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

Gordon Hanson

Lin Tian

Jonathan VogelUCLAUC San Diego

INSEAD

UCLA

October 2019

Abstract
In this paper, we study how occupation (or industry) tradability shapes local labormarket adjustment to immigration. Theoretically, we derive a simple condition underwhich the arrival of foreign-born labor into a region crowds native-born workers outof (or into) immigrant-intensive jobs, thus lowering (or raising) relative wages in theseoccupations, 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, wefind—consistent with our theory—that a local influx of immigrants crowds out employment of native-born workers in more relative to less immigrant-intensive nontradablejobs, but has no such effect across tradable occupations. Further analysis of occupationlabor 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, thereby confirming our model’s theoretical mechanism. We
then use the model to explore the quantitative consequences of counterfactual changes
in U.S. immigration on real wages at the occupation and 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 RossiHansberg for helpful comments. We thank the Russell Sage Foundation for financial support under Award
85-17-10. Hanson also acknowledges support from the Center on Global Transformation at UC San Diego.

1Introduction

How do the labor markets impacts of immigration differ across workers within an economy?
The literature has alternatively treated such impacts as varying at the national level according to a worker’s skill level (e.g., Borjas, 2003; Ottaviano and Peri, 2012), at the regional
level according to the attractiveness of a worker’s local labor market to arriving immigrants(e.g., Altonji and Card, 1991; Card, 2001), at the sectoral level depending on whether or
not a worker produces tradable manufactured goods or nontradable services (e.g., Dustmann
and Glitz, 2015), and at the occupational level depending on whether or not requirements
in a worker’s job (e.g., language, manual labor, math aptitude) are relatively favorable ordisfavorable to the foreign-born (Peri and Sparber, 2009; Hunt and Gauthier-Loiselle, 2010).
Although we now know that impacts vary by skill, region, sector, and occupation, we know
little about how effects across these dimensions interact to determine the employment andwage responses of native workers to an inflow of immigrants.
In this paper, we present theoretical analysis and empirical evidence showing how variation within regions in the tradability and foreign-labor-employment intensity of occupations,and across regions in the exposure to immigrant inflows, shape how immigration affects
native-born workers. To preview our approach, we consider the impact of an inflow offoreign-born labor in a U.S. region on employment and wages of U.S. native-born workers
across more relative to less immigrant-intensive occupations, and examine how adjustment
to labor inflows differs according to the tradability of occupations. 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 theoreticalcondition 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 findsupport for our model’s implications using cross-region and cross-occupation variation inchanges in labor allocations, total labor payments, and wages for the U.S. between 1980 and2012. Finally, we use our empirical estimates to calibrate our model in order to conduct
counterfactual exercises that quantitatively examine the impact of changes in immigration
on real wages both across occupations within regions and across regions.
Our model has three main ingredients. First, each occupation’s output is produced using
immigrant and native labor, where the two types of workers differ in their relative productivities across occupations and are imperfectly substitutable within occupations. Second,
heterogeneous workers select occupations (Roy, 1951), creating upward-sloping labor-supply
curves. 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. In thisframework, the response of occupational wages and employment to immigration is shapedby 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 theelasticity of local occupation output to local prices is low, the ratio of outputs across occupations is relatively insensitive to an inflow of immigrants. Factors reallocate away from
immigrant-intensive occupations, in which case foreign-born arrivals crowd the native-born
out of these lines of work. By contrast, low immigrant-native substitutability results in1

crowding in. Because factor proportions within occupations are insensitive to changes infactor supplies, market clearing requires that factors reallocate towards immigrant-intensive
jobs.1 In general, native-born workers are crowded out by an inflow of immigrants if andonly 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. Because each
occupation faces an upward-sloping labor-supply curve, crowding out (in) is accompanied bya 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. In response to immigration, the increase in output of immigrant-intensive occupations is larger and the reduction in price is smaller for
tradable than for nontradable tasks. The crowding-out effect of immigration on nativeborn workers is systematically weaker (or, equivalently, the crowding-in effect is stronger)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 tradables than within nontradables. Because these results on greater crowding out of natives byimmigrants within nontradables (compared to tradables) involve comparisons across native
workers within a region, they do not imply that native workers in immigrant-intensive jobs
within nontradables must lose from immigration.
We provide empirical support for the adjustment mechanisms 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). 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 Ipums over 1980 to 2012, we find that a local influxof immigrants crowds out employment of U.S. native-born workers in more relative to lessimmigrant-intensive occupations within nontradables, but has no such effect within tradables. 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 a larger increase in labor payments for immigrantintensive occupations in tradables when compared to nontradables, which is consistent withtradable occupations adjusting relatively more through changes in local output and nontradable occupations adjusting relatively more through changes in local prices. Analysis of wagechanges in response to immigration provides further support for our mechanism.
The empirical estimates guide parameterization of an extended version of our model,
which allows for geographic labor mobility (e.g., Borjas, 2006; Cadena and Kovak, 2016),
and relaxes restrictions (e.g., small open economy) used to obtain our analytic results. We
conduct counterfactual analyses to demonstrate numerically that our theoretical results arerobust to a range of generalizations and to evaluate how immigration affects regional wages
1

This is the classic Rybczynski (1955) effect, derived under fixed output prices, in which changes in factor
supplies draw native labor into expanding sectors and obviate the need for changes in wages. Empiricalevidence on this mechanism is mixed (Hanson and Slaughter, 2002; Gandal et al., 2004; and Gonzalez andOrtega, 2011). Foreign labor appears to be absorbed by within-industry rather than between-industry labor
reallocation (Card and Lewis, 2007; Lewis, 2011; and Dustmann and Glitz, 2015).

2and welfare both across occupations within regions and across regions. In one exercise, motivated by recent policy debates, we reduce the number 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 suchas Pittsburgh. More distinctively, for both education groups this shock raises wages fornative-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). Regarding welfare, reducing immigration lowers real wages for native-born workers
except in the most immigrant-intensive nontraded jobs in the most-exposed regions. In many
commuting zones, the within-CZ variation in wage changes across occupations dwarfs thevariation in average wage changes across CZs, which highlights the new sources of worker
exposure to immigration elucidated by our framework.
A second counterfactual exercise, in which we double high-skilled immigration, clarifies
how the geography of labor-supply shocks conditions labor-market adjustment. Because thespatial correlation of changes in occupation labor demand is higher in response to high-skill
immigration than in response to Latin American immigration, adjustment within tradables
more closely resembles adjustment within nontradables in the former case when comparedto the latter case. For the nontradable-tradable distinction in adjustment to be manifest,
regional labor markets must be differentially exposed to a particular shock.
The quantitative analysis also allows us to evaluate alternative explanations for our empirical result on greater immigrant crowding out of natives within tradables relative to within
nontradables. One is that crowding out occurs because immigrant-native substitution elasticities are higher in nontradable occupations than in tradables, rather than because the priceelasticity of output is lower in nontradables than in tradables. If we set the immigrant-native
substitution elasticity to be higher in nontradables than in tradables, there is stronger immigrant crowding-out within nontradables than within tradables but there are also counterfactual changes in total labor payments. Other explanations for stronger immigrant crowding
out within nontradables, such as relatively high factor adjustment costs or low supply elasticities in tradables, would have to confront the observation that over time employment shareschange by more across tradable jobs than across nontradable jobs.
Many scholars have considered how immigration and output tradability interact. Dustmann and Glitz (2015) find that in response to an influx of immigrants, native wages fall in
nontradables (non-manufacturing) but not in tradables (manufacturing); Peters (2017) findsthat manufacturing employment rises in regions that are more exposed to refugee inflows in
post-World War II Germany.2 While our analysis encompasses variation in impacts between
tradable and nontradable aggregates, this variation is orthogonal to the adjustments on which
we focus. Our theory implies that we should compare jobs within tradables—e.g., immigrantintensive 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.
In other work on immigration and trade, Ottaviano et al. (2013) examine a partial equi2

For contrasting results, see Hong and McLaren (2015).

3

librium model of a sector in which firms may hire native and immigrant labor domesticallyor offshore production. Freer immigration reduces offshoring and has theoretically ambiguous impacts on native sectoral 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.
In 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 or those with highimmigrant employment intensities. Industry case studies further support our framework’s
implications. A local influx of foreign labor crowds out native-born workers in immigrantintensive non-traded occupations, including manicurist services (Federman et al., 2006),
construction (Bratsberg and Raaum, 2012), and nursing (Cortes and Pan, 2014). While theseresults for nontradables appear to contradict the Ottaviano et al. (2013) finding of immigrantcrowding in of native workers for tradables, our theoretical model is fully consistent withstronger crowding in for tradables versus stronger crowding out for nontradables, thereby
rationalizing ostensibly discordant evidence on immigrant displacement of natives.
In related work on whether immigrant arrivals crowd out native-born workers on the job,
evidence of displacement effects is mixed (Peri and Sparber, 2011). While higher immigration occupations or regions do not in general have lower employment rates for native-bornworkers (Friedberg, 2001; 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. It is the
combination of immigrant intensity and nontradability that predisposes an occupation to
the crowding out of native labor by foreign labor.
Our analytic results on immigrant crowding out of native-born workers are parallel totheoretical insights on capital deepening in Acemoglu and Guerrieri (2008) and on offshoringin Grossman and Rossi-Hansberg (2008) and Acemoglu et al. (2015). The former paper, inaddressing 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 papers demonstratethat 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. Relative to these papers, we show that crowding out is weaker where local prices are less responsive
to local output changes, prove that differential output tradability creates differential local
price sensitivity, and provide empirical evidence consistent with these predictions.
Sections 2 and 3 present our benchmark model and comparative statics. Section 4 details
our empirical approach and results on the impact of immigration on the reallocation of nativeborn workers, changes in labor payments, 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.

4

2

Model

Our model 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, occupationaltasks are tradable, as in Grossman and Rossi-Hansberg (2008), and we incorporate variation
across occupations in tradability, which induces occupational variation in producer priceresponsiveness 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. Workers are either immigrant (i.e,foreign born) or domestic (i.e., native born), indexed by k = {I, D}. Workers are further
distinguished by their education level, indexed by e. Within each region there is a continuumof workers with a given education level, e, and nativity, k, indexed by ω ∈ Ωkre , each of whomkinelastically supplies one unit of labor. The measure of Ωkre is Nre. Each worker is employed3
in one of O occupations, indexed by o ∈ O.
Each region produces a non-traded final good combining the services of all occupations,
Yr =

X

1
η

µro (Yro )

η−1
η

η
! η−1

for all r,o∈O

where Yr is the absorption (and production) of the final good in region r, Yro is the absorptionof occupation o in region r, and η > 0 is the elasticity of substitution between occupationsin the production of the final good. The absorption of occupation o in region r is itself anaggregator of the services of occupation o across all origins,
Yro =

X

α−1
α

Yjro

α
! α−1

for all r, o,j∈Rwhere Yjro is the absorption within region r of region j’s output of occupation o and whereα > 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,
Qro = Aro

AIro LIro

 ρ−1
ρ

D
+ AD
ro Lro

ρ
 ρ−1
 ρ−1
ρ

for all r, o,(1)where Lkro is the efficiency units of type k workers employed in occupation o in region r;
Aro and Akro are the systematic components of productivity of all workers and of any type k
3

While we allow occupational choice to respond to immigration, we take worker education as given. See
Llull (2017) on how native education responds to immigration. Whereas in the model of this section the
supply of immigrant workers in a region is exogenous, in the empirical and quantitative analysis we allow it
to be endogenous; see Klein and Ventura (2009), Kennan (2013), di Giovanni et al. (2015), and Caliendo etal. (2017) for models of international migration based on cross-country wage differences.

5

worker, respectively, in this occupation and region; and ρ > 0 is the elasticity of substitution
between immigrant and domestic labor within each occupation.4
Let Ωkreo denote the set of type k workers with education e in region r employed inkand must satisfy the labor-market clearing condition
occupation o, which has measure Nreo
X
k
k
Nre
=
Nreo
.
o∈O
k
ε (ω, o) efficiency units of labor if employed in occupation
A worker ω ∈ Ωkre supplies Zreoko and region r, where Zreo denotes the systematic component of productivity and ε (ω, o)denotes the worker idiosyncratic component of productivity. The measure of efficiency unitsof type k workers with education e employed in occupation o within region r isZkk
ε (ω, o) dω for all r, e, o, k.
Lreo = Zreoω∈Ωkreo

Within each occupation, efficiency units of type k workers are perfect substitutes acrossworkers of all education levels.5 The measure of efficiency
P units of type k workers employedin occupation o within region r is thus given by Lkro = e Lkreo .
We assume that each ε (ω, o) is drawn independently from a Fréchet distribution withcumulative 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.6
The services of an occupation can be traded between regions subject to iceberg trade
costs, where τrjo ≥ 1 is the cost for shipments of occupation o from region r to region j
and we impose τrro = 1 for all regions r and occupations o. The quantity of occupation oproduced in region r must equal the sum of absorption (and trade costs) across destinations,Xτrjo Yrjo for all r, o.
(2)
Qro =
j∈R

We assume trade is balanced in each region, all markets are perfectly competitive, andlabor is freely mobile across occupations but immobile across regions (an assumption werelax in Section 5).
Four remarks regarding our approach are in order. First, our baseline model abstracts
from variation across occupations in the elasticity of substitution between immigrant anddomestic workers, ρ, which prevents such variation from being a source of differential adjustment to immigration within tradables as compared to within nontradables. In Section
4

All our analytic results hold if occupation production functions are instead common Cobb-Douglas
aggregators of our labor aggregate in (1) and a composite input.
5Because education groups specialize in different occupations, this assumption—similar to Llull(2017)—does not imply that immigration leaves the skill premium unchanged for native or immigrant workers. We examine changes in the skill premium in response to alternative changes in the relative supply of
immigrants in the counterfactual exercises presented in Section 6.
6
In 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), technological change and wage inequality (Burstein et al.,2016), and regional adjustment to trade shocks (Galle et al., 2015), among other topics in a rapidly expanding
literature. We assume a Fréchet distribution because it is convenient to derive our analytic comparative
statics and to parameterize the model in the presence of a large number (50) of occupations.

6

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. Second, the equilibrium conditions we derive are identical to those for a model 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 (see Appendix B).
In this alternative setting, the parameter ρ controls the extent of comparative advantage
between domestic and immigrant labor across tasks within occupations. Thus, while ourbaseline 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.7 Analogously, the trade elasticity in gravity models has alternative
micro-foundations (see, e.g., Arkolakis et al., 2012), which all generate similar aggregate
implications. Third, and by extension to the second remark, the equilibrium conditions wederive are identical to those for a model (e.g., Eaton and Kortum, 2002) in which occupation
output is produced using a continuum of varieties and regions’ outputs are perfect substitutes(up to a variety-specific productivity differential) within each variety. In this alternative setting, the parameter α controls the extent of comparative advantage across regions. Fourth,since we focus on long-run changes—1980 to 2012 in our empirics—we abstract from transition dynamics arising from costs to reallocating labor across occupations and (or) regions(e.g., Monras, 2015; Caliendo et al., 2017).

2.2

Equilibrium characterization

Final-good profit maximization in region r implies
 y −ηPro
Yr ,Yro = µro
Pr
where

(3)

1
! 1−η

Pr =

X

y 1−η
µro (Pro
)

(4)

o∈O
y
denotes the final good price, and where Pro
denotes the absorption price of occupation o inregion r. Optimal regional sourcing of occupation o in region j implies
−ατrjo Pro
Yrjo =
Yjo ,
(5)
y
Pjo

where

1
! 1−α

y
Pro
=

X

(τjro Pjo )1−α

,

(6)

j∈R
7
See Appendix C for a model in which imperfect substitutability between immigrant and native workers
at the occupation level emerges from imperfect substitutability between skilled and unskilled workers.

7and where Pjo denotes the output price of occupation o in region j. Equations (2), (3), and(5) implyX
y α−η
µjo (τrjo )1−α Pjo(Pj )η Yj .
(7)
Qro = (Pro )−αj∈RProfit maximization in the production of occupation o in region r implies

  1
1 
I
I 1−ρ
D
D 1−ρ 1−ρPro =Wro /Aro+ Wro /Aro
Aro
andLkro =

ρ−1
Aro Akro



k
Wro
Pro

(8)

−ρ
Qro ,

(9)

k
where Wrodenotes 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 and which we henceforthkrefer to as the occupation wage. A change in Wro
represents the change in the wage of a
type k and education e worker in region r who does not switch occupations (for fixed laborkdiffers from the average
efficiency units).8 Because of self-selection into occupations, Wrowage of type k workers with education e in region r who are employed in occupation o,
W agekreo . In Section 5.3 we use changes in average wages, W agekreo , across occupations toinfer indirectly how immigration affects (unobserved) occupation-level wages.
Worker ω ∈ Ωkre chooses to work in the occupation o that maximizes wage incomek k
Wro Zreo ε (ω, o). Idiosyncratic worker productivity implies that the share of type k workk
k
k
, is
/Nre
≡ Nreoers with education e who work in occupation o within region r, πreo


k θ+1
k
Wro
Zreo
k
πreo = P
 ,
k
k θ+1
Z
W
rej
rj
j∈O

(10)

k
. Total efficiency units supplied by workers in occupation o iswhich is increasing in Wro
θ
 θ+1
k
k
k
Lkreo = γZreo
πreo
Nre
,

where γ ≡ Γ

θ
θ−1



(11)

and Γ is the gamma function. Finally, trade balance impliesX

Pro Qro = Pr Yr for all r.

(12)

o∈O

 k
y
An equilibrium is a vector of prices {Pr , Pro , Pro},
wages
Wro , quantities produced and kconsumed {Yr , Yro , Yrjo , Qro }, and labor allocations Nreo
, Lkreo for all regions r, occupationso, worker types k, and education cells e that satisfy (3)-(12).
8Occupation switching by workers may mitigate the potentially negative impact of immigration on wages(Peri and Sparber, 2009). The envelope condition implies that given changes in occupation wages, this occuk
pation switching has no first-order effects on changes in individual wages, which solve maxo Wro× ε (ω, o) .
Because this holds for all workers, it also holds for the average wage across workers.

83Comparative statics

We next derive analytic results for the effects of infinitesimal changes in regional immigrantDI, and region × occupation productivity, Aro , on
and Nreand native labor supplies, Nreoccupation labor payments as well as factor allocations and occupation wages.9 We derive
our analytic results in a simplified version of our model. In Section 3.1 we describe model
restrictions and their implications. In Section 3.2 we hold regional labor supplies of natives
as well as region-occupation productivities fixed. In Section 3.3 we generalize these resultsby allowing native labor supplies and region-occupation productivities to change. Lowercase characters, x, denote the logarithmic change of any variable X relative to its initialk). Derivations and proofs are in Appendix A.
equilibrium level (e.g., nkre ≡ ∆ ln Nre

3.1

Restrictions imposed in analytics

To build intuition, we focus on a special case of the model that satisfies three restrictions.
First, we assume that each region operates as a small open economy. Second, we group occupations into sets in which they are equally traded. Third, we assume that distinct educationgroups within each worker nationality type (k = D, I) differ only in their absolute productivities (rather than in their relative productivities across occupations). Our quantitative
analysis in Section 5 dispenses with these restrictions.
Small open economy. We assume region r is a small open economy, in that it constitutes
a negligible share of exports and absorption in each occupation for each region j 6= r. This
assumption implies that, in response to a region r shock, prices and output elsewhere areunaffected: pyjo = pjo = pj = yj = 0 for all j 6= r and o. It does not imply that region r’s
producer prices are fixed. The log derivative of equation (6) is thusmpyro = (1 − Sro) promwhere Srodenotes region r’s share of imports in occupation absorption. Similarly, the log
derivative of equation (7) isxx
qro = −αpro + (1 − Sro) (α − η) pyro + (1 − Sro) (ηpr + yr )xxwhere Sro
≡ 1 − Srro
denotes region r’s share of exports in occupation output. Combining
these equations, we obtainx) (ηpr + yr )qro = −ro pro + (1 − Srowhere ro represents the the partial elasticity of demand for region r’s occupation o output
to its output price and is given byxmxmro = (1 − (1 − Sro) (1 − Sro)) α + (1 − Sro) (1 − Sro
) η.

(13)

ro is a weighted average of the elasticity of substitution across occupations, η, and theelasticity across origins, α > η, where the weight on the latter is increasing in the extent to
9Changes in productivity, Aro , are isomorphic to changes in demand, µro .

9which the services of occupation o are traded, as measured by the region r share of exports inxmoccupation output (Sro) and share of imports in occupation absorption (Sro). For occupationmx
o with infinite trade costs, Sro = Sro = 0, so that ro = η. More traded occupations—withmx—feature higher elasticities of demand for regional output toand Srohigher values of Sroprice (and lower sensitivities of regional price to output).10
Grouping occupations by trade shares. We assume that occupations are grouped into
sets, g = {T, N }, where region r’s export share of occupation output and import share ofoccupation absorption are common across all occupations in set g. N is the set of occupations
that produce nontraded services and T is the set of occupations that produce traded services,where all we require is that the latter is more tradable than the former. Because the export
share of occupation output and the import share of occupation absorption are assumed
common across occupations in g in region r, the elasticity of regional output to the regional
producer price, ro , is common across occupations in g. We denote by rg the elasticity ofregional output to the regional producer price for all o ∈ g, for g = {T, N }.11
Restricting comparative advantage. Finally, we assume that education groups withinkkeach k differ only in their absolute productivities, Zreo
= Zre
. This assumption implies thatkk
education groups within k are allocated identically across occupations: πreo
= πro
for
e.
 all
k
In this case, the vector of changes in labor supplies by education level in region r, nre e ,can be summarized by a single sufficient statistic,
nkr ≡

X Sk

reo

e

k
Sro

nkre ,(14)

with weights given by the share of labor income in region r and occupation o accruing to typek k
kk labor with education e, Sreo
≡ P WroWLkreo
0 k0 , relative to the share of labor income in region00ro Lre0 o
e ,k
P k
k
r and occupation o accruing to all type k labor, Sro= e Sreo. The right hand side of (14)kkkkdoes not vary across occupations because πreo
= πroimplies that Sreo
/Srois common acrossIo. Sro is the immigrant cost share in occupation o output in region r, which varies acrossoccupations within a region according to the Ricardian comparative advantage of immigrantI
and native workers across occupations within a region. From the definition of Sroand the
k
k
I
I
I
I
D
D
assumption that Zreo = Zre , we have that Sro ≥ Sro0 if and only if πro /πro0 ≥ πro /πro0 . Along I ρ−1  AI ρ−1
Aro
II
≥ ADro0
with (10), this implies Sro≥ Sro.
0 if and only if
AD
ro

3.2

ro0

Changes in immigrant labor supplyWe I now study the impact of infinitesimal changes in regional immigrant labor supplies,
nre e , on labor payments, factor allocations, and occupation wages across occupations
10

In Appendix A.3, we show that the absolute value of the partial own labor demand elasticity at theregion-occupation level is increasing in ro (consistent with Hicks-Marshall’s rules of derived demand) and,
therefore, trade shares, a result related to findings in Rodrik (1997) and Slaughter (2001).
11
Our results hold with an arbitrary number of sets. In the empirical analysis (see Appendix E), 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).

10within each group g.12 To focus on the implications of nIre , in this section we hold nativelabor supply and region-occupation productivities fixed; we study the impacts of changes innative labor supply and region-occupation productivity in Section 3.3.
revenues, Pro Qro , are equal to occupation labor payments, denoted by LPro ≡P Occupationkkke W agereo Nreo . We focus on labor payments because they are easier to measure in practicethanlabor supplies,
 I occupation quantities and prices. Infinitesimal changes in immigrant
nre e , generate differential changes in labor payments for any o, o0 ∈ g that are given by
lpro − lpro0 = I I(rg − 1) (θ + ρ) I
I
Sro − Sro0 nr Φ r ,θ + rg

(15)

 I
D
I
where ΦIr = wro− wro
nr denotes the elasticity of domestic relative to immigrant occupation wages (which are common across occupations in equilibrium under the assumptionkkthat Zreo= Zre) with respect to the supply of immigrants.13 We do not provide an explicit
I
solution for Φr ; rather, we assume that parameter values guarantee that the following law
of demand is satisfied: all else equal, an increase in immigrant labor supply, nIr ≥ 0, raises
the occupation wage of natives relative to the occupation wage of immigrants, ΦIr ≥ 0.14
Consider two occupations o, o0 ∈ g, where occupation o is immigrant intensive relative
I
I
> Sro
to o0 (i.e., Sro0 ). According to (15), an increase in the supply of immigrant workers inIregion r, nr > 0, increases labor payments in occupation o relative to o0 if and only if rg > 1.
Intuitively, an inflow of immigrants, nIr > 0, raises relative output and lowers relative prices
of immigrant-intensive occupations within g (i.e., within tradables or within nontradables).
A higher value of the elasticity of demand for region r’s occupation o output to its price, rg ,increases the size of relative output changes and decreases the size of relative price changes.
In response to an inflow of immigrants, nIr > 0, a higher value of rg therefore generates
a larger increase (or smaller decrease if rg < 1) in labor payments of immigrant-intensive
occupations. Because rT > rN , relative labor payments to immigrant-intensive occupations
increase relatively more within T than within N in response I to an inflow of immigrants.
Infinitesimal changes in immigrant labor supplies, nre e , generate differential changes
in labor allocations in occupations that are given by
nkreo − nkreo0 = I I(θ + 1) (rg − ρ) I
I
Sro − Sro0 nr Φ r ,θ + rg(16)

and changes in occupation wages that are given by
k
k
wro
− wro
0 =

 I I
rg − ρ I
I
Sro − Sro0 nr Φrθ + rg(17)k
Up to a first-order approximation, wro
is equal to the change in average income of workers who were
employed in occupation o in the initial equilibrium.
13
As shown in Appendix A, we obtain (15) as follows. We combine the results described above thatxDI
qro = −ro pro P+ (1 − Sro) (ηpr + yr ) and wro− wro= nIr ΦIr with the log derivatives of occupational

k k
D
I
D
I
output, qro =k Sro lro , and the profit maximization condition, lro − lro = −ρ wro − wro , to obtain
ρ
1 D
1
x
I I I
(1 − Sro) (ηpr + yr ) − roSronr Φr − rol . Combining the previous expression with the derivativepro = ro
P ro

k
k
k
k
k
of the labor supply equations, lro= θwro−θj∈O πrj wrj + nr , and the log derivative of the occupation

I
D
I
I
price, pro = 1 − Sro
wro
+ Sro
wro
, we obtain (15).
14
In Appendix A.4 we prove that ΦIr ≥ 0 if all occupations have common export and import shares.
12

11

for any o, o0 ∈ g and k ∈ {D, I}, where nIr is given by (14).15 By (16) and (17), an increase
immigrant labor supply, nIr > 0, decreases relative employment of type k workers and (forfinite θ) occupation wages in relatively immigrant-intensive occupations within g if and only
if rg < ρ. If rg < ρ, we have crowding out: an immigrant influx in r reallocates factors
away from immigrant-intensive occupations within g; if rg > ρ, we have crowding in: an
immigrant influx reallocates factors toward immigrant-intensive occupations within g.16
Because rT > rN , we can compare the differential employment response of more to lessimmigrant-intensive occupations in T and N : within T , immigration causes less crowdingout of (or more crowding into) occupations that are more immigrant intensive (comparedto the effect within N ). Similarly, because rT > rN , we can compare the differential
wage response of more to less immigrant-intensive occupations in T and N : within tradedoccupations 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 ). We next provide intuition for these results.
Labor reallocation between occupations within N or within T is governed by the extent
to which immigration is accommodated by expanding production of immigrant-intensive
occupations (rg ) or by substituting away from native towards immigrant workers withineach occupation (ρ). Consider two special cases. First, in the limit as rg → 0, output
ratios across occupations are fixed. To accommodate an increase in immigrant labor supply
requires increasing the share of each factor employed in domestic-labor-intensive occupations(while making each occupation more immigrant intensive). With immigration, immigrants
crowd out natives. Second, in the limit as ρ → 0, factor intensities within each occupation
are fixed. To accommodate immigration, the share of each factor employed in immigrantintensive occupations must rise (while the production of immigrant-intensive occupations
increases disproportionately). Now, immigration induces crowding in. More generally, alower value of rg − ρ generates more crowding out of (or less crowding into) immigrantlabor-intensive occupations in response to an increase in regional immigrant labor supply.
Consider next changes in relative occupation wages within N or within T . If θ → ∞,then all workers within each k and e are identical and indifferent between employment
in any occupation. In this knife-edge case, labor reallocates across occupations without
corresponding changes in relative occupation wages within k and e. The restriction that
θ → ∞ thus precludes studying the impact of immigration (or any other shock) on therelative 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 acrossoccupations. It is these changes in occupation wages that induce labor reallocation: in order
to induce workers to switch from occupation o to o0 , the occupation wage must increase in o0
relative to o, as shown in (17). Hence, factor reallocation translates directly into changes in
occupation wages. Specifically, if occupation o0 is immigrant intensive relative to occupationII
0o, Sro0 > Sro , and o, o ∈ g, then an increase in the relative supply of immigrant laborIin region r, nr > 0, decreases the occupation wage for domestic and immigrant labor in
occupation o0 relative to occupation o if and only if rg < ρ.
We emphasize that these analytic results apply to relative comparisons of occupations
15
16

These results follow similar steps to those outlined in Footnote 13.
See Appendix A.5 for results where education groups differ in relative productivities across occupations.

12within tradables and within nontradables. The quantitative analysis of Sections 5 and 6
allows us to evaluate the absolute impact on real wages and thereby fully characterize thelabor market consequences of immigrant inflows.

3.3

Changes in all labor supplies and occupation productivities

We now extend the analysis of Section 3.2 to allow native labor supply and occupation
productivity to vary along with immigrant labor supply. In the empirical analysis, we mustaccount for the presence of multiple shocks to region-occupation labor-market outcomes.
By generalizing equations (15), (16), and (17), the analysis will help guide our empirical
specification—in particular, by motivating the fixed-effects structure that we allow for in theestimation and by clarifying the exclusion restrictions required for identification—and willfurther demonstrate that our insights regarding the differential impacts within more and lesstraded sectors of an immigration shock apply equally well to other shocks.
Proposition 1. Infinitesimal changes in immigrant and native labor supplies (nkre ) andregion-occupation productivities (aro ), generate differential changes in labor payments (lpro ),k) for any o, o0 ∈ g andfactor allocations (nkreo ), and wages per efficiency unit of labor (wrok ∈ {D, I} that are given by (rg − 1) (θ + 1)
(rg − 1) (θ + ρ)IIw̃r Sro(aro − aro0 )
− Sro
+
0
rg + θrg + θ (rg − 1) (θ + 1)
(rg − ρ) (θ + 1)
II
nkreo − nkreo0 =w̃r Sro− Sro+(aro − aro0 )0rg + θrg + θ (rg − 1)
(rg − ρ)IIkkw̃r Sro− Sro(aro − aro0 ) ,
wro
− wro
+
0 =
0
rg + θrg + θlpro − lpro0 =

(18)
(19)
(20)

where
D
I
D
w̃r ≡ wro− wro
= ΦIr nIr + ΦD
r nr +XΦA
ro aro(21)

ois the change in the relative occupation wage for natives relative to immigrants, which isA
common across occupations; ΦIr , ΦDr , and Φro are the elasticities of this relative occupationkwage to the three types of shocks; and nr is defined in (14).
Analogous to the previous section, we do not explicitly solve for the change in relative
wages per efficiency unit, w̃r , and we assume that parameter values satisfy the law of demand:an increase in immigrant labor supply, nIr ≥ 0, or a decrease in native labor supply, nDr ≤ 0,
17
raises the relative occupation wage of natives, ΦIr ≥ 0 and ΦD≤0.
r
While our focus is on the differential impact of immigration on outcomes within moreversus less tradable occupational groups, our insights apply equally to the differential impactof native migration and region and occupation-specific changes in productivity. All else
equal, a decrease in the effective supply of native labor in region r, where nD
r is given byequation (14), has the same qualitative effects—on labor payments, factor allocations, andIn Appendix A.4 we prove that ΦIr = −ΦDr ≥ 0 if all occupations share common export and importshares (i.e. if there is a single g).
17

13

occupation wages—as an increase in the effective supply of immigrant labor, since the change
in the relative occupation wage of natives to immigrants, w̃r , is a sufficient condition for eachoutcome. Given w̃r , an increase in the relative productivity of occupation o within group gincreases occupation o labor payments, the share of factor k allocated to occupation o, andthe occupation o wage if and only if rg > 1, and these effects are stronger the higher is rg
if rg > 1. Changes in productivity may also affect outcomes indirectly through w̃r .18

4

Empirical Analysis

Guided by our theoretical model, we study the impact of immigration on labor market
outcomes at the occupation level in U.S. regional economies. We begin by using our analyticalresults on labor market adjustment to immigration to specify our estimating equation. These
results treat changes in productivity and in immigrant and native labor supplies as exogenous.
In practice, these changes may be jointly determined. 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. Although our analytical results predict how
occupational labor allocations, labor payments, and wages adjust to immigration, measuringchanges in occupation-level wages, as discussed in Section 2.2, is not straightforward becausechanges in observable wages reflect both changes in the occupation wage per efficiency unitof labor and self-selection of workers across occupations according to unobserved worker
productivity. Accordingly, we analyze immigration impacts on occupational labor allocations
and labor payments in this section and address wage changes in our quantitative exercises.

4.1

Specifications for Labor Allocations and Labor Payments

Combining (19) and (21), in Appendix A.3 we derive the following specification for changes
in the allocation of native workers in education cell e to occupation o—given at least two
occupations in each group g ∈ {T, N }—within region r:
D
D
D
D
nD
reo = ςrg ao + αreg + βr xro + βN r Io (N )xro + νro ,(22)

where we have decomposed the region-occupation productivity shock as aro ≡ ao + arg + ãro ,with ao the national-occupation component of the productivity shock, arg the region andoccupation-group-specific component of the shock, and ãro the region-occupation-specificDcomponent of the shock; ςrg , βrD , and βNr are region and group-specific treatment effects,
which are functions of model parameters; xro is the model-defined immigration shock; Io (N )Dequals one if occupation o is nontradable; αreg
is a function of model parameters that doesD
not vary across o; and νro is a structural residual. Specifically, the immigration shock
X
I
xro ≡
Sreo
nIre
(23)
e


summarizes how region and education-specific changes in immigration, nIre e , are transmitted to occupation o in region r via the initial immigrant intensity of ro in each education
D
I
In Appendix A.4 we show that ΦAro > 0 if and only if (πro − πro )r > 1 under the assumption that all
occupations share common export and import shares.
18

14

I
cell, Sreo
. The treatment effect of xro for tradable occupations in (22) isβrD =(rT − ρ) (θ + 1) I
Φr
rT + θwhich is negative, implying crowding out of natives by immigrants, if the substitutabilityof immigrant and native labor is large relative to the sensitivity of regional output to price(rT < ρ).19 The treatment effect for T differs from that for N by the term,
D
βN
r =

(θ + ρ) (θ + 1)
(rN − rT ) ΦIr(rN + θ) (rT + θ)

which is negative, implying stronger crowding out in nontradables relative to tradables,
since the sensitivity of regional output to price is greater for T than for N (rN < rT ). The
treatment effect of the national-occupation component of the productivity shock, ao , isςrg ≡(rg − 1) (θ + 1).
rg + θFinally, the structural residual isDνro≡ (rg − 1) (θ + 1)
(rg − ρ) (θ + 1) I
DSro ΦDãro ,
r n r + ar +
rg + θrg + θP
where ar ≡ o ΦAro aro is a weighted sum of region-occupation productivity shocks.
To simplify the estimation, we specify the regression equation,
D
D
D
D
D
nD
reo = αreg + αo + β xro + βN Io (N )xro + ν̃ro(24)

in which we impose regional homogeneity for the treatment effects in (22), which in turnDthat adds
changes the interpretation of the coefficients and generates a modified residual ν̃roD
to νro specification error generated by these parameter restrictions. By imposing uniformity
D
across regions for these coefficients in (24), β D and β D + βN
represent average treatment
effects for the immigration shock on native allocations. Because we estimate (24) separately
for low- and high-education labor allocations, we effectively allow the occupation fixed effect,D
αoD , and the treatment effects, β D and β D + βN
, to differ by education level.20
Our empirical exercise does not directly recover a combination of structural parameters
for two reasons. First, we transform (22) to (24) by estimating an average treatment effectacross regions. Second, (22) was derived under the assumption that education groups withinIeach k differ only in their absolute productivities, which implies that xro Srodoes not varyacross o. In practice, we construct xro without imposing this restriction. Our theoreticalD
model implies the sign restriction that β D > β D + βN
, which we test for explicitly. In thequantitative analysis, we use the estimated coefficients from (24) to discipline the calibrationof the structural parameters of an extended model.
As in the previous section, we assume that the law of demand holds, such that ΦIr > 0.
As we discuss in Appendix H, a logic similar to that underlying (24) applies to how an immigrant inflow
affects the allocation of foreign-born workers across occupations. In Appendix H, we present results on theimmigrant-employment allocation regressions that are the counterparts to (24) and Table 1 below.
19

20

15

Because regional shocks to occupation productivity and native labor supply are in theresidual in (24)—and do not enter the specification directly as regressors—the coefficientsthat we estimate on xro will capture not just the direct effect of immigration on nativelabor allocations but also any indirect effects of this immigration shock through its effecton the supply of native workers or the productivity of specific occupations at the regional
level.21 If, for instance, immigration induces regional migration of natives—a possibility
that our quantitative model in Section 5 accommodates explicitly—then the total effect of
the immigration shock on native allocations that we estimate in (24) may differ from thetheoretically defined partial effect in Proposition 1. Nevertheless, as long as a version of
the law of demand holds—i.e., accounting for the responses of productivity and native labor
supplies, an increase in immigrant supply raises the relative occupation wage of natives—ourresults that there is crowding out in g if and only if rg < ρ and that there is more crowding
out within N occupations than within T occupations still hold.
More pertinent to identifying the labor market impacts of immigration, immigrant inflows
for region r, nIr , may result from the endogenous location response of immigrants to regional
productivity or amenity shocks or to native labor supply. If this was the case, our estimatesD
would reflect not just our theoretically specified impact of immigration onof β D and βN
native allocations but also the direct effect of these regional shocks on native allocations.22
Estimating (24) therefore requires an instrumentation strategy to isolate variation in xro thatis orthogonal to the components of regional changes in native labor supply and occupation
productivities that are not themselves caused by immigrant inflows.
Based on a similar motivation to that underlying equation (24), we specify an expression
for changes in occupation labor payments,D
lpro = αrg+ ςrg ao + γxro + γN Io (N ) xro + ν̃ro ,(25)

in which we again estimate average treatment effects, γ and γN , for the immigration shock
xro . Following Proposition 1, the treatment effect for tradables γ will be positive if thesensitivity of regional output to price exceeds unity (rT > 1) and the differential treatment
effect for nontradables γN will be negative since the sensitivity of regional output to price isgreater for tradables than for nontradables (rN < rT ). Analogous to the above discussion,
identifying the impact of xro on labor payments requires an instrumentation strategy.
In the regression in (24), we 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. In the regression in (25), we estimate whether immigrant flows into a
region induce on average an increase or decrease in labor payments in relatively immigrantintensive occupations separately within tradables and within nontradables. This allows us toassess the mechanism in our model that generates differential crowding out within N and T
21

See, e.g., Borjas (2006) on the response of native outmigration to immigrant inflows. Other work suggeststhat inflows of foreign labor lead to higher land rents (Saiz, 2007), local agglomeration externalities (Kerrand Lincoln, 2010), and weaker incentives for firms to adopt labor-saving technologies (Lewis, 2011). Suchadjustments in costs and productivity appear to disproportionately affect manufacturing (Peters, 2017).
22
See, e.g., Cadena and Kovak (2016) on the responsiveness of immigration to local labor demand shocks.

16

occupations, which is that quantities are more responsive and prices less responsive to local
factor supply shocks in tradable than nontradable activities.

4.2

An instrumental variables approach

The immigration shock in (23) is a function of the inflows of immigrants in region r withineach education cell e, nIre , and the initial intensity of region-occupation ro in the employment
I. The residuals in turn contain the region-occupationof immigrants with education e, Sreo
specific productivity shock, ãro , and the interaction of region-occupation immigrant employment intensities with the average regional productivity shock, ar , and the regional nativelabor supply shock, nD
r . Endogeneity could arise from two sources: a correlation between
regional productivity or native labor supply shocks playing a role in determining the contemporaneous inflow of immigrants to a region, and (or) region-occupation productivity shocks
being a function of initial region-occupation immigrant employment intensities.
To construct an instrument for xro , we exploit the fact that nIre is the result of inflowsof immigrants from multiple source countries c. We leave unmodeled the cause of migrant
outflows from these countries. Inspired by literature on migration networks (e.g., Munshi,
2003), we allocate these aggregate inflows across regions according to historical settlement
patterns, as summarized in the identifying restrictions that we discuss below.
Following Altonji and Card (1991) and Card (2001), we instrument for xro usingx∗ro ≡

X
e

I
Sreo

I∗
∆Nre
I
Nre

I∗
where ∆Nreis a variant of the standard Card instrument that accounts for education-groupand region-specific immigration shocks,
X
I∗
Ic
−r
∆Nre
≡
fre
∆Nec
.
c
−r
Ic
Here, ∆Nec
is as defined above and fre
is the share of immigrants from source c witheducation e who lived in region r in the initial (or some earlier) period.23 Combining thetwo previous expressions, we obtainx∗ro ≡X X S I f Icec

reo re
−r
∆Nec
I
Nre

(26)

D
where x∗ro is a valid instrument in regressions (24) and (25) if it is uncorrelated with ν̃roand
ν̃ro , respectively.
A recent literature—Adao et al. (2018), Borusyak et al. (2018), and Goldsmith-Pinkham
et al. (2018)—explores identification and inference using shift-share instruments taking theform of (26). This literature formally specifies the data generating process that is responsible either for the “shifters” or the “shares” and argues that identification is obtained if either
23

In our extended model in Section 5, we introduce immigrant source countries so as to construct thesame instrument and run the same 2SLS regression on model-generated data to calibrate the model. Thisextension does not impact our analytic results yet does burden the notation.

17

the shifters or the shares are as good as randomly assigned. In our case, the shifters are
−r
I
Ic
I
given by ∆Nec
and the shares are given by Sreo
fre
/Nre
. For example, a sufficient set of
restrictions under which our instrument is valid is: (i) the predicted inflow of immigrants,I∗, is uncorrelated with the change in the supply of natives in r not induced by immigra∆NreI∗tion, (ii) the predicted inflow of immigrants, ∆Nre
, is also uncorrelated with the weighted
region productivity shock not induced by immigration, and (iii) the initial region-occupationI
immigrant employment intensity for each education cell e, Sreo
, is uncorrelated with theregion-occupation-specific productivity shock, ãro . Restrictions (i) and (ii)—which rule out
Dthat vary in thecorrelation between the components of x∗ro and of the structural residual νroIr dimension (and are interacted with Sreo ) and are not themselves functions of x∗ro —are likely
to hold if each region r is small in the sense that its specific shocks do not affect aggregate
immigration inflows across other regions and if the historical attraction of immigrants toIcparticular regions is due to pre-existing migration networks (i.e., fre
is not a function of recent shocks to native migration or regional productivity that persist into the current period).
D
Restriction (iii), which rules out correlation between the components of x∗ro and νrothat varyin the ro dimension, holds if deviations in region-occupation productivity—from the national
average within the occupation and the regional average within the occupation group—are
I 24.
not a function of past immigrant employment intensities across occupations, Sreo
In extended results, we examine the robustness of our results to dropping the largest
immigrant-receiving regions from the sample (which account for a substantial fraction of
immigrant inflows and whose shocks could plausibly affect immigration in the aggregate).
We also check whether current immigration shocks are correlated with past changes in labormarket outcomes to evaluate whether our results may be a byproduct of persistent regional
employment trends. Given the possibility that current immigration shocks are correlatedwith persistent regional employment trends, we also consider a modified Card instrumentin which we replace initial immigrant employment intensities for education cell e in regionoccupation ro with occupation-education immigrant employment intensities averaged over a
set of regions other than r and outside of r’s state, which creates the value,x∗ro ≡

X
e

I
S−reo

I∗
∆Nre
.
I
Nre

(27)

The alternative instrument in (27) helps address a well-known critique of the Card instrument
regarding the persistence of regional labor-demand shocks (Borjas et al., 1997).

4.3

Data

In our baseline analysis, we study changes in labor-market outcomes between 1980 and 2012.
In sensitivity analysis, we use 1990 and 2007 as alternative start and end years, respectively.
All data, except for occupation tradability, come from the Integrated Public Use Micro
Samples (Ipums; Ruggles et al., 2015). For 1980 and 1990, we use 5% Census samples; for2012, we use the combined 2011, 2012, and 2013 1% American Community Survey samples.
Our sample includes individuals who were between ages 16 and 64 in the year preceding
24
The three-decade period of our analysis helps address concerns that results based on the Card instrument
may conflate short-run and long-run impacts of immigration (Jaeger et al., 2018).

18

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). Each CZ is a clusterof counties characterized by strong commuting ties within and weak commuting ties acrosszones. There are 722 CZs in the mainland US.
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 arethose with a college degree (or four years of college) or more, whereas low-education workers
are those without a college degree. Although these education groups may seem rather aggregate, 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).25 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.
The aggregate share of immigrants in hours worked in our sample rises from 6.6% in 1980 to
16.8% in 2012.26 We construct the occupation-and-CZ-specific immigration shock in (24) and(25), xro , 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 thensummed over education groups. In constructing xro and its instrument, x∗ro , shown in (26),
we use three education groups; for the instrument we use 12 source regions for immigrants.27
Our baseline data include 50 occupations (see Table 5 in Appendix D).28 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 beoffshored.29 We group occupations into more and less tradable categories using the median25

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 educationor less tend to work in similar occupations, the some-college group may seem overly skilled for this category.
Results are similar if we shift some-college workers from the low-education to the high-education group.
26
Because we use data from the Census and ACS (which seek to be representative of the entire resident
population), 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 whoarrived in the U.S. as children (and attended U.S. schools) and those who arrived in the U.S. as adults. Our
results (in unreported analysis) are substantially unchanged using an alternative definition of immigrant
status in which we exclude foreign-born individuals who moved to the U.S. before the age of 18.
27
The education groups are less than a high-school education, high-school graduates and those with somecollege education, and college graduates. Relative to native-born workers, we create a third education category of less-than-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 SouthAmerica, China, Eastern Europe and Russia, India, Mexico, East Asia (excluding China), Middle East andSouth and Southeast Asia (excluding India), Oceania, Western Europe, and all other countries.
28
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 (http://www.ddorn.net/) and to combine small
occupations that are similar in education profile and tradability but whose size complicates measurement.
29
Goos et al. (2014) provide evidence supporting this measure. Their index of actual offshoring by occu-

19

so that there are 25 tradable and 25 nontradable entries (see Table 6 in Appendix D). 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.
In Table 7 in Appendix D, we compare the characteristics of workers employed in tradable and nontradable occupations. Whereas the two groups are similar in terms of theshares of employment of workers with a college education, by age and racial group, andin communication-intensive occupations (see, e.g., Peri and Sparber, 2009), tradable occupations do have relatively high shares of employment of male workers and workers inroutine- and abstract-reasoning-intensive jobs. High male and routine-task intensity arise
because tradable occupations are overrepresented in manufacturing. In 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 technologicalchange 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 toimmigration shocks (Peri and Sparber, 2009). In further checks, we use industries in placeof occupations, categorizing tradable industries to include agriculture, manufacturing, andmining, and nontradable industries to include services.
In Table 7 in Appendix D, we show that the national shares of immigrants in employment for nontradable and tradable occupations are similar, both in 1980 and in 2012. These
aggregates mask heterogeneity in two dimensions. First, the share of immigrants in total
employment varies widely across regions; see Figure 9 in Appendix D. For example, in 2012
the share of immigrants in total employment is highest in Miami, San Jose, and Yuma.
Second, within regions there is heterogeneity in immigrant cost shares across occupations,both within tradable and within nontradable jobs; see Figures 10 and 11, and Table 11 inAppendix D. For example, in Los Angeles in 2012, immigrant intensity among tradable
occupations is highest for textile machine operators, printing machine operators, and othermachine operators. Among nontradable occupations, immigrant intensity in 2012 is highest
among housekeeping, agricultural workers, cleaning and building services, and food preparation services. This variation in exposure to immigration across regions and occupations is
at the core of our empirical and quantitative analysis.
Finally, to provide context for our analysis of adjustment to immigration across occupations within tradables versus within nontradables in the estimation of (24) and (25), we
compare over our 1980 to 2012 time period the unconditional changes in employment sharesacross 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.30
Although these unconditional changes do not account for differences in the magnitude ofshocks affecting occupations in the two groups, the higher variability of employment changes
pation based on the European Restructuring Monitor is strongly and positively correlated with the BlinderKrueger measure. Given limited data on intra-country trade flows in occupation services, we use measuresof offshorability at the national level to capture tradability at the regional level, a correspondence which isimperfect. Our results are robust to using alternative cutoffs regarding which occupations are assigned to T
versus assigned to N and to defining tradability at the industry rather than occupation level.
30
If 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.

20

within T when compared to within N suggests that overall adjustment is no less sluggish
among tradable jobs than among nontradable jobs.31

4.4

Empirical Results on Labor Allocations and Labor Payments

In the specification for the allocation of native-born workers across occupations within CZs in(24), the dependent variable is the log change in CZ employment of native-born workers for an
education cell in an occupation and the independent variables are the CZ immigration shockto the occupation, shown in (23), this value interacted with a dummy for the occupation being
nontraded, and dummies for the occupation and CZ-occupation group. The regressions,which we run separately for low-education and high-education workers, are weighted by the
initial number of native-born workers in the education cell employed in the occupation in
the CZ; standard errors are clustered by state. We instrument for the immigration shockusing the value in (26), where we disaggregate the sum in specifying the instrument, suchthat we have three instruments per endogenous variable; we report Angrist and Pischke(2008) F-statistics for first-stage regressions with multiple endogenous variables. Table 1
presents results for equation (24). In the upper panel, we exclude the interaction term forthe immigration shock and the nontraded dummy, such that we estimate a common impact
coefficient across all occupations; in the lower panel we incorporate this interaction andallow xro to have differential effects across occupations within T and within N . For loweducation workers, column (1a) reports OLS results, column (2a) reports 2SLS results, andcolumn (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. In the upper panel,
all coefficients are negative: on average the arrival of immigrant workers in a CZ crowds out
native-born workers at the education-occupation level. The impact coefficient on xro is larger
in absolute value for high-education workers than for low-education workers, suggesting that
crowding out is stronger for the more-skilled. Referring to our analytic model, these results
are consistent with immigrant-native substitutability ρ being large relative to occupationoutput sensitivity to price rg (averaged across r and g).
In the lower panel of Table 1, we add the interaction between the immigration shock andthe nontradable indicator, as in (24), to allow for differences in crowding out within T andwithin N . The two groups are clearly delineated. In tradables, the 2SLS impact coefficient isclose to zero (0.002 for low-education workers, −0.03 for high-education workers) with narrowconfidence intervals. The arrival of immigrant workers crowds native-born workers neither
out of nor into tradable jobs. In nontradables, by contrast, the impact coefficient—the sumof the coefficients on xro and the xro Io (N ) interaction—is strongly negative. For both lowand high-education workers, in either the 2SLS or the reduced-form regression, the coefficientsum is significant at the 1% level. In nontradables, an influx of immigrant workers crowds
out native-born workers, consistent with our theoretical model in which the crowding-out
effects of immigration are stronger within N than within T .
31This observation poses a challenge to an alternative explanation for the greater immigrant displacementof natives within N versus within T : that the occupation supply elasticity is lower in T than in N . If
this were the case, one would expect, all else equal, employment changes across occupations within T to besmaller than those across occupations within N . Yet, in the data we observe the opposite.

21

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
Panel A
(1a)

(3a)

(4a)

OLS

(2a)
Low Ed
2SLS

RF

xro

-.088
(.065)-.150**(.069)

Obs
R-sq

33723
.822

33723
.822

AP F-stats (first stage)

(6a)

OLS

(5a)
High Ed
2SLS-.097**(.040)-.130***(.040)-.225***(.048)-.205***(.037)

33723
.822

26644
.68

26644
.679

26644
.68

136.10RF

105.67

Panel B
(1b)

(3b)

(4b)

OLS

(2b)
Low Ed
2SLS

RF

.089*
(.049)-.303***(.062).002(.089)-.296***(.102)

Obs
R-sq

33723
.836

Wald Test: P-values

0.00

xro
Io (N ) xro

AP F-stats (first stage)xro
Io (N ) xro

(6b)

OLS

(5b)
High Ed
2SLS.004(.060)-.234***(.090).022(.036)-.309***(.097)-.030(.066)-.374***(.126)-.018(.059)-.328***(.112)

33723
.836

33723
.836

26644
.699

26644
.699

26644
.699

0.00

0.00

0.00

0.00

0.00

102.77
75.21

RF

65.90
48.48

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, xro , is defined in (23); Io (N ) is a dummy variable for theoccupation being nontradable. All regressions include dummy variables for the occupation and theCZ-group (tradable, nontradable). Columns (1) and (4) report OLS results, columns (2) and (5) report
2SLS results using (26) to instrument for xro , 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. Robust standard errors (in parentheses) areclustered on state. Models are weighted by start of period CZ-occupation-education group native-born
population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 1: Allocation for domestic workers across occupations

22

Because the immigration exposure measure, xro , 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 nontradable occupations, interpreting coefficient magnitudes in Table 1 requires guidance. Consider the impact of an immigrant inflow
between 1980 and 2012 into high-immigration Los Angeles on two occupations within N ,high-immigrant intensity housekeeping (xro = 0.71), and low immigrant-intensity firefighting(xro = 0.06), where the difference in their occupation exposure is 0.65. Our results indicatethat for housekeeping relative to firefighting, we would see a 0.20 = 0.65×0.30 differential log
point employment reduction for low-education natives and a 0.24 = 0.65 × 0.37 differential
log point employment reduction for high-education natives. By contrast, because the 2SLS
coefficient on xro in column (2b) within T is a reasonably precisely estimated zero, we would
detect no differential domestic employment changes between any pair of tradable occupations, either in Los Angeles or elsewhere.32 These results do not address how immigration
affects tradables or nontradables in the aggregate, which is the focus of previous literature.
Our results highlight a new source of labor market exposure to immigration. Living ina high immigration region (e.g., Los Angeles) and preferring to work in immigrant-intensive
nontradable jobs (e.g., housekeeping) leaves one relatively exposed to foreign labor inflows,
whereas living in the same CZ but having a proclivity to work either in tradable jobs orin nontradable jobs that attract few immigrants leaves one comparatively less exposed. In
Section 6, we use our quantitative framework to interpret these coefficients, without imposing
the restrictions we make in Section 3.1, to determine the welfare consequences of differential
exposure to immigration, and to solve for wage effects across CZs.
The specification for the log change in total labor payments in (25) provides evidence
on the theoretical mechanism underlying differential immigrant crowding out of native-bornworkers in T versus N . In Table 2, we report estimates of γ, which is the coefficient on theimmigration shock, xro , and γN , which is the coefficient on the immigration shock interactedwith the nontradable-occupation dummy, Io (N ) xro . In all specifications, the coefficienton xro is positive and precisely estimated, consistent with the elasticity of local output tolocal prices in tradables being larger than one (rT > 1). Similarly, in all specifications thecoefficient on Io (N ) xro is negative and highly significant, is consistent with rT > rN .
Together, the results in Tables 1 and 2 verify both differential crowding out within T
versus within N and the mechanism in our model through which this difference is achieved.
The arrival of immigrant labor results in an expansion in output and a decline in prices ofimmigrant-intensive tasks both within tradables and within nontradables. Compared to N ,however, adjustment in T occurs more through output changes than through price changes.
Consequently, labor payments of immigrant-intensive occupations increase by more within
tradable than within nontradable jobs, as shown in Table 2. Consistent with this mechanism,
Table 1 shows that an immigration shock generates null effects on native employment within
T and negative effects on native employment within N .
32

Given a value of θ + 1—which is the elasticity of occupation wages to factor allocation, as shown inequation (20) and which we set at 2 in our quantitative model in Section 5—our theory allows us to use theseresults to interpret wage implications. Specifically, our results indicate that we would detect a 0.10 = 0.20/2
and a 0.12 = 0.24/2 log point reduction in domestic low-education and high-education wages in housekeeping
relative to firefighters in Los Angeles but no differential domestic wage changes between any two tradable
occupations in Los Angeles or elsewhere.

23

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
(2)
(3)
OLS
2SLS
RF
xro

.392***(.115)-.3512***(.116).380**(.166)-.398***(.137).320**(.131)-.324***(.092)

Obs
R-sq

34892
.897

34892
.897

34892
.897

Wald Test: P-values

0.38

0.85

0.96

Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

55.54
105.82

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, xro , is in(23); Io (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 xro , and column (3) replaces theimmigration shocks with the instruments. Robust standard errors (in parentheses) are clustered onstate. Models are weighted by start of period CZ-occupation population. For the Wald test, the null
hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke(AP) F-statistics for the first stage regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 2: Labor payments across occupations
Robustness. In Appendix E, we present alternative specifications in which we check forviolations of the identifying restrictions (i)-(iii) discussed in Section 4.2. Assumptions (i)and (ii) require that employment shocks to a region do not affect immigration inflows toother regions. When we drop the largest CZs, for which concerns about reverse causality
from local labor market shocks to immigrant inflows may be strongest, our results are materially unchanged; see Appendix E.1.3. Assumption (iii) would be violated if current regional
productivity shocks are correlated with past shocks that affected initial region-occupation
immigrant employment intensities. Reassuringly, our results are qualitatively unaltered when
we construct the instrument replacing initial immigrant employment intensities for a given
region with the corresponding intensities averaged over a set of regions other than this regionand outside of the region’s state, as in (27); see Appendix E.2. Our results would be similarlycompromised if the negative impact of the immigration shock on native allocations and totallabor payments was the byproduct of persistent region-occupation employment trends, as in
the Borjas et al. (1997) critique of the Card instrument. To examine the relevance of thiscritique for our analysis, we re-estimate (24) with a dependent variable that is the change
in the occupational employment of native workers over the 1950-1980 period, while keeping
the immigration shock defined over the 1980-2012 period, thus assessing whether confounding long-run region-occupation employment trends are present in the data. These exercises,
presented in Appendix E.1, reveal no evidence that current impacts of immigration on native24

born employment are simply the byproduct of continuing patterns of regional employment
growth.33 The results in Tables 1 and 2 also embody assumptions about which activities
are nontradable and which are tradable. In Table 1, we divide occupations into equal-sizedgroups of tradables and nontradables. In Appendix E.3, we explore alternative assumptions
about which occupations are tradable and which are not (and alternative occupation aggregation schemes). The corresponding regression results are very similar to those in Table 1.
Results are also similar, as reported in Appendix E.6, when we redo the analysis for regionindustries, rather than for region-occupations, and identify the tradability of industries as
discussed in Section 4.3.34 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 crowdingout 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 differential
crowding-out effect for low-education workers in nontradables weakens, but remains strong
for high-education workers in nontradables; see Appendix E.1.2.35 Finally, in Appendix E.4
we verify that our results are qualitatively unaffected by imposing alternative occupation
aggregations (to establish the robustness of our results to either expanding or contracting
the number of occupational groups) or by dropping routine- or communication-intensive 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).
Summary. The empirical results show that, in line with our theoretical model, there aredifferences in adjustment to labor supply shocks across occupations within tradables andwithin nontradables. The allocation regressions are consistent with immigrant crowding out
of native-born workers within nontradables (rN < ρ) and with neither crowding in nor
crowding out within tradables (rT ≈ ρ).

5

A Quantitative Framework

We next present a quantitative model in which we impose less restrictive assumptions thanin our baseline model of Section 2 (geographic mobility of native and immigrant workers,
many source countries for immigrants) and in our comparative static exercises in Section 3
33

The results in Appendix E.1 indicate that the 1980-2012 immigration shock has “impacts” on outcomesfor 1950-1980 with the opposite sign of impacts on outcomes for 1980-2012. One potential explanation forthis pattern, which data limitations prevent us from evaluating, is that the immigration shocks for the 19501980 and 1980-2012 time periods are negatively correlated. A major change in U.S. immigration law in 1965,
which in later decades helped redirect source countries for U.S. labor inflows from Europe to Asia and Latin
America, could be one cause of this negative correlation. Whereas immigrants as a share of the populationand labor force declined modestly from 1950 to 1980, these shares increased sharply in the following three
decades, consistent with a negative correlation between shocks in the 1950-1980 and 1980-2012 periods.
34
Immigration crowds out native-born employment in nontradables but not in tradables (although βN in(24) is always negative, it is significant in 2SLS and reduced-form regressions for high-education but not loweducation natives), while leading to a greater expansion of labor payments in immigrant-intensive occupations
in tradable than in nontradable industries (γN in (25) is significantly negative in all specifications).
35
Variation in parameter estimates across time periods should not be surprising. In (24), these parameters
are functions of output price elasticities 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.

25

(allowing for flexible occupational comparative advantage of education groups, large shocks,
non-negligible shares of regions in the national economy, variation in trade shares across tradable occupations). This extended model allows us to show numerically that our theoreticalresults of Section 3 hold under less restrictive assumptions; to calibrate model parameters
and assess quantitatively other model implications using the same two-stage least squares
approach on model-generated data as in the actual data; to conduct counterfactual exercises
in which we change immigrant stocks by source country; and to calculate absolute changes
in real wages by CZ (in addition to relative outcomes across occupations within regions,which are the focus of our empirical and theoretical analyses). In this section, we describe
our quantitative model, parameterize it, and evaluate additional quantitative implications.
In the following section, we conduct counterfactual exercises regarding U.S. immigration.

5.1

An Extended Model

We extend our model of Section 2 as follows. First, we introduce many source countries, c,from which immigrants originate. We assume that the systematic component of productivity,I
Zreo, does not depend on the immigrant’s source country c. Hence, given the measure ofIc, theimmigrants in education cell e from each source country in each P
region, denoted Nre
Ic
I
equations in our baseline model continue to hold, where Nre ≡ c Nre . We incorporate
source countries in order to calibrate the model to our two-stage least squares regressions
and to perform source-country-specific counterfactuals. Nevertheless, we do not model trade
between regions in our model—U.S. commuting zones—and the rest of the world.
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 ω living in region r
depends on amenities and the expected real wage from living there. Preferences for amenities
Dfor natives
from residing in region r are given by the product of a systematic component, Ure
Icwith education e and Ure
for immigrants with education e from source country c, and an
idiosyncratic preference shock, εr (ω, r), which is distributed Fréchet with shape parameterν > 1.36 We assume that each worker first draws her preference shocks across regions andchooses her region, and then draws her productivity shocks across occupations and chooses
her occupation. Under these assumptions, the measure of workers of type k (and source
country c for immigrants) with education e in region r is given by

ν

ν
I
D
Ic W agere
D W agere
Ure PrUre Pr
D
Ic
D
N
and
N
=
Nre
=P

ν NeIc ,


ν
e
re
D
I
P
D W ageje
Ic W agejej∈R Ujej∈R Uje
Pj
Pj
where NeD and NeIc denote the exogenous measure of education e workers of who are native and who are immigrantfrom source country c, respectively, across all regions (NeD =
P
P
D
Ic
Ic
r∈R Nre and Ne =r∈R Nre ). We take the aggregate measure of migrants from source
country c and education group e, NeIc , as given, leaving unmodeled the cause of migrant
outflows from the set of source countries.
36

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
provides a model-based motivation of our Card-type instrument.

26

In Appendix G.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.37 These changes are not
restricted to be infinitesimal as in Section 3. Three sets of inputs are required to solve thissystem. First, we require initial period of allocations across occupations for each workerktype and education cell in each region, πreo
; wage income of each worker type and educationkagekrecell as a share of total income by region, P NreN×W
k0 ×W agek0 , where the average wage of type k
e0 k0

re0

re0

workers with education e in region r (i.e., the total income of these workers divided by theirmass) is (independently of country of origin c and occupation o) given by
1
# θ+1

"
W agekre = γ

X


k θ+1

k
Zrej
Wrj

;

(28)

j∈O

labor allocations across regions for each worker type and education cell (and source country
y
×Pro
D
Ic
for immigrants), Nreand Nre; absorption shares by occupation in each region, P Y0 roy ;o Yro0 ×Pro0
and occupation bilateral exports relative to production and relative to absorption in eachregion. Second, we require values of parameters η (the substitution elasticity between occupations in production of the final good), α (the substitution elasticity between occupation
services from different regions in the production of a given service), ρ (the substitution elasticity between domestic and immigrant workers in production within an occupation), θ (thedispersion of worker productivity), and ν (the dispersion of worker preferences for regions).
Third, we require aggregate changes in the national number of natives and immigrants bysource country and education, N̂eD and N̂eIc , as well as changes in preferences for amenities
Ic
D.
and Ûreby region r, nativity, and education, Ûre

5.2

Calibration

We calibrate the model based on the U.S. data used in Section 4. We consider 722 regions(each of which corresponds to a CZ) within a closed national economy, 50 occupations (halftradable, half nontradable), two domestic education groups (some college or less, college
completed or more), and three immigrant education groups (less than high school, high schoolkagekrekgraduates and some college, and college graduates). The values of πreo
, P NreN×W
k0 ×W agek0 ande0 k 0

re0

re0

kc
Nre
in the initial equilibrium are obtained from Census and ACS data. We use the same 12
source regions for immigrants as in our empirical exercises.
In order to construct bilateral exports by occupation in each region, we assume thatoccupation demand shifters are common across regions for tradable occupations, µro = µo
for o ∈ T , and choose trade costs as follows. First, we assume that nontradable occupations
are subject to prohibitive trade costs across CZs (τrjo = ∞ for all j 6= r). Second, we assume
that bilateral trade costs for a given tradable occupation between a given origin-destination
pair are common across tradable occupations (given the absence of bilateral cross-CZ trade
data by occupation), τrjo = τrjo0 for all o, o0 ∈ T , and parameterize them using a standard
37

Specifically, we must solve for 72, 200 (2 × 50 × 722) occupation wage changes and 27, 436 ([2 + (3 ×12)] × 722) population changes.

27

Parameter values

θ α
1 7

ρ
4.6

η
1.65

ν
1.5

Table 3: Parameter values in quantitative analysis
gravity trade cost function: τrjo = τ̄ × ln (distancerj )δ for j 6= r. Given this assumption,
the elasticity of trade with respect to distance across CZs within the U.S. in our model isgiven by (1 − α)δ, where 1 − α is the trade elasticity introduced in equation (5). We set(1−α)δ = −1.29, as estimated in Monte et al. (2016) using data on intra-U.S. manufacturing
trade from the Commodity Flow Survey (CFS). We calibrate τ̄ to match the average export
share within tradables in our model (in the year 2012) to that in the 23 CFS regions (in theyear 2007) that closely align with our CZs, where we weight each CZ according to total labor
payments in tradables in the model and according to total shipments in manufactures in thedata. Further details are provided in Appendix G.2. Even though bilateral trade costs arecommon across tradable occupations, bilateral trade shares differ across occupations due tovariation in size and marginal costs across occupations and regions.38
We assign values to the parameters α, ν, θ, η, and ρ as follows. The parameter α − 1 isthe 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 in line with the estimates using regional data within the U.S. estimated in Donaldson(Forthcoming) and Donaldson and Hornbeck (2016). The parameter ν is the elasticity ofnative and immigrant spatial allocations with respect to native real wages across regions,nk −nkν = wk −wrek −prr0 e+p 0 . We set ν = 1.5, which falls in the middle of the range of estimates in the
r

r0

r

geographic labor mobility literature reviewed by Fajgelbaum et al. (2015). The parameterθ + 1 is the elasticity of occupation allocations with respect to occupation wages within
nk −nkro0
We set θ = 1 following analyses on worker sorting acrossa region, θ + 1 = wrok −w k .
roro0

occupations in the U.S. in Burstein et al. (2016) and Hsieh et al. (2016).39 Since estimatesof the elasticity of substitution between occupations, η, and the elasticity of substitution
between native and immigrant workers within occupations, ρ, are not available from existing
research, we calibrate them. To do so, we feed into our model national changes in natives andimmigrants by source country and education, N̂eD and N̂eIc , as well as changes in preferencesD
Ic
for amenities in region r by nativity and education, Ûreand Ûre, and solve for the fullgeneral equilibrium, allowing for endogenous movements of natives and immigrants between
regions and occupations. We choose N̂eD and N̂eIc to match observed changes between 1990
DIc
and 2012. We choose Ûreand Ûreto match changes in regional populations of each nativityD
I 40
and education cell observed between 1980 and 2012, N̂reand N̂re. We then run the 2SLS
employment-allocation regression in (24) on model-generated data. While (24) no longer
holds in the extended model, it provides useful “identified moments,” which we can match in38

We also consider a parameterization with free trade within tradables. We match our moments—excluding
trade shares—by setting α = 7, ρ = 6.8, and η = 1.85 (compared to our baseline parameterization α = 7,
ρ = 4.6, and η = 1.65). In unreported results, we obtain similar results to our baseline parameterization.
39
Our parameter θ corresponds to θ + 1 in Burstein et al. (2016) and Hsieh et al. (2016).
40
We do not need to back out the realization of these amenity shocks because the total number of natives
DI
and immigrants by education and region, N̂reand N̂re, are sufficient statistics for all calibrated moments.

28

our full model. In particular, the signs and relative magnitudes of the regression coefficientscontain information about the underlying structural parameters.
We choose η and ρ to target the extent to which immigration crowds in (out) native
employment within tradables and within nontradables, reported in the lower panel of Table
1: we target the coefficient on xro , β D = −0.01 (neither crowding in nor crowding out ofD
natives by immigrants in tradables), and the coefficient on Io (N )xro , βN
= −0.34 (crowdingout of natives by immigrants in nontradables), where each is the average of the 2SLS estimates across high- and low-education native workers. Replicating our empirical parameter
estimates requires values of ρ = 4.6 and η = 1.65. Table 3 reports calibrated parameter values and Table 4 reports the employment-allocation regressions using data generated by themodel.41 Comparing empirical estimates in Table 1 with estimates using model-generated
data in Table 4, we see that estimates of β D are similar for the two education groups inboth exercises (0.002 for low-education natives and −0.03 for high-education natives in theempirical estimates; −0.01 for low-education natives and −0.01 for high-education natives
Din the model-generated estimates). In mild contrast, estimates for βN
are modestly smaller
in absolute value for low relative to high-education natives in the empirical estimates (−0.30
versus −0.37) and modestly larger in absolute value for low relative to high-education natives
in model-generated estimates (−0.37 versus −0.31).
The intuition for the realized values of the parameters η and ρ can be understood using
the analytics in Section 3, although the restrictions under which these results are obtained
are partially relaxed here. Our assumption that trade shares are zero for within N implies
that the elasticity of regional output to the regional producer price for nontradables, rN ,equals η. The elasticity of regional output to the regional producer price for tradables, 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, rT is closer to α than to η. From Section
3, targeting β D ≈ 0 in the employment-allocation regression (no crowding in or out within
tradables for natives) requires that the elasticity of regional output to the regional producer
price within tradables, rT , equals the elasticity of substitution between native- and foreignborn workers within each occupation, ρ. Thus, ρ must be closer to α than to η, yieldingρ = 4.6. A higher value of ρ would imply crowding out within tradables, which is inconsistent
with our reduced-form estimates (see the alternative parameterization below).

xro
Io (N )xro
R-sq

Allocations
Low education High education-0.014-0.009-0.368-0.3100.985
0.983

Labor payments

Occupation wages

0.478-0.2640.977-0.011-0.202
0.946

Table 4: Regression results using model-generated data
D = −0.34.
Notes: Calibration targets: average low & high education for native workers: β D = −0.01 and βN

The R2 in the 2SLS regressions are high, suggesting that our reduced-form regressions have a good fit.
In order to match the lower R2 in the data, we would have to introduce random changes in productivities
by occupation and regions, Âro and Âkro .
41

29

D
The intuition for the value of η = 1.65 is similar. Targeting βN< 0 in the employmentallocation regression (crowding out for natives in N ) requires that η = rN < ρ. To demonstrate how the allocation regression shapes our choice of η beyond requiring that η < ρ,D
Figure 12 in Appendix I plots model-implied values of β D and βN
against the value of η if
we fix all other parameters at their baseline levels. As described above, β D is less responsiveDD
to changes in η than is βN. Therefore, the estimated value of βN
guides our choice of η.

5.3

Additional quantitative implications

To explore further the validity of our extended model, we perform a series of regressions using
model-generated data—where the implied moments are not targeted in the calibration—andcompare the estimated parameters to those we obtain when using actual data.
Labor allocations: In our baseline calibration, we target separately the lack of crowding inof natives by immigrants in tradables and the extent of crowding out of natives by immigrants
in nontradables. When we estimate a common impact coefficient across all occupations by
excluding the interaction term for the immigration shock and the nontraded dummy inmodel-generated data (as in the upper panel of Table 1), we obtain an average estimate,across low- and high-education natives, of −0.18 (versus −0.19 in the data).
Labor payments: Estimating the 2SLS labor-payments regression on model-generated data
yields a coefficient on xro of 0.48 and a coefficient on Io (N )xro , of −0.26, as shown in Table
4. These results are roughly in line with the coefficient on xro of 0.38 and the coefficient on
Io (N )xro of −0.40 estimated in the data and shown in column 3 of Table 2. Both in themodel and in the data, labor payments expand in immigrant-intensive occupations more in
tradable than in nontradable occupations.
Occupation wages: Our analytic results in (20) predict how occupation wages per efficiency
unit of native-born workers adjust to an inflow of foreign workers. Following the same steps
that led to specification (24) for the impact of foreign labor inflows on native labor allocationsin Section 4.1, this equation yields the following regression for native occupation wages:
D
D
D
wro
= α̃rg+ α̃oD + χD xro + χD
N Io (N ) xro + ν̃ro .

(29)

D
Unfortunately, in actual data we do not observe wro, wages per efficiency unit at the regionoccupation level. All we observe empirically is the change in the average wage for workers ina region-education-occupation cell, wageD
reo , which conflates changes in wages per efficiency
unit of labor with changes in wages driven by changes in the composition of workers in
the region-education-occupation cell, as workers select into or out of occupations and (or)regions in response to changing labor market conditions. Our assumption that each ε (ω, o)
is drawn independently from a Fréchet distribution yields the prediction that wageD
reo is not
systematically related to the immigration shock, since changes in selection exactly offset
changes in occupation wages under this distributional assumption.
We examine this prediction in Table 41 in Appendix F, which presents results from estiD
mating a version of equation (29) in which we replace the dependent variable, wro, with theDobserved change in the average wage for a region-occupation, wagereo . For high-education30

native workers, the 2SLS regression strongly supports the implications of the Fréchet distribution: immigration has no differential effects on the average wages of high-education natives
in more immigrant-intensive occupations either within tradable or nontradable occupations.
The results for low-education natives are mixed. Within nontradables, the 2SLS regression
supports the implications of the Fréchet distribution. However, within tradable occupations,the average wages of low-education natives rise in more immigrant-intensive occupations(but point estimates are small), inconsistent with our assumption of a Fréchet-distributionof idiosyncratic productivity draws.
Alternatively, rather than test for an implication of Fréchet, we can leverage the assumption of a Fréchet distribution to recover unobserved occupation wage changes fromchanges in observed native allocations and average occupation wages. Specifically, denoting
D D
Dby W ageDreo ≡ Wro Lreo /Nreo the average wage paid to native workers in region r, educatione, and occupation o, we have
−1
 θ+1
k k
k
W agekreo = γWro
Zreo πreo

which implies
1kd ln πreo
,
(30)
θ+1
k
k
where d ln πreodenotes the log change in πreo
between two equilibria. Using the previous
expression, we construct changes in native occupation wages using our calibrated value of θ =D
1 and observed values of wageD
reo and d ln πreo . Table 42 in Appendix F presents results fromestimating a version of equation (29) in which we use this constructed value of occupation
wage changes. The results are strongly consistent with our calibrated model’s predictions,displayed in Table 4. We observe no differential change in occupation wages in more relative
to less immigrant intensive tradable occupations for low or high-education natives and we
observe a greater decline in occupation wages in more relative to less immigrant intensive
nontradable occupations for low and high-education natives, where both results are consistent
with our empirical results on native labor allocations.
Alternative parameterizations of ρ. We consider two alternative parameterizations forthe value of ρ. In the first, we triple its value to ρ = 13.8 and hold fixed other parameters.
This alternative is motivated by the concern that our chosen value of the within-occupation
elasticity of substitution between native and immigrant labor, ρ, is lower than the aggregate version of this elasticity estimated by the empirical literature (e.g., Borjas et al., 2012;
Ottaviano and Peri, 2012).42 When raising ρ, the model still implies stronger crowding out
Dwithin nontradables compared to tradables (βN= −0.33), but it now generates the counterfactual result of crowding out within tradable occupations (β D = −0.124). In a second
parameterization, we assume that ρ differs exogenously and systematically between tradable,ρT , and nontradable, ρN , occupations. In this parametrization, we assume autarky in all
occupations (so that T = N ), fix η at our baseline level, and choose ρT = 1.3 < 3.7 = ρNtargeting the native labor allocation regression estimates. This alternative is motivatedby the concern that our finding of stronger crowding out within nontradables relative tokwro= wagekreo +42

Unlike the elasticity of substitution between immigrant and domestic workers within occupations ρ, theaggregate substitution elasticity is not a structural parameter in our model. When we estimate it using
model-generated data, it is roughly twice as high as our assumed value of ρ; see Appendix G.3.

31

within tradables could be a byproduct of higher immigrant-native substitution elasticities
in nontradables relative to tradables. In this case, however, the model has counterfactual
predictions for how labor payments respond to immigration. In particular, relative labor payments to immigrant-intensive occupations increase relatively more within nontradable than
within tradable occupations in response to an inflow of immigrants (γN = 0.068). 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).

6

Counterfactual Changes in Immigration

Using data for 2012 as the initial period, we consider two counterfactual changes in the
supply of immigrant workers, N̂eIc , which we motivate using proposed reforms in U.S. immigration policy. One potential change is to tighten U.S. border security and to intensify U.S.
interior enforcement, which would effectively reduce immigration from Latin America, thesource region that accounts for the vast majority of undocumented migration flows acrossthe U.S.-Mexico border. For illustrative purposes, 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 differentiallyaffects CZs that historically have attracted more immigration from Latin America. Labor
market adjustment to the shock takes the form of changes in occupational output prices andoccupational wages, a resorting of workers across occupations within CZs, and movementsof 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-bornworkers (Kerr and Lincoln, 2010). We operationalize this shock via a doubling of immigrants
in the U.S. (from all 12 source countries) with a college education.
In order to describe the results of our counterfactual exercises, it is useful to define ameasure of the aggregate exposure of region r to a change in immigration as
xIr =

X
e

0

I
ψre

I
∆Nre
,
I
Nre

(31)

0

I
I
k
k
where ψre≡ Nre
× W ageIre / e0 k0 Nre
0 × W agere0 is the share of immigrant workers withI
education e in region r in total labor payments in region r and where ∆Nreis the change
between the initial and final periods in education e labor supply of immigrants in region r.
The measure xIr 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.

P

6.1

50% Reduction of Latin American Immigrants

In this scenario, we halve the number of Latin American immigrants at the national level.
Ice
We set N̂eIc = 1 − 0.5×N
for c = South and Central America and c = Mexico for all
N Ice

education cells and we set N̂eIc = 1 for all other c’s and all education cells, where NeIc is thetotal number of region c immigrants with education e in the U.S. in 2012. Because Latin
32

Figure 1: 50% reduction in Latin American Immigrants: change in the real wage of
low-education native-born workers across CZs
American immigrants tend to have relatively low schooling, reducing immigration from theregion reduces the relative supply of less-educated labor. In 2012, 70.4% of working-age
immigrants from the region had 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: xIr
ranges from near 0 in several CZs to 0.17 in Miami and takes a value of 0.08 in Los Angeles,
a case we discuss below. This variation arises from differences across CZs in 2012 in theshare 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
across space in response to this shock, this spatial re-sorting plays little role in shaping xIr .43
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 inimmigrant labor supply) for low-education natives.44 We next examine the consequenceson the native education wage premium. These outcomes, which are the focus of muchprevious literature, capture differences across CZs in immigration impacts. They do notreveal within-CZ variation in exposure to factor supply shocks, which is the emphasis of
our paper. Figure 1, which depicts the spatial variation in the log change in average real
wages for less-educated native-born workers across commuting zones, reveals the expectedlarger impacts in CZs that are located in Florida, close to the U.S. border with Mexico, or
gateway regions for immigration, such as Atlanta, Chicago, and New York. Figure 2 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 ineach graph the x-axis is CZ exposure to the immigration shock, xIr . In response to an outflow
of Latin American immigrants, average native low-education real wages fall in all locations,from close to zero in the least-exposed CZs, to 1.4% in Los Angeles, and to 3.4% in Miami.
43

With changes in real wages across regions that are relatively small in comparison to the size of the shocks
that we feed in, labor reallocation across regions is minor relative to the large initial shock. Hence, all of ourresults in what follows are very similar to what we would obtain without geographic labor mobility.
44
To a first-order approximation, this change in real wages equals the change in utility of low-education
natives initially located in that region.

33

Figure 2: 50% reduction in Latin American Immigrants: change across CZs in real wage of
low-education (left) and in education wage premium (right) of native workers
These wage impacts arise because native and immigrant workers are imperfect substitutes,
such that reducing immigration from Latin America reduces native real wages.45 Moving to
the right panel of Figure 2, 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 1%. Less-educated foreignborn 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 ro tends to be lower than 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 3 describes differences
across occupations in adjustment to the immigration shock in nontradable and tradabletasks for the CZ of Los Angeles. The horizontal axis reports occupation-level exposure to
immigration, as measured by the absolute value of xro in (23). The vertical axis reports thechange 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
the absorption price index in Los Angeles. Even though real wages fall on average acrossoccupations for natives in Los Angeles, reducing immigration from Latin America helps
natives in the eight most-exposed nontradable occupations. The difference between average
45

We also consider a specification in which immigration
affects productivity via agglomeration effects.
Pkkk
Productivity is given by Zreo
= Z̄reoNrλ , where Nr = k,e Nreis the population in region r, and λ governs
the extent of regional agglomeration or congestion. We set λ = 0.05, in line with estimates in the literature(Combes and Gobillon, 2015). Whereas differences in employment and wage changes across occupations
within regions are largely insensitive to λ, the immigration-induced decline in average real wages is higher inmost CZs in the presence of agglomeration effects. For example, the real wage of low-education workers falls
by 1.9 (4.7) percentage point in Los Angeles (Miami), instead of 1.4 (3.4) percentage points in our baseline.

34

Figure 3: 50% reduction in Latin American immigrants: change in domestic occupation
wage (deflated by the price index) by occupation in Los Angeles, CA
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 (housekeeping) sees wages rise by 8.4 percentage points more thanthe 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. In particular, our across-job, within-CZ wagechange 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 2.
The adjustment process across tradable occupations differs markedly from that acrossnontradables. In Figure 3, the most-exposed tradable occupation (textile-machine operators)
sees real wages rise by just 2.0 percentage points more than the least-exposed tradable
occupations (social scientists). The most-least difference for occupations in wage adjustment
is thus 6.4 percentage points larger in nontradables than in tradables. While the real wage
for natives in Los Angeles rises in 8 out of 25 nontradable occupations, it only rises in one
out of 25 tradable occupations.
The patterns of wage adjustment by occupation that we describe are not specific to Los
Angeles. To characterize changes in wages across occupations in all CZs, Figure 4 plots thedifference in wage changes between the occupation that has the largest wage increase (orsmallest 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 4 reports comparisons among nontradable
occupations, while the right panel reports comparisons for tradable occupations. Consistent
with the case of Los Angeles in Figure 3, across CZs we see much more variation in wage
adjustment across jobs within nontradables than across jobs within tradables.46 Moreover,variation in wage adjustment across occupations in most CZs tends to be much larger thanvariation in real wages across CZs (displayed in Figure 2). Finally, Figure 13 in Appendix J
depicts the spatial variation in the difference in wage changes between the occupation thathas the largest wage increase and the occupation that has the smallest wage increase (or46

For given aggregate exposure to Latin American immigration (x axis in Figure 4), regions vary in thehighest–lowest occupation wage change (y axis) because occupation exposure varies across CZs.

35

Figure 4: 50% reduction in Latin American Immigrants: highest minus lowest occupation
wage increase across CZs in nontradable (left) and tradable (right) occupations
largest wage decrease) in nontradables across commuting zones. It shows a similar regional
concentration of impacts as for real wage changes in Figure 1, though with an attenuateddistance gradient as one moves away from the Southwest border and the coasts.

6.2

Doubling of High-Education Immigrants

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. If, on the other hand, allregions 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. Specifically, if within eachtradable occupation, shocks are highly correlated across regions, then local producer prices
will move together with absorption prices, as is the case for nontraded occupations. 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 a non-uniform change in labor supply across regions within
an occupation. Hence, the logic of asymmetric adjustment across occupations within tradables versus within nontradables to a local labor supply shock, which is the focus of oursmall open economy analytic results in Section 3, applies in our first counterfactual. The
experiment we consider in this section, an increase in high-skilled immigration, is closer to a
uniform increase in labor supplies across regions within an occupation. The consequence willbe less differentiation in adjustment across occupations within nontradables versus within
tradables. Characterizing such differentiation would have been difficult with the reduced
form empirical results alone. Assessing how adjustment across occupations within nontradables versus within tradables will differ across given realizations of immigration shocks is
made possible by filtering these shocks through our structural model.47
47

Even if all regions within the U.S. are identical, as long as there is trade between countries there will be afunctional difference in adjustment to shocks between tradable and nontradable occupations. By abstracting
away from trade with the rest of the world, we may understate differences between T and N .

36

Figure 5: Doubling of high education immigrants: change in the real wage of low-education
native-born workers across CZs

Figure 6: Doubling of high education immigrants: change across CZs in real wage of
low-education (left) and in education wage premium (right) of native workers
In this scenario, we double the number of immigrants with a college degree at the national
level, setting N̂eIc = 2 for e = 3 (immigrants with a college education) from all sources c.
As in the previous section there is large variation in aggregate exposure across regions in
response to this shock—with xIr ranging from roughly 0 to a high of 0.33 in San Jose andtaking 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.
In response to an inflow of college-educated immigrants, average native low-education real
wages rise in all locations, as seen in Figure 5 and the left panel of Figure 6, from as little
as 0.4 percentage points in the least-exposed CZs, to 3.3 percentage points in Los Angeles,
and to as much as 5.2 percentage points in San Jose. As in the previous exercise, this real
wage impact arises because native and immigrant workers are imperfect substitutes, so that
increasing high-education immigrants raises native real wages. In the right panel of Figure
6, we see that in response to the increase in relative supply of more-educated immigrantlabor, the education wage premium falls (and more so in CZs that are exposed to larger
37

Figure 7: Doubling of high education immigrants: change in domestic occupation wage
(deflated by the price index) by occupation in Los Angeles, CA

Figure 8: Doubling of high education immigrants: highest minus lowest occupation wage
increase across CZs in nontradable (left) and tradable (right) occupations
increases in skilled foreign labor). Consistent with the logic operating in the previous shock,this effect arises because more-educated immigrants and less-educated natives tend to workin dissimilar occupations and not because they are weakly substitutable within occupations.
Figure 7 describes differences across occupations in the adjustment of occupation wages
to the immigration shock separately for nontradable and tradable tasks in Los Angeles.
Since there is a positive inflow of immigrants, most occupations experience an increase inreal earnings. However, for the occupations that are most exposed to the labor inflow, real
wages decline in both nontradable and tradable occupations—in contrast to the previous
section. In sharp contrast with Figure 3, the difference in real wage adjustment between
the two sets of occupations is now rather modest. Regarding relative earnings within thetwo groups, wages for the most-exposed nontradable occupation (health assessment) fall by
7.5 percentage points more than for the least-exposed nontradable occupation (extractivemining). In tradables, the difference in wage changes between the most- and least-exposed38

occupation (natural sciences and fabricators, respectively) is 4.4 percentage points. Whereas
in the case of the previous counterfactual exercise the difference in wage changes between
the most and least immigration-exposed occupations was 6.4 percentage points larger in
nontradables than in tradables, the difference in Figure 7 is 3.1 percentage points.48
The patterns of wage adjustment by occupation that we describe is by no means specificto Los Angeles. Figure 8—which plots the difference in wage changes between the occupationthat 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—provides further evidence of
reduced differences in occupation wage adjustment between nontradables and tradables in
the high-skilled immigration experiment as compared to the Latin American immigration
experiment. In nontradable jobs, differences in wage changes range from 0 to 11 percentage
points, whereas in tradable jobs they range from 3 to 8 percentage points. In the regions thatare more exposed to high-skilled immigration, differences in wage changes are roughly only 2
percentage points higher within nontradable occupations than within tradable occupations,much smaller than in our first counterfactual.49

7

Conclusion

Empirical analysis of the labor market impacts of immigration has focused overwhelmingly
on how inflows of foreign-born workers affect average wages at the regional or educationgroup level. When working with a single-sector model of the economy, such emphases
are natural. Once one allows for multiple sectors or occupations and trade between labor markets, however, comparative advantage at the worker level immediately comes intoplay. Because foreign-born workers tend to concentrate in specific groups of jobs—computerrelated tasks for the high skilled, agriculture and labor-intensive manufacturing for the low
skilled—exposure to immigration will vary across native-born workers according to their favored occupation. That worker heterogeneity in occupational productivity creates variation
in how workers are affected by immigration is hardly a surprise. What is more surprising isthat the impact on native workers of occupation exposure to immigration varies within thesets of tradable and nontradable jobs. The contribution of our paper is to show theoretically
how this tradable-nontradable distinction arises, to identify empirically its relevance for locallabor-market adjustment to immigration, and to quantify its implications for labor-market
outcomes including changes in real wages in general equilibrium.
While our empirical analysis validates the differential labor-market adjustment patterns
within tradables and within nontradables predicted by our theoretical model, it is only in48

When we consider a partial equilibrium specification in which we solve for occupation wages in each CZ
assuming constant producer prices in all other locations, the difference in wage changes between the most andleast immigration-exposed occupations is 7.2 percentage points larger in nontradables than in tradables in
Los Angeles, which is much larger than 3.1 percentage when solving for all prices in full general equilibrium.
The differences between general and partial equilibrium are much smaller in our first counterfactual.
49
In Figure 8, there are CZs that have large changes in wages between occupations even though theiraggregate exposure to immigration is low. These CZs tend to have a small number of highly exposed
occupations, whereas their other occupations have little exposure. For these CZs, aggregate exposure to
immigration is not necessarily predictive of the difference in wage changes between occupations.

39the quantitative analysis that we see the consequences of this mechanism for wage levels andwelfare. Individuals who choose occupations that attract larger numbers of immigrants may
experience very different consequences for their real incomes, depending on whether theywork in tradable or nontradable activities. Workers drawn to less-tradable jobs are likely
to experience larger changes in wages in response to a given immigration shock, owing toadjustment occurring more through changes in occupational prices and less through changes
in occupational output. In contrast to recent literature, a worker’s region and education levelmay be insufficient to predict labor market impacts to changes in inflows of foreign labor.
Occupational abilities and preferences of workers may be of paramount importance, too.
Regarding immigration policy, the U.S. Congress has repeatedly considered comprehensive immigration reform, which would seek to legalize undocumented immigrants, prevent
future undocumented immigration, and reallocate visas from family members of U.S. residents to high-tech workers. Our analysis suggests that it would be shortsighted to see thesechanges simply in terms of aggregate labor-supply shocks, as is the tendency in the policy domain. They must instead be recognized as shocks whose occupational and regional
patterns of variation will determine which mechanisms of adjustment they induce.
We choose to study immigration because it is a measurable shock whose magnitude varies
across occupations, skill groups, regions, and time, thus providing sufficient dimensions ofvariation to understand where the distinction between tradable and nontradable jobs isrelevant. The logic at the core of our analytical approach is applicable to a wide range ofshocks, as shown in Proposition 1. Sector or region-specific changes in technology or labormarket institutions would potentially have distinct impacts within tradable versus within
nontradable activities, as well. For these distinct impacts to materialize, there must be
variation in exposure to shocks within tradable and within nontradable jobs and across local
labor markets, such that individual regions do not simply replicate the aggregate economy.

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43

Contents (Appendix)
I

Theoretical Appendix

1

A Derivation of analytic results
1
A.1 System in changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
A.2 Imposing the restrictions of Section 3.1 . . . . . . . . . . . . . . . . . . . . .
3
A.3 Proofs for Sections 3.2 and 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . .
4
A.4 Explicit solutions if all o have common trade shares . . . . . . . . . . . . . .
6
A.5 Relaxing restriction three: education-specific occupation comparative advantage 8
B Alternative occupation production function

9

C Imperfectly substitutable skilled and unskilled labor

11

II

13

Empirical Appendix

D Summary statistics and occupation details

13

E Robustness
E.1 Persistent regional trends and alternative periods . . . . . . . . . . . . . . .
E.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.3 The cutoff between tradable and nontradable occupations . . . . . . . . . . .
E.4 Alternative mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.5 Alternative occupation aggregations . . . . . . . . . . . . . . . . . . . . . . .
E.6 Industry analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20
22
29
32
36
40
43

F Wage analysis

46

III

48

Quantitative Model Appendix

G Additional details of the extended model
G.1 System of equilibrium equations in changes . . . . . . . . . . . . . . . . . . .
G.2 Bilateral trade and absorption shares . . . . . . . . . . . . . . . . . . . . . .
G.3 Aggregate elasticity of substitution between natives and immigrants . . . . .

48
48
50
53

H Immigrant occupation reallocation

54

I

Labor allocation analysis

56

J Counterfactual exercises

57

1

Part I

Theoretical Appendix
In Appendix A we derive the system of equations that allows us to solve for all endogenous
variables as a function of small changes in immigrant and natives supplies in every region
and education group and productivities in every region and occupation; we then solve for the
analytic results formally presented in Sections 3.2 and 3.3 as well as a range of other results
described throughout the paper. In Appendix B we provide an alternative set of assumptions on the occupation production that yield the same equilibrium equations as the CES
occupation production function in equation (1). In Appendix C we consider an isomorphic
formulation of our baseline model in which the imperfect substitution between immigrantand native workers within an occupation arises from imperfect substitution between skilled
and unskilled labor.

A

Derivation of analytic results

In Section A.1, we begin by deriving the system in changes for small changes in {nkre }r,e,k
and {aro }r,o for our baseline model of Section 2. We then impose the restrictions of Section
3.1 and simplify this system in changes in Section A.2. In Section A.3 we derive the analytic
results presented in Sections 3.2 and 3.3. In Section A.4 we solve explicitly for all endogenous
variables of interest in a special case of the model in Section A.2. Finally, in Section A.5 wedeviate from the model of Section A.2 in the other direction and provide additional results
in a version of the model that imposes fewer rather than more restrictions.

A.1

System in changes

Here we derive a system of equations that we use to solve for changes in endogenous variablesID
in response to infinitesimal changes in Nre, Nre, and Aro in every region r, education cell e,
and occupation o. We use lower case characters, x, to denote the log change of any variable
X relative to its initial equilibrium level: x = d ln X.
Log-differentiating equation (8) we obtain
X
k
k
wro
,
(32)
pro = −aro +Srok

P k Lkreo
kis the cost share of factor k (across all education cells) in occupation
where Sro≡ e WPreoro Qroo output in region r. Log differentiating equation (9), we obtain

D
I
D
I
lro
− lro
= −ρ wro
− wro
.
(33)
Combining equations (10) and (11) and log differentiating yields
!
X
k
k
k
k
wrj
+ nkre .
lreo= θwro
−θ
πrej

(34)

j∈O

Online Appendix 1

Log differentiating Lkro =P

ke Lreo , we obtain
k
=
lro

X Lk
e

reo k
l .
Lkro reo(35)

Log differentiating equation (10), we obtaink− (θ + 1)
nkreo = (θ + 1)wroXkk+ nkre .
wro
πro

(36)

m
pjo .
Sjro

(37)

o

Log differentiating equation (6), we obtainm) pro +
pyro = (1 − Sro

X
j6=r

P τ

Y

jro jromwhere Sjro
≡ joProis the share ofof region r’s absorption in occupation oyYroPthe valuemmthat originates in region j and Sro ≡ j6=r Sjro is regions r’s import share of absorption in
occupation o. Log differentiating equation (4) and using equation (37) yields
!
X
X
m
A
m
Sjro
pjo ,
(38)
Sro
(1 − Sro) pro +
pr =

o∈O

j6=r

y

A
= PPror YYrro denotes the share of occupation o in total absorption in region r.
where SroLog differentiating equation (7), we obtain
X


x
Srjo
qro = −αpro +(α − η) pyjo + ηpj + yj ,

(39)

j∈R
P τ

Y

rjo
x
is the share of the value of region r’s output in occupation o that iswhere Srjo
≡ roProrjo
Qrodestined for region j. Equations 39 and (37) yield
#
!
"
X
X

x
m
qro = −αpro +Srjo(α − η) 1 − Sjopjo +Sjm0 jo pj 0 o + ηpj + yj .

j 0 6=jj∈RLog differentiating equation (1) and using equation (9) we obtain
X
k k
lro .
qro = aro +SrokCombining the two previous expressions, we obtain
"
!
#
X
X
X

x
m
k k
lro = −αpro +Srjo(α − η) 1 − Sjopjo +Sjm0 jo pj 0 o + ηpj + yj .
qro = aro +Sro
j 0 6=j

j∈R

k

(40)
Log differentiating equation (12) yields
X
X

k
k
k
P
Sro
Sro
wro
+ lro
= pr + y r
o

(41)

k

Online Appendix 2

PPwhere Srodenotes the share of occupation o in total absorption in region r, Sro= PProrQYrro .
We can use equations (32), (33), (34), (35), (36), (38), (40), and (41) to solve for changeskkand bodies nkreo , occupation wages
and lroin employment allocations in efficiency units lreokwro , occupation prices pro and quantities qro , aggregate absorption price pr and quantity yr ,for all r, o and k.

A.2

Imposing the restrictions of Section 3.1

In Section 3.1, we impose three restrictions. First, we assume that region r is a small open
economy in the sense that it constitutes a negligible share of exports and absorption in eachmx
occupation for each region j 6= r. Specifically, we assume that Srjo
→ 0 and Sjro
→ 0 for all oand j 6= r. 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: pyjo = pjo = pj = yj = 0
for j 6= r. Therefore, given a shock to region r alone, equation (40) simplifies toXk kxqro = aro +Sro
lro = −ro pro + (1 − Sro) (ηpr + yr ) ,
(42)
k

where
x
m
x
m
ro ≡ (1 − (1 − Sro) (1 − Sro)) α + (1 − Sro) (1 − Sro
)η

(43)

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 whichxmthe services of an occupation are traded, as measured by Sro
and Sro. The parameter ro is
the partial demand elasticity of region r’s occupation o output to its output price. It is apartial elasticity because it holds fixed region r’s aggregate output and price index (but lets
it’s absorption price of occupation o change). Equation (38) simplifies to
X
A
m
Sro
(1 − Sro
) pro
(44)
pr =
o∈O

Second, we assume that occupations are grouped into two sets, g for g = {T, N }, where
x
m
0
x
x
m
x
= Sro
Sro
0 and Sro = Sro0 for all o, o ∈ g. According to (43), the assumption that Sro = Sro0m0mand Sro= Sro
0 for all o, o ∈ g implies that the elasticity of local output to the local producer
price, ro , is common across all occupations in g. We refer to rg as the common elasticityxx0
for all o ∈ g within region r. The assumption that that Sro= Sro
0 for all o, o ∈ g also impliesxthat the term (1 − Sro) (ηpr + yr ) in (42) is common across all occupations in g.50
Third, we restrict comparative advantage by assuming that education groups within eachkkk differ only in their absolute productivities, Zreo
= Zre
. This assumption and equation (10)kk
imply that education groups within k are allocated identically across occupations: πreo
= πrofor all e. Hence, equation (34) becomes
!
X
k
k
k
k
−θ
wrj
+ nkre .
lreo= θwroπrjj∈O50

Under the assumption that α is infinite, as in the Rybczynski theorem, ro is infinite and the assumptionthat r is a small open economy implies that pro = 0. In this case, we obtain our analytic results in Section
3.2 without requiring common trade shares across goods. Of course, in this case crowding in obtains.

Online Appendix 3

The previous expression and equation (35) yield51
!
X

k
k
lro
= θwro
−θ

k
k
πrj
wrj

+

X Sk

reo

e

j∈O

k
Sro

nkre .

kkkkUnder the assumption that Zreo
= Zre
, the ratio Sreo
/Srois common across o, so
!
X
k
k
k
k
lro
= θwro−θπrj
wrj+ nkr ,

(45)

j∈O

where the vector of changes in labor supplies by education level in region r,
summarized by a single sufficient statistic,
nkr ≡

X Sk

re

e

Srk

 k
nre e , isnkre ,

with weights given by the share of labor income in region r accruing to type k labor withk kk
≡ P WroWLkre0 Lk0 , relative to the share of labor income in region r accruing to
education e, Sree0 ,k0P ro kre0
all type k labor, Srk = e0 Sre
0.
Hence, under the first and third restrictions of Section 3.1, we can use equations (32),k(33), (36), (41), (42), (44), and (45) to solve for changes in employment allocations lroandkk
nro , occupation wages wro , occupation prices pro and quantities qro , and aggregate absorption
price pr and quantity yr , for all r, o and k. With shocks to region
 log changes in all r alone,endogenous variables are linear functions of shocks in region r: nIre e , nD
re e , and {aro }o .

A.3

Proofs for Sections 3.2 and 3.3

Deriving equations (18)-(21): Combining equations (33) and (45), we obtain
!
X
X

D
I
I
I
D D
(θ + ρ) wro
− wro
πrj
wrj
+ nIr − nD
=θ
πrj
wrj −
r
j∈O

(46)

j∈O

D
I
so that w̃r ≡ wro− wro
is common across occupations o. With shocks to region r alone, itfollows from the system of equation in changes that w̃r is a linear combination of region r
shocks, as in equation (21). We do not explicitly solve for the change in relative wages per
efficiency unit, w̃r , in general; we do so under the assumption of a single g in Section A.4.
Equation (42) is equivalent to

pro =
51


1
1
1 I I
1 D
x
D
(1 − Sro) (ηpr + yr ) −aro −Sro lro − lro
−
l .
ro
ro
ro
ro roIn this derivation, we use the following
X Lk
e

1
reo k
n = k P
Lkro reWro e0 Lkre0 o

X
e

k
Wro
Lk
reo
k0 k0
W
0
0
ro Lre0 o
e ,kk
and the definitions in the main text Sreo
≡P

k0 k0
X
e0 ,k0 Wro Lre0 oPS k nkkkWro e0 Lre0 o e reo re

P
k k
Wro
Lreo nkre =kand Sro≡ke Sreo .

P

Online Appendix 4

The previous expression and equation (33) yield
pro =

1
1 D
1
ρ I
x
) (ηpr + yr ) −(1 − Sroaro −Sro w̃r −
l ,
ro
ro
ro
ro rowhich, together with equation (32) yields




1
ro − 1ro − ρ
1 D
D
x
I
wro =
(1 − Sro ) (ηpr + yr ) +
aro +
Sro
w̃r −
l .
ro
ro
ro
ro roThe previous expression and equation (45) yieldro − ρro − 1DIwro =w̃r Sro +aroro + θro + θ
#
"
X
1
x
D D
.
(1 − Sro) (ηpr + yr ) + θπrj
wrj − nD+r
ro + θj∈O

(47)

We similarly obtain






ro − ρro − 1Iw̃r Sro − 1 +aroro + θro + θ
"
#
X
1
x
I
I
I
+
(1 − Sro ) (ηpr + yr ) + θ
πrj wrj − nr .
ro + θ
j

I
wro
=

(48)

Imposing the second restriction from Section (3.1), equations (36), (47), and (48) yield
equation (20), where rg = ro for all o ∈ g. Under the same restriction, equations (36)and (20) yield equation (19). Equations 19 and (20) simplify to equations (16) and (17) if
aro = aro0 for all o, o0 ∈ g and nD
re = 0 for all e.
Using equations (32) and (20), we obtainpro − pro0 = −


θ+1
θ+ρ
I
I
w̃r Sro− Sro−(aro − aro0 )0θ + rgθ + rg

for any o, o0 ∈ g. Combining the previous expression and equation (42), we obtainqro − qro0 = rg (θ + 1)
rg (θ + ρ)II+w̃r Sro− Sro(aro − aro0 )0θ + rgθ + rg

for any o, o0 ∈ g. The two previous expressions yield equation (18). Equation (18) simplifies
to equation (15) if aro = aro0 for all o, o0 ∈ g and nD
re = 0 for all e.
Deriving equation (22): Consider o, o0 ∈ g. Equation (19) implies
nkreo =

 (rg − 1) (θ + 1)
(rg − ρ) (θ + 1)
I
I
− Sro
+
w̃r Sro(aro − aro0 ) + nkreo00rg + θrg + θOnline Appendix 5

The previous expression is equivalent to
 k

k
k
πreo
(rg − ρ) (θ + 1)
πreo0 I
πreo
0
0
k
I
w̃r
nreo =
Sro − k Sro0kkπregrg + θ
πreg
πreg
 k

k
k
(rg − 1) (θ + 1) πreo0
πreo0
πreo
0
0
+
aro − k aro + k nkreo0krg + θ
πreg
πreg
πreg
P
πk 0 knreo0 denote the log change in labor allocated to g, and summing
Letting nkreg ≡ o0 ∈g πreokreg
the previous expression over all o0 ∈ g, we obtain!
!
X πk 0X πk 0
(
−
ρ)
(θ
+
1)
(
−
1)
(θ
+
1)
rg
rg
I
I
reo
reo
nkreo =
w̃r Sro
−
aro −
Sro
+
aro0 +nkreg
0kkrg + θ
π

+
θ
π
rg
o0 ∈g rego0 ∈g reg
The previous expression, equation (21), and aro ≡ ao + arg + ãro yield equation (22), where(rg − ρ) (θ + 1)
k
w̃r
αreg
≡−
rg + θ−X πk 0

I
reo
Sro
0
k
π
o0 ∈g regk(rg − 1) (θ + 1)
(rg − 1) (θ + 1) X πreo0
arg + nkreg .
aro0 +krg + θπ+θrg
o0 ∈g reg

The partial own labor demand elasticity: We can solve for the partial own labor
DD
demand elasticity at the level of the region-occupation, lro/wro, in which we allow for nativeand immigrant labor to reallocate across occupations and occupation prices to change, but
hold immigrant wages, aggregate output, and aggregate prices fixed. Combining equations(32), (33), and 42, we obtain

D
D
I
I
lro
/wro
= ro 1 − Sro+ ρSro.
This partial elasticity is increasing in ρ (as is standard) and also ro (consistent with HicksI
if and only if ρ > ro .
Marshall’s rules of derived demand). Moreover, it is increasing in Sro

A.4

Explicit solutions if all o have common trade shares

Here we consider a version of our baseline model in which we assume that there is a single
grouping of occupations so that all occupations o have a common export share of output,xm
Srx = Sro, and import share of absorption, Sro= Srm . This formulation nests the case inxmwhich bilateral trade costs are infinite, in which case Sro= Sro= 0 for all o.
DA
We begin by solving explicitly for w̃r and nreo . We then sign ΨIro , ΨDro , and Ψro .
Solving explicitly for w̃r and nkr . Equation (43) simplifies tor ≡ ro = (1 − (1 − Srx ) (1 − Srm )) α + (1 − Srx ) (1 − Srm ) η for all o.

(49)

Equations (47) and (49) imply
 X



X
r − 1 X D
11
r − ρ
D I
D Dw̃r
πro Sro +πro aro + (ηpr + yr ) (1 − Srx ) − nD
πro wro =
r
r
r
r r
o
o
o
Online Appendix 6

We similarly obtain from equations (48) and (49)


 X

X

r − 1 X I
ρ − r
1
1
I
I
I
I
w̃r
πro 1 − Sro +πro aro + (ηpr + yr ) (1 − Srx )− nIr .
πro wro =
r
r
r
r
o
o
o
The previous two expressions and equation (46) yield an explicit solution for w̃r ,


P
I
D
aro
− πro
+ θ (r − 1) o πro(θ + r ) nIr − nD
r
P
w̃r =
D
I
I
r (θ + ρ) + θ (ρ − r ) [1 + o (πro − πro ) Sro ]This can be re-expressed as X Aw̃r = ΦIr nIr − nD+Φro aro ,
r

(50)

o

where
ΦIr =
and
ΦA
ro =

θ + rP
D − πI ) S I ]r (θ + ρ) + θ (ρ − r ) [1 + o (πrororoθ (r − 1)
D
I
P
π
−
π
ro
ro
D − πI ) S I ]r (θ + ρ) + θ (ρ − r ) [1 + o (πrororoEquation (50) provides an explicit solution for the log change in the relative occupation
wage of natives to immigrants, w̃r , as a function of the relative log change in the supplyIDof immigrant toPnative workers,
 nr − nr , Iand theA log change in the change in occupation
DI
productivities, o πro − πro aro , where Φr and Φr represent the corresponding elasticities.
Finally, we can also solve explicitly for log changes in labor allocations as
"
!
!#
X
X
θ
+
1
I
D I
D
(r − ρ) w̃r Sro−πro
Sro + (r − 1) aro −
πro
aro
+ nD
nD
re
reo =
r + θ
ooSigning ΦIr . Here, we prove that ΦIr ≥ 0. Let
X
 I
I
D
zr ≡
πrj
− πrj
Srj .

(51)

j

The numerator of ΦIr is weakly positive. We consider two cases: (i) ρ ≥ r and (ii) ρ < r .
In the first case (ρ ≥ r ), we clearly have ΦIr ≥ 0, since zr ≤ 1. In thesecondcase (ρ ≥ r ),r ρ
1
zr ≥ 0 is a sufficient condition for ΦIr ≥ 0 since ΦIr ≥ 0 ⇐⇒ ρ−+ 1θ ≤ zr . Orderrroccupations such thatIIo ≤ o0 ⇒ Sro
≤ Sro
0.


I
I I
I I
D D
By definition, Sro= Wro
Lro WroLro + Wro
Lro . Equations (10) and (11) imply
1
! θ+1

k k
k k
Wro
Lreo = γNre
πreo

X


k θ+1

k
Wrj
Zrej

,

j∈O

Online Appendix 7kkwhich, together with our restriction that Zreo
= Zro
, yields
1
! θ+1
X

θ+1
k
k
k k
Wrjk
Zrj
Lro = γπro
Wro
Nrk ,
j∈O

where Nrk ≡ke Nre . Hence, we havePo ≤ o0 ⇒

D
D
πro
πro
0
≥
.
I
I
πro
πro0

(52)

P
k
Let Πkr (o) ≡ oo0 =1 πro. Condition (52) is equivalent to stating that ΠIr (o) dominates ΠDr (o)Iin terms of the likelihood ratio. This implies that Πr (o) (first-order) stochastically dominatesIΠDr (o). Since Sro is increasing in o, equation (51) therefore implies zr ≥ 0, which impliesΦIr ≥ 0 if ρ < r . Combining the two cases (ρ ≥ r and ρ < r ), we obtain the result that
ΦIr ≥ 0.
A
D
I
A
Signing ΦAro . Here, we prove that Φro > 0 ⇐⇒ (πro − πro )r > 1. The denominator of Φris strictly positive, since zr ≤ 1 and ρ, θ, r > 0. The numerator of ΦAr is positive if and onlyID
if (πro − πro )r > 1.

A.5

Relaxing restriction three: education-specific occupation comparative advantage

In our baseline analytic results we assumed that education cells did not differ in their relative
k
k
k
k
/Zreo
productivities across occupations: Zreo
0 = Zre0 o /Zre0 o0 (restriction 3). Here we discuss
the conditions for crowding in or out when we relax this assumption (as is the case in thedata we use in our quantitative analysis). We impose that aro = 0.
By equation (34) and (35),kklro= θwro
+

X Lk
e

reo
Lkro


−θwagekre + nkre ,

(53)

where
wagekre =

X

k
k
πreo
wro

o∈O

Equations (32), (33), and (42) (which do not use restriction 3) imply that
D
I
D
x
lro
+ (ρ − ro ) Srow̃ro = −ro wro+ (1 − Sro) (ηpr + yr )DIwhere w̃ro ≡ wro− wro. For two occupations o, o0 ∈ g,

 I

D
D
I
D
D
= (rg − ρ) Srow̃ro − Sro
lro
− lro
0 w̃ro0 .
0 + rg wro − wro0

(54)

k
k
k
k
Consider first the case in which Zreo
/Zreo
0 = Zre0 o /Zre0 o0 for k = D (satisfying restriction
D

LD

0
D
D
− lro
= Lreoand equation (53) implies that lro3) but not for k = I. In this case, LLreo
0 =
D
D
ro
0
ro

D
D
θ wro
− wro
0 . Using (33), (54) can be re-written as

D
D
wro
− wro
0 =


(rg − ρ) I
I
Sro w̃ro − Sro0 w̃ro0(rg + θ)
Online Appendix 8

D
D
D
D
0
If rg = ρ, then wro= wro
0 so by equation (34), lreo − lreo0 = 0 for o, o ∈ g; that is there isneither crowding in or out for native workers in g. If rg 6= ρ, then the sign and magnitudeI
DI
D− lreoof lreo
0 depends on Sro , Sro0 , w̃ro and w̃ro0 .
Consider now the more general case in which we do not impose restriction 3 for either
k = D or k = I. We aim to understand under what conditions ρ = rg implies neither
crowding in nor out in g, as under the assumption that restriction 3 holds. If ρ = rg , thenequation (54) (and the analogous equation for immigrant labor) implies that for o, o0 ∈ g,


k
k
k
k
=0
− lro
lro
0 + rg wro − wro0
which combined with equation (53) implies
1 X Lkreo Lkreo0kkkk
wro − wro0 =
−
n
θwage
−
re
re
rg + θ e
Lkro
Lkro0

(55)

for k = D, I and o, o0 ∈ g. If θwagekre − nkre is common across education levels e, then
k
0
k
k
k
wro
− wro
0 = lreo − lreo0 = 0 for all o, o ∈ g; that is, there is neither crowding in nor out
across occupations in g for worker k type.
We can use this result to understand why, in the calibrated model of Section 5 (in which
we do not impose restriction 3) setting rT ≈ ρ results roughly in neither crowding in nor
crowding out for natives workers within the set of tradable occupations, as in the model witha single education group. This is because immigration induces only small differential changes
across education groups in native population across space (via endogenous mobility of native
DDD
workers) and in average wages within a region: that is, nD
re ≈ nre0 and wagere ≈ wagere00
for all e, e . In contrast, in Section H of the Appendix we show that setting rT ≈ ρ implies
that immigrant workers reallocate systematically across tradable occupations in response to
an inflow of immigrants. As shown in Section H, this is also the case in the data when we
consider the allocation regressions for immigrant workers.

B

Alternative occupation production function

Here we provide an alternative set of assumptions on the occupation production that yield
the same equilibrium equations as the CES occupation production function in equation (1)(under the restriction, which we do not impose in our baseline model, that ρ > 1). For
simplicity, here we suppress region indicators.
Setup. Suppose that there are two factors of production, domestic labor and immigrantlabor, indexed by k = D, I, with wages per efficiency unit of labor within occupation o given
by WoD and WoI . Each occupation production function is itself a Cobb-Douglas combinationof the output of a continuum of tasks indexed by t ∈ [0, 1]. Workers within each k may differ
in their relative productivity across occupations, but not in their relative productivity acrosstasks within an occupation.
The production function of task t within occupation o is given by
Yo (t) = LD
o (t)



ZoD
t

1
 ρ−1

+ LIo (t)



ZoI
1−t

1
 ρ−1

,
Online Appendix 9where Lko (t) is employment of efficiency units of factor k in task t in occupation o and whereρ > 1. Therefore, domestic and immigrant efficiency units of labor are perfectly substitutablein the production of each task, up to a task-specific productivity differential. A lower value ofρ implies that this productivity differential is more variable across tasks. The cost function
implied by this production function is Co (z) = min{CoD (z), CoI (z)}, where the unit cost ofcompleting task t using domestic labor is
CoD (t) = WoD



t
ZoD

1
 ρ−1

,

whereas using immigrant labor it is
CoI (t) = WoI



1−t
ZoI

1
 ρ−1

.

The unit cost of producing each occupation equals its price and is given by
Z 1
ln Co (t)dt.
Po = exp0

Characterization. There exists a cutoff task, denoted by
to =

1
,
1 + Ho(56)

for which firms are indifferent between hiring domestic and immigrant workers, where Ho ≡woρ−1 zo−1 , wo ≡ WoD /WoI , and zo ≡ ZoD /ZoI . The set of tasks in occupation o in which firms
employ domestic workers is given by [0, to ) and the set of tasks in occupation o in whichfirms employ immigrant workers is given by (to , 1]. Moreover, the share of expenditure on
domestic labor in occupation o is simply to .
Given the cutoffs, we have

Z to
Z 1
D
I
ln Co (t)dt
Po = exp
ln Co (t)dt +
0

to



 1
1
WoI (ZoI ) 1−ρ Hoto ttoo (1 − to )1−to ρ−1 .

which can be expressed asPo = exp

11−ρ

The previous expression and equation (56) yieldPo = exp

1
1−ρ



1
WoI (ZoI ) 1−ρHo
1 + Ho1 ρ−1.

Together with the definition of Ho , we obtain


 1
1
Po = exp
ZoD (WoD )1−ρ + ZoI (WoI )1−ρ 1−ρ
1−ρ

(57)
Online Appendix 10

exactly as in Dekle et al. (2008).
In Appendix A.1, we use equation (1) to derive only two equations: (32) and (33). Log
differentiating equation (57) and using equation (56), we obtain
po = SoD woD + SoI woI ,where SoD = to and SoI = 1 − to , exactly as in equation (32). Moreover, the fact that to is
the share of expenditure on domestic labor, equation (56), and the definition of Ho together
imply

−ρ
LD
ZoD WoDo= I.
LIo
Zo WoI
Log differentiating the previous expression, we obtain equation (33).

C

Imperfectly substitutable skilled and unskilled labor

Here we consider an isomorphic formulation of our model of Section 2 in which the imperfect
substitution between immigrant and native workers within an occupation arises from imperfect substitution between skilled and unskilled labor. While this model is isomorphic to ourbaseline model, the impact of immigration depends on the skill mix of immigrants and theskill-intensity of occupations. For simplicity, here we abstract from changes in productivity
and we consider a version of the model with a single g, as in Section A.4.
Occupations are produced combining unskilled and skilled labor according to
Qro = Aro

AUor LUor

 ρ−1
ρ

+

ASor LSor

ρ
 ρ−1
 ρ−1
ρ

,

where Leor denotes efficiency units of workers with education e = U, S. Efficiency unitsof native and immigrant workers of a given education are perfect substitutes within aneI
occupation, Leor = LeDor + Lor , whereZekek
Lro = Zrε (ω, o) dω for all o, e, k,
ω∈Ωek
ro

Zrek denotes the systematic productivity of workers of type k = D, I and education e = U, S
(which is equal across occupations), Ωek
ro denotes the set of e, k workers in region r (withekmeasure Nro), and ε (ω, o) is drawn independently from
P aekFréchet distribution. The totalekmeasure of e, k workers in region r is given by Nr = Nro .
Under these assumptions, the ratio of efficiency units of native
immigrant
workers
 to eI

eI
eD eD
eI
with education e is equal across occupations, LeD
/L
=
N
Z
/
N
Z
.
Allocations
ro
ro
r
r
r
r
and occupation wages can be solved for given “aggregate” supplies of workers by education,
summing up immigrant and natives, Nre = NreD ZreD + NreI ZreI .
This framework is isomorphic to our baseline model, with education groups replacing
nativity groups. Hence, our baseline results on the impact of changes in the relative supplyof immigrant to native workers translate directly into results on changes in the relative
supply of low to high education workers. However, we remain interested in the impact ofimmigration.
Online Appendix 11

The resulting comparative statics on immigration are very similar to those in our baselinemodel. Specifically, consider changes in the supply of native or immigrant workers by eduand nIe
cation, nDer , which result in changes in aggregate supplies of workers by educationr
given byeI eI eI
N eD ZreD neD
r + Nr Zr nr
ner = r eD.
Nr ZreD + NreI ZreI

U
U U
U U
S S
Define the cost share of unskilled workers in occupation o as Sro= Wro
Lro / Wro
Lro + Wro
Lro .
Changes in allocations and occupation wages for any areeknek
ro − nro0 =(r − ρ) (θ + 1)
UUw̃r Sro− Sro0r + θandr − ρU
U
w̃r Sro− Sro
0 ,θ + rwhere the log change in the wage per efficiency unit of skilled to unskilled workers is w̃r =ΨUr nUr − nSr with ΨUr ≥ 0 defined analogously to ΨIr in our baseline model. According tothese results, an inflow of immigrants that increases the relative supply of unskilled workers,
nUr > nSr (which implies w̃r ≥ 0), decreases relative employment of type e, k workers and (forany finite value of θ) occupation wages in relatively unskill-intensive occupations (crowdingout) if and only if r < ρ.
ek
ek
wro
− wro
0 =

Online Appendix 12

Part II

Empirical Appendix
D

Summary statistics and occupation details

In this section we list the 50 occupations used in our baseline analysis, in Table 5. We
rank occupation tradability using our baseline measure from Blinder and Krueger (2013),
in Table 6. We provide balance tables across tradable and nontradable occupations using
1980 occupation characteristics and 2012 occupation characteristics, in Table 7. We list the
15 occupations that are the most and least intensive in low-education, middle-education,and high-education immigrants, in Tables 8, 9, and 10. We provide summary statistics forI
immigrant intensity, Sro, for the most and least tradable occupations both at the national
level and in Los Angeles, CA in Table 11. Finally, we provide summary statistics illustrating
the distribution of immigrant shares of regional employment in 1980 and 2012 in Figure
9, and the distribution across CZs of the within-region (i.e., across occupations) coefficientof variation in immigrant cost shares for 1980 and 2012, where we display this variation
separately for nontradable jobs in Figure 10 and for tradable jobs in Figure 11.

Online Appendix 13

List of the 50 occupations used in our baseline analysis
Executive, Administrative, and Managerial
Supervisors, Protective Services
Firefighting
Managerial Related
Social Scientists, Urban Planners and Architects
PoliceEngineers
GuardsMath and Computer Science
Food Preparation and Service
Health Service
Natural Science
Cleaning and Building Service
Health Assessment
Health Diagnosing and Technologists
Personal Service
Agriculture
Therapists
Teachers, Postsecondary
Vehicle Mechanic
Teachers, Non-postsecondary
Electronic Repairer
Librarians and Curators
Misc. Repairer
Construction Trade
Lawyers and Judges
Social, Recreation and Religious Workers
Extractive
Arts and Athletes
Precision Production, Food and Textile
Engineering Technicians
Precision Production, Other
Metal and Plastic Machine Operator
Science Technicians
Technical Support Staff
Metal and Plastic Processing Operator
Sales, All
Woodworking Machine Operator
Printing Machine Operator
Secretaries and Office Clerks
Records Processing
Textile Machine Operator
Office Machine Operator
Machine Operator, Other
Computer and Communication Equipment Operator Fabricators
Misc. Administrative Support
Production, OtherHousekeeping
Transportation and Material Moving

Table 5: Occupations for Baseline Analysis
Notes: We start with the 69 occupations based on the sub-headings of the 1990 Census Occupational Classification System
and aggregate up to 50 to concord to David Dorn’s occupation categorization (http://www.ddorn.net/) and to combine
occupations that are similar in education profile and tradability but whose small size creates measurement problems (given
the larger number of CZs in our data).

Online Appendix 14

Rank*
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

Most and least tradable occupations
Twenty-five most tradable occupations
Twenty-five least tradable occupations+
Fabricators
Social, Recreation and Religious Workers++
Printing Machine Operators
Cleaning and Building Service+
Metal and Plastic Processing Operator+
Electronic Repairer++
Woodworking Machine Operators
Lawyers and Judges+
Textile Machine Operator
Vehicle Mechanic+
Math and Computer Science
Police+Precision Production, Food and Textile
Housekeeping+
Records Processing
Teachers, Postsecondary+
Machine Operator, Other
Health Assessment+
Computer, Communication Equipment Operator
Food Preparation and Service+
Office Machine Operator
Personal Service+
Precision Production, Other
Firefighting+
Metal and Plastic Machine Operator
Related Agriculture+
Technical Support Staff
Extractive+
Science Technicians
Production, Other+Engineering Technicians
Guards+Natural Science
Construction Trade+
Arts and Athletes
Therapists+
Misc. Administrative Support
Supervisors, Protective Services+
Engineers
Teachers, Non-postsecondary
Social Scientists, Urban Planners and Architects
Transportation and Material Moving
Managerial Related
Librarians and Curators
Secretaries and Office Clerks
Health Service
Sales, All
Misc. Repairer
Health Technologists and Diagnosing
Executive, Administrative and Managerial

Table 6: The most and least tradable occupations, in order
Notes: *: for most (least) traded occupations, rank is in decreasing (increasing) order of tradability score; + : occupations that
achieve either the maximum or minimum tradability score.

Online Appendix 15

Tradable

Characteristics of Workers

Natives

1980
Immigrants

Share of female
Share of college and above
Share of non-white

0.49
0.17
0.10
0.44
0.33
0.23
0.45
0.30
0.27
0.46
0.31
0.20
0.11
0.41
0.35
0.24
0.07
0.24
0.33
0.47

0.47
0.23
0.25
0.37
0.40
0.23
0.39
0.22
0.22
0.03
0.33
0.18
0.22
0.35
0.40
0.24
0.10
0.22
0.28
0.03

Age distribution

16-32
33-49
50-65

Share in routine-intensive
Share in abstract-intensive
Share in communication-intensive
Total
Share of female
Share of college and above
Share of non-white
Nontradable

Age distribution
Share in routine-intensive
Share in abstract-intensive
Share in communication-intensive
Total

16-32
33-49
50-65

Total
0.49
0.17
0.11
0.44
0.33
0.23
0.44
0.29
0.27
0.50
0.31
0.20
0.12
0.41
0.35
0.24
0.07
0.24
0.32
0.50

Natives

2012
Immigrants

Total

0.51
0.34
0.17
0.30
0.37
0.33
0.40
0.34
0.34
0.37
0.42
0.34
0.18
0.28
0.39
0.33
0.07
0.28
0.41
0.46

0.46
0.43
0.57
0.25
0.48
0.28
0.35
0.27
0.27
0.07
0.38
0.24
0.50
0.24
0.49
0.27
0.11
0.19
0.25
0.10

0.51
0.34
0.24
0.29
0.39
0.32
0.39
0.33
0.33
0.44
0.41
0.32
0.24
0.28
0.40
0.32
0.08
0.26
0.39
0.56

Table 7: Characteristics of workers, 1980 in left panel and 2012 in right panel
Notes: Source for data is 1980 Census for the left panel and 2011-2013 ACS in the right panel. Values are weighted by annual hours worked times the sampling weight.

Online Appendix 16

Most and least immigrant-intensive occupations (low-education immigrants)
15 most immigrant-intensive occupations 15 least immigrant-intensive occupations
Agriculture
PoliceFood Preparation and Service
Firefighting
Woodworking Machine Operators
Textile Machine Operator
Housekeeping
Social Scientists, Urban Planners and Architects
Engineers
Arts and Athletes
Personal Service
Extractive
Precision Production, Other
Electronic Repairer
Guards
Metal and Plastic Machine Operator
Precision Production, Food and Textile
Misc. Repairer
Science Technicians
Metal and Plastic Processing Operator
Office Machine Operator
Teachers, Non-postsecondary
Printing Machine Operators
Technical Support Staff
Managerial Related
Health Technologists and Diagnosing
Librarians and Curators
Fabricators
Therapists
Cleaning and Building Service

Table 8: The 15 most and least immigrant-intensive occupations, defined in terms ofimmigrant earning shares at the national level, for low-education immigrants (less than ahigh-school education)

Most and least immigrant-intensive occupations (medium-education immigrants)
15 most immigrant-intensive occupations
15 least immigrant-intensive occupations
Housekeeping
Firefighting
Extractive
Arts and Athletes
PoliceFood Preparation and Service
Teachers, Postsecondary
Lawyers and Judges
Woodworking Machine Operators
Textile Machine Operator
Personal Service
Transportation and Material Moving
Social Scientists, Urban Planners and Architects Electronic Repairer
Precision Production, Other
Construction Trade
Health Assessment
Misc. Repairer
Health Service
Science Technicians
Office Machine Operator
Supervisors, Protective Services
Librarians and Curators
Machine Operator, Other
GuardsEngineers
Natural Science
Vehicle Mechanic
Therapists
Fabricators

Table 9: The 15 most and least immigrant-intensive occupations, defined in terms ofimmigrant earning shares at the national level, for medium-education immigrants (highschool graduates and some college education)

Online Appendix 17

Figure 9: Share of Immigrant Workers in total Commuting Zone Population
Most and least immigrant-intensive occupations (high-education immigrants)
15 most immigrant-intensive occupations 15 least immigrant-intensive occupations
Textile Machine Operator
Teachers, Non-postsecondary
Lawyers and Judges
Metal and Plastic Processing Operator
Health Diagnosing and Technologists
Firefighting
Housekeeping
Extractive
Precision Production, Other
Supervisors, Protective Services
PoliceMetal and Plastic Machine Operator
Health Service
Woodworking Machine Operators
Agriculture
Office Machine Operator
Science Technicians
Therapists
Food Preparation and Service
Social, Recreation and Religious Workers
Engineers
Sales, All
Vehicle Mechanic
Construction Trade
Transportation and Material Moving
Natural Science
Teachers, Postsecondary
Executive, Administrative, and Managerial
Health Assessment
Librarians and Curators

Table 10: The 15 most and least immigrant-intensive occupations, defined in terms ofimmigrant earning shares at the national level, for high-education immigrants (a college
degree or more)

Online Appendix 18

Iacross Nontradable Occupations within CZ
Figure 10: Coefficient of Variation of SroI
Figure 11: Coefficient of Variation of Sro
across Tradable Occupations within CZ

Online Appendix 19

I
Occupation Immigrant Intensity within CZ, Sro

LA

10 Most Tradable∗

19 Least Tradable∗∗

Occupations
Fabricators+
Printing Machine Operators+
Metal and Plastic Processing Operators+
Woodworking Machine Operators+
Textile Machine Operators
Math and Computer Science
Precision Production, Food and Textile
Records Processing
Machine Operators, Other
Computer, Communication Equipment Operators
Social, Recreation and Religious Workers
Cleaning and Building Service
Electronic Repairer
Lawyers and Judges
Vehicle Mechanic
PoliceHousekeeping
Teachers, Postsecondary
Health Assessment
Food Preparation and Service
Personal Service
Firefighting
Related Agriculture
Extractive
Production, Other
GuardsConstruction Trade
Therapists
Supervisors, Protective Services

.324
.153
.352
.457
.714
.125
.218
.136
.262
.104
.093
.242
.1
.055
.207
.054
.537
.148
.215
.337
.175
.027
.442
.11
.186
.08
.144
.11
.03

1980
All CZs
Mean Std. Dev.
.027
.054
.019
.051
.038
.133
.023
.09
.053
.103
.026
.086
.024
.034
.016
.024
.027
.058
.012
.024
.023
.037
.025
.042
.01
.022
.006
.031
.018
.033
.014
.048
.04
.068
.046
.056
.03
.046
.034
.044
.023
.031
.008
.026
.041
.077
.02
.06
.019
.033
.014
.031
.019
.031
.027
.087
.008
.066

LA
.628
.433
.646
.72
.899
.364
.464
.301
.589
.274
.284
.527
.267
.124
.441
.119
.823
.283
.484
.527
.325
.03
.679
.164
.374
.225
.396
.287
.117

2012
All CZs
Mean Std. Dev.
.068
.095
.042
.093
.053
.158
.073
.163
.14
.178
.053
.065
.085
.096
.03
.044
.11
.11
.034
.088
.032
.042
.076
.093
.025
.047
.019
.051
.039
.063
.016
.029
.165
.174
.109
.078
.042
.065
.092
.085
.05
.053
.01
.023
.142
.134
.042
.092
.043
.057
.026
.042
.054
.067
.037
.051
.016
.056

I
Table 11: Summary Statistics of Srofor the most and least tradable occupations in Los
Angeles and across all CZs
Notes: ∗ : the most tradable occupations ordered by decreasing tradability score; + : occupations that achieve the maximum
tradability score; ∗∗ : the least tradable occupations that achieve the minimum tradability score.

E

Robustness

In this section we conduct sensitivity analysis of our baseline regressions, where we start bypresenting results for the allocation regressions (baseline results are in Table 1) and follow
these with results for the labor payment regressions (baseline results are in Table 2).
First, in Section E.1, we examine evidence of persistent confounding trends and checkrobustness to alternative sample restrictions. By regressing outcomes over 1950 to 1980 on
the immigration shock over 1980 to 2012, we check whether our results may be contaminatedby secular regional trends in labor demand. Sensitivity to such trends is a common critiqueof the Card approach. We then vary the time period for our analysis, by changing the startyear or the end year, and the set of commuting zones included in the sample, by dropping thefive largest immigrant-receiving CZs. These exercises allow us to check whether our results
may be subject to confounding factors that are unique to our baseline 1980 to 2012 period
Online Appendix 20

and whether our results may be contaminated by the presence of these large CZs, shocks
to which may affect national immigration patterns. We discuss results for these analyses
in more detail below. In Section E.1, we also alter the start year and the end year of ouranalysis.
Second, in Section E.2, we consider alternative methods to construct our instrumentalIvariables. We replace initial immigrant cost shares in (26), Sreo
, with alternative cost sharesconstructed using data on regions with similar aggregate shares of immigrants (shares ofIforeigners out of total population) as region r, S−reo. Specifically, we first calculate the shareof immigrants in each region-education cell in 1980.52 For a given region r, we calculate
the absolute difference in the share of immigrants—for each education group—between r
and all the other regions that are not in the same state as r. We then take the averagevalue of the differences across the three education groups to obtain a single measure foreach of the out-of-state regions. Finally, we select the top 50 regions with the smallest
average difference in immigrant shares to construct the alternative immigrant cost share,I
S−reo, using the employment-weighted average immigrant cost shares for these 50 regions.
This check addresses concerns about the endogeneity of (initial) immigrant cost shares to(persistent) regional technology shocks In the second check, we replace our baseline costshares measured in 1980 with alternative cost shares measured as the average of 1970 and1980 values. This check addresses concerns about measurement error in cost shares. Because
the results for these alternative instruments are substantially the same as those reported in
Section 4.4 (both for the allocation regressions and for the labor payment regressions), we
do not discuss them further below.
Third, in Section E.3, we vary the definition of tradable and nontradable occupations.
The exercises we perform include (i) dropping the middle eight occupations in terms of
tradability, leaving 21 tradable and nontradable occupations; and (ii) redefining tradable
occupations as, instead of being those above the 50th percentile of tradability, being thoseeither above the 40th percentile of tradability or above the 60th percentile of tradability,
where the first alternative creates 30 tradable and 20 nontradable occupations and the second
creates 20 tradable and 30 nontradable occupations. Again, because these results are very
similar to those reported in Section 4.4 (both for the allocation and the labor payment
regressions), we do not discuss them in more detail below.
Fourth, in Section E.4, we present evidence to rule out alternative explanations for our
empirical results, by dropping workers employed in the top quartile of occupations in termsof intensity in routine tasks or by dropping workers in occupations in the top quartile ofoccupations in terms of intensity in communication tasks. The first restriction addresses
concerns about confounding factors related to pressures for automation in routine-intensive
jobs, while the second addresses concerns about the insulation of native workers from immigration impacts in jobs requiring language-based interaction. These results are also very
similar to those reported in Section 4.4 and we do not discuss them further.
Fifth, in Section E.5, we examine the sensitivity of the results to alternative aggregation schemes for the 50 occupations that we use in the analysis in order to verify that our
results are not somehow conditioned by the particular scheme that we employ (from 69 oc52

The education groups are less than a high-school education, high-school graduates and those with somecollege education, and college graduates.

Online Appendix 21

cupations based on the sub-headings of the 1990 Census Occupational Classification System,
up to 64 occupations that are consistent across time following David Dorn’s categorization(http://www.ddorn.net/) and combining agriculture related occupations, and then up to
50 occupations to combine occupations that are similar in education profile and tradability
but whose small size creates measurement problems, given the larger number of CZs in ourdata). When we either expand the set of occupations to 59—by breaking out all but the five
occupations with the smallest cell sizes at the tenth percentile across CZs in the 1980 Census—or contract the set of occupations to 41—by dropping all of our baseline occupations
that are aggregates of David Dorn’s categorization—we obtain results that are substantiallythe same as those in Section 4.4 and we do not elaborate on these findings.
Sixth, in Section E.6, we move from separating occupations according to their tradability to separating industries according to their tradability. Following convention, we
define tradable industries to include goods producing sectors—agriculture, manufacturing,and mining—and nontradable industries to include services. Our discussion of these results
is below.

E.1

Persistent regional trends and alternative periods

In Section E.1.1, we redefine the time period for the dependent variable to be changes over1950 to 1980, rather than over 1980 to 2012, while keeping the regressors the same. In thismanner, we check whether current immigration shocks relate to common changes in native
allocations and total labor payments in both the current period and the pre-period, which
if true could indicate that our results are the byproduct of persistent local labor demand
shocks (that drive both immigration and changes in local labor market outcomes). Because
region-occupation labor markets are subject to myriad shocks across space and time, we
recognize that the immigration flows on which we focus may not be the most importantshock affecting these units. Our intent in this section is, in the presence of many possible
shocks, to verify that our results on native allocations and total labor payments are not theresult of persistent regional labor demand shocks (such that our regressions would deliver
qualitatively similar impact coefficients no matter if the time period for the immigration
shock preceded or succeeded the change in outcomes to which they were matched).
Table 12 shows that the 2SLS-estimated impact of the current immigration shock on
the allocation of low-education native workers within tradable occupations in the pre-period
is negative and insignificant, whereas this impact is zero in our baseline results in Table
1. The analysis also yields a 2SLS coefficient on the immigration shock interacted with
the nontradable dummy that is positive and insignificant, as opposed to negative and precisely estimated in Table 1. Turning to high-education workers, the 2SLS coefficient on theimmigration shock in Table 12 is negative and significant, as opposed to zero in Table 1,
indicating that future immigration shocks, xro , are higher in tradable occupations with lower
past native employment growth; the 2SLS coefficient on the immigration shock interactedwith the nontradable dummy reverses sign from Table 1 and is positive and significant.
The null effects of immigration on native-born employment in tradable occupations and thecrowding-out effect of immigration on native-born employment in nontradable occupations
are thus not evident when we examine the correlation of current immigration shocks withpast changes in native-born employment.
Online Appendix 22

A potential explanation for the coefficient estimates in Table 1 having the opposite signs
from those in Table 12—in which the native employment change is for 1950-80 and the immigration shock is for 1980-2012—is that the immigration shock for 1980-2012 is negatively
correlated with the corresponding shock for 1950-80. We cannot test this hypothesis forthe same reason that we cannot estimate the impact of immigration shocks on native labormarket outcomes in the 1950-1980 period: we cannot construct the region-occupation immigration shock, xro , for the period 1950-1980. To construct xro , we require immigrant costI
. However, in the 1950 census, the vast majority of observations
shares by education cell, Sreo
are missing either education or income information.
In Table 13, we repeat the analysis in Table 12, now defining the outcome variable tobe the change in total labor payments by region and occupation over the 1950 to 1980
period. Whereas in our baseline Table 2 the immigration shock for 1980 to 2012 causes
a contemporaneous increase in labor payments to more immigrant-intensive occupations
within tradables and a null effect within nontradables, we see no such impact of the same
shock on outcomes for labor payments in the pre-period. The 2SLS coefficients in Table 13
show a zero effect of the current-period immigration shock on the pre-period change in labor
payments, either within nontradables or within tradables. We interpret the results in Tables
1 and 13 as evidence against the hypothesis that our results are the byproduct of persistent
local labor demand shocks that are responsible both for immigration inflows to a region andfor regional changes in occupational employment and labor payments.
In Section E.1.2, we alter the beginning year or the end year of our analysis. Whenaltering the end year from 2012 to 2007 in Tables 14 and 15, such that the sample period
now excludes the Great Recession and subsequent recovery, the results are qualitatively very
similar to those in Section 4.4: immigration leads to stronger crowding out of natives within
nontradables compared to within tradables and to a larger increase of total labor payments
within tradables compared to within nontradables. When altering the beginning year of theanalysis from 1980 to 1990 in Tables 16 and 17,53 there is still clear evidence among higheducation workers of stronger crowding out within nontradables relative to within tradables,
but among low-education workers evidence of stronger crowding out within nontradables
is weaker. While for the high-education group the 2SLS-estimated impact of immigration
on native allocations within nontradables is negative and precisely estimated, for the loweducation group it is close to zero and imprecise. The labor payments regressions, however,continue to show evidence of stronger output adjustment within tradables compared towithin nontradables. Within tradables, immigration leads to a significant increase in labor
payments in more immigrant-intensive occupations, whereas within nontradables this impact
is much smaller and statistically indistinguishable from zero.
Finally, in Section E.1.3, we rerun our allocation and labor payment regressions, excluding from the sample the five largest immigrant-receiving commuting zones (Los Angeles/Riverside/Santa Ana, New York, Miami, Washington, DC, and Houston). These CZs aremajor gateway cities for immigrants. It is conceivable that productivity shocks to immigrantintensive occupations in these localities could affect immigrant inflows in the aggregate for
Ic
When calculating x∗ro , allocations of immigrants by source country across regions, fre, are calculated∗Iusing 1980 data. When calculating xro and xro , immigration cost shares, Sreo , are calculated using 1990
data.
53

Online Appendix 23

the U.S., which could create a source of simultaneity bias in the estimation. In Tables 18
and 19 we see, however, that our are results are materially unchanged by excluding thesecommuting zones.
E.1.1

Persistent regional employment trends
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1950-1980
(1)
OLS

(2)
Low Ed2SLS-.290**(.141).314**(.124)-.405 -.460**(.327) (.217)
.184
.219
(.222) (.142)-.377* -.785***(.204)(.266).985*** 1.545***(.237)(.270)

Obs
R-sq

21669
.717

21669
.716

21669
.718

6420
.654

6420
.653

6420
.655

Wald Test: P-values

0.78

0.31

0.10

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

35.28
20.31

(3)

(1)

RF

OLS

(2)
High Ed
2SLS

(3)
RF
-.576***(.187)
1.162***(.199)

18.81
53.08

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 12: Testing for persistent trends in region-occupation employment growth

Online Appendix 24

Dependent variable: log change in labor payments in a region-occupation, 1950-1980
(1)
OLS

(2)
2SLS

(3)
RF

-.010
(.156).224(.177)-.005(.365).025(.341)-.179(.306).078(.267)

Obs
R-sq

23321
.808

23321
.808

23321
.808

Wald Test: P-values

0.01

0.91

0.45

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

42.58
23.04

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start ofperiod CZ-occupation population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 13: Testing for persistent trends in region-occupation employment growth
E.1.2

Alternative time periods
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2007
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.018
(.076)-.410***(.075)-.139(.160)-.352***(.115)-.125(.106)-.296**(.115)-.015-.024(.0436)(.076)-.353*** -.413**(.121)(.162)-.0212(.070)-.363**(.138)

Obs
R-sq

33291
.832

33291
.832

33291
.832

25876
.692

25876
.692

25876
.693

Wald Test: P-values

0.00

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro(2)
High Ed
2SLS

120.63
64.89

(3)
RF

67.24
66.80

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 14: Alternative period: 1980-2007

Online Appendix 25

Dependent variable: log change in labor payments in a region-occupation, 1980-2007
(1)
OLS

(2)
2SLS

(3)
RF

.355***(.107)-.392***(.124).353**(.139)-.457***(.132).261**(.106)-.345***(.083)

Obs
R-sq

34738
.888

34738
.888

34738
.887

Wald Test: P-values

0.51

0.12

0.12

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

64.02
104.47

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start ofperiod CZ-occupation population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 15: Alternative period: 1980-2007

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1990-2012
(1)
OLS

(2)
Low Ed
2SLS

RF

OLS

(2)
High Ed
2SLS.187**(.090)-.270**(.115).140 .191**(.103) (.077)
.015
-.007
(.374) (.231)-.048(.089)-.216**(.105)-.222*(.132)-.339***(.131)-.146(.119)-.305***(.112)

Obs
R-sq

33957
.776

33957
.776

33957
.776

28089
.601

28089
.600

28089
.602

Wald Test: P-values

0.25

0.60

0.36

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

64.13
21.33

(3)

(1)

(3)
RF

56.23
39.41

Notes: To construct the Card instrument, we use the 1980 immigrant distribution by source region and education.
Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 16: Alternative period: 1990-2012

Online Appendix 26

Dependent variable: log change in labor payments in a region-occupation, 1990-2012
(1)
OLS

(2)
2SLS

(3)
RF

.559***(.082)-.464***(.091).513***(.130)-.260*(.150).718***(.119)-.557***(.095)

Obs
R-sq

35127
.869

35127
.869

35127
.870

Wald Test: P-values

0.08

0.17

0.02

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

71.57
24.01

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start ofperiod CZ-occupation population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 17: Alternative period: 1990-2012
E.1.3

Dropping large commuting zones
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

(2)
High Ed
2SLS.088(.053)-.272***(.085).034(.091)-.351***(.080).025(.073)-.339***(.093).008(.043)-.225*(.087)-.051-.047(.072) (.059)-.2222* -.195(.129) (.116)

Obs
R-sq

33473
.827

33473
.827

33473
.827

26405
.687

26405
.687

26405
.687

Wald Test: P-values

0.04

0.00

0.00

0.00

0.00

0.01

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

29.86
27.66

(3)
RF

22.79
41.44

Notes: Drop 5 largest immigrant-receiving CZs: LA/Riverside/Santa Ana, New York, Miami, Washington DC,
Houston. Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 18: Dropping top 5 immigrant-receiving commuting zones

Online Appendix 27

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.284***(.074)-.207**(.088).155(.1056)-.189**(.096).129(.100)-.177*(.091)

Obs
R-sq

34642
.895

34642
.895

34642
.895

Wald Test: P-values

0.14

0.49

0.30

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

40.76
35.57

Notes: Drop 5 largest immigrant-receiving CZs: LA/Riverside/Santa Ana, New York, Miami,
Washington DC, Houston. Robust standard errors (in parentheses) are clustered on state. Models areweighted by start of period CZ-occupation population. For the Wald test, the null hypothesis is thatthe sum of the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics forthe first stage regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 19: Dropping top 5 immigrant-receiving commuting zones

Online Appendix 28

E.2

Instrumentation
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.089*
(.049)-.303***(.062).216(.167)-.810***(.241).126(.101)-.524***(.164).022(.036)-.309***(.097)-.096-.08(.126)(.085)-.992*** -.645***(.224)(.170)

Obs
R-sq

33723
0.84

33723
0.83

33723
0.84

26644
0.70

26644
0.69

26644
0.70

Wald Test: P-values

0.00

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

54.62
35.67

(2)
High Ed
2SLS

(3)
RF

46.42
49.07

Notes: S−reo is constructed using 50 out-of-state CZs with share of immigrants most similar to r. Robust standard
errors (in parentheses) are clustered on state. Models are weighted by start of period CZ-occupation-educationgroup native-born population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: *10%, ** 5%, ***1%.

Table 20: Using S−reo to calculate the instrument

Online Appendix 29

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

.089*
(.049)-.303***(.062)-.006(.095)-.290**(.117)

Obs
R-sq

33723
.836

Wald Test: P-values

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

OLS

(2)
High Ed
2SLS

RF

-.005
(.057)-.220**(.084).022(.036)-.309***(.097)-.068(.072)-.503***(.181)-.033(.047)-.227**(.101)

33723
.836

33723
.836

26644
.699

26644
.697

26644
.699

0.00

0.00

0.00

0.00

0.00

131.70
45.28

(3)

25.76
47.09

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 21: Using the average values in 1970 and 1980 to construct immigrant share of laborIpayments Sreo

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.392***(.115)-.351***(.116)

1.293***(.208)-1.212***(.204).727***(.169)-.648***(.149)

Obs
R-sq

34892
0.90

34892
0.89

34892
0.90

Wald Test: P-values

0.38

0.40

0.31

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

52.56
46.25

Notes: S−reo is constructed using 50 out-of-state CZs with share of immigrants most similar to r.
Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation population. For the Wald test, the null hypothesis is that the sum of the coefficients on
xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 22: Using S−reo to calculate the instrument
Online Appendix 30

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.392***(.115)-.351***(.116).593**(.236)-.635***(.225).352**(.154)-.374***(.138)

Obs
R-sq

34892
.897

34892
.897

34892
.897

Wald Test: P-values

0.38

0.58

0.68

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

175.6657.73

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start ofperiod CZ-occupation population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 23: Using the average values in 1970 and 1980 to construct immigrant share of laborIpayments Sreo

Online Appendix 31

E.3

The cutoff between tradable and nontradable occupations
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.238***(.059)-.439***(.096).152*(.085)-.477***(.095).116*(.067)-.391***(.087).087*(.051)-.396***(.110).036.046(.087)(.086)-.487*** -.420***(.131)(.116)

Obs
R-sq

28035
.827

28035
.827

28035
.827

21262
.692

21262
.691

21262
.692

Wald Test: P-values

0.02

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

74.19
56.58

(2)
High Ed
2SLS

(3)
RF

63.81
46.09

Notes: Include the top 21 most tradable (and least tradable) occupations, dropping 8 middle occupations. Robust
standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation-education group native-born population. For the Wald test, the null hypothesis is that the sum of
the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 24: Alternative tradability cutoff (21T and 21N)

Online Appendix 32

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.035
(.051)-.226***(.073)-.089(.086)-.248***(.082)-.041(.057)-.243***(.075)-.011(.031)-.303***(.093)-.065-.058(.055)(.048)-.383*** -.301***(.116)(.093)

Obs
R-sq

33723
.832

33723
.832

33723
.832

26644
.700

26644
.700

26644
.700

Wald Test: P-values

0.02

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

126.7355.62(2)High Ed
2SLS

(3)
RF

52.29
47.39

Notes: Separate 50 occupations into 30 tradable and 20 nontradable occupations. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation-education groupnative-born population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: *10%, ** 5%, ***1%.

Table 25: Alternative tradability cutoff (30T and 20N)

Online Appendix 33

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.232***(.059)-.393***(.084).144*(.085)-.290***(.083).114*(.066)-.228***(.073).087(.057)-.318***(.094).030.0481(.094)(.091)-.353*** -.322***(.118)(.113)

Obs
R-sq

33723
.840

33723
.84

33723
.839

26644
.698

26644
.698

26644
.699

Wald Test: P-values

0.01

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

72.34
53.20

(2)
High Ed
2SLS

(3)
RF

71.89
42.21

Notes: Separate 50 occupations into 20 tradable and 30 nontradable occupations. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation-education groupnative-born population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: *10%, ** 5%, ***1%.

Table 26: Alternative tradability cutoff (20T and 30N)

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.590***(.128)-.553***(.133).647***(.158)-.691***(.132).507***(.111)-.529***(.084)

Obs
R-sq

29122
.893

29122
.893

29122
.892

Wald Test: P-values

0.41

0.65

0.76

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

50.58
88.03

Notes: Include the top 21 most tradable (and least tradable) occupations, dropping 8 middle
occupations. Robust standard errors (in parentheses) are clustered on state. Models are weighted bystart of period CZ-occupation population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 27: Alternative tradability cutoff (21T and 21N)
Online Appendix 34

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.349***(.104)-.323***(.093).288*(.154)-.341***(.083).269**(.127)-.297***(.068)

Obs
R-sq

34892
.895

34892
.895

34892
.895

Wald Test: P-values

0.52

0.57

0.70

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

81.81
89.99

Notes: Separate 50 occupations into 30 tradable and 20 nontradable occupations. Robust standard
errors (in parentheses) are clustered on state. Models are weighted by start of period CZ-occupation
population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 28: Alternative tradability cutoff (30T and 20N)

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.605***(.132)-.563***(.124).677***(.163)-.680***(.122).522***(.114)-.503***(.085)

Obs
R-sq

34892
.902

34892
.901

34892
.901

Wald Test: P-values

0.31

0.97

0.78

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

55.32
65.89

Notes: Separate 50 occupations into 20 tradable and 30 nontradable occupations. Robust standard
errors (in parentheses) are clustered on state. Models are weighted by start of period CZ-occupation
population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 29: Alternative tradability cutoff (20T and 30N)
Online Appendix 35

E.4

Alternative mechanisms
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

(2)
High Ed
2SLS.083*(.044)-.304***(.097).137**(.066)-.435***(.083).110(.067)-.359***(.064)-.052(.036)-.221**(.092)-.075-.052(.061)(.057)-.326** -.290**(.128)(.115)

Obs
R-sq

32997
.822

32997
.822

32997
.822

24693
.706

24693
.706

24693
.707

Wald Test: P-values

0.01

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

82.28
63.32

(3)
RF

43.91
56.13

Notes: Drop workers in routine-intensive occupations, defined as occupations that have a routine intensity (Autorand Dorn, 2013) higher than 75% of all workers. Robust standard errors (in parentheses) are clustered on state.
Models are weighted by start of period CZ-occupation-education group native-born population. For the Wald test,
the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke(AP) F-statistics for the first stage regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 30: Dropping workers employed in routine-intensive occupations

Online Appendix 36

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.328**(.134)-.290**(.138).385*(.217)-.429**(.176).346*(.175)-.377***(.126)

Obs
R-sq

33817
.890

33817
.890

33817
.891

Wald Test: P-values

0.46

0.69

0.70

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

63.20
86.31

Notes: Drop workers in routine-intensive occupations, defined as occupations that have a routine
intensity (Autor and Dorn, 2013) higher than 75% of all workers. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation population.
For the Wald test, the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero.
We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: * 10%, **5%, ***1%.

Table 31: Dropping workers employed in routine-intensive occupations

Online Appendix 37

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012(1)(2)
Low Ed
OLS
2SLS
xro

(3)

(1)
OLS

(2)
High Ed
2SLS

RF

(3)
RF

.112*
(.066)-.296***(.074)-.047(.116)-.211*(.115)-.026(.082)-.200*(.103)-.015(.054)-.234***(.079)-.136(.088)-.342***(.120)-.116(.085)-.278***(.010)

Obs
R-sq

31172
.839

31172
.838

31172
.839

22972
.672

22972
.671

22972
.672

Wald Test: P-values

0.01

0.00

0.00

0.00

0.00

0.00

Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

63.60
95.72

120.90101.70Notes: Drop workers in communication-intensive occupations, defined as occupations that have a communication
intensity index (Peri and Sparber, 2009) higher than 75% of all workers. Robust standard errors (in parentheses)
are clustered on state. Models are weighted by start of period CZ-occupation-education group native-born
population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero.
We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: * 10%, ** 5%,***1%.

Table 32: Dropping workers employed in communication-intensive occupations

Online Appendix 38

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.444***(.119)-.364***(.126).408**(.168)-.326**(.160).378***(.135)-.311**(.127)

Obs
R-sq

31974
.883

31974
.883

31974
.882

Wald Test: P-values

0.12

0.33

0.25

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

66.80
113.15

Notes: Drop workers in communication-intensive occupations, defined as occupations that have acommunication intensity index (Peri and Sparber, 2009) higher than 75% of all workers. Robust
standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation population. For the Wald test, the null hypothesis is that the sum of the coefficients on
xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 33: Dropping workers employed in communication-intensive occupations

Online Appendix 39

E.5

Alternative occupation aggregations
Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.106**(.047)-.244***(.066).019(.089)-.245***(.073).018(.063)-.208***(.066)-.024(.032)-.264***(.088)

-.088
-.071
(.06)
(.052)-.336*** -.278***(.111)(.098)

Obs
R-sq

40218
.825

40218
.825

40218
.825

31069
.671

31069
.670

31069
.671

Wald Test: P-values

0.06

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

90.36
78.33

(2)
High Ed
2SLS

(3)
RF

39.79
100.35

Notes: From 50 occupations, we disaggregate all but the five occupations that have the smallest cell sizes at thetenth percentile across CZs in the 1980 Census. These are Social Scientists and Urban Planners, HealthDiagnosing, Adjusters and Investigators, Precision Textile, and Precision Wood. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation-education groupnative-born population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: *10%, ** 5%, ***1%.

Table 34: Disaggregating to 59 occupations

Online Appendix 40

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.375***(.103)-.302***(.108).359**(.147)-.346***(.119).301**(.118)-.285***(.090)

Obs
R-sq

41390
.889

41390
.889

41390
.888

Wald Test: P-values

0.08

0.85

0.75

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

58.65
99.70

Notes: From 50 occupations, we disaggregate all but the five occupations that have the smallest cell
sizes at the tenth percentile across CZs in the 1980 Census. These are Social Scientists and Urban
Planners, Health Diagnosing, Adjusters and Investigators, Precision Textile, and Precision Wood.
Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation population. For the Wald test, the null hypothesis is that the sum of the coefficients on
xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 35: Disaggregating to 59 occupations

Online Appendix 41

Dependent variable: log change in the employment of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed
2SLS

RF

OLS

.213***(.079)-.394***(.120).087(.124)-.436***(.127).095(.1163)-.391***(.111)-.050(.053)-.238***(.090)-.143-.113(.092) (.086)-.275** -.230*(.135) (.125)

Obs
R-sq

27475
.837

27475
.837

27475
.837

20565
.712

20565
.712

20565
.712

Wald Test: P-values

0.04

0.00

0.00

0.00

0.00

0.00

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

96.12
70.21

(2)
High Ed
2SLS

(3)
RF

53.21
94.91

Notes: Drop all nine baseline occupations that are aggregates of David Dorn’s categorization. Occupations
dropped are Social Scientists, Urban Planners and Architects, Health Technologists and Diagnosing, Secretaries
and Office Clerks, Records Processing, Misc. Administrative Support, Precision Food and Textile, Precision Other,
Production Other, and Transportation and Material Moving. Robust standard errors (in parentheses) areclustered on state. Models are weighted by start of period CZ-occupation-education group native-born population.
For the Wald test, the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero. We report
Angrist-Pischke (AP) F-statistics for the first stage regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 36: 41 occupations

Online Appendix 42

Dependent variable: log change in labor payments in a region-occupation, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.530***(.163)-.500***(.153).547**(.260)-.606***(.191).449**(.188)-.487***(.130)

Obs
R-sq

28447
.894

28447
.894

28447
.894

Wald Test: P-values

0.42

0.49

0.57

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

81.08
93.18

Notes: Drop all nine baseline occupations that are aggregates of David Dorn’s categorization.
Occupations dropped are Social Scientists, Urban Planners and Architects, Health Technologists andDiagnosing, Secretaries and Office Clerks, Records Processing, Misc. Administrative Support, Precision
Food and Textile, Precision Other, Production Other, and Transportation and Material Moving.
Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-occupation population. For the Wald test, the null hypothesis is that the sum of the coefficients on
xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 37: 41 occupations

E.6

Industry analysis

In this section, we report results for our labor allocation and labor payments regressions
applied to industries rather than to occupations. We categorize all goods-producing industries—agriculture, mining, and manufacturing—as tradable and all service-producing industries as non-tradable. In Table 38, we list the 34 industries considered in this analysis, basedon the sub-headings of the 1990 Census Industry Classification System. This alternative
industry-based classification has the advantage of using categories that are familiar to tradeeconomists in terms of the activities that are conventionally deemed tradable or nontradable.
It has the disadvantage, however, of excluding from tradables portions of the service sector
in which activity appears to be highly traded. Because these activities are often occupation
specific (e.g., programming software, managing businesses, designing buildings), we use an
occupation-based measure in our baseline analysis.54
54

Alternative categorizations of industry tradability include Mian and Sufi (2014), who measure tradability according to geographic Herfindahl-Hirschman Indexes, following the logic that more geographicallyconcentrated industries are likely to be more tradable. Relative to our approach, HHIs have the appealing
property of designating some services as tradable (e.g., finance and insurance), but the unappealing 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 and in unreported results in which we define
tradable (nontradable) industries as those with above (below) median HHIs.

Online Appendix 43

Tradable and non-tradable industries (goods vs. services)+
Tradable industries
Non-tradable industries
Agriculture, forestry and fisheries
MiningTransportation equipment
Professional and photographic equipment and watches
Petroleum and coal products
Toys, amusement, and sporting goods
Printing, publishing and allied industries
Apparel and other finished textile products
Manufacturing industries, others
Machinery and computing equipment
Rubber and miscellaneous plastics products
Textile mill products
Chemicals and allied products
Leather and leather productsElectrical machinery, equipment, and supplies
Furniture and fixtures
Tobacco manufactures
Food and kindred products
Lumber, woods products (except furniture)
Paper and allied products
Stone, clay, glass and concrete products

Retail trade
Personal services
Professional and related services
Transportation
Wholesale trade, durables
Wholesale trade, nondurables
Communications
Business and repair services
Finance, insurance, and real estateEntertainment and recreation services
Utilities and sanitary services

Table 38: Tradable and non-tradable industries
Notes: + : We group all goods, i.e. agriculture, mining and manufacturing, as tradable industries; and all services as
non-tradable industries. We drop the construction industry for this analysis.

When we revisit our baseline analyses using industries, Table 39 shows that our allocation
regressions are largely robust to using industries in place of occupations, and Table 40 showsthat our labor payments regressions are fully robust to replacing occupations with industries.
In the allocation regressions, the impact of the immigration shock on tradables is positive
but imprecisely estimated, consistent with the absence of crowding in or crowding out within
tradables in our baseline analysis. Of course, the elasticity of substitution between natives
and immigrants within industries need not take the same value as its counterpart within
occupations. Hence, the key prediction is for the interaction between the immigration shockand the nontradable dummy. This interaction term is negative and precisely estimated in all
regressions for high-education workers; while it is negative in all regressions for low-education
workers, it is only significant in the OLS specification. The results for our labor payments
regression applied to industries are very similar to our baseline results. There is a positive andsignificant effect of immigration on labor payments for more immigrant-intensive industries
within tradables and an effect within nontradables that is indistinguishable from zero.

Online Appendix 44

Dependent variable: log change in the employment of domestic workers in aregion-industry, 1980-2012(1)(2)
Low Ed
OLS
2SLS

(3)

(1)

RF

.244**(.117)-.347**(.137).571(.439)-.486(.418)

Obs
R-sq

22193
.827

Wald Test: P-values

0.35

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

OLS

(2)
High Ed
2SLS

RF

.609
(.410)-.474(.353).430***(.131)-.725***(.180).540(.395)-.963**(.489).576*(.293)-.887***(.323)

22193
.826

22193
.828

17203
.723

17203
.723

17203
.723

0.40

0.24

0.01

0.01

0.01

50.00
27.70

(3)

100.9215.06

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start of period
CZ-industry-education group native-born population. For the Wald test, the null hypothesis is that the sum of thecoefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage
regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 39: Domestic allocation of workers across industries using goods-producing industries
as tradable and service industries as non-tradable

Dependent variable: log change in labor payments in a region-industry, 1980-2012
(1)
OLS

(2)
2SLS

(3)
RF

.444**(.166)-.474**(.180).960**(.464)-.847*(.512).733**(.313)-.576*(.319)

Obs
R-sq

22014
.838

22014
.836

22014
.839

Wald Test: P-values

0.80

0.36

0.16

xro
Io (N ) xro

A-P F-stats (first stage)xro
Io (N ) xro

52.84
31.93

Notes: Robust standard errors (in parentheses) are clustered on state. Models are weighted by start ofperiod CZ-industry population. For the Wald test, the null hypothesis is that the sum of the coefficientson xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the first stage regressions.
Significance levels: * 10%, ** 5%, ***1%.

Table 40: Labor payments across industries using goods-producing industries as tradable
and service industries as non-tradable

Online Appendix 45

Dependent variable: change in the average wage of domestic workers in aregion-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed2SLS

RF.038***(.014)-.057**(.028).046**(.023)-.083(.052)

Obs
R-sq

33723
.639

Wald Test: P-values

0.34

xro
Io (N ) xro

AP F-stats (first stage)xro
Io (N ) xro

OLS

(2)
High Ed
2SLS

RF.038**(.017)-.076**(.037).003(.021).007(.028)-.008(.031)-.022(.037).001(.030)-.0189(.0311)

33723
.639

33723
.639

26644
.613

26644
.613

26644
.613

0.38

0.18

0.64

0.36

0.52

102.77
75.21

(3)

65.90
48.48

Notes: Observations are for CZ-occupation pairs. The dependent variable is the log change in the average
CZ-occupation wage for native-born workers; the immigration shock, xro , is in (23); Io (N ) is a dummy variable forthe 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 instrumentfor xro , and column (3) replaces the immigration shocks with the instruments. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation-education groupnative-born population. For the Wald test, the null hypothesis is that the sum of the coefficients on xro and
Io (N ) xro is zero. Significance levels: * 10%, ** 5%, ***1%.

Table 41: Average occupation wage for domestic workers

F

Wage analysis

To estimate regression 29 replacing unobserved occupation wages with observed average
wages and to estimate regression 30, we require measures of average wages by educationgroup, occupation, and CZ (reo) cell. 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 educational attainment, a quartic in years of potential experience, andall 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, occupation, and CZ. Finally, we use these values to calculate changes
in average wages in each reo cell.

Online Appendix 46

Dependent variable: log change in the constructed occupation wage of domestic workers ina region-occupation, 1980-2012
(1)

(3)

(1)

OLS

(2)
Low Ed2SLS

RF.075***(.023)-.189***(.038).039(.045)-.204***(.070)

Obs
R-sq

33723
.798

Wald Test: P-values

0.01

xro
Io (N ) xro

AP F-stats (first stage)xro
Io (N ) xro

OLS

(2)
High Ed
2SLS

RF

.033
(.031)-.171***(.050).019(.032)-.167***(.061)-.021(.057)-.234***(.087)-.006(.052)-.203***(.077)

33723
.797

33723
.797

26644
.712

26644
.711

26644
.712

0.01

0.00

0.00

0.00

0.00

102.77
75.21

(3)

65.90
48.48

Notes: Observations are for CZ-occupation pairs. The dependent variable is the constructed changes in native
occupation wages in (30); the immigration shock, xro , is in (23); Io (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 xro ,and column (3) replaces the immigration shocks with the instruments. Robust standard errors (in parentheses) areclustered on state. Models are weighted by start of period CZ-occupation-education group native-born population.
For the Wald test, the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero. Significancelevels: * 10%, ** 5%, ***1%.

Table 42: Constructed occupation wage for domestic workers

Online Appendix 47

Part III

Quantitative Model Appendix
G

Additional details of the extended model

In this section we present additional details of the extended model.

G.1

System of equilibrium equations in changes

We describe a system of equations to solve for changes in prices and quantities in the extended model. We consider the specification of the model that incorporates agglomeration
externalities governed by the parameter λ; see footnote 45. We use the “exact hat algebra”
approach that is widely used in international trade (Dekle et al., 2008). We denote with a“hat” the ratio of any variable between two time periods. The two driving forces are changes
in the national supply of foreign workers (denoted by N̂eI ) and domestic workers (denotedby N̂eD ).
We proceed in two steps. First, for a given guess of changes in occupation wages forDI
domestic and immigrant workers in each region,oro } and {Ŵro }, changes in the supply ofn {ŴD, and changes in the supply of immigrant
domestic workers by education in each region, N̂reonIc
, we calculate in each region
workers by education and source country in each region, N̂rer changes in the supply of immigrant workers by education e
I
=
N̂re

X N Ic

re
Ic
N̂re
,
I
Nre

c

changes in the total population in each region
N̂r =

X Nk

re

Nr
k,e

k
N̂re
,

changes in average group wages
ˆ k = N̂ λ
W age
re
r

X



k
k
πreo
Ŵro

θ+1

1
! θ+1

,

o

changes in occupation output prices
 1
 
1−ρ
  D 1−ρ 1−ρ
I
IIP̂ro = Sro Ŵro
+ 1 − Sro Ŵro,changes in allocations of workers across occupations
θ+1kN̂rλ Ŵro
k
π̂reo
=
θ+1 ,
ˆk
W agereOnline Appendix 48

changes in occupation output
Q̂ro =

1 X
P̂ro k,ekkˆ k N̂ k ,
W age
π̂reo
Sreo
re re

and change in aggregate expenditures (and income)Xkˆ k N̂ k .
Êr =
Sre
W age
re re
k,e
k
is defined as the total income share within region r of workers of group k, e (suchHere,PSrekk
is defined as the cost (or income) share within region r of workers= 1), Sreo
that k,e SrePIkdenotes the cost (or income)= 1), and Sroof group k, e in occupation o (such that k,e Sreo
P
I
I
I
I
share of immigrants in occupation o in region r (i.e. Sro = e Sreo). If Sro
= 0 (Sro= 1),ID= 1 (Ŵro= 1).
then we set Ŵro
Second, we update our guess of changes in occupation wages and changes in the supply
within each region r of domestic and immigrant workers by education (and, for immigrants,
also by source country) until the following equations are satisfied −α X α−η  η−1yxQ̂ro = P̂ro
Srjo
P̂jo
P̂j
Êj
j∈R

P
I
I
I
ˆ I I
1 − Sroe Sreo π̂reo W agere N̂re
=
P D D
I
ˆ D N̂ D
Sro
S
π̂
W
age
re re
e reo reo ˆ D ν
W agere
P̂r

D
N̂re
=P

D
Nje
j∈R NeD


Ic
N̂re
=P



ˆ D
W age
re
P̂j

ˆ I
W age
re
P̂r

Ic
Nje
Ic
j∈R Ne



I
Ŵro

!1−ρ

D
Ŵro

ν N̂eD

ν

ˆ I
W age
re
P̂j

ν N̂eIc

where changes in absorption prices are given by
y
P̂ro
=

X



1−α



1−η

m
Sjro
P̂jo

1
! 1−α

j∈R

P̂r =

X

A
y
Sro
P̂ro

1
! 1−η

o∈O
y

A
A
Here, Srois defined as the total absorption share in region r of occupation o, Sro≡ ProEYr ro ,x
Srjo
is the share of the value of region r’s output in occupation o that is destined for region j,

Online Appendix 49

Pro τrjo Yrjom, and Sjrois the share of the value of region r’s absorption within occupation
Pro QroP τjro Yjro 55m
Ic
Ic≡ joPro. If Nre= 0, then we set N̂re= 1.
o that originates in region j, Sjro
y
Yro
x
Srjo
≡

In this second step, we solve for |O|×|R| unknown occupation wage changes for domesticD
workers and the same for foreign workers. We
n alsoo solve for E × |R| unknown changes

Din population of domestic workers by region N̂re, and E IC × |R| unknown changes innoIc
population of immigrant workers by region N̂re, using the same number of equations.

D,
The inputs required to solve this system are: (i) values of initial equilibrium shares πreo
x
m
A
I
D
I
πreo , Sre , Sre , Sro , Sjro , Srjo and population levels for natives, immigrants by education andIcD; (ii) values of parameters θ, η, α, ν and λ; and (iii) values of changes, Nresource country Nre
in aggregate domestic supply by education N̂eD , and changes in aggregate immigrant supplykIby education and source country N̂eIc . We have omitted Sreo
and Srofrom the list of requiredkk
inputs because they can be immediately calculated given πreo and Sre
as
k
k
Sre
πreo
0
k
k0
k0 ,e0 Sre0 πre0 o

k
Sreo
=P

P I
k
I
equals both the share of labor income earned and the. In the model, πreo
= e Sreoand Sroshare of employment in occupation o by nativity k in region r (because average wages arekas the share of labor income.
equal across occupations). In practice, we measure πreo
In the next subsection we show that equilibrium price and quantity changes in the extended model coincide with those in the baseline version of our model if education groupskk
for all e).
= πrowithin each k are allocated identically across occupations (i.e. πreo

G.2

Bilateral trade and absorption shares

Given the difficulty of obtaining bilateral regional trade data by occupation that is required tomxconstruct initial equilibrium trade shares Sjro
and Srjo, we construct them given assumptions
on trade costs, as described in Section 5.2. For nontradable occupations, we assume thatx
trade costs are prohibitive across CZs (τrjo = ∞ for all j 6= r). This implies that Srro=mxm
Srro = 1 and Srjo = Srjo = 0 for all j 6= r. Absorption shares for each nontradableA
occupation, Sro, are given by
Pro Qro
A
Sro
=
,
Er
where occupation revenues, Pro Qro , are measured by labor payments of this occupation in thedata, and Er is equal to total expenditures in region r (which, by the assumption of balanced
trade, is equal to the sum of revenues—labor payments—across all occupations). For tradable
occupations, we assume instead that trade costs between a given origin-destination pairare common across occupations, τrjo = τrjo0 for all o, o0 ∈ T , and are parameterized asτrjo = τ̄ × ln (distancerj )ε for j 6= r. We also assume that occupation demand shifters are
55

In terms of our model’s primitive parameters, regions vary in their occupational output composition duekDIs
to variation in labor productivities, Akro and Treo
(for k = D, I and by education e); amenities, Ureand Ure(by source country and education group); and bilateral trade costs, τrj .

Online Appendix 50

common across regions for tradable occupations, µro = µo for o ∈ T . Equations (3) and (5)imply that region r’s sales to region j in occupation o are given by
y α−1 yPjo Yjo(58)
Erjo = (τrjo Pro )1−α Pjo


α−η
η−1
y
y
PjT
EjT ,
= µo (τrjo Pro )1−α Pjo
where ErT denotes total expenditures on tradable occupations in region r, which by tradebalance equals the sum of revenues across tradable occupations and is related to aggregate
expenditures and prices by ErT = Er (Pr /PrT )η−1 . We now describe how we solve for Erjo
given measures of ErT , τrjo , and Pro Qro and parameter values α, η.
 1
1−α
1−α
 1
y
y
1−η
1−η
Defining P̃ro = µo Pro, Erjo in equation (58) can be
and P̃jo = µo Pjo
n ore-written as a function of P̃ro ,  α−η

y η−1
y 1−α
PjT
EjT ,
Erjo = (τrjo )1−α P̃ro P̃jo(59)

where, by equations (4) and (6),
y
P̃jo
=

X

(τj 0 jo )1−α P̃j 0 o

j 0 ∈R

y
PjT

1−η

X

=

y
P̃jo

1−η
 1−α

o∈OT

Given measures of ErT , τrjo , and Pro Qro and parameter values α, η, we solve for OT × |R|
values of P̃ro using an equal number of equationsX
Pro Qro =
Erjo
(60)
j∈R

where Erjo is given by equation (59). Once we solve for tradable occupation prices P̃ro , wecalculate Erjo , which allows us to construct import, export and absorption shares as
Erjo
m
=P
Srjo
r0 Er0 jo
x
Srjo
=

and

Erjo
Pro QroPASro=j Ejro.
Er
The own export share of region r across all tradable occupations is defined asP
T Erroown
Sr = o∈O
ErT
Online Appendix 51

In our model calibration, we assume (1 − α)δ = −1.29 and set τ̄ to target a weighted averageof own export shares Srown across a selected subset of regions, as described next.
Measuring CZ-level export shares in tradables in the data. To measure CZ-level
trade shares within tradables, we use public tables from the 2007 Commodity Flow Survey(CFS), which include region-to-region trade flows. For each of the 49 CFS origin areas(henceforth CFS regions), this data includes the value of shipments that originate from the
CFS region and are destined to all U.S. destinations as well as the value of shipments thatoriginate from and are destined for the same CFS region. For each region we construct theown sales share, Srown , as the value of shipments that both originate from and are destinedfor the CFS region relative to the value of shipments that originate from the CFS region andare destined for all U.S. destinations. To concord these CFS regions to our CZs (of which
there are 722), we take the following steps. We overlay 2007 CFS regions with 1990 CZ
boundaries using QGIS. For each CFS region, we calculate the area of intersection and thearea of the union between the boundaries of the CFS region and the nearest CZ. We consider
a CFS region to be matched with a CZ if the area of the intersection of the two boundaries
is at least 70% of the area of the union of the two boundaries. Using this procedure, we
obtain 23 CFS regions that each match with one of our CZs, listed in Table 43. We thenconstruct the weighted average across these 23 CFS regions of the own sales share, weighingby the CFS region’s total sales destined for all U.S. destinations.

Online Appendix 52

CFS Area
Austin-Round Rock
Baltimore-Towson
Baton Rouge-Pierre Part
Beaumont-Port Arthur
Charleston-North Charleston
Cleveland-Akron-Elyria
Dayton-Springfield-Greenville
Detroit-Warren-Flint
Hartford-West Hartford-Willimantic
Jacksonville
Lake Charles-Jennings
LaredoLos Angeles-Long Beach-Riverside
Mobile-Daphne-Fairhope
New Orleans-Metairie-Bogalusa
Phoenix-Mesa-Scottsdale
Pittsburgh-New Castle
Raleigh-Durham-Cary
San Antonio
San Diego-Carlsbad-San Marcos
Seattle-Tacoma-Olympia
Tampa-St. Petersburg-Clearwater,
TucsonMatched CZ code
31201
11302
03500
32100
08202
15200
12501
11600
20901
07600
03700
31503
38300
11001
03300
35001
16300
01701
31301
38000
39400
06700
35100

Table 43: List of matched CFS regions and CZs

G.3

Aggregate elasticity of substitution between natives and immigrants

Because it is not a structural parameter in our model, in our parameterization we do nottarget the elasticity of substitution between domestic and immigrant workers with similar
education levels at the national level. Ottaviano and Peri, 2012 (henceforth OP) have estimated this parameter, σN , using annual variation in factor supplies and average wages at
the national level. In our notation, their estimating equation isln

W ageIet
1
NetD
=
I
+
I
+
ln
+ ιet
e
t
σN
W ageD
NetI
etwhere Ie and It are skill-group (OP leverages variation across education-experience cells
whereas we only have education cells in our model) and time effects. Differencing between
two time periods, the previous regression becomeswageIet − wageD
et = Ĩt +


1
I
nD
et − net + ι̃et .
σN

(61)

Online Appendix 53

To estimate this regression in data generated by our model, we take the following steps.
First, starting the 2012 equilibrium, we feed into our quantitative model the change innational supplies of immigrants within each education group and source country that we
consider in our two counterfactual exercises in Section 6, {nIce }e,c , and solve the model’s
general equilibrium. Second, since we have three immigrant and only two native educationgroups, within each region we aggregate wage changes across low- (high school dropout) andmedium- (high school graduate and some college) education immigrants to construct changes
in average wages for immigrants without a college degree by region. Similarly, since we have
many regions, we aggregate wage changes across CZs to construct national average wagechanges for immigrants with and without college degrees and for natives with and withoutcollege degrees. Finally, the parameters
exactly identified inequation (61),  Ĩt andIσN are then
I
D
I
D
I
D
where σN = nD
−
n
−
n
+
n
wage
−
wage
Ht
Ht
Lt
Lt
Ht
Ht − wageLt + wageLt . We recovera value of σN equal to 6.9 in the first and 8.6 in the second counterfactual exercise in Section
6. These estimates of σN are higher than the structural elasticity of substitution within
occupations, ρ = 4.6.

H

Immigrant occupation reallocation

In Section 4 we analyze empirically how native workers reallocate across occupations in
response to immigration. In this section, we analyze the reallocation of immigrant workers,
both in the extended model and in the data. We show that the predictions of our extended
model are qualitatively consistent with the data for all immigrant education groups: bothin the model and in the data there is stronger immigrant crowding out within nontradable
occupations than within tradable occupations, immigrants are crowded out of immigrantintensive nontradable occupations, and (unlike natives) immigrants are also weakly crowded
out of immigrant-intensive tradable occupations.56
At our baseline parameterization, we now show that our model predicts that a foreignlabor inflow generates crowding out of immigrants within tradable and stronger crowding outof immigrants in nontradable occupations (i.e., in response to an immigrant inflow, the sharesof immigrants employed in immigrant-intensive occupations decline within the tradable andthe nontradable groups, though more within the former than within the latter). We thenshow that we obtain qualitatively similar results empirically.
First using model-generated data from our extended model and then using Census/ACS
data, we estimate separately for the three immigrant education groups the regression,
I
I
I
nIro = αrg+ αoI + β I xro + βN
Io (N ) xro + νro.

(62)

Table 44 reports three sets of results for immigrant education groups when estimating regression (62) using model-generated data. First, we find more crowding out within nontradable
I
than within tradable occupations, βN< 0, consistent with our empirical results for natives.
I
Second, we find crowding out within nontradable occupations, β I + βN
< 0, again consistent56

We emphasize that crowding out does not imply that in response to an increase in the number of
immigrants, the employment level of immigrants in immigrant-intensive occupations falls, but instead thatthe share of immigrant employment in immigrant intensive occupations falls (across either T or N jobs).

Online Appendix 54

with our empirical results for natives. Finally, we find crowding out within tradable occupations, β I < 0, unlike our empirical results for natives. While two of these three results are
similar to our empirical (and quantitative) results for natives, the third is not.

xro
Io (N )xro
R-sq

Low Ed
−0.06
−0.19
1.00

Med Ed
−0.00
−0.31
0.99

High Ed
−0.06
−0.25
0.99

Table 44: Allocation for immigrant workers across occupations in model-generated data
Turning to Census/ACS data, Table 45 reports a corresponding set of estimation results
for the three immigrant education groups. First, we find more crowding out of immigrantI
workers within nontradable than within tradable occupations, βN< 0, for all educationgroups and across all empirical specifications, consistent with our quantitative results inI< 0, for
Table 44. Second, we find crowding out within nontradable occupations, β I + βN
all immigrant education groups and across all empirical specifications, again consistent with
our quantitative results in Table 44. Finally, we find some evidence of crowding out within
tradable occupations, consistent with our quantitative results in Table 44, although theseresults are somewhat less clear cut than in the model-generated data. Specifically, within
tradables we obtain statistically significant crowding out for high-education immigrants but
obtain imprecise estimates for both low- and medium-education immigrations (with one
positive and the other negative). In summary, our model’s predictions for immigrant allocations—reported in Table 44—are qualitatively consistent with immigrant allocations
observed in the data—reported in Table 45.
Dependent variable: log change in the employment of immigrant workers in aregion-occupation, 1980-2012
(1a)
OLS
xro

(2a)
Low Ed
2SLS

(3a)

(1b)

RF

OLS

.335
.652
.183
(.289)(.611)(.331)-1.425*** -2.044** -1.379***(.399)(.847)(.377)

Io (N ) xro-.213(.193)-.894***(.232)(2b)
Med Ed
2SLS

(3b)

(1c)

RF

OLS

-.376
-.255
(.309)(.193)-1.208*** -.850***(.353)(.133)(2c)
High Ed
2SLS-.825*** -1.391***(.172)(.266)-.472*** -.696**(.174)(.289)(3c)
RF-.962***(.198)-.404**(.180)

Obs
R-sq

5042
.798

5042
.797

5042
.799

13043
.729

13043
.728

13043
.73

6551
.658

6551
.649

6551
.662

Wald Test: P-values

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

AP F-stats (first stage)xro
Io (N ) xro

60.90
289.00

69.11
86.49

77.62
29.26

I
I
I
Notes: The table reports estimates of nIro = αrg+ αoI + β I xro + βN
Io (N ) xro + υroseparately for each education group. Robust standard errors (inparentheses) are clustered on state. Models are weighted by start of period CZ-occupation-education group foreigh-born population. For the Wald
test, the null hypothesis is that the sum of the coefficients on xro and Io (N ) xro is zero. We report Angrist-Pischke (AP) F-statistics for the firststage regressions. Significance levels: * 10%, ** 5%, ***1%.

Table 45: Allocation for immigrant workers across occupations
Finally, we remark that while our empirical results for immigrant allocations are consistent with our model-based predictions, it may appear puzzling that at our baseline parameter
Online Appendix 55

values our model predicts crowding out for immigrants within tradables (β I < 0) but neither crowding in nor out for natives within tradables (β D ≈ 0). How could immigration
lead to more crowding out among immigrants than among natives within tradables? To
be sure, the divergence between native and immigrant reallocations within tradable jobs isinconsistent with the analytic results for our model in Section 3, derived under the assumption that education cells do not differ in their relative productivities across occupations, inΦIr , iswhich case the impact parameter that indicates crowding out (in), β k ≡ (rg−ρ)(θ+1)
rg +θcommon across natives and immigrants. In subsection A.5, we provide an analytic resultthat suggests why divergence in results on crowding out for immigrants and natives becomes
possible once occupation comparative advantage differs between education groups. We show
in a special case in which rT = ρ (i.e., the output price elasticity in tradables equals theimmigrant-native substitution elasticity) that an influx of immigrants will induce neither
crowding in nor crowding out of natives (consistent with our results with only one educationgroup) but that it will induce crowding out for immigrants. Specifically, when rT = ρ, ourmodel’s prediction for reallocation for group k = D, I into (or out of) occupation o in region
P kθwagekre − nkre . Because
r contains an additional term, which is a linear function of e LLreokroDchanges in native average wages, wageD
re , and native supplies, nre , at the region-educationlevel do not vary much across regions with an immigrant influx, this term is small for natives. By contrast, this term is larger for immigrants since variation in wageIre and nIre acrossregions is larger. The presence of this additional term for immigrants (which is closer to zerofor natives) allows crowding out effects for natives and immigrants within tradables to bedissimilar. Note that as long as our Card instrument is valid, the presence of this additionalterm in the allocation regression does not complicate estimation because this regression is
reduced form. This reduced-form immigrant allocation regression provides useful identified
moments that we do not target and with which our model is qualitatively consistent, as weshow in Tables 44 and 45.

I

Labor allocation analysis

Figure 12 displays the results of estimating equation (24) using model-generated data. The
D
plots show the sensitivity of estimated values of β D and βN
to varying the value of η. See
Section 5.2 for further details on the calibration that produces these data.

Online Appendix 56

Figure 12: 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 represent the baseline valueof η = 1.65 and the value of α = 7.

JCounterfactual exercises

The figures below depict the spatial variation in the difference in wage changes between theoccupation that has the largest wage increase and the occupation that has the smallest wage
increase (or largest wage decrease) in nontradables across commuting zones, first, in Figure
13 for the counterfactual in which immigration from Latin America is reduced by 50%, and,second, in Figure 14 for the counterfactual in which immigration of high-skilled workers isdoubled. See Section 6 for further details.

Figure 13: 50% reduction in Latin American Immigrants: highest minus lowest occupation
wage increase for nontradable occupations across CZs

Online Appendix 57

Figure 14: Doubling of high education immigrants: highest minus lowest occupation wage
increase for nontradable occupations across CZs

Online Appendix 58