment shares (⁠$αi,c,1980e$⁠) times the change in exports by industry from 1980 to 1990 (⁠$γi,1980-1990e$⁠), such that $IVcexport=∑iαi,c,1980×γi,1980-1990e$⁠. The instrument then reflects a city-specific index of export exposure, based on a weighted average of industry-specific growth in exports per worker.⁸

A fourth instrument is based on patenting activity. Cities initially concentrated in particular technology classes may experience greater TFPR growth when there is greater patenting activity in those technologies nationwide.⁹ For each city, the instrument is defined by summing over all technology classes $i$⁠: the number of patent assignees per manufacturing worker in 1980 (⁠$αi,c,1980p$⁠, multiplied by the total number of patents filed nationwide between 1980 and 1990 (⁠$γi,c,1980-1990p$⁠) excluding patents from an assignee located in that city, such that $IVcpatent=∑iαi,c,1980p×γi,c,1980-1990p$⁠. This instrument captures the relative benefit of national patenting activity for cities that had more patenting activity in particular technology classes.¹⁰

The identification assumption is specific to each instrument, though the four instruments are constructed similarly, as the assumptions depend on which cities are disproportionately affected by which national changes. For our baseline instrument, the identification assumption is that changes in labor market and housing market outcomes in certain cities (with manufacturing output initially concentrated in industries that experience stronger nationwide TFPR gains) would otherwise have been similar, on average, to changes in other cities (with manufacturing output initially concentrated in industries that experience weaker nationwide TFPR gains). For the alternative instruments, the identification assumptions are that labor market and housing market outcomes would otherwise have changed similarly in cities that were differentially exposed to stock market appreciation, export growth, or patenting activity.

These identification assumptions are meaningfully distinct when, in practice, the four instrumental variables capture different sources of empirical variation in city TFPR growth. Table 1, panels A and B, shows the sample cities with the largest and smallest predicted changes in TFPR for each of the four instrumental variables. While there is some overlap in these lists, the cities predicted to experience the greatest TFPR growth between 1980 and 1990 based on the baseline instrument are not the same set of cities predicted to experience the greatest TFPR growth based on the stock market instrument, export instrument, or patent instrument. For example, the top three cities in predicted TFPR growth are all different across the baseline instrument (Richmond, Atlantic City, and Raleigh-Durham), stock market instrument (Greenville, Charlotte, Greensboro), export instrument (Lexington, Fort Collins, Binghamton), and patent instrument (Stamford, Washington, Wilmington). There is more overlap among cities predicted to experience the least TFPR growth between 1980 and 1990, particularly among cities with substantial exposure to the oil and gas industry that experienced negative shocks in the 1980s, and we later estimate that the estimates are not sensitive to controlling for cities’ baseline share in the oil and gas industry.

Table 1, panel C, lists which industries or technology classes are most influential in driving the variation for each instrument.¹¹ The instruments largely reflect nationwide shocks to different industries, which then affect different cities according to their baseline concentrations. Petroleum refining is influential for both the baseline IV and export IV, which may reflect shocks in the oil and gas industry that affect city TFPR through multiple channels, but our identification assumption does not rely on city TFPR changing only through differential exposure to trade shocks or other shocks.

Figure 2 shows pairwise correlations for all pairs of the four instruments, where each dot represents a city. The different instruments are statistically correlated in three of the six cases but reflect a great amount of independent variation, with pairwise regressions yielding $R$-squared values of 0.002, 0.358, 0.123, 0.014, 0.006, and 0.006.

Figure 3 shows four maps, one for each instrument, that illustrate the geographic variation in predicted changes in TFPR. Each instrument is divided into deciles, with darker shades reflecting higher values of the instrument (which predict greater increases in TFPR). The maps show that the instruments are not simply picking up local shocks common to each instrument and that there is geographic variation within nearby areas for each instrument.

Because the instrumental variables reflect different sources of empirical variation in predicted TFPR growth, the identification assumptions are also then meaningfully distinct in practice. We estimate overidentification tests that fail to reject that the 2SLS estimates are statistically the same across these instruments. Each instrumental variable estimates a particular local average treatment effect (LATE), which reflects variation in TFPR growth due to sectoral shifts that may be more long-lasting than all observed variation in TFPR that is a combination of permanent shocks and transitory shocks. The IV estimates may then be larger than the OLS estimates, even in the absence of omitted variable bias or measurement error, though in practice, we see little systematic mean reversion in TFPR growth from one decade to the next (appendix figure 2). Our estimates may be expected to reflect the impacts of average TFPR growth, sustained over longer periods, whereas alternative research designs based on temporary TFPR shocks may identify different relationships (e.g., if there is little time for migration responses).

Table 2 reports our baseline estimates, which instrument for changes in TFPR using the baseline instrumental variable. The estimated first-stage impact is reported at the bottom of the table, along with the $F$-statistic of the excluded instrument. Appendix table 2 reports corresponding OLS estimates.¹²

City employment responds substantially to local TFPR growth (panel A). A 1% increase in local TFPR is estimated to increase city employment by 2.38% in the medium run (column 1), by 4.16% in the long run (column 2), and by 4.03% in the longer run (column 3). These estimates suggest that it takes additional years for worker migration to respond to increased real wages and for housing construction to respond to increased demand, though this adjustment process was complete by 2000.

Panel B reports estimated impacts on annual earnings per worker. A 1% increase in local TFPR is associated with a 0.91% increase in earnings in the medium run (column 1), a 1.45% increase in earnings in the long run (column 2), and a 1.46% increase in earnings in the longer run (column 3). These estimated magnitudes are reduced-form effects of TFPR growth and, in particular, can be greater than 1 when worker in-migration and increased economic activity generate agglomeration spillovers (as in Greenstone, Hornbeck, & Moretti, 2010).

The estimated impacts on earnings are economically substantial. Given that real TFPR increased by 5.3% between 1980 and 1990 in the average city (appendix table 1), the IV estimates suggest that TFPR growth increased local earnings of full-time workers in the average sample city by 4.8% from 1980 to 1990, by 7.7% from 1980 to 2000, and by 7.7% from 1980 to 2010.

We expect increases in local housing costs to mitigate some portion of the estimated increases in local nominal earnings, given increases in employment that create additional demand for housing. Indeed, table 2 shows that increases in local TFPR are associated with substantially higher housing costs. A 1% increase in local TFPR leads to a 0.98% medium run increase in rental costs, a 1.47% long-run increase in rental costs, and a 1.09% longer-run increase in rental costs (panel B). The corresponding effects on home values are somewhat larger, 1.74% to 3.05% (panel C), which suggests some expectation of future increases in rental costs. The estimated long-run effect on employment which are relative to rent is 2.8, and relative to home value is 1.7, similar magnitudes to the median housing elasticity (2.1) and mean housing elasticity (2.3) of sample MSAs with housing supply elasticity data from Saiz (2010).

We test whether the estimated impact on housing costs is larger in cities with a more inelastic housing supply, as a validation exercise suggested by previous empirical research (Glaeser & Gyourko, 2005; Gyourko, 2009; Saiz, 2010). We find that the estimated impact on local housing costs is indeed somewhat greater in cities with a more inelastic housing supply (appendix table 3). A 1% increase in local TFPR leads to a 2.3% long-run increase in rents in cities with below-average housing elasticity and to a 1.2% increase in rents in cities with above-average housing elasticity.

We note that growth in TFPR may reflect a variety of factors, including both technological improvement and increases in demand that raise prices. The impacts of local TFPR growth operate through increases in local labor demand, similar to increases in quantity TFP growth (TFPQ), and so for our purposes, the important distinction between TFPR and TFPQ is not central and the empirical analysis draws on both sources of variation in TFPR.¹³

The estimated increases in local earnings (table 2, panel B) are partly mitigated by increases in housing costs (panel C), but it remains unclear how much local TFPR growth affects local purchasing power (defined as increases in earnings net of increases in local cost of living). We use a measure of local cost of living that follows the BLS method for measuring the nationwide CPI but adapted to vary at the city level.

The effect of local TFPR growth on local purchasing power is conceptually straightforward for renters. In cities with TFPR growth, renters pay increased housing rents that reduce their purchasing power in proportion to the importance of housing as a share of total expenditures. Renters also pay increased costs of other nontradable goods, which reduces their purchasing power in proportion to the importance of nontradable goods as a share of total expenditures.

Thus, we define the effect on renter purchasing power as the percent increase in local earnings (panel B) minus the properly weighted percent increase in local rent (table 2, panel C) and the properly weighted percent increase in local prices of nonhousing, nontradable goods. The proper weights correspond to the share of total expenditures that is spent on housing and nonhousing, nontradable goods, respectively. We derive this expression in appendix C and address the important data limitation that there are not high-quality city-level data on the local price of nonhousing, nontradable goods for most cities in our time period. We follow the approach of Moretti (2013) to impute changes in prices of nontradables based on changes in rents.¹⁴ In practice, this means that we estimate the impact on renters’ purchasing power as the estimated impact on log earnings minus 0.56 times log rent.

Panel E of table 2 reports that a 1% increase in local TFPR increases renters’ purchasing power by 0.36% in the medium run (column 1) and by 0.62% in the long run (column 2). Purchasing power increases for renters because nominal earnings increase by more than the weighted increase in cost of living. Comparing the increase in purchasing power to the increase in nominal earnings, however, renters lose roughly two-thirds of their earnings increases to higher costs for housing and other local goods and services.

For workers who owned their home prior to the increase in TFPR, estimating changes in purchasing power is conceptually more complicated because it depends on how one accounts for the increase in home equity value. A large literature has examined the financial consequences of homeownership, but we are not aware of a widely accepted measure of the effect of housing prices changes on homeowners’ purchasing power (Sinai & Souleles, 2005; Campbell & Cocco, 2007; Attanasio et al., 2009; Buiter, 2010; Mian, Rao, & Sufi, 2013; Ströbel & Vavra, 2019; Berger et al., 2018). Thus, we provide two bounds for how TFPR growth affects homeowners’ purchasing power (see appendix C for more details). In one extreme case (case A), we consider a homeowner whose purchasing power is insulated only from increases in local housing rents.¹⁵ In case A, we measure the impact on homeowners’ purchasing power as the estimated increase in earnings minus the properly weighted increase in the cost of nontradable goods (as calculated for renters, above).¹⁶ At the other extreme (case B), we consider a homeowner who is able to consume the wealth created by increased home value. In case B, we measure the impact on the homeowners’ purchasing power as the estimated increase in earnings, plus the properly weighted increase in rental return on the home, minus the properly weighted increase in the cost of nontradable goods.¹⁷

Panel E reports that when homeowners are insulated from rising housing costs (case A), a 1% increase in local TFPR is associated with a 0.68% increase in purchasing power in the medium run (column 1) and a 1.11% increase in purchasing power in the long run (column 2). These increases in purchasing power are almost twice as large as the increases in purchasing power for renters, who face increased housing costs. The gains to homeowners are substantially larger when homeowners benefit from the increase in housing costs (case B). We conclude that local productivity growth benefits local workers in large part through the housing market rather than through the labor market.

Table 3 reports the estimated impacts of local TFPR growth using the stock market IV (columns 1, 5, 9), export IV (columns 2, 6, 10), and patent IV (columns 3, 7, 11) in the same form as the baseline IV estimates in table 2. The bottom row reports the estimated first-stage coefficients, along with the $F$-statistic on the excluded instruments. The estimated impacts fluctuate somewhat across specifications, and the alternative instruments have less power than our baseline instrument, but the pattern of results is generally consistent. Combining the use of all four instruments, columns 4, 8, and 12 report similar estimates as our baseline IV specifications. Overidentification tests fail to reject that the different instruments are yielding statistically different estimates. That is, despite drawing on identifying variation from different cities and industries experiencing different shocks, the instrumental variable estimates do not yield statistically different estimates of how local TFPR growth directly affects local economic outcomes. In particular, the stock market instrument isolates variation in TFPR growth that would be largely unanticipated, and these estimates suggest that our baseline estimates were not skewed by the anticipation of TFPR growth.

Given the similarity in the long-run estimates (1980 to 2000) and longer-run estimates (1980 to 2010) in tables 2 and 3, the remainder of the paper focuses on the long-run estimates and reports medium-run estimates as a point of comparison.

Table 4 reports our baseline IV estimates separately by worker education group.¹⁸ We estimate larger impacts of local TFPR growth on the employment of more educated workers, particularly in the long run (panel A). By contrast, we estimate larger impacts on earnings of less educated workers (panel B). These estimates are consistent with the notion that more educated workers are more geographically mobile in response to local economic shocks (Bound & Holzer, 2000; Wozniak, 2010; Malamud & Wozniak, 2012; Diamond, 2016; Notowidigdo, 2020). As a consequence, local more educated workers benefit less from local TFPR growth (in percentage terms).¹⁹

Panel E reports increases in the purchasing power of less educated renters in the medium run and long run, and somewhat smaller and statistically insignificant increases in the purchasing power of more educated renters. Local college-educated workers receive more substantial increases in purchasing power if they were homeowners prior to the TFPR shock, however, and are thereby insulated from increased housing costs or otherwise benefit from increased home values.

These results suggest that productivity growth reduces inequality at the local level, in both nominal terms and adjusted for local cost of living. College-educated workers appear very responsive to local TFPR shocks, whereas less educated workers are less responsive, and the greater employment responses for more educated workers appear to dampen the local economic gains for more educated workers. In the context of a Rosen-Roback model, where workers have idiosyncratic preferences for location, this would be the case if worker preferences for locations are relatively more important for less educated workers.²⁰

Figure 4 shows the differential responsiveness of workers by education group and its relationship with the local college earnings premium. Panel A shows a decreasing relationship between the change in local college earnings premium and predicted growth in local TFPR (using our baseline instrument). Panel B shows an increasing relationship between the change in employment share of college workers and predicted growth in local TFPR. This figure summarizes the intuition for how local TFPR growth decreases local inequality due to spatial mobility: following an increase in labor demand from local TFPR growth, a relative increase in the supply of more educated workers contributes to a decline in the education earnings premium.²¹

Table 5 reports estimated impacts of local TFPR growth on the distribution of local earnings, measured as the difference in log earnings at the 90th and 10th percentiles (panel A). We then separate impacts on overall inequality into impacts on inequality within the upper portion of the distribution (panel B) and lower portion of the distribution (panel C). Panel A, row 1 reports that increased local TFPR is associated with substantial declines in local earnings inequality. The estimated magnitude implies that a 1% increase in local TFPR reduces the 90-10 earnings gap by 0.632%, or that earnings at the 10th percentile increase by 0.632% more than earnings at the 90th percentile. This impact on inequality occurs at the upper portion of the distribution (panel B), whereas there is little impact on earnings inequality at the lower portion of the distribution (panel C).²² These effects are larger in the long run, with a 1% increase in local TFPR reducing the 90-10 earnings gap by 0.998% and reducing the 90-50 earnings gap by 0.930%.

One way to interpret the economic magnitude of our estimated effects is to relate the estimated impacts of TFPR to cities’ elasticity of local labor supply. Local labor supply reflects how many workers are willing to live in a city for a given wage. Consider appendix figure 3, in which point 1 represents the equilibrium wage (⁠$w1$⁠) and equilibrium employment (⁠$N1$⁠) in a city before an increase in TFPR. An increase in TFPR then shifts local labor demand out from $D(TFP1)$ to $D(TFP2)$ and point 2 reflects the new equilibrium. By shifting labor demand, the TFPR shock identifies the slope of the function. The inverse elasticity of local labor supply is given by the ratio of the percent increase in earnings over the percent increase in employment. When this ratio is smaller, the supply of labor to this city is more elastic and the supply curve is flatter. This reflects workers being more willing to move from other cities (without requiring much higher wages), as well as the housing stock being more able to adjust upward (without requiring much higher housing prices).

From table 2, the estimated long-run impact on earnings (1.45), divided by the estimated long-run impact on employment (4.16), implies a long-run inverse elasticity of 0.35. This number reflects a relatively elastic local labor supply, indicating that in the long run, the U.S. labor force is fairly willing in this period to relocate to cities with better labor markets.²³

The local labor supply of college graduates is much more elastic than the local labor supply of high school graduates. The estimates by education group, from table 4, imply an inverse elasticity of 0.15 for college graduates and 0.38 for high school graduates.

We have been interpreting the estimated increases in employment as additional workers moving into the city, though increased employment could also reflect increased labor supply of existing city residents. Consistent with migration explaining most of the employment effect, we find that TFPR increases the level of employment and level of population by similar amounts (appendix figure 4).

Increases in manufacturing TFPR have a direct effect on the manufacturing sector, but also indirectly affect the local nonmanufacturing sector. Wage and employment growth in manufacturing increase the demand for local nontraded goods and services, and therefore employment in nonmanufacturing sectors (Moretti, 2010). The extent to which nonmanufacturing sectors are affected is informative about how much policies directed at the manufacturing sector might influence the broader local economy. Indeed, policy efforts to support local manufacturing are often justified by policymakers on these grounds.

Appendix table 6 reports that employment responds similarly in the manufacturing and nonmanufacturing sectors. These increases reflect a combination of in-migration and movement between sectors. We compute the implied multiplier effect of the manufacturing sector on the local nonmanufacturing sector, defined as the number of additional nonmanufacturing jobs created for each additional manufacturing job generated by TFPR gains.²⁴ From an increase in manufacturing TFPR that creates one manufacturing job, panel B reports an implied increase of 1.62 nonmanufacturing jobs. This estimate is consistent with estimates by Moretti (2010) based on a similar time horizon. A longer time horizon yields a larger multiplier, perhaps because it takes time for the effect of shocks in manufacturing to generate additional demand for local services. Over the long run, there is an implied increase of 2.21 nonmanufacturing jobs.

We can extend the outcome data back to 1970 for 110 cities of our main sample of 193 cities and estimate the relationship between 1970-to-1980 outcome changes and instrumented changes in TFPR from 1980 to 1990. Appendix table 7 shows similar pretrends in employment and negative pretrends in wages and housing costs (column 1). The estimates are similar to our baseline estimates when controlling directly for 1970-to-1980 changes in the outcome variable (columns 2 and 3).

City TFPR growth from 1980 to 1990 is not strongly correlated with city TFPR growth from 1990 to 2000, with a slight negative relationship that is statistically insignificant. Appendix table 8 reports similar long-run estimates when controlling for changes in TFPR from 1990 to 2000 (column 1) and instrumenting for this later change in TFPR with an analogous instrument for that later period (column 2). City TFPR growth from 1990 to 2000 itself has generally smaller and statistically insignificant effects, but the first stage is notably less robust for TFPR changes from 1990 to 2000.²⁵ The average impacts of TFPR growth may vary across time periods and contexts, based on where TFPR growth occurs and the characteristics of those places along with how TFPR growth translates into local labor demand. Indeed, we estimate that the effects of TFPR growth are concentrated in larger cities with less impact of TFPR growth on earnings and rents in smaller cities (appendix table 9, columns 1 and 2). The estimated effects of TFPR growth are more similar for cities that were previously growing at faster or slower rates (columns 3 and 4). Column 3 of appendix table 8 reports estimates from a long difference specification, regressing outcome changes from 1980 to 2000 on TFPR changes from 1980 to 2000 and instrumenting with the predicted change in TFPR from 1980 to 2000. The long difference specification may not reflect long-run effects, however, as changes in TFPR could occur any time between 1980 and 2000 and the estimated magnitudes are more similar to the medium-run estimates in table 2.

Appendix table 8 reports similar estimates when controlling for TFPR growth in cities within 500 miles, 250 miles, and 100 miles (columns 4–6), instrumenting using predicted TFPR growth in those cities based on their industry shares and industry-level TFPR growth. These specifications also effectively control for regional industry concentration, exploiting variation in relative local industry concentration within that particular city. Cross-city correlations may also affect the statistical inference. To allow for potential geographic correlation among nearby MSAs, appendix table 10 reports our baseline estimates when clustering the standard errors by state (42 clusters, columns 2 and 4) or contiguous MSA groupings (114 clusters, columns 1 and 3). Appendix table 11 reports estimates using the procedure developed by Adao, Kolesar, and Morales (2019) to allow for correlation across MSAs with similar baseline industry shares that vary by instrument in predicting city TFPR growth. The inference remains similar to our baseline estimates, consistent with the substantial spatial variation across cities with different industry shares.

The baseline estimates are not sensitive to controlling for cities’ total manufacturing share (appendix table 12, columns 1 and 5), as suggested by Borusyak, Hull, and Jaravel (2021) for similar research designs.²⁶ Columns 2 and 6 report estimates controlling for cities’ employment share in 1980 in broad industry categories outside of manufacturing. Columns 3 and 7 report estimates when controlling for cities’ 1980 employment share in the oil and gas industry, which experienced particularly negative shocks in the 1980s (table 1).

Given the estimated increases in local employment following local TFPR growth, one question is whether changes in worker composition are driving the estimated increases in annual earnings. Columns 4 and 8 of panel B in appendix table 12 report estimated impacts using individual-level data to condition on worker characteristics: age, age-squared, education, race, and gender. Panels C and D report similar estimated impacts on housing costs when using individual-level data to condition on physical characteristics of the home: the number of rooms and number of bedrooms, whether the home is part of a multi-unit structure, and the presence of a kitchen or plumbing.²⁷ These specifications are not our preferred models, however, because the changes in worker composition are endogenous and conditioning on endogenous responses to local TFPR growth can introduce bias.

When local employment increases in cities that experience relatively greater TFPR growth, some of those workers are drawn from other sample cities that make up the control group. The estimated relative effects on employment would then be biased upward, as the average comparison city is negatively affected, indirectly increasing wages and decreasing housing costs in comparison cities. We expect this contamination bias to be small, however, because there is little average indirect effect on comparison cities.²⁸ Some sample MSAs are more closely linked with particular other sample MSAs, whereby one MSA receives more than 10% or 5% of its migrants from that other MSA. Appendix table 13 reports estimates when aggregating the data from these MSAs and treating them as one observation (columns 1, 2, 5, 6). Columns 3 and 7 report medium-run and long-run estimates when combining contiguous MSAs into one MSA. Columns 4 and 8 report estimates when omitting region fixed effects, such that the comparison cities are all other sample MSAs.

Because each city is a small share of the total labor market, the indirect effects are spread across many cities and there is a negligible indirect impact on the average control city. In considering the sum of these small indirect effects on each other city, however, the total indirect effect may be substantial.

Estimates from section IV report how a local TFPR shock affects employment, wages, and housing costs in the city where the shock occurs, relative to other cities. These estimated direct effects on local outcomes are only part of the overall impact from a local TFPR shock, however, as the local TFPR shock also has indirect effects outside that particular city.

We propose a methodology for quantifying indirect effects generated through worker mobility. Our approach builds on the estimated direct effects, along with particular assumptions about the elasticity of labor demand and patterns of worker mobility.

Intuitively, local TFPR growth in one city (e.g., Houston) generates additional indirect impacts on labor markets and housing markets in other cities due to worker migration responses. Some migrants to Houston come from Dallas, which raises wages and lowers housing costs in Dallas given downward-sloping labor demand and an upward-sloping housing supply in Dallas. Dallas also experiences its own TFPR shock, as do other cities, but this indirect effect represents the pressure on labor markets and housing markets in Dallas from TFPR changes in Houston.

The magnitude of indirect effects depends on the magnitude of worker reallocation, and our estimates from section IV found substantial direct employment effects in response to local TFPR growth (particularly in the long run). We therefore expect the indirect effects to be substantial, and particularly large for more educated workers who are more mobile. Thus, we anticipate that local TFPR shocks will have different impacts on inequality at the aggregate level as compared to the direct effects on inequality at the local level.

For each sample city, we use our estimated direct effect on employment and data on city-to-city migration to estimate how TFPR growth in that city alone would induce employment changes in the other sample cities. We then use data on cities’ elasticity of housing supply, along with an assumption about the elasticity of labor demand, to quantify the indirect effects on housing costs and worker earnings in these other sample cities. We sum these indirect effects from TFPR growth in each sample city and compare this magnitude to the estimated direct effects on sample cities. Specifically, we proceed in three steps.

Step 1. For each of the 193 sample cities $c$⁠, we use estimates from section IV to calculate the number of workers drawn to city $c$ from 1980 to 2000 based on its growth in TFPR from 1980 to 1990. This number is the product of city $c$’s growth in TFPR from 1980 to 1990, times the estimated long-run impact on employment (table 2, panel A, column 2), times city $c$’s baseline employment in 1980 (appendix table 1).

Step 2. Given an increase in workers in city $c$⁠, we calculate the associated number of workers who would leave each of the other 192 cities $o$ due to TFPR growth in city $c$⁠. Because we do not observe where these workers would move from, in response to increasing TFPR in city $c$ only, we use data on observed city-to-city migration rates to characterize typical cross-city migration links. As a baseline assumption, we assume that workers are drawn to city $c$ from city $o$ in proportion to observed migration flows from 1975 to 1980 in the 1980 Census of Population.²⁹ For example, if Houston would have added 1,000 new workers between 1980 and 2000 (based on its TFPR gains from 1980 to 1990 and the estimated impact of local TFPR growth on local employment), and 5% of migrants to Houston were from Dallas from 1975 to 1980, then we calculate an induced decline of 50 workers in Dallas from TFPR growth in Houston (all else equal). As an alternative method for assigning migrant origins, we assume that workers moving to city $c$ are drawn from all other locations in proportion to their size (which holds fixed the relative sizes of other cities). As another method, we assign the share of migrants to city $c$ from city $o$ using predicted migrant flows from an estimated gravity equation.³⁰

Step 3. Given the induced change in employment in each other origin city $o$⁠, from TFPR growth in city $c$⁠, we calculate the resulting pressure on housing costs and earnings in city $o$⁠. For housing costs, we calculate the decline in households in city $o$⁠, based on the decline in workers and the average number of workers per household in city $o$⁠, and use the estimated city-level elasticities of housing supply from Saiz (2010).³¹ For earnings, our baseline calculations assume a constant elasticity of labor demand (⁠$-$0.15). We also report estimates allowing for heterogeneity across cities in the elasticity of labor demand due to variation in city industry mix.³² We assume no agglomeration economies, whereby changes in city employment would affect city TFPR (and then affect city employment, and so on).

These three steps provide an estimate of how a local TFPR change in each city $c$ indirectly affects wages and housing costs in each other city $o$ through worker mobility. We sum these indirect effects across all cities $o$⁠. We then sum the indirect effects from each city $c$ and compare these to the direct effects on all cities $c$⁠.