Tradability and the Labor-Market Impact of Immigration: Theory and Evidence from the U.S.

Transcription

1 Tradability and the Labor-Market mpact of mmigration: Theory and Evidence from the U.S. Ariel Burstein Gordon Hanson Lin Tian Jonathan Vogel UCLA UC San Diego Columbia University UCLA March 2018 Abstract n this paper, we study how occupation (or industry) tradability shapes local labormarket adjustment to immigration. Theoretically, we derive a simple condition under which the arrival of foreign-born labor into a region crowds native-born workers out of (or into) immigrant-intensive jobs, thus lowering (or raising) relative wages in these occupations, and explain why this process differs within tradable versus within nontradable activities. Using data for U.S. commuting zones over the period 1980 to 2012, we find that consistent with our theory a local influx of immigrants crowds out employment of native-born workers in more relative to less immigrant-intensive nontradable jobs, but has no such effect within tradable occupations. Further analysis of occupation labor payments is consistent with adjustment to immigration within tradables occurring more through changes in output (versus changes in prices) when compared to adjustment within nontradables, thus confirming our model s theoretical mechanism. We then use an extended quantitative model to interpret the magnitudes of our reducedform estimates and to aggregate up the consequences of counterfactual changes in U.S. immigration from the region-occupation level to the region-level. We thank Rodrigo Adao, David Atkin, Lorenzo Caliendo, Javier Cravino, Klaus Desmet, Jonathan Dingel, Ben Faber, Cecile Gaubert, Gene Grossman, Joan Monras, Michael Peters, and Esteban Rossi- Hansberg for helpful comments. We thank the Russell Sage Foundation for financial support under Award

2 1 ntroduction There is a large literature on the labor market impacts of international trade. 1 While this work has advanced far beyond the classical two-good, two-factor Heckscher-Ohlin (HO) model, modern analyses of, say, how trade with China affects U.S. wages and employment still invoke variation in factor intensities across producers, which is central to the HO framework. 2 By contrast, research on the labor market impact of immigration has been far less kind to classical trade theory. The Rybczynski Theorem (Rybczynski, 1955), the core HO result related to immigration, which predicts that factor prices and industry factor proportions are insensitive to changes in factor supplies and that between-industry factor movements are what deliver this insensitivity, is widely seen as being counterfactual. 3 n this paper, we present theoretical analysis and empirical evidence to show that variation in factor intensities, together with variation in the tradability of goods and services, matters for how native workers are affected by inflows of foreign labor. By allowing the labor-market effects of immigration to differ for aggregates of tradables and nontradables, we follow previous literature. The novelty of our approach is its focus on Rybczynksi-style adjustment mechanisms suitably generalized to allow for worker heterogeneity across job tasks and endogenous producer prices at the regional level which operate distinctly within tradables versus within nontradables. As we demonstrate, these mechanisms create new sources of variation in worker and regional exposure to labor supply shocks. To preview our approach, we consider the impact of a local influx of immigrants on U.S. native-born workers within the set of more relative to less immigrant-intensive occupations, where we incorporate variation in the tradability of goods and services as in recent models of offshoring (Grossman and Rossi-Hansberg, 2008). Although textile production and housekeeping, for instance, are each intensive in immigrant labor, textile factories can absorb increased labor supplies by expanding exports to other regions (with small corresponding price reductions) in a way that housekeepers cannot. We derive a simple theoretical condition under which the arrival of foreign-born labor crowds native-born workers into or out of immigrant-intensive jobs and explain why this process differs within the sets of tradable tasks (e.g., textiles) and nontradable tasks (e.g., housekeeping). Empirically, we find support for our model s implications using cross-region and cross-occupation variation in changes in labor allocations, total labor payments, and wages for the U.S. between 1980 and While we focus on occupations to match our model s emphasis on worker assignment to tasks, we also analyze industries separated by their tradability. Finally, we incorporate our insights into a generalized quantitative framework to provide structural interpretations of the mag- 1 For recent surveys of this work, see Harrison et al. (2011) and Autor et al. (2016). 2 See, e.g., Kovak (2012), Galle et al. (2015), Adao (2017), and Burstein and Vogel (2017). 3 See Hanson and Slaughter (2002) and Gandal et al. (2004) for evidence that economies do not absorb labor inflows by shifting toward labor-intensive industries and related analysis in Bernard et al. (2013) on regional covariation in factor prices and factor supplies. See Gonzalez and Ortega (2011) for recent analysis in a line of work dating back to Card (1990) on how sudden inflows of immigrant labor do not discernibly affect native wages and employment. For contrasting results on immigration and industry size, see Bratsberg et al. (2017). Card and Lewis (2007), Lewis (2011), and Dustmann and Glitz (2015) find that absorption of foreign labor occurs through within-industry and within-firm changes in factor intensities. Empirical work more in the spirit of Rybczynski examines how national factor supplies affect national specialization patterns (Harrigan, 1995; Bernstein and Weinstein, 2002; Schott, 2003; Romalis, 2004). 1

3 nitudes of our reduced-form estimates and to aggregate up from the region-occupation level to the region-level, where we capture impacts on regional wages and welfare. Our model has three main ingredients. First, each occupation is produced using a combination of immigrant and native labor, where the two types of workers may differ in their relative productivities across occupations and may be imperfectly substitutable within occupations. 4 Second, heterogeneous workers select occupations as in Roy (1951), giving rise to upward-sloping labor-supply curves. 5 Third, the elasticity of demand facing a region s occupation output with respect to its local price differs endogenously between more- and less-traded occupations. n this framework, the response of occupational wages and employment to an inflow of foreign-born labor depends on two elasticities: the elasticity of local occupation output to local prices and the elasticity of substitution between native and immigrant labor within an occupation. When the second elasticity is low, crowding in occurs, as in the classic Rybczynski (1955) effect. Because factor proportions within each occupation are insensitive to changes in factor supplies, market clearing requires that factors reallocate towards immigrant-intensive occupations. By contrast, a low elasticity of local occupation output to local prices means that the ratio of outputs across occupations is relatively insensitive to changes in factor supplies. Now, factors reallocate away from immigrant-intensive occupations, in which case foreign-born arrivals crowd the native-born out of these lines of work. More generally, native-born workers are crowded out by an inflow of immigrants if and only if the elasticity of substitution between native and immigrant labor within each occupation is greater than the elasticity of local occupation output to local prices. 6 Factor reallocation, in turn, is linked to changes in occupational wages. Because each occupation faces an upward-sloping labor-supply curve, crowding out (in) is accompanied by a decrease (increase) in the wages of native workers in relatively immigrant-intensive jobs. The tradability of output matters in our model because it shapes the elasticity of local occupation output to local prices. The prices of more-traded occupations are (endogenously) less sensitive to changes in local output. n response to an inflow of immigrants, the increase in output of immigrant-intensive occupations is larger and the reduction in price is smaller for tradable than for nontradable tasks. That is, adjustment to labor-supply shocks across tradable occupations occurs more through changes in output when compared to nontradables. The crowding-out effect of immigration on native-born workers, whatever its sign, is systematically weaker in tradable than in nontradable jobs. Since factor reallocation and wage changes are linked by upward-sloping occupational-labor-supply curves, an inflow of immigrants causes wages of more immigrant-intensive occupations to fall by less (or to rise by more) within tradable occupations than within nontradable occupations. 4 Comparisons between the degree of native-immigrant substitutability within occupations on which we focus and on prior estimates of an aggregate native-immigrant substitutability (Ottaviano and Peri, 2012; Borjas et al., 2012) are not well founded. This aggregate elasticity is not a structural parameter in our model. Nevertheless, we follow the approach of the prior literature to estimate this aggregate elasticity using data generated in our counterfactual exercises, which we discuss in Appendix H.5. 5 n marrying Roy with Eaton and Kortum (2002), our work relates to analyses on changes in labor-market outcomes by gender and race (Hsieh et al., 2016), the role of agriculture in cross-country productivity differences (Lagakos and Waugh, 2013), the consequences of technological change for wage inequality (Burstein et al., 2016), and regional adjustment to trade shocks (Caliendo et al., 2015; Galle et al., 2015). 6 The Rybczynski Theorem is a particular knife-edge case of our framework in which, amongst many other restrictions, the elasticity of local occupation output to local prices is assumed to be infinite. 2

4 We provide empirical support for the adjustment mechanism in our model by estimating the impact of increases in local immigrant labor supply on the local allocation of domestic workers across occupations in the U.S. We instrument for immigrant inflows into an occupation in a local labor market following Card (2001). Because we focus on adjustment across occupations within a region, we are able to control for regional and occupation-group time trends and thus impose weaker identifying assumptions than in standard applications of the Card approach. Using commuting zones to define local labor markets, measures of occupational tradability from Blinder and Krueger (2013) and Goos et al. (2014), and data from pums over 1980 to 2012, we find that a local influx of immigrants crowds out employment of U.S. native-born workers in more relative to less immigrant-intensive occupations within nontradables, but has no such effect within tradables. Stronger immigrant crowding out in nontradables satisfies a central prediction of our model. Additional support for the adjustment mechanism in our framework comes from occupation total labor payments, which in our model are proportional to occupational revenue. A regional inflow of foreign labor leads to larger increase in labor payments for immigrantintensive occupations in tradables when compared to nontradables, which is consistent with tradable occupations adjusting relatively more through changes in local output and nontradable occupations adjusting relatively more through changes in local prices. Analysis of wage changes in response to immigration provides further support for our mechanism. The empirical estimates guide the parameterization of an extended version of our model, which incorporates multiple education groups, allows for the geographic mobility of native and immigrant labor (Borjas, 2006; Cadena and Kovak, 2016), and relaxes the restrictions (small shocks and small open economy) we impose to obtain our analytic results. Using the model, we conduct counterfactual analyses which (i) provide structural interpretations of the magnitudes of our reduced-form empirical estimates, (ii) demonstrate that our qualitative results are robust to a wide range of generalizations, and (iii) obtain impacts on how immigration affects regional wages and welfare both across occupations within regions and across regions. n one of our exercises, motivated by current U.S. policy proposals, we consider a reduction of immigrants from Latin America, who tend to have low education levels and to cluster in specific U.S. regions. Unsurprisingly, the average wage of low-education relative to high-education native-born workers rises by more in high-settlement cities such as Los Angeles than in low-settlement cities such as Pittsburgh. More significantly, for both education groups this shock raises wages for native-born workers in more-exposed nontradable occupations (e.g., housekeeping) relative to less-exposed nontradable occupations (e.g., firefighting) by much more than for similarly differentially exposed tradable jobs (e.g., textile-machine operation versus technical support staff), consistent with the wage implications of differential immigrant crowding out of native-born workers within nontradables versus within tradables implied by our theoretical results. Reducing immigration also raises the local price index, thereby lowering real wages for native-born workers, except in the most immigrant-intensive nontraded occupations in the most-exposed regions. 7 n many commuting zones, the within- CZ variation in wage changes (i.e, across occupations) dwarfs the variation in average wage changes across CZs, which highlights the new sources of worker exposure to immigration 7 Also on the welfare gains from immigration, see Hong and McLaren (2015), Monras (2015), and Caliendo et al. (2017). 3

5 that are elucidated by our framework. The quantitative analysis also allows us to evalute alternative explanations for our empirical result on greater immigrant crowding out of natives within tradables relative to within nontradables. One such explanation is that crowding out occurs because immigrant-native substitution elasticities are higher in nontradable occupations than in tradables, rather than because, as we suppose, that the price elasticity of output is lower in nontradables than in tradables. f we set the immigrant-native substitution elasticity to be higher in nontradables than in tradables, there is, as expected, stronger immigrant crowding-out within nontradables than within tradables. However, these elasticity values generate counterfactual changes in total labor payments. Other explanations for stronger immigrant crowding out within nontradables, such as higher factor adjustment costs or lower supply elasticities in tradables compared to nontradables, would have to confront the observation that over time employment shares change by more across tradable jobs than across non-tradable jobs. Many scholars have considered the interaction between immigration and trade. n recent empirical work, Dustmann and Glitz (2015), Hong and McLaren (2015), and Peters (2017) study the impact of immigration on average native outcomes in an aggregate tradable (manufacturing) sector relative to an aggregate non-tradable (non-manufacturing) sector. Dustmann and Glitz (2015) find that in response to an influx of immigrants, average native wages fall in nontradables but not in tradables; Peters (2017) finds that the manufacturing share of employment rises in regions that are more exposed to refugee inflows in post-world War Germany. 8 While our analysis encompasses variation in impacts between tradable and nontradable aggregates which would account for why immigration induces larger declines in native wages and employment among housekeepers than among textile workers this variation is orthogonal to the Rybczynski-style effects on which we focus. To identify these effects, our theory says to compare jobs within tradables e.g., immigrant-intensive textiles versus non-immigrant-intensive technical support and jobs within nontradables e.g., immigrant-intensive housekeeping versus non-immigrant-intensive firefighting. We use such within-aggregate comparisons to validate our model empirically. 9 n other work on immigration and trade, Ottaviano et al. (2013) study a partial equilibrium model in which firms may hire native and immigrant labor domestically or offshore production. Freer immigration reduces offshoring and has theoretically ambiguous impacts on native employment, which empirically they find to be positive. Our paper characterizes when crowding out (in) occurs in a general equilibrium context, as well as how native employment and wage impacts differ for more and less tradable jobs. n line with our prediction for differential crowding out within tradables versus within nontradables, Cortes (2008) finds that a city-level influx of immigrants reduces the local prices of six immigrant-intensive non-traded activities while having a small and imprecisely estimated impact on the prices of tradables, either for those with low immigrant employment intensities or for those with high intensities. ndustry case studies further support our 8 Hong and McLaren (2015) find, in contrast, that immigrant inflows in U.S. regions lead to increases in total native employment, with no consistent difference in response between more and less tradable industries. 9 f one allows cross-country differences in technology to affect immigration, then foreign labor inflows may reduce real incomes in high-income countries such as the U.S. through adverse impacts on global relative prices (Davis and Weinstein, 2002). This insight relates to the broader result that the welfare consequences of factor inflows are tightly connected to their consequences for a country s terms of trade (Grossman, 1984). 4

6 framework. A local influx of foreign labor displaces (i.e., crowds out) native-born workers in immigrant-intensive non-traded occupations, including manicurist services (Federman et al., 2006), construction (Bratsberg and Raaum, 2012), and nursing (Cortes and Pan, 2014). While these results for nontradables appear to contradict the Ottaviano et al. (2013) finding of immigrant crowding in of native workers for tradables, our theoretical model is fully consistent with stronger crowding in for tradables versus stronger crowding out for nontradables, thereby rationalizing the ostensibly discordant evidence in the literature. 10 n broader work on whether immigrant arrivals displace native-born workers on the job, evidence of displacement effects is decidedly mixed (Peri and Sparber, 2011a). While higher immigration occupations or regions do not in general have lower employment rates for nativeborn workers (Friedberg, 2001; Card, 2005; Cortes, 2008), affected regions do see lower relative employment of native-born workers in manual-labor-intensive tasks (Peri and Sparber, 2009). Our analysis suggests that previous work, by imposing uniform adjustment for sectors that have similar factor intensities, incompletely characterizes immigration displacement effects. t is the combination of immigrant intensity and nontradability that predisposes an occupation to the crowding out of native labor by foreign labor. Our contribution is to build a theoretical framework that generates differential responsiveness of wages, employment, and total labor payments across activities separated by their immigrant intensity and their tradability, and to offer an empirical and quantitative evaluation of this framework. Our analytic results on immigrant crowding out of native-born workers are parallel to insights on capital deepening in Acemoglu and Guerrieri (2008) and on offshoring in Grossman and Rossi-Hansberg (2008). The former paper, in addressing growth dynamics, derives a condition for crowding in (out) of the labor-intensive sector in response to capital deepening in a closed economy; the latter paper demonstrates that a reduction in offshoring costs has both productivity and price effects, which are closely related to the forces behind crowding in and crowding out, respectively, in our model. As we show below, the forces generating crowding in within Acemoglu and Guerrieri (2008) and the productivity effect in Grossman and Rossi-Hansberg (2008) are closely related to the Rybczynski theorem. Relative to these papers, we provide more general conditions under which there is crowding in (out), show that crowding out is weaker where local prices are less responsive to local output changes, and prove that differential output tradability creates differential local price sensitivity. Sections 2 and 3 outline our benchmark model and present comparative statics. Section 4 details our empirical approach and results on the impact of immigration on the reallocation of native-born workers, changes in labor payments across occupations, and changes in wages for native-born workers. Section 5 summarizes our quantitative framework and discusses parameterization, while Section 6 presents results from counterfactual exercises. Section 7 offers concluding remarks. 10 One difference between our work and Ottaviano et al. (2013) is that whereas they find crowding in of natives by immigrants in tradables, we find neutral effects (neither crowding out nor crowding in). This distinction may be driven by our analysis being conducted at the regional level, which allows us to control for national-level occupation time trends, whereas the analysis in Ottaviano et al. (2013), because it is conducted at the national level, necessarily excludes such controls. 5

7 2 Model The model that we present combines three ingredients. First, following Roy (1951) we allow for occupational selection by heterogeneous workers, inducing an upward-sloping labor supply curve to each occupation and differences in wages across occupations within a region. Second, occupational tasks are tradable, as in Grossman and Rossi-Hansberg (2008), and we incorporate variation across occupations in tradability, which induces occupational variation in price responsiveness to local output. Third, as in Ottaviano et al. (2013), we allow for imperfect substitutability within occupations between immigrant and domestic workers. 2.1 Assumptions There are a finite number of regions, indexed by r R. Within each region there is a continuum of workers indexed by z Z r, each of whom inelastically supplies one unit of labor. Workers may be immigrant (i.e, foreign born) or domestic (i.e., native born), indexed by k = {, D}. The set of type k workers within region r is given by Zr k, which has measure Nr k. Each worker is employed in one of O occupations, indexed by o O. n Section 5 we extend this model by dividing domestic and immigrant workers by education and allowing for the imperfect mobility of labor across regions. 11 Each region produces a non-traded final good combining the services of all occupations, ( ) η Y r = µ 1 η ro (Y ro ) η 1 η 1 η for all r, o O where Y r is the absorption (and production) of the final good in region r, Y ro is the absorption of occupation o in region r, and η > 0 is the elasticity of substitution between occupations in the production of the final good. The absorption of occupation o in region r is itself an aggregator of the services of occupation o across all origins, Y ro = ( j R Y α 1 α jro ) α α 1 for all r, o, where Y jro is the absorption within region r of region j s output of occupation o and where α > η is the elasticity of substitution between origins for a given occupation. Occupation o in region r produces output by combining immigrant and domestic labor, Q ro = A ro ( (A ro L ro ) ρ 1 ρ + ( A D rol D ro ) ρ 1 ρ ) ρ ρ 1 for all r, o, (1) 11 While we allow occupational selection to respond to immigration, we take worker education levels as given. See Llull (2017) for an analysis that endogenizes native education choices in response to immigration. Whereas in the model the supply of immigrant workers in a region is exogenous, in the empirical analysis we treat it as endogenous; see Klein and Ventura (2009), Kennan (2013), di Giovanni et al. (2015), Desmet et al. (Forthcoming), and Caliendo et al. (2017) for models of international migration based on cross-country wage differences. n Appendix D we vary the model by allowing for an infinitely elastic supply of immigrants in each region-occupation pair (which fixes their wage). We show that the implications of that model for occupation wages of native workers and factor allocations in response to changes in the productivity of immigrants are qualitatively the same as those in our baseline model for changes in the number of immigrants. We also use this model to relate our results to those in Grossman and Rossi-Hansberg (2008). 6

8 where L k ro is the efficiency units of type k workers employed in occupation o in region r; A ro and A k ro are the systematic components of productivity of all workers and of any type k worker, respectively, in this occupation and region; and ρ > 0 is the elasticity of substitution between immigrant and domestic labor within each occupation. 12 n Appendix B, we present an alternative model that microfounds the imperfect substitutability of native and immigrant labor within occupations, in which occupation output is produced using a continuum of tasks and domestic and immigrant labor are perfect substitutes (up to a task-specific productivity differential) within each task. This setting in which immigrant and native workers endogenously specialize in different tasks within occupations yields an identical system of equilibrium conditions to those we consider in the main text, where the parameter ρ controls the extent of comparative advantage between domestic and immigrant labor across tasks within occupations. 13 Thus, while our baseline model imposes imperfect substitutability between immigrant and native workers at the occupation level, it can be grounded in a framework that entails perfect substitutability at the task level. Two further remarks regarding our approach are in order. A first is that our baseline model abstracts from variation across occupations in the elasticity of substitution between immigrant and domestic workers, ρ, which prevents such variation from being a source of differential adjustment to immigration within tradables as compared to within nontradables. n Section 5, we show that assuming a higher value of this elasticity for less traded occupations implies stronger crowding-out within this group (consistent with our data) but has counterfactual predictions for how labor payments and prices respond to immigration. A second is that while the literature has varying results on the substitutability of domestic and immigrant workers in the aggregate and at the national level (Borjas et al., 2012; Manacorda et al., 2012; Ottaviano and Peri, 2012), reasonable estimates suggest that the degree of aggregate substitutability between domestic and immigrant workers with similar education and experience levels at the national level is high, e.g. ranging from around 10 to 100 in Ottaviano and Peri (2012). Unlike the elasticity of substitution between immigrant and domestic workers within occupations ρ, this aggregate and national elasticity of substitution is not a structural parameter in our model. However, when we estimate it on data generated by our quantitative model, we find an elasticity of around 10, which is at the lower end of estimates in the empirical literature (see Appendix H.5). A worker z Zr k supplies ε (z, o) efficiency units of labor if employed in occupation o. 14 Let Zro k denote the set of type k workers in region r employed in occupation o, which has measure Nro k and must satisfy the labor-market clearing condition N k r = o O N k ro. 12 All our results hold if occupation production functions are common Cobb-Douglas aggregators of our labor aggregate in (1) and a composite input. 13 Analogously, the trade elasticity in gravity models has alternative micro-foundations (see e.g. Arkolakis et al., 2012), and they all result in similar aggregate implications. 14 Because our empirics focus on long-term labor adjustment, our theory abstracts from adjustment costs for workers reallocating between occupations (see e.g. Caliendo et al. (2015)). 7

9 The measure of efficiency units of factor k employed in occupation o in region r is L k ro = ε (z, o) dz for all r, o, k. z Z k ro We assume that each ε (z, o) is drawn independently from a Fréchet distribution with cumulative distribution function G (ε) = exp ( ε (θ+1)), where a higher value of θ > 0 decreases the within-worker dispersion of efficiency units across occupations. 15 The services of an occupation can be traded between regions subject to iceberg trade costs, where τ rjo 1 is the cost for shipments of occupation o from region r to region j and we impose τ rro = 1 for all regions r and occupations o. The quantity of occupation o produced in region r must equal the sum of absorption (and trade costs) across destinations, Q ro = j R τ rjo Y rjo for all r, o. (2) Although it plays little role in our analysis, we assume trade is balanced in each region. All markets are perfectly competitive, all factors are freely mobile across occupations, and, for now, all factors are immobile across regions (an assumption we relax in Section 5). 2.2 Equilibrium characterization We characterize the equilibrium under the assumption that L k ro > 0 for all occupations o and worker types k, since our analytic results are derived under conditions such that this assumption is satisfied. Final-good profit maximization in region r implies where P r = Y ro = µ ro ( P y ro P r ( o O ) η Y r, (3) µ ro (P y ro) 1 η ) 1 1 η denotes the final good price, and where Pro y denotes the absorption price of occupation o in region r. Optimal regional sourcing of occupation o in region j implies (4) where ( ) α τrjo P ro Y rjo = Y jo, (5) P y ro = ( j R P y jo (τ jro P jo ) 1 α ) 1 1 α, (6) 15 We make the assumption of a Fréchet distribution largely because it is convenient to derive our analytic comparative statics and to parameterize the model in the presence of a large number (50) of occupation choices (since it only requires one parameter, shaping how occupation wages change with occupation employment). See Adao (2017) for a non-parametric approach to estimate the distribution of idiosyncratic productivity. n Appendix G we provide reduced-form empirical evidence showing that the implications for average occupation wages of the Fréchet assumption perform well for high-education natives but have more mixed success for low-education natives. 8

10 and where P ro denotes the output price of occupation o in region r. Equations (2), (3), and (5) imply Q ro = (P ro ) α j R µ jo (τ rjo ) 1 α ( P y jo) α η (Pj ) η Y j. (7) Profit maximization in the production of occupation o in region r implies P ro = 1 ( (W ) A ro /A 1 ρ ( ) 1 ro + W D ro /Aro) D 1 ρ 1 ρ ro (8) and L k ro = ( ( ) ) A ro A k ρ 1 W k ρ ro ro Q ro, (9) where Wro k denotes the wage per efficiency unit of type k labor employed in occupation o within region r, which we henceforth refer to as the occupation wage. A change in Wro k represents the change in the wage of a type k worker in region r who does not switch occupations. 16 Because of self-selection into occupations, Wro k differs from the average wage earned by type k workers in region r who are employed in occupation o, W age k ro. Changes in region-occupation average wages W age k ro reflect both changes in wages per efficiency unit in region-occupation ro and the resorting of workers across occupations in region r. n Section 4.5 we show how we can use measures of changes in average wages across occupations at the region level to infer indirectly how immigration affects occupation-level wages. Worker z Zr k chooses to work in the occupation o that maximizes wage income Wro k ε (z, o). The assumptions on idiosyncratic worker productivity imply that the share of type k workers who choose to work in occupation o within region r, πro k Nro/N k r k, is P ro π k ro = ( W k ro ) θ+1 ( ) j O W k θ+1, (10) rj which is increasing in W k ro. Total efficiency units supplied by workers in occupation o is L k ro = γ ( ) πro k θ θ+1 Nr k, (11) where γ Γ ( θ θ 1) and Γ is the gamma function. Finally, trade balance implies P ro Q ro = P r Y r for all r. (12) o O An equilibrium is a vector of prices {P r, P ro, Pro}, y occupation wages { Wro} k, quantities { of occupation } services produced and consumed {Y r, Y ro, Y rjo, Q ro }, and labor allocations N k ro, L k ro for all regions r R, occupations o O, and worker types k that satisfy (3)-(12). 16 n response to a decline in an occupation wage, a worker may switch occupations, thus mitigating the potentially negative impact of immigration on wages, as in Peri and Sparber (2009). However, the envelope condition implies that given changes in occupation wages, occupation switching does not have first-order effects on changes in individual wages, which solve max o { W k ro ε (z, o) }. Because this holds for all workers, it also holds for the average wage across workers, as can be seen in equation (28). 9

11 3 Comparative statics We next derive analytic results for infinitesimal changes in regional labor supply, Nr and Nr D, and region occupation productivity, A ro, on occupation quantities, prices, and labor payments as well as factor allocation and occupation wages. 17 By totally differentiating the system of equations, we are not taking a stand on the extent to which changes in regional labor supply cause changes in productivity or vice versa. nstead, we are determining how outcomes of interest must respond to any combination of changes in labor supply and productivity. Of course, our empirical exercises will involve an instrumental variables strategy, which does require that we take a stand on the direction of causality in the estimation. To build intuition and identify how particular assumptions affect results, we start with the special case of a closed economy with fixed productivity in Section 3.1. We then generalize the results, first in Section 3.2 by allowing for trade between regions under the assumption that each region operates as a small open economy, and then in Section 3.3 by additionally allowing for changes in region occupation productivity. Lower case characters, x, denote the logarithmic change of any variable X relative to its initial equilibrium level (e.g. n k r ln Nr k ). Derivations and proofs are in Appendix A. 3.1 Closed economy n this section we assume that region r is autarkic: τ rjo = for all j r and o. We describe the impact of a change in labor supply first on occupation output, prices, and labor payments and then on factor allocation and occupation wages. 18 Changes in occupation quantities, prices, and labor payments. nfinitesimal changes in aggregate labor supplies, Nr D and Nr, within an autarkic region generate changes in relative occupation output quantities across two occupations o and o that are given by q ro q ro = η (θ + ρ) θ + η w r ( S ro S ro ) and changes in relative occupation output prices that are given by p ro p ro = 1 η (q ro q ro ) = θ + ρ θ + η w ( ) r S ro Sro, (14) where S ro W ro L ro W D ro LD ro +W ro L ro (13) is defined as the cost share of immigrants in occupation o output in region r (the immigrant cost share) and w r w D ro w ro denotes the log change in domestic relative to immigrant occupation wages (which is common across occupations). 19 The log 17 For given elasticities, changes in productivity, A ro, are isomorphic to changes in demand, µ ro. n what follows, we focus on productivity shocks. 18 We focus on changes in occupation wages because to a first-order approximation wro k is equal to changes in average income of workers employed in occupation o before the shocks. 19 n either the open or closed economy, variation in Sro across occupations is generated by variation in Ricardian comparative advantage of immigrant and native workers across occupations within a region. From the definitions of Sro and πro k Nro/N k r k, we have Sro Sro if and only if π ro/πro πd ro/πro D. Together ( ) with equation (10), we obtain the result that Sro Sro if and only if A ρ 1 ( ro A ) ρ 1. ro A D ro A D ro 10

12 change in domestic relative to immigrant occupation wages is given by w r = ( ) n r n D r Ψ n r, where Ψ n r θ + η ( (θ + ρ) η + θ (ρ η) 1 ( ) ) 0 j O π rj πrj D S rj is the absolute value of the elasticity of domestic relative to immigrant occupation wages to changes in their relative supplies. That Ψ n r 0 is an instance of the law of demand. With Ψ n r 0, an increase in the relative supply of immigrant workers in a region, n r > n D r, increases the relative wage of domestic workers in a region, w r 0, and makes all occupations more immigrant intensive. Despite common values of θ, η, and ρ, variation in Ψ n r across regions arises through regional variation in factor allocations and immigrant cost shares. Consider two occupations o and o, where occupation o is immigrant intensive relative to o (i.e., Sro > Sro ). According to (13) and (14), an increase in the relative supply of immigrant workers in region r, n r > n D r, increases the output and decreases the price in o relative to o. This result follows immediately from the fact that the occupation wage of immigrant workers relative to domestic workers falls equally in all occupations. Occupation revenues, P ro Q ro, are equal to occupation labor payments, denoted by LP ro k W agek ronro. k We focus on labor payments because they are easier to measure in practice than occupation quantities and prices. Equations (13) and (14) imply that small changes in aggregate labor supplies Nr D and Nr within an autarkic region generate changes in relative labor payments across two occupations o and o that are given by, lp ro lp ro = (η 1) (θ + ρ) θ + η w r ( S ro S ro ). (15) According to (15), an increase in the relative supply of immigrant workers in region r, n r > n D r, increases labor payments in relatively immigrant-intensive occupations if and only if η > 1. mportantly for what follows, a higher value of the elasticity of substitution across occupations, η, increases the size of relative output changes and decreases the size of relative price changes. n response to an inflow of immigrants, n r > n D r, a higher value of η generates a larger increase (or smaller decrease) in labor payments within immigrantintensive occupations, as we show in Appendix A.2. Changes in factor allocation and occupation wages. nfinitesimal changes in aggregate labor supplies N D r and N r within an autarkic region generate changes in relative labor allocations across two occupations o and o that are given by n k ro n k ro = θ + 1 θ + η (η ρ) w ( ) r S ro Sro and changes in relative occupation wages that are given by (16) w k ro w k ro = nk ro n k ro θ + 1 = 1 θ + η (η ρ) w ( ) r S ro Sro. (17) 11

13 By (16) and (17), an increase in the relative supply of immigrant workers, n r > n D r (which implies w r 0), decreases relative employment of type k workers and (for any finite value of θ) occupation wages in the relatively immigrant-intensive occupation if and only if η < ρ. f η < ρ, we have crowding out: an inflow of immigrant workers into a region induces factor reallocation away from immigrant-intensive occupations; if on the the other hand, η > ρ, we have crowding in: an immigrant influx induces factors to move towards immigrant-intensive occupations. Labor reallocation between occupations is governed by the extent to which immigration is accommodated by expanding production of immigrant-intensive occupations or by substituting away from native towards immigrant workers within each occupation. To provide intuition, consider two special cases. First, in the limit as η 0, output ratios across occupations are fixed. The only way to accommodate an increase in the supply of immigrants is to increase the share of each factor employed in domestic-labor-intensive occupations (while making each occupation more immigrant intensive). mmigration thus induces crowding out. Second, in the limit as ρ 0, factor intensities within each occupation are fixed. To accommodate immigration, the share of each factor employed in immigrant-intensive occupations must rise (while the production of immigrant-intensive occupations increases disproportionately). Now, immigration induces crowding in. 20 More generally, a lower value of η ρ generates more crowding out of (or less crowding into) immigrant-labor-intensive occupations in response to an increase in regional immigrant labor supply. Consider next changes in occupation wages. f θ, then all workers within each k are identical and indifferent between employment in any occupation. n this knife-edge case, labor reallocates across occupations without corresponding changes in relative occupation wages within k (taking the limit of (16) and (17) as θ converges to infinity). The restriction that θ thus precludes studying the impact of immigration (or any other shock) on the relative wage across occupations of domestic or foreign workers. For any finite value of θ i.e., anything short of pure worker homogeneity changes in occupation wages vary across occupations. t is precisely these changes in occupation wages that induce labor reallocation: in order to induce workers to switch to occupation o from occupation o, the occupation wage must increase in o relative to o, as shown in (17). Hence, factor reallocation translates directly into changes in occupation wages. Specifically, if occupation o is immigrant intensive relative to occupation o, Sro > S ro, then an increase in the relative supply of immigrant labor in region r decreases the occupation wage for domestic and immigrant labor in occupation o relative to occupation o if and only if η < ρ. Relation to the Rybczynski theorem. Our results on changes in occupation output and prices and on factor reallocation strictly extend the Rybczynski (1955) theorem. 21 n our 20 n the knife-edge case in which η = ρ, the immigrant intensity of each occupation moves one-for-one with the region s aggregate ratio of immigrants to native workers. New immigrants are allocated proportionately across occupations whereas the allocation of native workers remains unchanged. n Appendix A.2 we solve for the elasticity of factor intensities within each occupation with respect to changes in relative factor endowments, ( ( n D ro nro) / n D r nr). Factor intensities are inelastic if and only if η > ρ (and unit elastic if η = ρ). Moreover, a higher value of η decreases the responsiveness of domestic relative to immigrant occupation wages, Ψ n r. 21 Also on relaxing the assumptions underlying Rybczynski, see Wood (2012), who uses a two-country, two-factor, and two-sector model in which each country produces a differentiated variety within each sector. 12

14 context, in which occupation services are produced using immigrant and domestic labor, the theorem states that for any constant-returns-to-scale production function, if factor supply curves to each occupation are infinitely elastic (θ in our model and homogeneous labor in the Rybczynski theorem), there are two occupations (O = 2 in our model), and relative occupation prices are fixed (η in our closed-economy model and the assumption of a small open economy that faces fixed output prices in the Rybczynski theorem), then an increase in the relative supply of immigrant labor causes a disproportionate increase in the output of the occupation that is intensive in immigrant labor and a disproportionate decrease in the output of the other occupation. Specifically, if S r1 > S r2 and n r > n D r, then q r1 > n r > n D r > q r2 ; a corollary of this result is n k r1 = q r1 > n r > n D r > q r2 = n k r2 for k = D,. Under the assumptions of the theorem, factor intensities are constant in each occupation (as in the case of ρ 0 discussed above) and factor prices are independent of factor endowments, and factor-price insensitivity obtains (Feenstra, 2015). Hence, the only way to accommodate an increase in the supply of immigrants is to increase the share of each factor employed in the immigrant-intensive occupation. Taking the limit of equation (16) as θ and η both converge to infinity and assuming that O = 2, we obtain and q r1 = n k r1 = 1 π r1 π D r1 q r2 = n k r2 = (( 1 π D r1 ) n r ( 1 π r1) n D r ) 1 π r1 π D r1 ( π D r1 n r + π r1n D r f S r1 > S r2 which implies π r1 > π D r1 in the case of two occupations then we obtain the Rybczynski theorem and its corollary. n a special case of our model that is, nevertheless, more general than the assumptions of the Rybczynski theorem, we obtain a simplified version of our results above immigration induces crowding in or crowding out depending on a simple comparison of local elasticities in the absence of specific functional forms for production functions (see Appendix C). Hence, our results extend the Rybczynski theorem Small open economy We extend the analysis by allowing region r to trade. To make progress analytically, we impose two restrictions. We assume that region r is a small open economy, in the sense that it constitutes a negligible share of exports and absorption in each occupation for each region j r, and we assume that occupations are grouped into two sets, O (g) for g = {T, N}, where region r s export share of occupation output and import share of occupation absorption are common across all occupations in the set O (g). 23 We refer to N as the set of occupations 22 Acemoglu and Guerrieri (2008) assume that factor supply curves to each occupation are infinitely elastic (θ in our model), there are two occupations (O = 2 in our model), and the elasticity of substitution between factors is one (ρ = 1 in our model). They show that there is crowding in if η > 1 and crowding out if η < 1. n Appendix D, we relate our framework and results to Grossman and Rossi-Hansberg (2008). 23 Our results hold with an arbitrary number of sets. n the empirical analysis, we alter the effective number of sets by varying the size of occupations of intermediate tradability which are excluded from the analysis (from zero to one-fifth of the total number of categories). See the Appendix F. ) 13

15 that produce nontraded services and T as the set of occupations that produce traded services; all that is required for our analysis is that the latter is more tradable than the former. The small-open-economy assumption implies that, in response to a shock in region r only, prices and output elsewhere are unaffected in all occupations: p y jo = p jo = p j = y j = 0 for all j r and o. As we show in Appendix A.3, in this case the elasticity of region r s occupation o output to its price an elasticity we denote by ɛ ro is a weighted average of the elasticity of substitution across occupations, η, and the elasticity across origins, α > η, where the weight on the latter is increasing in the extent to which the services of an occupation are traded, as measured by the export share of occupation output and the import share of occupation absorption in region r. Therefore, more traded occupations feature higher elasticities of regional output to price (and lower sensitivities of regional price to regional output). 24 The assumption that the export share of occupation output and the import share of occupation absorption are each common across all occupations in O (g) in region r implies that the elasticity of regional output to the regional producer price, ɛ ro, is common across all occupations in O (g). 25 n a mild abuse of notation, we denote by ɛ rg the elasticity of regional output to the regional producer price for all o O (g), for g = {T, N}. nfinitesimal changes in aggregate labor supplies Nr D and Nr generate changes in occupation outputs, output prices, labor payments, factor allocations, and wages across pairs of occupations that are either in the set T or in the set N (i.e. o, o O (g)), which are given by equations (13), (14), (15), (16) and (17) except now η is replaced by ɛ rg. Changes in occupation quantities, prices, and labor payments. f o, o O (g), then changes in relative occupation quantities and prices are given by q ro q ro = ɛ rg (θ + ρ) θ + ɛ rg w r ( S ro S ro ) p ro p ro = θ + ρ θ + ɛ rg w r ( S ro S ro ), where, again, the log change in domestic relative to immigrant occupation wages, w r wro w D ro, is common across all occupations (both tradable and nontradable). n the extended version of the model in this section we do not provide an explicit solution for w r wro D wro. However, we assume that conditions on parameters satisfy the following version of the law of demand: n r n D r implies w r 0. The results comparing changes in occupation output and prices across any two occupations obtained in Section 3.1 now hold for any two occupations within the same set: an increase in the relative supply of immigrant workers, n r > n D r, increases the relative output and decreases the relative price of immigrant-intensive occupations. Moreover, we can compare the differential output and price responses of more to less immigrant-intensive occupations within T and N. Because ɛ rt > ɛ rn, the relative output of immigrant-intensive occupations increases relatively more within T than within 24 n Appendix A.3, we show that the absolute value of the partial own labor demand elasticity at the region-occupation level is increasing in ɛ ro and, therefore, trade shares. This result is related to Rodrik (1997) and Slaughter (2001), who consider how greater trade openness affects the elasticity of labor demand. 25 By assuming that export shares in region r are common across all occupations in O (g), we are assuming that variation in immigrant intensity, Sro, is the only reason why occupations within O (g) respond differently in terms of quantities, prices, and employment to a region r shock. 14

16 N, whereas the relative price of immigrant-intensive occupations decreases relatively less in T than in N. Similarly, if o, o O (g), then changes in relative labor payments are given by lp ro lp ro = (ɛ rg 1) (θ + ρ) θ + ɛ rg w r ( S ro S ro ). (18) Because ɛ rt > ɛ rn, relative labor payments to immigrant-intensive occupations increase relatively more within T than within N in response to an inflow of immigrants. Changes in factor allocation and occupation wages. f o, o O (g), then changes in relative labor allocations and occupation wages are given by n k ro n k ro = θ + 1 ɛ rg + θ (ɛ ( ) rg ρ) w r S ro Sro, (19) wro k wro k = 1 ( ) n k θ + 1 ro n k ro. (20) The results comparing changes in allocations across any two occupations obtained in Section 3.1 now hold for any two occupations within the same set: for a given elasticity between domestic and immigrant labor, ρ, the lower is the elasticity of regional output to the regional producer price, ɛ rg, the more that a positive immigrant labor supply shock causes workers to crowd out of (equivalently, the less it causes workers to crowd into) occupations that are more immigrant intensive. Because ɛ rt > ɛ rn, we can compare the differential response of more to less immigrant-intensive occupations in T and N: within T, immigration causes less crowding out of (or more crowding into) occupations that are more immigrant intensive (compared to the effect within N). The intuition for the pattern and extent of factor reallocation between any two occupations within a given set g = T or g = N is exactly the same as described in the closed economy presented in Section 3.1. On the other hand, the pattern and extent of factor reallocation between T and N depend on the full set of model parameters. Similarly, the result comparing changes in wages (for continuing workers) across two occupations obtained in Section 3.1 now holds for any two occupations within the same set. Because ɛ rt > ɛ rn, we can compare the differential response of more to less immigrantintensive occupations in T and N: within traded occupations T, immigration decreases occupation wages less (or increases occupation wages more) in occupations that are more immigrant intensive (compared to the effect within nontraded occupations N). 3.3 Productivity changes mmigration may also affect productivity (and vice versa). For example, an increase in foreign labor could result in local congestion externalities (e.g., Saiz, 2007), thereby reducing productivity, local agglomeration externalities (e.g., Kerr and Lincoln, 2010), thereby increasing productivity, or lower incentives for firms to adopt labor-saving technologies (e.g., Lewis, 2011), thereby affecting industry labor productivity. And these productivity effects may disproportionately affect manufacturing or tradables, as shown by Peters (2017) See Clemens et al. (2018) on the endogenous response of industry production technology to immigration in the case of U.S. agriculture following the end of the Bracero Program. 15

17 The results in Sections 3.1 and 3.2 extend to the case in which both labor supply, Nr and Nr D, and productivity, A ro, change. n general, whether in a closed or small open economy, the equations determining changes in occupation quatities, prices, labor payments, factor allocations, and wages remain unchanged, except for the inclusion of an additional additively separable term in a ro a ro (see Appendices A.2 and A.3). 27 All else equal, an increase in the relative productivity of occupation o within group g increases occupation o labor payments, the share of factor k allocated to occupation o, and the occupation o wage if and only if ɛ rg (or η in the closed economy) is greater than one. Under the assumption that productivity changes are common within g that is, a ro = a ro for all o, o O(g) none of our theoretical results changes qualitatively. This is an important observation, since much previous empirical work focuses on differential impacts of immigration on a tradables aggregate versus a nontradables aggregate with the important exception of Cortes (2008) and emphasizes the average response within tradables versus the average response within non-tradables of wages (e.g., Dustmann and Glitz, 2015) and/or allocations (e.g., Peters, 2017). n the context of our model, the assumptions embodied in previous work can be formalized as imposing common factor intensities and productivity growth rates across occupations within tradables and, separately, within nontradables: S ro = S ro and a ro = a ro for all o, o O(g). n this case, the variation within tradables and within non-tradables on which we focus is assumed away (i.e., relative changes across occupations within g are zero) and the remaining variation across an aggregate T and an aggregate N is not related to the Rybczynski-style mechanisms on which our analytic results and empirical exercises focus. Nevertheless, because our model incorporates this across T and N variation, we will control for it using a model-consistent approach in our empirical strategy. 4 Empirical Analysis Guided by our theoretical model, we aim to study the impact of immigration on labor market outcomes at the occupation level in U.S. regional economies. We begin by showing how to convert our analytical results on labor market adjustment to immigration into estimating equations. We then turn to an instrumentation strategy for changes in immigrant labor supply, discussion of data used in the analysis, and presentation of our empirical findings. Our analytical results include predictions for how occupational labor allocations, total labor payments, and wages adjust to immigration. The impact of an influx of foreign labor on an occupation depends on a triple interaction: the magnitude of the overall regional labor inflow (n r), the immigrant employment intensity of the occupation in the base year (Sro), and the tradability of tasks performed by workers in the occupation (o O(g) for g = T, N). The V strategy that we develop targets this interaction term. As discussed in Section 2.2, measuring changes in occupation-level wages is difficult because changes in observable wages reflect both changes in occupation wages and self-selection of workers across occupations according to unobserved worker productivity. Correspondingly, we begin this section with the more straightforward analysis of immigration impacts on occupational labor allocations 27 We continue to assume that parameters are such that a relative increase in immigrant labor reduces the relative wage of immigrants. This requires that any resulting productivity growth is not too biased towards (away from) immigrant-intensive occupations if ɛ rg > 1 (ɛ rg < 1). 16

18 and labor payments, before turning to address wages. 4.1 Specifications for Labor Allocations and Labor Payments The version of (19) that incorporates changes in productivity (equation (60) in Appendix A.3) provides a strategy for estimating the impact of immigration on changes in the regional allocation of native-born workers across occupations, n D ro. t can be rewritten as, n D ro = α D rg + θ + 1 ɛ rg + θ (ɛ rg ρ) w r S ro + θ + 1 ɛ rg + θ (ɛ rg 1) a ro for all o O (g), where α D rg is a fixed effect specific to region r and the group (i.e., tradable, nontradable) to which occupation o belongs. f the only shock in region r between time t 0 and t 1 > t 0 is to the supply of immigrants, n r, and if changes in native factor supply, n D r, and occupation productivity, a ro, are arbitrary region- and time-specific functions of changes in immigrant supply, then w r = ψ r n r, where we assume that parameter values satisfy ψ r > 0. Hence, we have n D ro = α D rg + θ + 1 ɛ rg + θ (ɛ rg ρ) ψ r n rs ro + ν D ro for all o O (g), where ν D ro = θ+1 ɛ rg+θ (ɛ rg 1) (a ro ā rg ) is a linear function of the deviation of the productivity change for occupation o in region r, a ro, from the average productivity change across occupations in the same group g and region r, ā rg. This can be expressed compactly as n D ro = α D rg + β D r x ro + β D Nr o (N) x ro + ν D ro, (21) where x ro = Sron r is the immigration shock to occupation o in region r (i.e., the immigrant cost share of occupation o at time t 0, Sro, times the percentage change in the overall supply of immigrant workers in region r, n r), and o (N) equals one if occupation o is nontradable. 28 The structure of our model maps region-level changes in immigrant labor supplies into regionoccupation-specific shocks, via the initial intensity of the region-occupation in immigrant labor interacted with the tradability of the occupation. 29 From section 3.2, we know that βr D < 0 in (21) if and only if ɛ rt < ρ (the price elasticity of regional output in tradables is less than the elasticity of substitution between native- 28 As we discuss in Appendix J, a logic similar to that underlying (21) applies to how an immigrant inflow affects the allocation of foreign-born workers across occupations. n Appendix J, we present results on the immigrant-employment allocation regressions that are the counterparts to (24) and Table 1 below. As with our findings on the allocation of native-born workers, the results on how immigration affects the allocation of foreign-born workers across occupations are consistent with our framework. 29 t is worth noting that the structural relationship in (21) does not imply that the immigrant influx raises immigrant employment shares in immigrant-intensive occupations. ndeed, the labor inflow may cause these shares to differentially rise or fall in more relative to less immigrant-intensive jobs. Accordingly, our measure of the shock in (21) is not the (endogenous) change in immigrant employment in an occupation, but rather the region-level immigrant influx interacted with the initial occupation immigrant-employment intensity. What our model does imply is that the immigration shock is correlated with changes in occupation prices (where this correlation is more negative within nontradables than within tradables), occupation output (where this correlation is more positive within tradables than within nontradables), and occupation total revenue (where this correlation is more positive within tradables than within nontradables). 17

19 and foreign-born labor within occupations). f νro D is uncorrelated with x ro within each g, then this would imply crowding out of native-born workers by immigrant labor in tradables: in response to an inflow of immigrants into region r, native-born employment in tradable occupations with higher immigrant cost shares contracts (on average) relative to those with lower immigrant cost shares. Similarly, we know that βr D + βnr D < 0 in (21) if and only if ɛ rn < ρ (where ɛ rn is the price elasticity of regional output in nontradables). f νro D is uncorrelated with x ro within each g, then this would imply crowding out in nontradables. Finally, a value of βnr D < 0 is equivalent to ɛ rt > ɛ rn (the price elasticity of regional output is higher in tradables than in nontradables). f νro D is uncorrelated with x ro within each g, then crowding out is stronger in nontradables than in tradables: in response to an immigrant inflow, native-born employment in nontradables contracts more (or expands less) on average in occupations with high relative to low immigrant cost shares compared to tradables. The version of equation (18) in Appendix A.3 that incorporates changes in productivity generates the corresponding specification for occupation labor payments, lp ro = α rg + γ r x ro + γ Nr o (N) x ro + ν ro, (22) where the left-hand side of (22) is the log change in total labor payments for occupation o in region r, α rg is a fixed effect specific to region r and the group (i.e., tradable, nontradable) to which occupation o belongs, and ν ro is a linear function of the deviation in productivity change for occupation o in region r from the average productivity change across occupations in the same group and region. From Section 3.2, we know that a value of γ r > 0 in (22) implies that ɛ rt > 1, and a value of γ Nr < 0 implies that ɛ rt > ɛ rn. Therefore, an estimate of γ Nr < 0 provides a means of establishing that the price elasticity of output is large in tradables relative to nontradables, in addition to the test of whether crowding out is stronger in nontradables than in tradables, βnr D < 0. n Section 5, we show that γ Nr < 0 is inconsistent with another force that can generate βnr D < 0 in our model (namely, that substitutability of immigrant and native workers is relatively weak in tradables). To apply (21) and (22) empirically, we must address issues suppressed in the theory but likely to matter in estimation. By doing so, we move from structural regressions in our analytical model to reduced-form regressions that are motivated by our model but that do not identify structural parameters; in our quantitative analysis we will calibrate parameter values by running the same non-structural regressions in data generated by our extended model (in which we also relax the assumptions imposed in Section 3). First, by focusing on a small open economy, we abstract from occupation shocks at the national level (e.g., economy-wide changes in technology or demand). To allow for these, we incorporate occupation fixed effects into the estimation. Second, by abstracting away from observable differences in worker skill, we assume that all workers, regardless of education level, draw their occupational productivities from the same distribution within each k = D, ; this implies that the pattern of native comparative advantage across occupations is fixed over time, in spite of large changes in native educational attainment. n our extended model in Section 5 we allow for heterogeneous patterns of comparative advantage across education groups both for natives and immigrants. n our reduced-form empirical exercises, we capture this as follows. For natives, we estimate (21) by education group (while estimating (22) for all education groups combined, consistent with that equation s connection to occupation 18

20 total revenues). For immigrants, we define the immigration shock x ro expansively as x ro e S reo Nre, (23) Nre where Nre is the population of immigrants with education e within region r in period t 0, Nre is the change in this population between t 0 and t 1, and Sreo is the share of total labor payments in occupation o and region r that goes to immigrants with education e in period t n (23), we specify the exposure of a region-occupation to an immigrant influx as a function of the education-group-specific change in immigrant labor supplies and the initial education-group- and occupation-group-specific cost shares for immigrants. 31 Summarizing the above discussion, regression specifications for changes in native-born employment and total labor payments derived from our analytical results take the form n D ro = α D rg + α D o + β D x ro + β D N o (N) x ro + ν D ro, (24) lp ro = α rg + α o + γx ro + γ N o (N) x ro + ν ro, (25) where n D ro is the log change in employment for native-born workers (disaggregated by education group) for occupation o in region r, lp ro is the log change in labor payments for occupation o in region r (across all education groups and including both foreign- and nativeborn workers), we define x ro using (23), and we incorporate occupation fixed effects, αo D and α o. 32 n (24) and (25) we impose common impact coefficients β D, βn D, γ, and γ N, such that the estimates of these values are averages of their corresponding region-specific values (βr D, βnr D, γ, γ N) in (21) and (22). When estimating (24) and (25), we weight by the number of native-born workers employed or total labor payments within r, o in period t 0. The regression in (24) allows us to estimate whether immigrant flows into a region induce on average crowding out or crowding in of domestic workers in relatively immigrant-intensive occupations separately within tradable and within nontradable occupations, thereby allowing us to test whether crowding-out is weaker (or crowding-in is stronger) in tradable relative to nontradable jobs. The regression in (25) allows us to estimate whether immigrant flows into a region induce on average an increase or decrease in labor payments in relatively immigrantintensive occupations separately within tradable and within nontradable occupations. This allows us to assess the mechanism in our model that generates differential crowding out within tradable and nontradable occupations, which is that quantities are more responsive and prices less responsive to local factor supply shocks in tradable than nontradable activities. 30 With only one education group, the only difference between S ron r and x ro is the use of log changes versus percentage changes, which makes little difference for our results. 31 Consistent with Peri and Sparber (2011b) and Dustmann et al. (2013), we allow foreign- and native-born workers with similar education levels to differ in how they match to occupations. 32 Since the immigration shock in (23) is normalized by initial population levels (and not current values), the specification in (24) avoids concerns over division bias (Peri and Sparber, 2011a). And since we estimate (24) by education group, the occupation fixed effects control for national changes in the demand for skill that vary across occupations (due, e.g., to occupation-specific changes in preferences or technology). 19

21 4.2 An instrumental variables approach n the theory, we allow for variation in both immigrant inflows and changes in occupation productivity; our objective in the empirical analysis is to identify the causal effect of an immigrant influx on native allocations across occupations and on occupation labor payments. nterpreted through the lens of our model, the error terms in (24) and (25) are deviations for occupation o from the average change in productivity or demand both (i) across occupations in the same group g in region r, and (ii) within occupation o across all commuting zones. n the estimation, these unobserved shocks to productivity or demand may affect both the employment and wages of native-born workers and the attractiveness of a region to immigrant labor. Consider region r that attracts high-education immigrants between periods t 0 and t 1. This region will have a higher value of x ro, which by construction is mechanically higher in occupations that are intensive in high-education immigrants. The overall regional inflow of high-education immigrants, N re, which is one component of x ro, may have been induced in part by region-and-occupation-specific demand or productivity shocks (demeaned at the region-group level and at the national-occupation level), implying that x ro may be correlated with ν D ro in (24) and with ν ro in (25). Measurement error in x ro may also be an issue, given small sample sizes for workers in some occupation-region cells. To identify the causal impact of immigrant inflows to a region on native outcomes, we follow Altonji and Card (1991) and Card (2001) and instrument for x ro using x ro e S reo N re N re (26) where N re is a variant of the standard Card instrument that accounts for education-group and region-specific immigration shocks, N re s f res N r es. Here, Nes r is the net immigrant inflow in the U.S. (excluding region r) from immigrantsource-region s and with education e between t 0 and t 1, and f res is the share of immigrants from source s with education e who lived in region r in period t We allow immigrants with different education and sources to vary in their spatial allocation, and allow immigrants with different education levels within a region to vary in their occupational allocation. The Card instrument, while widely used, is subject to criticism. One is that it may be invalid if regional labor-demand shocks persist over time (Borjas et al., 1997). Helpfully, this concern is less pressing in our context. n (24) and (25) we identify the parameters β, β N, γ, and γ N using variation across occupations within regions in the change in employment or labor payments. By including region-group fixed effects (αrg, D α rg ) in regressions in which the dependent variable is a long-period change, we control for time trends that are specific both to the region (r) and to tradable or nontradable occupations as a group (g). Our 33 Regarding measurement error, small cell sizes in pums data may imply that the immigrant cost share S reo used to construct x ro may be subject to sampling variation. n Appendix F, we report results using values of S reo averaged over the initial sample year (1980) and the preceding time period (1970), to help attenuate classical measurement error. The coefficient estimates are very similar to our main results. 20

22 analysis is thereby immune to region, occupation-group specific innovations that may drive immigration, such as long-run shocks to aggregate regional productivity or amenities. 34 The extended time period of our analysis, which uses time differences over the three decade period of 1980 to 2012, helps address further concerns that results based on the Card instrument may conflate short-run and long-run impacts of immigration (Jaeger et al., 2018). 4.3 Data n our baseline analysis, we study changes in labor-market outcomes between 1980 and n sensitivity analysis, we use 1990 and 2007 as alternative start and end years, respectively. All data, except for occupation tradability, come from the ntegrated Public Use Micro Samples (pums; Ruggles et al., 2015). For 1980 and 1990, we use 5% Census samples; for 2012, we use the combined 2011, 2012, and % American Community Survey samples. Our sample includes individuals who were between ages 16 and 64 in the year preceding the survey. Residents of group quarters are dropped. Our concept of local labor markets is commuting zones (CZs), as developed by Tolbert and Sizer (1996) and applied by Autor and Dorn (2013). Each CZ is a cluster of counties characterized by strong commuting ties within and weak commuting ties across zones. There are 722 CZs in the mainland U.S. For our first dependent variable, the log change in native-born employment for an occupation in a CZ shown in (24), we consider two education groups: high-education workers are those with a college degree (or four years of college) or more, whereas low-education workers are those without a college degree. These education groups may seem rather aggregate. However, note that in (24) the unit of observation is the region and occupation, where our 50 occupational groups already entail considerable skill-level specificity (e.g., computer scientists versus textile-machine operators). 35 We measure domestic employment as total hours worked by native-born individuals in full-time-equivalent units (for an education group in an occupation in a CZ) and use the log change in this value as our first regressand. We measure our second dependent variable, the change in total labor payments, as the log change in total wages and salaries in an occupation in a commuting zone. We define immigrants as those born outside of the U.S. and not born to U.S. citizens. 36 The aggregate share of immigrants in hours worked in our sample rises from 6.6% in 1980 to 16.8% in We construct the occupation-and-cz-specific immigration shock in (24) and 34 A remaining concern is possible correlation between innovations to employment or labor payments (ν D ro, ν ro ) and the initial share of immigrants in region-occupation labor payments (S reo), which is used in the instrument in (26) and which may occur if the region-occupations that experience larger subsequent native employment growth are ones in which immigrants were initially more concentrated. To address this threat to identification, in Appendix F we construct the instrument in (26) by replacing S reo with S reo, which is the share of immigrant workers in labor payments for occupation o and education group e in the U.S., excluding region r. Results again are qualitatively similar to those we report below. 35 We simplify the analysis by including two education groups of native-born workers. Because the divide in occupational sorting is sharpest between college-educated and all other workers, we include the some-college group with lower-education workers. Whereas workers with a high-school education or less tend to work in similar occupations, the some-college group may seem overly skilled to fit in this category. Reassuringly, results are very similar if we exclude some-college workers from the low-education group. 36 We obtain qualitatively similar findings (in unreported analysis) using an alternative definition of immigrant status in which we exclude foreign-born workers who moved to the U.S. before the age of Because we use data from the Census and ACS (which seek to be representative of the entire resident 21

23 (25), x ro, defined in (23), as the percentage growth in the number of working-age immigrants for an education group in CZ r times the initial-period share of foreign-born workers in that education group in total earnings for occupation o in CZ r, where this product is then summed over education groups. n constructing our instrument shown in equation (26), we consider three education groups and 12 source regions for immigrants. 38 Our baseline data include 50 occupations (see Table 6 in Appendix E). 39 We measure occupation tradability using the Blinder and Krueger (2013) measure of offshorability, which is based on professional coders assessments of the ease with which each occupation could be offshored. Goos et al. (2014) provide evidence supporting this measure. They construct an index of actual offshoring by occupation using the European Restructuring Monitor and find that it is strongly and positively correlated with the Blinder-Krueger measure. 40 We group occupations into more and less tradable categories using the median so that there are 25 tradable and 25 nontradable entries (see Table 7 in Appendix E). The most tradable occupations include fabricators, financial-record processors, mathematicians and computer scientists, and textile-machine operators; the least tradable include firefighters, health assessors, therapists, and vehicle mechanics. n Table 8 in Appendix E, we compare the characteristics of workers employed in tradable and nontradable occupations. Whereas the two groups are similar in terms of the shares of employment of workers with a college education, by age and racial group, and in communication-intensive occupations (see, e.g., Peri and Sparber, 2009), tradable occupations do have relatively high shares of employment of male workers and workers in routineand abstract-reasoning-intensive jobs. High male and routine-task intensity arise because tradable occupations are strongly overrepresented in manufacturing. n robustness checks, we use alternative cutoffs for which occupations are tradable and which are nontradable; drop workers in routine-task-intensive jobs, in which pressures for labor-saving technological change has been particularly strong (Lewis, 2011; Autor and Dorn, 2013); and drop workers in communication-task-intensive jobs, in which native workers may be less exposed to immigration shocks Peri and Sparber (2009). n further checks, we use industries in place population, whether in the U.S. legally or not), undocumented immigrants will be included to the extent that are captured by these surveys. An additional concern is that the matching of immigrants to occupations may differ for individuals who arrived in the U.S. as children (and attended U.S. schools) and those who arrived in the U.S. as adults. n Appendix F, we report results limiting immigrants to those who arrived in the U.S. at age 18 or above. Our results are substantially unchanged. 38 The education groups are less than a high-school education, high-school graduates and those with some college, and college graduates. Relative to native-born workers, we create a third education category of lessthan-high-school completed for foreign-born workers, given the preponderance of undocumented immigrants in this group (and the much larger proportional size of the less-than-high-school educated among immigrants relative to natives). The source regions for immigrants are Africa, Canada, Central and South America, China, Eastern Europe and Russia, ndia, Mexico, East Asia (excluding China), Middle East and South and Southeast Asia (excluding ndia), Oceania, Western Europe, and all other countries. 39 We begin with the 69 occupations from the 1990 Census occupational classification system and aggregate up to 50 to concord to David Dorn s categorization ( and to combine small occupations that are similar in education profile and tradability but whose size complicates measurement. 40 Given limited data on intra-country trade flows in occupation services, we use measures of offshorability at the national level to capture tradability at the regional level, a correspondence which is imperfect. We demonstrate that our results are robust to using alternative cutoffs regarding which occupations are designated as tradable and to defining tradability across industries rather than across occupations. 22

24 of occupations, categorizing tradable industries to include agriculture, manufacturing, and mining, and nontradable industries to include services. 41 To provide context for our analysis of adjustment to immigration across occuptions within tradables versus within nontradables in the estimation of (24) and (25), we compare here, over our 1980 to 2012 time period, the unconditional changes in employment shares across occupations within T and across occupations within N. The median absolute log employment change for occupations is 0.59 in nontradables, as compared to 0.65 in tradables. 42 Although these unconditional changes do not account for differences in the magnitude of shocks affecting occupations in the two groups, the higher variability of employment changes within T when compared to within N suggests that overall adjustment is no less sluggish among tradable jobs than among nontradable jobs. 43 Our later analysis of changes in wages requires measures of wages by occupation, education group, and CZ. To obtain these, we first regress log hourly earnings of native-born workers in each year on a gender dummy, a race dummy, a categorical variable for 10 levels of education attainment, a quartic in years of potential experience, and all pair-wise interactions of these values (where regressions are weighted by annual hours worked times the sampling weight). We take the residuals from this Mincerian regression and calculate the sampling weight and hours-weighted average value for native-born workers for an education group in a CZ (or for an occupation-education group in a CZ). Finally, we use these values to calculate changes in education-level wages in each CZ (or in each occupation-cz). 4.4 Empirical Results on Labor Allocations and Labor Payments The specification for the impact of immigration on the allocation of native-born workers across occupations within CZs is given in (24). We run all regressions separately for the loweducation group (some college or less) and the high-education group (college education or more). The dependent variable is the log change in CZ employment (hours worked) of nativeborn workers in an occupation and the independent variables are the CZ immigration shock to the occupation, shown in (23), this value interacted with a dummy for whether the occupation is nontraded, and dummies for the occupation and the CZ-occupation group. Regressions are weighted by the initial number of native-born workers (by education) employed in the occupation in the CZ, and standard errors are clustered by state. We instrument for the 41 Alternative categorizations of industry tradability include Mian and Sufi (2014), who measure tradability according to geographic Herfindahl-Hirschman ndexes, following the logic that more geographically concentrated industries are likely to be more tradable. Relative to our approach, HHs have the appealling property of designating some services as tradable (e.g., finance and insurance), but the unappealling property of designating some obviously tradable goods as nontradable (e.g., agriculture, food products, lumber, metal products, mining, non-metallic minerals, paper products, plastics). Nevertheless, we find qualitatively similar results using our designation of industry tradability (see Appendix F) and in unreported results in which we define tradable (nontradable) industries as those with above (below) median HHs. 42 f we instead examine the mean absolute log employment change (weighted by initial occupation employment shares), the corresponding values are 0.45 for nontradables and 0.48 for tradables. 43 This observation poses a challenge to an alternative explanation for the greater immigrant displacement of natives within N versus within T : that costs to switching occupations are higher (or, more generally, that the occupation supply elasticity is lower) in T than in N. f this were the case, one would expect, all else equal, employment changes across occupations within T to be smaller than those across occupations within N. Yet, in the data we observe the opposite. 23

25 immigration shock using the value in (26), where we disaggregate the sum in specifying the instrument, such that we have three instruments per endogenous variable. Table 1 presents results for equation (24). n the upper panel, we exclude the interaction term for the immigration shock and the nontraded dummy, such that we estimate a common impact coefficient across occupations; in the lower panel we incorporate this interaction and allow the immigration shock to have differential effects on tradable and nontradable occupations. For low-education workers, column (1a) reports OLS results, column (2a) reports 2SLS results, and column (3a) reports reduced-form results in which we replace the immigration shock with the instrument in (26), a pattern we repeat for high-education workers. n the upper panel, all coefficients are negative: on average the arrival of immigrant workers in a CZ crowds out native-born workers at the occupational level. The impact coefficient on x ro is larger in absolute value for high-education workers than for low-education workers, suggesting that crowding out is stronger for the more-skilled. n the lower panel of Table 1, we add the interaction term between the immigration shock and an indicator for whether the occupation is nontraded, as in (24), which allows for differences in crowding out within tradables and within nontradables. There is a clear delineation between these two groups. n tradable occupations, the impact coefficient is close to zero (0.009 for low-education workers, 0.03 for high-education workers) with narrow confidence intervals. The arrival of immigrant workers crowds native-born workers neither out of nor into tradable jobs. n nontradable occupations, by contrast, the impact coefficient the sum of the coefficients on x ro and the x ro o (N) interaction is strongly negative. For both lowand high-education workers, in either the 2SLS or the reduced-form regression, we reject the hypothesis that this coefficient sum is zero at a 1% significance level. n nontradables, an influx of immigrant workers crowds out native-born workers. These results are consistent with our theoretical model, in which the crowding-out effects of immigration are stronger within nontradable versus within tradable jobs. Because the immigration exposure measure, x ro, is the interaction between the immigrant inflow into a CZ and the initial immigrant intensity of an occupation and because we allow this term to matter differentially for tradable and for nontradable occupations, interpretating coefficient magnitudes for the variable requires some guidance. Here, we rely our analytic results. Consider the impact of the inflow of immigrants between 1980 and 2012 into highimmigration Los Angeles on two occupations within nontradables, a high-immigrant intensity activity, private household services with x ro = 0.71, and a low immigrant-intensive activity, firefighting with x ro = 0.06, such that the difference in their occupation exposure is Our results indicate that for personal services relative to firefighting, we would see a 0.20 = differential log point employment reduction for low-education natives and a 0.24 = differential log point employment reduction for high-education natives. When comparing native employment changes for occupations by immigrant intensity in tradables, however, we would observe much smaller differences. Because the 2SLS coefficient on immigration exposure in column (2b) of Table 1 is a reasonably precisely estimated zero, our results indicate that we would detect no differential domestic employment changes between any pair of tradable occupations, either in Los Angeles or elsewhere. 44 Note that these coefficients do 44 Given a value of θ + 1 which is the elasticity of occupation wages to factor allocation, as shown in equation (20) and which we set at 2 in our quantitative model in Section 5 our theory allows us to use these 24

26 Dependent variable: log change in the employment of domestic workers in a region-occupation, Panel A (1a) (2a) (3a) (4a) (5a) (6a) Low Ed High Ed OLS 2SLS RF OLS 2SLS RF x ro ** -.099** -.130*** -.229*** -.210*** (.065) (.069) (.041) (.040) (.047) (.037) Obs R-sq F-stat (first stage) Panel B (1b) (2b) (3b) (4b) (5b) (6b) Low Ed High Ed OLS 2SLS RF OLS 2SLS RF x ro.089* (.049) (.088) (.061) (.036) (.066) (.060) o (N) x ro -.303*** -.303*** -.238*** -.309*** -.373*** -.330*** (.062) (.101) (.091) (.097) (.126) (.113) Obs R-sq Wald Test: P-values F-stat (first stage) Notes: The estimating equation is (24). Observations are for CZ-occupation pairs (722 CZs 50 occupations). The dependent variable is the log change in hours worked by native-born workers in a CZ-occupation; the immigration shock, x ro, is defined in (23); o (N) is a dummy variable for the occupation being nontradable. All regressions include dummy variables for the occupation and the CZ-group (tradable, nontradable). Columns (1) and (4) report OLS results, columns (2) and (5) report 2SLS results using (26) to instrument for x ro, and columns (3) and (6) replace the immigration shock(s) with the instrument(s). Low-education workers are those with some college or less; high-education workers are those with at least a bachelor s degree. Standard errors (in parentheses) are clustered by state. For the Wald test, the null hypothesis is that the sum of the coefficients on x ro and o (N) x ro is zero. Significance levels: * 10%, ** 5%, ***1%. Table 1: Allocation for domestic workers across occupations 25

27 not address the effect of immigration on tradable or nontradable aggregates (e.g., employment or wages), which is the focus of much previous literature. These results highlight a new source of exposure to the labor market consequences of immigration. The combination of living in a high immigration region (e.g., Los Angeles) and having a proclivity to work in immigrant-intensive nontradable jobs (e.g., personal services) leaves one relatively exposed to foreign labor inflows, whereas living in the same CZ but having a proclivity to work either in tradable jobs or in nontradable jobs that attract few immigrants leaves one comparatively less exposed. n Section 6, we will use our quantiative framework to interpret these coefficients, in a generalized model and without imposing the restrictions we make in Section 3, to determine the welfare consequences of differential exposure to immigration, and to solve for wage effects across (rather than within) CZs. The specification for the log change in total labor payments in (25) provides support for the mechanism underlying differential immigrant crowding out of native-born workers in tradables versus nontradables. n Table 2, we report estimates of γ, which is the coefficient on the immigration shock, x ro, and γ N, which is the coefficient on the immigration shock interacted with the nontradable-occupation dummy, o (N) x ro. n all specifications, the coefficient on x ro is positive and precisely estimated, which is consistent with the elasticity of local output to local prices in tradables being larger than one (ɛ rt > 1). Similarly, in all specifications the coefficient on o (N) x ro is negative and highly significant, which implies that immigrant crowding out of natives is stronger within nontradables than within tradables (i.e., ɛ rt > ɛ rn ), which is consistent with the results in Table 1. Together, the results in Tables 1 and 2 verify both differential crowding out within tradables versus within nontradables and the key mechanism in our model through which this difference is achieved. n our model the arrival of immigrant labor results in an expansion in output and a decline in prices of immigrant-intensive tasks both within tradables and within nontradables. Compared to nontradables, however, adjustment in tradables occurs more through output changes than through price changes. Consequently, revenues and labor payments of immigrant-intensive occupations increase by more within tradable than within nontradable jobs, as does native employment. Consistent with this logic, Tables 1 and 2 show that, within tradables, an immigration shock generates null effects on native employment and an expansion in total labor payments for immigrant-intensive activities. n contrast, within nontradables, the immigration shock has a negative impact on native employment and no change in labor payments in more immigrant-intensive occupations. Robustness. The results in Tables 1 and 2 embody assumptions about instrument validity, which activities are nontradable and which are tradable, and the relevant time period for the analysis. n Appendix F, we present results for alternative specifications in which we examine the importance of these assumptions. Beginning with instrument validity, one concern about our estimation is that, by virtue of using a variant of the Card (2001) instrument, we are subject to the Borjas et al. (1997) critique that regional immigrant inflows are the result of secular trends in regional employment growth, which could complicate using past immigrant results to interpret wage implications. Specifically, our results indicate that we would detect a.10 = 0.20/2 and a 0.12 = 0.24/2 log point reduction in domestic low-education and high-education wages in personal services relative to electronic repairers in Los Angeles but no differential domestic wage changes between any two tradable occupations in Los Angeles or elsewhere. 26

28 Dependent variable: log change in labor payments in a region-occupation, (1) (2) (3) OLS 2SLS RF x ro.3918***.3868**.3266** (.1147) (.1631) (.1297) o (N) x ro *** *** *** (.1157) (.1362) (.0923) Obs R-sq Wald Test: P-values F-stat (first stage) Notes: The estimating equation is (25). Observations are for CZ-occupation pairs. The dependent variable is the log change in total labor payments in a CZ-occupation; the immigration shock, x ro, is in (23); o (N) is a dummy variable for the occupation being nontradable. All regressions include dummy variables for the occupation and the CZ-group (tradable, nontradable). Column (1) reports OLS results, column (2) reports 2SLS results using (26) to instrument for x ro, and column (3) replaces the immigration shocks with the instruments. Standard errors (in parentheses) are clustered by state. For the Wald test, the null hypothesis is that the sum of the coefficients on x ro and o (N) x ro is zero. Significance levels: * 10%, ** 5%, ***1%. Table 2: Labor payments across occupations settlement patterns to isolate exogenous sources of variation in future regional immigrant inflows. To examine the relevance of this critique for our analysis, we check whether our results are driven by pre-trends in occupational employment adjustment patterns. We repeat the estimation of (24), but now with a dependent variable that is defined as the change in the occupational employment of native workers over the period, while keeping the immigration shock defined over the period. This exercise allows us to assess whether future changes in immigration predict past changes in native employment, which would indicate the presence of confounding long-run regional-occupational employment trends in the data. These exercises, discussed in more detail in the Appendix, reveal no evidence that current impacts of immigration on native-born employment are merely a continuation of past employment adjustment patterns. We further examine the sensitivity of our estimates to constructing instruments using means of long lags of immigrant region-occupation cost shares (see note 33) or these cost shares measured excluding the region-occupation on which an observation is based (see note 34), also with little impact on our results. n the regressions in Table 1, we divide occupations into equal-sized groups of tradables and nontradables. n Appendix F, we explore alternative assumptions about which occupations are tradable and which are not (and alternative aggregation schemes for the 50 occupations in our sample). The corresponding regression results are very similar to those in Table 1. Results are also similar, as reported in the Appendix, when we redo the analysis for region-industries, rather than for region-occupations, and identify the tradability of industries as discussed in Section 4.3. mmigration induces crowding out of native-born employment in nontradable industries but not in tradable industries (while β N in (24) is always less than zero, it is significant in 2SLS and reduced-form regressions for high-education 27

29 natives but not for low-education natives), while leading to a greater expansion of labor payments in immigrant-intensive occupations in tradable than in nontradable industries (where γ N in (25) is significantly negative in all specifications). We also experiment with changing the end year for the analysis from 2012 to 2007, which falls before the onset of the Great Recession. Using this earlier end year yields results similar to our baseline sample period of strong immigrant crowding out of native-born workers in nontradable occupations and no crowding out in tradable occupations. When we alternatively change the start year from 1980 to 1990, the crowding-out effect weakens for low-education workers in nontradables, but remains strong for high-education workers in nontradables. 45 Finally, we verify that our results are unaffected by dropping routine- or communicationintensive occupations, to address concerns over the confounding effects of skill-biased technical change and the language-based adjustment mechanisms discussed in Peri and Sparber (2009); and the largest commuting zones, for which concerns about reverse causality from local labor demand shocks to immigrant inflows may be strongest. 4.5 Wage Changes for Native-born Workers Our analytical results predict how occupation wages per efficiency unit of native-born workers adjust to an inflow of foreign workers. Equation (20) yields a regression specification that takes the form w D ro = α D rg + α D o + χ D x ro + χ D N o (N) x ro + ν D ro, (27) following the same steps incorporating occupation fixed effects, imposing common slope parameters across regions, and measuring x ro using (23) that led from equation (19) to regression specification (24). A positive value of χ D would imply that an inflow of immigrants raises native occupation wages in more relative to less immigrant-intensive occupations within tradables, while a negative value of χ D N would imply that the impact of an inflow of immigrants on wages in immigrant-intensive native occupation is less positive (or more negative) within nontradables than within tradables. n the data we observe not changes in wages per efficiency unit at the occupation level, wro, D but rather changes in average wages by occupation, wage D ro. Under crowding out, an immigrant influx would tend to drive down the wage per efficiency unit in more-immigrantintensive occupations and also to drive out native-born workers whose unobserved characteristics give them relatively low productivity in these jobs. Absent knowledge of the distribution of worker productivity draws, the relative importance of these two forces is ambiguous, which complicates analysis of observed changes in occupation-level wages. 46 As a solution to the unobservability of occupation-level changes in wages per efficiency unit, we derive an estimating equation that allows us to use observed changes in average wages (across education groups) at the region level to infer indirectly the model s predictions 45 Variation in parameter estimates across time periods should not be surprising. n (21), these parameters are functions of output price elasticties and embodied native labor-supply and productivity elasticities; they will vary across time periods to the extent that trade shares or the component elasticities vary. 46 With a Fréchet-distribution of idiosyncratic productivity draws, these two forces exactly balance out, implying that changes in average wages are equal across occupations within a region for natives. n Appendix G, we discuss estimation results for the impact of immigration on region-occupation wages and their possible implications for the distribution of worker productivity. 28

30 for occupation-level wage changes, χ D and χ D N. Log-linearizing the average wage change of native workers in region r and taking into account that occupation switching does not have first-order effects on changes in individual wages (see footnote 16), yields wage D r = o O w D roπ D ro, The change in average wages across workers in a region is an average of changes in occupation wages weighted by initial employment shares. n our extended model of Section 5.1, in which there are multiple education groups e of native workers, the previous expression holds as wage D re = o O w D roπ D reo, (28) where wage D re is the change in average wages of native workers with education e in region r and πreo D is the allocation across occupations of these workers in the base year. Combining (27) and (28), we obtain wage D re = α rgπ D reo D + α o D πreo D (29) g o O(g) o O + χ D x ro πreo D + χ D N x ro o (N) πreo D + ν re D o O We estimate (29) proxying for region-group time trends α D rg (which cannot be identified since there are as many parameters as observations) using γ g x rg + ζ r for g = T, N, where x rg is the simple average value of x rg in region r across occupations in group g. 47 We present regression results for equation (29) in Table 3. The coefficient on the term xro o (N) π D reo, which captures the differential impact of immigration on changes in regional education-group average wages in nontradable compared to tradable occupations, is negative and precisely estimated in both 2SLS and reduced-form specifications. 48 This finding is consistent with immigrant crowding out of native-born workers within nontradables being stronger than within tradables. For tradable occupations, by contrast, the coefficient on the term x ro π D reo is positive and precisely estimated in the reduced-form and 2SLS specifications. Consistent with the employment-allocation regressions in which crowding out is stronger in nontradable than in tradable occupations the negative impact of immigration on regional wages appears to work more strongly through nontradables than through tradables. However, the positive coefficient on the tradable component of the immigration shock in the wage regressions is distinct from the employment regressions in which there are null effects of immigration on crowding out (in) of the native-born. 47 n Appendix we use data generated by our extended model of Section 5.2 to verify that there is a tight link between estimates of χ D and χ D N based on equations (27) and (29), and that the coefficients of the wage regression, the χs, are roughly equal to 1/ (θ + 1) times the coefficients of the allocation regression, the βs, as implied by our analytic expression (17). 48 After proxying for α rg, D we construct instruments for the four endogenous variables in (29) x ro π reo, D xro o (N) πreo D, x rt o O(T ) πd reo, and x rn o O(N) πd reo using instruments for x ro s as defined in (26). We first instrument x rg by calculating the simple averages of the instrument x ro across occupations within g = T, N. We then replace x ro, x rn,, and x rt in the four endogenous variables with their corresponding instruments to construct the instruments used in the 2SLS and reduced-form regressions. o O 29

31 (1) (2) (3) OLS 2SLS RF o O πd reox ro.602***.8986***.9678*** (.1101) (.139) (.1617) o O πd reo o (N) x ro *** *** *** (.1535) (.1779) (.2439) Obs R-sq Wald Test: P-values Notes: The estimating equation is (29). Observations are by CZ and education group (some college and less, bachelor s and more). The dependent variable is the education-group-specific log change in average wages for native-born workers in (28). Reported coefficients are for the immigration shock to all occupations, o O πd reox ro, and to nontradables, o O πd reo o (N) x ro. Coefficient estimates on other variables ( o O πd reo, x rt o O(T ) πd reo, x rn o O(N) πd reo) are suppressed. Column (1) reports OLS results, column (2) reports 2SLS results using (26) to construct instruments for the immigration shocks, and column (3) replaces the immigration shocks with the instruments. For the Wald test, the null hypothesis is that the sum of coefficients on o O πd reox ro and o O πd reo o (N) x ro are zero. F-stats for the first-stage are 41.87, 76.53, and 86.6 for the endogenous variables o O πd reox ro, o O πd reo o (N) x ro, x rt o O(T ) πd reo, and x rn o O(N) πd reo, respectively. Significance levels: * 10%, ** 5%, ***1%. Table 3: Change in average wage for native-born workers, The wage specifications in Table 3 are roughly analogous to the voluminous literature that takes a cross-area-study approach to estimating immigration wage effects, which tends to find null or small negative impacts of local-area immigrant inflows on wages for the native born (see, e.g., Blau and Mackie, 2016). Our specification differs in important respects from commonly estimated regressions, which do not distinguish shocks within tradable versus within nontradable occupations, as we do above by aggregating earning shocks across occupations into the O(T ) and O(N) sets. n Appendix G, we contrast our method with the common approach of assuming a single aggregate production sector, by estimating a regression for region-education-group wage changes in which the immigration shock is specified at the region-education-group level, without allowing for differential adjustment within T versus within N. Consistent with the literature, this specification yields a negative but small and insignificant effect of immigration on earnings. These findings highlight how the correlation between earnings and immigrant-driven labor supply shocks in the aggregate may hide substantial variation across occupations in the impact of these shocks, as well as differential adjustment within tradable and nontradable activities. Summary. The empirical results show that, in line with our theoretical model, there are differences in adjustment to labor supply shocks across occupations within tradables and within nontradables. The allocation and wage regressions are consistent with immigrant crowding out of native-born workers within nontradables (ɛ rn < ρ) and with less crowding out within tradables (ɛ rn < ɛ rt ). Whereas the allocation regression is consistent with neither crowding in nor crowding out within tradables (ɛ rt ρ), the average wage regression is consistent with crowding in within tradables (ɛ rt > ρ). We identify a new source of worker exposure to immigration variation in the proclivity to work in nontradable immigrant- 30

32 intensive occupations in high immigration regions which is not present in previous work. 5 A Quantitative Framework We next present an extended quantitative model, in which we impose less restrictive assumptions than in Section 3 (large shocks, large open economies, multiple labor skill groups, geographic mobility of native and immigrant workers), provide structural interpretations of our reduced-form empirical estimates, and evaluate changes in real wages by occupation and region. We further compare outcomes across CZs and between the sets of tradable and nontradable occupations, which are not the focus of our empirical and theoretical analyses. n this section, we describe how we parameterize our quantitative model; in the following section, we use the model to conduct counterfactual exercises regarding U.S. immigration. 5.1 An Extended Model We extend our model of Section 2 as follows. First, type k {D, } workers are now differentiated by their education level, indexed by e E k. The set of type k workers with education e in region r is Zre, k which has measure Nre k and which is endogenously determined for both domestic and immigrant workers as described below. The measure of efficiency units of type k workers with education e employed in occupation o within region r is L k reo = Treo k ε (z, o) dz for all r, e, o, k, z Z k reo where Treo k denotes systematic productivity for any type k worker with education e employed in occupation o and region r. We assume that immigration affects productivity only at the aggregate region level: productivity is given by Treo k = T reon k r λ, where N r = k,e N re k is the population in region r and λ governs the extent of regional agglomeration (if λ > 0) or congestion (if λ < 0). We maintain the same assumptions as in the one-education-group model on the distribution from which ε (z, o) is drawn, where for simplicity the parameter θ that controls the dispersion of idiosyncratic productivity draws is common across education groups, e. Within each occupation, efficiency units of type k workers are perfect substitutes across workers of all education levels. 49 The measure of efficiency units of type k workers employed in occupation o within region r is thus given by L k ro = e Lk reo. Output of occupation o in region r is produced according to (1). These assumptions imply that, for any ρ <, within each occupation immigrants and domestic workers are less substitutable than are type k workers with different levels of education. Under these assumptions, the share of type k workers with education e who choose to work in occupation o within region r, πreo, k is 49 This simplifying assumption, which allows us to avoid further nesting of workers with yet more substitution elasticities to calibrate, does not imply that education groups within nativity categories are perfectly substitutable at the aggregate level, since workers with different education levels concentrate in different occupations (see Llull 2017 for a similar assumption). We elaborate on this point below. Borjas (2003) and Piyapromdee (2017), among others, obtain related results for the impact of immigration on education-group wages by alternatively assuming that education and nativity groups are imperfect substitutes in an aggregate production function that does not specify heterogeneous tasks or occupations. 31

33 π k reo = ( T k reo W k ro) θ+1 ( ) j O T k rej Wrj k θ+1, (30) where Wro k is the wage per efficiency unit of type k labor, which is common across all education groups of type k employed in occupation o within region r. The efficiency units supplied by these workers in occupation o is ( ) L k reo = γtreo k θ π k θ+1 reo Nre. k (31) The average wage of type k workers with education e in region r (i.e., the total income of these workers divided by their mass) is W age k re = γ [ j O ] 1 θ+1 ( ) T k rej Wrj k θ+1 (32) which is also the average wage for these workers within each occupation. 50 A second extension is that native and immigrant workers choose in which region r to live. We follow Redding (2016) and assume that the utility of a worker z living in region r depends on ammenities and the expected real wage from living there. Ammenities from residing in region r are given by the product of a systematic component, A D re for natives with education e and A s re for immigrants with education e from source country s, and an idiosyncratic amenity shock, ε r (z, r), which is distributed Fréchet with shape parameter ν > 1. We assume that each worker first draws her amenity shocks across regions and chooses her region, and then draws her productivity shocks across occupations and chooses her occupation. We assume that the systematic component of productivity, Treo, does not depend on the immigrant s source country s, so that the allocation of workers across occupations, πreo, k and average wage, W age k re, do not vary by s and are given by (30), (31) and (32). 51 Under these assumptions, the measure of workers of type k (and source country s for immigrants) with education e in region r is given by N ks re = ( j R A ks re ( ) ν W age k re P r A ks je W age k je P j ) ν N ks e, where Ne ks denotes the exogenous measure of education e workers of type k (and source country s for immigrants) across all regions (Ne ks = r R N re ks ). The measure of immigrant workers with education e in region r is given by Nre = s S N s 50 Taking as given changes in the population of domestic and immigrant workers by education in each region, the equilibrium occupation price and quantity changes would then coincide with those in our baseline model if there are no agglomeration forces, λ = 0, and if education groups within each k are allocated identically across occupations (i.e., πreo k = πro k for all e E k ) with the aggregate supply of type k workers in region S k re r in the single education model set to n k r = e E n k k S re. Further details are presented in Appendix H.2. r k 51 We incorporate immigrant source countries into our quantitative model in order to conduct origin-specific counterfactuals (e.g., reducing the number of low-education Latin American immigrants). The assumption that immigrants with a given education level differ in their preferences across U.S. regions (based on their source country) but not in their pattern of comparative advantage across occupations mirrors the extensions to our empirical specifications and provides a model-based motivation of our Card-type instrument. re. 32

34 n Appendix H.1 we specify a system of equations to solve for changes between two time periods in prices and quantities in response to changes in exogenously specified national supplies of immigrant workers by education and source country. 52 These changes are not restricted to be infinitesimal as in the analytic results above. The inputs required to solve this system are: (i) initial period allocations across occupations for each worker type and education in each region by region, πreo, k wage income of each worker type and education as Nre a share of total income by region, k W agek re, allocations of workers across regions for e k N k re W agek re each worker type, education (and source country for immigrants), Nre ks, absorption shares by occupation in each region, Y ro P ro y, and bilateral exports relative to production and o Y ro P y ro relative to absorption by occupation in each region; and (ii) values of parameters η (the substitution elasticity between occupations in production of the final good), α (the substitution elasticity between services from different regions in the production of a given occupational service), ρ (the substitution elasticity between domestic and immigrant workers in production within an occupation), θ (the dispersion of worker productivity), ν (the dispersion of worker preferences for regions), and λ (the elasticity of aggregate productivity to population in each region); and (iii) changes in immigrant labor supply by education and source country, ˆN re. n Appendix H.3 we extend the analytic results of Section 3 to multiple education s groups, providing conditions under which immigration neither crowds in nor crowds out type k, e workers within tradable or nontradable jobs. 5.2 Calibration We calibrate the model based on the U.S. data used in our empirical analysis. We consider 722 regions (each of which corresponds to a given CZ) within a closed national economy, 50 occupations (half tradable, half nontradable), two domestic education groups (some college or less, college completed or more), and three immigrant education groups (high school dropouts, high school graduates and some college, and college graduates). The values of π k reo, Nre k W agek re e k N k re W agek re and N ks re in the initial equilibrium are obtained from Census and ACS data. We consider two aggregates of source countries for immigrants one for Latin American countries and one for all other countries which is sufficient to conduct our counterfactuals. n order to construct bilateral exports by occupation in each region, we assume that occupation demand shifters are common across regions for tradable occupations, µ ro = µ o for o O(T ), and choose trade costs as follows. First, we assume that nontradable occupations are subject to prohibitive trade costs across CZs (τ rjo = for all j r). Second, we assume that bilateral trade costs for a given tradable occupation between a given origindestination pair are common across tradable occupations (given the absence of bilateral cross-cz trade data by occupation), τ rjo = τ rjo for all o, o O(T ), and parameterize them using a standard gravity trade cost function: τ rjo = τ ln (distance rj ) ε for j r. Given this assumption, the elasticity of trade with respect to distance across CZs within the U.S. in our model is given by (1 α)ε, where 1 α is the trade elasticity introduced in equation (5). We set (1 α)ε = 1.29, as estimated in Monte et al. (2016) using data on intra-u.s. 52 Specifically, we must solve for 72, 200 ( ) occupation wage changes and 5, 776 ([2+(3 2)] 722) population changes. 33

35 θ α ρ η ν λ Parameter values Table 4: Parameter values in quantitative analysis manufacturing trade from the Commodity Flow Survey (CFS). We calibrate τ to match the average export share within tradables in our model (in the year 2012) to that in the 23 CFS regions (in the year 2007) that closely align with our CZs, where the average weighs each CZ according to total labor payments in tradables in the model and according to total shipments in manufactures in the data. Further details are provided in Appendix H We assign values to the parameters α, ν, θ, λ, η, and ρ as follows. The parameter α 1 is the partial elasticity of trade flows to trade costs. We set α = 7, yielding a trade elasticity of 6, in the mid range of estimates in the trade literature surveyed by Head and Mayer (2014) and, more importantly, in line with the estimates using regional data within the U.S. estimated in Donaldson (Forthcoming), Donaldson and Hornbeck (2016), and Fuchs (2018). The parameter ν is the elasticity of native and immigrant spatial allocations with respect to n k re nk r e native real wages across regions, ν =. We set ν = 1.5, which is in the middle wr k wk r pr+p r of the range of estimates in the geographic labor mobility literature reviewed by Fajgelbaum et al. (2015). The parameter θ + 1 is the elasticity of occupation allocations with respect to occupation wages within a region, θ + 1 = nk ro n k ro. We set θ = 1 following analyses wro k wk ro on worker sorting across occupations in the U.S. labor market in Burstein et al. (2016) and Hsieh et al. (2016). 54 We set λ = 0.05, in line with estimates in the local agglomeration economics literature reviewed in Combes and Gobillon (2015). Since estimates of the elasticity of substitution between occupations, η, and the elasticity of substitution between native and immigrant workers within occupations, ρ, are not readily available from existing research, we calibrate them. To best match our reduced-form employment-allocation regressions in which we instrument for immigrant allocation across space using a Card-like instrument, we feed into our model exogenous changes in immigrant supply by education and region between 1980 and 2012 predicted by the Card instrument, ˆN re N re = 1 + N re, where Nre is defined in Section 4, and leave the supply of native workers by education and region unchanged (in the counterfactuals in Section 6, we feed in national changes in immigrants by source country and education, and allow for endogenous regional movements of natives and immigrants). Using data generated by the extended model (taking into account the general equilibrium determination of producer prices by region and occupation), we then run the reduced-form employment-allocation regression in (24). While this reduced-form equation has no structural interpretation both because of our extensions described above and because we do not impose small open economy or small shock assumptions here it provides useful identified moments that we can match in our full model (see Nakamura and Steinsson, 2018). We choose η and ρ to target the extent to which 53 We also consider an alternative parameterization in which trade is free within tradables. We match our moments excluding trade shares by setting ρ = α = 7 and η = n unreported results, we show that in our counterfactual exercises the within CZ results for native reallocation and wage changes across occupations are similar, but the across CZ changes in real wages are smaller. 54 Our parameter θ corresponds to θ + 1 in Burstein et al. (2016) and Hsieh et al. (2016). 34

36 Allocation regression Labor payment regression Low education High education β D βn D γ γ N R-sq Table 5: Regression results using model-generated data Calibration targets: average low & high education for native workers β = 0; Average low & high education for native workers β D + β D N = immigration crowds in or crowds out native employment within tradables and within nontradables. Specifically, we target β D = 0 (neither crowding in nor crowding out of natives by immigrants in tradables) and β D + βn D = (crowding out of natives by immigrants in nontradables), where the latter is the average of the reduced-form estimates across high- and low-education native workers. Replicating our empirical parameter estimates implies values of ρ = 5.6 and η = Table 4 reports calibrated parameter values and Table 5 reports the employment-allocation regressions using data generated by the model. The intuition for the values that the parameters η and ρ are assigned can be understood using the analytics in Section 3.2, although the narrow restrictions under which these results are obtained are partially relaxed here. Our assumption that trade shares are zero for nontradable occupations implies that the elasticity of regional output to the regional producer price for nontradables, ɛ rn, is equal to η. The elasticity of regional output to the regional producer price for tradables, ɛ rt, is a weighted average of α and η, with the weight on α increasing in trade shares of tradable occupations, where trade shares are implied by the calibration procedure described above. Since tradable occupations have high trade shares, ɛ rt is closer to α than to η. According to our analytics in Section 3.2, targeting β D = 0 in the employment-allocation regression (no crowding out in tradables for low- and high-education natives) requires that the elasticity of regional output to the regional producer price within tradables, ɛ rt, equals the elasticity of substitution between native- and foreign-born workers within each occupation, ρ. t follows that ρ must be closer to α than to η, yielding ρ = 5.6. A higher value of ρ would imply crowding out in tradables, which is inconsistent with our reduced-form estimates (see the alternative parameterization below). The intuition for the value of η = 1.94 is similar. Targeting βn D < 0 in the employmentallocation regression (crowding out in nontradables for low- and high-education natives) requires that η = ɛ rn < ρ. To demonstrate how the allocation regression shapes our choice of η beyond requiring that η < ρ, Figure 1 displays the model-implied values of β D and βn D against the value of η if we fix all other parameters at their baseline levels. As described above, β D is less responsive to changes in η than is βn D. Therefore, the estimated value of βn D guides our choice of η. Although we do not directly target the labor-payments regression coefficients, the estimated coefficients in our model, reported in Table 5, are roughly in line with the reducedform labor-payments regression results in our data, reported in column 3 of Table 2. The 35

37 Figure 1: Estimates from allocation regression (model generated data) Figure varies η from 1 to 9, holding all other parameters at their baseline levels. The vertical lines represents the baseline value of η = 1.94 and the value of η = α = 7. resulting R-squared values for the allocation and labor payment regressions run on modelgenerated data are above Because these regressions are not structural, the tight fit does not follow directly from our modeling assumptions. nstead, the fit reflects the ability of the reduced-form employment-allocation and labor-payments regressions to summarize equilibrium occupational employments in the model. 55 Alternative parameterizations of ρ. We consider two alternative parameterizations in which we choose different values of ρ. n the first, we triple the value of ρ to ρ = 16.8 and hold fixed other parameters. When raising ρ, we continue to roughly match the extent of differential crowding out within nontradables compared to tradables, βn D = 0.294, but the model now generates the counterfactual result of crowding out within tradable occupations, β D = n the second parameterization, we assume that ρ differs exogenously and systematically between tradable, ρ T, and nontradable, ρ N, occupations. n this parametrization, we assume autarky in all occupations (so that ɛ T = ɛ N ), fix η at our baseline level, and choose ρ T = 1.9 < 4.7 = ρ N targeting the native factor allocation regression estimates. This alternative is motivated by the concern that our finding of stronger crowding out within nontradables relative to within tradables could be a byproduct of higher immigrant-native substitution elasticities in nontradables relative to tradables. n this case, however, the model has counterfactual predictions for how labor payments respond to immigration. n particular, relative labor payments to immigrant-intensive occupations counterfactually increase relatively more within nontradable than within tradable occupations in response to an inflow of immigrants, γ N = Similarly, prices of immigrant-intensive occupations do not fall relatively more within nontradable than within tradable occupations, which is inconsistent with evidence in Cortes (2008). 55 n Appendix we report estimates for the wage regressions (27) and (29) using model-generated data. 36

38 6 Counterfactual Changes in mmigration Using data for 2012 as the initial period, we consider two counterfactual changes in the s supply of immigrant workers, ˆN e, which we motivate using proposed reforms in U.S. immigration policy. One potential change is to tighten U.S. border security, which would reduce immigration from Latin America, the source region that accounts for the vast majority of undocumented migration flows across the U.S.-Mexico border. We operationalize this change by reducing the immigrant population from Mexico, Central America, and South America in the U.S. by one half. Following the logic of the Card instrument, this labor-supply shock will differentially affect commuting zones that historically have attracted more immigration from Latin America. Labor market adjustment to the immigration shock takes the form of changes in occupational output prices and occupational wages, a resorting of workers across occupations within CZs, and movements of native- and foreign-born workers between CZs. The second shock we consider is expanded immigration of high-skilled workers. The U.S. business community has advocated for expanding the supply of H1-B visas, the majority of which go to more-educated foreign-born workers (Kerr and Lincoln, 2010). We operationalize this shock via a doubling of immigrants in the U.S. with a college education. n order to describe the results of our counterfactual exercises, it is useful to define a measure of the aggregate exposure of region r to a change in immigration as x r = ψre Nre Nre, (33) where ψre Nre W age re/ e k N re k W agek re e is the share of immigrant workers with education e in region r in total labor payments in region r and where N re is the change between the initial and final periods in education e labor supply of immigrants in region r. The measure x r captures the change in effective labor supply in CZ r caused by changes in the local supply of immigrants, accounting for endogenous regional labor movements % Reduction of Latin American mmigrants n this scenario, we halve the number of Latin American immigrants at the national level,,latam,latam 0.5 Ne setting ˆN e = 1, where N,LatAm Ne,LatAm e corresponds to the total number of Latin American immigrants with education e in the U.S. in the period Because Latin American immigrants tend to have relatively low education levels, reducing immigration from the region amounts to a reduction in the relative supply of less-educated labor. n 2012, 70.4% of working-age immigrants from Mexico, Central America, and South America had the equivalent of a high-school education or less, as compared to 29.4% of non-latin American immigrants and 38.3% of native-born workers. There is large variation in aggregate exposure across regions in response to this shock with x r ranging from almost 0 to 0.18 in Miami and taking a value of 0.08 in Los Angeles, a case on which we focus below. This variation arises from differences across CZs in 2012 in the share of immigrants by education in total income and in the share of Latin Americans in the total number of immigrants by education. Although natives and immigrants reallocate 37

39 Figure 2: 50% reduction in Latin American mmigrants: change in the real wage of low-education native-born workers across CZs across space in response to this shock, this spatial re-sorting plays little role in shaping x r. 56 We first examine the consequences of a reduction in immigrants from Latin America on changes in average real wages (i.e., the change in average consumption for workers who begin in the region before and remain in the region after the the counterfactual change in immigrant labor supply) for low-education natives. 57 We next examine the consequences on the native education wage premium. These outcomes, which are the focus of much previous literature, capture differences across CZs in immigration impacts. They do not, however, reveal within-cz variation in exposure to factor supply shocks, which is the emphasis of our paper. Figure 2 depicts the spatial variation in the log change in average real wages for less-educated native-born workers across commuting zones, and reveals the expected larger impacts in CZs that are located in Florida, close to the U.S. border with Mexico, or gateway regions for immigration, such as the metro areas of Atlanta, Chicago, New York, and Washington, D.C. Figure 3 plots, on the y-axis, the log change in average real wages for less-educated native-born workers in the left panel and the log change in the education wage premium for native-born workers (college-educated workers versus workers with less than college) in the right panel, where in each graph the x-axis is CZ exposure to the immigration shock, x r. n response to an outflow of Latin American immigrants, average native loweducation real wages fall in all but six locations, from close to zero in the least-exposed CZs, 56 With changes in real wages across regions differing by no more than 5% and with ν = 1.5, there is not substantial labor reallocation across regions relative to the large intial shock. Hence, all of our results in what follows are very similar to the results that we would obtain without geographic labor mobility. 57 To a first-order approximation, this change in real wages equals the change in utility of low-education natives initially located in that region. 38

40 Figure 3: 50% reduction in Latin American mmigrants: change in real wage of low education domestic workers and change in education wage premium of domestic workers, across CZs to 1.6% in Los Angeles, and to as much as 4.1% in Miami. This real wage impact arises both because of agglomeration externalities and because native and immigrant workers are imperfect substitutes, such that reducing immigration from Latin America reduces native real wages. At calibrated parameter values, this real wage effect is largely transmitted through changes in region price indices rather through than changes in nominal wages. 58 Moving to the right panel of Figure 3, we see that because the immigration shock reduces the relative supply of less-educated immigrant labor and because less-educated immigrants are relatively substitutable with less-educated natives, the education wage premium falls (and more so in CZs that are exposed to larger reductions in immigration from Latin America). For example, in Miami and Los Angeles the education premium falls by roughly 0.8%. Less-educated foreign-born workers substitute more easily for less-educated natives than for more-educated natives both because less-educated native- and foreign-born workers tend to specialize in similar occupations and because ɛ rg ρ (which implies that native- and foreignborn workers are more substitutable within than across occupations). Our Roy model, in which education groups are perfect substitutes within occupations, endogenously generates aggregate patterns of imperfect substitutability between education groups. Our more novel results are for changes in wages at the occupation level, which capture variation in exposure to immigration across jobs within a CZ. Figure 4 describes differences across occupations in adjustment to the immigration shock in nontradable and tradable tasks for the CZ of Los Angeles. The horizontal axis reports occupation-level exposure to immigration, as measured by the absolute value of x ro in (23). The vertical axis reports the change in wage by occupation for stayers (native-born workers who do not switch between occupations nor migrate between CZs in response to the shock) deflated by the change in 58 See Figure 12 of Appendix H. Without agglomeration externalities (λ = 0), the real wage of loweducation workers falls by 1 percentage point in Los Angeles, instead of 1.6 percentage points in our baseline. 39

41 Figure 4: 50% reduction in Latin American immigrants: change in domestic occupation wage (deflated by the price index) by occupation in Los Angeles, CA the absorption price index in Los Angeles. Even though real wages fall on average across occupations for natives in Los Angeles, reducing immigration from Latin America helps natives in the six most-exposed nontradable occupations. The difference between average and extreme real wage changes reflects large differences in real wage changes according to occupation-level exposure to immigration across nontradable occupations. The most-exposed nontradable occupation (private household services) sees wages rise by 7.7 percentage points more than the least-exposed nontradable occupation (firefighting). This difference in wage changes across nontradable jobs dwarfs variation in immigration impacts between CZs, which are aggregations of occupation-wage changes. n particular, our across-job, within-cz wage change is large relative to the difference in real wage changes across CZs for low-education natives and relative to the difference in changes in the education wage premium between the most-exposed CZ and the least-exposed CZ, seen in the left and right panels of Figure 3. The adjustment process across tradable occupations differs markedly from that across nontradables. n Figure 4, the most-exposed tradable occupation (textile-machine operators) sees real wages rise by just 2.8 percentage points more than the least-exposed tradable occupations (social scientists). The most-least difference for occupations in wage adjustment is thus 4.9 percentage points larger in nontradables than in tradables. n contrast to nontradables, the real wage falls for natives in all tradable occupations in Los Angeles, even the most immigrant-intensive ones. The patterns of wage adjustment by occupation that we describe are not specific to the Los Angeles commuting zone. To characterize changes in wages across occupations in all CZs, Figure 5 plots the difference in wage changes between the occupation that has the largest wage increase (or smallest wage decrease) and the occupation that has the smallest wage increase (or largest wage decrease), on the vertical axis, against overall CZ exposure to the immigration shock, on the horizontal axis. The left panel of Figure 5 reports comparisons among nontradable occupations, while the right panel reports comparisons for tradable occupations. Consistent with the case of Los Angeles in Figure 4, across CZs we see substantially more variation in wage adjustment across jobs within nontradables than across jobs within 40

42 Figure 5: 50% reduction in Latin American mmigrants: highest occupation wage increase minus lowest occupation wage increase across CZs tradables. 59 Moreover, variation in wage adjustment across occcupations in most CZs tends to be much larger than variation in real wages across CZs (displayed in Figure 3). Figure 6 depicts the spatial variation in the difference in wage changes between the occupation that has the largest wage increase and the occupation that has the smallest wage increase (or largest wage decrease) in nontradables across commuting zones. t shows a similar regional concentration of impacts as for real wage changes in Figure 2, though with an attenuated distance gradient as one moves away from the Southwest border and the coasts. 6.2 Doubling of High-Education mmigrants The intuition we have developed for differences in adjustment across occupations within nontradables versus within tradables rests on labor supply shocks varying across regions or on factor allocations across occupations varying across regions. f, on the other hand, all regions within a national or global economy are subject to similar aggregate labor supply shocks and if labor is allocated similarly across occupations in all regions, there is no functional difference between nontradable and tradable activities. Each locality simply replicates the aggregate economy. Because immigrants from Latin America concentrate in specific U.S. commuting zones and specialize in different occupations across these commuting zones, the immigration shock we modeled in the previous section represents far from a uniform change in labor supply across region-occupation pairs. Hence, the logic of adjustment to a local labor supply shock applies when projecting differences in labor market adjustment mechanisms in nontradable versus tradable activities. The experiment we consider in this section, an increase in highskilled immigration, is closer to a uniform increase in labor supplies across region-occupation pairs, owing to more similar occupation employment patterns for immigrants in this skill category. The consequence will be less differentiation in adjustment across occupations 59 For a given level of aggregate exposure to Latin American immigration (x axis in Figure 5) there is large variation across regions in the highest minus lowest occupation wage change (y axis) because occupation exposure varies across commuting zones. 41

43 Figure 6: 50% reduction in Latin American mmigrants: highest occupation wage increase minus lowest occupation wage increase for nontradable occupations across CZs within nontradables versus within tradables. 60 n this scenario, we double the number of immigrants with a college degree at the national s level, setting ˆN e = 2 for e = 3 (immigrants with a college education) from all sources s. As in the previous section there is large variation in aggregate exposure across regions in response to this shock with x r ranging from roughly 0 to a high of 0.34 in San Jose and taking a value of 0.16 in Los Angeles. However, unlike in the previous section, high-education immigrants tend to work in similar occupations across commuting zones. n response to an inflow of college-educated immigrants, average native low-education real wages rise in all locations, as seen in Figure 8 and the left panel of Figure 9, from as little as 0.3 percentage points in the least-exposed CZs, to 3.3 percentage points in Los Angeles, and to as much as 5.3 percentage points in San Jose. As in the previous exercise, this real wage impact arises both because of agglomeration effects and because native and immigrant workers are imperfect substitutes, so that increasing high-education immigrants raises native real wages. Now, however, the relatively even spatial distribution of the immigration shock produces a map of real wage changes in Figure 8, which displays no clear geographic pattern when compared to the more regionally concentrated Latin American immigration shock depicted in Figure 2. n the right panel of Figure 9, we see that in response to the increase in relative supply of more-educated immigrant labor, the education wage premium falls (and more so in CZs that are exposed to larger increases in skilled foreign labor). Consistent with 60 Even if all regions within the U.S. are identical, as long as there is trade between countries there will be a functional difference between tradable and nontradable occupations in terms of within-occupation adjustment to shocks. By abstracting away from trade with the rest of the world in our counterfactual exercises, we may understate differences between tradables and nontradables. 42

44 Figure 7: Doubling of high education immigrants: highest occupation wage increase minus lowest occupation wage increase for nontradable occupations across CZs Figure 8: Doubling of high education immigrants: change in the real wage of low-education native-born workers across CZs 43