Modes of Migration Entry, Location Dependence, and the

Global Impacts of a skill-based US Immigration Reform

Chen Liu∗

University of California, San Diego

November 24, 2018

Please find the latest version here

Abstract

This paper develops a general equilibrium model of international migration to

analyze the economic consequences of changes in US immigration policy. Workers

choose where to live, which occupation to work, and a mode (from multiple types of

visa or illegal entry) to migrate, and the model allows heterogeneity in worker pro-

ductivity similarities across countries. Theoretically, I derive analytic expressions

for two sets of elasticity parameters, namely migration elasticity to migration cost,

and wage elasticity to migration supply — both of which are endogenous objects

of my model and are key in determining the impact of immigration policy changes.

I also show my model can undertake a realistic policy experiment in the form of

changes in the overall number of migration entries for each mode. Empirically, I

combine multiple data sources to estimate these variables and parameters that de-

termine these key elasticities, and quantify the impacts on global migration and

wages in many countries, had the U.S. shifted to a skill-based immigration system.

I find the migration and wage impacts are small both for the US and for foreign

countries. Due to migrants’ entry mode substitution, US illegal immigration in-

creases by 21%. I also find when heterogeneity in worker productivity similarities

is absent, the increase of US illegal immigration falls to 1/3 to 1/2 of the magnitude

increase in my benchmark model, while the impact of US wages would have been

doubled.

∗Ph.D Candidate, University of California, San Diego. Email address: chl110@ucsd.edu. I am thankful to myadvisor Gordon Hanson for invaluable insights and guidance. I am also grateful to Craig McIntosh, Gordon Dahl,Mitch Downey, David Lagakos, Marc Muendler, Paul Niehaus, Tommaso Porzio, Natalia Ramondo and seminarparticipants at the 24th Annual Conference of Freit-EIIT, Washington St. Louis (ESGC), WEAI graduate studentworkshop, and UC San Diego, for helpful comments. Generous research support was received from the NBERand the Alfred P. Sloan Foundation.

1

1 Introduction

Recent decades have seen rapid changes in immigration systems among developed countries.

Canada, Australia, and New Zealand, which previously admitted immigrants on the basis of

national origin or family ties, are now operating under systems that select immigrants based

mostly on education and occupational background.1 The United States, the country that re-

ceives the most immigrants, continues to prioritize immigration based on family ties to U.S.

citizens or residents, as it has for the past half century.2 In the US, there has been an on-going

debate of a skill-based immigration reform.3 Moving to a system that prioritizes highly-skilled

immigrants might suggest skill upgrading of US immigration. However, quantifying the im-

pact of this reform is challenging since individuals decide whether to live in the US, and which

types of visa they would acquire to migrate. As US immigration policy changes and the labor

markets adjust domestically and internationally, some may leave for other foreign destinations

or for home, some may stay in the US by adjusting the type of visa they acquire, while others

may stay without legal documentation. Yet, literature on the economics of immigration has not

come to capture these factors. The lack of quality data of measuring how US immigrants en-

tered and how their ways of entry differ across skill groups and across migrants from different

origin countries, make this task daunting.

This paper develops a general equilibrium model of international migration to analyze the

economic consequences of changes in US immigration policy. Workers choose where to live,

which occupation to work, and a mode (from multiple types of visa or illegal entry) to migrate,

and I allow heterogeneity in worker productivity similarities across countries. The model al-

lows aggregate migration elasticity differ across countries from where migrants can choose, re-

ferred as location dependence, where I provide micro-foundation as due to the heterogeneity in

worker productivity similarity across countries.4 Theoretically, I derive analytic expressions

for two sets of elasticity parameters, namely migration elasticity to migration cost, and wage

elasticity to migration supply — both of which are endogenous objects of my model and are

key in determining the impact of immigration policy changes. Empirically, I combine multiple

data sources to estimate these variables and parameters, and measure international migration

to OECD destinations by detailed occupations and modes of entry, for 115 countries of ori-

gin, and multiple education, gender groups. I show my model can undertake a realistic policy

experiment in the form of changes in the overall number of migration entries for each mode,

1The commonly used skill-based immigration system is the point system. Point system was first introducedby Canada in the 1960s and was adopted by Australia in 1989 and New Zealand in 1991. Recent adoptions ofpoint-based systems include: Sweden in 2003, Singapore in 2004, Hong Kong in 2006, Denmark in 2007, and theUK in 2008.

2The Immigration and Nationality Act of 1965 ended the national origin quota system and began awardingentry permits based on family ties with US citizens and residents.

3Proposal for a comprehensive skill-based reform has reflected in part by the Comprehensive ImmigrationReform Act of 2007, and more recently in 2017, the Reforming American Immigration for Strong Employment(RAISE) Act.

4For example, a stronger micro-level productivity similarity across the US labor markets than the similaritybetween the US to foreign countries, leads to a larger aggregate substitution to alternative US modes of entry andoccupations.

2

and quantify the impacts on global migration and wages both on immigrant -receiving and

-sending countries, had the U.S. shifted to a skill-based immigration system.

In my model, the migration elasticity in response to changes in mode-specific frictions dif-

fers endogenously across workers of different country of origin, and education groups, and de-

termines how the composition of US immigrants would change in response to policy changes.5

Three mechanisms are the keys. The first mechanism is which modes do immigrants use to

migrate to the US. I find increasing the employment-based migration entries would favor the

entry of college-educated Indian and Chinese the most. Perhaps surprisingly, college-educated

workers from Central America & Caribbean countries, instead of the sheer size of non-college

educated Mexicans, would be the most exposed to switch alternatives if family-based visa re-

duces.

The second mechanism is the attractiveness of other US migration modes, and how it differs

in comparing to the outside US options that immigrants could substitute to. This mechanism

is summarized by two factors. Firstly, the share of immigrants who migrate through alter-

native US modes of entry.6 I find that when reducing family-based visa of migration entries,

non-college-educated immigrants from Mexico, and Central America & Caribbean countries

are the most likely to substitute to illegal entry. The second factor is workers’ productivity sim-

ilarity across US labor markets, and how this similarity differs from the productivity similarity

between the US labor markets and foreign labor markets. I find the productivity similarity

across US labor markets is much stronger than the similarity between the US and competing

destination countries, whereas the similarity between the US and migration home country is

the weakest. This supports the location dependence hypothesis: the migration elasticity of sub-

stitution to US alternative labor markets is larger than those to competing destination countries

and home country.

The third, since the productivity similarity is weaker between the US and migration home

country than that between the US and competing destination countries, how the population

of each group are distributed among the rest of the world also matters: for groups whose

population are relatively more likely to live in competing destination countries than in home

country, their US migration stock is more responsive to policy changes. I find when increasing

employment-based visa entries, this mechanism operates in favor of college-educated work-

ers from Western & Northern Europe but acts against college-educated Indian. Evaluating all

forces together in my general equilibrium model, I find that reforming the US immigration

system would only have a modest level of composition impact on the national-origin and edu-

cation of US immigration.

To evaluate the wage impacts of immigration composition change, my model predicts na-

5This differs from previous studies which estimate a reduce-form parameter of migration elasticity, and assumeit is the same across workers from different countries of origin.; for example, see Mayda (2010), Grogger andHanson (2011), Belot and Hatton (2012), Ortega and Peri (2013).

6As a well-know feature in the literature, the share of labor allocation summarizes and is a sufficient statisticsof the costs and benefits of choosing each options relative to other alternatives.

3

tives’ wage elasticity differs endogenously across immigrants from different countries of ori-

gin, education, and gender groups. Immigrant groups who are more specialized in occupations

where US natives are underrepresented (overrepresented), an influx of their immigrants lead

to a less negative (or stronger positive) impact on US natives’ wage through factor substitution

(complementary). The intuition is in line with Costinot and Vogel (2010), Burstein, Morales

and Vogel (2015) where workers’ occupational comparative advantage determine their occu-

pation sorting and drive the group wage impact.7 I find among college education workers,

natives’ wage elasticity is the most negative to immigrants from English-speaking countries

such as UK and Canada, but the least negative to Indian; among non-college educated work-

ers, natives wage elasticity is the most negative to Mexican immigrants, but the least negative

to immigrants from western Europe. The result sheds some new light on immigrants from

which country of origin compete with US natives of the same education group the most.

I combine multiple data sources to measure the key variables that determine the impact

of immigration policy changes and are required to perform the counterfactual exercise. I use

micro-level census from multiple countries, international migration database from Institute for

Employment Research (IAB) database, and the Database on Immigrants in OECD countries

(DIOC), to measure international migration to OECD destination countries by occupations in

2010, for 115 countries of origin, and multiple education, gender groups. I also use these data

to estimate the average group wage earned in each country. For each group, I measure the frac-

tion of immigrants to the US by three broad types of visa entries including family-based visa,

employment-based visa, and refugee-based and diversity visa. I break down US immigrants

of each education and occupation group into each type of visa using the Yearbook of Immigra-

tion Statistics from the Department of Homeland Security, and the New Immigrant Survey. I

also measure a fourth type of mode status of undocumented or illegal status, which I apply the

algorithm developed in Borjas (2017) to identify illegal immigrant based on the Annual Social

and Economic Supplement (ASEC) sample of Current Population Survey (CPS).

I estimate several key model parameters using the Integrated Public Use Micro Samples

(Ruggles et al., 2015) and the New Immigrant Survey. I estimate the labor supply elastic-

ity across alternatives within a country — which governs the responsiveness of switching a

occupation-mode option within the US when the return to this option changes by 1 percent —

by relating the observed variation in the occupational share of US immigrants to immigrant-

sending countries’ education quality that is relevant to a given occupation.8 For example, I

examine how likely it is that Chinese-born US immigrants work in occupations where quan-

titative skill matters, relative to their Mexican counterparts, given the differences in national

education quality in mathematics. For the labor demand side, I estimate the occupational elas-

ticity of the substitution parameter — the inverse of which governs changes in relative wages

7Slightly different from Burstein et al. (2015), Galle et al. (2015) and Lee (2016), in which occupational compar-ative advantage shapes occupation sorting and determines the aggregate group wage responses, my model alsoallows the the occupational friction affects occupational sorting.

8The approach serves as a test of Roy comparative advantage hypothesis, and is the labor market analog ofCostinot et al. (2011).

4

in response to a 1% change in relative occupational labor — by relating changes in average

occupation wages to changes in total occupational hours during 1990-2015. I construct a Card-

type instrument based on the persistence in occupational specialization of US immigrants by

national origin, to measure the exogenous occupational labor supply in the absence of occupa-

tional labor demand or labor productivity changes. Finally, I estimate workers’ productivity

similarity parameters between the US and home country by exploring information on pre-

migration and post-migration wages from New Immigrant Survey (NIS).

I make two further assumptions in order to solve my model to evaluate the migration and

wage impact of changes in the overall number of mode-specific migration entries. First, for

a change in the overall number of mode-specific migration entries, my model absorbs these

changes by introducing a change of mode-specific migration friction that is the same across

national-origin groups. This assumption mirrors the fact that the majority of US visas have

been distributed without discrimination against immigrants’ national origin. Second, I assume

that the mode-specific migration friction (policy component) is multiplicative separable from

origin-destination-occupation-specific friction (non-policy component). The gain of this as-

sumption is to translate the level changes in mode-specific migration friction to proportional

changes, without knowing the initial equilibrium level migration frictions of each mode for

each group of workers, which are difficulty to identify from the data. I apply exact hat algebra

(Dekle, Eaton and Kortum, 2008) to solve the model in proportional changes, which enables

simulation of the counterfactual with only a few elasticity parameters, and parameters on pro-

ductivity similarity, without information on many model primitives.

To validate my model and assumptions made on solution methods, I introduce the number

of US visas granted since 1990 to the model and compare the model-generated cross-country

visa allocation with data.9 I find that simulating changes in entry mode by adjusting a common

mode-specific percentage change can generate a cross-country visa allocation that aligns well

with the data. This validation exercise also addresses the concerns about the violation of the

per-country ceiling rules of US immigration policy. I find that my model overpredicts the

number of visas acquired by countries that send large numbers of immigrants, but not by

much.10

Having established the validity of my model assumptions, I use the model to perform two

simulation exercises. First and as the main counterfactual exercise, I simulate a hypothetical

policy reform: reducing a total of 8 million of family- and refugee-based mode of migration

entries in 2010, but increase the same number of employment-based mode of migrants, so that

the overall number of legal US immigrants is unchanged. The number of 8 million mimic a

9The data is obtained from the Yearbook of Immigration Statistics from the Department of Homeland Security.10Simulating the model requires an assumption that US visas have been issued to immigrants without discrim-

ination on the basis of national origin. Strictly speaking, this assumption is invalid: For instance, only immigrantsfrom certain countries with low rates of immigration to the US are eligible for the diversity visa program andthere are also per-country immigration limits. In addition, the Immigration and Nationality Act (INA) limits law-ful permanent resident (LPR) admission from any single country to 7% of the total number of family-based andemployment-based admissions for each year. However, many categories are exempt from this limitation Wasem(2012). Section 4 provides details on per-country limits.

5

situation where the US visa distribution were shifted to the Canadian system since 1990, while

holding the overall number of visas issued unchanged.11

I find the migration and wage impacts are small both for the US and for foreign countries.

For non-college-educated US natives, wage increases 0.48% for males and increases 0.53% for

females; college-educated males experience a 0.16% wage loss, while female counterparts gain

0.30%. Because of the entry-mode substitution, the number of US illegal immigration increases

by 21%. For the same reasoning, there is little aggregate and distributional effects on Mexico

economy. I also find the college wage premium increases in India and East Asian countries, but

falls in Central American countries.

I perform a second counterfactual in which the legal system is reformed the same as in the

previous counterfactual, but increase the migration friction of illegal entry such that the num-

ber of illegal immigrants remains unchanged. Applying Gathmann (2008)’s estimates on the

elasticity of illegal migration costs (measured as smuggling prices) to line-watch hours, I relate

the calibrated the increase in migration friction of illegal entry to the extent to which the border

enforcement needs to be strengthened in order for the number of illegal immigrants remains

unchanged. I find the number of US-Mexico border patrol agents would need to increase by

8.6 to 11.6%, with $ 306-412 million additional salary expenses.

Finally, I study the extent to which have the location dependence resulted from the pro-

ductivity similarity structure at explaining the benchmark results. Specifically, I compare the

migration and wage effects predicted by my benchmark model with the effects predicted by

alternatives models which have independent productivity or productivity drawn from One-

layer CES correlation functions. I find the increase of US illegal immigration falls to 1/3 to 1/2

of the magnitude increase in my benchmark model, with a 7% increase predicted by the model

of independent productivity, and a 8-10% increase predicted by models with One-layer CES

correlation functions. I also find the US wages impacts are larger in all alternative models, and

would have been doubled in the model with independent productivity.

The paper is organized as follows: Section 2 relates this paper to previous literature; Section

3 presents the model, and Section 4 establishes the key variables and model parameters that

are the key determinants for the impact of immigration policy changes; Section 5 estimates the

entry mode share of US immigrants, and the model parameters; Section 6 discusses the coun-

terfactual exercise and the additional assumptions made to solve the model in proportional

changes, and Section 7 represents the quantitative results. Section 8 compares the results pro-

duced by different models, and highlight the quantitative role of location dependence. Section

9 concludes.11See Figure 4 in Section 7 for visa distribution issued by the US and by Canada.

6

2 Literature

This paper relates to several strands of literature in economics of immigration. A voluminous

literature has emerged to analyze the labor market impacts of immigration on receiving coun-

tries such as the US or European countries, and have have highlighted factors that are the key

in determining the labor market effects of immigration; for example Borjas (2003), Ottaviano

and Peri (2012).12 In contrast, only a few papers analyze the impacts on migration sending

countries; see (Borjas, 2008; Khanna and Morales, 2017). Another large strand of literature

study factors that determine international migration sorting and selection (Borjas, 1987; Grog-

ger and Hanson, 2011).13 In terms of analysis of immigration policy, much emphasis is on the

H-1B visa program and its associated consequences on the US labor market (Bound, Khanna

and Morales, 2017; Peri, Shih and Sparber, 2015) and innovation (Kerr and Lincoln, 2010).

My main difference from the previous literature is that I analyze a different yet equally im-

portant question: the impact of the permanent visa (green card) system reform. Although the

discussion of a potential skill-based US immigration reform has drawn enormous public and

political attention, there has been only a few papers try to shed light on this question quantita-

tively; for example, see Piyapromdee (2017).14 The study that is closest to mine is a concurrent

work by Chassamboulli and Peri (2018) who uses a two-country search model to analyze the

effects of US immigration reform. In their paper, individuals’ entry mode is exogenously as-

signed, and therefore, the model is silent to equilibrium substitution across entry modes.15 I

model endogenous migration selection and mode choice in a multi-country general equilib-

rium setting, and my results suggest that substitution to illegal entry is one of the key margin

of policy impact on the US labor market, and substitution to foreign countries drives the policy

impact on global economy. As another difference, Chassamboulli and Peri (2018) emphasizes

the differences in immigrants’ job matching across legal and illegal status, my approach em-

phasizes the heterogeneity in modes of entry and in occupation sorting for US immigrants

across national-origin and education groups.

To take my model to the data, I measure immigration at a more dis-aggregated level than

previous literature, in which I distinguish by multiple education groups, by multiple occupa-

tions as in Burstein et al. (2017), to various destinations and distinguish immigrants by their

country of origin as in Docquier, Ozden and Peri (2014), and also by multiple modes of migra-

12These factors include the elasticity of substitution between natives and immigrants (Ottaviano and Peri, 2012)and between education groups (Card, 2009); geographic and institutional frictions (Angrist and Kugler, 2003); thetradablility of occupations (Burstein, Hanson, Tian and Vogel, 2017); capital-skill complementarity (Lewis, 2011);internal migration and sector adjustments (Llull, 2013; Piyapromdee, 2017) and labor market dynamics (Monras,2015; Colas, 2017).

13Also see Chiquiar and Hanson (2005), Orrenius and Zavodny (2005), McKenzie and Rapoport (2007) andamong others on the self-selection of Mexican immigration to the US.

14See Borjas (1993) and Antecol, Cobb-Clark and Trejo (2003) for qualitative discussion of a skill-based US immi-gration reform. Piyapromdee (2017) introduces exogenous composition changes of US foreign-born labor supplyinto a single-country model, and performs a counterfactual exercise by exogenously changing the skill composi-tion of immigration to mimic a skill selective policy changes.

15In Chassamboulli and Peri (2018), individuals choose between the US and home country given the type ofentry mode they were assigned.

7

tion entry, including those who are undocumented. In contrast to Ottaviano and Peri (2012)

who model the aggregate immigrant-native substitution exogenously through nested CES pro-

duction function, my model allows a rich pattern of immigrant-native substitution to differ

endogenously across immigrants from different education and countries of origin groups.16

In terms of methodology, this paper relates to the broad literature of quantitative trade

models, and is close to Eaton and Kortum (2002) and its extensions to rapidly growing body

of work on Roy-like general equilibrium models; see Lagakos and Waugh (2013) and Hsieh,

Hurst, Jones and Klenow (2013).17 — analogous to the CES demand system of goods discussed

in Arkolakis, Costinot and Rodríguez-Clare (2012). I construct a multivariate Fréchet distribu-

tion with a three-layers nested-CES correlation function. My model implies a GEV system of

labor supply which belongs to the class of GEV demand system of goods introduced in Lind

and Ramondo (2018), and hence relaxing the independence irrelevant alternatives assumption im-

plied in the CES system.18 My analysis allows workers’ productivity similarity across locations

also play an important role in determining the aggregate migration elasticity of substitution. I

estimated these micro-level productivity, and my quantification emphasizes the quantitatively

importance of taking into account these productivity correlation in evaluating the labor market

outcomes.

Also from the methodological aspect, my paper evaluates the impact of international mi-

gration in a multi-country setting — similar as Docquier et al. (2014), Di Giovanni, Levchenko

and Ortega (2015), rather than studying the impact in a single-country setting as most of the

previous literature did. The advancement of these multi-country models is the ability to eval-

uate to the consequences of immigration globally. Differ from these two papers which assume

inelastic labor supply, I model endogenous migration selection, occupation and mode choice,

and, hence, allow the labor market to adjust both domestically and internationally. The model

that come closest to mine is Caliendo, Opromolla, Parro and Sforza (2017) who endogenize

migrants location choice in a dynamic general equilibrium model to study the impact of EU

accession. My model is a static, but has a new feature of location dependence on the pattern of

migration substitution, and also incorporates endogenous mode choice of migration entries.

16A few papers in the literature on immigration selection (Grogger and Hanson, 2011; Belot and Hatton, 2012;Bertoli et al., 2013) also distinguish immigrants by country of origin, but these papers doesn’t examine the labormarket impacts, and hence, silent to their differential impacts on the US natives’ labor market outcomes.

17Extensions have been developed to many scenarios, and most models imply a constant elasticity-of-substitution (CES) system of labor supply. Recent papers of Roy-like general equilibrium model include (butare not limited to), impacts of computerization on wage inequality (Burstein et al., 2015), the aggregate productiv-ity impacts of internal migration (Bryan and Morten, 2018), the distributional impacts of international trade (Galleet al., 2015; Lee, 2016), the aggregate and distribution effects of building urban infrastructure (Tsivanidis, 2018),and market adjustment to immigration in tradable and non-tradable occupations in the US (Burstein et al., 2017).These models assume independent productivity or correlated productivity drawn from a multivariate CDF withone-layer nested-CES correlation function. Two exceptional cases are Adao et al. (2018) and Adao et al. (2018).The former paper pursues a nonparameteric approach in a two-sector Roy model. The latter paper studies a rep-resentative household who decide what to consume and where to allocate its labor in each market. They allowthe labor supply elasticity to differ across sector and region, and distinguish the intensive and the extensive laborsupply elasticity.

18One interpretation of IIA is constant elasticity-of-substitution (CES) or also called proportional substitution,that is, an improvement in the attractiveness of an alternative would reduce the probabilities for all the otheralternatives by the same percentage in partial equilibrium.

8

3 A Equilibrium Model with Migration Entry Mode Choice

This section presents a general equilibrium model of international migration that has many

countries, occupations and modes of migration entry. Under perfect competition, each country

produces a final good using labor of various occupations. Workers are born at home country,

and choose where to live, which occupation to work, and a mode (a type of visa or illegal entry)

to migrate, by recognizing the costs of migration, their potential productivity, and the returns to

their productivity at each option. For each national-origin, education and gender group, work-

ers face the same migration costs to each destination, occupation and mode of entry. Workers

within each group draw an ex-ante identical but ex-post heterogeneous productivity for each

combination of destination, occupation and mode of entry. The within-country productivity

similarity between any pair of occupations and modes is the same, but differs from the similar-

ity to the productivity in a foreign country. Workers across groups differ in their productivity

distribution for which their productivity is drawn.

I index worker groups by s, occupation by o, mode of migration by m, foreign country by d

and home country by H . There is a fixed population Ls for each group. I assume countries are

open to immigration, but are closed to international trade.

3.1 Production

In each country d, a single final product is produced by combining occupational tasks using a

CES production function,

Yd =[∑

o

Ad,σLηd−1

ηdd,o

] ηdηd−1

,

where Ad,o is total factor productivity in country d and occupation o, and is assumed to be ex-

ogenous in the model. ηd denotes the elasticity of substitution across occupations of country d.

Ld,o is aggregate efficiency units of labor in destination country d and occupation o. I assume

natives and immigrants are perfect substitutes within each occupation o. Different from Borjas

(2003) and Ottaviano and Peri (2012) who impose the aggregate between-group substitution

through CES production function, my approach imposes perfect between-group substitution

in each narrowly defined occupation, and allows between-group substitution differs endoge-

nously not only across education and gender groups, but also across immigrants from different

countries of origin, as shown in Section 4.

3.2 Labor Productivity Distribution

For each country-of-origin, education and gender group s, a worker j draws a vector of poten-

tial productivity {~a} at each combination of destination d, occupation o, and mode of entry m.

The productivity vector follows a multivariate Fréchet distribution with three-layer nested CES

9

correlation function with the following cumulative distribution function (CDF)

F(~a; s)

= exp

{−

[∑H,F

(∑d

[ ∑m,o∈Od

(ad,m,o

/T sd,m,o

)− θ1−ρ] 1−ρ

1−σ) 1−σ

1−γ]1−γ}

,

This distribution is characterized by five set of parameters: T sd,m,o, θ, ρ, σ and γ, and belongs

to the class of generalized extreme value (GEV) distribution (McFadden, 1978). It generalizes

the widely used independent or the correlated multivariate Fréchet distribution generated by

the one-layer CES correlation Function in Fréchet-Roy literature. For example, when ρ = σ =

γ = 0, the productivity distribution becomes independently drawn across options as studied

in Galle, Rodriguez-Clare and Yi (2015), Burstein et al. (2015), Lee (2016).19 As another case

when ρ = σ = γ, the productivity are drawn from a multivariate distribution with a single-

layer CES correlation function as studied in Hsieh et al. (2013), Bryan and Morten (2018) and

Tsivanidis (2018).20 Same as these special cases, T sd,m,o and θ are the scale parameter and shape

parameter of marginal production distribution for group s at d-m-o, respectively. More general

than previous studies, I introduce three parameters, ρ, σ and γ. Each parameter takes value

between 0 and 1, and captures the productivity similarity between any pair of alternatives

within its nest. Next, I use the diagram below to illustrate the correlation structure of this

distribution. I use H to denote home country, F to denote the collection of foreign countries,

and OH and Od for the collection of options (occupations, modes) at home and foreign country,

respectively.

Several things are worth noticing. First, the nesting structure doesn’t indicate that indi-

viduals are making migration decision sequentially, but reflects the similarity in productivity

among alternatives resulted from researchers’ prior knowledge. In fact, the model assumes

workers choose location-mode-occupation simultaneously. Second, the nesting structure as-

sumes that within each nest, the productivity similarity between any pairs of alternatives are

the same. In particular, ρ controls the within-country productivity similarity across occupa-

tions and modes. σ governs productivity similarity between any pair of foreign countries in

the collection of F , and γ controls productivity similarity between home and any foreign coun-

try.21 Since productivity tends to be more similarity as we move from upper-level to lower-level

nest, hypothetically γ ≤ σ ≤ ρ.19Also see Ahlfeldt et al. (2015) and Monte et al. (2015) who assume independent Fréchet distribution of amenity,

instead of productivity. Notice when set ρ = σ = γ = 0, the cumulative distribution function becomes

F (~a; s) = exp

{−∑H,F

∑d

∑m,o∈O

(ad,m,o

/T sd,m,o

)−θ},

which is the CDF for independent Fréchet distribution.20When set ρ = σ = γ, the cumulative distribution function becomes

F (~a; s) = exp

{−[∑H,F

∑d

∑m,o∈O

(ad,m,o

/T sd,m,o

)− θ1−ρ]1−ρ

},

which is the multivariate Fréchet distribution generated by a single-layer CES correlation function.21The bivariate CDF of producitivty within each nest can be derived by evaluating the CDF at +∞ for any other

10

Workers

Home, H

o1 ∈ OH

Occupation o2 ∈ OH

o3 ∈ OH

Foreign Countries, F

d1 ∈ F

Country d2 ∈ F

d3 ∈ F

{m1, o1} ∈ Od2 {m3, o1} ∈ Od2

Mode & Occupation {m2, o1} ∈ Od2

Figure 1: Nested Correlation Structure

Note: H denotes home country, and OH is the set of occupations available at home country. F denotes the

collection of foreign countries which workers can choose to migrate to, d denotes a specific foreign country

in the collection of foreign countries F , and Od is the collection of mode of entry (m) and occupation (o)

options at foreign country d that a worker can choose. All these notation here are defined specific to each

group s, but I omit group subscript for notation simplicity.

Third, the productivity similarity between two lower-level alternatives of different nests

equals the productivity similarity of alternatives that lie in the same upper-level nest. For ex-

ample, the productivity similarity between an arbitrary occupation in foreign country and an

arbitrate occupation in home country, is governed by γ which is the productivity similarity

between home and any foreign country.22

I assume each of ρ, σ and γ is the invariant across all countries and groups.23 In Section 4, I

alternatives. For example the Bi-variate Fréchet CDF of two home country occupation productivity{aH,o1 , aH,o2

}is

F (aH,o1 , aH,o2 ; s) = F (+∞, ..., aH,o1 , aH,o2 , ...,+∞; s) = exp

{−[T sH,o1a

− θ1−ρ

H,o1+ T sH,o1a

− θ1−ρ

H,o1

]1−ρ},

where ρ captures the correlation between aH,o1 and aH,o2 .22Analygously, The Bi-variate Fréchet CDF of productivity

{ad,m,o, aH,o

}is

F (ad,m,o, aH,o; s) = exp

{−[T sd,m,oa

− θ1−γ

d,m,o + T sH,oa− θ

1−γH,o

]1−γ},

where r captures the correlation between ad,m,o and aH,o.23ρ, σ and γ can be specific to each nest and to each group s.

11

show analytically that a stronger micro-level workers’ productivity similarly across alternatives

in the same countries than the productivity similarity across countries, would lead to a larger

aggregate migration elasticity of substitution to those alternatives in the country, which I refer

as “location dependence".

Recall that T sd,m,o and θ are the scale parameter and shape parameter of marginal production

distribution for group s at d-m-o, respectively. A larger T sd,m,o corresponding to a higher average

level and also a fat upper tail of marginal productivity distribution, and a larger θ corresponds

to small within-group productivity dispersion (holding T sd,m,o the same). I assume θ is the same

across labor groups, but allow a large degree of heterogeneity in T sd,m,o.24

The heterogeneity in T sd,m,o can reflect group differences in occupational talents or skill

transferability. For example, Indian workers might be endowed with higher STEM occupa-

tional talents than Mexican workers. For another example, it is likely that Mexican workers

are more productive to work as lawyers in India than in the US for two reasons: there are lan-

guage barriers, and linguistic ability matters to work as lawyers. For all countries, I include

unemployment as an occupation option. Including the unemployment option is particularly

important for my study, as it absorbs the younger and elder migrants who manage to migrate

to the US, but are less likely to be in the labor force.

3.3 Migration Frictions

Labor movement is subject to frictions. I assume migration frictions take the iceberg cost form,

denoted as τ sd,m,o, i.e., if a worker from group s wants to migrate to destination d and work in

occupation o and enter through mode m, then a portion of 1 − τ sd,m,o of his/her income would

melt away.25 The multiplicative form of migration frictions keeps the model tractable, and has

been widely adopted to model migration choices (Borjas, 1987; Chiquiar and Hanson, 2005;

Bryan and Morten, 2018), and residential-commuting choices Ahlfeldt, Redding, Sturm and

Wolf (2015); Monte, Redding and Rossi-Hansberg (2015); Tsivanidis (2018).26

The model allows a large degree of heterogeneity in migration frictions. First, τ sd,m,o can be

specific by groups s, and varies by which destination country d to migrate. The s-d component

captures bilateral geographic, network ties and cultural barriers. Migration frictions can also

depend on occupation o, which captures the differential occupation-level labor market friction.

More importantly, τ sd,m,o depends on the type of mode of entry m, and allowing the interaction

between mode type and bilateral cost components. For example, under a family-preference

system — as in the US — the family-mode entry friction is presumably lower for Mexican who

have established strong migration networks in the US than Indian who have not.

24See Lee (2016) and Tsivanidis (2018) who allow θ to be specific across groups.25τsd,m,o can nest factors such as political unrest, natural disaster in immigrant-sending countries (Mahajan and

Yang, 2017).26Both Borjas (1987) and Chiquiar and Hanson (2005) assume additive migration cost on the log of perceived

wage, which also implies migration costs as a fixed portion of income loss.

12

3.4 Aggregate Migration Flow

Denote wd,o as the wage per efficiency unit of labor in country d and occupation o. For worker

j who draws productivity as,jd,m,o, he/she choose d-m-o by solving

max{d,m,o}

{wd,o × as,jd,m,o × τsd,m,o},

As shown in McFadden (1978) , the joint probability for group s to choose a foreign country

d ∈ F , mode m and occupation o is

Πsd,m,o,F =

φd,m,o∑m′,o′∈Od φd,m′,o′

× Φd∑d′∈F Φd′

×

[∑d′∈F Φd′

] 1−σ1−γ

[∑d′∈F Φd′

] 1−σ1−γ

+[∑

o′∈OH φH,o′] 1−ρ

1−γ. (1)

where φd,m,o =

(T sd,m,owd,oτ

sd,m,o

) θ1−ρ

, Φd =

(∑m′,o′∈Od φd,m′,o′

) 1−ρ1−σ

. All these notations are spe-

cific to s which I omit the subscript for notation simplicity. The first term in equation (1) rep-

resents the probability of choosing m and o, conditional on living in country d ∈ F ; the second

term represents the probability of living in country d, conditional on living abroad, denoted

as Πsd|F ; and the last term is the marginal probability of living abroad, denoted as Πs

F . With a

slight difference, the joint probability of choosing home country H and occupation o is

ΠsH,o =

φH,o∑o′∈O′ φH,o′

×

[∑o′∈O′ φH,o′

] 1−ρ1−γ

[∑d′∈F Φd′

] 1−σ1−γ

+[∑

o′∈OH φH,o′] 1−ρ

1−γ

3.5 Average Group Wages

The multivariate Fréchet distribution implies that each element asd,m,o follows a margin Fréchet

distribution with scale parameter T sd,m,o, and shape parameter θ, for any specific d, m and o.27

Then the average group efficiency units of labor employed in country d, at occupation o, and

that migrate through mode m equals

E[asd,m,o|d,m, o

]= Γ

(1− 1

θ

)· T sd,m,o ·

(Πsd,m,o,F

)− 1−ρθ,

where Γ(·) denotes the gamma function. In contrast with the inverse Mill’s ratio generated

by the log normal truncation distribution (Heckman, 1979; Borjas, 1987), the expected value

from the truncated Fréchet distribution has a simple functional form, captured by the term(Πsd,m,o,F

)− 1−ρϑ

in my case.28 It says, first, that the smaller the fraction of workers who are

selected into a cell, the greater the positive selection bias in terms of the efficiency units of27The statement is obtained by evaluating the multivariate Cumulative Density Function (CDF) at +∞ for any

other options but d-m-o.28See Head (2013) for a survey of truncated distribution and the functional form of truncation moments.

13

labor. The intuition is that when the barrier to enter a given labor market is high or its return is

low, only the most productive workers find it optimal to work in the market; however, as the

barrier falls or the return rises, the market would absorb less-productive workers as well, thus

lowering the degree of positive selection. This prediction is in line with the recent findings

that immigrants from countries that sent a smaller fraction of their population to the US are

on average better educated (Lazear, 2017). The second feature of the term(

Πsd,m,o,F

)− 1−ρϑ

, says

that as the fraction of workers who work in a given cell increases, the skill-selectivity bias falls

faster when productivity is highly dispersed — θ is small.

The average wage of workers working in occupation σ under mode m in country κ can be

expressed as

W sd,m,o = wd,o · E

[asd,m,o|d,m, o

]= Γ

(1− 1

θ

)· T sd,m,o · wd,o ·

(Πsd,m,o,F

)− 1−ρθ

Different from the literature which predicts the average wage earned by a given group is a

constant across all occupations or sectors (Hsieh et al., 2013; Burstein et al., 2015; Galle et al.,

2015), my model allows gaps in average occupational wages by introducing frictions.

3.6 General Equilibrium

The model primitives are characterized by country-occupation-specific total factor productivity

Ad,o, bilateral and mode-specific iceberg migratory costs τ sd,m,o, the stock of labor force in each

origin-education group Ls, the elasticity of substitution across occupations in each country, ηd,

Fréchet scale parameters T sd,m,o, shape parameter θ, and three correlation parameters ρ, σ, and γ.

The CES production function implies the labor demand at country d and occupation o is

Ldemandd,o =

1

wηdd,oYdA

ηdd,o.

The total efficiency units of labor supplied in country d and occupation o are aggregated over

natives and immigrants of all country-of-origin, education, and gender groups, and aggregate

over immigrants who enter through each mode.

Lsupplyd,o =

1

wd,o

∑s

∑m

W sd,m,o · Ls · Πs

d,m,o,F .

Given the set of model primitives, a competitive equilibrium in a global economy consists of

the labor allocation to country-mode-occupation, Πsd,m,o, the average efficiency units of labor in

each country-occupation-mode, E[asd,m,o|d,m, o

]and average wagesW s

d,m,o, the wage efficiency

unit of labor at each d-o market wd,o equalizes the labor demand with labor supply, such that

Lsupplyd,o = Ldemand

d,o .

14

4 Endogenous Elasticities

This section analyzes establish the key variables and model parameters that determine the im-

pact of immigration policy changes by analyzing three sets of endogenous elasticity. In particu-

lar, the first set of elasticity analyzes factors that drive the direct policy impact on demographic

composition of US immigration;29 the second set of elasticity analyzes factors that determine

the substitution patterns to other modes of entry, to other foreign countries and to home coun-

try as family-entry mode become more restrictive; the third set of elasticity isolates factors that

determine wage elasticity to immigration, and analyzes how it differs across immigrants from

different countries of origin within each education group.

4.1 Migration Elasticity to the US

This subsection analyzes factors that drive the direct policy impact on demographic compo-

sition of US immigration when family-based mode of entries become more restrictive, while

relaxing the barrier of employment-based entries. Without loss of generality, I abstract the oc-

cupation dimension. First consider a special case of my model with σ = 0 and γ = 0.30 For a

small change of US migration friction of mode m, the partial equilibrium migration elasticity

in response to migration friction changes has the following form:

∂Πsd,F

Πsd,F

/∂τ sd,mτ sd,m

= θ × Πsm|d,F ×

(1− Πs

d,F

)(2)

where Πsd,F is the unconditional probability of s population that live in the US (d). Equa-

tion (2) says, for example, increasing the number of employment-based visas, captured by∂τsd,mτsd,m

(1) would disproportionately increase immigration from group s who intensively use

employment-based visa to migrate — i.e., Πsm|d,F is larger; (2) would induce a large response if

the productivity is less dispersed — i.e., θ is large; and (3) would disproportionately increase

immigration from group s who have a larger fraction of population living outside the US (thus

the size of potential migrants is larger) — i.e., 1−Πsd,F is larger. Since 1−Πs

d,F is generally close

to 1, and θ is a constant, the cross-group variation in migration elasticity is mainly driven by

Πsm|d,F .

The intuition behind is that the relative migration friction across entry modes determines

migration sorting across mode of entry, and drives migration responses to policy shock. For

example, when employment-entry mode friction decreases, on one hand, groups that face rel-

atively high friction in employment-entry mode are less affected, as the majority would still

optimally migrate to the US through other modes. On the other hand, groups that face rela-

tively low friction in employment-entry would be very responsive to the policy changes.

29By direct impact, I mean it does not take into account general equilibrium adjustments.30The value of ρ doesn’t affect the elasticity analyzed in subsection (A).

15

Next, consider the general case with σ 6= 0 , γ 6= 0.31 The migration elasticity in response to

migration friction changes take the following form

∂Πsd,F

Πsd,F

/∂τ sd,mτ sd,m

= θ × Πsm|d,F ×

[1

1− σ

(1− Πs

d|F

)+

1

1− γΠsd|F

(1− Πs

F

)]. (3)

It is evident that equation (3) generalizes the result of the previous special case in equation (2).

In particular, equation (3) distinguishes two sources of potential migrants rather than treating

the entire outside US population equally. These two sources of migration are those who live

in competing foreign destinations, captured by 1 − Πsd|F , and those who live in home country,

captured by 1 − ΠsF . The latter further proportionally divided among foreign countries, and

hence the term Πsd|F re-scales the size of the potential global migrants using the US share.32

Another important distinction of equation (3) is that a stronger micro-level productivity

similarity parameter between migration source location and the US, leads to a larger aggregate

migration elasticity regarding to its corresponding potential migration source. As it shows

that the term 11−σ applies to the size of population live abroad, and 1

1−γ applies to population

resides in home country.33 In Section 5, I show σ > γ. The implication is that when increasing

employment-based visa entries, groups whose population are relatively more likely to live

in competing destination countries than in home country, the stronger productivity similarity

between foreign destinations and the US has an amplifying effect to absorb their migrants to the

US. This mechanism operates in favor of college-educated workers from Western & Northern

Europe but acts against college-educated Indian.

Finally, ρ is not involved in the migration elasticity analyzed here. The implication is that

the widely used Fréchet productivity based on the one-layer CES correlation function would

predict exactly the same relative migration elasticity across groups as the case of independent

Fréchet productivity.34

4.2 The Elasticity of Substitution to Alternative Options

When reducing the number of US family-based visas, the switchers who previously find family-

based visa optimal but no long do, could instead choose to live in home countries, or migrate to

other foreign destinations, or stay in the US through an alternative mode. This subsection stud-

ies factors that determine the elasticity of substitution to each of these three sets of alternatives,

respectively. Without loss of generality, I abstract the occupation dimension. All elasticities

presented are again, partial equilibrium elasiticities holding wage constant.

31Again ρ can take any value between 0 to 1.32This result is driven by the model assumption that the pairwise productivity correlation is the same across all

foreign countries, so IIA applies within each nest.33The monotonicity in equation (3) also implies the migration elasticity in models with correlated productivity

is larger than the model of independent productivity.34As I set the number of immigrants for each entry mode as fixed in counterfactual exericse, only the relative

migration elasticity matters for US immigration composition change.

16

1) The Elasticity of Substitution to Home Country

Consider reducing a certain number of US family-based visa, captured by a decrease in migra-

tion friction in family-entry mode. The elasticity of substitution to home country h is

∂ΠsH

ΠsH

/∂τ sd,mτ sd,m

= − θ

1− γΠsd,m,F . (4)

The variation of ∂ΠsHΠsH

/∂τsd,mτsd,m

across different groups is determined by the fraction of workers live

in the US and migrate using family mode (Πsd,m,F ), which captures the size of switchers (relative

to group population) due to the policy change. The other two factors that affect this elasticity

are γ and θ, and are common across groups. A more similar labor productivity between the US

and migration home country (a larger γ) would lead to a larger aggregate elasticity of substi-

tution from US to migration home country. As is already discussed from previous discussion,

a less dispersed productivity (a larger θ) corresponds a more elastic substitution pattern.

2) The Elasticity of Substitution to Foreign Countries

Again, for a decrease in migration friction in family-entry mode, the elasticity of substitution

to any competing foreign destination d′ ∈ Cf has the following form

∂Πsd′,F

Πsd′,F

/∂τ sd,mτ sd,m

= − θ

1− γΠsd,m,F −

θ(σ − γ)

(1− σ)(1− γ)Πsd,m|F . (5)

Comparing to equation (4), equation (5) has an additional term, − θ(σ−γ)(1−σ)(1−γ)

Πsd,m|F which is due

to the difference in productivity similarity between the US and competing destination coun-

tries, to the similarity between the US and home country. Two important implications arrive.

First, to the current example, family-visa switchers of each group s would be disproportion-

ately absorbed by foreign destinations relative to home country, if and only if σ > γ. Second,

the proportional substitution pattern (the IIA property) holds within the collection of foreign

competing destinations, but as long as σ 6= γ, IIA no longer holds between home and foreign

countries.

It is also worth noting that the cross-group variation in∂Πs

d′,FΠsd′,F

/∂τsd,mτsd,m

is not only determined

by the relative size of switchers (Πsd,m,F ), but also by the size of population live in foreign coun-

tries (ΠsF ).35 Again, when σ > γ, groups that have a relative large share of population live

abroad, the stronger productivity similarity between foreign destinations and the US would

have an amplifying effect for migrants to substitute to competing foreign destinations. This

amplifying effect is the strongest for workers from South American countries to European

countries.

3) The Elasticity of Substitution to Alternative Mode in the US

35By conditional probability, Πsd,m|F =

Πsd,m,FΠsF

.

17

Again, for the same policy shock, the elasticity of substitution to alternative entry mode m′

in the US take the below form

∂Πsd,m′,F

Πsd,m′,F

/∂τ sd,m,Fτ sd,m,F

= − θ

1− γΠsd,m,F −

θ(σ − γ)

(1− σ)(1− γ)Πsd,m|F −

θ(ρ− σ)

(1− ρ)(1− σ)Πsm|d,F . (6)

Comparing to equation (5), equation (6) has an additional term, − θ(ρ−σ)(1−ρ)(1−σ)

Πsm|d,F , which is due

to the difference in productivity similarity across alternatives within the US, and the productiv-

ity correlation between US and foreign country. Two implications follow. First, to the current

example, family-visa switchers of each group s would be disproportionately absorbed by al-

ternative US mode of entry relative to competing foreign destinations, if and only if ρ > σ.

Second, the proportional substitution pattern (the IIA property) holds across US alternatives,

but as long as ρ 6= σ, IIA no longer holds between US alternatives and foreign countries.

It is also worth noting that the cross-group variation in∂Πs

d′,m′,FΠsd′,m,F

/∂τsd,mτsd,m

is not only deter-

mined by the relative size of switchers (Πsd,m,F ) and the relative size of population live in for-

eign countries (ΠsF ), but also the relative size of population live in the US Πs

d,F .36 Again, when

ρ > σ, groups that have a relative large share of population live in the US, the productivity

similarity have an amplifying effect for migrants to substitute to alternative US mode of entry.

Unsurprisingly, this amplifying effect is the strong for workers from Mexico, Central American

& Caribbean countries.

4) A Special Case, ρ = σ = γ

In a case when ρ = σ = γ, the elasticity of substitution in equation (4), (5) and (6) all

becomes − θ1−γ × Πs

d,m,F which follows exact the same as a model with single-layer CES corre-

lation productivity draws. As a more special case of the independent productivity draws, i.e.,

ρ = σ = γ = 0, these elasticity of substitution all equal to −θ × Πsd,m,F . In either case, the IIA

property is present.

4.3 Between-group Wage Elasticity

This subsection analyzes the occupation specialization of US immigrants by each group s, and

relates occupation specialization to the competition between natives and immigrants? To illus-

trate this mechanism, I provide the analytic expression of the partial equilibrium cross-wage

elasticity between two groups as a function of the share of occupations for each group. The ulti-

mate cross-wage elasticity I use to illustrate this shows by what percentage the wage earned by

US natives would change in response to an increase in the same efficiency units of immigrant

labor from different countries of origin.

Consider s1 US natives and s2 as immigrants from an arbitrary origin and demographic

36By conditional probability, Πsm|d,F =

Πsd,m,FΠsd,F

.

18

group. I use o and o′ to denote occupations. The goal is to obtain the wage elasticity earned

by natives in response to changes in the immigrant labor supply of type s2. The derivation of

cross-group wage elasticity relies on the following equality:

∂Ws1

Ws1

/∂Ls2Ls2

=∑o

[∂Ws1

∂Lo

LoWs1

× ∂Lo∂Ls2

Ls2Lo

]=∑o

[(∑o′

∂Ws1

∂wo′

wo′

Ws1

× ∂wo′

∂Lo

Lowo′

)× ∂Lo∂Ls2

Ls2Lo

](7)

whereWs1 is the average group wage earned by natives; Ls2 is the total efficiency unit of type-s2

immigrant workers; and Lo is the total efficiency unit of labor in occupation o. wd,o is the wage

unit in occupation o. The two equal signs in equation (7) hold by the chain rule.37 Appendix

B.5 provides the expressions and derivations for each elasticity that appears in equation (7).

Equation (7) captures the partial equilibrium wage elasticity which is the first-order effect of

native wage response, without taking into account the equilibrium adjustment of occupation

and location switching. To make a 1% increase in Mexican immigrants comparable to a 1%

increase in immigrants from a small sending country such as Tonga, I normalize the cross-

group wage elasticity by efficiency units of immigrants such that the normalized cross-group

wage elasticity is as follows:

∂Ws1

Ws1

/∂Ls2

1=

1

η

∑o

[(Ro − Πs1

o|d) ×Πs2o|d

Lo︸︷︷︸percentage changes in occupational employment

], (8)

where Ro denotes the occupational wage bills as a share of the total, capturing the size of

the occupation throughout the entire economy. Πs1o|d and Πs2

o|d are the fractions of natives and

immigrants that work in occupation o conditional on living in the US, respectively. η is the

elasticity of substitution across occupations.

Equation (8) says a Πs2o|d

/Lo percentage change in the occupation labor supply induced by a

unit immigration influx of group s2 would lead to a net complementary effect on US natives, s1,

if native workers are underrepresented in this occupation, such that Ro − Πs1o|d > 0. Otherwise,

the substitution effect dominates. The aggregate natives’ wage response to a unit immigration

influx from group s2 is then obtained by summing over the response to labor supply increases

over all occupations and scaling by the inverse of occupation elasticity of substitution, 1η.

Equation (8) sheds light on an important question: Immigrants from which country and

demographic group benefit/hurt natives the most, in partial equilibrium? The implication

is that US natives lose more from an influx of immigrants who specialize in the occupation

where natives are the most over-represented, in the sense that Ro − Πso|d is the most negative

for US natives.38 The implication provides a different perspective, as it might be supposed

37The first equality states that the wage earned by natives in response to changes in immigrant labor supplyequals the sum product of natives’ wage elasticity in response to changes in occupations’ labor supply and the oc-cupational labor elasticity to changes in type-s2 immigration workers. The second equality holds by re-expressingnatives’ wage elasticity to occupation labor supply as the sum product of natives’ wage elasticity to occupationwage unit and the elasticity of occupation wage unit to the occupation labor supply induced by immigrants.

38This can be mapped into a linear optimization problem such that one picks vector values of Πo|s2,κ such that

19

that immigrants present the greatest competition for natives if their occupational shares are the

same. However, if occupational shares are exactly the same between immigrants and natives,

my model predicts that an immigration influx would have zero impacts on natives’ wage.

In Appendix D.1, I use the general equilibrium model to show that within the same ed-

ucation level, immigrant-to-native substitution differs substantially by immigrants’ national

origin. Driven by differential occupational specialization, I find that increasing the number of

college-educated Indian immigrants would benefit US natives the most on average, while the

average wage impacts earned by US natives would suffer the largest loss in response to a same

efficiency unit increase in non-college-educated Mexican immigrants.

5 Estimating Model Parameters

The previous section shows the main determinants of the three key sets of elasticities which

determine the impacts of shifting family-based visas to employment-based visas on migration

composition, on migration pattern of substitution, and on wages. This section estimates some

of the key variables and parameters that determine these elasticities. Specifically, Section 5.1

estimates the entry mode share to the US by each country of origin, education and occupation

group. Section 5.2, 5.3 and 5.4 discuss estimation of the five elasticity parameters θ, η, ρ, σ, γ.

5.1 Estimating the Entry Mode of US Immigrants

The empirical content of “entry modes" of my analysis is the types of mode status that an

individual has in 2010. The types of counterfactual that my model can undertake are exoge-

nous changes in the overall number of mode-specific migration entries in 2010, which reflects

changes of US immigration policy made in the past. My focus on year 2010 is due to data

availability and better quality.

I consider 4 types of migration mode of entry: three of them are permanent visas including

a family-based mode, denoted as mf ; an employment-based mode, denoted as me; and any

other legal entry, which include refugee, diversity, and other type of permanent visas, denoted

as mo (referred as refugee-based mode hereafter). I also consider an illegal mode status, de-

noted as mi. The three legal mode reflect the types of permanent visa status that an individual

has in 2010, whereas illegal status indicates if an individual is in illegal status in 2010.39 For

∂Ws1

Ws1

/∂Ls2

1 is maximized or minimized. This results in a corner solution:

Πs2o|d =

{1, if o = argmaxo′{

Ro−Πs2o′|d

Lo′}.

0, other o.

39In 2010, there is around 11.4 million US illegal immigrants, accounting about 30% of the total US immigrantpopulation.

20

individuals who initially entered the US through temporary or illegal mode, but managed to

obtain a family-based visa by year 2010, I track them as family-based visa mode immigrants.

My analysis does not measure temporary visas due to the data challenge of identifying

temporary work visa holders in the overall immigration stock.40 It is important to note that

although temporary work visas is one of the primary channel through which immigrants ac-

quire permanent visa status,41 owing to the numerical limits and limited duration of stay, the

share of temporary work visa holders in the overall immigration stock is small in 2010.42 Over

a 20-year time span of which I experiment the US immigration policy change, nearly all of

those who initially arrived with temporary work visas would either have converted to one of

the mode status I considered, or have left the US.

I estimate Πsm|d,o for each of the four entry modes in two steps and combine three data

sources: Annual Socioeconomic and Economic Supplement (ASEC-CPS), the Yearbook of Im-

migration Statistics, and the New Immigrants Survey (NIS). First, I use the ASEC-CPS sample

2010 and follow Borjas (2017) to generate a dummy variable which identifies illegal immi-

grants. Simplifying the probabilistic method from Passel and Cohn (2016), Borjas defines a

foreign-born worker as a legal immigrant if he/she satisfies at least one condition of many, and

classifies the remaining immigrants as undocumented or illegal. For example, an individual

is defined as legal if he/she receives Social Security benefits, Medicaid, Medicare, or military

insurance. Appendix C lists the detailed conditions for filtering legal immigrants. To avoid

overestimating the number of high-skilled immigrants in the illegal immigration population, I

further filter legal immigrants by assuming that an immigrant is legal if he or she has a mas-

ter’s, professional or doctoral degree or works in a skill-intensive occupation. Based on this

identifier, I obtain estimates of the fraction of legal and illegal immigrants in each group s,

conditional on working in occupation o.

In the second step, I break down legal immigrants into the three aforementioned visa cat-

egories for each group s in each occupation o. I draw data from the New Immigrant Survey

(NIS), which is a survey based on a sample of 8,573 immigrants granted lawful permanent res-

idence in 2003, and includes individual records of education, age, gender, occupational back-

ground, and class of visa admission. As the NIS data might not be population representative, I

assign a nation-mode-specific weight to each NIS observation such that the visa share for each

immigrant-sending country exactly matches the moments implied from the Yearbook of Immi-

gration Statistics during 1996-2015. In addition, to improve estimation precision, I pool males

40One measurement challenge is that the DHS reports temporary work visas by country of origin based onthe number of border crossing (I-94) forms in a given year, subject to the issues of multiple counting. Anotherchallenge is that the existing data doesn’t observe share of temporary visa holders who convert to permanentvisas or left the country by country of origin.

41According to the Yearbook of Immigration Statistics, each year about half of the overall permanent visa areawarded to immigrants who are adjusted status, which are those who converts from temporary to permanentvisas.

42For example, the H-1B has a three-year duration and is renewable once; the H2-visa has a one-year durationand some can be renewed for up to 3 years; the L-visa has a three-year duration and is extendable to a maximumof 5-7 years. By excluding temporary work visa categories, my calculation proportionately allocates the numberof workers who have temporary status in 2010 across the four modes considered.

21

and females within each national-origin and education group, cluster national origins into 12

countries/regions, and aggregate NIS occupations into the three widely used broad categories

— cognitive, routine, and manual occupations.43 I then assign the conditional probability of

each legal mode estimated in aggregated cells (12 regions,two education levels, three occupa-

tions) to finer cells (115 countries of origin, two education levels, gender, 28 occupations) to

match my model dimension in the quantitative exercise, while assuming the conditional prob-

ability is invariant within each broad aggregate. Appendix C.2 provides details on matching

the aggregated ACS and NIS occupations.

It is important to note that the moment estimated using ASEC-CPS data is based on the

stock of US immigrants, but the DHS and the NIS sample reflect migration inflow over a 20-

year time span and a one-year flow in 2003, respectively. To combine these estimates, I assume

that the sorting to visa categories or illegal entry for immigrants from each specific immigrant-

sending country is stable over time, and hence, the moments implied from DHS data apply to

he overall stock of US legal immigrants. I also assume that within each visa category, the occu-

pation and education selectivity for immigrants from each specific immigrant-sending country

is stable over time, and hence, again the moments implied from NIS sample apply to the over-

all stock of US legal immigrants. For each group, the share of the aggregate legal visa relative

to illegal entry is implied from ASEC-CPS, and the share of each legal visa is implied from

the Yearbook of Immigration Statistics. Given the number of immigrants from each country or

origin and migration through each legal mode, the NIS sample breaks down the numbers to

education and occupation cells. Because of these, the estimates of Πsm|d,o are less sensitive to the

problem of a small, under-representative NIS sample.44

Figure 2 presents the mode entry share of US immigrants for major origin countries/regions

and two education groups, Πsm|d.

45 The left panel focuses on non-college-educated US immi-

grants, and it shows systematic differences in their mode entry share across countries of ori-

gin. Two points are worth mentioning. First, immigrants from Mexico, Central American &

Caribbean countries are less likely to migrate with an family-based visa than immigrants from

Southeast Asian countries, and Northern European countries (EU hereafter). Family-based en-

try accounts for 46.4% of non-college-educated Mexican immigrants, 44.2% of Central America

immigrants, in comparing to 69.8% and 55.0% of their counterparts from Southeast Asian and

EU countries, respective. This indicates that, when reducing the number of family-based visas,

the share of US immigrants who are exposed to switch alternatives is smaller for those from

Mexico, Central America & Caribbean countries than those from Southeast Asian and EU coun-

tries. Second, Illegal entry is of high importance for Mexico and Central American immigrants,

accounting for over 49.9% of the total for Mexico and 31.5% of the total for Central American

43The 12 countries/regions are Canada, China, India, Korea, Mexico, Central America & the Caribbean, EasternEurope, Europe, the Middle East & Africa, Oceania, Southeast Asia and South America.

44Hendricks & Schoellman (2016) show that the NIS sample of US immigrants tends to be younger, bettereducated and lower paid, and to underrepresent Mexican-born immigrants.

45I pool male and female within each origin and education group in plotting Figure 2. According to conditionalprobability, Πs

m|d can be computed as∑o Πs

o|dΠsm|d,o.

22

immigrants. According to equation (6), it suggests that Mexican, and Central American immi-

grants are more likely to substitute to illegal entry than other immigrants, as family-visa entry

become more restrictive.

0

.2

.4

.6

.8

1

Shar

e of

imm

igra

nts

by m

ode

SE Asia EU

Centra

l Ameri

ca

Mexico

Non-College

0

.2

.4

.6

.8

1

Shar

e of

imm

igra

nts

by m

ode

Centra

l Ameri

ca

Mexico

China

India

College

Family Employment

Refugee Undocumented

Figure 2: Mode distribution by origin and education group

College-educated US immigrants from different countries of origin also differ dramatically

in their mode entry share, as shown in the right Panel of Figure 2. Comparing to the left Panel,

employment-based visas appear to be a much more important channel for college-educated

immigrants than for non-college-educated ones. Immigrants from India and China are much

more likely to enter with an employment-based visa than immigrants from Mexico and Central

American & Caribbean and Southeast Asian countries. Employment-based entry accounts for

47.2% of college-educated Indian immigrants, 39.4% of Chinese immigrants, in comparing to

7.7% of their Mexican counterparts, and 3.2% of those from Central American & Caribbean

countries. According to equation (3), this indicates that, when increasing employment-based

visas, the size of US immigrants from India and China would rise much faster than those from

Mexico, in percentage term. Also note that the majority of College-educated US immigrants

from Central American & Caribbean, and Mexico enter with a family-based visa, indicating a

large share of US immigrants from these groups are exposed to switch as family-based mode

of entries become restrictive.

23

5.2 Estimating Labor Supply Elasticity

θ/

(1 − ρ) is the labor supply elasticity within a country, and governs the responsiveness of

switching a occupation-mode option within a country when the return to this option changes

by 1 percent. I estimate this parameter by relating the observed variation in the occupational

share of US immigrants to immigrant-sending countries’ education quality that is relevant to

a given occupation. This approach is referred as revealed comparative approach analogous to

Costinot et al. (2011) who estimate trade elasticities. To carry out this approach, I assume the

scale parameter of labor productivity does not depend on m, meaning some workers can be

more productive if working with a family-based visa than with illegal status, but the marginal

productivity distribution is the same across all modes m. I denote labor productivity as T sd,o.

Using equilibrium condition in equation (1), I obtain theory-consistent specification by tak-

ing the occupational share of US immigrants, Πso|d, relative to a baseline group and to a baseline

occupation, o′, and taking the logarithm to have

logΠso|dus

Πs′o|dus

/Πso′|dus

Πs′o′|dus

=θ

1− ρ· log

T sdus,oT s′

dus,o

/T sdus,o′

T s′

dus,o′+

θ

1− ρ· log

∑m τ

sdus,m,o∑

m τs′dus,m,o

/∑m τ

sdus,m,o′∑

m τs′dus,m,o′

46,

where the term θ1−ρ · log

∑m τsdus,m,o∑m τs

′dus,m,o

/∑m τs

dus,m,o′∑m τs

′dus,m,o′

captures the unobserved friction component.

Since the denominator of the dependent variable, logΠso′|dus

Πs′o′|dus

, is invariant within each ν group

and thus will be knocked out by group fixed effects, the regression model would be identical if

one estimated the following specification

logΠso|dus

Πs′o|dus

=θ

1− ρ· log

T sdus,oT s′

dus,o

+ αs + εsdus,o, (9)

where αs are group fixed effects and the baseline group s′ denotes US natives. To measure

occupational productivity for each labor group in the US, T sdus,o, I assume workers’ productiv-

ity is determined by three dimensional abilities: quantitative skill, scientific knowledge, and

language ability. In addition, each type of ability differs in terms of its importance when per-

forming tasks required for each occupation, where the importance of ability for each occupa-

tion is measured using the O*NET variables of tasks intensities. I draw three O*NET variables

(mathematical reasoning ability, mathematics knowledge, and mathematics skill) to measure

the importance of quantitative ability; three variables (science skill, complex problem solv-

ing, and critical thinking) to measure the importance of scientific knowledge, and six variables

(speaking skill, writing skill, oral comprehension, oral expression, written comprehension, and

written expression) to measure the importance of language ability. The detailed definition on

each O*NET variable is described in Appendix C.3.

The O*NET and Census occupational codes match nicely, as both use the SOC occupation

46This specification is consistent with empirical finding evidence which suggests the occupation sorting of USimmigrants in not based purely on occupational comparative advantages (Patel and Vella, 2013).

24

code. I transform each of the O*NET variables to a percentile ranking based on the SOC occu-

pation code. Then I collapse the labor-hour weighted average for 28 aggregate occupations to

obtain the desired skill-importance measurement. I denote αmath,o, αscience,o, and αlinguistic,o as

the importance of math ability, scientific knowledge, and language ability, respectively,47 and

measure T sdus,o as

T sdus,o = αmath,o ·math + αscience,o · science + αlinguistic,o · linguistic proximity.

The math and science variables are based on the Program for International Student Assess-

ment (PISA), which is an international assessment of 15-year-old students on subjects such as

mathematics, science, reading, etc. The PISA data has been collected every three years since

2000. I compute the arithmetic average for each country over all periods for which data is avail-

able to include as many countries as possible. This leaves me with PISA data for 74 countries,

which results in 68 countries after merging with IPUM-ACS.48 I use the average PISA math

and science scores in the baseline estimation and use the percentile PISA scores as alternative

measurement.

Variable linguistic proximity is obtained from Melitz and Toubal (2014), who measure country-

to-country linguistic proximity used in the Automatic Similarity Judgement Program (ASJP).

ASJP advances the tree approach, or language distance measurement, by forming automatic

comparison of language-to-language linguistic distance that is based on the pronunciation of

words across languages, rather than relying on prior subjective used language families. The

language-to-language linguistic proximity measurement is mapped to the desired country-to-

country linguistic proximity by a weighting matrix, with each element being the product of

the population share that speaks each of the top two most widely spoken languages in each

country. I extract information on linguistic proximity from each country that sends emigrants

to the US. I re-scale the three variables — math, science, and linguistic proximity — to apply a

value from 0-1 to measure T sdus,o.49

Analogous to the "log gravity" regression in international trade literature, running an OLS

estimation on equation (9) has an important limitation of sample selection problem of "zero".

The log regression omits country-occupation observation pairs whenever the group-to-occupation

matching is not observed in the data. OLS thus tends to underestimate the elasticity, if those

“zeros” are the country-occupation pairs which have the least comparative advantage such that

labor-occupation sorting is not realized in the data. I use a pseudo-maximum-likelihood (PML)

estimator to estimate the parameter, based on a sample formed by a pairwise combination of

47The baseline results are estimated using transformed percentile O*NET task intensity. The results are similarif I use the raw O*NET standardized score measurement.

48PISA data for Malta, Montenegro, Slovenia, Qatar, and Tunisia were available but immigrants’ country ofbirth are not reported in IPUM-ACS. I also drop India, since India has only participated in the survey once, in2009, and pulled out in 2012 because of concerns that the questions were not socio-culturally appropriate forIndian students.

49For the math and science variables, a value close to 1 corresponds to a higher math or science ability. Forvariable linguistic proximity, a value close to 1 indicates a close proximity to the language spoken in the US.

25

country and occupation, irrespective of whether the country-to-occupation labor match is not

observed in the US labor market. Since the available country measurements of math, science,

and language ability place greater emphasis on the cognitive dimension of ability and vary

less among low-skill jobs in terms of their importance in task intensive, I restrict the sample to

those who have a college degree or higher. In addition, I break down education into bachelor’s

degree and advanced degree to increase the sample size.

Table 1: Estimation results on θ1−ρ

OLS PML

θ1−ρ 3.103*** 3.655***

(0.161) (0.173)

Num. of Obs. 3213 3698

Notes: Equation (9) is estimated using samples formed by non-zero pairwise combinations of 68 origin

countries, 28 occupations, and two educational degrees. The OLS estimator is performed without having

observation "zeros", while the PML estimator is performed with those "zeros". Standard errors are reported

in parentheses. I include a fixed effect for observation which includes college degree in education.

Table 1 reports the results. The PML estimation is performed on a larger sample size than

the OLS estimation, as it includes all pairwise combinations formed by the country-occupation-

degree unit. Unsurprisingly, it estimates a value of 3.66 greater than the value estimated by

OLS, which equals 3.10. Both estimates are statistically significant at a 1% level. To address the

concern that the results are not driven by small immigrant-sending countries, I cluster small

sending-countries into a single regional unit and re-estimate equation (9).50 I also use percentile

PISA scores to measure T sdus,o. As reported in Table 10 in Appendix A, the results are robust in

all scenarios.

My approach of estimating θ1−ρ also serves as a validation on the model hypothesis that

occupation comparative advantage determines occupation sorting. Several papers argue that

workers’ occupational sorting results from labor-occupation comparative advantages (Lagakos

and Waugh, 2013; Burstein et al., 2015), while others argue that market distortion and occu-

pational barriers shape occupation sorting across different race and gender groups in the US

(Hsieh et al., 2013), and affect immigrants across various ethnic groups (Oreopoulosa, 2011).

My result corroborates the occupation comparative advantage hypothesis.

50Regions in the analysis include the following large sending countries: Brazil, Canada, China, Colombia,France, Germany, Hong Kong, Japan, Korea, Mexico, Peru, Poland, Russia, Spain, Taiwan, UK, US, and Venezuela;aggregate regions include Central America, Eastern Europe, the Middle East and North Africa, Oceania countries,South America, Southern Europe, Southeast Asia, Sub-Saharan Africa, and Western Europe.

26

5.3 Estimating Labor Demand Elasticity for the US

Differentiating the CES production function for the US with respect to Ld,o, yields an equi-

librium condition which links the occupational wage unit wd,o with the total efficiency unit

of equilibrium occupational labor, Ld,o, and the elasticity of substitution across occupations,

η. Since neither wd,o nor Ld,o is observed, I substitute wd,o with the ratio between the average

occupational wage Wd,o and the average occupational efficiency units, and substitute Ld,o with

the product of occupational hoursHd,o and the average occupational efficiency units. I omit the

notation for destination d by focusing on the US. Exploring time variation during 1990-2015, I

obtain the following equation to estimate η:

logWo,t

Wo′,t= −1

ηlog

Ho,t

Ho′,t+ εo,t.

51 (10)

The term εo,t = log Ao,tAo′,t

+ (1 − 1η) log Eo,t

Eo′,tcaptures the mixture in year t of the unobserved

occupational demand and the aggregate occupational labor productivity at year t. I draw from

the US micro-census 5% sample in 1990 and 2000 and the 1% American Community Survey

sample in 2005, 2010, and 2015 to measure Wo,t using the average occupational hourly wage,

and measure Ho,t as the overall occupational labor hours in each time period. Each sample is

restricted to 18-65-year-olds.

The endogeneity issue is that the unobserved occupational demand and labor productiv-

ity affect both the equilibrium occupation wages and the equilibrium occupation labor hours.

Literature has mostly addressed this type of endogeneity issue using a Card-type instrumental

variable predicted by exogenous supply-push factors. For example, Card (2001) predicts the

exogenous labor supply based on persistence in spatial sorting of US immigrants by country

of origin. Multiple extended versions of the Card instrument have been developed based on

persistence in spatial-occupation sorting (Burstein et al., 2017) or spatial-sector sorting of US

immigrants by countries of origin (Colas, 2017).

51The estimating equation (10) is obtained by first taking the first-order condition on the CES production func-tion with respect to Lo to have

wo = Ao · Y1η · L−

1η

o ,

where Lo is the aggregate occupation efficiency unit of labor, and wo is wage efficiency units per labor. Sinceneither the wage efficiency unit, wo nor the total efficiency units of labor, Lo is observed, I rewrite wo = Wo

Eo, and

Lo = HoEo. Wo denotes the average hourly occupational wage; Eo denotes the average occupational efficiency

unit per hour; and Ho denotes the aggregate occupational labor hours. I rearrange to obtain Wo = Ao · Y1η ·H−

1η

o ·E

1− 1η

o . I normalize it by a baseline occupation o′ and take the logarithm to obtain

logWo

Wo′= −1

ηlog

Ho

Ho′+ log

AoAo′

+ (1− 1

η) log

EoEo′

.

Let εo = log AoAo′

+ (1− 1η ) log Eo

Eo′be the unobserved component.

27

Table 2: OLS AND 2SLS ESTIMATION RESULTS ON ηus

OLS IV FIRST STAGE

Panel A: w/o Trend and Occupation dummy interaction

− 1η

-0.403*** -0.457*** 0.523***

(0.026) (0.034) (0.039)

Num. of Obs. 112 112 112

Panel B: with Trend and Occupation dummy interaction

− 1η

-0.329*** -0.412*** 0.549***

(0.027) (0.036) (0.047)

Num. of Obs. 112 112 112

Notes: Equation (10) is estimated based on 28 occupations for four-year periods including 2000, 2005, 2010,

and 2015. Standard errors are reported in parentheses. The standard errors of η are calculated using the

Delta Method as discussed in detail in footnote 49.

To be consistent with my model, which segments the US national labor market by occupa-

tion, I construct a Card-type instrumental variable based on persistence in origin-occupation

sorting of US immigrants over time (Lafortune and Tessada, 2010; Hanson and Liu, 2016). The

constructed instrumental variable captures the exogenous occupational labor supply in the ab-

sence of changes in occupational labor demand or in labor productivity since 1990. I denote

the instrumental variable as log Ho,t

Ho′,t, where

Ho,t = Ho,1990 +∑s

[Πso,1990|d ×∆Hs−

d,o,t

], t ∈ {2000, 2005, 2010, 2015}.

Πso,1990|d is the share of natives or immigrants in group swho work in occupation o. Ho,1990 is the

total occupation hours in 1990. ∆Hs−d,o,t is the change in the total hours of US workers in group

s between 1990 and year t, excluding those who work in occupation o. I estimate equation

(10) using four-year periods (in 2000, 2005, 2010 and 2015) and 28 broad occupations which are

consistent with the categories used in the simulation.

Table 2 shows the results estimated using OLS and two-stage least squares (2SLS) in panel

A without adding trend and occupation dummy interaction, and in panel B which adds trend

and occupation dummy interaction. Adding occupation trend aims to approximate the unob-

served demand shifts by an occupational specific time trend as in (Katz and Murphy, 1992).

The estimates become larger (less negative) after controlling occupation trend, presumably

explained by the skill reversal since 2000 (Beaudry et al., 2016). Unsurprisingly, the OLS re-

gression leads to an upward bias of − 1η

for both specification. My preferred estimation result

28

is -0.457, obtained from the 2SLS regression in Panel A. It implies a value of η equal to 2.188

(standard error=0.162, which is smaller than the OLS estimate of 2.481. The first-stage regres-

sion also shows strong positive correlation, with an R2 of 0.62 and a coefficient of 0.523 that is

statistically significant at the 1% confidence level.52 My estimates lie within the range of values

obtained in the literature. Burstein et al. (2015) estimate a value of elasticity of substitution

across 30 US occupations between 1.78 and 2. Hsieh et al. (2013) estimate the value of elasticity

of substitution across 67 US occupations to be 3.

5.4 The Values of Productivity Correlation Parameters

The Value of γ: I estimate the productivity correlation between the US and immigrant home

country using NIS data. NIS reports immigrants’ pre-migration wages as well as the post-

migration wage earned in the US.53 The survey has information on individuals’ hours worked

per week, weeks worked per year, and also have fully flexible to report their wage at various

frequency (hour, week, month, annual) and based on the currency that they were paid. I calcu-

late pre-migration and post-migration hourly wages, and convert these wage variables in US

dollars using the exchange rate data from Penn World Tables (PWT 7.1). Following Schoellman

and Hendricks (2016), I exclude individuals whose hourly wage fall outside the range $ 0.01 to

$ 1, 000.

Since skill is paid at the same wage within a country, the correlation between pre-migration

at home country and post-migration wages in the US reflects the correlation of productivity

across these locations. I estimate the wage correlation for each migration sending country

separately, and then take the average over all sending countries to obtain a value of aver-

age correlation coefficient around 0.28. It is important to point out that ρ, σ and γ are not

exactly equal the correlation coefficient parameter, but is a function of it. Specifically, 1 − γ =√1− Cor(adus,oi , aH,oj); see (Cameron and Trivedi, 2005). This implies γ = 1−

√1− 0.28 = 0.15.

The Value of σ: My intuition of calibrating σ is motivated in Figure 3. The vertical axis is

for each national-origin group, the ratio between the number of migrants who migrate to the

US from foreign competing destination countries during 1995-2000 and the number of migrants

who live in these foreign countries in 1995. The horizontal axis is the ratio but for home country

residence. The 45-degree line is plotted by the blue dashed line. I use the variable on the state or

country of residence 5 years ago available in US Census 2000 to measure the 5-year migration

flow from foreign destination to the US.

As most points lie further above the 45-degree line, US immigrants are much more dispro-

portionately drawn from population who live abroad than those who live at home country.52The implied standard error is derived according to the Delta method, given that the negative inverse function

is a continuous mapping. The first is calculated as 0.026 ∗ 10.4032 = 0.160, while the second is calculated as 0.034 ∗

10.4572 = 0.162.

53These two variables from NIS dataset has recently explored by Schoellman and Hendricks (2016) to study thegain of migration.

29

On average, for every 1000 people who were residence in OECD countries in 1995, 30 of them

migrated to the US during 1995-2000; in contrast 5 out of 1000 home country residence migrate

to the US during the same period. This observation coincides with the intuition pointed out in

equations (4) and (5), and is informative to the value of σ, relative to γ.

ChinaSaudi ArabiaBrazil

Japan

RomaniaPhilippines

Korea

Colombia

Nicaragua

Ireland

CanadaCosta Rica

Ecuador

New Zealand

Guatemala

Haiti

Albania

Dominican Republic

Honduras

Barbados

Cuba

Mexico

El Salvador

Trinidad and Tobago

Jamaica

0

.03

.06

.09

.12

.15

The

Mig

ratio

n Sh

are

of R

esid

ence

in F

orei

gn C

ount

ries

0 .03 .06 .09 .12 .15The Migration Share of Residence in Home Country

Figure 3: The number of Migrants as a Share of Residence by Home and by Foreign Countries

Consider a change in wage unit, in terms of ∂wdwd

. Since wage units and migration frictions

enter symmetrically into equation (1), the results in equation (4) and (5) apply. Take difference

between these two to have

∆Πsd′,f

Πsd′,f

− ∆Πsh

Πsh

= − θ(σ − γ)

(1− σ)(1− γ)Πsd|f

∆wdwd

.

US Census 2000 asks individual the state or country of residence 5 years ago. Using this in-

formation, I measure migration flows to the US during 1995-2000 by those who migrate from

other foreign destinations, and those who came from home countries. I also obtain the number

of population live in each OECD countries excluding the US in 1995, based on the brain-drain

dataset collected by Institute for Employment Research (IAB). Combining these two informa-

tion, I compute∆Πs

d′,fΠsd′,f

and ∆ΠshΠsh

. I also measure Πsd|f , the fraction of population live in non-US

foreign countries in 1995 based on IAB database, and measure ∆wdwd

using WDI GDP per capital

growth in the US. This gives σ = 0.35.

The Value of ρ and θ: Recall that I obtain the value of θ1−ρ = 3.66 in Section 5.2. To separate

out these two parameter values, I perform maximum likelihood estimation (MLE) on the dis-

tribution of the wage residual obtained by running the wage earned by US workers on a set of

education, gender, marital status, and occupation dummy variables. I obtain θ = 1.47 which

lies in the range of estimates in the previous literature, and further implies ρ = 0.6.

30

6 Quantitative Exercises

The goal of this paper is to quantify how a skill-based US immigration reform — which shifts

visas from family- and refugee- based to employment-based categories — would change the

composition of US immigrants, the pattern of international labor movements, and the wage

structures in the US and in foreign countries. Recall that in the static model, the empirical

content of the “entry modes” is interpreted as the type of mode status that an individual has

in a given year (2010 in my analysis), and therefore the type of counterfactuals my model can

undertake are exogenous changes in the aggregate number of migrants in each mode status in

that year, which reflects changes of immigration policy made in the past. The counterfactual

exercise reduces a total of 8 million family- and refugee- mode migrants while increasing the

same number of employment-mode migrants. This experiment mimics a situation had the US

switched to the Canadian visa regime in 1990. I discuss how I measure the counterfactual shock

in details in Section 6.1.

Taking the model to the data in year 2010, I consider workers from 115 countries of ori-

gin, two educational levels (college and non-college), and two gender groups, resulting in a

total of dim(s) = 460 labor groups in the analysis. I consider a version of world economy

with dim(d) = 13 countries or aggregated regions, including four individual countries — the

US, Canada, India, and Mexico — while pooling other countries in nine aggregate regions —

Africa, Central America, East Asia, Eastern Europe, the Middle East and South Asia, Ocea-

nia, OECD Europe, Southeast Asia, and South America. I treat the US, Canada, Oceania, and

OECD Europe as both source and destination countries of migration, while the other countries

are treated only as source countries.54

For the US, I divide occupations into 29 categories, including an unemployment option. I

group detailed US occupations reported using variable OCC1990 by their similarity in task con-

tents. Table 9 in Appendix A shows the 28 occupation group are distinct in terms of their task

contents as provided by the Dictionary of Occupational Titles’s (DOT) task variable. I use the

American Community Survey (ACS) five-year sample, 2009-2013, from the Integrated Public

Use Microdata Series (IPUMS) USA (Ruggles et al., 2015) to measure the occupational share in

terms of total hours worked and average occupational hourly wage by each origin, education,

and gender group. For foreign countries, I have 20 broad occupational categories for Mexico

and India, and 9 occupations for other countries based on the one-digit International Standard

Classification of Occupations (ISCO88). I measure the share of occupations and average wage

earned by each group for each country/region mainly using Integrated Public Use Microdata

Series (IPUMS) International in year 2010, and International, Luxembourg income study (LIS),

and supplement with occupational share for immigrants using the Database on Immigrants in

OECD countries (DIOC). I also use the brain-drain dataset from the Institute for Employment

Research (IAB) to measure bilateral migration rates by gender and education groups. Section

54Omitting south-to-south migration is not a limitation of the model, but is due to the data challenge in mea-suring south-to-south migration.

31

C.1 discuss the data source and measurement of migration rate and labor market variables in

details.

In the benchmark results, I assign θ = 3.66 and ηus = 2.18 for the US, as estimated in Section

5. I assume the occupational elasticity of substitution is the same across all foreign countries,

and set it to equal to ηo = 0.9, following Goos et al. (2014). In addition, I set ρ = 0.6, σ = 0.35

and γ = 0.15.

Section 6.1 defines the benchmark counterfactual exercise; Section 6.2 expresses the solution

method of using the Exact Hat Algebra Approach (Dekle et al., 2008). I impose multiplicative

separable assumption on migration friction when solve my model in changes. This assumption

greatly simplifies the the model simulation without knowing the level on the policy component

of migration frictions specific to each mode of entry, which are difficulty to identify from the

data. Section 6.3 perform a validation exercise by taking the number of US visas granted since

1990 to the model, and show that despite my solution method impose a strong multiplicative

separable assumption on migration frictions, my model can generate a cross-country visa allo-

cation that aligns well with the data.55

6.1 Benchmark Counterfactual Reform

I simulate the benchmark counterfactual as follows: holding the total number of visas issued

unchanged since 1990, but reallocating visas from family-based and refugee-based categories

to employment-based categories such that the visa distribution exactly matches the Canadian

system as in Figure 4 below. The migration friction through the illegal channel is unchanged

between the actual and the counterfactual economy.

0

20

40

60

80

100

Sha

re o

f Vis

a in

%

Employment Family OtherSource: Department of Homeland Security and Statistics Canada

US Canada

Figure 4: Share of Lawful Permanent Residents in the US and Canada by 3 Visa Categories

Note: The visa distribution for the US is calculated based on Yearbook of Immigration Statistics 1996-2015.

The data for Canada is obtained from Canadian Statistics, 2011-2013.

55Under multiplicative separable assumption, I solve the model by adjusting a common mode-specific costchange to match the exogenous policy changes of visa number by categories.

32

Let Q denote the total number of visas granted since 1990, while PCANm and PUS

m denote the

visa distributions for Canada and the US, respectively, as in Figure 4. The policy changes in the

aggregate number of mode entry, Qm is defined as

∆Qm = Q× (PCANm − PUS

m ), m ∈{mf ,me,mo

}. (11)

This implies a reduction in the number of family- and refugee- mode migrants by 7.2 and 0.8

million, respective, and an increase in the number of employment-mode migrants by 8 million.

Given the exogenous policy shock as ∆Q ={∆Qmf ,∆Qmo ,∆Qme

}, the model absorbs these

changes by introducing ∆τ ={∆τmf ,∆τmo ,∆τme

}. In particular, I assume ∆τmf , ∆τmo are in-

variant in national origin, education, gender and occupation, mirroring the fact that US family-

and refugee- based visas have been distributed without discrimination against immigrants’

demographic characteristics such as nationality, education, gender and occupation. To reflect

Canadian point system’s emphasis on education and occupation specialty, I apply ∆τme > 0

only to workers who have college-educated and above and to skill-intensive occupations.56

Per-country ceiling: Absorbing changes in the aggregate number of mode specific migrants by

a mode-specific cost change may raise concerns about the violation of the per-country ceiling

rules. According to Immigration and Nationality Act (INA), the rule limits the annual law-

ful permanent resident (LPR) admission from any single country to 7% of the total number

of family-based and employment-based admissions in certain categories. However, the pur-

pose of the per-country ceiling is to avoid visa monopolization by a few countries rather than

set a limit on the number of visas from each country (Wasem, 2012), other categories are not

subject to this rule. For example, 75% of the visas allocated to spouses and children of LPRs

are not subject to the per-country ceiling; oversubscribed countries may surpass the limit for

employment-based immigrants as long as visas are available (Kandel, 2016). In practice, Mex-

ico has acquired over 20% of the overall LPRs during 1991-2000 and over 15% during 2001-2010.

As a validation, Section 6.3 shows that my model-generated cross-country visa allocation does

not overpredict the number of visas acquired by large immigrant-sending countries by much.

6.2 Solution Method

I solve the equilibrium in terms of proportional changes using the Exact Hat Algebra Approach

developed in Dekle et al. (2008). My solution method is slightly different from the conven-

tional approach used in the literature, which measures policy or economic shocks in terms of

model fundamentals externally, and then introduces the changes of model fundamentals (as

the shocks) to the model. I introduce exogenous policy shock as Qm, while matching it by

56The occupations where ∆τme > 0 applies are Math & Science, Engineers, Health Professional, Social Scientists,Computer System Analysts, Computer Software Developers, Management, Executive Managerial, Lawyers andJudges.

33

introducing ∆τ and solving them endogenously from the general equilibrium conditions.

Defining variables X = X′

X, where X ′ denotes the counterfactual equilibrium variables and

X denotes the equilibrium variables of the initially observed economy in year 2010, I express

equilibrium labor flow in terms of proportional changes as follows:

Πsm,o,d,F =

φd,m,o∑m′,o′∈Od

(φd,m′,o′Πm′,o′|d,F

) × Φd∑d′∈F

(Φ

1−ρ1−σd′ Πd′|F

) × ΨF

ΨHΠH + ΨFΠF

57, (12)

where φd,m,o =

(T sd,m,owd,oτ

sd,m,o

) θ1−ρ

, Φd =

[∑m′,o′∈Od

(φd,m′,o′Πm′,o′|d,F

)] 1−ρ1−σ

, and

ΨF =

[∑d′∈F

(Φ

1−ρ1−σd′ Πd′|F

)] 1−σ1−γ

, ΨH =

[ ∑o′∈OH

(φh,o′Πo′|H

)] 1−ρ1−γ

.

Again, all these notations in changes are specific to s, but I omit the subscript for notation sim-

plicity. Analogous to equation (1), the first terms in equation (12) represents the proportional

changes in probability of choosing m and o, conditional on living in country d ∈ F ; the second

term represents the proportional changes in probability of living in country d, conditional on

living abroad; and the last term is the proportional changes in the marginal probability of living

abroad. The proportional changes in wages is

W sd,m,o = T sd,m,o · wd,o ·

(Πsd,m,o,F

)− 1−ρθ

(13)

In the case when T sd,m,o = τ sd,m,o = 1, the changes in average group wage in country d is the

same across all occupations and modes, and equals

W sd =

[Φρ−σ1−ρd Ψ

σ−γ1−σF

(ΨHΠH + ΨFΠF

)] θ1−ρ

(14)

The proportional changes of labor supply is

Lsupplyd,o =

1

wd,o

∑s

∑mW

sd,m,o · Ls · Πs

d,m,o,fWsd,m,o · Ls · Πs

d,m,o,F∑s

∑mW

sd,m,o · Ls · Πs

d,m,o,F

. (15)

57Analogously, the proportional changes in marginal probability of staying home country H and working inoccupation o is,

ΠsH,o =

φH,o∑m′,o′∈Od

(φd,m′,o′Πm′,o′|d,F

) ×[∑

m′,o′∈Od

(φd,m′,o′Πm′,o′|d,F

)] 1−ρ1−γ

ΨFΠF + ΨHΠH

.

34

The proportional changes in labor demand is

Ldemandd,o =

1

wηdd,oYdA

ηdd,o.

58 (16)

In addition, the changes in the aggregate number of migrants in each mode status ∆Qm as

measured in Section 6.1 is absorbed by ∆τ such that

∆Qm =∑s

∑o

Ls · Πsd,m,o · (Πs

d,m,o − 1), s ∈ non-US, m ∈{mf ,me,mo

}. (17)

The system of equations (17) introduce three equations and three more unknowns, namely

∆τmf ,∆τmo ,∆τme . Ideally, if knowing the level of migration friction τ sd,m,o, one would translate

∆τ ={∆τmf ,∆τmo ,∆τme

}to proportional changes of migration friction for each groups s, 59

and solve ∆τ together with wd,o, Πsd,m,o, and W s

d,m,o from the system of equations (12) – (17).

However, τ sd,m,o and T sd,m,o are not separately identified from the data.

To carry out the counterfactual exercise, I impose a multiplicative separable assumption on

migration frictions to the US, as follows

τ sdus,m,o = τ sdus,o × τdus,m

The first term captures the non-policy component of migration friction, which is independent

across modes. It is unchanged between the observed equilibrium and the counterfactual, i.e.,

τ sdus,o = 1. The second term captures policy-related migration friction, which can be a function

of mode only. What this assumption rules out is the possibility that US immigration policy

preferentially selects workers from a specific country of origin to work in some occupations or

migrate through a given mode.

Although imposing a strong multiplicative separable assumption on migration frictions,

the gain is that the level changes of ∆τ are translated to proportional changes τ without know-

ing the level of τ sd,m,o. In addition, the frictions in illegal entry and in other countries are un-

changed in the counterfactual, so that τ sd,mi,o = 1 for illegal mode mi, and τ sdf ,m,o = 1, where dfrefer to any countries other than the US.60

Given exogenous policy shock ∆Qm ={∆Qmf ,∆Qmo ,∆Qme

}, I can solve τ =

{τmf , τmo , τme

},

58 Where

Yd =

∑s

∑o

∑mW

sd,m,o · Ls ·Πs

d,m,o,fWsd,m,o · Ls · Πs

d,m,o,F∑s

∑o

∑mW

sd,m,o · Ls ·Πs

d,m,o,F

.

59One can map the level to proportional changes using

τsd,m,o =τsd,m,o − ∆τm

τsd,m,o

60I am aware that eliminating family-based visas would increase the number of attempts at illegal border cross-ing, and, hence, the ratio of border patrol officers per illegal attempt would fall. Here, I assume that τsd,mi,o is afunction of the number of border patrol officers, instead of police officers per illegal attempt.

35

and wd,o, Πsd,m,o, and W s

d,m,o from systems of (12) – (17)61 without knowing information on oc-

cupation total factor productivity in each country (Ad,o), occupation labor productivity in each

country by groups and modes (T sd,m,o), the level of illegal migration frictions (τ sd,mi,o), the level

of migration frictions at countries other than the US (τ sdf ,m,o), the non-policy related migration

frictions in the US (τ sdus,o). Since these fundamentals are unchanged between the counterfactual

and the observed equilibrium, I set Ad,o = T sd,m,o = τ sdus,o = τ sd,mi,o = τ sdf ,m,o = 1. Performing

counterfactual simulation requires parameter values on{θ, η, ρ, σ, γ

}, and data on the share of

US immigrants that enters through each mode in each occupation and by labor groups (Πsm|d,o),

the bilateral migration rates (Πsd) to each country, the share of population live in each foreign

destination (Πsd|F ) conditional on those who live abroad, the occupational shares of immigrants

in each country(Πso|d), the average occupational wages earned in the US by labor groups and

by mode of entry (W sdus,m,o

), and the average occupation wages earned by immigrants in other

countries (W sdf ,o

).62

6.3 Validation

The subsection performs model-based validation exercises to compare the model-generated

visa allocation across immigrant-sending countries with the observed visa allocation since

1990. The goal is to show that, despite my solution method depends crucially on two assump-

tions 1) the US visas have been distributed without discrimination against immigrants’ nation-

ality (captured by a national-origin invariant change of mode-specific migration friction)63, and

2) the multiplicative separable assumption of migration frictions, my model together with the

solution method can generate predictions of visa allocation across immigrant-sending coun-

tries that align well with the data.

I obtain the aggregate number of US visas issued since 1990, and perform the following

four separate counterfactual exercises: (a) had family-based visas not been issued since 1990;

(b) had employment-based visas not been issued since 1990; (c) had refugee and diversity visas

not been issued since 1990; and (d) had all types of permanent visas not been issued since

1990. Each counterfactual keeps the migration friction of illegal entry unchanged, but absorbs

changes in the aggregate number of migrants in each mode by a proportional changes of mi-

gration friction associated with that mode.

Figure 5 plots, for each counterfactual, the predicted visa allocation across countries (on the

vertical axis) against the actual allocation (on the horizontal axis) for the 114 sending countries61To solve equilibrium efficiently, notice that equilibrium changes in labor allocation and wages — in equations

(12) and (13) — are functions of changes in the wage efficiency unit of labor wd,o. I solve the equilibrium in changesof wd,o using the system of equations (15) and (16) for each country and occupation labor market.

62Appendix B.2 shows that solving the model in proportional changes does not require information on the entrymode share, or the average occupation wage by modes for immigrants to other destination countries.

63The non-discrimination against national-origin, education assumption tends to be violated in practice to someextent. For example, only immigrants from certain countries with low rates of immigration to the US are eligiblefor the diversity visa program. In addition, there are per-country visa limits. Although many visa categories arenot subject to this limit as mentioned previously, there is still a concern about the extent to which my model mightoverpredict the visa share acquired by large immigrant-sending countries.

36

considered in this study; both axes are plotted in log scale. The blue dashed line is the 45-

degree line. One worth-mentioning take-away from Figure 5 is that my model together with

the solution method predicts visa allocation across immigrant-sending countries that align well

with the data. In the case of family-based visas displayed in panel (a), employment-based visas

displayed in panel (b), and overall visas displayed in panel (d), the dots align well with the 45-

degree line. The Pearson correlation coefficient equals 0.984 for the family-based visa, 0.987 for

the employment-based visa, and equals 0.956 in terms of the overall visa allocation.

Although the assumption of a common change in mode-specific friction tends to be vio-

lated in the case of the diversity visa, the predicted refugee and diversity visa allocation fits

reasonably well with the data, as shown in panel (c). The implied Pearson correlation coeffi-

cient equals 0.644. Appendix E reproduce the plot in Figure 9 excluding outliers, to rule out

the possibility that outliers drive the strong positive correlation. The calculation shows that the

correlation remains high.

ISLCYP

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(a) Family visas

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(b) Employment visas

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(d) All visas

Figure 5: Predicted vs. actual visa allocation across countries of origin

Another important take-away from validation exercise is that, although my model over-

predicts the number of visas acquired by countries that send large numbers of immigrants, it

does not do so by much. On the aggregate level, the share of overall visas which have been

allocated to Mexican immigrants since 1990 is 16.8%, which far exceeds the 7% per-country

37

ceiling.64 My model predicts that 21.3% of all visas will be allocated to Mexicans, an overpre-

diction that seems to be within acceptable ranges. In each detailed category, my model also

produces a reasonable prediction of visa categories that certain countries are likely to monopo-

lize. For example, for the family-based category, my model predicts that 28.9% of visas will be

allocated to Mexicans, compared to 23.1% in the data. For the employment-based category, my

model predicts that 19.9% and 9.8% of visas will be allocated to people from India and China,

respectively; these shares are slightly smaller than the observed data of a 20.8% and 11.3%,

respectively.

7 Quantitative Results

Solving the system of equations (12) - (17) leads to τmf = 0.93, τme = 1.39 and τmo = 0.97,

meaning that the counterfactual migration friction are changed such that the take-home wage

rate for family, employment, and other legal modes of migration become 93%, 139% and 97%,

respectively, of the take-home wage in the initial equilibrium. The rest of this section presents

the quantitative results of benchmark simulation. Section 7.1 discusses the impacts of policy

reform on the US in terms of changes in the composition of immigrants, and the impacts on

wages and occupational structure. Section 7.2 analyzes the impacts on the global economy.

7.1 The Impacts on the US

(A) The Composition Changes of US Immigrants

On National-origin and Education Composition of US Immigrants: Table 3 compares the

composition change of US immigrants between the observed and counterfactual economy.

Each value represents the number of immigrants for a specific national-origin and education

group as a share of the total US foreign-born population. The major migration sending coun-

tries from each continent are listed.64As discussed in an earlier section, this is because many visa categories are not subject to this restriction.

38

Table 3: Share of Foreign-born US Workers by Country of Origin and Education

Observed Economy Counterfactual Economy

Region/country All Non-

college

College All Non-

college

College

Mexico 32.1% 30.3% 1.8% 27.9% 26.2% 1.7%

Central America & Caribbean 17.7% 15.1% 2.6% 14.9% 12.7% 2.2%

East Asia 9.3% 4.2% 5.1% 12.4% 3.4% 9.0%

India 5.5% 1.2% 4.3% 9.7% 0.9% 8.8%

Southeast Asia 10.1% 6.3% 3.8% 9.1% 4.9% 4.2%

South America 7.2% 5.0% 2.2% 6.7% 4.1% 2.6%

Western & Northern Europe 4.4% 2.5% 1.9% 5.2% 2.0% 3.2%

ALL IMMIGRANTS 71.9% 28.1% 59.9% 40.1%

Notes: each value represents the number of immigrants in a given national origin and education group, as

a share of the total US foreign-born individuals. Male and female are aggregated in each national origin

and education group.

A few things are worth noting. First, the counterfactual policy reform improves the educa-

tion composition of US immigrants as shown in the last row of Table 3. The share of college-

educated immigrants increases from 28.1% to 40.1% as shown in the last row. Second, the

national-origin mix of US immigrants also changes. The largest decline is in Mexican immi-

grants, whose share in US immigration falls from 32.1% to 27.9%. The immigration share of

Central American and Caribbean-born workers also falls, from 17.7% to 14.9%. The share de-

clines slightly for immigrants from Southeast Asia, South America. The share of Indian-born

immigrants increases the most, from 5.5% to 9.7%. East Asian countries also see a significant

increase in emigrants to the US from 9.3% to 12.4%. There are is a modest increase of US mi-

grants from Western and Northern Europe. Results for other countries and regions are reported

in Appendix A Table 11.

Third, the changes in the share of foreign-born US workers follow the same sign among

most countries of a continent. Specifically, the share falls among all Central American and

Caribbean, South American, Southeast Asia, Eastern Europe, Middle Eastern and African coun-

tries, while it rises among all East Asian, OECD Europe countries. This great similarity among

countries in each continent reflects the similarity in their entry mode share for migration.

Guided by the discussion in Section 4, the results in Table 3 are not only determined by

which mode do workers use to migrate to the US, but also depends on the similarity in labor

productivity across countries, what fraction of workers live abroad relative to home country —

as shown in equation (3), and the equilibrium substitution to alternative US migration modes

— as shown in equation (6).

39

(B) Substitution to Alternative Modes of Entry

The impact on the composition changes of US immigrants reported in Table 3 is not large as

one might expect due to the entry mode substitution. Next I show in in columns 2 and 3 of Table

4, the number of US migrants increased in alternative mode status as a share of the total number

of US family- and refugee- based legal visas reduced, for non-college educated immigrants

from Mexico, Central American & Caribbean, and South America. Results starting in column

4 report the share the of immigrant who switch to other countries, and will be discussed in a

later section.

Table 4: The number of US Migrants Increased in Alternative Options as a Share of the Numberof US Family- and Refugee- based Visas Reduced by Major Non-college Educated Groups

In the US Received by Foreign economies

Origin countries Employment

visa

Illegal entry EU Oceania Canada Home

country

Mexico 1.63% 48.13% 0.10% 0% 0.04% 50.10%

CA. & CARIBBEAN 2.46% 33.59% 3.09% 0.02% 0.46% 60.38%

Honduras 3.62% 61.86% 0.12% 0% -0.01% 34.41%

Guatemala 3.53% 57.95% 0.08% 0% 0.01% 38.42%

El Salvador 3.63% 55.55% 0.12% 0.63% 0.24% 40.40%

Dominican republic 1.13% 24.10% 3.86% 0% 0.12% 70.78%

Jamaica 4.68% 22.70% 9.60% 0.03% 3.09% 59.90%

South America 15.23% 46.08% 5.18% 0.25% 1.97% 31.30%

Notes: The values are the changes in the number of workers toward each mode or destination as a share of

the total number by which US family and other legal visas were reduced.

Since the equilibrium occupational wage reduction at foreign countries are much smaller

than to the decline in family entry mode frictions to the US,65 it indicates that the switchers are

mostly those who no longer find family- or refugee-based visas optimal. Therefore, I interpret

the values reported in Table 4 as the share of family- or refugee-based visa Rejectees that switch

to each alternative options such as employment-based visas or illegal entry.

Among non-college educated immigrants from Mexico, Central American & Caribbean,

and South America, switching to illegal status is the primary channel for remaining in US. As

the primary source of US non-college educated immigrants, 48.13% of Mexicans would switch

from family- or refugee-based visa to illegal entry. The share of visa rejectees that to illegal

entry is also notable in Central American & Caribbean, and South America countries, and most

notable among immigrants from Honduras, Guatemala, and El Salvador, with 61.86%, 57.95%

65Model Solution shows the τmf = 0.93, τmo = 0.97. In contrast, the largest occupation wage decline at foreigncountries is wd,o = 0.9954, which takes place in Mexico at service occupations.

40

and 55.55% of choosing to remain in US with illegal status, respectively.

Again guided by the formula in equation (6) of Section 4, the result is not only determined

by which mode do workers use to migrate to the US (Πsd,m,F ), what fraction of workers live

abroad (ΠsF ) and live in the US (Πs

d,F ),66 but also depends on the productivity similarity across

US mode status and how this productivity similarity differs from that to foreign countries

(ρ− σ), and to home country (σ − γ).

On Illegal Immigrants to the US:

According to the Department of Homeland Security (DHS), there are 11.4 million undoc-

umented foreign-born population reside in the United States in 2010, and this number has

held steady since the end of the Great Recession (Passel and Cohn, 2016). As an unintended

consequence of a skill-based immigration reform, I find the number of US illegal immigration

increases by 21%, roughly 2.4 million more US illegal immigrants. Of these, approximately

1.4 million are from Mexico, accounting for 58.3% of the overall increase. Central America &

Caribbean account for 576 thousand. The number of illegal immigrants from South America

and Southeast Asia increases slightly, by 96 and 85 thousand, respectively.

(C) Wage and Occupational Employment

On US wages: When investigating the changes of average group wage, I am aware that the

changes can come from the equilibrium wage impacts, workers’ reallocation behavior across

occupations, and the change in the composition of US immigrants for each group. The effect

of interest lies in impacts on the average group wage caused by the first two sources: the

changes in average group wage, holding the composition constant. I compute the average

wage changes for each US native groups using equation (14). To compute the average wage

change for foreign-born groups, while holding the average group productivity constant, I use

the following formula

W sd =

∑o,mW

sd,m,oΠ

sd,m,oW

sd,m,oΠ

sd,m,o

(Πsd,m,o

) 1θ∑

o,mWsd,m,oΠ

sd,m,o

/∑o,m Πs

d,m,oΠsd,m,o∑

o,m Πsd,m,o

.

In the first term, W sd,m,o absorbs changes in equilibrium wage units and the composition changes

of workers in cell d-m-o; the term Πsd,m,o captures the reallocation of labor across occupations,

and the term(

Πsd,m,o

) 1θ

corrects for the selection bias.67 The second term captures the changes

66Recall using conditional probability, Πsd,m|F in equation (6) can be rewritten as Πs

d,m,F

/ΠsF , and Πs

d,m|F in

equation (6) can be rewritten as Πsd,m,F

/Πsd,F .

67It terms out one can simplifies the above formula as

W sd =

∑o,mW

sd,m,oΠ

sd,m,owd,oΠ

sd,m,o∑

o,mWsd,m,oΠ

sd,m,o

/∑o,m Πs

d,m,oΠsd,m,o∑

o,m Πsd,m,o

.

41

of migration population size.

Table 5 reports the average wage impacts of each education-gender group for US natives

and Mexican, Indian and Chinese immigrants. For US natives, wage increases for 0.48% for

non-college educated males and increases 0.53% for females. College educated males experi-

ence a 0.16% wage loss, while females gain 0.30%. For US immigrants workers, non-college

educated Mexican immigrants experience the largest wage gain by around 0.7%; although

smaller than the gain of Mexican immigrants, non-college educated Chinese and Indian im-

migrants also gain, with non-college educated females gain more than males.

Table 5: Wage impact of US workers by major groups

National origin Non-college

male

Non-college

female

College male College female

US natives 0.48% 0.53% -0.16% 0.30%

Mexican 0.69% 0.70% -0.34% 0.25%

Indian 0.20% 0.50% -2.32% -1.64%

Chinese 0.50% 0.62% -2.26% -1.43%

Among college-educated immigrants, the adverse impacts are concentrated mainly among

Indian and Chinese immigrants, and are stronger for males than for females. Indian and Chi-

nese male immigrants suffer a wage loss of 2.32% and 2.26%, respectively. The wage loss for

females is 1.64% for Indians, and 1.43% for Chinese. Mexican immigrants experience a small

wage gain, equaling 0.34% for males, while females gain by 0.25%. The differential wage im-

pacts across US workers reflects group differences in occupation sorting, as shown in equation

(8) of Section 4. Table 12 of Appendix A shows the wage impacts of US immigrants from other

countries of origin.

US Occupation Structure: I investigate the changes in US employment structure for each of

28 broad occupations. I first focus on the four STEM occupations included. Figure 10 shows

the changes in the occupational employment share of college-educated national-origin groups

that experience substantial changes (vertical axis), against their values in log revealed compar-

ative advantage (horizontal axis).68 The general finding is that 20-30% of STEM jobs switch

from college-educated US natives to Indian and Chinese counterparts. The line of best fit is

upward sloping among all four occupations, promoting the degree of labor-occupation spe-

cialization and suggesting an improvement of efficiency in labor-occupation allocation among

68I restrict the plot to college-educated labor groups, and aggregate countries into 13 regions by pooling malesand females together. Non-college educated groups are excluded from the plot to keep it informative. Sincenon-college educated workers are rarely employed in skill-intensive occupations, they play only a small role ininfluencing the efficiency labor-occupation allocation.

42

STEM occupations.

I then look at another four skill-intensive occupations: executive managers, health profes-

sionals, social scientists, and lawyers and judges — and restrict the sample to college-educated

national-origin groups. As displayed in Figure 11, the slope of the line fit becomes more flat

compared to that among STEM occupations. The occupation composition changes are larger

among health professionals, lawyers and judges, but smaller among the other two occupations.

The slope of the line fit suggests that the efficiency of the labor-occupation allocation does not

change much for executive managers and social scientists, while it improves slightly for health

professional. The allocation becomes less efficient for lawyers and judges.

Figure 12 replicates the plot of eight low-skilled occupations but focuses on non-college

educated national-origin groups.69 Overall, 3-5% of low-skill jobs switched from non-college

educated workers from Mexico, Central American & Caribbean to non-college educated US na-

tives. The slope of line fit is negative in all eight plots, suggesting a lesser degree of occupation

specialization by the labor group, and, hence, a less efficient allocation among low-skill occu-

pations due to policy reform. I also show changes among the other 12 occupations in Figure 13

of Appendix F, and the changes in their occupation structures are small.

7.2 Global Impacts

This subsection analyzes the impacts on global economies. I first examine how policy reform

affect the global labor movement. After that, I discuss the labor market impacts on migration

sending countries, with an emphasis on India, Mexico, Central American & Caribbean coun-

tries, and competing destinations — namely, OECD Europe, Canada and Oceania countries.

(A) The Global Labor Movement

I shed light on two questions regarding on the location resettlement of US family- and refugee-

based visa rejectees, and on the source of employment-mode college-educated immigrants.

Relocation of US Visa Rejectees: Return to columns 4-7 of table 4 which reports the number of

US family- and refugee-based legal visas rejectees absorbed by each foreign country as a share

of the total. One evident result is that among non-college educated switchers who are from

Mexico, or Central American & Caribbean countries, the predominate share resettle to their

home country. In contrast, a very small share of switchers substitute to other foreign destina-

tions. For Central America & Caribbean non-college educated immigrants, 60.38% relocate to

their home countries, compared to 3.09% + 0.02% + 0.46% = 3.57% of those who choose foreign

destinations. Also, 50.10% of Mexican non-college educated immigrants choose to resettle to

home country, in contrast to 0.10%+ 0.04% =0.14% that choose abroad. Although 31.30% of

69By the same reasoning, college-educated workers are unimportant to the labor supply in low-skill occupa-tions, and, therefore, are not included in the plot.

43

non-college educate switchers from South America countries relocate to home countries, there

is a substantial fraction around 5.18% + 0.25% + 1.97% = 7.4% of total are bound for foreign

destinations. These results are guided by the formula in equation (4) and (5) of Section 4, and

is mainly driven by the well-documented fact that less-educated workers are immobile (Doc-

quier et al., 2009; Grogger and Hanson, 2011).

Source of Newly Attracted Talent to the US: Table 6 displays the number of college-educated

workers reduced from each mode or from each country as a share of the number of US college-

educated employment-mode immigrants increased, by each national origin groups. I focus on

immigrants born in India, East Asia, and Western & Northern Europe, which are the regions

that absorb a substantial share of employment-based visas.70

Table 6: SOURCE OF INFLOW OF EMPLOYMENT-MODE, COLLEGE-EDUCATED WORKERS TOTHE US

IN THE US FROM FOREIGN ECONOMIES

ORIGIN COUNTRIES FAMILY-MODE REGUFEE-MODE EU OCEANIA CANADA HOME

COUNTRY

India 20.48% 2.57% 2.66% 0.82% 2.68% 69.80%

East Asia 27.74% 4.73% 1.41% 1.11% 2.78% 60.30%

China 21.51% 6.14% 1.76% 1.46% 3.51% 64.96%

Taiwan 34.75% 4.96% 0.61% 0.82% 2.17% 54.15%

Japan 26.82% 3.74% 2.26% 0.81% 0.83% 62.99%

Korea 28.55% 4.34% 0.91% 0.77% 1.84% 61.11%

Western & Northern Europe 28.95% 4.59% 4.57% 5.88% 54.60%

United Kingdom 27.96% 1.95% - 9.51% 7.62% 51.53%

Germany 30.23% 8.23% - 1.58% 4.46% 54.03%

Italy 32.86% 4.62% - 2.32% 6.95% 52.81%

Notes: Each value is the number of workers reduced in each mode or destination as a share of the total

number by which employment-based visas increased.

The results are guided by the elasticity formula presented in equation (4) — (6) of Section

4. One worth mentioning result is that the major proportion of newly attracted talents are

from immigrants’ home countries. 69.8% and 60.3% of newly attracted Indian-born and East

Asian- born talents are from home countries. Comparing to India and East Asian countries,

Western & Northern European born workers are relatively less likely to be drawn from their

home countries, reflecting that the substantial fraction of their college-educated natives live

abroad in 2010. Because of this, there is about 4.57% + 5.88% = 10.45% of Western & Northern70Among employment-based visas issued during 1996-2015 (excluding spouses or children), 20.34% were allo-

cated to workers from India, 10.9% from China, 11.3% from other East Asian countries and 9.8% from Western &Northern European countries.

44

European born newly attracted talents come from competing destination countries including

Australia, New Zealand, and Canada.

Another important source of the employment-based visa recipients are those who substi-

tute from family- and refugee-based visas to employment-based visas. The number of visa-

mode switchers account for 28.95%+4.59% = 33.54% of the total number of employment-mode

migrants increased for college-educated workers from Western & Northern European, 27.74%

+ 4.73% = 32.4% for those from East Asian countries, and 20.48% + 2.57% = 23.05% for those

from India.

(B) The Labor Market Impacts on Immigrant-sending Countries

The Panel A of Table 7 reports the impacts of labor force on four sending countries/regions

— Mexico, Central America, India, and East Asia, by education and gender groups. The im-

pacts differ systematically across countries. Central America & Caribbean countries experi-

ence an increase of labor force for all education and gender groups. The increase is larger

for college-educated workers than non-college educated ones, and larger for females than for

males. There is a 4.67% increase in the college-educated female labor force, in comparing to a

1.65% increase for college-educated males, and to a 1.27% and 1.04% increase for non-college

educated females and males, respectively. This corresponds to the fact shown in Figure 2 that

78% of college-educated US immigrants from Central America & Caribbean countries migrate

through family-based visas, in contrast to 41% of non-college educated counterparts who do

so.

Surprisingly, though Mexico is the country that sends the most immigrants to the US, the

impacts on the Mexican labor force are fairly small. College-educated workers have become

slightly more scarce: the non-college educated Mexican labor force increases by 1.71% and 1.54

% for male and female, respectively, in contrast to a 0.24% decrease and a 0.84% increase for

college-educated males and females, respectively. The modest increase of non-college educated

Mexican labor force is mainly due to the large degree of substitution to illegal entry, as shown

in Table 4.

The Panel A of Table 7 also shows that India and East Asia would experience a loss of their

college-educated labor force. The impacts are larger for India, which loses 4.29% of its college-

educated males, and 3.04% of its college-educated females from the labor force, versus East

Asian countries, which lose 3.15% of their college-educated males and 1.92% of their college-

educated females. The impacts on the non-college educated labor force are small in India and

East Asian countries.

45

Table 7: IMPACTS ON LABOR FORCE AND WAGES AT SENDING COUNTRIES/REGIONS

Country/RegionNon-college

Male

Non-college

Female

College

Male

College

Female

Panel A: Labor Force Impacts

Mexico 1.71% 1.54% -0.24% 0.84%

Central America & Caribbean 1.04% 1.27% 1.65% 4.67%

India 0.44% 0.49% -4.29% -3.04%

East Asia 0.10% 0.03% -3.15% -1.92%

Panel B: Wage Impacts

Mexico -0.23% -0.20% 0.06% -0.06%

Central America & Caribbean 0.03% -0.05% -0.23% -0.59%

India -0.21% -0.23% 0.63% 0.52%

East Asia -0.01% -0.01% 0.42% 0.24%

Notes: The results are obtained by setting ηus = 2.18, ηo = 0.9 and θ = 3.66. Each percentage value is

computed by subtracting one from the proportional change. For Central America & Caribbean and East

Asia, the changes in labor force is calculated as the average over all countries within that region.

With a modest level of changes in labor force, the wage impacts are small in immigrant-

sending countries. I calculate the average group wage changes based on equation (14), and

report the results in Panel B of Table 7. Again, following the intuition discussed in equation

(7), India and Central America & Caribbean countries experience larger changes in its wage

structure than other immigrant-sending countries. However, the college wage premium rises

for the former but declines for the latter. In India, wages rises by 0.63% among college educated

males and by 0.52% among college educated females, while they fall by around 0.2% among

non-college-educated workers. In Central America & Caribbean countries, wage falls by 0.59%

among college educated females and by 0.23% among college educated males, while they are

almost unchanged among non-college educated workers.

The wage impacts are small in Mexico and East Asian countries. In Mexico, non-college ed-

ucated wage declines by around 0.2%, while the wage of college educated workers are almost

unchanged. College wage premium rises among East Asian countries, although the impacts

all fall in a smaller magnitude than India. Table 13 in Appendix A reports the results for other

sending countries regions where I find the impacts are very small.

(C) The Labor Market Impacts on Competing Destination Countries

I next examine the impacts competing destination countries in terms of labor force changes,

as represented in Panel A of Table 14, and in terms of wage, as as represented in Panel B.

46

Panel A breaks down the labor force changes by native-born and foreign-born, and by edu-

cation and gender groups. All three destinations would lose college-educated labor force, with

a larger percentage loss for foreign-born than for native-born. Australia and New Zealand ex-

perience the largest proportional decrease in foreign-born workers, by 11.43% for males and

6.31% for females. Although the impacts fall in slightly small magnitude, foreign-born college-

educated males fall by 9.03% and 8.25% in Canada and Western & Northern European coun-

tries, respectively, and falls by 4.27% and 4.06% for female counterparts, respectively. Canada

experiences the largest decrease in its native college-educated labor force, by 4.78% for males

and 3.09% for females.

There is a slight increase in the non-college educated labor force increases in all three

economies for all education and gender groups, and the increase in percentage is larger for

foreign-born than for native-born. However, the changes on non-college educated counter-

parts are small in magnitude comparing to that of the college-educated labor force.

Panel B reports the impacts of wage earned by natives in each of the three competing des-

tination countries. Consistent with the changes in relative skill abundance reported in Panel

A, Canada experience larger changes in its wage structure than other immigrant-destination

countries. The wages rises by 0.59% among college educated males and by 0.43% among col-

lege educated females, while they fall by around 0.09% to 0.14% among non-college-educated

workers. The wage distribution also becomes more unequal in Western & Northern European

countries, Australia and New Zealand, although their impacts magnitude are smaller than the

impact in Canada.

8 The Role of Productivity Correlations

I quantify the extent to which have the productivity correlation structure at explaining the

benchmark results. Table 8 compares the results obtained from my benchmark model pre-

sented in Column (4), to a model with independent productivity draws presented in Column

(1), and to a model where productivity is drawn from one-layer CES correlation CDF with

ρ = σ = γ = 0.15 shown in Column (2), and to a model which productivity is drawn from

one-layer CES correlation CDF with ρ = σ = γ = 0.6 shown in Column (3).

All models predicts a much smaller increase of US illegal immigration and a larger wage

impacts than the benchmark model. In Panel A, US illegal immigration increases by 7.5% for a

model of independent productivity, by 8.0% and 10.1% for models of the correlation parameter

equaling 0.15 and 0.6, respectively, in comparing to 20.5% in benchmark model.

In all models, Non-college-educated male and female gain the most; college-educated fe-

male also gain, whereas College-educated male lose as shown in Panel B. The wage impact

is the largest in the case of independent productivity, and is the smallest for the benchmark

model. The former case predicts the wage earned by non-college educated natives would in-

47

crease by about 1%, where such wage increases fall by half in the latter case. Comparing results

across Column (1), (2) and (3), the wage impacts become smaller as the correlation parameter

rises. These differences are due to the models’ difference in workers’ occupation elasticity of

switching, which equals θ1−ρ in these alternative models, and hence the model has a stronger

mitigation effect of occupation adjustments on wages as the value of ρ rises. Also worth em-

phasizing that the model which predicts results of Column (3) allows the same elasticity of

switching across the US occupations as the benchmark model, and therefore their differences

in wage impacts is due to the additional illegal immigrants predicted in the benchmark model.

Table 8: RESULTS ACROSS DIFFERENT MODELS

Independent

Productivity

One-layer CES

Correlated Productivity

Three-layer nested-CES

Correlated Productivity

ρ = σ = γ = 0 ρ = σ = γ = 0.15 ρ = σ = γ = 0.6 ρ = 0.6, σ = 0.28, γ = 0.15

(1) (2) (3) (4)

Panel A: The Percentage Increase of the Overall US Illegal Immigration

7.5% 8.0% 10.1% 20.5%

Panel B: US Natives Wages

Non-college Male 1.01% 0.94% 0.61% 0.48%

Non-college female 1.02% 0.94% 0.61% 0.53%

College Male -0.37% -0.34% -0.20% -0.16%

College Female 0.49% 0.46% 0.31% 0.30%

Panel C: The Substitution of Non-college-educated Switchers, Mexico-born

Illegal entry 17.3% 18.3% 22.9% 48.1%

Competing Destinations 0.09% 0.09% 0.07% 0.14%

Mexico 82.0% 80.1% 76.2 % 50.1%

Panel D: The Source Newly Attracted College-educated Immigrants, India-born

Family-based Visa 10.8% 11.0% 11.6% 20.5%

Competing Destinations 1.97% 1.99% 2.08% 6.16%

India 86.3% 86.1% 85.4% 69.8%

Panel C shows that the substitution pattern of Mexico-born non-college educated visa re-

jectees. The results predicted by these alternative models are in the similar range, but differ

substantially from the results obtained by the benchmark model. This is consistent with the

partial equilibrium analysis in Section 4 that a model of independent productivity or of a one-

layer CES correlation CDF, each imposes a common elasticity of substitution to all alternatives,

whereas the benchmark model allows differential elasticity of substitution to each nest of al-

ternatives, as guided by the expression in equation (6) of Section 4. From Column (1) to Col-

umn (3), the share of Mexico-born Non-college educated visa rejectees who substitute to illegal

entry is 17.3%, 18.3% and 22.9%, respectively, in comparing to 48.1% predicted by the bench-

mark model. The results highlight the quantitative importance of having a nested productivity

correlation structure. In particular, the stronger productivity similarity across US alternatives

48

generate a large elasticity of substitution to the US, than to competing destinations, than to

immigrant-home country.

Panel D presents the source of newly attracted India-born college-educated immigrants.

Following the same intuition as the results in Panel, alternative models predicted results are

in the similar range, but differ significantly from the benchmark model prediction, which

indicates a substantial larger degree of substitution from US family-based visa rejectees to

employment-based visas, a larger share of immigrants drawn from competing destinations,

but a smaller fraction from home country.

9 Conclusion

This paper aims to shed light on the economic consequences of adopting a skill-based immi-

gration reform in the US. My contribution to the literature is to introduce a new framework

for immigration with endogenous mode of entry that can undertake a more realistic policy

experiment in the form of changes in the overall number of migration entries for each mode.

Quantifying the impacts had the U.S. shifted to a skill-based immigration system in the past, I

find the migration and wage impacts are small both for the US and for foreign countries. My

model also has a rich structure of workers’ productivity similarities across different nests of

alternatives, and my results highlight the quantitative importance of capturing productivity

similarity differences across locations.

My model can be extended to answer a series of questions related to immigration reform,

including: the welfare consequences of the 2004 EU enlargement, the economic consequence

of Immigration Act of 1990, the fiscal impacts of skill-based immigration reform, the optimal

immigration policy from the US welfare perspective. I intend to address some these questions

in future research.

49

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54

A TABLES

Table 9: DOT Occupation Task Intensity of 28 US Occupations

Occupation MATH DCP STS FINGDEX EYEHAND FOREIGN-BORN SHARE

Math & Science 0.941 0.820 0.776 0.447 0.350 28.9

Engineers 0.931 0.854 0.713 0.735 0.530 22.2

Health Professional 0.918 0.780 0.267 0.994 0.689 25.4

Social Scientists, Lecturers 0.881 0.839 0.235 0.214 0.244 25.8

Computer System Analysts 0.874 0.827 0.478 0.184 0.340 24.9

Computer Software Developers 0.872 0.668 0.872 0.189 0.171 37.9

Management Related 0.839 0.827 0.508 0.300 0.226 13.8

Lawyers and Judges 0.819 0.534 0.179 0.103 0.05 5.6

Teachers Except Postsecondary 0.804 0.924 0.141 0.340 0.350 6.8

Therapists 0.769 0.786 0.410 0.903 0.586 15.1

Executive, Managerial 0.753 0.878 0.260 0.285 0.361 14.4

Health Assistants 0.749 0.555 0.691 0.839 0.547 25.6

Technicians 0.746 0.511 0.745 0.642 0.540 15.4

Sales Representatives, Finance & Business 0.710 0.734 0.264 0.282 0.315 13.2

Editors Reports, Clergy & Arts 0.689 0.636 0.320 0.468 0.355 12.4

Mechanics, Repairers 0.636 0.459 0.811 0.810 0.652 20.2

Precision Workers 0.602 0.743 0.571 0.582 0.548 18.7

Construction Workers 0.553 0.564 0.681 0.643 0.750 17.8

Administrative & Financial Clerks 0.547 0.530 0.699 0.799 0.173 16.7

Information, Record & Distribution Clerks 0.500 0.521 0.430 0.348 0.260 14.4

Sales Representatives, Commodities 0.465 0.453 0.317 0.425 0.372 10.7

Equipment Operators 0.457 0.378 0.471 0.884 0.140 15.7

Farm & Agriculture 0.399 0.713 0.327 0.279 0.797 8.9

Machine Operators 0.347 0.312 0.643 0.618 0.598 21.3

Personal & Cleaning Service Workers 0.330 0.611 0.286 0.350 0.634 19.8

Food Preparation & Service 0.306 0.489 0.387 0.352 0.450 24.9

Protective Service 0.257 0.615 0.139 0.075 0.812 6.9

Transportation Workers 0.229 0.264 0.343 0.271 0.834 24.5

Notes: Each DOT task measurement value is the average of percentile values for detailed occupation codes.

The five variables presented here are those widely used DOT task variables (Autor et al., 2003). Math is

defined as general educational development in mathematics to measure non-rountine analytic tasks. DCP

is direction, control and planning, measuring non-routine interactive tasks. STS is the variable set limits,

tolerances or standards to measure routine cognitive tasks. FINGDEX is the variable of finger dexterity to

measure rountine manual tasks. EYEHAND is the variable eye-hand-foot coordination to measure non-

routine manual tasks.

55

Table 10: Estimation Results on θ

Panel A: OLS log regression

1) country-occupation as observational unit

θ 3.103*** 3.230*** 3.288***

(0.161) (0.173) (0.177)

PISA Score average 75 pctle 90 pctle

Num. of Obs. 3213 2998 2998

2) region-occupation as observational unit

θ 2.850*** 2.888*** 2.937***

(0.161) (0.207) (0.214)

PISA Score average 75 pctle 90 pctle

Num. of Obs. 1433 1377 1377

Panel B: Pseudo-maximum-likelihood (PML)

1) country-occupation as observational unit

θ 3.655*** 3.807*** 3.896***

(0.071) (0.077) (0.079)

PISA Score average 75 pctle 90 pctle

Num. of Obs. 3213 3429 3429

2) region-occupation as observational unit

θ 3.827*** 3.860*** 3.941***

(0.114) (0.120) (0.124)

PISA Score average 75 pctle 90 pctle

Num. of Obs. 1508 1450 1450

Notes: The full sample is formed by pairwise combination of 64 origin countries, 28 occupations and two

education degree groups (college-degree, and advanced degree). The sample used to run the log regression

excludes origin-occupation pairs for which there is no worker-occupation match observed in the data. The

sample of pseudo-maximum-likelihood estimation is based on origin-occupation pairs and includes ‘zeros’.

Panels A2) and B2) groups small countries into 8 regions and replicate OLS and PML estimation using

region-occupation as observational units. Standard errors are reported in parentheses.

56

Table 11: Share of Foreign-born US Workers by Country of Origin and Education

Observed Economy Counterfactual Economy

Region/country All Non-

college

College All Non-

college

College

Mexico 32.1% 30.3% 1.8% 27.9% 26.2% 1.7%

Central America & Caribbean 17.7% 15.1% 2.6% 14.9% 12.7% 2.2%

El Salvador 3.6% 3.4% 0.2% 3.2% 3.0% 0.2%

Guatemala 2.4% 2.3% 0.1% 2.1% 2.0% 0.1%

Cuba 2.5% 1.9% 0.6% 2.1% 1.6% 0.5%

Dominican republic 2.4% 2.1% 0.4% 1.9% 1.6% 0.3%

Jamaica 1.7% 1.3% 0.4% 1.4% 1.0% 0.4%

East Asia 9.3% 4.2% 5.1% 12.4% 3.4% 9.0%

China 4.1% 2.1% 2.0% 5.7% 1.6% 4.1%

Korea 2.7% 1.2% 1.5% 3.5% 1.0% 2.5%

India 5.5% 1.2% 4.3% 9.7% 0.9% 8.8%

Southeast Asia 10.1% 6.3% 3.8% 9.1% 4.9% 4.2%

Philippines 4.6% 2.3% 2.3% 4.5% 1.8% 2.7%

Vietnam 3.5% 2.6% 1.0% 2.6% 1.9% 0.7%

South America 7.2% 5.0% 2.2% 6.7% 4.1% 2.6%

Colombia 1.8% 1.2% 0.6% 1.5% 0.9% 0.6%

Ecuador 1.2% 1.0% 0.2% 1.0% 0.8% 0.2%

Brazil 1.0% 0.6% 0.4% 1.0% 0.5% 0.5%

Western & Northern Europe 4.4% 2.5% 1.9% 5.2% 2.0% 3.2%

Germany 1.0% 0.6% 0.4% 1.2% 0.5% 0.7%

United Kingdom 0.7% 0.4% 0.3% 0.9% 0.3% 0.6%

Mid-East & Southwest Asia 4.8% 2.5% 2.3% 4.9% 2.0% 2.9%

Iran 0.9% 0.4% 0.5% 0.9% 0.3% 0.6%

Pakistan 0.9% 0.4% 0.5% 0.9% 0.3% 0.6%

Eastern Europe 4.3% 2.3% 2.0% 4.3% 1.9% 2.4%

Poland 1.1% 0.8% 0.3% 1.1% 0.6% 0.5%

Russia 0.8% 0.3% 0.5% 0.7% 0.2% 0.5%

Africa 2.3% 1.3% 1.0% 2.2% 1.0% 1.2%

Canada 1.7% 0.8% 0.9% 2.2% 0.7% 1.5%

TOTAL 100% 71.9% 28.1% 100% 55.2% 44.8%

Notes: each value represents the number of immigrants in a given national origin and education group, as

a share of the total US foreign-born individuals. I restrict the sample to those who are 18 - 64 year old. Male

and female are aggregated in each national origin and education group.

57

Table 12: Wage Impacts of US Workers for Other Immigrant-sending Countries

National origin Non-college male Non-college

female

College male College female

El Salvador 0.65% 0.71% -0.21% 0.27%

Korea 0.22% 0.53% -0.94% -0.15%

Vietnam 0.40% 0.61% -1.60% -0.56%

Philippines 0.41% 0.67% -0.53% 0.35%

Canada 0.05% 0.46% -0.94% -0.16%

Germany 0.04% 0.47% -0.98% -0.35%

Colombia 0.46% 0.63% -0.47% 0.04%

58

Table 13: Impacts on Labor Force and Wages in Other Immigrant-sending Countries

Country/RegionNon-college

Male

Non-college

Female

College

Male

College

Female

Panel A: Labor Force Impacts

South America 0.13% 0.13% -1.19% -0.57%

Southeast Asia 0.19% 0.21% -1.06% -0.48%

East Europe 0.11% -0.76% -0.18% -0.47%

Africa 0.02% 0.02% -0.39% 0.05%

Middle east 0.07% 0.08% -1.07% -0.62%

Panel B: Wage Impacts

South America -0.04% -0.03% 0.16% 0.10%

Southeast Asia -0.06% -0.06% 0.20% 0.14%

East Europe -0.03% 0.11% 0.15% 0.12%

Africa -0.002% -0.002% 0.04% 0.01%

Middle east -0.02% -0.03% 0.20% 0.16%

Notes: The results are obtained by setting ηus = 2.18, ηo = 0.9 and θ = 3.66. Each percentage value is

computed by subtracting one from the proportional change in labor force. For each region, the changes in

labor force and wages are calculated as the average over all countries within that region.

59

Table 14: IMPACTS ON LABOR FORCE AND WAGES IN OTHER DESTINATIONS

Country/Region NativityNon-college

Male

Non-college

Female

College

Male

College

Female

Panel A: Labor Force Impacts

Canada Natives 0.43% 0.41% -4.78% -3.09%

Foreign 2.05% 2.35% -9.03% -4.27%

Western & Northern Europe Natives 0.20% 0.19% -2.22% -1.31%

Foreign 0.76% 0.53% -8.25% -4.06%

Oceania Natives 0.13% 0.09% -1.07% -0.37%

Foreign 1.74% 2.00% -11.43% -6.31%

Panel B: Wage Impacts

Canada Natives -0.14% -0.09% 0.59% 0.43%

Western & Northern Europe Natives -0.07% -0.06% 0.34% 0.24%

Oceania Natives -0.05% -0.03% 0.19% 0.12%

Notes: The results are obtained by setting ηus = 2.18, ηo = 0.9 and θ = 3.66. Each percentage value is

computed by subtracting 1 from the proportional change. For OECD Europe and Oceania, the changes in

labor force and wages are calculated as the average over all countries within that region.

60

B Derivation and Proofs

B.1 Equilibrium Derivations

Derivation on the expression of Πsd,m,o,F

The expression in equation (1) can be derived by applying the probabilistic choice formula

in Theorem 1 of (McFadden, 1978). Also see Lind and Ramondo (2018) who study the class of

multivariate θ-Fréchet distribution. According to Theorem 1 of (McFadden, 1978), for a random

vector(ε1, ε2, ...εn

)that has the joint distribution function as

F(ε1, ε2, ..., εn

)= exp

{−G

(eε1 , eε2 , ..., eεn

)},

where the function G(x1, x2, ....xn) satisfies a number of assumptions including nonnegativity,

homogeneity of degree one, mixed partial derivatives that are continuous, nonpositive for even

order and nonnegative for odd order, and unboundness such that limxj→∞G(x1, x2, ....xn) =∞,

then in a random utility model where Uj = Vj + εj , the choice probability has close form as

P (choose j) = eVj ·Gj(x1, x2, ....xn)

∣∣∣{x=eV }

G(eV1 , eV2 , ...., eVn)(18)

where Gj(x1, x2, ....xn) = ∂G(x1,x2,....xn)∂xj

. Recall that the logarithm of Gumbel distribution is

Fréchet distribution, therefore to apply the results to my case, I substitute x by log(x), to have

in my case

G(~xd,m,o

)= exp

{−

[∑H,F

(∑d

[∑m,o

x− 1

1−ρd,m,o

] 1−ρ1−σ) 1−σ

1−γ]1−γ}

,

Following (18) and replace{eV1 , eV2 , ..., eVn

}by{..., φ

1θd,m,o, ...

}to have Πs

d,m,o,F

=

φd,m,o

(∑H,F

[∑d

(∑m,o φd,m,o

) 1−ρ1−σ] 1−σ

1−γ)−γ[∑

d

(∑m,o φd,m,o

) 1−ρ1−σ] 1−σ

1−γ−1(∑m,o φd,m,o

) 1−ρ1−σ−1

φθ

1−ρ−1

d,m,o(∑H,F

[∑d

(∑m,o φd,m,o

) 1−ρ1−σ] 1−σ

1−γ)1−γ

=φd,m,o∑m,o φd,m,o

×

∑d

(∑m,o φd,m,o

) 1−ρ1−σ

∑d

(∑m,o φd,m,o

) 1−ρ1−σ×

[∑d

(∑m,o φd,m,o

) 1−ρ1−σ] 1−σ

1−γ

∑H,F

[∑d

(∑m,o φd,m,o

) 1−ρ1−σ] 1−σ

1−γ

where φd,m,o =

(T sd,m,owd,oτ

sd,m,o

) θ1−ρ

.

61

B.2 Equilibrium in Proportional Changes

Derivation of Equilibrium in Proportional Changes

Πsm,o|d =

φ′

d,m,o∑m′,o′ φ

′d,m,o

/φd,m,o∑m′,o′ φd,m,o

=φd,m,o∑

m′,o′ φd,m′,o′Πm′,o′|d(19)

where φd,m,o = (T sd,m,owd,oτsd,m,o)

ρ1−σ

Πsd|F =

[∑m′,o′ φ

′

d,m′,o′

] 1−ρ1−σ/[∑

m′,o′ φd,m′,o′] 1−ρ

1−σ

∑d′

[∑m′,o′ φ

′d′,m′,o′

] 1−ρ1−σ/∑

d′

[∑m′,o′ φd′,m′,o′

] 1−ρ1−σ

=

[∑m,o φd,m′,o′Πm,o|d,F

] 1−ρ1−σ

∑d′

[∑m,o φd,m′,o′Πm,o|d,F

] 1−ρ1−σ

Πd′|F

(20)

The second equality in (20) holds since[∑

m′,o′ φ′

d,m′,o′

]=[∑

m′,o′ φd,m,o

][∑m′,o′ φd,m′,o′Πm′,o′|d,F

]which is the denominator of equation (19).

ΠsF =

(∑d′

[∑m′,o′ φ

′

d′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ/(∑

d′

[∑m′,o′ φd,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

∑H,F

(∑d′

[∑m′,o′ φ

′d,m′,o′

] 1−ρ1−σ

) 1−σ1−γ/∑

H,F

(∑d′

[∑m′,o′ φd,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

=

(∑d′

[∑m′,o′ φ

sd′,m′,o′Πm′,o′|d′

] 1−ρ1−σ

Πd′|F

) 1−σ1−γ

(∑d′

[∑m′,o′ φ

sd′,m′,o′Πm′,o′|d′

] 1−ρ1−σ

Πd′|F

) 1−ρ1−σ

ΠF +

([∑o′ φ

sH,o′Πo′|H

] 1−σ1−γ

) 1−σ1−γ

ΠH

The second equality holds, again from the denominator of equation (20).(∑d′

[∑m′,o′

φ′

d′,m′,o′

] 1−ρ1−σ

)=

(∑d′

[∑m′,o′

φd′,m′,o′] 1−ρ

1−σ

)(∑d′

[∑m,o

φd,m′,o′Πm,o|d

] 1−ρ1−σ

Πd′|h

)

Mode Independence: An important advantage of using the Exact Hat Algebra to solve the

model is that, when τ sd,m,o = 1, neither Πsd,m,o nor W s

d,m,o are functions of Πsm,o|d,F . The impli-

cation is that, since migration friction is unchanged in counterfactual status, solving counter-

factual policy changes doesn’t need any information on Πsm,o|d,F for foreign countries which are

difficult to estimate. Πsm,o|d,F only appears in Φd which can be simplified as

Φsd =

[∑m′,o′

φsd,m′,o′Πsm′,o′|d,f

]=

[∑o′

wθ

1−ρd,o Πs

o|d,F

[∑m′

T sd,m′,o′(τ sd,m′,o′

) θ1−ρ

Πsm′|d,o′,F

]]

When T sd,m′,o′ = τ sd,m′,o′ = 1, Φsd =

[∑o′ w

θ1−ρd,o Πs

o|d,F

].

62

B.3 Derivation of Migration Elasticity

Derivation of∂Πsd,FΠsd,F

/∂τsd,mτsd,m

By the definition of conditional probability, we can write Πsd,F = Πs

d|F · ΠsF . Applying the

product rule to take derivatives with respect to τ sd,m, we have

∂Πsd,F

∂τ sd,m=∂Πs

d|F

∂τ sd,mΠsF + Πs

d|F∂Πs

F

∂τ sd,m, (21)

Taking derivative on ΠsF , with respect to τ sd,m, to have

∂ΠsF

∂τ sd,m=

θ

1− γ

∑H,F

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

−

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

∑H,F

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

×

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ−1[∑

m′,o′ φsd′,m′,o′

] 1−ρ1−σ−1 φsd,m,o

τsd,m

∑H,F

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

=θ

1− γ1− Πs

F

τ sd,m

φsd,m,o∑m′,o′ φ

sd′,m′,o′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

∑H,F

(∑d′

[∑m′,o′ φ

sd′,m′,o′

] 1−ρ1−σ

) 1−σ1−γ

According to the close-form formula of labor allocation, the last three fraction terms equals

Πsm|d,F , Πs

d|F , and ΠsF , respectively. This derivative is

∂ΠsF

∂τ sd,m=

θ

1− γΠsm|d,FΠs

d|FΠsF

(1− Πs

F

)1

τ sd,m. (22)

Similar, taking derivative on Πsd,F with respect to τ sd,m, one could show that

∂Πsd|F

∂τ sd,m=

θ

1− σΠsm|d,FΠs

d|F

(1− Πs

d|F

) 1

τ sd,m, (23)

Plugging equation (22) and (23) to equation (21), one can show

∂Πsd,F

∂τ sd,m= θΠs

m|d,FΠsd|fΠ

sF

[1

1− σ(1− Πs

d|F ) +1

1− γ(1− Πs

F )Πsd|F

]1

τ sd,m. (24)

63

Multiplying byτSd,mΠsd,F

, to obtain the following elasticity

∂Πsd,F

Πsd,F

/∂τ sd,mτ sd,m

= θ × Πsm|d,F ×

[1

1− σ

(1− Πs

d|F

)+

1

1− γΠsd|F

(1− Πs

F

)].

B.4 Derivation on the Elasticity of Substitution

Elasticity of Substitution to Home Country

Take derivative for the formula of ΠsH with respect to τ sd,m, one could directly have

∂ΠsH

ΠsH

/∂τ sd,mτ sd,m

= − θ

1− γΠsd,m,F

Elasticity of Substitution to a foreign country d′

By the definition of conditional probability, we can write Πsd′,F = Πs

d′|F · ΠsF . Applying the

product rule to take derivatives with respect to τ sd,m, we have

∂Πsd′,F

∂τ sd,m=∂Πs

d′|F

∂τ sd,mΠsF + Πs

d′,F

∂ΠsF

∂τ sd,m(25)

Take derivative on Πsd′|F with respect to τ sd,m to have

∂Πsd′|F

∂τ sd,m=

θ

1− σΠsm|d,FΠs

d|FΠsd′|F

1

τ sd,m(26)

Plugging (26) and to equation (25) to have

∂Πsd′,F

Πsd′,F

/∂τ sd,mτ sd,m

= − θ

1− γΠsd,m,F −

θ(σ − γ)

(1− σ)(1− γ)Πsd,m|F

Elasticity of Substitution to an Alternative Mode m′

By the definition of conditional probability, we can write Πsd,m′,F = Πs

m′|d,FΠsd,F . Applying the

product rule to take derivatives with respect to τ sd,m, we have

∂Πsd,m′,F

∂τ sd,m=∂Πs

m′|d,F

∂τ sd,mΠsd,F + Πs

m′|d,F∂Πs

d,F

∂τ sd,m. (27)

Take derivative on Πsm′|d,F with respect to τ sd,m to have

∂Πsm′|d,F

∂τ sd,m= − θ

1− ρΠsm′|d,FΠs

m|d,F1

τ sd,m. (28)

Plugging equation (28) and (24) to equation (27) to have

∂Πsd,m′,F

Πsd,m′,F

/∂τ sd,m,Fτ sd,m,F

= − θ

1− γΠsd,m,F −

θ(σ − γ)

(1− σ)(1− γ)Πsd,m|F −

θ(ρ− σ)

(1− ρ)(1− σ)Πsm|d,F

64

B.5 Derivation of Cross-wage Elasticity

To build intuition, I first present the following expressions and discuss some key properties

below.

(a) The sets of elasticity provided in equation (7) have the following expression such that∂Lo∂Ls

LsLo

= ∂Ws

∂wowoWs

= Πso|d.

∂wo′

∂Lo

Lowo′

=

1ηRo − 1

η, if ω = σ,

1ρRo, if ω 6= σ.

where Ro denotes the occupational labor wage bill as a share of the total, which captures

the occupation size in the entire economy.

(b) Thea average group-s wage elasticity in response to changes in occupation labor, and its

sign is determined as

∂Ws

Ws

/∂LoLo

=Ro − Πs

o|d

η=

< 0, if Ro < Πs

o|d,

> 0, if Ro > Πso|d,

= 0, if Ro = Πso|d.

(c) The ∂Ws

Ws

/∂LoLo

is monotonically decreases in Πso|d.

The expression of ∂Ws

Ws

/∂LoLo

is derived according to∑

o′∂Ws

∂wo′

wo′Ws× ∂wo′

∂LoLowo′

. It embeds a substi-

tution and a complementary effect which is inherited from the CES production function. The

intuition of b) is that the difference between Ro and Πso|d captures the occupation specialization

of s workers relative to the US economy. If s workers are disproportionately employed in at o,

such that Ro < Πso|d, substitution effect dominates. Therefore an increase of o occupation labor

leads to a wage decline of s workers. Complementary effects dominate when Ro > Πso|d. Also

notice that in a special case when Ro = Πso|d, the substitution and complementary effects are

fully offset.

c) says that the more specialized of a group of workers in occupation o such that Πso|d is

larger, the larger the adverse wage impacts in response to an increase in the labor supply

of o occupation. Following equation (7), obtaining the expression of cross-wage elasticity is

straightforward. Cross-group wage elasticity is derived by showing the analytical expression

of ∂Lo∂Ls

LsLo

, ∂Ws

∂wo′

wo′Ws

and ∂wo′∂Lo

Lowo′

. Below provide detailed steps for calculating each elasticity.

1. Derivation of ∂Lo∂Ls

LsLo

It is straightforward that the occupation labor elasticity in response to the labor supply of

group s, denoted as ∂Lo∂Ls

LsLo

, equals the occupation employment share of s workers, denoted as

65

Λso. Since ∂Lo

∂Ls= Πs

o|d, the conclusion follows immediately since Πso|d

LsLo

= Λso.71

2. Derivation of ∂Ws

∂wo′

wo′Ws

I show that ∂Ws

∂wo′

wo′Ws

= Πso′|d. Holding other model primitives constant, such that τ sd,m,o′ =

T sd,m,o′ = 1, and with a small change in ∆wo′ and wd,o = 1 for other occupations when o 6= o′,

one has

Ws + ∆Ws

Ws

=[(wo′ + ∆wo′

wo′

)θP so′|d +

∑o 6=o′

Πso|d

] 1θ

=[(wo′ + ∆wo′

wo′

)θΠso′|d + 1− Πs

o′|d

] 1θ,

subtracting 1 from both sides of the above equation and applying the Taylor expansion such

that(wo′+∆wo′

wo′

)θ= 1 + θ

∆wo′wo′

+ O(∆wo′wo′

). I rewrite

∆Ws

Ws

=[(

1 + θ∆wo′

wo′+ O(

∆wo′

wo′))Πso′|d + 1− Πs

o′|d

] 1θ − 1 =

[1 + θ

∆wo′

wo′Πso′|d + O(

∆wo′

wo′)Πs

o′|d

] 1θ − 1,

applying the Taylor expansion again to have

∆Ws

Ws

= 1 +∆wo′

wo′Πso′|d +

1

θO(

∆wo′

wo′)Πs

o′|d − 1 =∆wo′

wo′Πso′|d +

1

θO(

∆wo′

wo′)Πs

o′|d,

multiplying by wo′∆wo′

and limiting the change to be infinitely small to have

∂Ws

∂wo′

wo′

Ws

= Πso′|d +

1

θO(1)Πs

o′|d = Πso′|d.

3. Deriving the Expression of ∂wo′∂Lo

Lowo′

I show that the elasticity of wage unit in response to changes in occupation labor supply

has the expression below. Differentiating the CES production function with respect to Lo to

have

wo =[∑

o

AoLη−1η

o

] 1η−1AoL

− 1η

o ,

and then differentiate the above equation with respect to Lo to have

∂wo∂Lo

=1

η

[∑o

AoLη−1η

o

] 2−ηη−1AoL

− 2η

o −1

η

[∑o

AoLη−1η

o

] 1η−1AoL

− 1η−1

o ,

71 ∂Lo∂Ls

= Πso|d because an infinitesimal changes in Lo does not cause general equilibrium effects of changes in

wage units and labor re-allocation. In other word, holding wage units unchanged, the increasing amount of laborwill sorting into occupation exactly the same way as the initial equilibrium.

66

multiplying Lowo

on both sides to have

∂wo∂Lo

Lowo

=

1η

[∑oAoL

η−1η

o

] 2−ηη−1AoL

η−2η

o − 1η

[∑oAoL

η−1η

o

] 1η−1AoL

− 1η

o[∑oAoL

η−1η

o

] 1η−1AoL

− 1η

o

=1

ρAoL

η−1η

o

[∑o

AoLη−1η

o

]−1 − 1

η

=1

ηRo −

1

η

where Ro denotes the wage bill earned by workers in o occupation. The last equality holds as

it is straightforward to show that, under a CES production function

Ro =AoL

η−1η

o

[∑oAoL

η−1η

o

] 1η−1

Y= AoL

η−1η

o

[∑o

AoLη−1η

o

]−1.

Analogously, I obtain the cross-elasticity expression when o′ 6= o by first differentiating the CES

production function with respect to Lo′ to have

wo′ =[∑

o

AoLη−1η

o

] 1η−1Ao′L

− 1η

o′ ,

and then differentiating the above equation with respect to Lo to have

∂wo′

∂Lo=

1

ηAoAo′L

− 1η

o L− 1η

o′

[∑o

AoLη−1η

o

] 2−ηη−1 ,

multiplying Lowo′

on both sides to have

∂wo′

∂Lo

Lowo′

=

1ηAoAo′L

1− 1η

o L− 1η

o′

[∑oAoL

η−1η

o

] 2−ηη−1[∑

oAoLη−1η

o

] 1η−1Ao′L

− 1η

o′

=1

ηAoL

1− 1η

o

[∑o

AoLη−1η

o

]−1=

1

ηRo.

In sum, I obtain

∂wo′

∂Lo

Lowo′

=

1ηRo − 1

η, if o′ = o,

1ρRo, if o′ 6= o.

whereRo is occupational labor wage bill as a share of the total wage bill. It captures the occupa-

tion size relative to the entire economy. The result comes exclusively from the CES production

function. Notice that the own-wage elasticity is always negative since Ro < 1 due to the substi-

tution effect, whereas cross-wage elasticity is always positive due to the complementary effect.

67

C Data Description

As discussed in section 6.3, the empirical exercise has dim(κ) = 13 economies, dim(ν) = 460

labor groups, dim(σus) = 28 occupation categories for the US economy plus one other option

which is unemployment or not in labor force. dim(σo) = 20 for India and Mexico and 9 for the

others. I consider immigrants born from dim(ν) = 115 countries. These 115 countries together

account for more than 95% of migrants to the US. I consider four education and gender groups

including non-college female, non-college male, college female and college male.

C.1 Labor Market and Migration Data

I draw data from the censuses and labor force survey of multiple countries to measure occupa-

tional shares and the average wage earned by labor groups. I also use the brain-drain dataset

from the Institute for Employment Research (IAB) to measure bilateral migration rates.

US labor market: I use the American Community Survey (ACS) five-year sample, 2009-2013,

from the Integrated Public Use Microdata Series (IPUMS) USA (Ruggles et al., 2015) to measure

the occupational share and average occupational wage earned by each origin, education, and

gender group. I restrict the sample to individuals who are 18-64 years old, and aggregate the

ACS education categories into two broad groups: non-college educated and college-educated

and above. I also pool the detailed ACS occupations into 28 aggregate categories, based on

similarities in the contents of their tasks. In addition to the 28 occupations, I include another

option: employment or unemployment. Table 9 in Appendix C shows how distinct the 28

occupations are in terms of their task contents as provided by the Dictionary of Occupational

Titles’s (DOT) task variable.

For each group s, I measure the occupational share in terms of total hours worked and

calculate the average hourly wage in each occupation. To do that, I weigh each observation

using the following weights adjusted by hours worked as

Adjusted Weights =Census weight×weeks worked× usual hours per week

2000

I modify wages by adjusting the IPUMS variable INCWAGE (the annual wage and salary in-

come) as follows:

Hourly Wage =Annual Wage and Salary IncomeWeeks Worked×Hours per week

Variables of weeks worked in IPUMS Census are reported in intervals. I use the middle point

of each interval to approximate the number of weeks worked in the previous year. The aver-

age occupational wage for each group reflects the mixture of equilibrium wage unit and the

occupational labor composition. To impute the average occupational wage by mode of en-

68

try, I assume the average occupational wage earned by each group is invariant across all legal

modes. I then use ASEC-CPS data to calculate the wage earned by legal and illegal immigrants

relative to all immigrants in each of the 28 occupations. Finally, I multiply the relative wage

ratio by the average occupational wage earned by each group estimated from ACS, to compute

the average occupational wage earned by each group and by each mode.

Foreign labor market: I measure the share of occupations and average wage earned by groups

for each country/region. I calculate these variables for the three individual foreign countries

— Canada, Mexico, and India — from the Integrated Public Use Microdata Series (IPUMS)

International in year 2010. For each of the nine regions, I extract data from IPUMS – Interna-

tional, Luxembourg income study (LIS) to measure these variables for natives. When data on

immigrants is unavailable, I supplement with the Database on Immigrants in OECD countries

(DIOC) to measure the occupational share for immigrants in OECD destinations.72

I group the detailed occupational categories into 20 broad occupational categories for Mex-

ico and India. I use the one-digit International Standard Classification of Occupations (ISCO88)

for the other economies, which provides me common occupational categories across countries,

in order to cluster the countries into nine regions. Since Canadian census reports individuals’

place of birth by aggregate regions, I use the DIOC database, rather than the Canadian census,

to measure the occupational share of Canadian immigrants from many countries of origin at

1-digit ISCO code. Details of the data sources used for foreign countries are provided in Table

15 in Appendix C. When wage variables are missing from IPUM-International or LIS, I com-

bine DIOC data with the Occupational Wages around the World (OWW) Database to impute

the average group wage earned by immigrants as an occupational-share weighted average of

occupational wage,73 and calculate the population-weighted average within each region.

Migration data: I measure the migration rate to each destination by group in year 2010 using

the brain-drain dataset collected by the Institute for Employment Research (IAB). Assuming

that the US, OECD, Oceania countries, and Canada are the only migration-receiving countries,

I compute the fraction of workers who stay in their home country by labor group.

C.2 Occupation Aggregation

ACS Occupation aggregation: I aggregate the ACS occupation codes into 28 occupations for

the US economy to pool together jobs with similar task intensities and maintain consistency

with the broad IPUMS occupation definitions. Table 9 shows the five widely used Dictionary

of Occupational Titles (DOT) tasks measurements. They are: General education development72The data in the DIOC database is jointly collected by the OECD and the World Bank from census data from

around year 2010 and covers characteristics of immigration to 33 OECD destination countries from more than 150countries. The cross-tabulated data is publicly available on the OECD website.

73The OWW Database is collected by Freeman and Oostendorp from information on earnings by occupation inthe International Labor Organization’s (ILO) October Inquiry Survey.

69

(GED), Direction, control and Planning (DCP), Set limits, tolerance and vocational preparation

(STS), Eye-hand-foot coordination (EHF) and Finger dexterity (FINGER). The last column of

table 9 shows the fraction supplied by foreign-born workers at each of the 28 occupations.

To ensure that the occupations are consistent with the aggregation used in NIS sample, I

further group the above 28 occupations into three broad occupations as follows:

• Cognitive occupations: math and science; engineers; health professional; social scientists,

lecturers; computer system analyst; computer software developers; management related;

lawyers and judges; executive, managerial.

• Routine occupations: teachers, except postsecondary; therapists; health assistants; tech-

nicians; sales representatives, finance and business; editors reporters, clergy, arts; admin-

istrative and financial clerks; information, record and distribution clerks; sales represen-

tatives, commodities.

• Manual occupations: mechanics, repairers; precision workers; construction; equipment

operators; farm and agriculture; machine operators; personal and cleaning service work-

ers; food preparation and service; protective service; transportation.

I use the 1-digit International Standard Classification of Occupations (ISCO88) code to cre-

ate nine broad occupation categories for the other 12 economies. The purpose is to have con-

sistent occupational categories for foreign countries, easing the tasks of clustering countries

into regions. The nine occupations are Legislators, Senior Officials and Mangers, Professionals,

Technicians and associate professional, Clerks, Service workers and Salespeople, Skilled Work-

ers, Craft and Related Trade Workers, Machine Operators and Assemblers, and Elementary

Occupations.

Occupation aggregation of New Immigrant Survey: The New Immigrant Survey (NIS) con-

tains 30 detailed occupations, excluding the military occupations. To merge the NIS occupa-

tions with ACS, I aggregate them into three broad occupation categories as follows:

• Cognitive occupations: executive, administrative and managerial; management related;

mathematical and computer scientists; engineers, architects and surveyors; engineering

and related technicians; life and physical scientists; social scientists and related workers;

life, physical and social science technicians; Lawyers, judges and legal support workers;

health diagnosis and treating practitioners.

• Routine occupations: counselors, social and religious workers; teachers; education, train-

ing and library workers; entertainers and performers, sports and related workers; media

and communication workers; health care technical and support; sales and related work-

ers; office and administrative support workers.

• Manual occupations: protective service, food preparations and serving related; cleaning

and building service; entertainment attendants and related workers; personal care and

70

service workers; farming, fishing and forestry; construction trades and extraction work-

ers; installation, maintenance, and repair workers; production and operating workers;

food preparation; machine setters, operators and tenders; transportation and material

moving workers.

C.3 Definition on O*NET Variables

I draw from O*NET variables, including three on quantitative ability, 3 on science knowledge

and 6 on language ability. The definition of those variables are provided below. The three

quantitative variables are:

1. Mathematical reasoning ability: the ability to understand and organize a problem and

then to select a mathematical method or formula to solve the problem.

2. Mathematics knowledge: knowledge of numbers, their operations, and interrelationships

including arithmetic, algebra, geometry, calculus, statistics, and their applications.

3. Mathematics skill: using mathematics to solve problems.

The three science knowledge variables are:

1. Science skill: using scientific rules and methods to solve problems

2. Complex problem solving: identifying complex problems and reviewing related infor-

mation to develop and evaluate options and implement solutions.

3. Critical thinking: using logic and reasoning to identify the strengths and weaknesses of

alternative solutions, conclusions or approaches to problems.

The six language ability variables are:

1. Speaking skill: talking to others to convey information effectively.

2. Writing skill: communicating effectively in writing as appropriate for the needs of the

audience.

3. Oral comprehension: the ability to listen to and understand information and ideas pre-

sented through spoken words and sentences.

4. Oral expression: the ability to communicate information and ideas in speaking so others

will understand.

5. Written comprehension: the ability to read and understand information and ideas pre-

sented in writing.

6. Written expression: the ability to communicate information and ideas in writing so others

will understand.

71

C.4 Labor Market Variables for Foreign Countries/Regions

Information on employment and wages in the other 12 economies is mainly measured based

on IPUMS International, or the Luxembourg income study (LIS). I supplement Occupational

Wages around the World (OWW) Database to measure wage whenever wage information is

not available, and supplement with the Database on Immigrants in OECD countries (DIOC) to

measure the share of occupation employment for immigrants whenever the variables on place

of birth are not available.74 After that, I compute the average wage and occupation employment

for the aggregated regions, weighted by the population size of countries in each region. The

table below provides detailed information on the set of countries which has been considered,

and the data source that I used to measure their variables.

Table 15: Data source and countries included for each aggregated region

Country Wage Pω|ν,κ Lν,κ, Pκ|ν Countries included and year

Mexico IPUM-Intl IPUMS-Intl IPUMS-Intl, IAB Mexico(2010)

India LIS LIS LIS, IAB India(2011)

Canada OWW-DIOC DIOC DIOC, IAB Canada(2010)

Central America IPUM-Intl IPUMS-Intl IAB, Barro & Lee Costa Rica(2011), Dominican Republic(2010), El

Salvador(2007), Nicaragua(2005), Panama(2010)

South America IPUM-Intl IPUMS-Intl IAB, IAB, Barro &

Lee

Argentina(2010), Brazil(2010), Bolivia(2001),

Colombia(2005), Ecuador(2010), Peru(2007)

OECD Europe OWW, DIOC DIOC DIOC, IAB, Barro

& Lee

Austria, Belgium, Denmark, Finland, France,

Germany, Greece, Ireland, Italy, Norway, Portu-

gal, Spain, Sweden, Switzerland (all 2010)

Oceania OWW, DIOC DIOC DIOC, IAB, Barro

& Lee

Australia(2010)

Africa IPUM-Intl IPUM-Intl IAB, Barro & Lee Cameroon(2005), Ghana(2010), Liberia(2008),

Malawi(2008), Mali(2009), Mozambique(2007),

Nigeria(2010), South Africa(2011), South Su-

dan(2008), Sudan(2008), Zambia(2010)

East Europe IPUM-Intl+LIS IPUM-Intl+LIS IAB, Barro & Lee Czech Republic(2010), Estonia(2010), Hun-

gary(2009), Poland(2010), Russia(2010), Ser-

bia(2010), Slovak Republic(2010), Slovenia(2010)

East Asia IPUM-Intl+LIS IPUM-Intl+LIS IAB, Barro & Lee Japan(2008), Korea(2006), Taiwan(2010)

Southeast Asia IPUM-Intl IPUM-Intl IAB, Barro & Lee Cambodia(2008), Indonesia(2010), Viet-

nam(2009)

Middle East &

southwest Asia

IPUM-Intl+LIS IPUM-Intl+LIS IAB, Barro & Lee Armenia(2011), Bangladesh(2011), Jordan(2004),

Iran(2006), Pakistan(1998), Palestine(2007),

Turkey(2000)

• IAB shorthands for IAB brain-drain data available at Institute for Employment Research.

C.5 The Algorithm of Generating Illegal Migrants Identifiers

I follow Borjas (2017) to generate an identifier for illegal US immigrants. Borjas defines a legal

immigrant as someone for whom one of the following nine conditions holds, and then treating

74Since Occupational Wages around the World (OWW) database provide the occupation wages at each country,I use group specific occupational share as the weights to impute the average group wages at each country.

72

the residual sample as illegal immigrants.

1. That person arrived before 1980;

2. That person is a citizen;

3. That person receives Social Security benefits, SSI, Medicaid, Medicare, or Military Insur-

ance;

4. That person is a veteran, or is currently in the Armed Forces;

5. That person works in the government sector;

6. That person resides in public housing or receives rental subsidies, or that person is a

spouse of someone who resides in public housing or receives rental subsidies;

7. That person was born in Cuba (as practically all Cuban immigrants were granted refugee

status before 2017);

8. That person’s occupation requires some form of licensing (such as physicians, registered

nurses, air traffic controllers, and lawyers);

9. That person’s spouse is a legal immigrant or citizen.

This algorithm may result in highly skilled immigrants being over-represented in the illegal

population, since high-skill workers are less likely to have arrived before 1980 or to receive

government benefits. Using this algorithm, 20.3% of illegal immigrants have college degree

and above, and 14% of illegal immigrants work in skill-intensive occupations, such as executive

management, engineers, computer and research scientists, etc. I add two conditions to filter

legal immigrants. An immigrant is legal if one the following condition holds

1. An individual has a masters’, professional or Doctoral degree

2. An individual works in skill-intensive occupation such as executive manager, mathemat-

ical and computer scientists, electrical engineer, social scientists and urban planners, and

computer software developers.

73

D Immigrant-native Substitution

I provide evidence to show, how would immigrants’ differential occupation specialization im-

plies the differences in immigrant-native substitution across immigrants’ national origins and

education groups, in general equilibrium. I use the model to simulate 50 counterfactuals. Each

counterfactual simulates the average wage impacts for natives in response to migration in-

flow growth of 100,000 — either non-college or college-educated workers — from one of the

25 major sending countries, holding constant the stock of US immigrants from other countries

and education groups. Each time, I introduce a change in occupation and mode-neutral policy

shock τν,κus for each group such that ν immigrants increase by 100,000.

D.1 Simulation Immigrant-native Substitution

UK

DEU

TTO

LAO

GUY

BRANIC

POL

CAN

PER

KORIND

ECU

COLHTIJAM

HND

CUB

CHNDOMPHL

GTMVNM

SLVMEX

-.04

-.03

-.02

-.01

0

Wag

e ch

ange

s (%

), no

n-co

llege

nat

ives

.5 1 2 5 40Share of total immigrants (%)

(a) Native wages to immigrants, NCL

HTIPER

UK

BRA

POL

UKR

DOMHKG

PAK

JPN

DEU

IRN

JAM

RUSCUB

COLTWN

CAN

VNM

KORMEXCHN

PHL

IND

-.04

-.03

-.02

-.01

0

Wag

e ch

ange

s (%

), co

llege

nat

ives

0 2 4 6Share of total immigrants (%)

(b) Native wages to immigrants, CL

Figure 6: Immigrant-native Substitution, within Each Education Group

Figure 6 plots the share of US immigrants of each national-origin and education group (on

x-axis), against the simulated changes in non-college US native wages in response to non-

college immigration influx (on the y-axis) in the left panel, and against the simulated changes

in college-educated US native wages in response to college-educated immigrants (on the y-

axis) in the right panel. Two points are worth noting from Figure 6. First, within the same

education group, natives’ wages fall in response to an immigration influx. Comparing across

the two panels, the natives’ wage falls more among the non-college education groups than the

college-educated groups, in general. Second, the left panel shows that natives wage falls more

in response to immigrants from Mexico and EI Salvador, which have sent large numbers of

non-college immigrants. The opposite pattern is displayed in the right panel, as it shows that

natives wage falls less in response to immigrants from India and the Philippines, which have

sent more college-educated immigrants.

74

UKDEUTTO

LAO

GUYBRANIC

POL

CAN

PERKORIND

ECUCOL

HTIJAM

HNDCUBCHN

DOMPHL

GTMVNMSLV

MEX

0

.03

.06

.09

Wag

e ch

ange

s (%

), co

llege

nat

ives

.5 1 2 5 40Share of total immigrants (%)

(a) Native wages to NCL immigrants

HTIPER

UK

BRA

POL

UKR

DOM

HKGPAK

JPN

DEUIRN

JAM

RUS

CUBCOL

TWN

CAN

VNMKOR

MEX

CHN

PHL

IND

0

.03

.06

.09

Wag

e ch

ange

s (%

), no

n-co

llege

nat

ives

0 2 4 6Share of total immigrants (%)

(b) Native wages to CL immigrants

Figure 7: Immigrant-native Substitution, within Each Education Group

Figure 7 plots the simulated changes in US native wages to immigrants cross education

groups. The left panel shows the wage changes earned by US college-educated natives in

response to an influx of non-college-educated immigrants, while the right panel shows the

wage changes earned by US non-college-educated natives in response to an influx of college-

educated immigrants. Two additional features are worth noting. First, in cross-education

groups, natives wage increase in response to an influx of immigrants. Comparing across the

two panels, the wage gain of college-educated natives in response to a cross-education immi-

gration influx is larger than the wage gain of non-college natives.

Second, the left panel shows that the wage gain of non-college-educated natives is more

clustered, as the orange circles are more concentrated vertically; while the wage gain of college-

educated natives is more scattered as the green triangles are more dispersed vertically in the

right panel.

Figure 8 replicates the previous plot, but looks at the average earnings of US natives in

response to an immigration influx. It displays the simulated changes in the wage earned by

US natives averaged over all education and gender groups, against the number immigrants

from a given country-education group as a share of the overall US immigrants. Each orange

circle denotes a counterfactual of a 100,000 inflow of non-college educated immigrants from a

given country, and each green triangle denotes a counterfactual of a 100,000 inflow of college-

educated immigrants from a given country.

Two things are worth noting from Figure 8. First, the average earnings of US natives are

negatively affected by an increase in non-college educated immigrants, irrespective of their

country of origin; whereas an increase in college educated immigrants leads to a gain in the

average wage earned by US workers. In addition, the green triangles are more dispersed verti-

cally than the orange circles, indicating that college-educated immigration inflow from differ-

ent countries is more heterogeneous in affecting natives wage than that of non-college immi-

grants. Second, there is a systematic difference across education groups between the number of

immigrants that the US has received from a given origin country and the extent to which their

75

UKDEUTTOLAOGUYBRANICPOL

CAN

PERKORIND

ECUCOLHTIJAMHNDCUBCHNDOMPHLGTMVNM SLV MEX

HTIPER

UK

BRAPOL

UKR

DOM

HKGPAK

JPN

DEUIRN

JAM

RUS

CUBCOL

TWNCAN

VNMKOR

MEX

CHN

PHL

IND

-.02

0

.02

.04

.06

Ave

rage

nat

ive

wag

e ch

ange

s (%

)

.5 1 2 5 40Share of total immigration (%)

Non-college migrantsCollege educated migrants

Figure 8: Simulated Changes in the average wage earned by US natives in response to an influxof immigrants, against immigrants as a share of the total US immigrants

immigrants impact native wages. In the case of non-college educated workers, countries that

have sent a larger number of non-college workers to the US, such as Mexico and EL Salvador,

their workers tend to be stronger substitutes for US natives. However, the opposite case holds

among college-educated immigrants: In the case of countries that have sent a larger number

of college workers to the US, such as India and China, their workers have a stronger positive

impact on natives wages.

76

E Additional Validation Evidence

I show that the stronger correlation found in the validation exercise is not driven by outliers.

I replicate the plots by excluding Mexico in panel (a) for family-visa, excluding India in panel

(b) for employment visa, excluding Cuba in panel (c) and excluding Mexico in panel (d). Table

16 also shows the correlation coefficients from each figure. Unsurprisingly, a strong correlation

remains.

Table 16: Correlation When Excluding Outliers

Panel (a) (b) (c) (d)

Correlation 0.959 0.971 0.536 0.947

ISLCYP

COD

LBY

EST

FIN

AUT

HRVNORDNK

ZMB

TONBELPRYLVA

ARE

ZWE

SGPCHE

SVKDZA

TGO

TZA

GMB

MDACZESDNUGA

BRBNZL

GRC

LKAKWT

NLDSWESAU

LTU

PRT

SEN

HUNFJI

KAZ

BLZ

LAO

URY

SLECMR

AFGBUR

ARMMYS

IRLESP

MNE

NPLLBR

ZAF

PAN

IRQCHL

BGR

BOLAUSIDN

ITA

CRI

ALB

TURFRASYR

RUS

MARKENYEM

NICISR

HKGKHMARGROUEGY

JOR

THA

DEUCUB

UKR

JPNVEN

TWN

GHA

TTOHNDIRNGUY

POLBRAGBR

CAN

BGD

GTMECU

KOR

PERPAK

SLVHTIJAMCOL

VNMINDDOMCHN

PHL

.003

.01

.05

.1

.2

Mod

el-p

redi

cted

allo

catio

n

.003 .01 .05 .1 .2Actual data

(a) Family visa

TON

CUB

CODTGO

GMB

FJI

EST

LAO

YEM

ISLSDNLBY

BLZCYPLBRLVA

KHMBRB

SLE

NIC

SENMDADZAPRYCMRALB

HRVNOR

ZMBBURUGAKAZCZELTUTZA

HTIPAN

AFG

AUT

ARMSVKURYFIN

MNE

ZWE

RUS

MAR

GUYKWT

GRC

CRIDNK

ARE

JOR

VNMPRT

HUN

NZLBELSAUGHA

DOMCHESYR

IRQ

CHLSWEBGRSGPIRL

KEN

HND

THALKABOLNLDESPIDNTTOJAM

EGY

HKG

NPL

MYSUKR

GTM

AUS

ITA

ROU

BGD

TURIRNSLVPERARGZAFECUISR

FRAPOLDEU

VENCOLJPNTWN

PAKBRA GBR

CAN

MEXPHLKORCHN

.003

.01

.05

.1

.2M

odel

-pre

dict

ed a

lloca

tion

.003 .01 .05 .1 .2Actual data

(b) Employment visa

CYPISL

NOR

BLZBRBDNK

PRYTON

PRT

FIN

CZE

SGP

GUY

PAN

BEL

KOR

AUT

JAM

SWE

EST

LBY

NLD

ZMB

CRIIRLGRC

NZL

CHL

HKG

URYCHE

ARE

TTO

HUN

SVK

BOLKWT

DOM

LVA

ESP

ITA

SEN

ISR

GMB

YEM

GBRSAU

AUSZWE

JOR

PHL

TWN

FRAZAF

JPN

SYRARG

ECUKHM

CAN

BRA

UGA

MYSFJI

HND

TZALTU

LKA

LAO

KAZDZA

HRVIDN

TGO

RUS

TUR

POL

MNE

DEU

ROU

PAK

SLE

PER

COD

VEN

MDAMARBGR

ARMGHAAFGCMR

IND

BGD

SDNALB

THA

LBRKEN

COL

NPL

EGY

NIC

VNMGTMHTI

MEX

IRN

BURIRQ

SLVUKR

CHN

CUB

.003

.01

.05

.1

.2

Mod

el-p

redi

cted

allo

catio

n

.003 .01 .05 .1 .2Actual data

(c) Refugee, Diversity and other

ISLCYPLBY

EST

TONNORFIN

AUT

PRY

ZMB

LVA

DNK

BRB

BEL

CZESVK

ARE

GMB

CHE

ZWE

SGPBLZ

GRC

NZL

UGA

PRT

TZAHRVKWTSEN

URY

DZA

SWEHUNSAUFJINLD

LTU

TGO

LAO

COD

IRL

KAZ

PAN

LKA

ESPCHLCRI

MDASLE

MYSBOL

MNE

AUS

YEM

ITA

SYR

CMR

AFGARM

SDN

IDNZAF

KHM

RUS

BGR

HKG

FRA

JORTURMARLBR

ISR

ALB

ARGROU

NPL

TTO

KEN

NIC

HNDGUYJPN

GHATHA

BUR

DEUTWN

EGYVEN

IRQ

POLECU

BGDBRAIRNUKR

PERGTM

GBR

CAN

PAK

JAMHTISLVKORCOL

VNM

CUB

DOM

PHLINDCHN

.003

.01

.05

.1

.2

Mod

el-p

redi

cted

allo

catio

n

.003 .01 .05 .1 .2Actual data

(d) All visas

Figure 9: Model-predicted vs. actual visa allocation across countries, by type of visa

77

F Structure Changes in Other Occupations

INDCHN

CANSEAEEUCA OCMEXEA

US

EU MEAFSA

-.3

-.1

.1

.3D

if in

em

ploy

men

t sha

re

0 1 2 3Log comparative advantage

Computer Software Developers

IND

CHNCANSEAEEUCA OCMEX EA

US

EU MEAFSA

-.3

-.1

.1

.3

Dif

in e

mpl

oym

ent s

hare

0 1 2 3Log comparative advantage

Computer System Analysts

INDCHN

CANSEAEEUCA OCMEXEA

US

EUMEAFSA

-.3

-.1

.1

.3

Dif

in e

mpl

oym

ent s

hare

0 1 2 3Log comparative advantage

Math & ScienceIND

CHNCANSEA EEUCA OCMEX EA

US

EUMEAFSA

-.3

-.1

.1

.3

Dif

in e

mpl

oym

ent s

hare

0 1 2 3Log comparative advantage

Engineers

Figure 10: LINEAR DIFFERENCE OF EMPLOYMENT SHARE AGAINST LOG COMPARATIVE AD-VANTAGES FOR STEM OCCUPATIONS

INDCHN CANSEAEEUCA OCMEXEA

US

EUMEAFSA

-.2

-.1

0

.1

.2

Dif

in e

mpl

oym

ent s

hare

-1.5 -.5 .5 1.5Log comparative advantage

Executive, Managerial

INDCHN CANSEAEEUCAOCMEX

EA

US

EU MEAFSA

-.2

-.1

0

.1

.2

Dif

in e

mpl

oym

ent s

hare

-1.5 -.5 .5 1.5Log comparative advantage

Health Professionals

IND CHNCANSEA EEUCA OCMEX EA

US

EUMEAFSA

-.2

-.1

0

.1

.2

Dif

in e

mpl

oym

ent s

hare

-1.5 -.5 .5 1.5Log comparative advantage

Social Scientists

IND CHN CANSEA EEUCA OCMEXEA

US

EUMEAFSA

-.2

-.1

0

.1

.2

Dif

in e

mpl

oym

ent s

hare

-1.5 -.5 .5 1.5Log comparative advantage

Lawyers and Judges

Figure 11: LINEAR DIFFERENCE OF EMPLOYMENT SHARE AGAINST LOG COMPARATIVE AD-VANTAGES FOR NON-STEM SKILL-INTENSIVE OCCUPATIONS

78

US

SEA EEUSAEACA

ME EU

MEX

IND CANAF OCCHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2 3Log comparative advantage

Construction

US

SEAEEU SAEACA

ME EU

MEX

IND CANAF OCCHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2 3Log comparative advantage

Farm & Agriculture

US

SEAEEUSAEA

CAMEEU

MEXINDCAN AFOC CHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2 3Log comparative advantage

Personal & Cleaning Service

US

SEAEEUSAEACAMEEU

MEX

INDCAN AFOC CHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2 3Log comparative advantage

Food Preparation & Service

US

SEAEEUSAEA

CAMEEU

MEX

INDCAN AFOC CHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2Log comparative advantage

Machine operators

US

SEAEEUSAEACA

MEEU

MEX

IND CANAFOCCHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2Log comparative advantage

Mechanics, Repairers

US

SEAEEUSA EACAMEEUMEX

INDCAN AFOC CHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2Log comparative advantage

Precision workers

US

SEA EEUSAEACA

MEEUMEX

INDCAN AFOC CHN

-.05

0

.05

Dif

in e

mpl

oym

ent s

hare

-2 0 2Log comparative advantage

Transportation

Figure 12: LINEAR DIFFERENCE OF EMPLOYMENT SHARE AGAINST LOG COMPARATIVE AD-VANTAGES FOR LOW-SKILL OCCUPATIONS

79

US, L

SEA, LEEU, LSA, LEA, LCA, LME, LEU, LMEX, LIND, LCAN, LAF, LOC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Admin & Fin. Clerks

US, LSEA, LEEU, LSA, LEA, LCA, LME, LEU, LMEX, LIND, L CAN, LAF, L OC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Editors, Clergy, Arts

US, L

SEA, LEEU, LSA, LEA, LCA, L

ME, L EU, LMEX, LIND, L CAN, LAF, LOC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Equipment Operators

US, L

SEA, LEEU, LSA, LEA, L

CA, L

ME, LEU, LMEX, LIND, LCAN, L AF, LOC, LCHN, LIND, HCHN, HCAN, H

SEA, H

EEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, H AF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Health Assistants

US, L

SEA, LEEU, LSA, LEA, LCA, L

ME, LEU, LMEX, LIND, LCAN, LAF, LOC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Record Clerks

US, L

SEA, LEEU, LSA, LEA, LCA, LME, LEU, LMEX, LIND, LCAN, LAF, LOC, LCHN, LIND, HCHN, HCAN, H

SEA, HEEU, HCA, HOC, HMEX, H

EA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Management Related

US, LSEA, LEEU, LSA, LEA, L

CA, LME, LEU, LMEX, LIND, LCAN, L AF, LOC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, H CA, HOC, H MEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Protective ServiceUS, L

SEA, LEEU, LSA, LEA, L

CA, LME, LEU, L

MEX, L

IND, LCAN, LAF, LOC, LCHN, L

IND, HCHN, HCAN, H SEA, HEEU, HCA, HOC, H MEX, HEA, HUS, HEU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Commodities Sales

US, L

SEA, LEEU, L SA, LEA, LCA, L

ME, LEU, L

MEX, L

IND, LCAN, LAF, L OC, LCHN, LIND, HCHN, H CAN, HSEA, HEEU, H CA, HOC, H MEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Finance & Business SalesUS, L

SEA, L EEU, LSA, LEA, LCA, L

ME, L EU, L

MEX, L

IND, L CAN, LAF, L OC, LCHN, LIND, HCHN, HCAN, HSEA, H EEU, HCA, HOC, H MEX, HEA, HUS, HEU, HME, HAF, H SA, H

-.03

-.01

.01

.03

-2 0 2

TeachersUS, L

SEA, LEEU, LSA, LEA, L

CA, LME, LEU, L

MEX, L

IND, LCAN, LAF, LOC, LCHN, LIND, HCHN, HCAN, HSEA, HEEU, HCA, HOC, HMEX, HEA, H

US, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

TechniciansUS, L

SEA, L

EEU, LSA, LEA, LCA, L

ME, LEU, L

MEX, L

IND, LCAN, LAF, LOC, L CHN, LIND, HCHN, HCAN, H SEA, HEEU, HCA, HOC, H MEX, HEA, HUS, H

EU, HME, HAF, HSA, H

-.03

-.01

.01

.03

-2 0 2

Therapists

Figure 13: LINEAR DIFFERENCE OF EMPLOYMENT SHARE AGAINST LOG COMPARATIVE AD-VANTAGES FOR OTHER 12 OCCUPATIONS

Comparing to the aforementioned STEM and low-skill occupations in which immigrants are

overrepresented, the changes in labor composition are far less dramatic among the other 12

occupations, as presented in Figure 13. The plot is based on labor groups of both non-college

and college-educated and above for 13 aggregate regions. Eight out of 12 occupations exhibits

downward slopes. A positive slope is found for equipment operators occupation, and flat lines

in other occupations such as editors, clergy & Arts, and protective service occupations.

80

G On US-Mexico Border Enforcement

There has been an active policy debate concerning whether to offer a path to legality for the

11 million undocumented immigrants currently in the United States. Opponents argue that

the 1986 Immigration Reform and Control Act (IRCA), which enabled more than 3 million

illegal immigrants to obtain legal status, has not reduced illegal immigration. Instead, they

argue, this amnesty has incentivized more illegal immigration by raising expectations about

future legalization. My results show that a skill-based immigration reform would increase the

number of undocumented immigrants by about 2.3 million. Therefore, to avoid intensifying the

current debate, such a reform would have to be accompanied by additional border enforcement

or protections.

In this section, I discuss the extent to which the US would need to increase border en-

forcement if a skill-based reform were to be implemented, in order to maintain current levels

of illegal immigration. I address this question by performing an alternative counterfactual in

which the legal mode of entry is reformed the same way as the baseline counterfactual, but

border enforcement increases such that the number of illegal migrants stays unchanged.

Again, I set ηus = 2.18, θ = 3.66 and ηo = 0.9 to solve the alternative counterfactual with

proportional changes to the system of equations (12)-(17).75 Unsurprisingly, the impacts on

equilibrium wage units and US wages are almost the same as those of the baseline counterfac-

tual. I also find τmi = 0.937, meaning that there needs to be an increase in migration friction

of illegal crossing so that, on average, the take-home wage rate of a worker entering the US

illegally drops to 93.7% of the take-home wage rate in the actual economy.

Next, I relate the simulated changes in illegal migration frictions, τmi , to a required increase

in the number of border patrol agents. I pursue this goal in two steps. First, I calculate the

percentage changes in smuggling prices that are implied from the simulated result of τmi =

0.937. Second, I borrow the elasticity of smuggling prices to linewatch hours (hours that border

agents spend watching the border) estimated by Gathmann (2008) to obtain the additional

number of border patrol agents needed. Gathmann combines Mexican Migration Project data

and enforcement records from the Department of Homeland Security to analyze the effects of

US border build-up on the market for illegal border crossing. She finds that a 1 percent increase

in linewatch hours in a particular city, on average, would result in a 0.27 percent increase in the

smuggling price in that city and a 0.22 percent increase in the smuggling price in neighboring

cities.

The first step calibrates the level of τm. Since the majority of illegal immigrants entered

the US through the Mexican border, I calculate τm based on the labor-country-mode allocation

of the less-educated Mexican population. To facilitate the calibration, I assume a simplified

version of my model that abstracts away the occupation dimension. I use the equilibrium

75This introduces an additional unknown, τmi , to match the additional equality restriction introduced in thesystem of equations (17) for illegal mode.

81

allocation in equation (1) to compare the fraction of illegal Mexican immigrants who stay in

Mexico, and rearrange to obtain

τmi =(Πus,mi

Πmex

) 1ϑ · Tmexwmex

Tuswus

I omit subscript s since I am fixing the group in this analysis as Mexican non-college-educated

workers. For the same reason, I also omit subscript d, and denote the illegal migration friction

from Mexico to the US as τmi . I assume no friction for Mexicans to live in their home country,

so that the iceberg migration cost to home country equals 1. Πus,mi is Mexican illegal immigra-

tion as a share of Mexico’s non-college-educated population, and Πmex is the share of Mexican

non-college-educated workers who stay in Mexico. To calibrate τmi , I proxy Tuswus with the av-

erage wage earned by non-college-educated US illegal immigrants, measured using the ASEC-

CPS 2010 sample, and proxy Tmexwmex with the average wage earned by non-college-educated

workers in Mexico, calculated from Mexican Census 2010 data. As before, I set θ = 3.66.

This calculation gives τmi = 0.27, further implying that smuggling prices need to increase

by 6.34% to match changes of τmi = 0.937. To deal with the spillover effects of border enforce-

ment on smuggling prices in neighboring cities, I assume the linewatch hours are increased

proportionally across cities. As an upper bound estimate, I assume that there is spillover across

only across one neighboring city; and as a lower bound estimate, I assume spillover across two

neighboring cities. This implies that the number of US-Mexico border patrol agents would

need to increase by 8.6− 11.6%.

What are the implications for government spending on protecting the US-Mexico border?

According to the Congressional Budget Justification 2010, Border Security and Control has

more than 20,000 full-time employees and a total staffing budget of about USD 3.56 billion, in

addition to expenditures on facilities capital, construction and maintenance amounting to USD

1.92 billion. The number of full-time employees stationed on the US-Mexico border account for

about 90% of the total.76 This implies an increase of USD 306-412 million in salary expenses.

If a constant labor-capital ratio assignment along the border is assumed, this facilities, capital

expenses and maintenance costs would therefore increase by USD 165-222 million.

76I assume that 90% of total salary and capital expenses are allocated to the US-Mexico border.

82

H Sensitivity to Parameter Values

This section analyzes the results’ sensitivity to the two elasticity parameters estimated in Sec-

tion 6.3: the labor supply elasticity θ and the labor demand elasticity ηus. I will hold the occu-

pation elasticity of substitution to equal 0.9 for foreign countries.

Alternative θ: I apply two alternative approaches to estimate ϑ, both of which explore the

parametric Fréchet assumption on US wage distribution. First, I use the method of the matching

coefficient of variation, as proposed by Hsieh et al. (2013), who rely on the functional form

of the first and the second moments of the Fréchet distribution. I calibrate the parameter by

matching the following moment restriction:

Var[W]

E[W]2 =

T 2d,m,o ·

[Γ(1− 2/θ

)− Γ

(1− 1/θ

)2]

T 2d,m,o · Γ[1− 1/θ]2

=Γ(1− 2/θ

)Γ(1− 1/θ

)2 − 1,

I estimate the LHS moments using ACS 2009-2012 for the hourly earnings of all observations,

while excluding individuals who earn below the federal minimum wage. This gives θ = 3.14.

Again, I focus on the sample of individuals who earn at least the federal minimum wage with

positive hours worked.

I also use an alternative θ value equal to 1.7 as estimated in Burstein et al. (2015), and a large

value of 5, and holding ηus = 2.18 and ηo = 0.9 as in the baseline. Table 17 reports the wages of

US natives by demographic groups, as well as the impacts on US output. The wage responses

seem less sensitive to θ, and a predominant feature is that the output increases with respect to

θ. This is because θ governs the dispersion of group productivity. A larger θ corresponds to

a smaller dispersion of within-group productivity, and hence average productivity of Chinese

and Indian immigrants would decline slowly as the US attracts more talents from countries

such as India and China.

Alternative ηus: I assign values ranging from 0.9-5 while holding θ = 3.66 and ηo = 0.9 for

other foreign countries. As captured by equation (8), the average wage is more responsive to

changes in the relative labor supply when ηus is small. Results are reported in Table 17.

83

Table 17: WAGE IMPACT ON US NATIVES BY EDUCATION AND GENDER GROUPS, WITH AL-TERNATIVE ηus AND θ AND SETTING ηo=0.9

θ ηus Non-college

male

Non-college

female

College male College

female

Output

1.7 2.18 0.64% 0.73% -0.31% 0.29% 0.27%

3.14 2.18 1.10% 1.22% -0.40% 0.52% 1.77%

5 2.18 1.14% 1.24% -0.34% 0.54% 2.87%

3.66 0.9 1.68% 1.81% -0.56% 0.74% 1.82%

3.66 1.5 1.37% 1.49% -0.46% 0.63% 2.01%

3.66 4 0.77% 0.86% -0.27% 0.39% 2.38%

3.66 5 0.66% 0.74% -0.23% 0.3% 2.45%

84

I Model Extension

I.1 Imperfect Substitution of Undocumented Immigrants

I present a version of model in which natives and legal immigrants are perfect substitutes in

each occupation, while undocumented immigrants are imperfect substitutes for them. Again,

the final good is produced according to occupation CES technology in each country d.

Yd =[∑

o

Ad,oLηd−1

ηdd,o

] ηdηd−1

,

the overall efficiency units of labor in each country and occupation are aggregated according

to

Ld,o =[αd,o,gL

µd−1

µdκ,σ,n + αd,o,uL

µd−1

µdd,o,u

] µdµd−1

,

natives or legal immigrants are denoted by subscript n, and illegal immigrants are denoted by

subscript u. Also denote the wage efficiency unit per labor as wd,o,n for natives and legal im-

migrants, and as wd,o,u for illegal immigrants. µd denotes the elasticity of substitution between

two types of workers in each occupation. The aggregate migration flow resembles as in (1)

with the only difference is the wage unit wd,o,n and wd,o,u applies to each corresponding mode.

The overall efficiency units of labor supply for undocumented immigrants can be expressed

as

Lsupplyd,o,u =

∑s

E[ asd,mu,o ] · Ls · Πsd,mu,o =

1

wd,o,u

∑ν

W sd,mu,o · Lν · Π

sd,mu,o.

The labor demand for undocumented immigrants can be expressed as

Ldemandd,o,u =

1

wµκd,o,u

1

wηdd,oYdA

ηdd,oα

µdd,o,u

where wd,o =[α

1µdd,o,nw

1−µdd,o,n + α

1µdd,o,uw

1−µdd,o,u

]. The labor demand and supply for legal immigrants

follows similar functional form. wd,o,n and wd,o,u clear the market for legal and illegal workers,

respectively.

I.2 Imperfect Substitution Between Native and Immigrants

This subsection presents an another extension of the model in which immigrants and natives

are imperfect substitutes, but legal and illegal immigrants are perfect substitutes. Again, the

final good is produced according to occupation CES technology in each country d. The overall

efficiency units of labor in each country and occupation are aggregated according to

Ld,o =[αd,o,nL

λd−1

λdd,o,n + αd,o,fL

λd−1

λdd,o,f

] λdλd−1

,

85

where subscript n denotes natives, and f denotes immigrants. Also denote the wage efficiency

unit per labor as wd,o,n for natives, and as wd,o,f for immigrants. λd denotes the elasticity of

substitution between immigrants and natives in each occupation. The aggregate migration

flow resembles as in (1) with the only difference is the wage unit wd,o,n and wd,o,f applies to

each corresponding mode.

The overall efficiency units of labor supply for immigrants is

Lsupplyd,o,f =

∑s

E[ asd,m,o|κ, σ,m] · Ls · Πsd,m,o =

1

wd,o,f

∑ν

W sd,m,o · Ld · Πs

d,m,o.

The overall efficiency units of labor supply for natives can be expressed analogously, denoted

as Lsupplyd,o,n . The efficiency units of labor demanded at each market is given from the nested-CES

as

Ldemandd,o,f =

1

wλdd,o,f

1

wηdd,oYdA

ηdd,oα

λdd,o,f

Similarly, the labor demand for native can be expressed as

Ldemandd,o,n =

1

wλdd,o,n

1

wηdd,oYdA

ηdd,oα

λdd,o,n

where wd,o =[α

1µdd,o,fw

1−µdd,o,f +α

1µdd,o,nw

1−µdd,o,n

]. wd,o,f clears the market such that Ldemand

d,o,f = Lsupplyd,o,f , and

wd,o,n clears the market such that Ldemandd,o,n = L

supplyd,o,n .

I.3 Trade in Occupations

Finally, I present an extension of the model with trade in occupation in a Armington fashion

following the labor demand side of the recent work in Burstein et al. (2017). The aggregate

production function is still the same as

Yd =[∑

o

Ad,oYη−1η

d,o

] ηη−1

where Yd,o is the absorption of tasks o in country d, and is assumed to be a CES aggregator of

tasks across countries

Yd,o =[∑

c

Yα−1α

c,d,o

] αα−1

where Yc,d,o is the task produced by country c and shifted to d. α > ρ is the elasticity of sub-

stitution between countries for task o. The task output Qd,o is a linear function of the overall

efficient unit of labor. Also assume the the factor productivity equals 1 and is absorbed by Ad,o,

implying the per-unit price of the task equals the wage efficiency unit per labor, pd,o = wd,o. The

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optimality condition and CES lead to the following equilibrium characterization:

Yd,o =( pd,opd

)−ηYd, pd =

[∑σ

Aηd,op1−ηd,o

] 11−η

Yc,d,o =(dc,d,opc,o

pd,o

)−αYd,o, pd,o =

[∑c

dc,d,ow1−αd,o

] 11−α

where pd is price of final goods in country d, and pd,o is the absorption price in country d and

occupation o. Next, the demand of total efficiency units of labor in country d and occupation o

is

Ldemandd,o = w−αd,o

∑c

d1−αc,d,op

α−ηc,o pηcYc

the supply side of the labor market remains the same as that in the baseline model. Again wd,oequalizes labor demand and supply.

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