QUANTIFYING THE IMPACTS OF A SKILL-BASED US IMMIGRATION REFORM

Transcription

1 QUANTIFYING THE IMPACTS OF A SKILL-BASED US IMMIGRATION REFORM Chen Liu February 7, 2018 JOB MARKET PAPER Abstract Immigration policy is under scrutiny in many high-income countries. This paper develops a multi-country general equilibrium model to analyze the economic consequences of changes in immigration policy regimes. The model can undertake policy-relevant counterfactual by using data on visa share, and can map the aggregate visa changes to endogenous migration composition and wage changes. Assembling micro-level census data from many countries, and data on international migration flow, I estimate and validate the model, and use the model to simulate a counterfactual of a hypothetical skill-based US immigration reform in a world economy of migrants from 115 origin countries and four education and gender groups. I find that had the US changed from the current family-preference immigration system to a system that mimics Canada s emphasis on high-skilled workers in 1990, it would increase the average wage of US natives by 0.9%, narrow US college premium and gender wage gap. As an unintended consequence, US illegal immigration increases by 7%. I also find heterogeneous impacts across foreign countries: the college wage premium increases in India, falls in Central American countries. Despite Mexico is the largest immigrant-sending country to the US, surprisingly, the aggregate and distributional effects on Mexico are small. Ph.D Candidate, University of California, San Diego. address: chl110@ucsd.edu. I am thankful to my advisor 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 seminar participants at the 24th Annual Conference of Freit-EIIT, Washington St. Louis (ESGC), WEAI graduate student workshop, and UC San Diego, for helpful comments. Generous research support was received from the NBER and the Alfred P. Sloan Foundation. 1

2 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, family ties, or refugee status, are now operating under systems that select immigrants based mostly on education, and occupational background (referred to as a skill-based system). 1 The United States, the country that receives 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 As the level of low-skilled US immigrants surged from the early 1990s until the recession, policy debates on comprehensive immigration reform became more active in the past decade. 3 Perceivably, moving from the current US immigration system to a system that prioritizes highly-educated immigrants, would update the skill composition of US immigration. However, since workers may adjust the way through which they migrate to the US in response to economic condition or policy changes, the impacts on US economy might not as large as one might expect. This paper assembles data from many countries micro-level census and data on international migration flow, to perform three empirical exercises to gain understanding on the economic consequences of changes in the US immigration visa regime, both on US and foreign economies. First, I estimate the share of migration mode through which immigrants migrate to the US, for each country of origin, education, and gender groups. Second, I develop a multicountry general equilibrium model of international migration, in which workers choose which country to live, which occupation to work and which mode (the types of visa or illegal entry) to migrate. The model can undertake policy-relevant counterfactual by using data on visa share, can simulate the impacts on international migration flow and wages when there is a change in the aggregate number of visa for a specific category. 4 Third, I structurally estimate and validate the model, and use the estimated model to simulate a hypothetical US immigration reform in which the US had moved to a system that mimics Canada s emphasis on high-skill immigration since I have four main results when shifting eight million family-based visa to employmentbased category. 5 First, the share of college-educated US immigrants increases from 28% to 45%. The skill upgrading predicted in this study is considerably smaller than a counterfactual, which replaces the same number of non-college-educated immigrants by college-educated 1 A commonly used skill-based immigration system is the point system. Point system was first introduced by Canada in the 1960s and was adopted by Australia in 1989 and New Zealand in Recent adoptions of pointbased systems include: Sweden in 2003, Singapore in 2004, Hong Kong in 2006, Denmark in 2007, and the UK in The Immigration and Nationality Act of 1965 ended the national origin quota system and began awarding entry permits based on family ties with US citizens and residents. 3 Proposal for a comprehensive skill-based reform has reflected in part by the Comprehensive Immigration Reform Act of 2007, and more recently, the Reforming American Immigration for Strong Employment (RAISE) Act. 4 This differs from previous literature which can experiment a counterfactual by exogenously changing the level or the composition of immigration. For example, see papers including Bound et al. (2017), Burstein et al. (2017), Piyapromdee (2017), Llull (2013), Colas (2017). 5 The number of eight million is implied from a counterfactual which reallocates visas to employment-based categories such that the visa distribution exactly matches the Canadian system, while holding the total number of visas issue unchanged since

3 ones. 6 Second, the average wage earned by US natives increases by 0.9%. The counterfactual policy changes would also narrow the US college premium and gender wage gap. Third, the level of US illegal immigration increases by 7%. Finally, the effects are heterogeneous across immigrant-sending countries. Wage inequality rises in India, falls in Central American countries. Surprisingly, as the largest immigrant-sending country to the US, there is small aggregate and distributional effects on Mexico. The model allows a large dimension of heterogeneity. There are many countries that differ in productivity. There are many groups defined by a different combination of characteristics, such as national-origin, education, and gender groups. Each group differs in the cost of migrating to each destination through each mode of entry (referred to as migration friction), and also differs in their occupation comparative advantage. I use the model to show that two central elasticity parameters in immigration literature each of which has been studied as a single reduce-form parameter vary systematically across immigrants national-origin, education, and gender groups. These two elasticity parameters are migration elasticity in response to migration frictions, and natives wage elasticity in response to immigration. The heterogeneity in these two elasticity parameters is crucial in determining the impacts of visa regime changes on migration flow and wages. In particular, the heterogeneous migration elasticity determines how the national-origin, education, and gender composition of US immigrants would change in response to changes in visa regime; 7 and the heterogeneity in natives wage elasticity informs which immigrant groups compete with US natives the most. The heterogeneous migration elasticity is driven by group differences in how intensively they use each mode to migrate to the US. In the model, the relative migration friction across entry modes rationalizes migration sorting across mode of entry, and drives migration responses to policy shock through two channels. For example, when family-entry mode friction increases, which simulates a reduction of family visas, immigrant groups who face relatively high friction in family-entry mode are less affected, as the majority would still optimally migrate to the US through other modes. I find that Mexican immigrants are not affected as much as expected, since more than half of Mexican immigrants migrate to the US illegally. The relative migration frictions also determine the extent to which immigrants switch to alternative modes of entry. As it becomes harder to migrate through family-entry mode, groups who face a relatively low friction in illegal mode are more likely to switch to illegal crossing. I find that the pattern of switching to illegal crossing is the strongest among Mexican immigrants, mitigating the net changes of Mexico-to-US migration flow. Those two channels together explains the small impacts on Mexico. The heterogeneous natives wage elasticity in response to immigrant groups is driven by the extent to which occupation specialization differs between immigrants and natives. I show that even within the same education and gender characteristics, natives wage response to the same level of change in immigration vary dramatically by immigrants national-origin. In particular, an increase in the number of Indian college-educated immigrants who specializes in 6 The share of college-educated immigrants would rise to 56% in a counterfacutal which replace eight million non-college-educated immigrants by college-educated ones. 7 In one strand of literature, Mayda (2010), Grogger and Hanson (2011), Belot and Hatton (2012), Ortega and Peri (2013) estimate a reduce-form parameter of migration elasticity. In another strand of literature, Ottaviano and Peri (2012) estimates a single elasticity parameter of immigrant-native substitution. 3

4 occupations that US natives are underrepresented in, would, on average, lead to a strong positive impact on US natives wage through factor complementary. In addition, complementary effects are stronger for non-college than college groups, and for female than male. 8 In contrast, by increasing to the same level of Mexican college-educated immigrants who specialize in occupations that US natives are over-represented in, would have a negative impact on US natives wage through factor substitution. I estimate the labor demand and supply elasticity of the model mainly using the Integrated Public Use Micro Samples (IPUMS, Ruggles et al. (2015)). First, I identify the labor supply elasticity which governs the responsiveness of choosing a country-occupation-mode option 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. 9 For example, I examine how likely it is that Chinese-born US immigrants work in occupations where quantitative 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 elasticity of the substitution parameter the inverse of which governs changes in relative wages in response to a 1% change in relative occupational labor by relating changes in average occupation wages to changes in total occupational hours during I construct a Card-type instrument based on the persistence in occupational specialization of US immigrants by national origin (Lafortune and Tessada, 2010; Hanson and Liu, 2016), to capture the exogenous occupational labor supply in the absence of occupational labor demand or labor productivity changes. I validate the assumption by taking the number of US visas granted since 1990 to the model and comparing the model-generated cross-country visa allocation with data from the Department of Homeland Security. I find that simulating changes in entry mode by adjusting a common mode-specific cost change in my model can generate a cross-country visa allocation that aligns well with the data. I also find 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 the model, I use the estimated model to perform two simulation exercises. First, I simulate the migration and welfare impacts of the baseline counterfactural: holding the total number of visas issued unchanged since 1990, but reallocating visas to employment-based categories among college-educated workers in skill-intensive occupations such that the visa distribution matches the Canadian system. 11 This exercise keeps counterfactual border enforcement unchanged. The results indicate that US illegal immigration 8 The intuition is in line with Costinot and Vogel (2010), Burstein et al. (2015), Galle et al. (2015) and Lee (2016), in which occupational comparative advantage shapes occupation sorting and determines the aggregate group wage responses. My model also allows the possibility that the friction of working in each occupation affects occupational sorting. 9 The approach serves as a test of Roy comparative advantage hypothesis, and is the labor market analog of Costinot et al. (2011). 10 Simulating the model requires an assumption that US visas have been issued to immigrants without discrimination on the basis of national origin. Strictly speaking, this assumption is invalid: For instance, only immigrants from certain countries with low rates of immigration to the US are eligible for the diversity visa program and there are also per-country immigration limits. In addition, the Immigration and Nationality Act (INA) limits lawful permanent resident (LPR) admission from any single country to 7% of the total number of family-based and employment-based admissions for each year. However, many categories are exempt from this limitation Wasem (2012). Section 2.5 provides details on per-country limits. 11 See Figure 3 in Section 6 for visa distribution. 4

5 increases due to the adjustments in entry mode. I perform a second counterfactual in which the legal system is reformed as in the baseline, and to learn to what extent the border enforcement needs to be increased such that the number of illegal immigrants remains unchanged. Despite the fact that the model has a large number of primitives such as migration costs, total factor productivities, and labor-occupational productivity, applying exact hat algebra (Dekle et al., 2008) which solves the model in proportional changes enables simulation of the counterfactual with only two sets of elasticity parameters: the labor supply elasticity and the labor demand elasticity. I consider migrants from 115 countries of origin, two education levels (college and non-college), and two gender groups, and simulate a model by aggregating the world to 13 countries/regions, multiple occupations, and four modes of entry. The data required include: for each national origin, education level and gender group, their occupation choices and average wages in each country, the number of workers who live in each country, and the mode entry share among those who live in the US. I measure the set of labor market variables using census microdata from more than 80 countries and obtain international migration stocks and the occupational share of immigrants from the Institute for Employment Research (IAB) database and the Database on Immigrants in OECD countries (DIOC), respectively. I estimate the entry mode share for US immigrants by national origin based on the Annual Social and Economic Supplement of the Current Population Surveys (ASEC) and the Yearbook of Immigration Statistics from the Department of Homeland Security (DHS), while supplementing with data from the New Immigrant Survey (NIS) to obtain conditional moments on mode entry by education group and by occupation. This paper relates to several strands of literature. Some studies examine how a skill-based US immigration reform would affect immigration composition by comparing the observable characteristics of immigrants in the US with Canada or Australia countries that filter immigrants based on education, occupational specialty, and language ability (Borjas, 1993; Antecol et al., 2003). US higher education institutions and temporary visas (H-1B or F-1 student visa) both play an important role in determining the inflow of high-skill US immigrants (Bound, Demirci, Khanna and Turner, 2015). However, we still lack a complete understanding of how a comprehensive immigration reform of the permanent visa system would affect immigration composition and the welfare in a global general equilibrium context. My model advances the literature on immigration selection (Borjas, 1987; Orrenius and Zavodny, 2005; Grogger and Hanson, 2011) by incorporating entry mode to a general equilibrium Roy model. The results emphasize the importance of incorporating entry mode into analysis of immigration policy reform. That is, if abstracting entry mode from the model, one would over-predict the economic impacts of skill-based immigration reform. This paper also relates to literature on the labor market impacts of immigration, which is mostly based on reduced-form approaches and highlights the key factors that determine the effects of immigration. These factors include substitutability among education groups (Card, 2009) and between natives and immigrants (Cortes, 2008; Ottaviano and Peri, 2012); the relative skill abundance of natives (Borjas, 2003; Lewis, 2011); geographic and institutional frictions (Angrist and Kugler, 2003); and skill transferability of immigrants (Schoellman and Hendricks, 2016). Other work incorporates sector adjustments using structural approaches (Llull, 2013; 5

6 Bound, Khanna and Morales, 2017; Piyapromdee, 2017; Colas, 2017). 12 My model takes into account the above factors but departs from the previous literature with analysis of immigration in a multi-country setting 13, and, hence, can speak to the consequences of immigration globally analogous to the multi-country general equilibrium analysis which has been widely used in international trade literature, e.g., Eaton and Kortum (2002). 14 Regarding multi-country analysis of international migration, my paper is perhaps most closely related to the analysis of EU enlargement studied by Caliendo, Opromolla, Parro and Sforza (2017). This paper differs from their work in two important dimensions. First, by modeling mode of entry, I can take data on mode entry share to the quantitative model and to analyze immigration policy change. This turns out to be important as I find the equilibrium mode adjustment to illegal entry is an important margin US immigration policy changes. Second, my model allows a larger dimension of heterogeneity than Caliendo et al. (2017). I use the model to show that two central elasticity parameters in immigration literature, vary systematically across immigrants national-origin, education, and gender groups. Finally, this paper relates to the rapidly expanding body of literature on Roy-like general equilibrium models. Building on Lagakos and Waugh (2013) and Hsieh, Hurst, Jones and Klenow (2013), extensions have studied the impacts of computerization on wage inequality (Burstein, Morales and Vogel, 2015), the distributional impacts of international trade (Adão, 2015; Galle et al., 2015; Lee, 2016) 15, and market adjustment to immigration in tradable and non-tradable occupations in the US (Burstein, Hanson, Tian and Vogel, 2017). 16 The literature offers different hypotheses as to what determines differences in labor-to-occupation allocations across labor groups. I use a revealed comparative advantage approach to estimate labor supply elasticity, which also serves as a validation test of Roy s comparative advantage hypothesis. I find supportive evidence of the Roy s comparative advantage hypothesis based on the occupational sorting of US immigrants. The paper is organized as follows: Section 2 presents the model and key model predictions; Section 3 discusses the datasets used in the simulation exercise; Section 4 estimates the labor supply and demand elasticities of the model; and Section 5 presents the performance of a validation exercise. The results for baseline counterfactual policy impacts on the US and on global economies are presented in Section 6. Section 7 shows an alternative counterfactual in which the US also increases government expenditures on border enforcement, maintaining the total 12 Literature has also emphasized factors such as the capital-skill complementarity (Lewis, 2011), and industry expansion (Lewis, 2005) and the tradablility of occupations (Cortes, 2008; Burstein et al., 2017) at local labor market. Piyapromdee (2017) performs a counterfactual exercise by exogenously changing the skill composition of immigration to mimic a skill selective policy changes. Colas (2017) analyzes labor market adjustments to immigration in a dynamic setting. 13 Di Giovanni, Levchenko and Ortega (2015) considers a global general equilibrium model with trade and exogenous migration flow. My model differs from this paper by allowing an upward sloping labor supply curve with endogenous migration selection. Also see Khanna and Morales (2017) who conduct a two-country general equilibrium analysis of H-1B program on Indian IT sector boom. 14 Various versions of Eaton and Kortum (2002) include multi-sector extensions as in Costinot et al. (2011), multinational production as in Ramondo and Rodríguez-Clare (2013), cross-sector interdependence of intermediate inputs as in Caliendo and Parro (2015), and multi-sector with Roy selection as in Redding (2016), Galle et al. (2015), Lee (2016), among others. 15 An exception is Adão (2015), who pursues a nonparameteric approach in a two-sector setting. 16 Lagakos and Waugh (2013) first brought Fréchet productivity into a two-sector Roy model to study crosscountry differences in agricultural labor productivity. Hsieh et al. (2013) extended this literat ure to a multioccupation Roy model to study misallocation in the US from 1960 to

7 number of illegal migrants. Section 8 concludes. 2 MODEL My model simplifies the real world as an economy with many competitive labor markets a standard setting that is prevalent in wage inequality and immigration literature (Katz and Murphy, 1992; Borjas, 2003). I extend this setting to include multiple countries and to consider that the labor markets of each country are distinguished by occupations, rather than by education-experience groups. I allow an upward sloping labor supply curve generated from the Roy selection (Lagakos and Waugh, 2013; Hsieh et al., 2013), while extending it to incorporate international migration with multiple modes of entry. The model has many national-origin, education and gender groups, which differ in two major aspects. First, for a given destination country, groups differ in their relative costs of migration across modes. For example, it may be cheaper for some groups to migrate illegally than to migrate with a family-based visa. Second, groups differ in their relative occupational productivity. For example, some groups may be more productive than others if they work as computer scientists rather than lawyers. Countries are open to immigration, but are closed to international trade. 17 I denote destination country by κ, occupation by and the mode of migration by m. I also denote national-origin, education, and gender groups by ν. 2.1 Production In each country κ, a single final product is produced by combining occupational tasks using a CES production function, [ ρκ 1 ] ρκ ρκ 1 ρκ Y κ = A κ, L, where ρ κ denotes the elasticity of substitution across occupations of country κ. L κ, is aggregate efficiency units of labor in destination country κ and occupation. At each occupation, natives and immigrants are perfect substitutes. A κ, is total factor productivity in country κ and occupation, and is assumed to be exogenous in the baseline model. κ, 2.2 Labor Supply In practice, immigration policy imposes numerical limits on visas and selects immigrants based on a variety of principles such as family ties, educational background, and refugee status. For example, 65-70% of US visas are granted to family-preference categories, while around 60% of Canadian visas are issued to economic and employment categories. Building upon the Roy model, the labor supply side of my model incorporates the entry mode of immigration to capture this feature of immigration policy. The empirical part considers three entry modes, includ- 17 Ottaviano et al. (2013) jointly analyzes immigration and offshoring in a partial equilibrium setting. Burstein et al. (2017) analyzes the trade adjustments to immigration at the local labor market in the US, while treating immigrants as exogenous. My analysis omits international trade due to the data challenge of measuring trade in occupations globally. 7

8 ing family-based visa, employment-based visa, and refugee and diversity visa. Since US illegal immigration accounts for 30% of the total, I also consider illegal entry. Section 3 discusses the empirical content of each entry mode. For each country-of-origin, education and gender group ν, the potential productivity of working in country κ, occupation, and in mode status m follows a marginal Fréchet productivity distribution that has the cumulative distribution function: { P (η ν,κ,,m < z) = exp T ϑν,κ,z } ϑ 18. All marginal productivity distributions are independent across κ and. Each marginal distribution is characterized by two parameters: ϑ and T ν,κ,. ϑ governs the shape of the productivity distribution. Holding T ν,κ, constant, a larger ϑ corresponds to small within-group dispersion, and, hence, workers switching among options is more responsive to economic shocks. I assume ϑ is the same across labor groups. 19 T ν,κ, is the scale parameter, with a larger T ν,κ, corresponding to a higher average level and also a fat upper tail of productivity if group ν works in destination country κ and occupation. I assume T ν,κ, 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. As will be discussed in Section 4, this assumption allows me to estimate ϑ using a revealed comparative advantage approach. T ν,κ, reflects the mixture of occupational talents and skill transferability. Variation in T ν,κ, may result from differences in countries education quality, countries emphases across educational subjects, and the extent to which certain skills are important in performing occupational tasks. For example, immigrants from countries that place more emphasis on math and science (e.g., China), will tend to be more productive in occupations where knowledge in math and science are important. I include whether the immigrant is unemployed in options in. 20 It is important to consider immigrants employment status, since unemployed immigrants account for over 10% of all immigrants. In either case, the Fréchet distribution is that of the reservation wage. 2.3 Location, Occupation and Mode Choices Workers choose κ--m by maximizing their net perceived earnings. I use Ω κ, to denote the wage per efficiency unit of labor in country κ and occupation. Migration is subject to iceberg migration costs, denoted as τ ν,κ,,m. The interpretation of τ ν,κ,,m is that if a worker from group ν wants to migrate to destination κ and work in occupation through mode m, then for every 18 Alternatively, the model remain tractable using a multivariate Fréchet productivity as in Hsieh et al. (2013). However, since later I will estimate labor supply elasticity which is a composite function of the Fréchet shape and correlation parameters (instead of separately identify them), my results are indifferent between independent and correlated Fréchet draws. 19 Estimating ϑ would be challenging if they were allowed to vary across groups. See Appendix of Burstein et al. (2015) and Lee (2016), which use the maximum likelihood estimator (MLE) to recover group-specific ϑ from wage distributions. A concern with this approach is that the estimation is based on a self-selected sample and is subject to selection bias. It also neglects the specific context of Roy selection. 20 In the case where corresponds to employed or unemployed, A κ, = 0 in the production function. 8

9 dollar he/she earns, 1 τ ν,κ,,m would melt away. 21 The multiplicative form of migration frictions is aimed at keeping the model tractable and has been widely adopted in the literature on immigration self-selection; for example, see Borjas (1987), Chiquiar and Hanson (2005). 22 τ ν,κ,,m is driven by a mix of factors such as bilateral geographic and cultural barriers, migration networks, immigration policy, etc. Immigration policy might ease costs of certain modes of entry or favor workers with certain skills or occupational specialties while restricting others. It also determines how much immigrant-sending countries characteristics such as migration network and political unrest are valuable in a specific mode of entry. For example, under a familypreference system as in the US the family-mode entry friction is lower for countries that have established strong migration networks in the US than countries that have not. In contrast, for a system that prioritizes skilled workers for example, the Canadian or Australian systems the entry friction in employment-based mode is likely to be lower than family-based mode, and is even lower among highly educated workers with certain occupational specialties. τ ν,κ,,m also include factors such as political unrest, natural disaster in immigrant-sending countries (Mahajan and Yang, 2017). Given the Fréchet distribution assumption, the fraction of group ν working in country κ at occupation, and migrating through mode m, has a closed form as follows: P κ,,m ν = T ϑ ν,κ,ω ϑ κ,τ ϑ ν,κ,,m κ m T ϑ ν,κ, Ω ϑ κ, τ ϑ ν,κ,,m, (1) Throughout this paper, I use the notation P to denote conditional probability. Summing over options within a destination country to obtain the bilateral migration rate for group ν, P κ ν = m T ν,κ,ω ϑ ϑ κ,τν,κ,,m ϑ. κ m T ϑ ν,κ, Ω ϑ κ, τ ϑ ν,κ,,m In addition, among ν immigrants who work in occupation, the mode through which immigrants in a given occupation entered the US depends on the ϑ-adjusted frictions of entering through that mode relative to the sum of those frictions in any other modes, P m ν,κ, = τ θ ν,κ,,m m τ θ ν,κ,,m. (2) In the model, each conditional probability P is explained by the ϑ-adjusted average benefits of being in one cell relative to the sum of benefits over all cells. 23 The functional form of the partial equilibrium prediction is consistent with the empirical literature on migration; see Grog- 21 For the worker who draws η ν,κ,,m (i) efficiency unit of labor productivity, the wage she would earn if she chooses to live in country κ and work in occupation with mode status m equals τ ν,κ,,m Ω κ, η ν,κ,,m (i). 22 Literature on immigration selection assumes an additive migration cost on the log of perceived wage. For example, recall that in the seminal paper by Borjas (1987), the take-home wage net of migratory costs at destination are written as log w 1 c = µ 1 + ε 1 c, where c is assumed to be a constant across workers. Chiquiar and Hanson (2005) also assume log additive migration costs, but they increase with respect to education. In my model, taking the logarithm of τ ν,κ,,m Ω κ, η ν,κ,,m (i) will result in the same function form as in those papers. However, my model is more flexible, as it allows migration costs to be specific to each origin, education, and gender group, as well as host country, occupation, and mode of migration. 23 Appendix B.1 also provides the expression of conditional probability that will be used in the simulation exercises, including P κ, ν, P κ,m ν, P ν,κ, P m ν,κ, P m ν,κ, and P,m ν,κ. 9

10 ger and Hanson (2011), Kennan and Walker (2011), and Monte, Redding and Rossi-Hansberg (2015). In Appendix B.1, I present the expression for other conditional probabilities that will be extensively analyzed in Section 2.5. The Fréchet distribution implies that the average group efficiency units of labor employed in country κ, at occupation, and that migrate through mode m equals E[ η ν,κ,,m κ,, m] = Γ(1 1 ϑ ) T ν,κ,[p κ ν P,m ν,κ ] 1 ϑ, 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 [P κ ν P,m ν,κ ] 1 ϑ in my case. 24 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 of 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 experimental evidence of positive migration selection on unobservable ability (McKenzie, Stillman and Gibson, 2010) 25, and is consistent 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 [P κ ν P,m ν,κ ] 1 ϑ, 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 under mode m in country κ can be expressed as W,m ν,κ = Γ(1 1 ϑ ) T ν,κ, Ω κ, [P κ ν P,m ν,κ ] 1 ϑ. 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 occupation and mode-specific frictions. 2.4 General Equilibrium The model primitives are characterized by country-occupation-specific total factor productivity A κ,, bilateral and mode-specific iceberg migratory costs τ ν,κ,ω,m, the stock of labor force in each origin-education group L ν, Fréchet productivity location parameter T ν,κ,, Fréchet shape parameter ϑ, and the elasticity of substitution across occupations in each country, ρ κ. 24 See Head (2013) for a survey of truncated distribution and the functional form of truncation moments. 25 McKenzie et al. (2010) finds Tongan immigrants to New Zealand are positively selected in terms of both observed and unobserved skills. 10

11 The CES production function implies the labor demand in each country κ and occupation is L demand κ, = 1 Y Ω ρκ κ A ρκ κ,. κ, The total efficiency units of labor supplied in each destination and occupation market are aggregated over natives and immigrants of all country-of-origin, education, and gender groups, and among immigrants who enter through each mode. L supply κ, = ν E[ η ν,κ,,m κ,, m] L ν P κ,,m ν = 1 W,m ν,κ L ν P κ,,m ν. 26 Ω κ, m ν m Given the primitives Λ, a competitive equilibrium in a global economy consists of the locationoccupation-mode sorting of ν workers P κ,,m ν, bilateral migration rate P κ ν, and the average wages earned by ν workers in country κ, occupation and mode m, W,m ν,κ. The wage efficiency unit of labor at each κ- market Ω κ, equalizes the labor demand with labor supply such that L supply κ, = L demand κ,. 2.5 Model Intuition I illustrate the model s mechanism of how the model generate two central elasticity parameters, each is heterogeneous across groups. The first is migration elasticity in response to migration frictions, and the second is natives wage elasticity to immigration. The first set of elasticities informs how the demographic composition of US immigration would change due to policy shocks, and the second shows, within each skill group, which countries immigrants are the closest substitutes for US natives. (A) Migration elasticity to migration friction Consider a special case of the model in which I assume migration friction doesn t depend on o. The partial equilibrium migration elasticity (holding wage units unchanged) in response to migration friction changes has the following form: / P κ ν τν,κ,m ) = ϑ (1 P κ ν P m ν,κ. (3) P κ ν τ ν,κ,m Equation (3) says that reducing the number of family-based visas (1) would disproportionately reduce immigration from ν who are more likely to enter with a family-based visa i.e., P m ν,κ is larger; (2) would disproportionately reduce immigration from ν who have a small fraction of population living in the US i.e., P κ ν is smaller; and (3) would have a large location response if the productivity is highly dispersed i.e., ϑ is small. As I will estimate in Section 3, 78% of college-educated Central American immigrants entered the US through the family mode, compared to 35% of their Indian counterparts. This indicates that, when reducing family-based visas, the number of US immigrants from Central American and Caribbean countries would fall more than two times faster than for those from India, in percentage term. 26 The second equality holds because the total expenditures on labor equal the products of wage efficiency per unit and the overall efficiency units of labor. 11

12 The intuition is that the relative migration friction across entry modes rationalizes migration sorting across mode of entry, and drives migration responses to policy shock. For example, when family-entry mode friction increases, immigrant groups who face relatively high friction in family-entry mode are less affected, as the majority would still optimally migrate to the US through other modes. (B) Cross-wage elasticity So far, I have illustrated the mechanism of how visa regime changes would modify the national origin mix of US immigration. As the occupation specialization of US immigrants differs by country of origin, how would it affect differences in native-immigrant competition? To illustrate 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 ultimate 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 ν 1 US natives and ν 2 as immigrants from an arbitrary origin and demographic group. I use and ω 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 ν 2. The derivation of cross-group wage elasticity relies on the following equality: W ν1 W ν1 / Lν2 L ν2 = [ Wν1 L L W ν1 L L ] ν2 = L ν2 L [ ( ω W ν1 Ω ω Ω ω W ν1 Ω ω L ) L L ] ν2 L Ω ω L ν2 L where W ν1 is the average group wage earned by natives; L ν2 is the total efficiency unit of type-ν 2 immigrant workers; and L is the total efficiency unit of labor in occupation. Ω ω is the wage unit in occupation ω. The two equal signs in equation (4) hold by the chain rule. 27 Appendix B.4 provides the expressions and derivations for each elasticity that appears in equation (4). Equation (4) captures the partial equilibrium wage elasticity which is the first-order effect of native wage response, but not 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 Tonga, I normalize the cross-group wage elasticity by efficiency units of immigrants such that the normalized cross-group wage elasticity is as follows: W ν1 W ν1 / Lν2 1 = 1 ρ [ P ν2,κ (R P ν1,κ) L }{{ } percentage changes in occupational employment (4) ], (5) where R denotes the occupational wage bills as a share of the total, capturing the size of the occupation throughout the entire economy. P ν1,κ and P ν2,κ are the fractions of natives and immigrants that work in occupation, respectively. ρ is the elasticity of substitution across 27 The first equality states that the wage earned by natives in response to changes in immigrant labor supply equals the sum product of natives wage elasticity in response to changes in occupations labor supply and the occupational labor elasticity to changes in type-ν 2 immigration workers. The second equality holds by re-expressing natives wage elasticity to occupation labor supply as the sum product of natives wage elasticity to occupation wage unit and the elasticity of occupation wage unit to the occupation labor supply induced by immigrants. 12

13 occupations. Equation (5) says a P ν 2,κ L percentage change in the occupation labor supply induced by a unit immigration influx of group ν 2 would lead to a net complementary effect on US natives, ν 1, if native workers are underrepresented in this occupation, such that R P ν1,κ > 0. Otherwise, the substitution effect dominates. The aggregate natives wage response to a unit immigration influx from group ν 2 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, 1. ρ Equation (5) 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 R P ν,κ is the most negative for US natives. 28 The implication provides a different perspective, as it might be supposed that immigrants present the greatest competition for natives if they work in the same occupation i.e., 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 education 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. In Appendix D.2, I also analyze a simple two-occupation case in which the difference in immigrant-to-native substitution can be related to the difference in occupational comparative advantages. My approach is distinct from previous literature on immigrant-native substitution in two aspects. First, the literature uses a reduced-form parameter the elasticity of substitution of the production function to study immigrant-native substitution. However, economists often argue that immigrants and natives are imperfect substitutes, using evidence that they specialize in different occupations (Peri and Sparber, 2009). I measure their substitution from the labor supply side using cross-wage elasticity, and pin down these parameters by using data on occupational share. In line with the insights of Costinot and Vogel (2010) and Burstein et al. (2015), comparative advantage causes occupational specialization and, hence, governs the betweengroup substitution. Second, since the occupational specialization of US immigrants with the same education differs dramatically across countries of origin (Lafortune and Tessada, 2010; Hanson and Liu, 2016), my approach allows the substitution between immigrants and natives within the same skill group to differ across immigrants national origin, rather than clustering immigrants only by skill groups. 28 This / can be mapped into a linear optimization problem such that one picks vector values of P ν2,κ such that W ν1 L ν2 W ν1 1 is maximized or minimized. This results in a corner solution: P ν2,κ = { 1, if = argmax ω { Rω P ω ν,κ L ω }. 0, other. 13

14 (C) The role of ϑ and ρ ϑ plays two roles in the model. First, as shown in equations (3) and (??), ϑ is the labor supply elasticity and governs the responsiveness of choosing a country-occupation-mode option when the monetary returns to that option change by 1%. The second is a property from the truncated Fréchet distribution. ϑ governs how fast the migration-occupation selectivity bias responds to changes in the size of the selected sample (workers who choose a given country and occupation). As described in equation (8), when within-group productivity is highly dispersed, i.e., ϑ is large, the average group productivity is less responsive to changes in the size of the sample. ρ is the labor demand elasticity and governs the responsiveness of relative occupational labor demand when the relative wage changes by 1%. The inverse of ρ acts as a multiplier in determining the wage responses, as shown in equation (5). For an extreme case, as ρ becomes large enough the relative wage is invariant to changes in relative labor supply, as workers in different occupations are perfect substitutes. The estimation of these two parameters is presented in Section Equilibrium Using Exact Hat Algebra To solve equilibrium conditions in terms of proportional changes, I define variables X = X C X 0, where X C denotes the counterfactual equilibrium variables and X 0 denotes the equilibrium variables of the initially observed economy in year I then express equilibrium labor flow in terms of proportional changes as follows: P κ,,m ν = T ν,κ, ϑ Ω ϑ κ, τ ν,κ,,m ϑ ϑ κ m T Ω. (6) ν,κ, ϑ κ, P 0,κ,,m ν An important observation from equation (6) is that P κ,,m ν does not depend on model primitives such as T ν,κ,, τ ν,κ,,m. Instead, these model primitives enter the function only in terms of P κ,,m ν, implying that information about P κ,,m ν is sufficient to capture these model primitives. Analogously, proportional changes for the migration rate, average wages, and labor market clearing conditions can be obtained as follows: P κ ν = ϑ T Ω ϑ ν,κ, κ, P 0, ν,κb ν,κ, ϑ κ T Ω, (7) ν,κ, ϑ κ, P 0,κ, νb ν,κ, where B ν,κ, = ] ϑ m [ τ ν,κ,,m P 0,m ν,κ,, and the proportional changes in average wages take the form 1 { } 1 ϑ Ŵ,m ν,κ = Tν,κ, Ωϑ τ κ, P 0, ν,κb ν,κ, P 1 ϑ κ ν (8) ν,κ,,m 14

15 Â ρκ 1 ρκ κ, Ω κ, Ŷκ = ν m W 0,,m ν,κl 0,ν P 0,κ,,m ν Ŵ,m ν,κ Lν Pκ,,m ν ν m W 0,,m ν,κl 0,ν P 0,κ,,m ν 29, κ,. (9) The expressions for P ν,κ, P κ, ν, P,m ν,κ can be obtained analogously, and the detailed derivation is provided in Appendix B.2. Burstein et al. (2015) and Redding (2016) show that the model with an elastic labor supply can be solved in changes by applying the exact hat algebra first recognized by Dekle et al. (2008) in international trade literature. The great advantage is that it requires little information on model primitives. In this case, I need two elasticity parameters: demand elasticity ρ and labor supply elasticity ϑ. Consider an exogenous immigration policy shock in terms of {Q m }, where Q m denotes changes in the number of entrants for each mode. Then, given parameter values of ϑ, ρ κ and data on {W,m ν,κ }, {P κ ν }, {P ν,κ }, {P m ν,κ, }, and setting Âκ, = T ν,κ,ω = 1, since they are unchanged in the counterfactual, the goal is to solve Ω κ,, P ν,κ, P κ ν, Ŵ,m ν,κ, and τ ν,κ,,m from the system of equations (6) (9), 30 and set the restrictions to match the exogenous changes in mode entry as follows: L ν P κ,,m ν ( P κ,,m ν 1) = Q m, ν foreign-born, m. (10) ν In general, the system of equations (6) (10) does not yield a unique solution, because one can adjust τ ν,κ,,m to shift certain visas across groups (ν) or across occupations () so that the changes in mode entry still match Q m at each mode. In the counterfactual exercise presented later, I simulate changes in migration frictions that are invariant across ν and for the family-based and refugee-based modes. For the employment-based mode, I also allow a common change in migration friction that applies only to certain occupations and education groups. The counterfactual simulation reduces the number of unknowns in τ ν,κ,,m to equal to the number of restrictions in (10), to yield a unique solution with respect to a given policy shock {Q m } Relation to Existing Models My model assumes that labor is the only input factor in production and perfect substitution between immigrants and natives within each occupation, similar to Card (2001). Existing pa- 29 where Ŷ κ = ν,,m W 0,,m ν,κl 0,ν P 0,κ,,m ν Ŵ,m ν,κ Lν Pκ,,m ν ν,,m W 0,,m ν,κl 0,ν P 0,κ,,m ν, 30 To solve equilibrium efficiently, I notice that equilibrium changes in labor allocation and wages equations (6) (8) are functions of changes in the wage efficiency unit of labor Ω κ,. This allows us to express P ν,κ, P κ ν and Ŵ ν,κ in terms of Ω κ, and solve the equilibrium in changes Ω κ, using the system of equations (9) for each country and occupation labor market. 31 To see this, consider that in partial equilibrium (i.e., Ω κ, = 1), the number of unknowns in the system of equations (10), which is dim(ν) dim() dim(m), far exceeds the number of equations in system (10), which is dim(m). Also notice that the system of equations (10) is linear in τ ϑ ν,κ,,m. Thus, reducing the number of unknowns in τ ν,κ,,m to equal the number of restrictions in (10) satisfies the necessary condition of having a unique solution. Computation shows convergence of iteration and thus my simulation yields a unique solution. However, my focus in this paper is not to theoretically investigate the sufficient and necessary conditions for the unique equilibrium to exist. 15