# Immigration, Search and Redistribution: A Quantitative Assessment of Native Welfare

Immigration, Search and Redistribution: A Quantitative Assessment of Native Welfare Abstract What are the welfare effects of immigration on low-skilled and high-skilled natives? To address this question, we develop a general equilibrium model featuring two skill types, search frictions, wage bargaining, and a welfare state that redistributes income through unemployment benefits and the provision of public goods. Our quantitative analysis suggests that, in all 20 countries studied, immigration attenuates the effects of search frictions. The resulting gains tend to outweigh the welfare costs of redistribution. Immigration has increased native welfare in almost all countries. In two-thirds of countries, both high- and low-skilled natives have benefited from the presence of immigrants, contrary to what models without search frictions or redistribution predict. Average total welfare gains from migration are 1.25% and 1.00% for high- and low-skilled natives, respectively. 1. Introduction Many OECD countries have experienced high immigration rates during the last two decades. Foreign-born workers now make up a significant share of their labor forces. The overall economic effects of immigration on the native population are debated. Based on simple models of factor complementarity, economists have long been optimistic about the existence of a net immigration surplus for natives (Borjas 1995). They have also been aware of factor price adjustment effects of immigration (Borjas 2003) and of the possible consequences for welfare states (Razin and Sadka 2000). However, once we simultaneously account for labor market frictions and redistributive fiscal policies, the net effect of immigration on native welfare is harder to calculate. To our knowledge, no previous paper on the effects of immigration has taken into account both production complementarities under imperfect competition in the labor market and fiscal redistribution. This paper begins to fill this gap. We document that host OECD countries differ with respect to the size and structure of their immigrant populations. They also differ with respect to their labor market and redistributive institutions. To study how this heterogeneity shapes outcomes for incumbent populations, we develop a parsimonious model that incorporates key aspects of this heterogeneity. We use a setup with search and matching frictions that includes skill heterogeneity, wage bargaining and a welfare state that taxes labor income to provide unemployment benefits and engages in redistributive policies. We calibrate our model separately for 20 OECD countries to evaluate the effects of different migration scenarios on the welfare of different sections of the native and immigrant populations. The effect of immigration on labor market outcomes and welfare is likely to hinge on four important features of immigrants and host countries. First, it depends on how the skill composition of the immigrant labor force differs from that of natives. By the complementarity channel, additional supply of a certain type of workers negatively affects other workers of the same type (substitutes) and positively affects workers of different types (complements). For example, a new inflow of low-skilled immigrants reduces wages of low-skilled natives and increases those of high-skilled natives. In about a third of the surveyed countries, the share of tertiary educated is larger for immigrants than for natives. In several countries, including France, Germany, and the United Kingdom, however, that share is substantially smaller for immigrants than for natives. The second key fact relates to the relative wage levels of immigrants and natives. In all 20 countries, low-skilled natives earn a wage premium over low-skilled immigrants. In 17 out of 20 countries, high-skilled natives earn more than high-skilled immigrants. In the remaining three countries, high-skilled natives and immigrants earn about the same. Wage gaps may reflect differences in labor productivity, but they may also relate to differences in the outside option of natives relative to migrants. These two determinants of wage gaps have different implications on the labor market effects of immigrants. The third fact relates to unemployment risk. In most countries, both low- and high-skilled immigrants are much more likely to be unemployed than natives of the same skill level. All countries in our sample provide some unemployment insurance, albeit at different levels of generosity. Such systems lead to net redistribution from the group with lower unemployment rates to the group with higher unemployment rates. Fourth, the size of government (measured by the share of taxes or public expenditures in gross domestic product (GDP)) has important implications on the fiscal effect of immigrants and varies significantly across countries. Although fiscal effects of migration have been the subject of some research and much public debate, to the best of our knowledge the welfare state has not been included into a general equilibrium model featuring skill heterogeneity and labor market frictions. These features describe four different margins through which immigrants affect native welfare. In our quantitative analysis, we capture all of them. To this end, we must go beyond the complementarity and labor market competition channels of the canonical frictionless model. We need a setup in which wages and unemployment rates can differ for workers with similar educational attainments, and where the public sector redistributes income to the unemployed and to low-income individuals through unemployment benefits and through the provision of public goods. To this end, we present a model that combines a production function featuring skill complementarity with a labor market characterized by search and matching frictions. Competitive firms create vacancies for high- or low-skilled workers and cannot target immigrants or natives ex ante. Natives and immigrants are perfect substitutes within each skill group, but may differ with respect to their productivity. For a given level of education, our model also allows immigrants to differ from natives with respect to their outside options (for example due to different costs of search for employment while unemployed) and their exogenous job breakup rate, which for immigrants is in part driven by remigration. Through these differences, the model explains the empirical fact that foreign-born workers face higher unemployment risk than natives and have lower wages. In equilibrium, immigration affects native welfare through four channels. Two of them work through the labor market: The traditional complementarity channel affects wages through relative supply of skills, whereas a job-creation channel arises because an increase in the share of immigrant workers affects the incentives for job creation by firms. This job-creation channel was first pointed out by Chassamboulli and Palivos (2014). Its impact on native employment depends crucially on differences between natives and immigrants regarding productivity and outside options. Redistribution also works through two channels: one through unemployment benefits and another through proportional taxes and lump-sum transfers. How these channels affect native welfare depends on the relative skill composition of immigrants, as well as on the design of labor market institutions and the public sector. Although it is impossible to obtain closed-form solutions for our full general equilibrium setup, analytical results are available for simplified versions of our model. We calibrate the parameters of our model to match 11 salient empirical moments we have collected for 20 OECD countries circa 2011. We use the quantitative model to study the welfare implications of the following four exercises: (i) an increase in immigration equal to 1 percentage point of the labor force, keeping the skill composition of the immigrant population fixed and starting from the 2011 status quo; (ii) an increase of the same size, but only of low-skilled immigrants; (iii) a hypothetical no-immigrant situation (autarky) relative to the status quo in 2011, and (iv) a change in migrant shares and skill composition equivalent to the changes between 2011 and 2014. Although we find welfare effects to be heterogeneous across countries and skill groups, in most cases the effects of a marginal increase of immigrants—as in experiment (i)—are positive for natives. In the case of an increase in the stock of unskilled immigrants only—as in experiment (ii)—the impact on welfare of low-skilled natives is usually negative. However, it is small (on average on the order of one-tenth of a percentage point), and the average welfare effect for all natives is zero. In 19 of 20 countries, welfare effects of total migration relative to autarky—as experiment in (iii)—are positive for natives in terms of the utilitarian social welfare function. Positive effects on labor market efficiency tend to outweigh costs coming from the welfare state, especially in countries where transfers are relatively unimportant. We include important extensions analyzing the different impact of immigrants on native welfare when their productivity is lower than natives’ and when part of the public spending is on nonrival goods such as defense and debt servicing. Finally, to better understand the relative quantitative importance of the different mechanisms present in our framework, we perform a simulated comparative statics exercise. For this purpose, based on observational data, we draw a vector of moments for 10,000 artificial economies, calibrate our model to each of them, and run regressions to obtain conditional correlations between these moments and native welfare, which is our variable of interest. Wage and unemployment gaps between immigrants and natives, as well as the size of government, are found to be important determinants of the welfare effects of immigration. A simpler model with competitive labor markets and no government cannot deliver this result. Our paper is related to at least four strands of research. First, a large empirical literature studies the wage effects of immigration.1 Using increasingly sophisticated approaches based on dividing the labor market into cells to estimate own- and cross-elasticities of substitution, this literature simulates the effect of immigration through the complementarity channel.2 Second, some recent papers apply a structural empirical framework to a setup where wages are set noncompetitively. For instance, D’Amuri, Ottaviano, and Peri (2010); Felbermayr, Geis, and Kohler (2010); Brücker and Jahn (2011); and Brücker, Jahn, and Upward (2014) postulate, in reduced form, that wages are decreasing functions of unemployment rates. Although these models do allow for unemployment, the labor market imperfections are not microfounded, and the role of labor market institutions is not explicitly modeled. Moreover, these studies do not have any role for the government and do not discuss welfare. Chassamboulli and Palivos (2014) address the shortcomings related to missing microfoundations of labor market imperfections and study immigration in a search-and-matching model in which immigrants have inferior outside options compared to natives. Bargaining results in lower wages for immigrants, which encourages firms to create more vacancies for all workers. In this way, immigration can attenuate the effects of labor market frictions for natives.3 In this paper, we generalize the model presented in Chassamboulli and Palivos (2014). We allow heterogeneity between immigrants and natives in employment duration, thereby allowing unemployment rates to be different between natives and immigrants of the same skill level. We also extend the quantitative exercise to a sample of 20 countries. The literature on the wage effects of immigration also abstracts from the fiscal effects of immigration. This is the focus of a separate literature. Calibrating dynamic equilibrium models featuring demographics and fiscal policy for the United States and Sweden, Storesletten (2000, 2003) find that immigration can strongly benefit natives when immigrants are middle aged and have sufficiently high employment rates. Actual immigration, however, may differ from such a composition; immigration may turn out to be a burden for the native taxpayer.4 Dustmann and Frattini (2014) provide a comprehensive analysis of the net fiscal contribution of immigrants in the United Kingdom and find an overall positive impact. Virtually all papers in this literature abstract from a microfounded modeling of labor market imperfections. They instead use an “accounting approach” based on observed taxes and transfers, without considering labor market interactions and the equilibrium responses of the economy. Finally, a handful of papers evaluate the welfare gains from immigration within a general equilibrium framework. Benhabib and Jovanovic (2012) use a model with human capital externalities similar to Lucas (1990) to estimate the level of international migration that maximizes world welfare. They find that global migration flows ought to be much larger than they are today. di Giovanni, Levchenko, and Ortega (2015) quantify the welfare effects of international migration in a model that incorporates total factor productivity and skill differences, within a Melitz (2003) framework of international trade with a home market effect. Klein and Ventura (2007, 2009) analyze the effects of international migration driven by productivity differences, in models where capital is mobile in the long run. They find substantial gains from migration, accruing in large part to the immigrants themselves. Docquier, Ozden, and Peri (2014), instead, evaluate wage and employment gains from immigration and emigration for nonmigrants in all OECD countries. These papers assume Walrasian labor markets and do not include a public sector. In addition to affecting wages and fiscal budgets, large-scale immigration may be capitalized in rents and property values. Like other papers on the wage effects of immigration, we abstain from modeling this mechanism. As most land is owned by native citizens, changes in rents can be expected to generate winners and losers within the native population but largely cancel out at the level of aggregate native income. Nonetheless, such a distributional conflict could be a reason why tenants may be worried about increases in immigration. Glazer, Kanniainen, and Poutvaara (2008) present a model in which utility depends on housing location and other consumption, and land is heterogeneous. They show that if a utilitarian government does not care about the welfare of landowners, it may tax the rich more once they become mobile in order to push rents down. The remainder of this paper is structured as follows. Section 2 presents cross-country variation of measures related to migration and institutions in 20 OECD countries. Section 3 presents our model. Section 4 discusses our calibration strategy and presents our quantitative results and extensions. Section 5 concludes. 2. Cross-Country Summary Statistics In this section, we document cross-country heterogeneity in the labor market performance of immigrants and in relevant institutions. These summary statistics motivate our modeling approach and play a central role in our quantitative exercise. 2.1. Immigrants in the Labor Force Table 1 provides summary statistics on eight important measures that characterize immigration, the labor market, and the generosity of welfare states in the 20 countries of our sample.5 Row [1] of Table 1 shows that immigrants represent a substantial percentage of the labor force in the countries considered, with the average across countries standing at about 17%, the lowest equal to 10% (Portugal), and the highest as large as 39% (Luxembourg).6 Row [2] refers to the skill composition of immigrants relative to natives. On average, the share of tertiary-educated among immigrants is almost the same as the share of tertiary educated among natives, revealing similar average skill composition. However, there is substantial heterogeneity across countries. In Canada, this share for immigrants is 1.63 times the share of college-educated natives. In Slovenia, the share for college-educated immigrants is only 0.40 times that of natives. Based on this heterogeneity in relative skill patterns, we expect different distributional effects of immigration in different countries. Table 1. Summary statistics of moments of interest. Variable Average 75th PCTL 25th PCTL Top value (country) Bottom value (country) [1] Share of immigrants 17.1% 17.9% 13.4% 39.1% 9.9% in the labor force (Luxembourg) (Portugal) [2] Share of tertiary educated, 0.99 1.16 0.78 1.63 0.40 immigrants rel. to natives (Canada) (Slovenia) [3] Low-skilled average wage, 0.86 0.90 0.78 0.99 0.72 immigrants rel. to natives (Canada) (Greece) [4] High-skilled average wage, 0.86 0.93 0.81 1.01 0.64 immigrants rel. to natives (Switzerland) (Italy) [5] Low-skilled unemployment, 1.62 2.07 1.23 2.43 0.91 immigrants rel. to natives (Switzerland) (United States) [6] High-skilled unemployment, 2.19 2.78 1.69 3.50 1.14 immigrants rel. to natives (Austria) (Portugal) [7] Replacement ratio 38.9% 49.8% 26.6% 62.9% 21.9% (benefits/wages) (Belgium) (Greece) [8] Public spending 45.3% 49.7% 41.0% 54.8% 33.4% as share of GDP (Denmark) (Switzerland) Variable Average 75th PCTL 25th PCTL Top value (country) Bottom value (country) [1] Share of immigrants 17.1% 17.9% 13.4% 39.1% 9.9% in the labor force (Luxembourg) (Portugal) [2] Share of tertiary educated, 0.99 1.16 0.78 1.63 0.40 immigrants rel. to natives (Canada) (Slovenia) [3] Low-skilled average wage, 0.86 0.90 0.78 0.99 0.72 immigrants rel. to natives (Canada) (Greece) [4] High-skilled average wage, 0.86 0.93 0.81 1.01 0.64 immigrants rel. to natives (Switzerland) (Italy) [5] Low-skilled unemployment, 1.62 2.07 1.23 2.43 0.91 immigrants rel. to natives (Switzerland) (United States) [6] High-skilled unemployment, 2.19 2.78 1.69 3.50 1.14 immigrants rel. to natives (Austria) (Portugal) [7] Replacement ratio 38.9% 49.8% 26.6% 62.9% 21.9% (benefits/wages) (Belgium) (Greece) [8] Public spending 45.3% 49.7% 41.0% 54.8% 33.4% as share of GDP (Denmark) (Switzerland) Data sources: See Appendix B for details. PCTL: Percentile. View Large Table 1. Summary statistics of moments of interest. Variable Average 75th PCTL 25th PCTL Top value (country) Bottom value (country) [1] Share of immigrants 17.1% 17.9% 13.4% 39.1% 9.9% in the labor force (Luxembourg) (Portugal) [2] Share of tertiary educated, 0.99 1.16 0.78 1.63 0.40 immigrants rel. to natives (Canada) (Slovenia) [3] Low-skilled average wage, 0.86 0.90 0.78 0.99 0.72 immigrants rel. to natives (Canada) (Greece) [4] High-skilled average wage, 0.86 0.93 0.81 1.01 0.64 immigrants rel. to natives (Switzerland) (Italy) [5] Low-skilled unemployment, 1.62 2.07 1.23 2.43 0.91 immigrants rel. to natives (Switzerland) (United States) [6] High-skilled unemployment, 2.19 2.78 1.69 3.50 1.14 immigrants rel. to natives (Austria) (Portugal) [7] Replacement ratio 38.9% 49.8% 26.6% 62.9% 21.9% (benefits/wages) (Belgium) (Greece) [8] Public spending 45.3% 49.7% 41.0% 54.8% 33.4% as share of GDP (Denmark) (Switzerland) Variable Average 75th PCTL 25th PCTL Top value (country) Bottom value (country) [1] Share of immigrants 17.1% 17.9% 13.4% 39.1% 9.9% in the labor force (Luxembourg) (Portugal) [2] Share of tertiary educated, 0.99 1.16 0.78 1.63 0.40 immigrants rel. to natives (Canada) (Slovenia) [3] Low-skilled average wage, 0.86 0.90 0.78 0.99 0.72 immigrants rel. to natives (Canada) (Greece) [4] High-skilled average wage, 0.86 0.93 0.81 1.01 0.64 immigrants rel. to natives (Switzerland) (Italy) [5] Low-skilled unemployment, 1.62 2.07 1.23 2.43 0.91 immigrants rel. to natives (Switzerland) (United States) [6] High-skilled unemployment, 2.19 2.78 1.69 3.50 1.14 immigrants rel. to natives (Austria) (Portugal) [7] Replacement ratio 38.9% 49.8% 26.6% 62.9% 21.9% (benefits/wages) (Belgium) (Greece) [8] Public spending 45.3% 49.7% 41.0% 54.8% 33.4% as share of GDP (Denmark) (Switzerland) Data sources: See Appendix B for details. PCTL: Percentile. View Large 2.2. Labor Market Outcomes of Natives and Immigrants Native and immigrant workers also differ in their labor market outcomes. Rows [3] and [4] in Table 1 show that across the countries in our sample, the average wage received by immigrants is typically lower than the one received by natives of the same skill class. Using European Union Statistics on Income and Living Conditions (EU-SILC) and Census data, both for high- and low-skilled workers,7 the average yearly wage paid to immigrants equals 86% of that paid to natives, with large cross-country heterogeneity. For example, there is no wage gap for low-skilled immigrants in Canada and high-skilled immigrants in Switzerland. The wage gap is highest in Greece for low-skilled workers and Italy for high-skilled workers. The lower wages for immigrants relative to similarly skilled natives could derive from different factors. First, the wage gaps could be due to lower bargaining power of migrants. Second, even within the same skill class, migrants may have lower productivity than natives because of poorer language skills or imperfect portability of human capital (Poutvaara 2008). Although several studies document that the native-immigrant wage gap declines with years spent in the host country, most of them find a positive native/immigrant wage gap that persists even after many years of linguistic and skill assimilation.8 This wage difference affects the value to the firm of a job filled by a migrant. It can be higher or lower than the value of a job filled with a native, depending on whether the bargaining effect or the productivity effect dominates.9 Rows [5] and [6] of Table 1 report summary statistics on unemployment rates of immigrants compared to natives, within the groups of low- and high-skilled workers. Differences are substantial, in particular for the highly skilled. Cross-country heterogeneity is large, too. On average, the likelihood of unemployment for an immigrant is 1.6 times (for low skilled) and 2.2 times (for high skilled) the corresponding likelihood for a native. Unemployment gaps are largest in Switzerland for the low skilled and in Austria for the high skilled, and lowest in the United States for the low skilled and in Portugal for the high skilled. These discrepancies in unemployment rates are consistent with immigrants facing higher job destruction rates than natives, a fact documented in the empirical literature for several countries, as we discuss below. Ceteris paribus, the shorter expected duration of a match with an immigrant, due to a variety of reasons, reduces incentives for vacancy creation. 2.3. Welfare State Characteristics Different wages and unemployment rates between natives and immigrants have important implications: First, they open the door for immigration to affect job creation incentives; second, they may generate redistribution through taxation and unemployment benefits. The relative importance of unemployment benefits as a redistribution channel between natives and immigrants depends on equilibrium unemployment rates and on the generosity of benefits. Following the literature, we measure this as the average replacement ratio, that is, the size of unemployment benefits as a percentage of after-tax wage income.10 Row [7] of Table 1 shows this rate averages 39% and varies from 63% in Belgium to 22% in Greece. The generosity of unemployment benefits changes the effective bargaining power of workers, their wages, and the degree of labor market tightness. The overall scale of fiscal redistribution is quantitatively more relevant. Many European countries engage in substantial redistribution. Government spending as a share of GDP, which we report in Row [8] of Table 1, is a simple measure of the redistributive role of governments.11 Government spending as a share of GDP averages 45%, ranging between 33% (Switzerland) and 55% (Denmark). Although transfers and public goods may imply redistribution toward migrants, they also alter the distributional effects of immigration on natives of different skill levels. 3. Model We model each country as an economy populated by native and immigrant workers, has perfectly mobile physical capital, and produces one output good. In the tradition of papers on the impact of immigrants on national labor markets (Borjas 2003; Ottaviano and Peri 2012) and recent multicountry extensions (Docquier et al. 2014; di Giovanni et al. 2015), we take the stock of international migrants as an exogenous variable. There is a single final output good and two intermediate goods. The government redistributes income through unemployment benefits and a lump-sum transfer. Taxes are a linear function of wage income. Utility is linear in consumption. 3.1. Production The final output good Y, whose price is normalized to unity, is produced using capital K and a composite input good Z. In turn, good Z is produced using a Constant elasticity of substitution (CES) combination of two intermediate inputs. We denote them by YL and YH, and assume them to be linear functions of employment of low- and high-skilled workers, respectively. This is common in the macro labor literature that analyzes skill premia and skill bias (see, Katz and Murphy 1992; Acemoglu 2002; Autor, Katz, and Kearney 2006). More precisely, the supply side is characterized by the following expressions: \begin{eqnarray} Y &=& AK^{\alpha }Z^{1-\alpha },\alpha \in \left( 0,1\right) \nonumber\\ Z &=& \left[ xY_{L}^{\rho }+\left( 1-x\right) Y_{H}^{\rho }\right] ^{\frac{1}{ \rho }},\rho \in \left( 0,1\right) \nonumber\\ Y_{i} &=& \sum _{j\in \left\lbrace N,I\right\rbrace } ( 1-u_{ij}) \pi _{ij}Q_{ij},i\in \left\lbrace L,H\right\rbrace , \end{eqnarray} (1) where α is the output elasticity of capital, A denotes total factor productivity, ρ governs the elasticity of substitution between the low-skill-intensive intermediate input YL and the high-skill-intensive intermediate input YH, x ∈ (0, 1) is a productivity parameter, Qij is the supply of different types of labor, with i ∈ {L, H} indexing skills (high and low levels of education) and j ∈ {N, I} distinguishing native (N) and immigrant (I) workers. Finally, uij is the unemployment rate and πij is labor productivity (effectiveness) for group i × j.12 Expression (1) implies that natives and migrants of the same skill level are perfect substitutes in production and that two different types of skill sets, usually identified with workers who completed a college education and workers who did not complete a college education, are sufficient to capture the main differences in workers’ roles in production. This bipartition is typical of models that identify education-based skills (e.g., Goldin and Katz 2008; Card 2009; Docquier et al. 2014), and it recognizes that workers with a completed college education and those without a college education are performing different productive roles associated, most likely, with cognitive-analytical abilities (the first group) and noncognitive abilities (the second group). This distinction acknowledges the crucial complementarity in production between workers with a (completed) college education and those without a (completed) college education, which is at the core of modeling labor demand and labor supply in the last decades (e.g., Autor et al. 2006). Recently, Autor and Dorn (2013) and Goos, Manning, and Salomons (2009) have shown how distinguishing between “routine” and “service” tasks within skill classes can shed light on the role of technological change in explaining wage polarization. We do not follow this task-based approach because our main focus is on the labor supply side rather than on labor demand, and because it would be difficult to empirically assess the suitability of immigrants for either task in the available cross-country data. Rather, we simply analyze average wage and employment effects for workers without distinguishing by productive tasks.13 Becausewe assume capital to be freely mobile internationally, the return to capital is determined on world markets. The simplest assumption about capital ownership is that each individual owns an equal share of capital invested across countries to mirror exactly the cross-country distribution of capital that equates its marginal return across countries. Hence, the stock of capital owned by natives of a country is given by $${\bar{K}}$$ and its amount and return do not change with immigration (although its cross-country allocation will). The amount of capital used in production by a country may differ from $${\bar{K}}$$. It is determined by the usual first-order condition r + δ = αAKα − 1Z1 − α, where r + δ is the user cost of capital given by the sum of the interest rate on a risk-free asset and the depreciation rate of capital. Hence, gross capital income R generated in the economy is given by $$R\equiv (r+\delta )K=\alpha AK^{\alpha }Z^{1-\alpha }=\alpha Y.$$ (2) Intermediate goods are produced under perfect competition. So, their prices equal their marginal contributions to the production of the final good Y, namely \begin{eqnarray} p_{L} =AK^{\alpha }(1-\alpha )xY_{L}^{\rho -1}\left[ xY_{L}^{\rho }+(1-x)Y_{H}^{\rho }\right] ^{\frac{1-\alpha -\rho }{\rho }}, \end{eqnarray} (3) \begin{eqnarray} p_{H} =AK^{\alpha }(1-\alpha )(1-x)Y_{H}^{\rho -1}\left[ xY_{L}^{\rho }+(1-x)Y_{H}^{\rho }\right] ^{\frac{1-\alpha -\rho }{\rho }}. \end{eqnarray} (4) The production function of the intermediate goods is very simple: Once a worker of group i × j (i ∈ {L, H}, j ∈ {N, I}) has been hired, he or she produces πij units of the good Yi. The labor market, however, is not competitive, and therefore wages are not equal to intermediate goods prices. 3.2. Labor Markets There is a separate labor market for each skill type (H and L for high skilled and low skilled) so that natives and immigrants of the same skill level compete for the same jobs. Firms post vacancies specific to a skill. Depending on the numbers of vacancies and unemployed workers in each market, matches are formed continuously. The total supply of workers in labor market i is taken as exogenous and given by Qi = ∑j∈{N, I}Qij, i ∈ {H, L}. Immigration represents an exogenous change in the number of foreign-born workers QiI. Strictly speaking, the changes in the stock of foreign born are equilibrium outcomes, deriving from the interaction of immigration policies and the potential supply of immigrants. However, given the current immigration restrictions in OECD countries and the potential economic gains from migration for non-OECD immigrants (estimated to be on average two to three times as large as the migrant’s wage income at home, as found in Clemens, Montenegro, and Pritchett 2010; see also Gibson, McKenzie, and Stillman 2010 and Clemens 2013), an exogenous relaxation of immigration quotas by a few percentage points of the host country population will certainly imply that the quotas remain binding.14 By the same token, migration pressure will not change as a consequence of the migration flows that we consider. Feedback effects will be irrelevant and therefore we believe that maintaining a policy-determined exogenous change in the number of immigrants is rather reasonable. Matching Process. Firms post vacancies in skill-specific markets (H and L). At the time in which the firm pays the cost to open a vacancy, it cannot target immigrants or natives. When firms and workers meet and negotiate, however, immigrants and natives are distinguishable and may be offered different wages. In other words, firms cannot direct their search activities ex ante (when they post vacancies), but can treat immigrants and natives differently ex post (at the wage determination stage). This assumption follows Chassamboulli and Palivos (2014) and explains immigrant-native wage gaps appealing to the intuitive idea that immigrants have a different, perhaps weaker, bargaining position than natives.15 Therefore, in our model, there are four types of workers and two labor markets (for high- and low-skilled workers). At each instant of time, a mass Vi of open vacancies and a mass Ui = ∑j∈{N, I}Uij of unemployed workers exist in each labor market i. Below, M denotes the flow contact rate as a function of Ui and Vi. For each market, we use a standard constant returns-to-scale matching function, increasing in both its arguments, concave and homogeneous of degree 1: $$M(U_{i},V_{i})=\xi U_{i}^{\varepsilon }V_{i}^{1-\varepsilon }, \,\,\, i = H,L,$$ (5) where ε ∈ (0, 1) is the matching elasticity and ξ is a scale parameter. Labor market tightness is defined as θi ≡ Vi/Ui, measuring the number of vacancies per unemployed person. The rate at which firms fill vacancies is Mi/Vi = q(θi) = ξθ−ε. The rate at which unemployed workers find jobs is Mi/Ui = m(θi) = ξθ1−ε. Higher market tightness makes it easier for the unemployed to find a job and harder for a firm to fill a vacancy. Existing matches are broken at the exogenous rate sij, which may differ between natives and migrants, and across skill types. Differences in separation rates between natives and immigrants may at least in part come from the fact that immigrants are more likely to remigrate, that is, to return to their home country or to migrate to other locations, due to exogenous events. As their families are often in different locations, their status is more precarious and they have less attachment to their current location. Hence, we consider the separation rates of immigrants as the sum of exogenous remigration rates and standard separation rates. Empirically, we will measure remigration rates as including return to the home country or a move to a different country or region (internal migration is part of what constitutes remigration to the extent that workers separate from their employers). We capture remigration rates as part of the separation rates of immigrants as follows: $$s_{iI}=\bar{s}_{iI}+\psi _{j}$$ where ψj denotes the remigration probability of migrants of type j. We will discuss in Section 4.1 the plausible values of ψj based on data on international remigration. The parameter siI plays a key role for job creation incentives from the perspective of the firm (see below), but from the firm’s perspective it is irrelevant whether the separation of the worker takes place because he or she moves domestically or internationally,16 or because of other exogenous reasons, captured by $$\bar{s}_{iI}$$. Bellman Equations. Under these assumptions, the Bellman (asset) equations determining the value of an open vacancy $$J_{i}^{V}$$ to a firm producing good i can be written as follows: $$rJ_{i}^{V}=q(\theta _{i})\left[ \varphi _{iN}J_{iN}^{F}+\varphi _{iI}J_{iI}^{F}-J_{i}^{V}\right] -c_{i}.$$ (6) The flow value of an open vacancy, $$rJ_{i}^{V}$$ (where r denotes the risk-free interest rate), has no index j because firms cannot direct their search ex ante to natives or immigrants. From an ex ante perspective, whether the vacancy is filled by an immigrant or a native worker is not known to the firm and depends on the share of immigrants among the unemployed of a particular skill group. In equation (6), the value of a vacancy depends on expected capital gains, which equal the probability the vacancy is turned into a filled job, represented by the rate q(θi), multiplied by the value of the filled job, minus the value of the open vacancy. The variable φij ≡ Uij/(∑jUij) denotes the share of workers of skill level i and of type j (either immigrants or natives) among those searching for a job. We then need to subtract the flow cost of an open vacancy, ci, denoted in terms of the numéraire good. The flow value of a filled vacancy, $$J_{ij}^{F}$$, can be written as follows: $$rJ_{ij}^{F}=\pi _{ij}p_{i}-w_{ij}-s_{ij}\left[ J_{ij}^{F}-J_{i}^{V}\right] .$$ (7) The flow value of a filled vacancy is equal to its rate of return, net of the wage paid to the worker (πijpi − wij), minus the expected capital loss occurring if the match between worker and firm is broken. The exogenous separation occurs at rate sij and entails a loss equal to the difference between the value of a filled vacancy and that of an open vacancy, that is, $$J_{ij}^{F}-J_{i}^{V}$$. Unlike the value of an open vacancy, the value of a filled vacancy depends both on the skill i ∈ {H, L} and on the type of the worker j ∈ {I, N}. For workers, we can then define Bellman equations determining the value of employment and unemployment. The flow value of employment can be written as $$rJ_{ij}^{E}=g+rk_{ij}+\left( 1-t\right) w_{ij}-s_{ij}\left[ J_{ij}^{E}-J_{ij}^{U}\right] .$$ (8) The flow value of employment is given by the sum of a lump-sum per-capita transfer g, capital income rkij, the after-tax wage (1 − t)wij, where t is a proportional tax rate on labor income, minus the expected capital loss arising from job destruction. This loss occurs at rate sij and is equal to the difference between the value of employment and that of unemployment, that is, $$J_{ij}^{E}-J_{ij}^{U}$$. The flow value of unemployment can be written as $$rJ_{ij}^{U}=g+rk_{ij}+b_{ij}+h_{ij}+m(\theta _{i})\left[ J_{ij}^{E}-J_{ij}^{U}\right] .$$ (9) The flow value of unemployment is equal to the transfer g, capital income rkij, unemployment benefits bij, which will be determined from wages and replacement rates, as well as the term hij, which denotes the utility value of being unemployed, capturing the fact that the utility effect of unemployment may not be fully captured by monetary benefits. These must satisfy bij + hij < wij(1 − t). We set hij to zero for natives $$( h_{\mathit {HN}}=h_{\mathit {LN}}=0)$$. The value of hiI will be negative for immigrants if they experience larger disutility from unemployment due to being outside their home country.17 Alternatively, the disutility from unemployment hiI for immigrants can be interpreted to reflect higher utility costs of searching for employment (as pointed out by Chassamboulli and Palivos 2014) because of less advantageous social network and more limited knowledge of labor market institutions, which increase the effort needed to search for a job while unemployed. The flow value of unemployment also needs to include the expected capital gain arising from a successful match: the difference between the value of employment and that of unemployment. The probability that an umployed worker finds a job is given by m(θi). Wage Bargaining. We assume that firms post vacancies until the value of posting a vacancy drops to zero. The free entry condition, $$J_{i}^{V}=0$$, applies to vacancies in both skill classes. As it is customary in the literature, we assume a simple Nash bargaining model for wage determination.18 Wages are bargained efficiently once a match has been formed, and the identity of the matched worker, native or immigrant, has been revealed. Let the bargaining power of the worker be β ∈ (0, 1); then, the worker receives the share β of the total surplus of the match $$( J_{ij}^{E}+J_{ij}^{F}-J_{ij}^{U}-J_{i}^{V})$$. Incorporating the free entry condition, Nash bargaining implies $$\left( 1-\beta \right) \left( J_{ij}^{E}-J_{ij}^{U}\right) =\beta J_{ij}^{F}.$$ (10) As usual in this type of model, we focus on the steady state, that is, the situation where the flows into and out of unemployment are equal to each other for each type of worker: \begin{equation*} s_{ij}(Q_{ij} - U_{ij}) = m(\theta_{i})U_{ij}\ {\rm for}\ i \in \{H, L\} \ {\rm and}\ j \in \{N, I\}. \end{equation*} Thus, we obtain $$U_{ij}\!=\!\frac{s_{ij}}{s_{ij}+m(\theta _{i})}Q_{ij},\text{ and }E_{ij}=\frac{ m(\theta_{i})}{s_{ij}+m(\theta_{i})}Q_{ij};\text{for}\,i \in \lbrace H,L\rbrace \text{ and }j\in \lbrace N,I\rbrace ,$$ (11) where Eij is total employment in labor market cell i × j. Higher labor market tightness and lower separation rates lead to lower equilibrium unemployment. 3.3. Public Sector We consider a very simple government budget constraint. This allows for fiscal effects from immigration.19 The government collects income by raising proportional taxes on labor income. We assume that capital income is not taxed.20 The government uses its revenues to finance the payment of unemployment benefits and of the lump-sum transfer g, which may be viewed as a publicly provided rival good.21 Therefore, the government budget constraint is $$\sum _{i}\sum _{j}b_{ij}U_{ij}+g\sum _{i}\sum _{j}Q_{ij}=t\sum _{i} \sum _{j}w_{ij}E_{ij}.$$ (12) The left-hand side of equation (12) corresponds to government expenditures, given by the sum of total unemployment benefits and lump-sum transfers. The right-hand side corresponds to government revenues. We will treat bij and g as exogenous and let t adjust to satisfy (12).22 In the comparative static simulations of Section 4.2, we set the values of bij and g to their baseline values, and let t adjust in response to migration.23 3.4. Equilibrium Job-Creation Conditions. Combining the Bellman equations (6) and (7), along with the free entry condition $$J_{i}^{V}=0$$, we derive, for each labor market i, a relationship between labor market tightness θi and the expected present discounted value of the job surplus to the firm: $$q(\theta _i)\sum _{j\in \left\lbrace N,I\right\rbrace }\varphi _{ij}\frac{\pi _{ij}p_{i}-w_{ij}}{r+s_{ij}}-c_{i}=0.$$ (13) This can be seen as a job creation condition. It states that the flow cost of an open vacancy ci must be equal to the expected profit from a job filled with either a native or a migrant, πijpi − wij, weighted by the probability of the candidate being either a native or an immigrant φij, discounted at the specific effective discount rate r + sij, and multiplied by the probability of the vacancy being filled q(θi). The expected surplus to the firm from opening a vacancy can be high because market tightness is low, because the worker has high productivity πij, because he or she is paid a low wage wij, or because he or she has a low separation rate sij. This points at two channels through which immigrants affect labor markets for natives. If immigrants are paid a lower wage than natives with the same productivity, an increase in their share φiI increases the firm’s surplus and in equilibrium it must increase job creation and labor market tightness θi. However, if immigrants have larger separation rates sij, an increase in their share φiI decreases the firm’s surplus and induces less job creation. Wage Equations. Substituting the value functions (9) and (8) into (10), and because the free entry condition implies $$J_{ij}^{F}=( \pi _{ij}p_{i}-w_{ij}) /( r+s_{ij})$$ from (7), we can write the wage rate as \begin{eqnarray} w_{ij} &=& \beta \frac{r+s_{ij}+m\left( \theta _{i}\right) }{( r+s_{ij}) \left[ 1-t\left( 1-\beta \right) \right] +\beta m( \theta _{i}) }\pi _{ij}p_{i} \nonumber\\ &&+\,\left( 1-\beta \right) \frac{r+s_{ij}}{( r+s_{ij}) \left[ 1-t\left( 1-\beta \right) \right] +\beta m( \theta _{i}) }( b_{ij}+h_{ij}) . \end{eqnarray} (14) The lower the worker’s bargaining power β, the closer the wage is to the outside option. If β = 0, wij = (bij + hij)/(1 − t), which is exactly the outside option. As β approaches unity, the worker’s income approaches the product of her labor πijpi and the outside option becomes irrelevant. Moreover, the tighter the market, the larger the weight on πijpi (given that m΄(θi) > 0), because workers have a stronger effective bargaining position.24 It is also straightforward to show that, for a given equilibrium value of labor market tightness, higher separation rates are associated with lower wages. If we adjust the separation rates of two groups in such a way that market tightness is unaffected, the group with a higher separation rate is going to have lower equilibrium wages. Equations (13) and (14) show that heterogeneity between native and immigrant workers in their productivity πij and in their separation rates sij (to be understood as including remigration probabilities) has effects operating in a similar way, although in opposite directions. Lower productivity of migrants and higher separation rates represent a downward shift of the job creation curve in a graph relating wages and labor market tightness. A lower outside option hij also commands lower wages. Definition of Equilibrium. The equations above define a set of ten equilibrium conditions: one first-order condition governing the optimal capital stock (2), two profit maximizing conditions on goods markets (3) and (4), the government budget constraint (12), two job-creation conditions (13), and four wage equations (14). We use them to solve for ten equilibrium values: $$\lbrace K;p_{L},p_{H};t;\theta _{L},\theta _{H};w_{\mathit {LN}},w_{\mathit {LI}},w_{\mathit {HN}},w_{\mathit {HI}}\rbrace .$$ Knowing θi, we can get Uij and Eij from (11). Choosing the price of the final output good as the numéraire implies a restriction on goods prices pL and pH, which makes either (3) or (4) redundant by Walras’ Law.25 Existence and Uniqueness. As in other applications of search-and-matching models, existence requires parameter constellations that ensure that the surplus from a filled job is nonnegative (Pissarides 2000). In our Online Appendix, we discuss sufficient conditions for existence. In particular, we require πij(1 − t) > bij + hij, which implies a positive match surplus.26 For uniqueness, we additionally need the value of ρ and the flow value of vacancy posting to be sufficiently high. Necessary conditions are difficult to derive, given the complicated feedback mechanisms in the model. However, assuming a joint normal distribution, we have drawn 1,000 artificial economies that reproduce our sample of 20 OECD countries in terms of means and variances of targeted moments. We find that an equilibrium exists in all cases. Moreover, our numerical algorithm always converges to the same equilibria regardless of whether we choose very high or very low initial values for our endogenous variables. 3.5. Analytical Results Without a Public Sector The model outlined above captures several mechanisms through which natives’ outcomes are affected by the characteristics and size of the immigrant population. It is too complex for a full-fledged analytical solution. Therefore, we analyze it numerically. However, before we do so, we present analytical results for a simplified version. Proposition 1. Let us abstract from a public sector so that g = bij = 0, and assume natives and immigrants are identical except for the possibility that immigrants have worse outside options so that sij = si, πij = 1, and hiI < 0. Then, the model implies: an inflow of immigrants with the same skill composition as natives increases wages and decreases unemployment rates of natives, and therefore increases native welfare; an inflow of immigrants of skill i will unambiguously benefit natives of skill i΄ ≠ i. Depending on parameters, it may also benefit natives of skill i; a worsening of the outside option of immigrants increases wages of natives and decreases unemployment rates for all workers and increases welfare of natives. Proof. See Appendix A. Result (i) is relatively straightforward. In a model where immigrants have worse outside options than natives (but have the same productivity and break-up rates), immigrants affect natives through skill complementarity and through their effect on vacancy creation. The skill complementarity channel is inactive if immigrants have the same skill distribution as natives. The job creation channel is driven by immigrants’ lower outside option, implying the firm’s surplus is larger. A higher share of immigrants, therefore, encourages firms to create more vacancies. The resulting tighter labor market implies lower unemployment rates and higher wages for natives. The intuition for (ii) is also straightforward: Without a government, an inflow of immigrants of skill i will affect natives of skill i΄ ≠ i only through the factor complementarity channel, which is unambiguously positive. On the other hand, this model cannot deliver sharp predictions concerning the effect on natives of the same skill as immigrants. The reason is that there are two counteracting effects at work: a factor competition effect (negative for natives) and a vacancy creation effect (positive for natives). The latter will tend to dominate when natives have high unemployment rates and when wage gaps between immigrants and natives are large. The result in (iii) is driven by the same mechanism as (i): The surplus from the match the firm gets is a negative function of the outside option of the worker. And because vacancies cannot be directed to immigrants or natives, the additional vacancies benefit natives as well. Although Proposition 1 illustrates effects already present in Chassamboulli and Palivos (2014), the next result is not part of their analysis. Proposition 2. Let us abstract from a public sector so that g = bij = 0, and assume natives and immigrants are identical except for separation rates so that hiI = 0, πij = 1, and siI > siN. Then, the model implies: an inflow of immigrants with the same skill composition as natives decreases wages and increases unemployment rates of all natives, therefore decreasing native welfare; an inflow of immigrants of skill i will unambiguously reduce the welfare of natives of skill i and may have either a positive or a negative effect on natives of skill i΄ ≠ i; an increase in the separation rate for immigrants negatively affects welfare of all natives, through both wages and unemployment rates. Proof. See intuition below and further details in Appendix A. The intuition for the result in (i) above is the same (in the opposite direction) as the intuition for result (i) of Proposition 1. The only effect of a balanced immigrant inflow is brought about by the vacancy creation effect, which is negative in this case because the value to the firm of a vacancy matched with an immigrant is lower than the value of one matched with a native due to immigrants’ higher separation rates. Here, a larger number of immigrants imply that the firm’s expected surplus from a match is lower, which reduces the number of posted vacancies and lowers market tightness, putting downward pressure on wages and upward pressure on unemployment of natives. The first part of the result in (ii) arises from negative effects driven by both the factor competition and the vacancy creation channels. The effect on natives of the other skill type is indeterminate and depends on whether the inflow of immigrants of the other type results in an increase or decrease in the number of filled jobs of that type. Result (iii) follows the same intuition: If immigrants have higher separation rates, expected surplus and welfare for workers of the same skill class will be lower. Through production complementarity, there will also be a spillover effect for natives of different skills. The two propositions above illustrate the mechanisms at work in the labor markets of our model and emphasize the importance of immigrants’ outside options and separation rates in determining their impact on natives. Next, we will simulate welfare effects using our fully fledged model and employ country-level moments for the calibration of the parameters. 4. Quantitative Analysis We parameterize the model for each of the 20 countries included in our analysis. Our main object of interest is group-specific per-capita welfare $$\mathcal {W}_{ij}$$: $$\mathcal {W}_{ij}=(1-U_{ij})(1-t)w_{ij}+U_{ij}(b_{ij}+h_{ij})+rk_{ij}+g.$$ (15) It consists of four parts: (i) after-tax income multiplied by the probability of being employed, (ii) the unemployment benefit and the nonmonetary utility of being jobless multiplied by the probability of being unemployed, (iii) capital income, and (iv) the lump-sum transfer g. We are also interested in average native or immigrant welfare, which we define as follows: $$\mathcal {W}_{j}=\sum _{i}(Q_{ij}/\sum _{i}Q_{ij})\mathcal {W}_{ij}$$. 4.1. Calibration External Parameters. In the calibration, we tie model parameters to empirical counterparts and moments obtained from the data. First, we set unemployment benefits bij equal to the net wage wij(1 − t) times the observable country-specific replacement rate ϱ so that bij = ϱwij(1 − t). Second, we assume all capital in a country in the premigration equilibrium to be native owned so that $${\bar{K}}=K$$. We determine this value using information on the user cost of capital and on the observable capital share, α. Because our small open economy assumption fixes the return to capital, and capital per person does not vary in the comparative statics, the assumption that domestic capital is fully native owned is without loss of generality. GDP is denoted by Y so that $${\bar{K}}=\alpha Y/( r+\delta )$$. Third, we normalize cL = 0.5.27 This leaves us with a total of 27 exogenous parameters to be determined: {Qij, sij, πij, hiI, ϱ, cH, ξ, A, x, G, β, ε, ρ, r, δ, α, ψ}, with i ∈ {H, L} and j ∈ {N, I}.28 There are two types of parameters in the model. Some can be directly equated to their empirical counterparts or can be taken from the literature. Others are obtained by matching a set of moments in the data. Moreover, although most model parameters vary across countries, some are assumed to be fixed. Table 2 below lists those model parameters that we take from the literature or observe directly in standard databases. We follow Petrongolo and Pissarides (2001) and most of the search literature in setting the bargaining power of workers, β, equal to the elasticity of the matching function, ε, ensuring the Hosios condition is met. The parameter, ρ, determining the elasticity of substitution between the high-skill-intensive and the low-skill-intensive good is set in line with Ottaviano and Peri (2012) at ρ = 0.5, which corresponds to an elasticity of 2. The user cost of capital (r + δ) is about 12% per year, or about 1% per month, following Chassamboulli and Palivos (2014) and related papers in the literature. Table 2. Parameters taken from available data or the literature. Parameter Description Mean S.D. Source Parameters without country variation β Worker bargaining power 0.5 n.a. Petrongolo and Pissarides (2001) ε Matching elasticity 0.5 n.a. Petrongolo and Pissarides (2001) ρ Parameter governing the substitution elasticity 0.5 n.a. Ottaviano and Peri (2012) r Interest rate (monthly) 0.004 n.a. Chassamboulli and Palivos (2014) δ Depreciation rate (monthly) 0.0061 n.a. Chassamboulli and Palivos (2014) ψ Remigration rate 0.0100 n.a. OECD International Migration (monthly) Outlook Parameters varying across countries ϱ Replacement rate 0.39 0.13 OECD Benefits and Wages α Capital share 0.35 0.05 OECD Labour Cost Indicators $$Q_{\mathit {LN}}$$ Low-skilled natives 0.72 0.07 Eurostat, Census, HILDA $$Q_{\mathit {HN}}$$ High-skilled natives 0.28 0.07 Eurostat, Census, HILDA $$Q_{\mathit {LI}}$$ Low-skilled immigrants 0.15 0.08 Eurostat, Census, HILDA $$Q_{\mathit {HI}}$$ High-skilled immigrants 0.06 0.05 Eurostat, Census, HILDA Parameter Description Mean S.D. Source Parameters without country variation β Worker bargaining power 0.5 n.a. Petrongolo and Pissarides (2001) ε Matching elasticity 0.5 n.a. Petrongolo and Pissarides (2001) ρ Parameter governing the substitution elasticity 0.5 n.a. Ottaviano and Peri (2012) r Interest rate (monthly) 0.004 n.a. Chassamboulli and Palivos (2014) δ Depreciation rate (monthly) 0.0061 n.a. Chassamboulli and Palivos (2014) ψ Remigration rate 0.0100 n.a. OECD International Migration (monthly) Outlook Parameters varying across countries ϱ Replacement rate 0.39 0.13 OECD Benefits and Wages α Capital share 0.35 0.05 OECD Labour Cost Indicators $$Q_{\mathit {LN}}$$ Low-skilled natives 0.72 0.07 Eurostat, Census, HILDA $$Q_{\mathit {HN}}$$ High-skilled natives 0.28 0.07 Eurostat, Census, HILDA $$Q_{\mathit {LI}}$$ Low-skilled immigrants 0.15 0.08 Eurostat, Census, HILDA $$Q_{\mathit {HI}}$$ High-skilled immigrants 0.06 0.05 Eurostat, Census, HILDA Notes: We normalize the size of the native labor force to unity: $$Q_{\mathit {LN}}+Q_{\mathit {HN}}=1$$. Data sources: see Appendix B for details. View Large Table 2. Parameters taken from available data or the literature. Parameter Description Mean S.D. Source Parameters without country variation β Worker bargaining power 0.5 n.a. Petrongolo and Pissarides (2001) ε Matching elasticity 0.5 n.a. Petrongolo and Pissarides (2001) ρ Parameter governing the substitution elasticity 0.5 n.a. Ottaviano and Peri (2012) r Interest rate (monthly) 0.004 n.a. Chassamboulli and Palivos (2014) δ Depreciation rate (monthly) 0.0061 n.a. Chassamboulli and Palivos (2014) ψ Remigration rate 0.0100 n.a. OECD International Migration (monthly) Outlook Parameters varying across countries ϱ Replacement rate 0.39 0.13 OECD Benefits and Wages α Capital share 0.35 0.05 OECD Labour Cost Indicators $$Q_{\mathit {LN}}$$ Low-skilled natives 0.72 0.07 Eurostat, Census, HILDA $$Q_{\mathit {HN}}$$ High-skilled natives 0.28 0.07 Eurostat, Census, HILDA $$Q_{\mathit {LI}}$$ Low-skilled immigrants 0.15 0.08 Eurostat, Census, HILDA $$Q_{\mathit {HI}}$$ High-skilled immigrants 0.06 0.05 Eurostat, Census, HILDA Parameter Description Mean S.D. Source Parameters without country variation β Worker bargaining power 0.5 n.a. Petrongolo and Pissarides (2001) ε Matching elasticity 0.5 n.a. Petrongolo and Pissarides (2001) ρ Parameter governing the substitution elasticity 0.5 n.a. Ottaviano and Peri (2012) r Interest rate (monthly) 0.004 n.a. Chassamboulli and Palivos (2014) δ Depreciation rate (monthly) 0.0061 n.a. Chassamboulli and Palivos (2014) ψ Remigration rate 0.0100 n.a. OECD International Migration (monthly) Outlook Parameters varying across countries ϱ Replacement rate 0.39 0.13 OECD Benefits and Wages α Capital share 0.35 0.05 OECD Labour Cost Indicators $$Q_{\mathit {LN}}$$ Low-skilled natives 0.72 0.07 Eurostat, Census, HILDA $$Q_{\mathit {HN}}$$ High-skilled natives 0.28 0.07 Eurostat, Census, HILDA $$Q_{\mathit {LI}}$$ Low-skilled immigrants 0.15 0.08 Eurostat, Census, HILDA $$Q_{\mathit {HI}}$$ High-skilled immigrants 0.06 0.05 Eurostat, Census, HILDA Notes: We normalize the size of the native labor force to unity: $$Q_{\mathit {LN}}+Q_{\mathit {HN}}=1$$. Data sources: see Appendix B for details. View Large An important parameter is the exogenous remigration rate ψ for immigrants,29 which accounts for a major part of the difference between immigrant and native separation rates. OECD (2008) presents various estimates of remigration rates over the first five years since arrival. Unfortunately, there are such data for very few countries, which prevent us from including worker-type or country-specific rates. In our baseline calibration, for each county, we use the median rate, but we also produce results based on the high or low values reported in OECD (2008). The cross-country median is 45% (close to the remigration rate in the United Kingdom).30 These five-year rates imply that monthly separation rates for migrants are about 1 percentage point higher than for natives.31 Table 2 also presents means and standard deviations of exogenous parameters we take from the data that vary by country. We use data on the average replacement rate, ϱ, from the OECD Benefits and Wages data base. We allow capital shares, α, to vary by country. Finally, we use observed data on immigrant stocks, Qij. Without loss of generality, we normalize the native labor force of each country to one.32 Calibration of Unobserved Model Parameters. We pin down the remaining parameters of the model to ensure the baseline equilibrium of our model matches a number of empirical moments. We have 11 such moments (Table 3), but need to determine 15 parameters {sij, πij, hiI, cH, ξ, A, x, G}.33 Thus, we face an identification problem. It arises because the same combination of wages and unemployment rates for natives and immigrants of each skill type can be obtained with different combinations of break-up rates sij, productivity levels πij, and values of unemployment hiI. Table 3. Matched moments. Moment Source Mean S.D. Moments without country variation Average job duration, low skilled (months) Chassamboulli and Palivos (2014) 29.4 n.a. Average job duration, high skilled (months) Chassamboulli and Palivos (2014) 52.6 n.a. Moments varying across countries Native wage premium, low skilled EU-SILC, Censuses, HILDA 1.179 0.112 Native wage premium, high skilled EU-SILC, Censuses, HILDA 1.177 0.146 Skilled-unskilled wage ratio, native workers EU-SILC, Censuses, HILDA 1.541 0.227 Unemployment rate low-skilled natives EU and Canadian LFS, CPS, HILDA 0.082 0.035 Unemployment rate low-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.124 0.046 Unemployment rate high-skilled natives EU and Canadian LFS, CPS, HILDA 0.040 0.022 Unemployment rate high-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.079 0.034 Government expenditures as % of GDP IMF 0.453 0.059 Real per capita GDP, US = 1 (PPP) World Bank WDI 0.823 0.289 Moment Source Mean S.D. Moments without country variation Average job duration, low skilled (months) Chassamboulli and Palivos (2014) 29.4 n.a. Average job duration, high skilled (months) Chassamboulli and Palivos (2014) 52.6 n.a. Moments varying across countries Native wage premium, low skilled EU-SILC, Censuses, HILDA 1.179 0.112 Native wage premium, high skilled EU-SILC, Censuses, HILDA 1.177 0.146 Skilled-unskilled wage ratio, native workers EU-SILC, Censuses, HILDA 1.541 0.227 Unemployment rate low-skilled natives EU and Canadian LFS, CPS, HILDA 0.082 0.035 Unemployment rate low-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.124 0.046 Unemployment rate high-skilled natives EU and Canadian LFS, CPS, HILDA 0.040 0.022 Unemployment rate high-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.079 0.034 Government expenditures as % of GDP IMF 0.453 0.059 Real per capita GDP, US = 1 (PPP) World Bank WDI 0.823 0.289 Notes: All shares refer to working age population, aged 15–64 years. For unemployment rates, we use 2005–2011 averages. See Appendix B for details. All moments are constructed for each of our 20 countries. View Large Table 3. Matched moments. Moment Source Mean S.D. Moments without country variation Average job duration, low skilled (months) Chassamboulli and Palivos (2014) 29.4 n.a. Average job duration, high skilled (months) Chassamboulli and Palivos (2014) 52.6 n.a. Moments varying across countries Native wage premium, low skilled EU-SILC, Censuses, HILDA 1.179 0.112 Native wage premium, high skilled EU-SILC, Censuses, HILDA 1.177 0.146 Skilled-unskilled wage ratio, native workers EU-SILC, Censuses, HILDA 1.541 0.227 Unemployment rate low-skilled natives EU and Canadian LFS, CPS, HILDA 0.082 0.035 Unemployment rate low-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.124 0.046 Unemployment rate high-skilled natives EU and Canadian LFS, CPS, HILDA 0.040 0.022 Unemployment rate high-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.079 0.034 Government expenditures as % of GDP IMF 0.453 0.059 Real per capita GDP, US = 1 (PPP) World Bank WDI 0.823 0.289 Moment Source Mean S.D. Moments without country variation Average job duration, low skilled (months) Chassamboulli and Palivos (2014) 29.4 n.a. Average job duration, high skilled (months) Chassamboulli and Palivos (2014) 52.6 n.a. Moments varying across countries Native wage premium, low skilled EU-SILC, Censuses, HILDA 1.179 0.112 Native wage premium, high skilled EU-SILC, Censuses, HILDA 1.177 0.146 Skilled-unskilled wage ratio, native workers EU-SILC, Censuses, HILDA 1.541 0.227 Unemployment rate low-skilled natives EU and Canadian LFS, CPS, HILDA 0.082 0.035 Unemployment rate low-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.124 0.046 Unemployment rate high-skilled natives EU and Canadian LFS, CPS, HILDA 0.040 0.022 Unemployment rate high-skilled immigrants EU and Canadian LFS, CPS, HILDA 0.079 0.034 Government expenditures as % of GDP IMF 0.453 0.059 Real per capita GDP, US = 1 (PPP) World Bank WDI 0.823 0.289 Notes: All shares refer to working age population, aged 15–64 years. For unemployment rates, we use 2005–2011 averages. See Appendix B for details. All moments are constructed for each of our 20 countries. View Large First, we standardize the effectiveness of natives such that πiN = 1. In order to solve the indeterminacy problem, we need to assume that immigrants have a certain relative effectiveness vis-à-vis natives. Although relative effectiveness is hard to measure, we begin by considering the case in which—once we control for skills—immigrants and natives have the same productivity; namely, πiI = 1. As we allow the empirical moments in the data to determine sij and hiI, even with identical effectiveness of immigrants and natives, our model is rich enough to capture a nontrivial effect of immigrants on job creation. Moreover, empirical results by LaLonde and Topel (1991), Borjas and Friedberg (2009), and the survey by Kerr and Kerr (2011) show immigrants are paid less than natives, even after controlling for observable productivity drivers such as education and language. Thus, we consider the skill level as the main determinant of productivity and assume that wage differentials are driven by other types of heterogeneity. We investigate the effects of allowing for productivity differences between immigrants and natives in a sensitivity analysis in Section 4.3.1. We calibrate the remaining parameters so that our model exactly reproduces the set of moments for each country. Table 4 presents average and cross-country standard deviations of the calibrated parameters. Differences in unemployment rates between natives and immigrants are mainly explained by the higher separation rates of immigrants, due to remigration. After accounting for average international remigration probabilities, in fact, differences in pure separation rates are small for both low-skilled and high-skilled workers and are compatible with larger internal remigration shocks for immigrants. We use data on international remigration only, because we lack reliable data on internal migration, but internal mobility may play a role as well. To the extent that internal mobility is higher for immigrants, our measure of ψj may underestimate the true value. The parameters $$h_{\mathit {LI}}$$ and $$h_{\mathit {HI}}$$ are mostly negative, capturing worse outside options for immigrants. This is revealed by the lower equilibrium wage for immigrants.34 Three exceptions are high-skilled immigrants in Australia, Switzerland, and the United States, for which the values of $$h_{\mathit {HI}}$$ are positive. Table 4. Calibrated parameter values. Parameter Description Mean S.D. ξ Match efficiency parameter 0.419 0.182 A Total factor productivity 0.569 0.110 x Low skill share in production of intermediates 0.514 0.048 $$c_{\mathit {H}}$$ Cost of a high skill vacancy 0.723 0.552 g Public expenditures (per capita) 0.328 0.119 $$\bar{s}_{\mathit {LN}}$$ Monthly job separation rate, low-skilled natives 0.030 0.003 $$\bar{s}_{\mathit {LI}}$$ Monthly job separation rate, low-skilled immigrants 0.040 0.012 $$\bar{s}_{\mathit {HN}}$$ Monthly job separation rate, high-skilled natives 0.016 0.002 $$\bar{s}_{\mathit {HI}}$$ Monthly job separation rate, high-skilled immigrants 0.025 0.009 $$h_{\mathit {LI}}$$ Unemployment disutility for low-skilled immigrants −0.973 1.091 $$h_{\mathit {HI}}$$ Unemployment disutility for high-skilled immigrants −1.602 1.246 Parameter Description Mean S.D. ξ Match efficiency parameter 0.419 0.182 A Total factor productivity 0.569 0.110 x Low skill share in production of intermediates 0.514 0.048 $$c_{\mathit {H}}$$ Cost of a high skill vacancy 0.723 0.552 g Public expenditures (per capita) 0.328 0.119 $$\bar{s}_{\mathit {LN}}$$ Monthly job separation rate, low-skilled natives 0.030 0.003 $$\bar{s}_{\mathit {LI}}$$ Monthly job separation rate, low-skilled immigrants 0.040 0.012 $$\bar{s}_{\mathit {HN}}$$ Monthly job separation rate, high-skilled natives 0.016 0.002 $$\bar{s}_{\mathit {HI}}$$ Monthly job separation rate, high-skilled immigrants 0.025 0.009 $$h_{\mathit {LI}}$$ Unemployment disutility for low-skilled immigrants −0.973 1.091 $$h_{\mathit {HI}}$$ Unemployment disutility for high-skilled immigrants −1.602 1.246 Notes: Summary statistics of parameters calibrated on empirical moments for 20 countries. Separation rates exclude remigration rates. View Large Table 4. Calibrated parameter values. Parameter Description Mean S.D. ξ Match efficiency parameter 0.419 0.182 A Total factor productivity 0.569 0.110 x Low skill share in production of intermediates 0.514 0.048 $$c_{\mathit {H}}$$ Cost of a high skill vacancy 0.723 0.552 g Public expenditures (per capita) 0.328 0.119 $$\bar{s}_{\mathit {LN}}$$ Monthly job separation rate, low-skilled natives 0.030 0.003 $$\bar{s}_{\mathit {LI}}$$ Monthly job separation rate, low-skilled immigrants 0.040 0.012 $$\bar{s}_{\mathit {HN}}$$ Monthly job separation rate, high-skilled natives 0.016 0.002 $$\bar{s}_{\mathit {HI}}$$ Monthly job separation rate, high-skilled immigrants 0.025 0.009 $$h_{\mathit {LI}}$$ Unemployment disutility for low-skilled immigrants −0.973 1.091 $$h_{\mathit {HI}}$$ Unemployment disutility for high-skilled immigrants −1.602 1.246 Parameter Description Mean S.D. ξ Match efficiency parameter 0.419 0.182 A Total factor productivity 0.569 0.110 x Low skill share in production of intermediates 0.514 0.048 $$c_{\mathit {H}}$$ Cost of a high skill vacancy 0.723 0.552 g Public expenditures (per capita) 0.328 0.119 $$\bar{s}_{\mathit {LN}}$$ Monthly job separation rate, low-skilled natives 0.030 0.003 $$\bar{s}_{\mathit {LI}}$$ Monthly job separation rate, low-skilled immigrants 0.040 0.012 $$\bar{s}_{\mathit {HN}}$$ Monthly job separation rate, high-skilled natives 0.016 0.002 $$\bar{s}_{\mathit {HI}}$$ Monthly job separation rate, high-skilled immigrants 0.025 0.009 $$h_{\mathit {LI}}$$ Unemployment disutility for low-skilled immigrants −0.973 1.091 $$h_{\mathit {HI}}$$ Unemployment disutility for high-skilled immigrants −1.602 1.246 Notes: Summary statistics of parameters calibrated on empirical moments for 20 countries. Separation rates exclude remigration rates. View Large 4.2. Results In our simulations, we focus on the welfare effects of immigrants on native workers. We study four scenarios, having year 2011 as our baseline year: (i) an increase in the stock of migrants by 1% of the labor force, holding skill structures constant, (ii) an inflow as in (i) but assuming all new immigrants are unskilled, (iii) a hypothetical situation in which all foreign-born workers left their host countries, and (iv) immigration as observed between 2011 and 2014. 4.2.1. The Effects of Immigration With Constant Skill Composition We begin by simulating the welfare effects of an increase in the immigrant stock by 1% of the baseline labor force relative to the 2011 baseline level, leaving the skill composition of immigrants unchanged. In other words, we inflate the immigrant labor force holding skill shares constant so that the proportion of high skilled among immigrants remains the same before and after the change. We use this setup to study the welfare results obtained from progressively richer models to provide insights regarding different mechanisms. Beginning with the simplest version in which immigrants are essentially identical to natives within skill groups and where there is no government, we gradually add all of the features of our framework. This procedure illustrates the relative role of each “ingredient” in shaping the effect on native welfare. To save space, Table 5 provides results for two countries only, the United States and Germany, in each of the increasingly complex models. We report welfare effects on natives and immigrants in all countries for the complete model in Table 6. Table C.2 in our Appendix provides full country coverage on the stripped-down model variants. Table 5. Native welfare effects of a 1 percentage point increase in migration: different models. United States Germany $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W} _{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Model 1: Only complementarity effects 0.00% 0.01% −0.02% 0.00% −0.05% 0.11% Model 2: Adding wage heterogeneity 0.04% 0.08% 0.00% 0.07% 0.03% 0.17% Model 3: Adding unemployment heterogeneity 0.04% 0.08% 0.00% 0.02% −0.03% 0.12% Model 4: Adding redistribution through bij 0.05% 0.08% 0.01% 0.02% −0.02% 0.12% Model 5: Adding redistribution through g 0.05% 0.06% 0.03% −0.01% −0.03% 0.04% United States Germany $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W} _{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Model 1: Only complementarity effects 0.00% 0.01% −0.02% 0.00% −0.05% 0.11% Model 2: Adding wage heterogeneity 0.04% 0.08% 0.00% 0.07% 0.03% 0.17% Model 3: Adding unemployment heterogeneity 0.04% 0.08% 0.00% 0.02% −0.03% 0.12% Model 4: Adding redistribution through bij 0.05% 0.08% 0.01% 0.02% −0.02% 0.12% Model 5: Adding redistribution through g 0.05% 0.06% 0.03% −0.01% −0.03% 0.04% View Large Table 5. Native welfare effects of a 1 percentage point increase in migration: different models. United States Germany $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W} _{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Model 1: Only complementarity effects 0.00% 0.01% −0.02% 0.00% −0.05% 0.11% Model 2: Adding wage heterogeneity 0.04% 0.08% 0.00% 0.07% 0.03% 0.17% Model 3: Adding unemployment heterogeneity 0.04% 0.08% 0.00% 0.02% −0.03% 0.12% Model 4: Adding redistribution through bij 0.05% 0.08% 0.01% 0.02% −0.02% 0.12% Model 5: Adding redistribution through g 0.05% 0.06% 0.03% −0.01% −0.03% 0.04% United States Germany $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W} _{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Model 1: Only complementarity effects 0.00% 0.01% −0.02% 0.00% −0.05% 0.11% Model 2: Adding wage heterogeneity 0.04% 0.08% 0.00% 0.07% 0.03% 0.17% Model 3: Adding unemployment heterogeneity 0.04% 0.08% 0.00% 0.02% −0.03% 0.12% Model 4: Adding redistribution through bij 0.05% 0.08% 0.01% 0.02% −0.02% 0.12% Model 5: Adding redistribution through g 0.05% 0.06% 0.03% −0.01% −0.03% 0.04% View Large Table 6. Welfare effects of a 1 percentage point increase in immigration: full model. Natives Incumbent immigrants Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_I$$ $$\mathcal {W}_{\mathit {LI}}$$ $$\mathcal {W}_{\mathit {HI}}$$ Australia 0.01% 0.06% −0.08% −0.01% 0.09% −0.11% Austria −0.03% −0.03% −0.03% 0.19% 0.20% 0.11% Belgium −0.02% −0.03% −0.01% 0.12% 0.12% 0.12% Canada 0.04% 0.08% −0.08% 0.08% 0.11% 0.03% Denmark 0.06% 0.11% −0.05% 0.18% 0.27% 0.10% Estonia 0.05% 0.07% 0.02% 0.24% 0.16% 0.37% France 0.02% 0.00% 0.05% 0.09% 0.09% 0.08% Germany −0.01% −0.03% 0.04% 0.06% 0.02% 0.20% Greece 0.07% 0.02% 0.18% 0.26% 0.22% 0.48% Ireland 0.05% 0.10% −0.03% 0.18% 0.16% 0.21% Italy 0.07% 0.05% 0.14% 0.37% 0.30% 0.81% Luxembourg −0.02% −0.03% −0.01% 0.04% 0.05% 0.02% Netherlands −0.01% −0.03% 0.02% 0.10% 0.07% 0.19% Portugal 0.08% 0.09% 0.07% 0.21% 0.15% 0.37% Slovenia 0.02% −0.04% 0.17% 0.04% 0.01% 0.22% Spain 0.04% −0.01% 0.12% 0.18% 0.10% 0.42% Sweden −0.02% −0.01% −0.04% 0.08% 0.10% 0.04% Switzerland −0.04% −0.03% −0.04% 0.00% 0.03% −0.06% United Kingdom 0.00% −0.03% 0.05% 0.06% −0.03% 0.21% United States 0.05% 0.06% 0.03% 0.09% 0.14% 0.03% Average 0.02% 0.02% 0.03% 0.13% 0.12% 0.19% Median 0.02% 0.00% 0.02% 0.10% 0.10% 0.16% Natives Incumbent immigrants Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_I$$ $$\mathcal {W}_{\mathit {LI}}$$ $$\mathcal {W}_{\mathit {HI}}$$ Australia 0.01% 0.06% −0.08% −0.01% 0.09% −0.11% Austria −0.03% −0.03% −0.03% 0.19% 0.20% 0.11% Belgium −0.02% −0.03% −0.01% 0.12% 0.12% 0.12% Canada 0.04% 0.08% −0.08% 0.08% 0.11% 0.03% Denmark 0.06% 0.11% −0.05% 0.18% 0.27% 0.10% Estonia 0.05% 0.07% 0.02% 0.24% 0.16% 0.37% France 0.02% 0.00% 0.05% 0.09% 0.09% 0.08% Germany −0.01% −0.03% 0.04% 0.06% 0.02% 0.20% Greece 0.07% 0.02% 0.18% 0.26% 0.22% 0.48% Ireland 0.05% 0.10% −0.03% 0.18% 0.16% 0.21% Italy 0.07% 0.05% 0.14% 0.37% 0.30% 0.81% Luxembourg −0.02% −0.03% −0.01% 0.04% 0.05% 0.02% Netherlands −0.01% −0.03% 0.02% 0.10% 0.07% 0.19% Portugal 0.08% 0.09% 0.07% 0.21% 0.15% 0.37% Slovenia 0.02% −0.04% 0.17% 0.04% 0.01% 0.22% Spain 0.04% −0.01% 0.12% 0.18% 0.10% 0.42% Sweden −0.02% −0.01% −0.04% 0.08% 0.10% 0.04% Switzerland −0.04% −0.03% −0.04% 0.00% 0.03% −0.06% United Kingdom 0.00% −0.03% 0.05% 0.06% −0.03% 0.21% United States 0.05% 0.06% 0.03% 0.09% 0.14% 0.03% Average 0.02% 0.02% 0.03% 0.13% 0.12% 0.19% Median 0.02% 0.00% 0.02% 0.10% 0.10% 0.16% Notes: All columns refer to our full model, that is, Model 5 as of Table 5. View Large Table 6. Welfare effects of a 1 percentage point increase in immigration: full model. Natives Incumbent immigrants Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_I$$ $$\mathcal {W}_{\mathit {LI}}$$ $$\mathcal {W}_{\mathit {HI}}$$ Australia 0.01% 0.06% −0.08% −0.01% 0.09% −0.11% Austria −0.03% −0.03% −0.03% 0.19% 0.20% 0.11% Belgium −0.02% −0.03% −0.01% 0.12% 0.12% 0.12% Canada 0.04% 0.08% −0.08% 0.08% 0.11% 0.03% Denmark 0.06% 0.11% −0.05% 0.18% 0.27% 0.10% Estonia 0.05% 0.07% 0.02% 0.24% 0.16% 0.37% France 0.02% 0.00% 0.05% 0.09% 0.09% 0.08% Germany −0.01% −0.03% 0.04% 0.06% 0.02% 0.20% Greece 0.07% 0.02% 0.18% 0.26% 0.22% 0.48% Ireland 0.05% 0.10% −0.03% 0.18% 0.16% 0.21% Italy 0.07% 0.05% 0.14% 0.37% 0.30% 0.81% Luxembourg −0.02% −0.03% −0.01% 0.04% 0.05% 0.02% Netherlands −0.01% −0.03% 0.02% 0.10% 0.07% 0.19% Portugal 0.08% 0.09% 0.07% 0.21% 0.15% 0.37% Slovenia 0.02% −0.04% 0.17% 0.04% 0.01% 0.22% Spain 0.04% −0.01% 0.12% 0.18% 0.10% 0.42% Sweden −0.02% −0.01% −0.04% 0.08% 0.10% 0.04% Switzerland −0.04% −0.03% −0.04% 0.00% 0.03% −0.06% United Kingdom 0.00% −0.03% 0.05% 0.06% −0.03% 0.21% United States 0.05% 0.06% 0.03% 0.09% 0.14% 0.03% Average 0.02% 0.02% 0.03% 0.13% 0.12% 0.19% Median 0.02% 0.00% 0.02% 0.10% 0.10% 0.16% Natives Incumbent immigrants Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_I$$ $$\mathcal {W}_{\mathit {LI}}$$ $$\mathcal {W}_{\mathit {HI}}$$ Australia 0.01% 0.06% −0.08% −0.01% 0.09% −0.11% Austria −0.03% −0.03% −0.03% 0.19% 0.20% 0.11% Belgium −0.02% −0.03% −0.01% 0.12% 0.12% 0.12% Canada 0.04% 0.08% −0.08% 0.08% 0.11% 0.03% Denmark 0.06% 0.11% −0.05% 0.18% 0.27% 0.10% Estonia 0.05% 0.07% 0.02% 0.24% 0.16% 0.37% France 0.02% 0.00% 0.05% 0.09% 0.09% 0.08% Germany −0.01% −0.03% 0.04% 0.06% 0.02% 0.20% Greece 0.07% 0.02% 0.18% 0.26% 0.22% 0.48% Ireland 0.05% 0.10% −0.03% 0.18% 0.16% 0.21% Italy 0.07% 0.05% 0.14% 0.37% 0.30% 0.81% Luxembourg −0.02% −0.03% −0.01% 0.04% 0.05% 0.02% Netherlands −0.01% −0.03% 0.02% 0.10% 0.07% 0.19% Portugal 0.08% 0.09% 0.07% 0.21% 0.15% 0.37% Slovenia 0.02% −0.04% 0.17% 0.04% 0.01% 0.22% Spain 0.04% −0.01% 0.12% 0.18% 0.10% 0.42% Sweden −0.02% −0.01% −0.04% 0.08% 0.10% 0.04% Switzerland −0.04% −0.03% −0.04% 0.00% 0.03% −0.06% United Kingdom 0.00% −0.03% 0.05% 0.06% −0.03% 0.21% United States 0.05% 0.06% 0.03% 0.09% 0.14% 0.03% Average 0.02% 0.02% 0.03% 0.13% 0.12% 0.19% Median 0.02% 0.00% 0.02% 0.10% 0.10% 0.16% Notes: All columns refer to our full model, that is, Model 5 as of Table 5. View Large Table 5 begins with the simulated effects of Model 1, which features the classical complementarity only. In this case, by setting hij = 0; siI = siN; bij = 0; and g = 0, we eliminate the effects of any labor market heterogeneity and the public sector. This setup corresponds to more traditional models such as those by Borjas (2003), Ottaviano and Peri (2012), or Docquier et al. (2014).35 We find overall welfare effects on natives $$\mathcal {W}_{N}$$ are positive but very close to zero both in Germany and the United States. However, effects on specific skill groups are more pronounced. High-skilled natives in Germany see a 0.11% increase in their welfare, whereas low-skilled natives lose 0.05%. In the United States, high-skilled individuals lose 0.02%, whereas low-skilled individuals gain 0.01%. This pattern reflects the fact that, in the United States, the skill composition of the stock of immigrants approximately resembled that of natives as of 2011, whereas in Germany it was biased toward unskilled workers. Model 2 accounts for observed immigrant-native wage differences by allowing for differences in the outside option of immigrants and natives (i.e., hiI ≠ 0). This model is similar to Chassamboulli and Palivos (2014), adding the job creation effect of immigrants described in Proposition 1. In both the United States and Germany, this channel adds incentives to create jobs, meaning that immigration can lead to lower unemployment rates. Average native welfare increases by 0.07% in Germany and by 0.04% in the United States. Moreover, in both countries both skill groups benefit from immigration. When looking at all countries (Table C.2 in the Appendix), both skill groups experience gains in 14 out of 20 countries when the job creation channel is present. In the remaining six cases, a distributive conflict remains, often due to the skill composition of migrants being heavily tilted toward the high skilled, for whom the job creation channel is less important. Model 3 matches the heterogeneity in the ratio between natives’ and immigrants’ unemployment rates by allowing different separation rates (i.e., siI ≠ siN). Matches with migrants have a shorter expected duration as documented in the literature reviewed in Section 4.1. Whatever the reason for such short duration in a model with costly search, this feature weakens both the strength of the vacancy creation effect and of the complementarity channel. The introduction of this channel has a very small effect in the United States, whereas it reduces the total immigration surplus to less than a third in Germany. The reason lies in the high unemployment rates among German immigrants relative to natives, which implies higher separation rates for immigrants in the model, and hence a much reduced job creation effect from immigration. Unemployment rates of natives and immigrants are almost identical in the United States; hence, this channel is not at work. Model 4 further adds unemployment benefits, (bij > 0), financed with taxes on labor income. Model 5, the most comprehensive variant, also includes the general redistribution channel with lump-sum transfers, (g > 0), financed by taxes. Both in Germany and in the United States, unemployment benefits generate relatively little redistribution and do not change welfare effects by much.36 Introducing other public expenditures matters more. This is particularly true in Germany, where the overall native welfare effect turns negative, mostly due to much lower gains for the high skilled. In the United States, public transfers are less relevant, so their introduction has no major effect on native welfare gains. Table C.2 shows that the presence of a redistributive welfare state is important in many other countries, turning an aggregate gain into a loss in 7 of 20 countries. Table 6 shows the welfare effects for all countries when using the full model (Model 5). Natives in most countries benefit from a marginal increase in the immigrant share of the labor force. However, in Austria, Belgium, Germany, Luxembourg, the Netherlands, Sweden and Switzerland, native welfare falls. In these cases, welfare gains turn negative for natives because of general redistribution, which plays a larger role than unemployment benefits. Countries with initially high unemployment rates (Italy, Greece, Portugal) are among those benefiting most from the job-creation channel. In all countries, welfare effects are relatively small in absolute value, ranging between −0.04% (Switzerland) and +0.08% (Portugal), averaging +0.02%. Table 6 also shows that incumbent immigrants benefit from additional immigration in most countries.37 They benefit strongly from the vacancy creation effect and do not suffer much from increased redistribution as their incomes are lower than those of natives. Therefore, in a non-Walrasian market, the vacancy creation effect can turn the conventional wisdom upside down: incumbent immigrants, even if potentially competing with new immigrants, may actually gain from immigration rather than being the group losing the most. 4.2.2. The Effects of Low-Skilled Immigration Cross-country differences in the native welfare effects discussed in the previous section depend not only on the labor market and institutional features of each country, but also on the type of shock we analyze. In order to isolate the first aspect and to investigate how institutions and labor markets of different countries may react to the same shock, we now look at the native welfare effects arising from an increase of 1 percentage point of the labor force,38 all made up of low-skilled immigrants. The size of the shock is the same as the one we analyze in Section 4.2.1, but the skill composition of the additional immigrants is different.39 Table 7 presents native welfare effects from this simulation, where we add this additional shock to our baseline (year 2011) calibrated model. Table 7. Native welfare effects of low skilled migration. Increase in the migrant stock $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 3.7% −0.02% −0.15% 0.22% Austria 4.4% −0.02% −0.07% 0.19% Belgium 4.6% −0.04% −0.14% 0.15% Canada 4.0% −0.03% −0.11% 0.21% Denmark 7.2% 0.01% −0.08% 0.21% Estonia 5.7% 0.01% −0.11% 0.21% France 6.6% 0.02% −0.07% 0.20% Germany 5.5% −0.01% −0.10% 0.20% Greece 6.1% 0.09% 0.00% 0.29% Ireland 5.5% −0.05% −0.18% 0.15% Italy 7.4% 0.09% 0.04% 0.31% Luxembourg 1.5% −0.05% −0.16% 0.13% Netherlands 6.1% −0.02% −0.12% 0.18% Portugal 9.0% 0.02% −0.06% 0.26% Slovenia 6.6% 0.03% −0.07% 0.26% Spain 4.6% 0.01% −0.12% 0.21% Sweden 4.6% −0.03% −0.12% 0.16% Switzerland 2.4% −0.03% −0.17% 0.20% United Kingdom 6.0% −0.02% −0.19% 0.20% United States 6.3% 0.02% −0.12% 0.24% Average 5.4% 0.00% −0.10% 0.21% Median 5.6% −0.02% −0.11% 0.20% Increase in the migrant stock $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 3.7% −0.02% −0.15% 0.22% Austria 4.4% −0.02% −0.07% 0.19% Belgium 4.6% −0.04% −0.14% 0.15% Canada 4.0% −0.03% −0.11% 0.21% Denmark 7.2% 0.01% −0.08% 0.21% Estonia 5.7% 0.01% −0.11% 0.21% France 6.6% 0.02% −0.07% 0.20% Germany 5.5% −0.01% −0.10% 0.20% Greece 6.1% 0.09% 0.00% 0.29% Ireland 5.5% −0.05% −0.18% 0.15% Italy 7.4% 0.09% 0.04% 0.31% Luxembourg 1.5% −0.05% −0.16% 0.13% Netherlands 6.1% −0.02% −0.12% 0.18% Portugal 9.0% 0.02% −0.06% 0.26% Slovenia 6.6% 0.03% −0.07% 0.26% Spain 4.6% 0.01% −0.12% 0.21% Sweden 4.6% −0.03% −0.12% 0.16% Switzerland 2.4% −0.03% −0.17% 0.20% United Kingdom 6.0% −0.02% −0.19% 0.20% United States 6.3% 0.02% −0.12% 0.24% Average 5.4% 0.00% −0.10% 0.21% Median 5.6% −0.02% −0.11% 0.20% Data sources: see Appendix B for details. View Large Table 7. Native welfare effects of low skilled migration. Increase in the migrant stock $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 3.7% −0.02% −0.15% 0.22% Austria 4.4% −0.02% −0.07% 0.19% Belgium 4.6% −0.04% −0.14% 0.15% Canada 4.0% −0.03% −0.11% 0.21% Denmark 7.2% 0.01% −0.08% 0.21% Estonia 5.7% 0.01% −0.11% 0.21% France 6.6% 0.02% −0.07% 0.20% Germany 5.5% −0.01% −0.10% 0.20% Greece 6.1% 0.09% 0.00% 0.29% Ireland 5.5% −0.05% −0.18% 0.15% Italy 7.4% 0.09% 0.04% 0.31% Luxembourg 1.5% −0.05% −0.16% 0.13% Netherlands 6.1% −0.02% −0.12% 0.18% Portugal 9.0% 0.02% −0.06% 0.26% Slovenia 6.6% 0.03% −0.07% 0.26% Spain 4.6% 0.01% −0.12% 0.21% Sweden 4.6% −0.03% −0.12% 0.16% Switzerland 2.4% −0.03% −0.17% 0.20% United Kingdom 6.0% −0.02% −0.19% 0.20% United States 6.3% 0.02% −0.12% 0.24% Average 5.4% 0.00% −0.10% 0.21% Median 5.6% −0.02% −0.11% 0.20% Increase in the migrant stock $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 3.7% −0.02% −0.15% 0.22% Austria 4.4% −0.02% −0.07% 0.19% Belgium 4.6% −0.04% −0.14% 0.15% Canada 4.0% −0.03% −0.11% 0.21% Denmark 7.2% 0.01% −0.08% 0.21% Estonia 5.7% 0.01% −0.11% 0.21% France 6.6% 0.02% −0.07% 0.20% Germany 5.5% −0.01% −0.10% 0.20% Greece 6.1% 0.09% 0.00% 0.29% Ireland 5.5% −0.05% −0.18% 0.15% Italy 7.4% 0.09% 0.04% 0.31% Luxembourg 1.5% −0.05% −0.16% 0.13% Netherlands 6.1% −0.02% −0.12% 0.18% Portugal 9.0% 0.02% −0.06% 0.26% Slovenia 6.6% 0.03% −0.07% 0.26% Spain 4.6% 0.01% −0.12% 0.21% Sweden 4.6% −0.03% −0.12% 0.16% Switzerland 2.4% −0.03% −0.17% 0.20% United Kingdom 6.0% −0.02% −0.19% 0.20% United States 6.3% 0.02% −0.12% 0.24% Average 5.4% 0.00% −0.10% 0.21% Median 5.6% −0.02% −0.11% 0.20% Data sources: see Appendix B for details. View Large The second column of Table 7 shows the increase in the immigrant stock from a shock that is as large as 1 percentage point of the labor force. The following columns show that welfare effects for the average native worker are very heterogeneous. Despite additional immigrants being all low skilled, in 9 out of our 20 countries average effects are positive, whereas they are negative in the remaining 11 countries. The average effect across all countries is very close to zero. The countries with positive effects include the United States (largely because of its relatively low taxation and low immigrant unemployment), France, Spain and Italy (because of the beneficial effects that immigration can have on labor markets where frictions are more severe). An additional inflow of low-skilled immigrants tends to hurt low-skilled natives and benefit high-skilled natives, showing that skill complementarity tends to be quantitatively more important than public transfers. 4.2.3. The Total Effects of Immigration In this section, instead of investigating the effects of a relatively small change in the immigrant share, we compare the status quo as of 2011 with a hypothetical autarky situation in which countries have no foreign-born workers. The left part of Table 8 presents the results. Countries that showed positive marginal effects in Table 6, such as Italy, Portugal, Greece and Ireland, are also among those exhibiting the largest gains in the status quo relative to the no immigration scenario. High native unemployment rates and large immigrant wage gaps lead to strong beneficial job creation effects. Moreover, the job creation effect has a much more important role when considering these substantial differences in immigration: We find positive overall effects in 19 out of our 20 countries, whereas only 13 countries show positive marginal effects. The median and average welfare effects of total immigration are both close to +1%, with magnitudes varying strongly across countries. Table 8. Native welfare effects of observed migration flows. Status quo vs. Autarky 2014 vs. 2011 Welfare effects Migrant shares High skilled Welfare effects Countries $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ 2011 2014 2011 2014 $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 21.0% 22.0% 42.9% 43.7% 0.06% 0.18% −0.16% Austria 1.77% 1.74% 1.94% 18.3% 19.8% 16.8% 29.4% 0.34% 1.04% −2.61% Belgium 1.70% 1.37% 2.30% 17.8% 18.9% 27.5% 30.4% 0.14% 0.31% −0.17% Canada 1.19% 1.79% −0.57% 19.9% 20.8% 32.2% 36.3% 0.28% 0.61% −0.70% Denmark 1.90% 2.39% 0.86% 12.0% 13.5% 46.8% 52.7% 0.23% 0.54% −0.42% Estonia 1.47% 1.47% 1.46% 14.7% 13.0% 36.3% 40.9% −0.04% 0.14% −0.36% France 0.77% 0.52% 1.27% 13.0% 13.0% 22.8% 28.1% 0.11% 0.33% −0.33% Germany 0.31% −0.07% 1.23% 15.3% 16.4% 18.7% 18.8% 0.02% 0.00% 0.07% Greece 2.02% 1.40% 3.51% 14.0% 12.7% 13.2% 15.6% −0.11% 0.05% −0.48% Ireland 1.77% 2.30% 0.95% 15.3% 16.3% 48.1% 50.1% 0.14% 0.31% −0.12% Italy 1.87% 1.64% 2.97% 11.8% 13.3% 11.0% 12.0% 0.22% 0.24% 0.15% Luxembourg 0.72% 0.45% 1.15% 39.1% 40.5% 32.2% 45.8% 0.62% 2.41% −2.09% Netherlands 0.48% 0.23% 0.98% 14.0% 14.0% 25.2% 24.9% −0.01% −0.02% 0.02% Portugal 1.27% 1.23% 1.41% 9.9% 10.3% 19.4% 24.9% 0.36% 0.57% −0.37% Slovenia 0.52% −0.20% 2.30% 13.1% 13.3% 9.7% 7.7% −0.03% −0.16% 0.28% Spain 1.90% 0.96% 3.43% 17.7% 15.9% 21.5% 24.3% −0.03% 0.23% −0.45% Sweden 0.63% 0.77% 0.34% 17.8% 19.8% 32.6% 36.7% 0.09% 0.35% −0.45% Switzerland −0.14% 0.04% −0.46% 29.2% 30.6% 30.6% 35.9% 0.07% 0.80% −1.18% United Kingdom 0.35% −0.22% 1.10% 14.2% 15.4% 31.3% 32.2% 0.09% 0.10% 0.07% United States 0.80% 0.97% 0.53% 13.5% 13.8% 31.7% 33.1% 0.08% 0.17% −0.05% Average 1.08% 1.00% 1.25% 17.1% 17.7% 27.5% 31.2% 0.13% 0.41% −0.47% Median 0.99% 1.10% 1.19% 15.0% 15.7% 29.1% 31.3% 0.09% 0.27% −0.35% Status quo vs. Autarky 2014 vs. 2011 Welfare effects Migrant shares High skilled Welfare effects Countries $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ 2011 2014 2011 2014 $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 21.0% 22.0% 42.9% 43.7% 0.06% 0.18% −0.16% Austria 1.77% 1.74% 1.94% 18.3% 19.8% 16.8% 29.4% 0.34% 1.04% −2.61% Belgium 1.70% 1.37% 2.30% 17.8% 18.9% 27.5% 30.4% 0.14% 0.31% −0.17% Canada 1.19% 1.79% −0.57% 19.9% 20.8% 32.2% 36.3% 0.28% 0.61% −0.70% Denmark 1.90% 2.39% 0.86% 12.0% 13.5% 46.8% 52.7% 0.23% 0.54% −0.42% Estonia 1.47% 1.47% 1.46% 14.7% 13.0% 36.3% 40.9% −0.04% 0.14% −0.36% France 0.77% 0.52% 1.27% 13.0% 13.0% 22.8% 28.1% 0.11% 0.33% −0.33% Germany 0.31% −0.07% 1.23% 15.3% 16.4% 18.7% 18.8% 0.02% 0.00% 0.07% Greece 2.02% 1.40% 3.51% 14.0% 12.7% 13.2% 15.6% −0.11% 0.05% −0.48% Ireland 1.77% 2.30% 0.95% 15.3% 16.3% 48.1% 50.1% 0.14% 0.31% −0.12% Italy 1.87% 1.64% 2.97% 11.8% 13.3% 11.0% 12.0% 0.22% 0.24% 0.15% Luxembourg 0.72% 0.45% 1.15% 39.1% 40.5% 32.2% 45.8% 0.62% 2.41% −2.09% Netherlands 0.48% 0.23% 0.98% 14.0% 14.0% 25.2% 24.9% −0.01% −0.02% 0.02% Portugal 1.27% 1.23% 1.41% 9.9% 10.3% 19.4% 24.9% 0.36% 0.57% −0.37% Slovenia 0.52% −0.20% 2.30% 13.1% 13.3% 9.7% 7.7% −0.03% −0.16% 0.28% Spain 1.90% 0.96% 3.43% 17.7% 15.9% 21.5% 24.3% −0.03% 0.23% −0.45% Sweden 0.63% 0.77% 0.34% 17.8% 19.8% 32.6% 36.7% 0.09% 0.35% −0.45% Switzerland −0.14% 0.04% −0.46% 29.2% 30.6% 30.6% 35.9% 0.07% 0.80% −1.18% United Kingdom 0.35% −0.22% 1.10% 14.2% 15.4% 31.3% 32.2% 0.09% 0.10% 0.07% United States 0.80% 0.97% 0.53% 13.5% 13.8% 31.7% 33.1% 0.08% 0.17% −0.05% Average 1.08% 1.00% 1.25% 17.1% 17.7% 27.5% 31.2% 0.13% 0.41% −0.47% Median 0.99% 1.10% 1.19% 15.0% 15.7% 29.1% 31.3% 0.09% 0.27% −0.35% Data sources for 2014 data: EU LFS, ACS, Hilda, and Census data. See Appendix B for details. View Large Table 8. Native welfare effects of observed migration flows. Status quo vs. Autarky 2014 vs. 2011 Welfare effects Migrant shares High skilled Welfare effects Countries $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ 2011 2014 2011 2014 $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 21.0% 22.0% 42.9% 43.7% 0.06% 0.18% −0.16% Austria 1.77% 1.74% 1.94% 18.3% 19.8% 16.8% 29.4% 0.34% 1.04% −2.61% Belgium 1.70% 1.37% 2.30% 17.8% 18.9% 27.5% 30.4% 0.14% 0.31% −0.17% Canada 1.19% 1.79% −0.57% 19.9% 20.8% 32.2% 36.3% 0.28% 0.61% −0.70% Denmark 1.90% 2.39% 0.86% 12.0% 13.5% 46.8% 52.7% 0.23% 0.54% −0.42% Estonia 1.47% 1.47% 1.46% 14.7% 13.0% 36.3% 40.9% −0.04% 0.14% −0.36% France 0.77% 0.52% 1.27% 13.0% 13.0% 22.8% 28.1% 0.11% 0.33% −0.33% Germany 0.31% −0.07% 1.23% 15.3% 16.4% 18.7% 18.8% 0.02% 0.00% 0.07% Greece 2.02% 1.40% 3.51% 14.0% 12.7% 13.2% 15.6% −0.11% 0.05% −0.48% Ireland 1.77% 2.30% 0.95% 15.3% 16.3% 48.1% 50.1% 0.14% 0.31% −0.12% Italy 1.87% 1.64% 2.97% 11.8% 13.3% 11.0% 12.0% 0.22% 0.24% 0.15% Luxembourg 0.72% 0.45% 1.15% 39.1% 40.5% 32.2% 45.8% 0.62% 2.41% −2.09% Netherlands 0.48% 0.23% 0.98% 14.0% 14.0% 25.2% 24.9% −0.01% −0.02% 0.02% Portugal 1.27% 1.23% 1.41% 9.9% 10.3% 19.4% 24.9% 0.36% 0.57% −0.37% Slovenia 0.52% −0.20% 2.30% 13.1% 13.3% 9.7% 7.7% −0.03% −0.16% 0.28% Spain 1.90% 0.96% 3.43% 17.7% 15.9% 21.5% 24.3% −0.03% 0.23% −0.45% Sweden 0.63% 0.77% 0.34% 17.8% 19.8% 32.6% 36.7% 0.09% 0.35% −0.45% Switzerland −0.14% 0.04% −0.46% 29.2% 30.6% 30.6% 35.9% 0.07% 0.80% −1.18% United Kingdom 0.35% −0.22% 1.10% 14.2% 15.4% 31.3% 32.2% 0.09% 0.10% 0.07% United States 0.80% 0.97% 0.53% 13.5% 13.8% 31.7% 33.1% 0.08% 0.17% −0.05% Average 1.08% 1.00% 1.25% 17.1% 17.7% 27.5% 31.2% 0.13% 0.41% −0.47% Median 0.99% 1.10% 1.19% 15.0% 15.7% 29.1% 31.3% 0.09% 0.27% −0.35% Status quo vs. Autarky 2014 vs. 2011 Welfare effects Migrant shares High skilled Welfare effects Countries $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ 2011 2014 2011 2014 $$\mathcal {W}_{N}$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 21.0% 22.0% 42.9% 43.7% 0.06% 0.18% −0.16% Austria 1.77% 1.74% 1.94% 18.3% 19.8% 16.8% 29.4% 0.34% 1.04% −2.61% Belgium 1.70% 1.37% 2.30% 17.8% 18.9% 27.5% 30.4% 0.14% 0.31% −0.17% Canada 1.19% 1.79% −0.57% 19.9% 20.8% 32.2% 36.3% 0.28% 0.61% −0.70% Denmark 1.90% 2.39% 0.86% 12.0% 13.5% 46.8% 52.7% 0.23% 0.54% −0.42% Estonia 1.47% 1.47% 1.46% 14.7% 13.0% 36.3% 40.9% −0.04% 0.14% −0.36% France 0.77% 0.52% 1.27% 13.0% 13.0% 22.8% 28.1% 0.11% 0.33% −0.33% Germany 0.31% −0.07% 1.23% 15.3% 16.4% 18.7% 18.8% 0.02% 0.00% 0.07% Greece 2.02% 1.40% 3.51% 14.0% 12.7% 13.2% 15.6% −0.11% 0.05% −0.48% Ireland 1.77% 2.30% 0.95% 15.3% 16.3% 48.1% 50.1% 0.14% 0.31% −0.12% Italy 1.87% 1.64% 2.97% 11.8% 13.3% 11.0% 12.0% 0.22% 0.24% 0.15% Luxembourg 0.72% 0.45% 1.15% 39.1% 40.5% 32.2% 45.8% 0.62% 2.41% −2.09% Netherlands 0.48% 0.23% 0.98% 14.0% 14.0% 25.2% 24.9% −0.01% −0.02% 0.02% Portugal 1.27% 1.23% 1.41% 9.9% 10.3% 19.4% 24.9% 0.36% 0.57% −0.37% Slovenia 0.52% −0.20% 2.30% 13.1% 13.3% 9.7% 7.7% −0.03% −0.16% 0.28% Spain 1.90% 0.96% 3.43% 17.7% 15.9% 21.5% 24.3% −0.03% 0.23% −0.45% Sweden 0.63% 0.77% 0.34% 17.8% 19.8% 32.6% 36.7% 0.09% 0.35% −0.45% Switzerland −0.14% 0.04% −0.46% 29.2% 30.6% 30.6% 35.9% 0.07% 0.80% −1.18% United Kingdom 0.35% −0.22% 1.10% 14.2% 15.4% 31.3% 32.2% 0.09% 0.10% 0.07% United States 0.80% 0.97% 0.53% 13.5% 13.8% 31.7% 33.1% 0.08% 0.17% −0.05% Average 1.08% 1.00% 1.25% 17.1% 17.7% 27.5% 31.2% 0.13% 0.41% −0.47% Median 0.99% 1.10% 1.19% 15.0% 15.7% 29.1% 31.3% 0.09% 0.27% −0.35% Data sources for 2014 data: EU LFS, ACS, Hilda, and Census data. See Appendix B for details. View Large In 14 of our 20 countries, there is no distributive conflict among natives. This highlights the importance of the job-creation effect over the simple complementarity effect, which is always positive for one and negative for the other group. Australia, Canada, and Switzerland, whose immigrant composition is most skewed in favor of high-skilled workers, are the only countries showing negative effects on the welfare of high-skilled natives. In a model with complementarity effects only, we would find negative effects that are larger in absolute terms for highly skilled native workers. In our model, these negative complementarity effects are moderated by the fiscal effect and the job creation effect, which benefit high-skilled natives. Compared to a standard neoclassical model with skill complementarity, our model helps us understand why high-skilled natives may not oppose skill-biased immigration. In Germany, Slovenia and the United Kingdom, there are negative (albeit very small) effects on the welfare of the low skilled. 4.2.4. The Effects of Recent Flows: 2014 Versus 2011 The comparison of the status quo with a hypothetical autarky scenario reveals the total welfare gains from international mobility. The next exercise investigates the effects of changing the immigrant stocks and their skill compositions so as to account for the changes that took place between 2011 (our baseline year) and 2014, for each of the 20 countries we analyze. As shown in Table 8, Estonia, Greece, and Spain are the only countries where the share of immigrants in the workforce fell noticeably from 2011 to 2014.40 Except for the Netherlands and Slovenia, all countries experienced an increase in the share of high-skilled among immigrants. Our simulation finds that 15 of 20 countries experienced positive effects on aggregate native welfare, and in three of these countries both low- and high-skilled natives benefited.41 Because migration has been relatively skilled in most countries, and because of fiscal transfers, the low skilled have benefited in 18 out of 20 countries. They experienced an average welfare increase of 0.41%, whereas high-skilled natives have experienced an average welfare loss of 0.47%, with negative effects in 15 countries. The positive effects for the low skilled and the small positive effects on native welfare are consistent with the findings of Docquier et al. (2014), who look at earlier years.42 The small magnitude of the wage effects is also consistent with Ottaviano and Peri (2012) for the United States, Glitz (2014) for Germany, and Dustmann et al. (2013) for the United Kingdom. The simulation of the welfare effects of immigration between 2011 and 2014 shows positive average effects on per capita income of natives. 4.2.5. A Linear Decomposition of Welfare Effects Our simulations show that the effects of immigration on native welfare depend in complicated ways on labor market characteristics, composition of the immigrant inflow and redistributive institutions of the host countries. In this section, we use a parsimonious regression analysis based on Monte-Carlo-type simulations to investigate the relative importance of the channels at work in our model. We first create a sample of 10,000 artificial economies, each described by a 15-element vector of characteristics (initial labor force shares of natives and migrants, wage gaps, unemployment rates, GDP per capita, government shares, etc.).43 We draw these “moments” from a jointly distributed normal distribution $${\mathcal N}({\mu },{\Sigma })$$, where μ is a (15-dimensional) vector of means and Σ is the corresponding variance-covariance matrix, both generated from the observed data for our 20 OECD countries.44 Then, we calibrate the model parameters of the artificial economies such that they match the drawn characteristics, following the same procedure as in the sections above. We next simulate the effects of an increase in migration equal to 1 percentage point of the labor force of our artificial countries. This exercise creates observations on 10,000 artificial economies, which by construction are characterized by the same summary statistics as the 20 real OECD economies. With these data, we run a simple ordinary least squares (OLS) regression (for all natives, and then separately by skill) where we explain welfare gains by various country characteristics (these are simple transformations of the 15 random variables). More precisely, we run the following regression: $$\Delta \ln \mathcal {W}_{iN}=\sum _{k}\beta _{k}\ln X_{ik}+u_{i},$$ (16) where $$\Delta \ln \mathcal {W}_{iN}$$ denotes the proportional welfare gain for natives in economy i, Xik is an i × k matrix of country characteristics, and ui is an error term capturing specification error.45 Regression (16) is a way of obtaining quantitative comparative statics results and is by no means a test of the model. The standardized beta coefficients presented in Table 9 summarize the conditional correlation of a certain country characteristic with the native welfare effect of immigration.46 Table 9. Native welfare gains by skill, semilog moment regression. Dependent variable: welfare gains of natives from a 1% point increase in immigrant stock (1) (2) (3) All Natives Low Skilled High Skilled Native/immigrant wage gap, skilled 0.086*** 0.065*** 0.124*** [6.38] [4.88] [10.15] Native/immigrant wage gap, unskilled 0.102*** 0.066*** 0.152*** [6.75] [4.44] [11.11] Native/immigrant unemployment gap, skilled −0.016 −0.015 −0.017 [−1.22] [−1.18] [−1.42] Native/immigrant unemployment gap, unskilled −0.096*** −0.081*** −0.114*** [−5.64] [−4.84] [−7.41] Share of immigrants in the labor force −0.145*** −0.111*** −0.195*** [−10.57] [−8.17] [−15.65] Share of tertiary educated: Immigrant/native ratio 0.058*** 0.176*** −0.347*** [4.57] [13.89] [−29.96] Share of tertiary educated among natives 0.007 0.001 0.019* [0.62] [0.08] [1.83] Replacement rate 0.051*** 0.058*** 0.039*** [3.06] [3.49] [2.61] Government expenditures as share of GDP −0.062*** −0.052*** −0.074*** [−4.36] [−3.69] [−5.70] Observations 10,000 10,000 10,000 R2 0.042 0.057 0.213 Dependent variable: welfare gains of natives from a 1% point increase in immigrant stock (1) (2) (3) All Natives Low Skilled High Skilled Native/immigrant wage gap, skilled 0.086*** 0.065*** 0.124*** [6.38] [4.88] [10.15] Native/immigrant wage gap, unskilled 0.102*** 0.066*** 0.152*** [6.75] [4.44] [11.11] Native/immigrant unemployment gap, skilled −0.016 −0.015 −0.017 [−1.22] [−1.18] [−1.42] Native/immigrant unemployment gap, unskilled −0.096*** −0.081*** −0.114*** [−5.64] [−4.84] [−7.41] Share of immigrants in the labor force −0.145*** −0.111*** −0.195*** [−10.57] [−8.17] [−15.65] Share of tertiary educated: Immigrant/native ratio 0.058*** 0.176*** −0.347*** [4.57] [13.89] [−29.96] Share of tertiary educated among natives 0.007 0.001 0.019* [0.62] [0.08] [1.83] Replacement rate 0.051*** 0.058*** 0.039*** [3.06] [3.49] [2.61] Government expenditures as share of GDP −0.062*** −0.052*** −0.074*** [−4.36] [−3.69] [−5.70] Observations 10,000 10,000 10,000 R2 0.042 0.057 0.213 Notes: Standardized beta coefficients; t-stats in brackets. *p < 0.1, **p < 0.05, ***p < 0.01. All regressors are in logs. Artificial economies obtained by sampling from a joint normal distribution. View Large Table 9. Native welfare gains by skill, semilog moment regression. Dependent variable: welfare gains of natives from a 1% point increase in immigrant stock (1) (2) (3) All Natives Low Skilled High Skilled Native/immigrant wage gap, skilled 0.086*** 0.065*** 0.124*** [6.38] [4.88] [10.15] Native/immigrant wage gap, unskilled 0.102*** 0.066*** 0.152*** [6.75] [4.44] [11.11] Native/immigrant unemployment gap, skilled −0.016 −0.015 −0.017 [−1.22] [−1.18] [−1.42] Native/immigrant unemployment gap, unskilled −0.096*** −0.081*** −0.114*** [−5.64] [−4.84] [−7.41] Share of immigrants in the labor force −0.145*** −0.111*** −0.195*** [−10.57] [−8.17] [−15.65] Share of tertiary educated: Immigrant/native ratio 0.058*** 0.176*** −0.347*** [4.57] [13.89] [−29.96] Share of tertiary educated among natives 0.007 0.001 0.019* [0.62] [0.08] [1.83] Replacement rate 0.051*** 0.058*** 0.039*** [3.06] [3.49] [2.61] Government expenditures as share of GDP −0.062*** −0.052*** −0.074*** [−4.36] [−3.69] [−5.70] Observations 10,000 10,000 10,000 R2 0.042 0.057 0.213 Dependent variable: welfare gains of natives from a 1% point increase in immigrant stock (1) (2) (3) All Natives Low Skilled High Skilled Native/immigrant wage gap, skilled 0.086*** 0.065*** 0.124*** [6.38] [4.88] [10.15] Native/immigrant wage gap, unskilled 0.102*** 0.066*** 0.152*** [6.75] [4.44] [11.11] Native/immigrant unemployment gap, skilled −0.016 −0.015 −0.017 [−1.22] [−1.18] [−1.42] Native/immigrant unemployment gap, unskilled −0.096*** −0.081*** −0.114*** [−5.64] [−4.84] [−7.41] Share of immigrants in the labor force −0.145*** −0.111*** −0.195*** [−10.57] [−8.17] [−15.65] Share of tertiary educated: Immigrant/native ratio 0.058*** 0.176*** −0.347*** [4.57] [13.89] [−29.96] Share of tertiary educated among natives 0.007 0.001 0.019* [0.62] [0.08] [1.83] Replacement rate 0.051*** 0.058*** 0.039*** [3.06] [3.49] [2.61] Government expenditures as share of GDP −0.062*** −0.052*** −0.074*** [−4.36] [−3.69] [−5.70] Observations 10,000 10,000 10,000 R2 0.042 0.057 0.213 Notes: Standardized beta coefficients; t-stats in brackets. *p < 0.1, **p < 0.05, ***p < 0.01. All regressors are in logs. Artificial economies obtained by sampling from a joint normal distribution. View Large Column (1) of Table 9 shows that the native/immigrant wage gaps are the most important positive determinants of the overall native welfare gains from immigration. Increasing the high- and low-skilled wage gaps by one standard deviation leads to an increase in the welfare gains by 0.09–0.10 standard deviations, respectively. This result shows the strength of the job creation effect, whereas the wage gap is mainly driven by different outside options. The second most important positive driver is the skill ratio between natives and immigrants: Relatively highly educated immigrants are associated with larger gains.47 The replacement rate ranks third: a higher replacement rate increases the gains as immigrants’ job-creating effects are stronger if labor market frictions are initially more pronounced. This effect dwarfs the negative redistributive role of replacement rates. The preexisting share of immigrants in the labor force turns out to be the most important negative determinant of the welfare gains (standardized beta of −0.15). This suggests that there may be an immigrant share at which the (usually) positive welfare effects of immigrants estimated in the previous section may turn negative. The logic for this result relates to infra-marginal effects: If additional immigration raises the wages of incumbent migrants, firms’ incentives to create jobs fall and the marginal value of immigration for natives is diminishing. Immigrant/native unemployment gaps also reduce the welfare gains of immigration, as expected, because they hamper the job-creating role of immigrants and increase transfers to immigrants. Government expenditures as a share of GDP rank as the third most important negative determinant of welfare gains. Results are qualitatively similar for welfare gains of low-skilled (column 2) and high-skilled natives (column 3), with the exception of the effects of immigrant skill composition, which are as expected because of complementarity effects. The relative skill composition of immigrants is the dominant determinant of welfare gains: The larger the share of immigrants with tertiary education, the higher the welfare gains for the low skilled and the smaller the gains for the high skilled. The associated standardized betas are large at 0.18 for low skilled and −0.35 for high skilled. The classical complementarity channel is still important for quantifying the distributive consequences of migration but matters much less for overall native welfare gains. Larger wage gaps are associated with larger welfare gains, and the generosity of unemployment benefits matters more for low-skilled than for high-skilled natives because of the former group’s higher unemployment risk. 4.3. Sensitivity Analyses 4.3.1. Immigrant-Native Productivity Gaps So far, we have assumed no productivity differences between immigrants and natives of the same skill level, setting πij = 1. In this robustness check, we introduce a parameter η, which makes the immigrant/native productivity gap proportional to the observed wage gap between immigrants and natives: We posit πiN/πiI − 1 = η(wiN/wiI − 1). Setting πiN = 1, this implies πiI = [η(wiN/wiI − 1) + 1]−1 ≤ 1. In the absence of a wage gap (i.e., wiN = wiI) or with η = 0, one has πiI = 1(as assumed in our baseline). On the other hand, with η = 1, the entire wage gap is explained by a productivity gap. Previous research (e.g., LaLonde and Topel 1991; Borjas and Friedberg 2009; Kerr and Kerr 2011) suggests that a significant part of the immigrant/native wage gap persists after controlling for skills and human capital. Hence, it seems plausible to expect η to lie closer to zero than to one. Figure 1 plots the level of η for which the overall native welfare gain due to immigrants, as shown in the second column of Table 8 for the case η = 0, changes sign. For example, in Canada, immigration would be beneficial for natives even if virtually the whole native/immigrant wage gap were due to productivity differences (within skill groups). In contrast, in Germany or Sweden, the gain would turn negative with an η larger than 0.13 or 0.20, respectively. Overall, Figure 1 indicates the assumption that πij = 1 is not essential in countries toward the top of the figure to obtain a positive welfare effect from immigration, whereas if immigrants’ productivity is significantly lower than that of comparable natives, countries toward the bottom may not experience the gains indicated by the model. The fact that the model is sensitive to an unidentified parameter calls for a cautious interpretation of some of our results. However, many of the considered countries (and notably Canada and the United States) would still gain from immigration, even if half of the wage differential between natives and immigrants was due to productivity differences. Figure 1. View largeDownload slide Critical value of $${\eta}$$ at which immigration gain changes sign. We denote by η* the level of η for which the overall native welfare gain resulting from the total observed stock of immigrants changes sign. Australia is excluded because no solution for η* exists. Due to the fact that wage gaps are very small in Australia, no productivity difference consistent with those wage gaps can eliminate the gains we find. In other words, the gains for natives we find are unaffected by productivity differences as they enter our model specifications. Figure 1. View largeDownload slide Critical value of $${\eta}$$ at which immigration gain changes sign. We denote by η* the level of η for which the overall native welfare gain resulting from the total observed stock of immigrants changes sign. Australia is excluded because no solution for η* exists. Due to the fact that wage gaps are very small in Australia, no productivity difference consistent with those wage gaps can eliminate the gains we find. In other words, the gains for natives we find are unaffected by productivity differences as they enter our model specifications. 4.3.2. Nonrival Public Spending So far, we have assumed public spending to be exclusively on rival goods. We find this defensible for scenarios that involve a long time span (e.g., the comparison between a hypothetical autarky situation with the observed status quo) and on basis of footnote 21. However, over shorter horizons and for small changes in immigrant shares, a fraction of public spending may be on nonrival public goods. To capture this possibility, we modify the government budget constraint to include spending on a nonrival (or “pure”) public good $$\bar{G}$$, which is independent of the size of the labor force: $$\sum _{i}\sum _{j}b_{ij}U_{ij}+\tilde{g}\sum _{i}\sum _{j}Q_{ij}+\bar{G} =t\sum _{i}\sum _{j}w_{ij}E_{ij}.$$ (17) As pointed out by Dustmann and Frattini (2014) and others, separating public spending into rival and nonrival public goods is difficult in practice. However, most studies agree that military spending and the service of government debt do not vary with migration, at least in the short run. Using World Bank data and averaging over 2005–2011, in our 20 countries governments spend on average 2.0% of GDP for interest payments (Greece spends the most: 5.2%) and 1.6% of GDP for the military (the United States spend the most: 4.2%).48 Compared to our baseline specification, we keep the same total size of the government as share of GDP, but allow it to include “pure” public goods. Table 10 reports results from simulations equivalent to the first three columns of Table 6, the only difference being that Table 10 allows for nonrival public goods as described above. Because of the nonrival nature of “pure” public goods, per capita expenses on these goods decrease with the size of the labor force. Therefore, all welfare effects now turn out larger than in our baseline specification. On average, native welfare gains are now 0.06%, whereas the corresponding effects without “pure” public goods are 0.02%. Five of the seven countries with negative average effects in the baseline simulation of Table 6 now display a positive effect, with the two remaining negative numbers being very close to zero. Although necessarily stylized, largely because we look at many countries, our exercise suggests that the composition of public spending may play an important role in shaping the native welfare effects of immigration. Table 10. Native welfare effects from one p.p. increase, with nonrival public spending. Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.04% 0.09% −0.05% Austria 0.00% 0.00% 0.00% Belgium 0.02% 0.01% 0.05% Canada 0.07% 0.10% −0.04% Denmark 0.09% 0.14% −0.02% Estonia 0.07% 0.08% 0.04% France 0.06% 0.04% 0.11% Germany 0.02% −0.01% 0.08% Greece 0.15% 0.10% 0.29% Ireland 0.07% 0.12% −0.01% Italy 0.13% 0.11% 0.22% Luxembourg −0.01% −0.03% 0.00% Netherlands 0.02% 0.00% 0.05% Portugal 0.13% 0.13% 0.14% Slovenia 0.05% −0.01% 0.20% Spain 0.07% 0.01% 0.15% Sweden 0.01% 0.02% −0.01% Switzerland −0.02% −0.02% −0.02% United Kingdom 0.05% 0.01% 0.10% United States 0.12% 0.12% 0.11% Average 0.06% 0.05% 0.07% Median 0.06% 0.03% 0.05% Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.04% 0.09% −0.05% Austria 0.00% 0.00% 0.00% Belgium 0.02% 0.01% 0.05% Canada 0.07% 0.10% −0.04% Denmark 0.09% 0.14% −0.02% Estonia 0.07% 0.08% 0.04% France 0.06% 0.04% 0.11% Germany 0.02% −0.01% 0.08% Greece 0.15% 0.10% 0.29% Ireland 0.07% 0.12% −0.01% Italy 0.13% 0.11% 0.22% Luxembourg −0.01% −0.03% 0.00% Netherlands 0.02% 0.00% 0.05% Portugal 0.13% 0.13% 0.14% Slovenia 0.05% −0.01% 0.20% Spain 0.07% 0.01% 0.15% Sweden 0.01% 0.02% −0.01% Switzerland −0.02% −0.02% −0.02% United Kingdom 0.05% 0.01% 0.10% United States 0.12% 0.12% 0.11% Average 0.06% 0.05% 0.07% Median 0.06% 0.03% 0.05% Notes: “p.p.” denotes “percentage point”. We analyze a skill-neutral increase in immigration equal to 1 percentage point of the labor force, compared to 2011. Appendix B discusses data sources. View Large Table 10. Native welfare effects from one p.p. increase, with nonrival public spending. Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.04% 0.09% −0.05% Austria 0.00% 0.00% 0.00% Belgium 0.02% 0.01% 0.05% Canada 0.07% 0.10% −0.04% Denmark 0.09% 0.14% −0.02% Estonia 0.07% 0.08% 0.04% France 0.06% 0.04% 0.11% Germany 0.02% −0.01% 0.08% Greece 0.15% 0.10% 0.29% Ireland 0.07% 0.12% −0.01% Italy 0.13% 0.11% 0.22% Luxembourg −0.01% −0.03% 0.00% Netherlands 0.02% 0.00% 0.05% Portugal 0.13% 0.13% 0.14% Slovenia 0.05% −0.01% 0.20% Spain 0.07% 0.01% 0.15% Sweden 0.01% 0.02% −0.01% Switzerland −0.02% −0.02% −0.02% United Kingdom 0.05% 0.01% 0.10% United States 0.12% 0.12% 0.11% Average 0.06% 0.05% 0.07% Median 0.06% 0.03% 0.05% Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.04% 0.09% −0.05% Austria 0.00% 0.00% 0.00% Belgium 0.02% 0.01% 0.05% Canada 0.07% 0.10% −0.04% Denmark 0.09% 0.14% −0.02% Estonia 0.07% 0.08% 0.04% France 0.06% 0.04% 0.11% Germany 0.02% −0.01% 0.08% Greece 0.15% 0.10% 0.29% Ireland 0.07% 0.12% −0.01% Italy 0.13% 0.11% 0.22% Luxembourg −0.01% −0.03% 0.00% Netherlands 0.02% 0.00% 0.05% Portugal 0.13% 0.13% 0.14% Slovenia 0.05% −0.01% 0.20% Spain 0.07% 0.01% 0.15% Sweden 0.01% 0.02% −0.01% Switzerland −0.02% −0.02% −0.02% United Kingdom 0.05% 0.01% 0.10% United States 0.12% 0.12% 0.11% Average 0.06% 0.05% 0.07% Median 0.06% 0.03% 0.05% Notes: “p.p.” denotes “percentage point”. We analyze a skill-neutral increase in immigration equal to 1 percentage point of the labor force, compared to 2011. Appendix B discusses data sources. View Large 4.3.3. Utility From Unemployment In the baseline version of our model, we set utility effects of unemployment for native workers to zero: We assume $$h_{\mathit {LN}}=0$$ and $$h_{\mathit {HN}}=0$$, as in Chassamboulli and Palivos (2014). We now perform a sensitivity analysis where we investigate the extent to which our results are robust to changing this assumption. In particular, we set the values of $$h_{\mathit {LN}}$$ and $$h_{\mathit {HN}}$$ to around 10% and around 25% of unemployment benefits, respectively. We use both positive and negative values so that we can investigate the possible roles of utility gains and utility losses from unemployment. We then run the same exercise as in Section 4.2.1 (we investigate effects of an increase in migrant shares equal to 1 percentage point of the labor force) for each of the new values, and look at whether estimated welfare effects for natives are different. Table C.5 in our Appendix presents the results of this sensitivity analysis on welfare gains for all natives, low-skilled natives and high-skilled natives separately. Even values of $$h_{\mathit {LN}}$$ and $$h_{\mathit {HN}}$$ as high as one-fourth of unemployment benefits hardly affect the welfare effects implied under our benchmark calibration. 5. Conclusions The impact of immigration on wages, employment, and welfare of natives depends on the characteristics of immigrants and on the institutions of the host country. Most research on the economic effects of immigration, however, assumes perfectly competitive labor markets and abstracts from redistribution. In this paper, we propose a model that addresses these two issues. In most countries, immigrants earn lower wages than natives and face higher unemployment risk, given similar observable skills. However, there is substantial heterogeneity across countries with regard to size and skill composition of the immigrant stock, their labor market performance, and institutional features, implying different impacts on natives. We develop a sufficiently flexible model to capture these facts. Our point of departure is a search-and-matching model, inspired by Chassamboulli and Palivos (2014), where firms cannot discriminate between immigrants and natives ex ante. However, when a match is formed, wage bargaining accounts for immigrants’ lower outside options and lower expected match duration. These two ingredients imply that the share of immigrants affects job creation, with consequences for wages and unemployment rates of native workers. We also add a redistributive government to the model. As stressed in the public finance literature, migration may generate a fiscal transfer from natives who typically hold higher paying jobs and are less likely to be unemployed. Our model accounts for that. Indeed, time and again, surveys show that unemployment and fiscal transfers are very important determinants of native attitudes toward migration (Boeri 2010).49 Introducing search frictions into a model with skill complementarity has quantitatively important implications for the welfare effects of immigration. When immigrant workers have inferior outside options, immigration boosts firms’ incentives to create vacancies; this can benefit all workers (natives and incumbent immigrants) and can increase the immigration surplus. Part of this advantage is eroded by the fact that matches with immigrants typically have shorter duration. However, our quantitative exercise suggests that the net effect from the two channels is positive in virtually all countries in our sample and is sometimes substantial. Interestingly, this job creation effect seems more important in countries whose domestic labor market institutions are more conducive to native unemployment. The benefits from immigration deriving from labor market imperfections tend to be quantitatively more important than the classical complementarity channel. In addition, in the presence of search frictions and wage bargaining, immigration need not create a distributional conflict between high- and low-skilled natives as in the classical model. Nonetheless, the composition of the immigrant workforce relative to natives is still the main predictor of skill-specific welfare effects for natives. We also find that the presence of a redistributive welfare state makes immigration less attractive to natives. Finally, accounting for all channels through which immigration affects natives, the latter are better off with the current migration stocks than in a hypothetical situation with no immigrants in 19 out of 20 countries. Our “macro” approach based on the structural calibration of a model on data from several countries complements previous reduced-form, one-country analyses of the effects of immigration. Still, there are many ways in which our analysis framework can be extended. For example, our analysis is silent on the role of intergenerational considerations. Given that intergenerational transfers are large, populations of OECD countries are aging and immigrants are young, immigration could play a considerable role in alleviating the burden that aging populations will place on OECD countries in the coming decades. The magnitude of such gains depends crucially on future return migration, on whether return migrants receive the accumulated pensions and on immigrants’ future health care costs. It is important to point out that these mechanisms can be expected to strengthen our main result that OECD countries have gained from immigration. They might also turn some of the estimated negative effects to positive, for example in scenarios that analyze the effects of recent inflows or hypothetical future inflows. We have preferred to err on the side of caution and refrained from making speculative assumptions about future return migration; future developments in life expectancy and about the extent to which immigrants’ potentially higher fertility rates could help to alleviate demographic challenges so that our welfare effects hold also in the absence of such additional gains. We hope that further research will continue to combine micro- and macroapproaches to answer the relevant policy questions about the economic impact of migration. Appendix A: Analytics of Simplified Models A.1. Proposition 1 Before we can discuss this specific result, we need to derive a few equations, which are simplifications of the model we presented in the main text. Assuming separation rates are the same for immigrants and natives, the ratio of natives and immigrants among employed and unemployed is the same as their ratio in the labor force: Immigrants and natives have the same chance of getting matched with a firm and the same probability of making a transition from employment to unemployment (because they have the same split rates). In this case, φiI is equal to QiI/(QiI + QiN), that is, the share of immigrants in the labor force. The ratio YH/YL that determines the marginal productivity of each type of workers can then be written as follows: $$\frac{Y_{H}}{Y_{L}}=\frac{m(\theta _{H})[ s_{L}+m(\theta _{L})] }{ m(\theta _{L})[ s_{H}+m(\theta _{H})] }\ast \frac{Q_{\mathit {HN}}+Q_{\mathit {HI}}}{ Q_{\mathit {LN}}+Q_{\mathit {LI}}}.$$ (A.1) In equilibrium, the vacancy/employment ratio is si/q(θi). Substituting (A.1) into (3) and (4), we can write the two equilibrium conditions for equilibrium market tightness, θH and θL explicitly: \begin{eqnarray} p_{L}^{BE}& =& xA[ x+(1-x)( \Lambda (\theta _{H},\theta _{L})\Omega ) ^{\rho }] ^{\frac{1-\rho }{\rho }} \nonumber\\ &=&\frac{\varphi _{\mathit {LI}}h_{\mathit {LI}}}{1-t}+c_{L}\frac{( r+s_{L}) ( 1-t( 1-\beta) ) +\beta \xi \theta _{L}^{1-\varepsilon }}{ \xi \theta _{L}^{-\varepsilon }( 1-\beta) ( 1-t) } \end{eqnarray} (A.2) \begin{eqnarray} p_{H}^{BE}& =&\left( 1-x\right) A\left[ x\left( \Lambda (\theta _{H},\theta _{L})\Omega \right) ^{-\rho }+(1-x)\right] ^{\frac{1-\rho }{\rho }} \nonumber\\ & =& \frac{\varphi _{\mathit {HI}}h_{\mathit {HI}}}{1-t}+c_{H}\frac{\left( r+s_{H}\right) \left( 1-t\left( 1-\beta \right) \right) +\beta \xi \theta _{H}^{1-\varepsilon }}{ \xi \theta _{H}^{-\varepsilon }\left( 1-\beta \right) \left( 1-t\right) }, \end{eqnarray} (A.3) where the term \begin{equation*} \Lambda (\theta _{H},\theta _{L})=\frac{\xi \theta _{H}^{1-\varepsilon } \left[ s_{L}+\xi \theta _{L}^{1-\varepsilon }\right] }{\xi \theta _{L}^{1-\varepsilon }\left[ s_{H}+\xi \theta _{H}^{1-\varepsilon }\right] } \end{equation*} depends positively on the tightness of market H and negatively on the tightness of market L. The term \begin{equation*} \Omega =\frac{Q_{\mathit {HN}}+Q_{\mathit {HI}}}{Q_{\mathit {LN}}+Q_{\mathit {LI}} } \end{equation*} is the supply of highly educated relative to less educated workers. This term may also be affected by immigration if the skill-mix among immigrants differs from that of natives. Case i. When the inflow of immigrants is balanced (the ratio of low to high skilled is the same as in the original native population), it will not affect Ω, and because immigrants of each type are as productive as natives, there is also no effect through Λ(θH, θL). The left-hand side of equation (A.2) remains the same. The right-hand side of the same equation will need to adjust to the increase in $$\varphi _{\mathit {LI}}$$. Because this change has no first-order impact on the left-hand side of equation (A.2), we can write the partial derivative of θL with respect to $$\varphi _{\mathit {LI}}$$ for the right-hand side of equation (A.2): \begin{multline} \frac{\partial {\theta _{L}}}{\partial {\varphi _{\mathit {LI}}}}=-\frac{d/d\varphi _{\mathit {LI}}}{ d/d\theta _{L}}\\ =\frac{\frac{h_{\mathit {LI}}}{1-t}}{c_{L}\frac{(1-\varepsilon )\beta \xi \theta _{L}^{-\varepsilon }(\xi \theta _{L}^{-\varepsilon }(1-\beta )(1-t))-[(r+s_{L})(1-t(1-\beta ))+\beta \xi \theta _{L}^{1-\varepsilon }][(1-\beta )(1-t)\xi (-\varepsilon )\theta _{L}^{-\varepsilon -1}]}{[\xi \theta _{L}^{-\varepsilon }(1-\beta )(1-t)]^{2}}}. \end{multline} (A.4) The sign of this derivative will be driven by the sign of the term \begin{eqnarray} (1-\varepsilon )\beta \xi \theta _{L}^{-\varepsilon }(\xi \theta _{L}^{-\varepsilon }(1&-&\beta )(1-t))-[(r+s_{L})(1-t(1-\beta ))\nonumber\\ &&+\,\beta \xi \theta _{L}^{1-\varepsilon }][(1-\beta )(1-t)\xi (-\varepsilon )\theta _{L}^{-\varepsilon -1}], \end{eqnarray} (A.5) which simplifies to \begin{eqnarray} [\beta (1-\beta )(1&-&\varepsilon )\xi ^{2}+\beta \xi \varepsilon (1-\beta )(1-t)]\theta _{L}^{-2\varepsilon }\nonumber \\ &&+\xi \varepsilon (r+s_{L})(1-t(1-\beta ))(1-\beta )(1-t)\theta _{L}^{-\varepsilon -1}>0. \end{eqnarray} (A.6) Equivalently, using equation (A.3), we find $$\frac{\partial {\theta _{H}}}{\partial {\varphi _{\mathit {HI}}}}=-\frac{d/d\varphi _{\mathit {HI}}}{ d/d\theta _{H}}>0.$$ (A.7) This confirms the intuition that as the number of immigrants increases without changing the ratio between high- and low-skilled workers, the value of a vacancy goes up because immigrants leave a higher surplus to the firm. Because we have a free-entry condition ensuring the equilibrium value of a vacancy remains zero, more vacancies will be created compared to the total number of workers, thereby increasing market tightness in both markets. As market tightness increases in both markets, unemployment rates for natives will decrease, because $$U_{iN}=\frac{s_{i}}{s_{i}+m(\theta_{i})}Q_{iN} \, \text {for }i=H,L.$$ (A.8) In this equation, the arrival of new immigrants will only affect the unemployment rate through θi. As θi increases, m(θi) also increases (the probability to find a job is higher the tighter the market is), which reduces the unemployment rate of natives. Evaluating the effects on equilibrium wages is only slightly more complicated. We use our wage bargaining equation, observing that the match surplus will be a positive function of market tightness, that is, ∂pi/∂θi > 0. We are interested in the effect of a change in market tightness on wages of natives: $$\frac{\partial w_{iN}}{\partial \theta _{i}}=\beta p_{i}\frac{m^{\prime }(\theta _{i})[(r+s_{i})(1-t(1-\beta ))+\beta m(\theta _{i})]-[r+s_{i}+m(\theta _{i})\beta m^{\prime }(\theta _{i})]}{[( r+s_{i}) ( 1-t( 1-\beta) ) +\beta m\left( \theta _{i}\right) ]^{2}}.$$ (A.9) After a few simple steps, this simplifies to $$\frac{\partial w_{iN}}{\partial \theta _{i}}=\beta m^{\prime }(\theta _{i})[(1-\beta )(r+s_{i})p_{i}(1-t)].$$ (A.10) Therefore, $$\frac{\partial w_{iN}}{\partial \theta _{i}}>0\text{ if and only if } p_{i}(1-t)>0,$$ (A.11) which is true in our model. Case ii. A change in the outside option of immigrants affects labor market tightness through the same channel discussed above, namely vacancy creation effects. If the outside option for immigrants worsens, unemployment of natives falls and wages of natives increase. In particular, consider a decrease in hiI (i.e., an increase in its absolute value). Note that hiI only enters equations (A.2) and (A.3) when it is multiplied by φiI. Therefore, the effect of a change in hiI is analytically equivalent to a change in φiI. Either having more immigrants or changing the outside option of current immigrants has the same qualitative effect. Therefore, the effects of labor market tightness on unemployment rates and wages of natives are equivalent to the analysis above. For clarity of exposition, let us consider an inflow of less-skilled immigrants, focusing on the effects on high-skilled natives. An increase in $$Q_{\mathit {LI}}$$ will affect Ω in equation (A.3). By reducing the relative size of the high-skilled population, it will increase market tightness in the high-skilled market. From equation (A.3), we can look at the effect of an increase in θH on pH: $${\small \frac{\partial {p_{H}}}{\partial {\theta _{H}}}\!=\! c_{H}\frac{\frac{ (1-\varepsilon )\beta \xi ^{2}(1-\beta )(1-t)}{\theta _{H}^{2\varepsilon }} +\varepsilon [(r+s_{H})(1-t(1-\beta ))+\frac{\beta \xi }{\theta _{H}^{\varepsilon -1} }]\frac{\xi (1-\beta )(1-t)}{ \theta _{H}^{\varepsilon +1}}}{ [\xi \theta _{H}^{-\varepsilon }(1-\beta )(1-t)]^{2}}\ge 0},$$ (A.12) so that higher labor market tightness of high-skilled workers is associated with a larger equilibrium surplus from the match, lower unemployment rates, and higher wages for high-skilled natives. Case iii. The effect on natives of skill i΄ ≠ i is entirely driven by the complementarity channel, which is positive from the concavity of the production function, as in Borjas (1995). A.2. Proposition 2 Results (i) and (ii) operate through identical mechanisms, as in the case of Proposition 1, with the fundamental difference that the effect of larger migration stocks on the expected surplus from a match is now negative. Given this equivalence, we focus on (iii). For simplicity, consider a situation in which immigrants and natives have identical separation rates initially. We then increase split rates of immigrants of one type and look at the effects on natives. Naturally, the stronger effects will be on the immigrants themselves. However, our focus is primarily on natives, which means we are focusing on the indirect effect of separation rates, which operate through the job creation margin. If immigrants have higher separation rates than natives, this means the surplus from being matched with an immigrant is lower because match duration is shorter on average. Note we are ruling out the firm targeting either natives or immigrants when it creates a vacancy. Therefore, from the free-entry condition, $$rJ_{i}^{V}=-c_{i}+q(\theta _{i})\left[ \varphi _{iN})J_{iN}^{F}+\varphi _{iI}J_{iI}^{F}-J_{i}^{V}\right] =0 .$$ (A.13) We see that as the value of a filled vacancy falls, equilibrium labor market tightness will have to fall in order for the equality to hold. Intuitively, in order for firms to break even in an environment where they get a lower surplus from the match, the market will have to adjust so the probability of filling a vacancy is larger for firms. In other words, at higher separation rates for immigrants, less vacancies get created and equilibrium market tightness is lower. The rest of the discussion in this paragraph follows from the results on labor market tightness, which is the channel through which separation rates of immigrants affect labor markets of natives.50 Below, we discuss the effects on wages and unemployment rates. These are generated by differences in separation rates, but because they operate though labor market tightness, they have been previously looked at in the context of search models. Higher separation rates for immigrants—which bring about lower equilibrium labor market tightness—generate higher unemployment rates for natives. Unemployment rates for natives of skill i are $$u_{iN}=\frac{s_{iN}}{s_{iN}+m(\theta _{i})}.$$ (A.14) Because m(θi) is increasing in θi (in our model we use the functional form m(θi) = ξθ1−ε), the unemployment rate of natives will be higher when equilibrium market tightness is lower, even though the separation rates of natives are unchanged. We next discuss the effect of separation rates of immigrants on wages of natives, operating once again through market tightness. Let us write gross wages of natives as a function only of market tightness and exogenous parameters: $$w_{iN}=\beta \frac{r+s_{iN}+\xi \theta ^{1-\varepsilon }}{( r+s_{iN}) ( 1-t( 1-\beta ) ) +\beta \xi \theta ^{1-\varepsilon }}p_{i} .$$ (A.15) We want to investigate the sign of ∂wiN/∂θi. It is straightforward to see the term on the right-hand side of equation (A.15) is increasing in θi. The price pi = pi(θi) is a positive function of labor market tightness, and it is easy to show that the expression (β(r + siN + ξθ1−ε))/((r + siN)(1 − t(1 − β)) + βξθ1−ε) is also a positive function of θi. Therefore, an increase in the separation rates of immigrants, reducing labor market tightness, also lowers wages for natives. Within a wage bargaining framework, wages are a convex combination of the surplus from the match and the outside option of the worker. Lower labor market tightness also lowers the value of the outside option (because it is harder to find a job when unemployed), the price of the intermediate good is lower, and its weight is also lower (because the expected value of a match following the current match is lower). Summarizing, through its negative effects on labor market tightness, higher separation rates for immigrants result in higher unemployment rates and lower wages not only for immigrants, but also for natives of the same skill class. These dynamics will also have second-order spillover effects of the same sign on native workers of a different skill class, operating through equations (3) and (4), governing prices of the intermediate goods. Lower employment of one skill level corresponds to a lower price in the other sector, due to complementarity. The mechanism feeds on itself and moves the system along a saddle path to a new steady state. Therefore, our model predicts that larger separation rates for immigrants in one sector will lower wages and increase unemployment of natives of the same skill level, as well as those of natives of a different skill level. Appendix B: Data Sources Our quantitative analysis uses data of population shares (skill shares of the labor force in each country, percentage of foreign-born individuals in each country, and skill shares among immigrants), wages (skill premia and immigrant wage gaps by skill level), unemployment rates, generosity of the unemployment insurance scheme, GDP per capita, and size of the public sector. For each of these, we list our data sources below. Following Chassamboulli and Palivos (2014) and Krusell, Ohanian, Rios-Rull, and Violante (2000), we define skilled workers as those workers who hold a Bachelor degree (or equivalent) or above. Population Shares. For all of the E.U. countries in our analysis, we have used information on population shares from the 2012 Eurostat Yearbook (data for 2011), restricting our sample to individuals between 15 and 64 years of age with skill information derived from the International Standard Classification of Education (ISCED) education classification system. From the Eurostat Yearbook, we use data on the share of low-skilled among natives, the share of low-skilled among immigrants, and the share of foreign born in the population. For the United States, equivalent population shares are constructed using the Public Use Micro File dataset from the 2005 US Census. Similarly, for Canada, we construct population shares using the Micro File version of the 2006 Canadian Census. In both cases, we then update the data using American Community Survey and Labor Force Survey. For Australia, we use the 2011 wave of the panel dataset Household, Income and Labor Dynamics in Australia (HILDA) representative survey.51 Unemployment Rates. Table C.1 presents descriptive figures for unemployment rates by skill class and by immigration status. For all E.U. countries and Switzerland, we have used descriptive data from the E.U. Labour Force Survey (LFS). For Germany, there is no information on country of birth in the European Labour Force Survey so we used nationality, for 2005–2011. For the United States, we used the Current Population Survey for 2005–2011. For Canada, because the LFS does not include migration information, we constructed unemployment rates by skill level for 2005–2011, and then used the 2006 Census Microfiles to construct unemployment rates for immigrants and natives. We then constructed trends using the census data and the LFS data together. For Australia, we use data from the HILDA Survey from 2005 to 2011 (Waves 5-11). For wage gaps and unemployment rates, we average data over this period to maximize comparability across countries and minimize the role of business cycle and short-term fluctuations, given that the focus of our study is on steady-state comparisons. Wages. For E.U. countries, we constructed a measure of the wage gap between low- and high-skilled native workers and of the gaps between immigrant and native workers (by skill) using the European Union Statistics on Income and Living Conditions (EU-SILC) for years 2005–2011 (2010 for Ireland).52 For the United States, Canada and Australia, we use the same datasets that we used for population shares, see above. Government Expenditures. We take expenditures as share of GDP from the World Economic Outlook Database of the International Monetary Fund. For each country, we take an average for 2005–2011 to make sure that heterogeneity across countries is not driven by asymmetries in the respective business cycles. Expenses on the Military and on Interests on Government Debt. We use the latest version of the World Development Indicators of the World Bank to get data on military spending and interest payments to service the government debt. We construct averages for all years between 2005 and 2011 to make sure that our results are not driven by current business cycle conditions. We use the sum of expenses for the military and payments to service the public debt as a conservative measure of the magnitude of “pure” public goods. Replacement Rates. In order to parameterize the level of unemployment benefits for each country, we use data on the average net replacement rates from the OECD Benefits and Wages Dataset, averaging net replacement rates (NRR)53 for 2005–2011 to smooth out business cycle fluctuations. GDP. We use data on 2011 GDP (PPP in international dollars) from the World Development Indicators of the World Bank. Capital Share. We calculate the capital share α for each country as one minus the annual labor income share, which is available from the “Unit Labour Costs—Annual Indicators” dataset of the OECD. We average capital shares over the period 2005–2011 again to get a measure that does not reflect a country’s specific position along the business cycle. Remigration Rates. We calculated monthly remigration rates using data on the share of reemigration rates five years after arrival from Table III.1 from OECD (2008). Because of data limitations, we are unable to use different values for different countries and are also unable to make remigration rates duration dependent, which is likely to be the case in reality. Stocks and Skill Compositions, 2011–2014. In order to perform this exercise, we need information on the stock of immigrants and on their skill composition in 2011. Our data sources are the EU LFS for European countries, the American Community Survey for the United States (where we take account of the different sample characteristics between the sample and the US Census by equating growth rates rather than levels). For Australia, we need to use HILDA data from 2013 and impute data for 2014 using previous growth rates. For Canada, to the best of our knowledge, there is no dataset that can be used for this purpose, which is more recent than the 2011 Census. We therefore use linear trends to extrapolate levels in 2014. Fortunately, both Australia and Canada are countries that have migration policies that have been very stable over longer periods of time, and we are therefore confident that our imputations do not deliver misleading results. Appendix C: Summary Statistics and Additional Results Table C.1. Summary statistics for country-specific moments. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) $$\frac{Q_{\mathit {LN}}}{Q_N}$$ QI $$\frac{Q_{\mathit {LI}}}{Q_I}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {LN}} }$$ $$\frac{w_{\mathit {LN}}}{w_{\mathit {LI}}}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {HI}}}$$ $$u_{\mathit {LN}}$$ $$u_{\mathit {LI}}$$ $$u_{\mathit {HN}}$$ $$u_{\mathit {HI}}$$ $$\frac{\bar{b}}{W(1-t)}$$ GDP $$\frac{G+B}{GDP}$$ $$\frac{rD}{GDP}$$ $$\frac{M}{GDP}$$ Countries Australia 0.70 0.21 0.57 1.40 1.01 1.00 0.04 0.05 0.01 0.03 0.43 39.7 0.36 0.010 0.019 Austria 0.83 0.18 0.83 1.35 1.34 1.18 0.04 0.10 0.02 0.06 0.52 42.2 0.50 0.025 0.008 Belgium 0.68 0.18 0.72 1.44 1.29 1.14 0.08 0.20 0.03 0.10 0.63 38.8 0.52 0.034 0.011 Canada 0.80 0.20 0.68 1.81 1.01 1.19 0.09 0.09 0.04 0.07 0.26 40.4 0.41 0.018 0.012 Denmark 0.71 0.12 0.53 1.37 1.18 1.16 0.06 0.12 0.03 0.08 0.57 40.9 0.55 0.016 0.014 Estonia 0.69 0.15 0.64 1.52 1.16 1.35 0.12 0.14 0.05 0.09 0.24 22.0 0.41 0.001 0.019 France 0.71 0.13 0.77 1.45 1.17 1.04 0.10 0.16 0.05 0.10 0.49 35.2 0.55 0.024 0.023 Germany 0.74 0.15 0.81 1.40 1.13 1.16 0.09 0.16 0.03 0.11 0.44 39.5 0.46 0.016 0.013 Greece 0.75 0.14 0.87 1.68 1.39 1.38 0.13 0.15 0.09 0.15 0.22 25.8 0.49 0.052 0.028 Ireland 0.66 0.15 0.52 1.61 1.07 1.24 0.11 0.16 0.04 0.08 0.54 41.7 0.44 0.020 0.006 Italy 0.86 0.12 0.89 1.56 1.34 1.57 0.08 0.11 0.05 0.08 0.23 32.6 0.49 0.044 0.017 Luxembourg 0.64 0.39 0.68 1.42 1.29 1.08 0.04 0.07 0.02 0.04 0.30 89.0 0.41 0.003 0.006 Netherlands 0.70 0.14 0.75 1.39 1.13 1.15 0.04 0.09 0.02 0.06 0.39 42.8 0.48 0.017 0.014 Portugal 0.83 0.10 0.81 2.08 1.09 1.22 0.10 0.14 0.08 0.09 0.52 25.4 0.47 0.029 0.019 Slovenia 0.76 0.13 0.90 1.49 1.12 1.06 0.07 0.08 0.04 0.05 0.26 27.0 0.44 0.014 0.014 Spain 0.67 0.18 0.79 1.55 1.30 1.34 0.17 0.23 0.08 0.16 0.42 32.0 0.43 0.015 0.011 Sweden 0.69 0.18 0.67 1.24 1.21 1.13 0.08 0.16 0.03 0.11 0.42 41.5 0.51 0.011 0.012 Switzerland 0.68 0.29 0.69 1.44 1.17 0.99 0.03 0.08 0.02 0.05 0.34 51.3 0.33 0.006 0.007 UK 0.62 0.14 0.69 1.52 1.04 1.15 0.08 0.10 0.03 0.06 0.29 35.7 0.43 0.023 0.023 USA 0.70 0.14 0.68 2.11 1.15 1.00 0.10 0.09 0.03 0.04 0.27 48.1 0.40 0.026 0.042 Statistics Mean 0.72 0.17 0.72 1.54 1.18 1.18 0.08 0.12 0.04 0.08 0.39 39.6 0.45 0.020 0.016 Median 0.70 0.15 0.71 1.47 1.16 1.15 0.08 0.11 0.03 0.08 0.40 39.6 0.45 0.018 0.014 S.d. 0.07 0.07 0.11 0.23 0.11 0.15 0.04 0.05 0.02 0.03 0.13 13.9 0.06 0.012 0.008 Min 0.62 0.10 0.52 1.24 1.01 0.99 0.03 0.05 0.01 0.03 0.22 22.0 0.33 0.001 0.006 Max 0.86 0.39 0.90 2.11 1.39 1.57 0.17 0.23 0.09 0.16 0.63 89.0 0.55 0.052 0.042 S.d./mean 0.09 0.39 0.15 0.15 0.09 0.12 0.43 0.37 0.55 0.33 0.40 0.40 0.13 0.61 0.53 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) $$\frac{Q_{\mathit {LN}}}{Q_N}$$ QI $$\frac{Q_{\mathit {LI}}}{Q_I}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {LN}} }$$ $$\frac{w_{\mathit {LN}}}{w_{\mathit {LI}}}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {HI}}}$$ $$u_{\mathit {LN}}$$ $$u_{\mathit {LI}}$$ $$u_{\mathit {HN}}$$ $$u_{\mathit {HI}}$$ $$\frac{\bar{b}}{W(1-t)}$$ GDP $$\frac{G+B}{GDP}$$ $$\frac{rD}{GDP}$$ $$\frac{M}{GDP}$$ Countries Australia 0.70 0.21 0.57 1.40 1.01 1.00 0.04 0.05 0.01 0.03 0.43 39.7 0.36 0.010 0.019 Austria 0.83 0.18 0.83 1.35 1.34 1.18 0.04 0.10 0.02 0.06 0.52 42.2 0.50 0.025 0.008 Belgium 0.68 0.18 0.72 1.44 1.29 1.14 0.08 0.20 0.03 0.10 0.63 38.8 0.52 0.034 0.011 Canada 0.80 0.20 0.68 1.81 1.01 1.19 0.09 0.09 0.04 0.07 0.26 40.4 0.41 0.018 0.012 Denmark 0.71 0.12 0.53 1.37 1.18 1.16 0.06 0.12 0.03 0.08 0.57 40.9 0.55 0.016 0.014 Estonia 0.69 0.15 0.64 1.52 1.16 1.35 0.12 0.14 0.05 0.09 0.24 22.0 0.41 0.001 0.019 France 0.71 0.13 0.77 1.45 1.17 1.04 0.10 0.16 0.05 0.10 0.49 35.2 0.55 0.024 0.023 Germany 0.74 0.15 0.81 1.40 1.13 1.16 0.09 0.16 0.03 0.11 0.44 39.5 0.46 0.016 0.013 Greece 0.75 0.14 0.87 1.68 1.39 1.38 0.13 0.15 0.09 0.15 0.22 25.8 0.49 0.052 0.028 Ireland 0.66 0.15 0.52 1.61 1.07 1.24 0.11 0.16 0.04 0.08 0.54 41.7 0.44 0.020 0.006 Italy 0.86 0.12 0.89 1.56 1.34 1.57 0.08 0.11 0.05 0.08 0.23 32.6 0.49 0.044 0.017 Luxembourg 0.64 0.39 0.68 1.42 1.29 1.08 0.04 0.07 0.02 0.04 0.30 89.0 0.41 0.003 0.006 Netherlands 0.70 0.14 0.75 1.39 1.13 1.15 0.04 0.09 0.02 0.06 0.39 42.8 0.48 0.017 0.014 Portugal 0.83 0.10 0.81 2.08 1.09 1.22 0.10 0.14 0.08 0.09 0.52 25.4 0.47 0.029 0.019 Slovenia 0.76 0.13 0.90 1.49 1.12 1.06 0.07 0.08 0.04 0.05 0.26 27.0 0.44 0.014 0.014 Spain 0.67 0.18 0.79 1.55 1.30 1.34 0.17 0.23 0.08 0.16 0.42 32.0 0.43 0.015 0.011 Sweden 0.69 0.18 0.67 1.24 1.21 1.13 0.08 0.16 0.03 0.11 0.42 41.5 0.51 0.011 0.012 Switzerland 0.68 0.29 0.69 1.44 1.17 0.99 0.03 0.08 0.02 0.05 0.34 51.3 0.33 0.006 0.007 UK 0.62 0.14 0.69 1.52 1.04 1.15 0.08 0.10 0.03 0.06 0.29 35.7 0.43 0.023 0.023 USA 0.70 0.14 0.68 2.11 1.15 1.00 0.10 0.09 0.03 0.04 0.27 48.1 0.40 0.026 0.042 Statistics Mean 0.72 0.17 0.72 1.54 1.18 1.18 0.08 0.12 0.04 0.08 0.39 39.6 0.45 0.020 0.016 Median 0.70 0.15 0.71 1.47 1.16 1.15 0.08 0.11 0.03 0.08 0.40 39.6 0.45 0.018 0.014 S.d. 0.07 0.07 0.11 0.23 0.11 0.15 0.04 0.05 0.02 0.03 0.13 13.9 0.06 0.012 0.008 Min 0.62 0.10 0.52 1.24 1.01 0.99 0.03 0.05 0.01 0.03 0.22 22.0 0.33 0.001 0.006 Max 0.86 0.39 0.90 2.11 1.39 1.57 0.17 0.23 0.09 0.16 0.63 89.0 0.55 0.052 0.042 S.d./mean 0.09 0.39 0.15 0.15 0.09 0.12 0.43 0.37 0.55 0.33 0.40 0.40 0.13 0.61 0.53 Notes: $$Q_{\mathit {LN}}/Q_N$$ is the share of low-skilled among natives. $$Q_I=Q_{\mathit {LI}}+Q_{\mathit {HI}}$$ is the number of immigrants in the labor force relative to the number of natives. $$Q_{\mathit {LI}}/Q_I$$ is the share of low-skilled among immigrants. $${w_{\mathit {HN}}}/{w_{\mathit {LN}}}$$ is the skill premium among natives. $${w_{\mathit {LN}}}/{w_{\mathit {LI}}}$$ is the native/immigrant wage ratio for low skilled. $${w_{\mathit {HN}}}/{w_{\mathit {HI}}}$$ is the native/immigrant wage ratio for high skilled. uij are unemployment rates for each skill level for immigrants and natives. $${\bar{b}}/{W(1-t)}$$ denotes the average replacement rate: ratio between benefits and average wages (OECD data). In column 11, we use OECD data for net replacement rates. GDP is per capita GDP PPP for year 2011 in current international dollars (in 1,000s). In column 13, B denotes total expenditures on unemployment benefits, and therefore our implied empirical measure of G denotes a public good in an inclusive sense, including all transfers and public expenses apart from unemployment insurance schemes. $${rD}/\mathit {GDP}$$ denotes interest payment on public debt as share of GDP, on average between 2005 and 2011. $${M}/\mathit {GDP}$$ denotes public spending on the military as share of GDP, on average between 2005 and 2011. These two measures are also included in our measure of G in column 13. For the USA, data from IPUMS 2005 Census. For Canada, data from the 2006 Census and 2005–2012 LFS (with data referring to 2011). For E.U. countries: Eurostat data for population shares, EU-SILC and EU-LFS for wage gaps. View Large Table C.1. Summary statistics for country-specific moments. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) $$\frac{Q_{\mathit {LN}}}{Q_N}$$ QI $$\frac{Q_{\mathit {LI}}}{Q_I}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {LN}} }$$ $$\frac{w_{\mathit {LN}}}{w_{\mathit {LI}}}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {HI}}}$$ $$u_{\mathit {LN}}$$ $$u_{\mathit {LI}}$$ $$u_{\mathit {HN}}$$ $$u_{\mathit {HI}}$$ $$\frac{\bar{b}}{W(1-t)}$$ GDP $$\frac{G+B}{GDP}$$ $$\frac{rD}{GDP}$$ $$\frac{M}{GDP}$$ Countries Australia 0.70 0.21 0.57 1.40 1.01 1.00 0.04 0.05 0.01 0.03 0.43 39.7 0.36 0.010 0.019 Austria 0.83 0.18 0.83 1.35 1.34 1.18 0.04 0.10 0.02 0.06 0.52 42.2 0.50 0.025 0.008 Belgium 0.68 0.18 0.72 1.44 1.29 1.14 0.08 0.20 0.03 0.10 0.63 38.8 0.52 0.034 0.011 Canada 0.80 0.20 0.68 1.81 1.01 1.19 0.09 0.09 0.04 0.07 0.26 40.4 0.41 0.018 0.012 Denmark 0.71 0.12 0.53 1.37 1.18 1.16 0.06 0.12 0.03 0.08 0.57 40.9 0.55 0.016 0.014 Estonia 0.69 0.15 0.64 1.52 1.16 1.35 0.12 0.14 0.05 0.09 0.24 22.0 0.41 0.001 0.019 France 0.71 0.13 0.77 1.45 1.17 1.04 0.10 0.16 0.05 0.10 0.49 35.2 0.55 0.024 0.023 Germany 0.74 0.15 0.81 1.40 1.13 1.16 0.09 0.16 0.03 0.11 0.44 39.5 0.46 0.016 0.013 Greece 0.75 0.14 0.87 1.68 1.39 1.38 0.13 0.15 0.09 0.15 0.22 25.8 0.49 0.052 0.028 Ireland 0.66 0.15 0.52 1.61 1.07 1.24 0.11 0.16 0.04 0.08 0.54 41.7 0.44 0.020 0.006 Italy 0.86 0.12 0.89 1.56 1.34 1.57 0.08 0.11 0.05 0.08 0.23 32.6 0.49 0.044 0.017 Luxembourg 0.64 0.39 0.68 1.42 1.29 1.08 0.04 0.07 0.02 0.04 0.30 89.0 0.41 0.003 0.006 Netherlands 0.70 0.14 0.75 1.39 1.13 1.15 0.04 0.09 0.02 0.06 0.39 42.8 0.48 0.017 0.014 Portugal 0.83 0.10 0.81 2.08 1.09 1.22 0.10 0.14 0.08 0.09 0.52 25.4 0.47 0.029 0.019 Slovenia 0.76 0.13 0.90 1.49 1.12 1.06 0.07 0.08 0.04 0.05 0.26 27.0 0.44 0.014 0.014 Spain 0.67 0.18 0.79 1.55 1.30 1.34 0.17 0.23 0.08 0.16 0.42 32.0 0.43 0.015 0.011 Sweden 0.69 0.18 0.67 1.24 1.21 1.13 0.08 0.16 0.03 0.11 0.42 41.5 0.51 0.011 0.012 Switzerland 0.68 0.29 0.69 1.44 1.17 0.99 0.03 0.08 0.02 0.05 0.34 51.3 0.33 0.006 0.007 UK 0.62 0.14 0.69 1.52 1.04 1.15 0.08 0.10 0.03 0.06 0.29 35.7 0.43 0.023 0.023 USA 0.70 0.14 0.68 2.11 1.15 1.00 0.10 0.09 0.03 0.04 0.27 48.1 0.40 0.026 0.042 Statistics Mean 0.72 0.17 0.72 1.54 1.18 1.18 0.08 0.12 0.04 0.08 0.39 39.6 0.45 0.020 0.016 Median 0.70 0.15 0.71 1.47 1.16 1.15 0.08 0.11 0.03 0.08 0.40 39.6 0.45 0.018 0.014 S.d. 0.07 0.07 0.11 0.23 0.11 0.15 0.04 0.05 0.02 0.03 0.13 13.9 0.06 0.012 0.008 Min 0.62 0.10 0.52 1.24 1.01 0.99 0.03 0.05 0.01 0.03 0.22 22.0 0.33 0.001 0.006 Max 0.86 0.39 0.90 2.11 1.39 1.57 0.17 0.23 0.09 0.16 0.63 89.0 0.55 0.052 0.042 S.d./mean 0.09 0.39 0.15 0.15 0.09 0.12 0.43 0.37 0.55 0.33 0.40 0.40 0.13 0.61 0.53 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) $$\frac{Q_{\mathit {LN}}}{Q_N}$$ QI $$\frac{Q_{\mathit {LI}}}{Q_I}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {LN}} }$$ $$\frac{w_{\mathit {LN}}}{w_{\mathit {LI}}}$$ $$\frac{w_{\mathit {HN}}}{w_{\mathit {HI}}}$$ $$u_{\mathit {LN}}$$ $$u_{\mathit {LI}}$$ $$u_{\mathit {HN}}$$ $$u_{\mathit {HI}}$$ $$\frac{\bar{b}}{W(1-t)}$$ GDP $$\frac{G+B}{GDP}$$ $$\frac{rD}{GDP}$$ $$\frac{M}{GDP}$$ Countries Australia 0.70 0.21 0.57 1.40 1.01 1.00 0.04 0.05 0.01 0.03 0.43 39.7 0.36 0.010 0.019 Austria 0.83 0.18 0.83 1.35 1.34 1.18 0.04 0.10 0.02 0.06 0.52 42.2 0.50 0.025 0.008 Belgium 0.68 0.18 0.72 1.44 1.29 1.14 0.08 0.20 0.03 0.10 0.63 38.8 0.52 0.034 0.011 Canada 0.80 0.20 0.68 1.81 1.01 1.19 0.09 0.09 0.04 0.07 0.26 40.4 0.41 0.018 0.012 Denmark 0.71 0.12 0.53 1.37 1.18 1.16 0.06 0.12 0.03 0.08 0.57 40.9 0.55 0.016 0.014 Estonia 0.69 0.15 0.64 1.52 1.16 1.35 0.12 0.14 0.05 0.09 0.24 22.0 0.41 0.001 0.019 France 0.71 0.13 0.77 1.45 1.17 1.04 0.10 0.16 0.05 0.10 0.49 35.2 0.55 0.024 0.023 Germany 0.74 0.15 0.81 1.40 1.13 1.16 0.09 0.16 0.03 0.11 0.44 39.5 0.46 0.016 0.013 Greece 0.75 0.14 0.87 1.68 1.39 1.38 0.13 0.15 0.09 0.15 0.22 25.8 0.49 0.052 0.028 Ireland 0.66 0.15 0.52 1.61 1.07 1.24 0.11 0.16 0.04 0.08 0.54 41.7 0.44 0.020 0.006 Italy 0.86 0.12 0.89 1.56 1.34 1.57 0.08 0.11 0.05 0.08 0.23 32.6 0.49 0.044 0.017 Luxembourg 0.64 0.39 0.68 1.42 1.29 1.08 0.04 0.07 0.02 0.04 0.30 89.0 0.41 0.003 0.006 Netherlands 0.70 0.14 0.75 1.39 1.13 1.15 0.04 0.09 0.02 0.06 0.39 42.8 0.48 0.017 0.014 Portugal 0.83 0.10 0.81 2.08 1.09 1.22 0.10 0.14 0.08 0.09 0.52 25.4 0.47 0.029 0.019 Slovenia 0.76 0.13 0.90 1.49 1.12 1.06 0.07 0.08 0.04 0.05 0.26 27.0 0.44 0.014 0.014 Spain 0.67 0.18 0.79 1.55 1.30 1.34 0.17 0.23 0.08 0.16 0.42 32.0 0.43 0.015 0.011 Sweden 0.69 0.18 0.67 1.24 1.21 1.13 0.08 0.16 0.03 0.11 0.42 41.5 0.51 0.011 0.012 Switzerland 0.68 0.29 0.69 1.44 1.17 0.99 0.03 0.08 0.02 0.05 0.34 51.3 0.33 0.006 0.007 UK 0.62 0.14 0.69 1.52 1.04 1.15 0.08 0.10 0.03 0.06 0.29 35.7 0.43 0.023 0.023 USA 0.70 0.14 0.68 2.11 1.15 1.00 0.10 0.09 0.03 0.04 0.27 48.1 0.40 0.026 0.042 Statistics Mean 0.72 0.17 0.72 1.54 1.18 1.18 0.08 0.12 0.04 0.08 0.39 39.6 0.45 0.020 0.016 Median 0.70 0.15 0.71 1.47 1.16 1.15 0.08 0.11 0.03 0.08 0.40 39.6 0.45 0.018 0.014 S.d. 0.07 0.07 0.11 0.23 0.11 0.15 0.04 0.05 0.02 0.03 0.13 13.9 0.06 0.012 0.008 Min 0.62 0.10 0.52 1.24 1.01 0.99 0.03 0.05 0.01 0.03 0.22 22.0 0.33 0.001 0.006 Max 0.86 0.39 0.90 2.11 1.39 1.57 0.17 0.23 0.09 0.16 0.63 89.0 0.55 0.052 0.042 S.d./mean 0.09 0.39 0.15 0.15 0.09 0.12 0.43 0.37 0.55 0.33 0.40 0.40 0.13 0.61 0.53 Notes: $$Q_{\mathit {LN}}/Q_N$$ is the share of low-skilled among natives. $$Q_I=Q_{\mathit {LI}}+Q_{\mathit {HI}}$$ is the number of immigrants in the labor force relative to the number of natives. $$Q_{\mathit {LI}}/Q_I$$ is the share of low-skilled among immigrants. $${w_{\mathit {HN}}}/{w_{\mathit {LN}}}$$ is the skill premium among natives. $${w_{\mathit {LN}}}/{w_{\mathit {LI}}}$$ is the native/immigrant wage ratio for low skilled. $${w_{\mathit {HN}}}/{w_{\mathit {HI}}}$$ is the native/immigrant wage ratio for high skilled. uij are unemployment rates for each skill level for immigrants and natives. $${\bar{b}}/{W(1-t)}$$ denotes the average replacement rate: ratio between benefits and average wages (OECD data). In column 11, we use OECD data for net replacement rates. GDP is per capita GDP PPP for year 2011 in current international dollars (in 1,000s). In column 13, B denotes total expenditures on unemployment benefits, and therefore our implied empirical measure of G denotes a public good in an inclusive sense, including all transfers and public expenses apart from unemployment insurance schemes. $${rD}/\mathit {GDP}$$ denotes interest payment on public debt as share of GDP, on average between 2005 and 2011. $${M}/\mathit {GDP}$$ denotes public spending on the military as share of GDP, on average between 2005 and 2011. These two measures are also included in our measure of G in column 13. For the USA, data from IPUMS 2005 Census. For Canada, data from the 2006 Census and 2005–2012 LFS (with data referring to 2011). For E.U. countries: Eurostat data for population shares, EU-SILC and EU-LFS for wage gaps. View Large Table C.2. Welfare effects for natives of a 1 percentage point increase in immigration. Model 1 Model 2 Model 3 Model 4 Model 5 Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.01% 0.08% −0.13% 0.01% 0.09% −0.12% 0.00% 0.08% −0.13% 0.00% 0.08% −0.13% 0.01% 0.06% −0.08% Austria 0.00% 0.00% 0.01% 0.08% 0.09% 0.07% 0.05% 0.05% 0.04% 0.04% 0.04% 0.04% −0.03% −0.03% −0.03% Belgium 0.00% −0.04% 0.06% 0.09% 0.07% 0.12% 0.03% 0.01% 0.06% 0.03% 0.01% 0.07% −0.02% −0.03% −0.01% Canada 0.01% 0.09% −0.20% 0.04% 0.11% −0.13% 0.03% 0.10% −0.14% 0.03% 0.10% −0.14% 0.04% 0.08% −0.08% Denmark 0.01% 0.14% −0.22% 0.09% 0.21% −0.13% 0.05% 0.17% −0.17% 0.07% 0.19% −0.16% 0.06% 0.11% −0.05% Estonia 0.00% 0.04% −0.06% 0.09% 0.12% 0.05% 0.07% 0.10% 0.03% 0.08% 0.11% 0.03% 0.05% 0.07% 0.02% France 0.00% −0.05% 0.09% 0.07% 0.04% 0.12% 0.03% −0.01% 0.08% 0.04% 0.00% 0.10% 0.02% 0.00% 0.05% Germany 0.00% −0.05% 0.11% 0.07% 0.03% 0.17% 0.02% −0.03% 0.12% 0.02% −0.02% 0.12% −0.01% −0.03% 0.04% Greece 0.01% −0.09% 0.19% 0.15% 0.07% 0.31% 0.13% 0.05% 0.29% 0.15% 0.06% 0.31% 0.07% 0.02% 0.18% Ireland 0.01% 0.11% −0.13% 0.07% 0.15% −0.04% 0.04% 0.13% −0.07% 0.05% 0.15% −0.08% 0.05% 0.10% −0.03% Italy 0.00% −0.02% 0.10% 0.14% 0.12% 0.25% 0.13% 0.10% 0.23% 0.13% 0.11% 0.24% 0.07% 0.05% 0.14% Luxembourg 0.00% −0.02% 0.04% 0.03% 0.02% 0.06% 0.02% 0.00% 0.05% 0.02% 0.00% 0.05% −0.02% −0.03% −0.01% Netherlands 0.00% −0.04% 0.06% 0.06% 0.03% 0.12% 0.03% 0.00% 0.09% 0.03% 0.00% 0.09% −0.01% −0.03% 0.02% Portugal 0.00% 0.02% −0.06% 0.08% 0.08% 0.06% 0.05% 0.06% 0.04% 0.08% 0.09% 0.04% 0.08% 0.09% 0.07% Slovenia 0.01% −0.11% 0.27% 0.07% −0.04% 0.30% 0.06% −0.05% 0.29% 0.06% −0.05% 0.30% 0.02% −0.04% 0.17% Spain 0.01% −0.09% 0.13% 0.13% 0.04% 0.25% 0.08% −0.01% 0.19% 0.09% 0.01% 0.21% 0.04% −0.01% 0.12% Sweden 0.00% 0.01% −0.02% 0.08% 0.10% 0.04% 0.02% 0.04% −0.01% 0.02% 0.04% −0.01% −0.02% −0.01% −0.04% Switzerland 0.00% −0.01% 0.02% 0.02% 0.03% 0.02% 0.00% 0.01% 0.00% −0.01% −0.01% −0.01% −0.04% −0.03% −0.04% UK 0.00% −0.06% 0.07% 0.05% −0.02% 0.12% 0.03% −0.04% 0.11% 0.03% −0.03% 0.11% 0.00% −0.03% 0.05% USA 0.00% 0.01% −0.02% 0.04% 0.08% 0.00% 0.04% 0.08% 0.00% 0.05% 0.08% 0.01% 0.05% 0.06% 0.03% Average 0.00% 0.00% 0.01% 0.07% 0.07% 0.08% 0.05% 0.04% 0.05% 0.05% 0.05% 0.06% 0.02% 0.02% 0.03% Median 0.00% −0.02% 0.03% 0.07% 0.08% 0.06% 0.04% 0.05% 0.04% 0.04% 0.04% 0.04% 0.02% 0.00% 0.02% Model 1 Model 2 Model 3 Model 4 Model 5 Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.01% 0.08% −0.13% 0.01% 0.09% −0.12% 0.00% 0.08% −0.13% 0.00% 0.08% −0.13% 0.01% 0.06% −0.08% Austria 0.00% 0.00% 0.01% 0.08% 0.09% 0.07% 0.05% 0.05% 0.04% 0.04% 0.04% 0.04% −0.03% −0.03% −0.03% Belgium 0.00% −0.04% 0.06% 0.09% 0.07% 0.12% 0.03% 0.01% 0.06% 0.03% 0.01% 0.07% −0.02% −0.03% −0.01% Canada 0.01% 0.09% −0.20% 0.04% 0.11% −0.13% 0.03% 0.10% −0.14% 0.03% 0.10% −0.14% 0.04% 0.08% −0.08% Denmark 0.01% 0.14% −0.22% 0.09% 0.21% −0.13% 0.05% 0.17% −0.17% 0.07% 0.19% −0.16% 0.06% 0.11% −0.05% Estonia 0.00% 0.04% −0.06% 0.09% 0.12% 0.05% 0.07% 0.10% 0.03% 0.08% 0.11% 0.03% 0.05% 0.07% 0.02% France 0.00% −0.05% 0.09% 0.07% 0.04% 0.12% 0.03% −0.01% 0.08% 0.04% 0.00% 0.10% 0.02% 0.00% 0.05% Germany 0.00% −0.05% 0.11% 0.07% 0.03% 0.17% 0.02% −0.03% 0.12% 0.02% −0.02% 0.12% −0.01% −0.03% 0.04% Greece 0.01% −0.09% 0.19% 0.15% 0.07% 0.31% 0.13% 0.05% 0.29% 0.15% 0.06% 0.31% 0.07% 0.02% 0.18% Ireland 0.01% 0.11% −0.13% 0.07% 0.15% −0.04% 0.04% 0.13% −0.07% 0.05% 0.15% −0.08% 0.05% 0.10% −0.03% Italy 0.00% −0.02% 0.10% 0.14% 0.12% 0.25% 0.13% 0.10% 0.23% 0.13% 0.11% 0.24% 0.07% 0.05% 0.14% Luxembourg 0.00% −0.02% 0.04% 0.03% 0.02% 0.06% 0.02% 0.00% 0.05% 0.02% 0.00% 0.05% −0.02% −0.03% −0.01% Netherlands 0.00% −0.04% 0.06% 0.06% 0.03% 0.12% 0.03% 0.00% 0.09% 0.03% 0.00% 0.09% −0.01% −0.03% 0.02% Portugal 0.00% 0.02% −0.06% 0.08% 0.08% 0.06% 0.05% 0.06% 0.04% 0.08% 0.09% 0.04% 0.08% 0.09% 0.07% Slovenia 0.01% −0.11% 0.27% 0.07% −0.04% 0.30% 0.06% −0.05% 0.29% 0.06% −0.05% 0.30% 0.02% −0.04% 0.17% Spain 0.01% −0.09% 0.13% 0.13% 0.04% 0.25% 0.08% −0.01% 0.19% 0.09% 0.01% 0.21% 0.04% −0.01% 0.12% Sweden 0.00% 0.01% −0.02% 0.08% 0.10% 0.04% 0.02% 0.04% −0.01% 0.02% 0.04% −0.01% −0.02% −0.01% −0.04% Switzerland 0.00% −0.01% 0.02% 0.02% 0.03% 0.02% 0.00% 0.01% 0.00% −0.01% −0.01% −0.01% −0.04% −0.03% −0.04% UK 0.00% −0.06% 0.07% 0.05% −0.02% 0.12% 0.03% −0.04% 0.11% 0.03% −0.03% 0.11% 0.00% −0.03% 0.05% USA 0.00% 0.01% −0.02% 0.04% 0.08% 0.00% 0.04% 0.08% 0.00% 0.05% 0.08% 0.01% 0.05% 0.06% 0.03% Average 0.00% 0.00% 0.01% 0.07% 0.07% 0.08% 0.05% 0.04% 0.05% 0.05% 0.05% 0.06% 0.02% 0.02% 0.03% Median 0.00% −0.02% 0.03% 0.07% 0.08% 0.06% 0.04% 0.05% 0.04% 0.04% 0.04% 0.04% 0.02% 0.00% 0.02% Notes: Models are defined as in Table 5. View Large Table C.2. Welfare effects for natives of a 1 percentage point increase in immigration. Model 1 Model 2 Model 3 Model 4 Model 5 Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.01% 0.08% −0.13% 0.01% 0.09% −0.12% 0.00% 0.08% −0.13% 0.00% 0.08% −0.13% 0.01% 0.06% −0.08% Austria 0.00% 0.00% 0.01% 0.08% 0.09% 0.07% 0.05% 0.05% 0.04% 0.04% 0.04% 0.04% −0.03% −0.03% −0.03% Belgium 0.00% −0.04% 0.06% 0.09% 0.07% 0.12% 0.03% 0.01% 0.06% 0.03% 0.01% 0.07% −0.02% −0.03% −0.01% Canada 0.01% 0.09% −0.20% 0.04% 0.11% −0.13% 0.03% 0.10% −0.14% 0.03% 0.10% −0.14% 0.04% 0.08% −0.08% Denmark 0.01% 0.14% −0.22% 0.09% 0.21% −0.13% 0.05% 0.17% −0.17% 0.07% 0.19% −0.16% 0.06% 0.11% −0.05% Estonia 0.00% 0.04% −0.06% 0.09% 0.12% 0.05% 0.07% 0.10% 0.03% 0.08% 0.11% 0.03% 0.05% 0.07% 0.02% France 0.00% −0.05% 0.09% 0.07% 0.04% 0.12% 0.03% −0.01% 0.08% 0.04% 0.00% 0.10% 0.02% 0.00% 0.05% Germany 0.00% −0.05% 0.11% 0.07% 0.03% 0.17% 0.02% −0.03% 0.12% 0.02% −0.02% 0.12% −0.01% −0.03% 0.04% Greece 0.01% −0.09% 0.19% 0.15% 0.07% 0.31% 0.13% 0.05% 0.29% 0.15% 0.06% 0.31% 0.07% 0.02% 0.18% Ireland 0.01% 0.11% −0.13% 0.07% 0.15% −0.04% 0.04% 0.13% −0.07% 0.05% 0.15% −0.08% 0.05% 0.10% −0.03% Italy 0.00% −0.02% 0.10% 0.14% 0.12% 0.25% 0.13% 0.10% 0.23% 0.13% 0.11% 0.24% 0.07% 0.05% 0.14% Luxembourg 0.00% −0.02% 0.04% 0.03% 0.02% 0.06% 0.02% 0.00% 0.05% 0.02% 0.00% 0.05% −0.02% −0.03% −0.01% Netherlands 0.00% −0.04% 0.06% 0.06% 0.03% 0.12% 0.03% 0.00% 0.09% 0.03% 0.00% 0.09% −0.01% −0.03% 0.02% Portugal 0.00% 0.02% −0.06% 0.08% 0.08% 0.06% 0.05% 0.06% 0.04% 0.08% 0.09% 0.04% 0.08% 0.09% 0.07% Slovenia 0.01% −0.11% 0.27% 0.07% −0.04% 0.30% 0.06% −0.05% 0.29% 0.06% −0.05% 0.30% 0.02% −0.04% 0.17% Spain 0.01% −0.09% 0.13% 0.13% 0.04% 0.25% 0.08% −0.01% 0.19% 0.09% 0.01% 0.21% 0.04% −0.01% 0.12% Sweden 0.00% 0.01% −0.02% 0.08% 0.10% 0.04% 0.02% 0.04% −0.01% 0.02% 0.04% −0.01% −0.02% −0.01% −0.04% Switzerland 0.00% −0.01% 0.02% 0.02% 0.03% 0.02% 0.00% 0.01% 0.00% −0.01% −0.01% −0.01% −0.04% −0.03% −0.04% UK 0.00% −0.06% 0.07% 0.05% −0.02% 0.12% 0.03% −0.04% 0.11% 0.03% −0.03% 0.11% 0.00% −0.03% 0.05% USA 0.00% 0.01% −0.02% 0.04% 0.08% 0.00% 0.04% 0.08% 0.00% 0.05% 0.08% 0.01% 0.05% 0.06% 0.03% Average 0.00% 0.00% 0.01% 0.07% 0.07% 0.08% 0.05% 0.04% 0.05% 0.05% 0.05% 0.06% 0.02% 0.02% 0.03% Median 0.00% −0.02% 0.03% 0.07% 0.08% 0.06% 0.04% 0.05% 0.04% 0.04% 0.04% 0.04% 0.02% 0.00% 0.02% Model 1 Model 2 Model 3 Model 4 Model 5 Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.01% 0.08% −0.13% 0.01% 0.09% −0.12% 0.00% 0.08% −0.13% 0.00% 0.08% −0.13% 0.01% 0.06% −0.08% Austria 0.00% 0.00% 0.01% 0.08% 0.09% 0.07% 0.05% 0.05% 0.04% 0.04% 0.04% 0.04% −0.03% −0.03% −0.03% Belgium 0.00% −0.04% 0.06% 0.09% 0.07% 0.12% 0.03% 0.01% 0.06% 0.03% 0.01% 0.07% −0.02% −0.03% −0.01% Canada 0.01% 0.09% −0.20% 0.04% 0.11% −0.13% 0.03% 0.10% −0.14% 0.03% 0.10% −0.14% 0.04% 0.08% −0.08% Denmark 0.01% 0.14% −0.22% 0.09% 0.21% −0.13% 0.05% 0.17% −0.17% 0.07% 0.19% −0.16% 0.06% 0.11% −0.05% Estonia 0.00% 0.04% −0.06% 0.09% 0.12% 0.05% 0.07% 0.10% 0.03% 0.08% 0.11% 0.03% 0.05% 0.07% 0.02% France 0.00% −0.05% 0.09% 0.07% 0.04% 0.12% 0.03% −0.01% 0.08% 0.04% 0.00% 0.10% 0.02% 0.00% 0.05% Germany 0.00% −0.05% 0.11% 0.07% 0.03% 0.17% 0.02% −0.03% 0.12% 0.02% −0.02% 0.12% −0.01% −0.03% 0.04% Greece 0.01% −0.09% 0.19% 0.15% 0.07% 0.31% 0.13% 0.05% 0.29% 0.15% 0.06% 0.31% 0.07% 0.02% 0.18% Ireland 0.01% 0.11% −0.13% 0.07% 0.15% −0.04% 0.04% 0.13% −0.07% 0.05% 0.15% −0.08% 0.05% 0.10% −0.03% Italy 0.00% −0.02% 0.10% 0.14% 0.12% 0.25% 0.13% 0.10% 0.23% 0.13% 0.11% 0.24% 0.07% 0.05% 0.14% Luxembourg 0.00% −0.02% 0.04% 0.03% 0.02% 0.06% 0.02% 0.00% 0.05% 0.02% 0.00% 0.05% −0.02% −0.03% −0.01% Netherlands 0.00% −0.04% 0.06% 0.06% 0.03% 0.12% 0.03% 0.00% 0.09% 0.03% 0.00% 0.09% −0.01% −0.03% 0.02% Portugal 0.00% 0.02% −0.06% 0.08% 0.08% 0.06% 0.05% 0.06% 0.04% 0.08% 0.09% 0.04% 0.08% 0.09% 0.07% Slovenia 0.01% −0.11% 0.27% 0.07% −0.04% 0.30% 0.06% −0.05% 0.29% 0.06% −0.05% 0.30% 0.02% −0.04% 0.17% Spain 0.01% −0.09% 0.13% 0.13% 0.04% 0.25% 0.08% −0.01% 0.19% 0.09% 0.01% 0.21% 0.04% −0.01% 0.12% Sweden 0.00% 0.01% −0.02% 0.08% 0.10% 0.04% 0.02% 0.04% −0.01% 0.02% 0.04% −0.01% −0.02% −0.01% −0.04% Switzerland 0.00% −0.01% 0.02% 0.02% 0.03% 0.02% 0.00% 0.01% 0.00% −0.01% −0.01% −0.01% −0.04% −0.03% −0.04% UK 0.00% −0.06% 0.07% 0.05% −0.02% 0.12% 0.03% −0.04% 0.11% 0.03% −0.03% 0.11% 0.00% −0.03% 0.05% USA 0.00% 0.01% −0.02% 0.04% 0.08% 0.00% 0.04% 0.08% 0.00% 0.05% 0.08% 0.01% 0.05% 0.06% 0.03% Average 0.00% 0.00% 0.01% 0.07% 0.07% 0.08% 0.05% 0.04% 0.05% 0.05% 0.05% 0.06% 0.02% 0.02% 0.03% Median 0.00% −0.02% 0.03% 0.07% 0.08% 0.06% 0.04% 0.05% 0.04% 0.04% 0.04% 0.04% 0.02% 0.00% 0.02% Notes: Models are defined as in Table 5. View Large Table C.3. Sensitivity analysis: t fixed, g adjusts. Autarky vs. status quo welfare effects What adjusts: Tax rate t (baseline) Government expenditures g Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 0.24% 1.28% −1.76% Austria 1.77% 1.74% 1.94% 1.74% 1.74% 1.74% Belgium 1.70% 1.37% 2.30% 1.64% 1.41% 2.06% Canada 1.19% 1.79% −0.57% 1.17% 1.86% −0.88% Denmark 1.90% 2.39% 0.86% 1.82% 2.46% 0.46% Estonia 1.47% 1.47% 1.46% 1.45% 1.51% 1.36% France 0.77% 0.52% 1.27% 0.75% 0.53% 1.20% Germany 0.31% −0.07% 1.23% 0.33% −0.08% 1.33% Greece 2.02% 1.40% 3.51% 1.99% 1.42% 3.36% Ireland 1.77% 2.30% 0.95% 1.71% 2.44% 0.57% Italy 1.87% 1.64% 2.97% 1.84% 1.65% 2.77% Luxembourg 0.72% 0.45% 1.15% 0.74% 0.37% 1.30% Netherlands 0.48% 0.23% 0.98% 0.49% 0.22% 1.01% Portugal 1.27% 1.23% 1.41% 1.22% 1.30% 0.95% Slovenia 0.52% −0.20% 2.30% 0.52% −0.21% 2.33% Spain 1.90% 0.96% 3.43% 1.87% 0.98% 3.31% Sweden 0.63% 0.77% 0.34% 0.64% 0.77% 0.38% Switzerland −0.14% 0.04% −0.46% −0.13% −0.04% −0.28% United Kingdom 0.35% −0.22% 1.10% 0.36% −0.24% 1.14% United States 0.80% 0.97% 0.53% 0.79% 1.05% 0.37% Average 1.08% 1.00% 1.25% 1.06% 1.02% 1.14% Median 0.99% 1.10% 1.19% 0.98% 1.17% 1.17% Autarky vs. status quo welfare effects What adjusts: Tax rate t (baseline) Government expenditures g Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 0.24% 1.28% −1.76% Austria 1.77% 1.74% 1.94% 1.74% 1.74% 1.74% Belgium 1.70% 1.37% 2.30% 1.64% 1.41% 2.06% Canada 1.19% 1.79% −0.57% 1.17% 1.86% −0.88% Denmark 1.90% 2.39% 0.86% 1.82% 2.46% 0.46% Estonia 1.47% 1.47% 1.46% 1.45% 1.51% 1.36% France 0.77% 0.52% 1.27% 0.75% 0.53% 1.20% Germany 0.31% −0.07% 1.23% 0.33% −0.08% 1.33% Greece 2.02% 1.40% 3.51% 1.99% 1.42% 3.36% Ireland 1.77% 2.30% 0.95% 1.71% 2.44% 0.57% Italy 1.87% 1.64% 2.97% 1.84% 1.65% 2.77% Luxembourg 0.72% 0.45% 1.15% 0.74% 0.37% 1.30% Netherlands 0.48% 0.23% 0.98% 0.49% 0.22% 1.01% Portugal 1.27% 1.23% 1.41% 1.22% 1.30% 0.95% Slovenia 0.52% −0.20% 2.30% 0.52% −0.21% 2.33% Spain 1.90% 0.96% 3.43% 1.87% 0.98% 3.31% Sweden 0.63% 0.77% 0.34% 0.64% 0.77% 0.38% Switzerland −0.14% 0.04% −0.46% −0.13% −0.04% −0.28% United Kingdom 0.35% −0.22% 1.10% 0.36% −0.24% 1.14% United States 0.80% 0.97% 0.53% 0.79% 1.05% 0.37% Average 1.08% 1.00% 1.25% 1.06% 1.02% 1.14% Median 0.99% 1.10% 1.19% 0.98% 1.17% 1.17% Notes: Results are equivalent to those in the first three of Table 8. View Large Table C.3. Sensitivity analysis: t fixed, g adjusts. Autarky vs. status quo welfare effects What adjusts: Tax rate t (baseline) Government expenditures g Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 0.24% 1.28% −1.76% Austria 1.77% 1.74% 1.94% 1.74% 1.74% 1.74% Belgium 1.70% 1.37% 2.30% 1.64% 1.41% 2.06% Canada 1.19% 1.79% −0.57% 1.17% 1.86% −0.88% Denmark 1.90% 2.39% 0.86% 1.82% 2.46% 0.46% Estonia 1.47% 1.47% 1.46% 1.45% 1.51% 1.36% France 0.77% 0.52% 1.27% 0.75% 0.53% 1.20% Germany 0.31% −0.07% 1.23% 0.33% −0.08% 1.33% Greece 2.02% 1.40% 3.51% 1.99% 1.42% 3.36% Ireland 1.77% 2.30% 0.95% 1.71% 2.44% 0.57% Italy 1.87% 1.64% 2.97% 1.84% 1.65% 2.77% Luxembourg 0.72% 0.45% 1.15% 0.74% 0.37% 1.30% Netherlands 0.48% 0.23% 0.98% 0.49% 0.22% 1.01% Portugal 1.27% 1.23% 1.41% 1.22% 1.30% 0.95% Slovenia 0.52% −0.20% 2.30% 0.52% −0.21% 2.33% Spain 1.90% 0.96% 3.43% 1.87% 0.98% 3.31% Sweden 0.63% 0.77% 0.34% 0.64% 0.77% 0.38% Switzerland −0.14% 0.04% −0.46% −0.13% −0.04% −0.28% United Kingdom 0.35% −0.22% 1.10% 0.36% −0.24% 1.14% United States 0.80% 0.97% 0.53% 0.79% 1.05% 0.37% Average 1.08% 1.00% 1.25% 1.06% 1.02% 1.14% Median 0.99% 1.10% 1.19% 0.98% 1.17% 1.17% Autarky vs. status quo welfare effects What adjusts: Tax rate t (baseline) Government expenditures g Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% 0.24% 1.28% −1.76% Austria 1.77% 1.74% 1.94% 1.74% 1.74% 1.74% Belgium 1.70% 1.37% 2.30% 1.64% 1.41% 2.06% Canada 1.19% 1.79% −0.57% 1.17% 1.86% −0.88% Denmark 1.90% 2.39% 0.86% 1.82% 2.46% 0.46% Estonia 1.47% 1.47% 1.46% 1.45% 1.51% 1.36% France 0.77% 0.52% 1.27% 0.75% 0.53% 1.20% Germany 0.31% −0.07% 1.23% 0.33% −0.08% 1.33% Greece 2.02% 1.40% 3.51% 1.99% 1.42% 3.36% Ireland 1.77% 2.30% 0.95% 1.71% 2.44% 0.57% Italy 1.87% 1.64% 2.97% 1.84% 1.65% 2.77% Luxembourg 0.72% 0.45% 1.15% 0.74% 0.37% 1.30% Netherlands 0.48% 0.23% 0.98% 0.49% 0.22% 1.01% Portugal 1.27% 1.23% 1.41% 1.22% 1.30% 0.95% Slovenia 0.52% −0.20% 2.30% 0.52% −0.21% 2.33% Spain 1.90% 0.96% 3.43% 1.87% 0.98% 3.31% Sweden 0.63% 0.77% 0.34% 0.64% 0.77% 0.38% Switzerland −0.14% 0.04% −0.46% −0.13% −0.04% −0.28% United Kingdom 0.35% −0.22% 1.10% 0.36% −0.24% 1.14% United States 0.80% 0.97% 0.53% 0.79% 1.05% 0.37% Average 1.08% 1.00% 1.25% 1.06% 1.02% 1.14% Median 0.99% 1.10% 1.19% 0.98% 1.17% 1.17% Notes: Results are equivalent to those in the first three of Table 8. View Large Table C.4. Sensitivity analysis: average separation rates from German data. Autarky vs. status quo welfare effects Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% Austria 1.77% 1.74% 1.92% Belgium 1.71% 1.38% 2.30% Canada 1.20% 1.79% −0.57% Denmark 1.91% 2.40% 0.86% Estonia 1.47% 1.48% 1.45% France 0.77% 0.52% 1.27% Germany 0.31% −0.06% 1.22% Greece 2.03% 1.41% 3.51% Ireland 1.79% 2.32% 0.96% Italy 1.87% 1.64% 2.97% Luxembourg 0.73% 0.45% 1.14% Netherlands 0.48% 0.24% 0.97% Portugal 1.30% 1.26% 1.44% Slovenia 0.52% −0.20% 2.30% Spain 1.91% 0.97% 3.43% Sweden 0.63% 0.78% 0.33% Switzerland −0.14% 0.04% −0.46% United Kingdom 0.36% −0.21% 1.10% United States 0.79% 0.96% 0.53% Average 1.08% 1.01% 1.25% Median 1.00% 1.11% 1.18% Autarky vs. status quo welfare effects Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% Austria 1.77% 1.74% 1.92% Belgium 1.71% 1.38% 2.30% Canada 1.20% 1.79% −0.57% Denmark 1.91% 2.40% 0.86% Estonia 1.47% 1.48% 1.45% France 0.77% 0.52% 1.27% Germany 0.31% −0.06% 1.22% Greece 2.03% 1.41% 3.51% Ireland 1.79% 2.32% 0.96% Italy 1.87% 1.64% 2.97% Luxembourg 0.73% 0.45% 1.14% Netherlands 0.48% 0.24% 0.97% Portugal 1.30% 1.26% 1.44% Slovenia 0.52% −0.20% 2.30% Spain 1.91% 0.97% 3.43% Sweden 0.63% 0.78% 0.33% Switzerland −0.14% 0.04% −0.46% United Kingdom 0.36% −0.21% 1.10% United States 0.79% 0.96% 0.53% Average 1.08% 1.01% 1.25% Median 1.00% 1.11% 1.18% Notes: Results are equivalent to those in the first three columns of Table 8, with average separation rates from SIAB microdata for Germany. View Large Table C.4. Sensitivity analysis: average separation rates from German data. Autarky vs. status quo welfare effects Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% Austria 1.77% 1.74% 1.92% Belgium 1.71% 1.38% 2.30% Canada 1.20% 1.79% −0.57% Denmark 1.91% 2.40% 0.86% Estonia 1.47% 1.48% 1.45% France 0.77% 0.52% 1.27% Germany 0.31% −0.06% 1.22% Greece 2.03% 1.41% 3.51% Ireland 1.79% 2.32% 0.96% Italy 1.87% 1.64% 2.97% Luxembourg 0.73% 0.45% 1.14% Netherlands 0.48% 0.24% 0.97% Portugal 1.30% 1.26% 1.44% Slovenia 0.52% −0.20% 2.30% Spain 1.91% 0.97% 3.43% Sweden 0.63% 0.78% 0.33% Switzerland −0.14% 0.04% −0.46% United Kingdom 0.36% −0.21% 1.10% United States 0.79% 0.96% 0.53% Average 1.08% 1.01% 1.25% Median 1.00% 1.11% 1.18% Autarky vs. status quo welfare effects Countries $$\mathcal {W}_N$$ $$\mathcal {W}_{\mathit {LN}}$$ $$\mathcal {W}_{\mathit {HN}}$$ Australia 0.24% 1.26% −1.72% Austria 1.77% 1.74% 1.92% Belgium 1.71% 1.38% 2.30% Canada 1.20% 1.79% −0.57% Denmark 1.91% 2.40% 0.86% Estonia 1.47% 1.48% 1.45% France 0.77% 0.52% 1.27% Germany 0.31% −0.06% 1.22% Greece 2.03% 1.41% 3.51% Ireland 1.79% 2.32% 0.96% Italy 1.87% 1.64% 2.97% Luxembourg 0.73% 0.45% 1.14% Netherlands 0.48% 0.24% 0.97% Portugal 1.30% 1.26% 1.44% Slovenia 0.52% −0.20% 2.30% Spain 1.91% 0.97% 3.43% Sweden 0.63% 0.78% 0.33% Switzerland −0.14% 0.04% −0.46% United Kingdom 0.36% −0.21% 1.10% United States 0.79% 0.96% 0.53% Average 1.08% 1.01% 1.25% Median 1.00% 1.11% 1.18% Notes: Results are equivalent to those in the first three columns of Table 8, with average separation rates from SIAB microdata for Germany. View Large Table C.5. Sensitivity analysis: effects of one percentage point increase in migration when unemployment has nonmonetary utility costs for natives. All natives Low skilled natives High Skilled Natives hN 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 Australia 0.012% 0.012% 0.012% 0.011% 0.013% 0.059% 0.059% 0.059% 0.058% 0.060% −0.079% −0.080% −0.078% −0.081% −0.077% Austria −0.030% −0.030% −0.030% −0.029% −0.030% −0.028% −0.028% −0.029% −0.028% −0.029% −0.034% −0.036% −0.033% −0.037% −0.032% Belgium −0.024% −0.027% −0.021% −0.031% −0.016% −0.034% −0.036% −0.032% −0.038% −0.030% −0.005% −0.011% 0.000% −0.018% 0.010% Canada 0.036% 0.036% 0.037% 0.036% 0.037% 0.075% 0.075% 0.075% 0.075% 0.076% −0.079% −0.079% −0.079% −0.079% -0.078% Denmark 0.057% 0.054% 0.061% 0.050% 0.066% 0.108% 0.106% 0.111% 0.103% 0.115% −0.052% −0.056% −0.047% −0.062% −0.038% Estonia 0.049% 0.048% 0.050% 0.046% 0.053% 0.066% 0.065% 0.067% 0.064% 0.068% 0.019% 0.017% 0.021% 0.015% 0.026% France 0.015% 0.010% 0.021% 0.003% 0.031% −0.003% −0.007% 0.001% −0.012% 0.008% 0.053% 0.045% 0.062% 0.034% 0.079% Germany −0.012% −0.015% −0.009% −0.019% −0.004% −0.035% −0.037% −0.032% −0.041% −0.028% 0.043% 0.040% 0.048% 0.035% 0.055% Greece 0.068% 0.067% 0.070% 0.064% 0.074% 0.023% 0.022% 0.024% 0.021% 0.024% 0.178% 0.173% 0.183% 0.167% 0.193% Ireland 0.047% 0.045% 0.049% 0.042% 0.054% 0.098% 0.096% 0.100% 0.094% 0.103% −0.033% −0.035% −0.029% −0.039% −0.023% Italy 0.067% 0.066% 0.067% 0.065% 0.069% 0.052% 0.052% 0.053% 0.051% 0.053% 0.135% 0.133% 0.138% 0.130% 0.142% Luxembourg −0.024% −0.024% −0.024% −0.024% −0.024% −0.034% −0.034% −0.034% −0.033% −0.034% −0.008% −0.008% −0.008% −0.009% −0.008% Netherlands −0.010% −0.011% −0.009% −0.012% −0.008% −0.025% −0.026% −0.024% −0.027% −0.023% 0.020% 0.018% 0.021% 0.016% 0.024% Portugal 0.083% 0.076% 0.091% 0.068% 0.108% 0.085% 0.079% 0.093% 0.072% 0.107% 0.073% 0.064% 0.085% 0.054% 0.113% Slovenia 0.020% 0.018% 0.021% 0.016% 0.023% −0.040% −0.041% −0.039% −0.042% −0.037% 0.167% 0.165% 0.170% 0.161% 0.175% Spain 0.040% 0.037% 0.044% 0.033% 0.050% −0.010% −0.012% −0.007% −0.016% −0.004% 0.121% 0.116% 0.127% 0.110% 0.136% Sweden −0.017% −0.018% −0.015% −0.021% −0.011% −0.006% −0.008% −0.005% −0.010% −0.003% −0.037% −0.040% −0.034% −0.044% −0.029% Switzerland −0.036% −0.035% −0.036% −0.035% −0.037% −0.034% −0.033% −0.035% −0.033% −0.036% −0.038% −0.038% −0.038% −0.038% −0.038% UK 0.005% 0.004% 0.006% 0.002% 0.007% −0.029% −0.030% −0.028% −0.032% −0.026% 0.049% 0.048% 0.049% 0.047% 0.051% USA 0.045% 0.045% 0.046% 0.044% 0.046% 0.057% 0.058% 0.057% 0.059% 0.056% 0.027% 0.025% 0.029% 0.023% 0.032% Average 0.020% 0.018% 0.022% 0.015% 0.025% 0.017% 0.016% 0.019% 0.014% 0.021% 0.026% 0.023% 0.029% 0.019% 0.036% Median 0.017% 0.015% 0.021% 0.014% 0.027% −0.005% −0.007% −0.002% −0.011% 0.003% 0.019% 0.018% 0.021% 0.016% 0.025% All natives Low skilled natives High Skilled Natives hN 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 Australia 0.012% 0.012% 0.012% 0.011% 0.013% 0.059% 0.059% 0.059% 0.058% 0.060% −0.079% −0.080% −0.078% −0.081% −0.077% Austria −0.030% −0.030% −0.030% −0.029% −0.030% −0.028% −0.028% −0.029% −0.028% −0.029% −0.034% −0.036% −0.033% −0.037% −0.032% Belgium −0.024% −0.027% −0.021% −0.031% −0.016% −0.034% −0.036% −0.032% −0.038% −0.030% −0.005% −0.011% 0.000% −0.018% 0.010% Canada 0.036% 0.036% 0.037% 0.036% 0.037% 0.075% 0.075% 0.075% 0.075% 0.076% −0.079% −0.079% −0.079% −0.079% -0.078% Denmark 0.057% 0.054% 0.061% 0.050% 0.066% 0.108% 0.106% 0.111% 0.103% 0.115% −0.052% −0.056% −0.047% −0.062% −0.038% Estonia 0.049% 0.048% 0.050% 0.046% 0.053% 0.066% 0.065% 0.067% 0.064% 0.068% 0.019% 0.017% 0.021% 0.015% 0.026% France 0.015% 0.010% 0.021% 0.003% 0.031% −0.003% −0.007% 0.001% −0.012% 0.008% 0.053% 0.045% 0.062% 0.034% 0.079% Germany −0.012% −0.015% −0.009% −0.019% −0.004% −0.035% −0.037% −0.032% −0.041% −0.028% 0.043% 0.040% 0.048% 0.035% 0.055% Greece 0.068% 0.067% 0.070% 0.064% 0.074% 0.023% 0.022% 0.024% 0.021% 0.024% 0.178% 0.173% 0.183% 0.167% 0.193% Ireland 0.047% 0.045% 0.049% 0.042% 0.054% 0.098% 0.096% 0.100% 0.094% 0.103% −0.033% −0.035% −0.029% −0.039% −0.023% Italy 0.067% 0.066% 0.067% 0.065% 0.069% 0.052% 0.052% 0.053% 0.051% 0.053% 0.135% 0.133% 0.138% 0.130% 0.142% Luxembourg −0.024% −0.024% −0.024% −0.024% −0.024% −0.034% −0.034% −0.034% −0.033% −0.034% −0.008% −0.008% −0.008% −0.009% −0.008% Netherlands −0.010% −0.011% −0.009% −0.012% −0.008% −0.025% −0.026% −0.024% −0.027% −0.023% 0.020% 0.018% 0.021% 0.016% 0.024% Portugal 0.083% 0.076% 0.091% 0.068% 0.108% 0.085% 0.079% 0.093% 0.072% 0.107% 0.073% 0.064% 0.085% 0.054% 0.113% Slovenia 0.020% 0.018% 0.021% 0.016% 0.023% −0.040% −0.041% −0.039% −0.042% −0.037% 0.167% 0.165% 0.170% 0.161% 0.175% Spain 0.040% 0.037% 0.044% 0.033% 0.050% −0.010% −0.012% −0.007% −0.016% −0.004% 0.121% 0.116% 0.127% 0.110% 0.136% Sweden −0.017% −0.018% −0.015% −0.021% −0.011% −0.006% −0.008% −0.005% −0.010% −0.003% −0.037% −0.040% −0.034% −0.044% −0.029% Switzerland −0.036% −0.035% −0.036% −0.035% −0.037% −0.034% −0.033% −0.035% −0.033% −0.036% −0.038% −0.038% −0.038% −0.038% −0.038% UK 0.005% 0.004% 0.006% 0.002% 0.007% −0.029% −0.030% −0.028% −0.032% −0.026% 0.049% 0.048% 0.049% 0.047% 0.051% USA 0.045% 0.045% 0.046% 0.044% 0.046% 0.057% 0.058% 0.057% 0.059% 0.056% 0.027% 0.025% 0.029% 0.023% 0.032% Average 0.020% 0.018% 0.022% 0.015% 0.025% 0.017% 0.016% 0.019% 0.014% 0.021% 0.026% 0.023% 0.029% 0.019% 0.036% Median 0.017% 0.015% 0.021% 0.014% 0.027% −0.005% −0.007% −0.002% −0.011% 0.003% 0.019% 0.018% 0.021% 0.016% 0.025% Notes: In all exercises, $$h_{\mathit {LN}}=h_{\mathit {HN}}$$, so we simply denote them by hN. A negative value of hN means that we are introducing a utility, because hN enters the value of being unemployed positively. The values of 0.02 and 0.05 are around 10% and 25% of average unemployment benefits received by natives in our 20 countries, respectively. View Large Table C.5. Sensitivity analysis: effects of one percentage point increase in migration when unemployment has nonmonetary utility costs for natives. All natives Low skilled natives High Skilled Natives hN 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 Australia 0.012% 0.012% 0.012% 0.011% 0.013% 0.059% 0.059% 0.059% 0.058% 0.060% −0.079% −0.080% −0.078% −0.081% −0.077% Austria −0.030% −0.030% −0.030% −0.029% −0.030% −0.028% −0.028% −0.029% −0.028% −0.029% −0.034% −0.036% −0.033% −0.037% −0.032% Belgium −0.024% −0.027% −0.021% −0.031% −0.016% −0.034% −0.036% −0.032% −0.038% −0.030% −0.005% −0.011% 0.000% −0.018% 0.010% Canada 0.036% 0.036% 0.037% 0.036% 0.037% 0.075% 0.075% 0.075% 0.075% 0.076% −0.079% −0.079% −0.079% −0.079% -0.078% Denmark 0.057% 0.054% 0.061% 0.050% 0.066% 0.108% 0.106% 0.111% 0.103% 0.115% −0.052% −0.056% −0.047% −0.062% −0.038% Estonia 0.049% 0.048% 0.050% 0.046% 0.053% 0.066% 0.065% 0.067% 0.064% 0.068% 0.019% 0.017% 0.021% 0.015% 0.026% France 0.015% 0.010% 0.021% 0.003% 0.031% −0.003% −0.007% 0.001% −0.012% 0.008% 0.053% 0.045% 0.062% 0.034% 0.079% Germany −0.012% −0.015% −0.009% −0.019% −0.004% −0.035% −0.037% −0.032% −0.041% −0.028% 0.043% 0.040% 0.048% 0.035% 0.055% Greece 0.068% 0.067% 0.070% 0.064% 0.074% 0.023% 0.022% 0.024% 0.021% 0.024% 0.178% 0.173% 0.183% 0.167% 0.193% Ireland 0.047% 0.045% 0.049% 0.042% 0.054% 0.098% 0.096% 0.100% 0.094% 0.103% −0.033% −0.035% −0.029% −0.039% −0.023% Italy 0.067% 0.066% 0.067% 0.065% 0.069% 0.052% 0.052% 0.053% 0.051% 0.053% 0.135% 0.133% 0.138% 0.130% 0.142% Luxembourg −0.024% −0.024% −0.024% −0.024% −0.024% −0.034% −0.034% −0.034% −0.033% −0.034% −0.008% −0.008% −0.008% −0.009% −0.008% Netherlands −0.010% −0.011% −0.009% −0.012% −0.008% −0.025% −0.026% −0.024% −0.027% −0.023% 0.020% 0.018% 0.021% 0.016% 0.024% Portugal 0.083% 0.076% 0.091% 0.068% 0.108% 0.085% 0.079% 0.093% 0.072% 0.107% 0.073% 0.064% 0.085% 0.054% 0.113% Slovenia 0.020% 0.018% 0.021% 0.016% 0.023% −0.040% −0.041% −0.039% −0.042% −0.037% 0.167% 0.165% 0.170% 0.161% 0.175% Spain 0.040% 0.037% 0.044% 0.033% 0.050% −0.010% −0.012% −0.007% −0.016% −0.004% 0.121% 0.116% 0.127% 0.110% 0.136% Sweden −0.017% −0.018% −0.015% −0.021% −0.011% −0.006% −0.008% −0.005% −0.010% −0.003% −0.037% −0.040% −0.034% −0.044% −0.029% Switzerland −0.036% −0.035% −0.036% −0.035% −0.037% −0.034% −0.033% −0.035% −0.033% −0.036% −0.038% −0.038% −0.038% −0.038% −0.038% UK 0.005% 0.004% 0.006% 0.002% 0.007% −0.029% −0.030% −0.028% −0.032% −0.026% 0.049% 0.048% 0.049% 0.047% 0.051% USA 0.045% 0.045% 0.046% 0.044% 0.046% 0.057% 0.058% 0.057% 0.059% 0.056% 0.027% 0.025% 0.029% 0.023% 0.032% Average 0.020% 0.018% 0.022% 0.015% 0.025% 0.017% 0.016% 0.019% 0.014% 0.021% 0.026% 0.023% 0.029% 0.019% 0.036% Median 0.017% 0.015% 0.021% 0.014% 0.027% −0.005% −0.007% −0.002% −0.011% 0.003% 0.019% 0.018% 0.021% 0.016% 0.025% All natives Low skilled natives High Skilled Natives hN 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 0 −0.02 0.02 −0.05 0.05 Australia 0.012% 0.012% 0.012% 0.011% 0.013% 0.059% 0.059% 0.059% 0.058% 0.060% −0.079% −0.080% −0.078% −0.081% −0.077% Austria −0.030% −0.030% −0.030% −0.029% −0.030% −0.028% −0.028% −0.029% −0.028% −0.029% −0.034% −0.036% −0.033% −0.037% −0.032% Belgium −0.024% −0.027% −0.021% −0.031% −0.016% −0.034% −0.036% −0.032% −0.038% −0.030% −0.005% −0.011% 0.000% −0.018% 0.010% Canada 0.036% 0.036% 0.037% 0.036% 0.037% 0.075% 0.075% 0.075% 0.075% 0.076% −0.079% −0.079% −0.079% −0.079% -0.078% Denmark 0.057% 0.054% 0.061% 0.050% 0.066% 0.108% 0.106% 0.111% 0.103% 0.115% −0.052% −0.056% −0.047% −0.062% −0.038% Estonia 0.049% 0.048% 0.050% 0.046% 0.053% 0.066% 0.065% 0.067% 0.064% 0.068% 0.019% 0.017% 0.021% 0.015% 0.026% France 0.015% 0.010% 0.021% 0.003% 0.031% −0.003% −0.007% 0.001% −0.012% 0.008% 0.053% 0.045% 0.062% 0.034% 0.079% Germany −0.012% −0.015% −0.009% −0.019% −0.004% −0.035% −0.037% −0.032% −0.041% −0.028% 0.043% 0.040% 0.048% 0.035% 0.055% Greece 0.068% 0.067% 0.070% 0.064% 0.074% 0.023% 0.022% 0.024% 0.021% 0.024% 0.178% 0.173% 0.183% 0.167% 0.193% Ireland 0.047% 0.045% 0.049% 0.042% 0.054% 0.098% 0.096% 0.100% 0.094% 0.103% −0.033% −0.035% −0.029% −0.039% −0.023% Italy 0.067% 0.066% 0.067% 0.065% 0.069% 0.052% 0.052% 0.053% 0.051% 0.053% 0.135% 0.133% 0.138% 0.130% 0.142% Luxembourg −0.024% −0.024% −0.024% −0.024% −0.024% −0.034% −0.034% −0.034% −0.033% −0.034% −0.008% −0.008% −0.008% −0.009% −0.008% Netherlands −0.010% −0.011% −0.009% −0.012% −0.008% −0.025% −0.026% −0.024% −0.027% −0.023% 0.020% 0.018% 0.021% 0.016% 0.024% Portugal 0.083% 0.076% 0.091% 0.068% 0.108% 0.085% 0.079% 0.093% 0.072% 0.107% 0.073% 0.064% 0.085% 0.054% 0.113% Slovenia 0.020% 0.018% 0.021% 0.016% 0.023% −0.040% −0.041% −0.039% −0.042% −0.037% 0.167% 0.165% 0.170% 0.161% 0.175% Spain 0.040% 0.037% 0.044% 0.033% 0.050% −0.010% −0.012% −0.007% −0.016% −0.004% 0.121% 0.116% 0.127% 0.110% 0.136% Sweden −0.017% −0.018% −0.015% −0.021% −0.011% −0.006% −0.008% −0.005% −0.010% −0.003% −0.037% −0.040% −0.034% −0.044% −0.029% Switzerland −0.036% −0.035% −0.036% −0.035% −0.037% −0.034% −0.033% −0.035% −0.033% −0.036% −0.038% −0.038% −0.038% −0.038% −0.038% UK 0.005% 0.004% 0.006% 0.002% 0.007% −0.029% −0.030% −0.028% −0.032% −0.026% 0.049% 0.048% 0.049% 0.047% 0.051% USA 0.045% 0.045% 0.046% 0.044% 0.046% 0.057% 0.058% 0.057% 0.059% 0.056% 0.027% 0.025% 0.029% 0.023% 0.032% Average 0.020% 0.018% 0.022% 0.015% 0.025% 0.017% 0.016% 0.019% 0.014% 0.021% 0.026% 0.023% 0.029% 0.019% 0.036% Median 0.017% 0.015% 0.021% 0.014% 0.027% −0.005% −0.007% −0.002% −0.011% 0.003% 0.019% 0.018% 0.021% 0.016% 0.025% Notes: In all exercises, $$h_{\mathit {LN}}=h_{\mathit {HN}}$$, so we simply denote them by hN. A negative value of hN means that we are introducing a utility, because hN enters the value of being unemployed positively. The values of 0.02 and 0.05 are around 10% and 25% of average unemployment benefits received by natives in our 20 countries, respectively. View Large Acknowledgments We would like to thank the editor and four anonymous referees for excellent comments and suggestions. We are also grateful for comments and suggestions from Simone Bertoli, from seminar participants in Clermont-Ferrand, Nottingham, Munich, Bayreuth, and Linz, and from participants of LAGV, IIPF, EEA and of the OECD Migration conference in 2014, and ESPE in 2015. We thank Robert Breunig and Syed Hasan for providing summary statistics for Australia. Financial support by the Leibniz Association (SAW-2012-ifo-3) is gratefully acknowledged. Felbermayr is a Research Fellow at CESifo, Peri is a Research Fellow at CESifo and IZA and a Research Associate at NBER, Poutvaara is a Research Fellow at CESifo, CReAM and IZA. Notes The editor in charge of this paper was Dirk Krueger. Footnotes 1 Longhi, Nijkamp, and Poot (2008) provide a meta-analysis of estimates. In his survey, Hanson (2009) criticizes that the literature is characterized by a “near obsession” with wages. 2 For example, Borjas (2003), Ottaviano and Peri (2012) and the references therein. 3 An older theoretical literature suggests that immigrants generate efficiency gains by weakening the bargaining power of labor unions; see Schmidt, Stilz, and Zimmermann (1994). Borjas (2001) argues that immigrant workers react more flexibly to differences in job opportunities than native workers because they are not tied to any specific location, thereby smoothing labor market frictions. Angrist and Kugler (2003) conclude that low labor market flexibility increases the negative effects of immigration in Europe. 4 In many countries there has been a fierce debate about the net fiscal contribution of immigrants. For Germany, see Sinn et al. (2001) and Bonin (2002). 5 We have been able to compile a set of comparative and reliable moments for 16 E.U. member states, plus Switzerland, the United States, Canada and Australia. The data are taken from national censuses or similar sources and generally refer to the year 2011. See Appendix B for details. 6 The countries in our sample have a larger share of immigrants than the average OECD country, which has 10%. 7 In all of our analysis, we define skills based on educational attainment. Highly skilled workers are those with (any completed) tertiary education. 8 This is especially true in Europe; see Kerr and Kerr (2011). 9 An alternative possibility, which we rule out in this paper, is classical employer discrimination, whereby the additional surplus from employing an immigrant compensates the firm for its “distaste” of employing immigrants. 10 This stylized measure abstracts from many complications of real-life unemployment insurance systems but is the only harmonized measure available. 11 We find this a better measure than the share of income transfers in GDP. Many publicly provided goods, like health care, schooling, and infrastructure, provide benefits independent from the recipient’s income. Taxes, however, are income dependent, thereby entailing an important redistributive component. 12 Acemoglu (2002) and Ottaviano and Peri (2012) use a similar structure. In contrast, Chassamboulli and Palivos (2014) assume that capital is needed only in the production of the high-skilled good. This implies a positive correlation between relative employment of skilled and unskilled, and the capital share. In our sample of 20 countries, this correlation is not statistically significant, and so we follow Acemoglu (2002). 13 We rule out complementarity effects within skill groups. This assumption implies that the positive wage impact on natives may be understated. See the debate in Ottaviano and Peri (2012). 14 The only exception to this situation are the internal migration flows between Western European countries which have been free for the period considered. For all other countries, and especially for migration from non-OECD to OECD countries, restrictions are generally binding, as high migration pressure shows. 15 A possible alternative is to allow for directed search by firms, implying separate labor markets for immigrants and natives. In that case, however, we should consider immigrants and natives as two different factors of production, and hence focus on immigrants’ substitutability with natives. That complementarity channel is analyzed in Ottaviano and Peri (2012), while here we assume it away, opting for a more conservative assumption (as in Borjas 2003). Interestingly, if immigrants and natives are not different factors ex-ante (i.e., they are perfect substitutes), it makes sense for them to match with the same opening so that the firm will not target them specifically. This is what produces the job-creation effect if immigrants are more valued by the firm. 16 From the workers’ point of view, return migration affects their welfare level to the extent that the value associated with this remigration event differs from that in the host country. However, in our Online Appendix we show that all equilibrium outcomes are unaffected by the value of remigration provided that that value does not depend on whether remigration follows an employment spell or an unemployment spell. Because the value of remigration does not play a role for any of the outcomes we investigate, simply for notational conciseness we assume it to be equal to the value of unemployment in the home country, without loss of generality. The unemployment rate is not directly affected by the remigration rate, because in the steady-state of our model remigration must be compensated by new arrivals. In terms of the writing of the model, this is equivalent to interpreting the remigration shock to immigrants as relating to the exogenous relocation within the host country. The Bellman equations in the body of the text therefore do not explicitly include remigration, but are also valid for a model with an exogenous probability of remigration that affects both employed and unemployed immigrants. 17 It could be argued that hij should be a positive value of leisure, as those without a job have more time available. However, the social psychologist Jahoda (1981) highlights that employment provides several important nonmonetary payoffs, including social contacts beyond the family. There is evidence of significant utility costs of unemployment for the United States and the United Kingdom (Blanchflower and Oswald 2004), and for Germany (Winkelmann and Winkelmann 1995; Schöb 2012), which suggest a negative value of hij. Chassamboulli and Palivos (2014) make the same assumption. In Section 4.3.3 we present the results of a sensitivity analysis where we evaluate the extent to which this assumption affects our results. We find our results to be very robust to changing $$h_{\mathit {LN}}$$ and $$h_{\mathit {HN}}$$. 18 Note that the model features an implicit minimum wage which is equal to the outside option (bij + hij)/(1 − t). 19 Given the static structure of the model, we are able to analyze fiscal redistribution between high- and low-skilled workers, and between employed and unemployed workers, but not between generations. Immigration may change the age profile of the population and hence affect intergenerational redistribution, but this is not the focus of this paper. 20 The optimality of zero taxation of capital income follows from our small open economy assumption. In addition, because we assume capital is distributed evenly among natives and returns to capital do not change with migration, introducing a proportional taxation of capital income would not have any first-order qualitative effects on our results. 21 Assuming the government additionally provides a pure public good would increase the gains of immigration mechanically, as costs would be distributed over a larger population. Our baseline formulation provides conservative estimates on potential benefits of immigration. In our data, regressing the log of public expenditures on the log of population size produces a coefficient of 1.03 (t-statistic: 18.66; R-squared: 0.95). This is consistent with our baseline hypothesis that government expenditures can be expressed in terms of per capita transfers, the role for pure public goods being limited. In a sensitivity analysis (Section 4.3.2), we consider defense and the service of public debt as nonrival components of public spending. 22 We calculate unemployment benefits using data on replacement rates and wages. 23 Table C.3 reports results based on an alternative specification, in which t is fixed and g adjusts to satisfy the budget constraint. Results are very similar. 24 Utility obtained from public goods consumption drops out of (14) because public goods are enjoyed irrespective of employment status. 25 This restriction is equivalent to setting the price index equal to 1 in the production function system (1), that is, P = A−1(r + δ)αΠ1 − α(α−α(1 − α)α−1) with $$\Pi =(p_{L}^{\rho /( \rho -1) }x^{1/( 1-\rho ) }+p_{H}^{\rho /( \rho -1) }(1-x)^{1/( 1-\rho )})^{\rho /( 1-\rho) }$$. 26 In our Online Appendix, we also impose siI > siN, which is always met in the data but is certainly not necessary. 27 We checked that this is just a normalization by changing the value of cL and verified that results are unaffected. 28 We were unable to find reliable data on remigration probabilities that are skill specific, so we will need to use an average value for both low-skilled and high-skilled immigrants. 29 We drop the subscript because we are not able to distinguish this by skill in our data. 30 Several other studies find similar remigration rates. Jensen and Pedersen (2007) estimate a five year return rate of 55% for Denmark. Bratsberg, Raaum, and Røed (2010) estimate a 50% remigration rate for Norway. Bijwaard, Schluter, and Wahba (2014) estimates a remigration of 47% for the Netherlands in the window 1999–2007. Recent studies for the United States (Cadena and Kovak 2016) and Germany (Schündeln 2014) show that immigrants also exhibit larger internal mobility, relative to natives, and less attachment to their location. These facts are consistent with larger exogenous mobility of immigrants. 31 Only a few studies present direct evidence on job separation rates for natives relative to immigrants. Using Swedish data, Arai and Vilhelmsson (2004) find that immigrants have higher chances of becoming unemployed compared to natives. Sá (2011) presents cross-country evidence from the E.U. LFS showing employment duration tends to be shorter for immigrants. Dustmann, Glitz, and Vogel (2010) provide evidence that immigrants have higher separation rates compared with natives of similar skill levels in Germany, and argue that this depends on remigration. Hirsch and Jahn (2015) also use German data and find higher separation rates into nonemployment for immigrants. Carrasco and Garcia-Perez (2015) find that average employment duration for natives is significantly longer than for immigrants in Spain, using 2000–2014 data. 32 We construct the four population shares from the immigrant share of the working-age population, the skill ratio of native and immigrant labor force, and this normalization. 33 Out of the 11 empirical moments, 10 are linearly independent. We have country-specific information on job duration by skill only for the United States and Germany. In our baseline calibration, we use the United States values for all countries. Table C.4 in the Appendix reports results obtained from using German microdata for all countries instead. This choice only makes a negligible quantitative difference. 34 In reality, it is likely that unemployment benefits packages are better for natives than for immigrants, and therefore that some of what the differences in the disutility from unemployment may pick up are differences in benefits. 35 These models do not feature search frictions on the labor market, whereas our Model 1 does. 36 The small effect of adding unemployment insurance is a robust finding across our entire country sample (see Table C.2 in the Appendix). 37 Table 6 reports welfare effects on immigrants already in the receiving country as of 2011. Therefore, in this exercise we do not consider the welfare gains for new immigrants arising from comparing welfare in their country of origin and their destination country. Such gains are likely to be much larger than our estimates in most cases. 38 This is comparable in magnitude to the labor force effect of the population of refugees to Germany in 2015. 39 Because of data limitations, we are unable to investigate the case in which a certain fraction of high-skilled immigrants enters a segment of the labor market that outs them in competition with low-skilled natives rather than high-skilled natives, due to “downgrading”, which is a well-documented phenomenon in the migration literature, see Dustmann, Frattini, and Preston (2013) among others. If some of the high-skilled immigrants “downgrade” this effectively increases the share of low-skilled immigrants. We believe this exercise can then be informative on what such an intermediate scenario may look like. 40 Shares in France and in the Netherlands fell very slightly. 41 In three of the five countries in which the native welfare decreased, this resulted from a decrease in the share of immigrants in the workforce, and in the remaining two from a decrease in the share of high-skilled among immigrants. 42 Those authors simulate the labor market effects of immigrants in a model featuring competitive labor markets. They focus on net immigration between 1990 and 2000 into OECD countries. Their study does not feature labor market frictions, the job creation channel or the income redistribution effects. However, it allows for potentially positive productive externalities from the concentration of high skilled. 43 The country moments are those listed in the lower half of Table 2 and the nine moments that vary across countries in Table 3 (job duration has no country variation). This gives us a total of 15 moments. 44 We truncate the distribution at μk ± 2σk to avoid realizations that are ruled out by parameter restrictions. 45 The log-linear specification of (16) is an approximation of the nonlinear relationship implied by our model. 46 Standardized beta coefficients measure the impact of an independent variable on the dependent variable in units of standard deviations, that is, $$\hat{\beta } _{k}\sigma ( \ln X_{k}) /\sigma ( \Delta \ln \mathcal {W} _{N})$$. Results from running the same regression on observational data for our 20 economies rather than on simulated data are in line with those of Table 9. 47 On the other hand, the share of tertiary educated among natives is unimportant once educational attainments of immigrants relative to natives are taken into account. 48 Table C.1 reports the value of military spending and interest payments as share of GDP in each country. 49 In contrast, the same data from the European Social Survey indicate the wage effects of immigration are relatively unimportant, despite their prominent role in the economic literature. 50 We are abstracting from the fiscal channel here, which adds a further mechanism: If immigrants have higher separation rates, they will have higher equilibrium unemployment rates, which imply larger transfers from natives even in the absence of wage gaps. 51 See Wooden and Watson (2007) and Breunig, Hasan, and Salehin (2013). 52 We thank Eurostat for providing us with summary statistics based on the EU-SILC dataset. 53 We use the Net Replacement Rates summary measure provided by the OECD, and defined as the average of the net unemployment benefit replacement rates for two earnings levels, three family situations, averaged over 60 months of unemployment and excluding Social Assistance and Housing Benefits. 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# Immigration, Search and Redistribution: A Quantitative Assessment of Native Welfare

, Volume 16 (4) – Aug 1, 2018
52 pages