Intergenerational Mobility and the Political Economy of Immigration

Intergenerational Mobility and the Political Economy of Immigration Henning Bohn Armando R. Lopez-Velasco April 2017 Abstract Flows of US immigrants are concentrated at the extremes of the skill distribution. We develop a dynamic political economy model consistent with these observations. Individuals care about wages and the welfare of their children. Skill types are complementary in production. Voter support for immigration requires that the children of median-voter natives and of immigrants have suffi ciently dissimilar skills. We estimate intergenerational transition matrices for skills, as measured by education, and find support for immigration at high and low skills, but not in the middle. In a version with guest worker programs, voters prefer high-skilled immigrants but low-skilled guest workers. Keywords: immigration, political economy model, overlapping generations, intergenerational mobility, guest workers JEL: F22, E24 We thank Finn Kydland, Peter Rupert, Giulio Zanella, Shawn Knabb, Stephen Trejo, Pia Orrenius, Carlos Zarazaga, Erick French and Julian Neyra for valuable comments and discussions. We also thank the comments by Nicola Pavoni as well as of two anonymous referees. All remaining errors are our own. Corresponding Author. Department of Economics, University of California Santa Barbara; Santa Barbara CA 93106; and CESifo network. Phone (805) 893-4532. E-mail: henning.bohn@ucsb.edu. Homepage: http://www.econ.ucsb.edu/~bohn Department of Economics, 253 Holden Hall. Texas Tech University. Lubbock, TX. Phone (806) 834-8436. Email: ar.lopez@ttu.edu. Webpage: https://sites.google.com/site/armandolopezvelascowebpage

1 Introduction Stylized facts of international migration are that immigrants tend to be concentrated at the extremes of the skill distribution (high and low) and that high- and low-skilled immigrants are treated very differently. Many countries allow or even encourage immigration of high-skilled workers, but they prohibit low-skilled immigration or only accept low-skilled foreigners temporarily (e.g., as guest workers or by allowing illegal immigrants subject to instant deportation to stay). We examine the political economy of immigration in a dynamic model in which natives care about their children and recognize that immigration influences the labor market for current and future generations. Skill types are complementary and the majority of natives is medium-skilled. Hence from a static perspective, the native majority benefits from foreign workers with skills far from the middle, both high and low. The challenge is to explain the differential treatment of high and low skilled foreigners. A common argument is that natives worry about low-skilled migrants relying on welfare, whereas the high-skilled pay more taxes. Our model includes a simple tax-transfer system to account for this, but we find the welfare argument unconvincing, at least for countries like the US that exclude migrants from most welfare benefits. Our main contribution is to provide an alternative explanation: Using U.S. data on generational mobility, we show that children of unskilled workers tend to compete in the labor market with the children of medium-skilled natives. In contrast, children of high-skilled workers have a skill distribution more complementary to the children of medium-skilled natives. Hence concern about children can provide a positive theory of why highskilled workers are allowed to enter permanently, i.e., with their children, whereas low-skilled workers are not accepted permanently. 1 Our data analysis focuses on the US. Since 1970, about 60% of immigrants are either "highskilled" (BA degree or more) or "low-skilled" (less than High School degree), while the rest is "medium-skilled" (High School degree or some college). Because the share of medium-skilled individuals in the US population is more than 50%, the amount of high-skilled and low-skilled individuals as percentage of their native counterparts is larger than for the middle group. For example, for the decade of the 90 s, we estimate that there were 5.65 low-skilled (net) immigrants per 1000 unskilled natives in the US, about 2.02 medium-skilled per 1000 native medium skilled, and 4.15 high-skilled immigrants per 1000 skilled US natives. 2 In a 30 year period these numbers would account for immigration quotas of roughly 18%, 6% and 13%, when compared to the composition of the native population. A diffi culty in interpreting these flow data is that control over immigration is highly imperfect. 1 Undocumented workers are typically confined to low skilled work and cannot easily settle down as families, being under a constant threat of deportation. Hence it can be argued that de facto tolerance of illegal immigrants is similar to a guest worker program for unskilled workers. 2 See appendix for details on these numbers. We use the terms "unskilled" and "low-skilled" interchangeably; and we use "skilled" and "high-skilled" in the same manner. 2

Observed immigration is arguably a combination of legal and illegal flows, and of job-related and other flows. 3 To interpret the data, we set up a political-economy model to derive predictions about optimal immigration under alternative asumptions, and we examine under what conditions the model provides a positive theory. The model has three types of labor inputs defined as low-, medium- and high-skilled; and two types of migrants, permanent immigrants and temporary guest workers. Each worker supplies one unit of their work-type to the production process, earns a wage, pays proportional taxes that are then redistributed via lump-sum, has children according to a fertility profile that depends on skill and place of birth. The model is calibrated to match the transition matrix of intergenerational skill transmission for natives and immigrants in the US. The calibrated demographic process for the US is such that with or without immigration, the medium-skilled type would be the absolute majority in each generation. Immigration policy is defined by a set of quotas indexed by skill level and type of immigration permit (permanent vs guest-worker). Votes over immigration policy occur before the skill type of children is revealed. Immigrants don t have the right to vote, but the children of immigrants are citizens identical in everything to natives, which in turn have the right to vote. We use Markov Perfect as the equilibrium concept, as it is common in the literature of dynamic political economy. Our analysis initially sets aside guest workers and focuses on the more challenging problem of modelling permanent immigration. We show that the medium-skilled majority chooses a positive level of unskilled immigration, zero medium-skilled migration, and substantial high-skilled immigration. Thereafter, we add the possibility of guest workers, which is straightforward in our setting because guest workers do not raise intertemporal issues. We show that in the presence of guest workers and (full) immigration, the medium-skilled majority chooses a guest worker program but no immigration for low-skilled foreigners, no immigration nor guest workers at the medium skill level, and immigration but no guest workers for high-skilled foreigners. U.S. immigration policy and recent reform proposals are broadly consistent with our model. For the last several decades, the U.S. has in effect accepted significant low-skill immigration by tolerating undocumented workers, minimized medium-skilled immigration by restricting undocumented workers to menial jobs, and encouraged high-skilled immigration by providing work visas (notably, the H1B program). In our model, the difference between guest workers and immigrants is whether or not children are excluded from the workforce either by border controls that keep children out, by expelling families that get in, or by some other means. We view the feasiblity of exclusions and the willingness to separate families as beyond the scope of our model, as decisions that involves a mix of diplomatic, altruistic and other non-economic motives and views about human rights. Changes in 3 In the US, a significant share of immigration involves non-working family members of earlier immigrants who have attained citizenship. We do not model family unification, but the phenomenon is consistent with our premise that intergenerational issues are central to thinking about immigration. 3

immigration policy reforms are therefore interpreted as shifts between policies that are economically optimal under different feasible sets as constrained by preferences about enforcement. From this perspective, recent (pre-2016) US immigration policy is consistent with optimization under the constraint that expulsions and family separations are unacceptable, i.e., over immigration without guest workers. The pre-2016 reform discussion favored creating a guest worker program for unskilled workers and increasing the immigration of the high skilled. 4 Both changes would increase the utility of medium-skilled natives (if feasible) and are thus consistent with our model. We interpret the Trump election as a shift towards stricter enforcement of restrictions on low- and medium-skilled immigration 5 and possibly as shift towards low skilled guest workers. Although President Trump initially expressed an intent to reduce all immigration drastically (which would be inconsistent with our model), Congress will be needed to enact reforms and the President s position seems to be softening. Thus we maintain that, campaign rhetoric notwithstanding, future U.S. policy will likely allow for substantial high skilled immigration and for some low skilled immigrants or guest workers. Two important objects in the model and of independent interest in this paper are the matrices of intergenerational mobility for natives and for immigrants, which we estimate from the General Social Survey. This survey collects information on education data on the respondents and their parents, and it also identifies whether the parents are foreign born, among other variables. The data required for our purposes is available since 1977. We find that on average the children of unskilled and medium-skilled parents do better than their native counterparts, while there is no statistical difference for children of high-skilled parents. Consistent with this, Card, DiNardo and Estes (2000) find with regression analysis that children of immigrants (second generation immigrants) have on average higher schooling comparable education level. We now elaborate on findings of the paper. and wages than children of native parents with Among other findings we show that the intergenerational mobility of children of low-skilled workers can be a major determinant for the political support of low-skill immigration by the medium-skilled majority. In this case 2 nd generation immigrants from low-skilled parents mostly 4 Major attempts at overhauling immigration include the Comprehensive Immigration Reform Act in 2006 which passed the Senate but not the House of Representatives (H1B visas would increase from 65,000 to 115,000, plus an annual increase each year). The Secure Borders, Economic Oportunity and Immigration Reform Act that was introduced in 2007 but never voted on proposed a merit based point system where skills was one of the most important criterions for points, and the Border Securiy, Economic Opportunity and Immigration Modernization Act in 2013 which in addition to moving to a point-based system, proposed to increase the H1B visas from 65,000 to 205,000. All of these legislation projects also included some form of guest worker program or temporary visa category for low skilled workers. 5 Medium-skilled immigration is an issue because minimizing it requires monitoring of programs meant to allow high-skilled immigration, notably the H1B program. President Trump has suggested reducing the number of HB1 visas and increasing the salary level required to apply. Currently, the number of H1B visas is capped (with exceptions for researchers/professors at universities), when applications exceed the cap, visas subject to the cap are allocated via lottery. The lottery suggests that current policy is not maximizing applicant quality. Hence restrictions that raise the skill requirement are not necessarily inconsistent with our model. Under the model, all medium skilled immigration is attributed to limited enforcement and non-economic (primarily family related) motives. 4

"complement" the children of medium-skilled natives. Also the higher the probability that children of low-skilled immigrants become medium-skilled, the lower the low-skilled immigration quota that is politically chosen because 2 nd generation immigrants from low-skilled parents are mostly "substitutes" of the children of medium-skilled natives. Since we estimate that on average children of unskilled immigrants have a higher probability of upward mobility, and a lower probability of becoming medium-skilled or staying unskilled than natives, these effects help explain why the US allows significant quantities of unskilled immigrants. Another way to put this is the following. If children of unskilled immigrants had on average the same probability of becoming skilled as the unskilled natives, the number of unskilled immigrants allowed in equilibrium would decrease considerably from current flows. In addition, the model suggests that intergenerational mobility of 2 nd generation immigrants from skilled parents is not as important for the admission of skilled individuals, but does matter for the choice of immigration over guest worker permits. If the children of the high-skilled immigrants were mostly concentrated in the medium-skill group and therefore competing in the most likely state with the children of the majority, the medium skill voters would choose guest worker permits for the high skilled as opposed to full immigration. Finally, given that we establish this equilibrium result with a preference of high-skill immigration over high-skill guest workers, our models show that the medium-skilled majority wouldn t want to restrict high-skill immigration from its current level (but increase it if possible). This is because high-skilled immigrants and a large fraction of their children have skills that are complementary to the native majority. The paper is organized as follows. Section 1.1 reviews the literature, in section 2 we present the model and the equilibrium concept. Section 3 presents the empirical evidence on intergenerational mobility and fertility profiles of natives and immigrants. Section 4 presents the calibration of the model as well as some important results from the calibration exercise. In section 5, we use the model to ask applied questions. Section 6 does sensitivity analysis. Section 7 concludes. 1.1 Related Literature This paper is closely related to Ortega s politico-economic models on immigration with intergenerational mobility (2005, 2010). Ortega (2005) identifies political-economic trade-offs of immigration in a model with two skill levels and skill upgrading while abstracting from redistribution issues. Ortega (2010) extends his previous model by allowing agents to vote over immigration and redistribution in a richer model with alternative immigration regimes. While we build on the insights in Ortega s work, we show that a generalization to three skill types implies different trade-offs, produces new conceptual insights, and raises interesting quantitative questions that cannot be addressed in a model with two skill types. We also show how our model can be used to explain voter preferences for immigration versus guest workers, at each skill level. Specifically, we use three instead of two skill levels for the following reasons: (1) the composi- 5

tion of unskilled workers (as traditionally defined as education level lower than a college degree) is very different for natives and immigrants: a high percentage of immigrants has much lower schooling than natives in this category; (2) the three-type classification helps to document that most immigration to the US is in the extreme types of the skill distribution; (3) the demographic profiles (mobility & fertility) of natives and immigrants are statistically different, particularly for the unskilled group; (4) the model with three skill types has a natural middle. Moreover, the middle type turns out to be the majority, which yield predictable voting outcomes. The resulting theory is centrally about the economic trade-offs and voting incentives of the medium-skilled majority, and not about the political trade-off identified by Ortega (2005). Other related literature on equilibrium political-economic models of immigration includes the seminal work of Benhabib (1996) on immigration policy under heterogeneous agents. Dolmas and Huffman (2004) study the interaction of immigration and redistribution. Sand and Razin (2007) study the joint determination of immigration and social security with a Markov perfect equilibrium concept, which we also use in this paper. Cohen, Razin and Sadka (2009), study the theory and empirical relation between the size of the welfare state and the composition of the immigration flows in a static model. Bohn and Lopez-Velasco (2015) study immigration games when immigrants have a larger fertility rate than natives. On the dynamic fiscal effects of immigration there are papers by Storesletten (2000) and Lee and Miller (2000). Ben Gad (2004) studies dynamic aspects of immigration related to capital accumulation. The paper is also related to the macroeconomic literature where current voters foresee the consequences of their choices on the future behavior of voters. Some examples include Krusell and Rios-Rull (1999) and Hassler et.al (2003). Empirical studies on the intergenerational mobility of immigrants include Borjas (1992) and Card, DiNardo and Estes (2000). On the economics of guest worker programs Djajić (2014) has discussed welfare implications of low skilled guest workers, the optimal design of temporary migration programs has been discussed by Schiff (2007) and Djajić, Michael and Vinogradova (2013). Regarding preferences over immigration, Dustmann and Preston (2005) find empirically that competition in the labor market, the effects of immigration on the public burden, and effi ciency considerations of immigration shape immigration attitudes. Mayda (2006) concludes that both economic variables (mainly labor market outcomes in her analysis) and non-economic variables shape the attitudes of natives toward immigration, and non-economic variables do not alter the labor market results. The paper by Card, Dustmann and Preston (2009) concludes that immigration preferences are shaped not only by the economic effects of immigration, but by externalities associated to the changes on the composition of the population induced by immigration policies. This is one of the main arguments in our paper: that the current and future composition of the population is affected by the composition of the immigration flows and their different-from-natives demographic profiles (mobility and fertility), which in addition to the welfare state and labor market effects would then shape views on immigration, and that ultimately can dictate policy. 6

2 The Model 2.1 Demographics Adults live for one period, work full-time, and have children. Individuals are grouped by skill level and immigration status. There are three skill types, which will earn different wages: low-skilled workers (type 1), medium-skilled (type 2) and high-skilled (type 3). Domestic-born individuals (henceforth: natives) can vote, as can their children. Immigrants cannot vote, but their childen are considered natives, and as such have the right to vote. Guest workers also cannot vote and they are assumed to leave their children abroad or return to their countries of origin. population dynamics. 6 They matter only for current-period labor supply and have no impact on There is intergenerational mobility across skill types: a child s skill level as adult has a distribution that depends on the skill type and immigration status of his/her parents. Children are assumed not to take any economic decisions. Skill is realized at the start of adulthood. We assume throughout that a majority of natives is medium-skilled. (The assumption will be justified in the calibration of the model.) Thus policy is set by the medium-skilled. The other skill levels are relevant not for voting, but because medium-skilled parents do not know their chidrens skill when voting over immigration. Hence they care about the impact of immigration on future labor supply at all skill levels. 7 To model population dynamics, let N i,t denote the numbers of natives of skill-type i in period t, let θ I it 0 denote the quota of immigrants of skill type i as a percentage of the native group of the same skill, and let θ G it 0 denote the quotas of guest workers of skill type i (for i = 1, 2, 3), again as percentage of natives. Let θ it = θ I it + θ G it denote total migrants. Let natives have η i children, whereas immigrants have η I i children. Let q ij denote the probability that the child of a native parent of skill type i will have skill type j (i, j = 1, 2, 3). Similarly, let q I ij be the probability that the children of an immigrant parent of skill type i will have skill type j. These fertility profiles and transition probabilities are estimated below by skill levels and nativity. With these definitions, the evolution of the native population by skill type is N i,t+1 = 3 j=1 which includes the children of immigrants. ( ) ηj q ji + η I jqjiθ I I jt Nj,t, for i = 1, 2, 3, (1) Key state variables in the voting analysis will be 6 The defining property for our purposes is the exclusion of their children. For example, if undocumented immigrants and their children were forced to return to their country of origin, these "immigrants" would be treated in effect as guest workers. 7 Due to the assumed medium-skill majority, our paper has a quite different focus than the literature on the political economy of immigration, which examines under what conditions immigration might change voting majorities (e.g. Ortega (2010)). 7

the implied ratios of low- and high- relative to medium-skilled population, x 1t = N 1,t /N 2,t and x 3t = N 3,t /N 2,t. For reference below, we define a more compact vector notation. Let intergenerational transition matrices for native and immigrants be q 11 q 12 q 13 q11 I q12 I q13 I Q = q 21 q 22 q 23 and Q I = q21 I q22 I q I 23. (2) q 31 q 32 q 33 q31 I q32 I q33 I The cells are probabilities. For example, q 13 is the probability that a child of a low-skilled native parent will be high-skilled. Hence the rows (denoted Q [i] and Q I [i], respectively) add up one. Define the population vector N t = (N 1t, N 2t, N 3t ), where denotes a transpose. Define the vector of population ratios X t = N t /N 2t = (x 1t, 1, x 3t ) (with dummy x 2t 1). Define policy vectors θ I t = (θ I 1t, θ I 2t, θ I 3t), θ G t = (θ G 1t, θ G 2t, θ G 3t), θ t = θ I t + θ G t (dimension 1 3), and Θ t = (θ I t, θ G t ) (dimension 1 6). Then population and population ratios have the dynamics N t+1 = S t N t, and (3) X t+1 = (S t X t )/(S t[2] X t ), (4) where S t = S(θ I t ) = Q η + ( Q I) ηi diag { θ I t }, S t[2] is the second row of S t, η = diag {η 1, η 2, η 3 }, and η I = diag { η I 1, η I 2, η I 3}. Policy overall is defined by the vector Θ t. Constraints on policy are imposed by the available supply of migrants and by the country s ability or inability to prevent guest workers from settling down as immigrants. Limits on the supply of migrants are modeled as upper bounds θ it θ max i with θ max i > 0 (i = 1, 2, 3). The bounds also ensure that policy spaces are compact. For a wealthy country like the U.S., the economically most relevant constraint is the supply of high-skilled migrants, θ max 3. We assume throughout that the supply of low- and medium-skilled migrants is effectively unlimited; this is implemented by setting θ max 1 and θ max 2 high enough to be non-binding. If a country cannot prevent guest workers from settling down as immigrants, all migrants turn into immigrants and the supply of guest workers effectively equals zero. Combining these constraints, we consider three main policy settings: Setting (I) assumes that the supply of high-skilled immigrants is effectively unlimited and that all migrants can and will settle as immigrants. The former is arguably unrealistic and turns out to have implausible implications, but it is instructive as starting point, because it treats type-3 like the others and is therefore least restrictive. Setting (II) assumes a fixed "small" supply of high-skilled immigrants (θ max 3 ), small enough to be a binding constraint; as in (I), all migrants are immigrants. This setting yields the most 8

interesting results about equilibrium immigration and it will highlight the importance of intergenerational mobility. 8 Setting (III) adds guest workers to the policy choices in (II), so policy can set separate quotas for immigrants and guest workers at each skill level. 2.2 Production Labor inputs are combined to produce output via a production function F, Y t = F (L 1t, L 2t, L 3t ), (5) where F has constant returns to scale and L it is the total labor supply of type i at time t. 9 We assume that F has partial derivatives F i > 0 and F ii < 0, F ij > 0 for i, j = 1, 2, 3. Wages w it = F i equal the respective marginal products of labor. Each agent supplies one unit of their labor-type inelastically. Natives, immigrants, and guest workers are assumed to be perfect substitutes within each skill category, 10 which defines the labor supply of type i as L it = N it ( 1 + θ I it + θ G it) = Nit (1 + θ it ), for i = 1, 2, 3. (6) Note that immigrants and guest workers of each type have the same impact on labor supply. Hence policy Θ t enters only through the sums θ it. Constant returns to scale imply that wages depend only on the labor supply ratios z 1t = L 1t L 2t = x 1t 1 + θ 1t 1 + θ 2t and z 3t = L 3t L 2t = x 3t 1 + θ 3t 1 + θ 2t. Hence wages depend on the elements of X t and of θ t, which we write as w it = w i (X t, θ t ) = w i (z 1t, z 3t ), for i = 1, 2, 3. (7) For the numerical analysis, we assume F has the constant-elasticity-of-substitution form (CES), 8 As extension, we examine a more general setting with wage-elastic supply of high-skilled immigrants, and we examine the ramifications of alternative supply elasticities. The results are similar to case (ii) but more complicated. Hence the main analysis focus on the polar cases (i) and (ii). 9 We abstract from capital inputs. An alternative interpretation is that production has constant scale returns over capital and labor in an open economy with exogenous required (world) return to capital. Then capital would vary in a way that output net of capital costs is a function F with constant returns to labor. For example, suppose production is Q = AK α Y 1 α, where A is technology, K is aggregate capital and Y is composite labor given by (5), and suppose r is an exogenous world interest rate. Then K = ( αa ) α r ) 1 1 α Y varies with Y, so Q rk = A Y with A = (1 α)a ( αa 1 α r. Setting A = 1 is without loss of generality, so we obtain (5). 10 There is evidence by Ottaviano and Peri (2012) that immigrants and natives for a same level of schooling/experience are not perfect substitutes. Borjas (2009) argues that for all practical purpose they can be considered perfect substitutes. For the present purpose out of simplicity we assume that they are perfect substitutes. 9

Y t = [φ 1 (L 1t ) ρ + φ 2 (L 2t ) ρ + φ 3 (L 3t ) ρ ] 1 ρ, (8) where the elasticity of substitution between labor types is ε = 1. and Cobb-Douglas, Leontief, and perfect substitution are special cases of this function. The parameters φ i are calibrated below so that w 1t < w 2t < w 3t holds under benchmark conditions. There is one technical complication. Because the wage premiums w 3t w 2t and w 2t w 1t depend on relative labor supplies, wage premiums could be negative for some immigration policies (e.g., if high θ 3 raises L 3t /L 2t and reduces w 3t relative to w 2t ). We rule out negative wage premiums by assuming agents may work in any job with a lower skill requirement than their own; i.e., the high-skilled can work in medium- or low-skilled jobs, the medium-skilled can work as low-skilled. 11 This assumption ensures that wages satisfy w 1t w 2t w 3t for all states and policies (X t, θ t ). 12 2.3 Redistributional Taxes The model includes a simple tax-transfer system. Though the fiscal effects of immigration are not our focus, the fiscal costs of low-skilled immigrants have been emphasized in the literature, and hence their omission would raise questions. To capture the fiscal impact of immigration in a simple way, we assume an exogenous tax rate τ on wages that is redistributed lump-sum. Tax payments are τ w it. The lump-sum transfer is b t = τ w t, where w t = Σ3 i=1x it (1 + θ it ) w it Σ 3 i=1 x it (1 + θ it ) is the average wage. High-skilled workers are net contributors to the system and low-skilled workers are net beneficiaries, as they have above- and below-average wages, respectively. Medium-skilled workers may have wages above or below the average, depending on relative productivities and labor supplies. Hence their net contribution may be positive or negative. Since w t depends on the elements of X t and of θ t, one may write w t = w (X t, θ t ). 2.4 Preferences Utility of a skill-type i agent depends on its own consumption (c it ) and on the expected utility of their children (v jt+1 ). Consumption is derived from after-tax wages plus transfers: c it = (1 τ) w it + b t, for i = 1, 2, 3. (9) 11 This is consistent with the identification of skills by schooling level (as traditionally interpreted in the literature), because schooling is acquired sequentially. Ortega (2005) makes the same assumption in a setting with two skill levels. 12 The job assignment is straightforward but tedious to formalize and therefore is relegated to the appendix. In the calibration, wage premiums are strictly positive except in case of extremely large (unrealistic) immigration and for X t far from the steady state. Thus agents normally work at their own skill levels. 10

There are no bequests or other financial linkages across cohorts. Overall utility for each type is obtained recursively from v it = u (c it ) + β 3 q ij v jt+1, for i = 1, 2, 3. (10) j=1 where β > 0 is a scalar that governs the strength of the altruism motive; the sum can be interpreted as expected value E [v t+1 ( ) i] = 3 j=1 q ijv jt+1 conditional on parental type i. 2.5 Equilibrium The transition matrices and fertility rates in this paper are such that the medium-skilled remains the majority each period, irrespective of the immigration quotas (justified with the empirical demographic profiles in the calibration stage). Hence they dictate immigration policy every period. The main equilibrium concept used is Markov perfect equilibrium (MPE), where the state of the system is described by the composition of the native population (X t ). In the MPE the equilibrium strategies are a function of the state but not of the history of the game. Under this equilibrium concept -typically used in dynamic political economic games, agents fully incorporate the expected induced effects on future policy due to changes in the current policy. In other words, when making a voting decision the agents consider how future generations will respond to changes in current policy. For the medium skilled workers, who set policy, a strategy maps the state X t into a policy choice Θ t Ω Θ, where Ω Θ is a compact policy space (e.g., one of the cases defined in Section 2.1). The medium-skilled have a majority if x 1t + x 3t < 1. To work with compact sets, we use Ω X = {(x 1, 1, x 3 ) x 1 0, x 3 0, x 1 + x 3 1} as domain of X t. An equilibrium is then defined as follows: Definition. A politico-economic equilibrium is a policy rule P : Ω X Ω Θ that defines Θ = P (X) and a triplet of value functions (v1, v2, v3) such that for all X Ω X : i) Given the policy rule P and implied rules θ = p (X) and θ I = p I (X), continuation values are given by vi (X) = u i (X, p (X)) + β 3 q ijvj (Ψ (X, P (X))) (11) j=1 for i = 1, 2, 3, where u i (X, θ) = u [(1 τ)w i (X, θ) + τ w (X, θ)] and ii) The policy rule P solves: Ψ ( X, p I (X) ) = (S(p I (X))X)/(S [2] (p I (X))X) (12) P (X) = arg max Θ Ω Θ { u 2 (X, θ) + β 11 3 ( ( q 2j v ))} j Ψ X, θ I. (13) j=1

iii) Ψ ( X, p I (X) ) {(x 1, 1, x 3 ) x 1 0, x 3 0, x 1 + x 3 < 1}. The definition requires that the value functions vi, which are the expected lifetime utilities of type-i agents, are consistent with the population process and with the state of the economy induced by P. The policy P maximizes the expected lifetime utility of medium skilled natives (type i = 2), which are the voting majority. Since types 1 and 3 do not control policy, their value functions (v1 and v3) are computed under the policy set by type-2. The optimization takes into account that type-2 offspring might be type-1 or 3 in the next generation, as well as the response of the next generation to the induced state (which is Ψ ( X, p I (X) ) ). For completeness, condition (iii) states that type-2 will retain its majority in the next period; this is not a binding constraint in the analysis below. Note that there may be multiple policies that solve (13) and yield the same utility. Notable, wages are unchanged if migration is increased marginally at all skill levels in a way that relative labor supplies (z 1t, z 3t ) remain constant. Voter are generally not indifferent if this occurs through immigration, because immigration impacts their children. Voters are indifferent, however, if labor supplies were increased proportionally by guest workers. In our three policy settings, policies are nonetheless generically unique: in (I) and (II) because there are no guest workers, and in (III) because of a limited supply of high-skilled migrants. 13 2.6 Static Analysis: β = 0 or Guest Workers Only Dynamic effects would be absent if agents did not care about their offspring (if β = 0) or if all migrants were guest workers (if θ I it = 0 exogenously for i = 1, 2, 3). Under both assumptions, agents would vote to maximize utility from current consumption. Since the medium-skilled are the majority, policy in equilibrium would maximize c 2. We discuss these two special cases briefly, mainly to provide intuition; proofs and more details (notably, tedious case distinctions) are relegated to the appendix. For the discussion here, assume positive wage premiums and w 2 w (which holds empirically). Consumption depends on immigration policy through wages and transfers. On the margin, c i θ j = (1 τ) w i θ j + τ w θ j ; i, j = 1, 2, 3. (14) where time subscripts are omitted to reduce clutter. The wage effects w i θ j are negative for a guest workers of the same type as the native and positive for a guest worker of a different type. Transfers 13 To cover non-generic exceptions (e.g., if Q I = Q and η I = η), we adopt Ortega s (2005) tie-breaker that indifferent voters unanimously choose the policy with the minimal total number of migrants. This can be justified as selecting the unique policy that would be optimal with an infinitesimal cost of processing work permits or with an infinitesimal element of decreasing returns to scale. The multiplicity issue motivates in part (apart from plausibility) why we do not study guest workers combined with unlimited supply of high skilled migrants. 12

τw are increased if the guest worker has a skill that earns an above average wage ( w θ i > 0 iff w i > w), and decreased otherwise. Applied to the medium-skilled majority (c 2 ), one finds: (a) c 2 θ 3 > 0, because more high-skilled labor increases both w 2 and w. Hence high skilled migrants are admitted until θ 3 = θ max 3. (b) c 2 θ 2 < 0, because more medium-skilled labor reduces w 2 and (under w 2 w) reduces transfers. Hence medium skilled migrants are not admitted, θ 2 = 0. (c) c 2 θ 1 0 is ambiguous because more low-skilled labor increases w 2 but reduces w. Hence θ 1 = 0 for some θ 1 (0, θ max 1 )). may have corner solutions (0 or θ max 1 ) or an interior solution (if c 2 θ 1 One can show that θ 1 is decreasing in τ, as consistent with Razin et al. s (2011) insight that welfare discourages low skilled immigration. 14 These findings determine unique immigration quotas when there are no guest workers (setting (II) with β = 0). Then θ I i = θ i (i = 1, 2, 3), which means high skilled immigrants are admitted, medium skilled immigrants are not admitted, and low skilled immigrants may or may not be admitted, depending on parameters. Similarly, if all migrants were guest workers (θ I i = 0 exogenously), one would obtain θ G i = θ i ; since guest workers leave, this applies for all β 0. High skilled guest workers would be admitted, possibly low skilled guest workers, but not medium skilled guest workers. Alternatively, suppose there are separate quotas for immigrants and guest workers (setting (III)) and β = 0. Since wages depend on migration only through the sums θ j = θ I j + θ G j, voters are indifferent about immigrants versus guest workers. Overall, the wage and tax effects documented in this section provide a motive for voters to support high and (at not too high tax rates) low skilled migration. The indifference between immigrants and guest workers for β = 0 shows that strict preferences for immigrants or for guest workers in the general model must be driven entirely by voter concerns about their children. 3 Empirical Evidence 3.1 Intergenerational Mobility Matrices Many studies about intergenerational mobility use transition matrices in order to analyze the relative position of people in the income distribution compared to that of their parents. Such studies typically suffer from possible life-cycle effects and a small number of observations (PSID, NLS for example). Since we are interested in the intergenerational mobility of individuals based on skills, we focus on the education levels of individuals and their parents in studying intergenerational mobility. 14 See appendix for more analysis. In principle, it is possible that θ 3 < θ max 3 (but only if w 2 = w 3 ) and/or that θ 2 > 0 (but only if w 2 > w). Positive wage premiums require (in the static case, not in general) binding θ max 3, which rules out setting (I). 13

We use the General Social Survey (GSS) for this matter, which is an annual survey since 1972. Starting in 1977, this survey captures the schooling level of the respondent s parents (in addition to the respondent s schooling). The survey also identifies whether the respondents and their parents were born in the US. Hence, we can estimate transition matrices and perform some statistical tests for natives and children of first generation immigrants. We consider individuals who were born on or after 1945 and whose age at the time of the interview was between 25 and 55 years old. 15 The education variable used to classify individuals is based on whether the individuals (either respondent or his/her parents) obtained any of the following degrees: less than high school, high school, junior college, college and grad school. We classify individuals as 2nd generation immigrants, whose transition matrix we are interested in, if the respondent was born in the US but any of the parents were born outside the US. 16 Natives in turn are individuals whose parents were born in the US. For the transition matrices we define an individual as "unskilled" if his/her education is less than a high school degree, "medium-skilled" as either having a high-school or a junior college degree, and "skilled" for individuals with college degrees and beyond. For individuals with information on both parents, we use the maximum degree obtained by any of them. Under these filters, the total number of observations is 18, 999 for natives and 1, 447 for immigrants. The transition matrices Q and Q I are estimated from the GSS as follows. For each of their elements q ij and q I ij, the estimate is the number of children with corresponding education level i and parents with education level j divided by the total number of parents with educational level j. The empirical frequencies differ somewhat across subsamples in the GSS (e.g. for men and women; see appendix); but since they do not differ greatly -and we cannot reject that they are different for native men and women, our main calibration uses results for all men and women, given by.256.663.081.211.594.195 Q =.062.707.231, QI =.067.633.299. (15).010.397.593.022.325.653 The first two rows of the transition matrices show that the children of unskilled and medium skilled immigrants to the US appear to be more "successful" than natives. For unskilled parents, children of immigrants have a lower probability of staying unskilled, and a higher probability of 15 We cap it at 55 because of a well know relationship between mortality and education level, and also because using older individuals from the early years of the GSS means using observations who were born early in the 1900 s. We use individuals born on or after 1945 as their average schooling years starting with that cohort has remained approximately constant (see the appendix for schooling statistics in the GSS). 16 We could classify second generation immigrants as those respondents born in the US whose both parents (rather than only one) were born outside the US. We don t do this because 1) the number of observations greatly decreases for second generation immigrants (from 1447 to 530) and 2) because the numbers don t appear to be significantly different according to the unskilled, medium-skilled, skilled classification used in this paper. The appendix shows the estimated matrices under this definition. 14

upward mobility. Indeed, children of unskilled natives have an 8% probability of becoming skilled, while for the children of unskilled immigrants it is almost 20%. Given medium-skilled parents, the differences are not as marked as in the unskilled case but their odds seem to be slightly better. We test formally if the probability distributions for natives and children of immigrants are statistically the same, conditional on the skill of the parents. That is, we test if row i in matrix Q is statistically the same as row i in Q I. For all i, the null hypothesis is rejected at the 1% level. 17 We also test for the equality of both matrices, with a test given by summing over the statistic for each row test. 18 The null hypothesis that the transition matrices are the same is also rejected at the 1% level. Further analysis with more disaggregated data (reported in detail in the appendix) indicates that: (i) children of low-skilled immigrants are significantly more likely to become high-skilled than the children of natives (q13 I > q 13 ); (ii) children of natives and immigrant with skilled parents have similar skill distributions for most partitions of the data; (iii) for children of medium-skilled workers, differences between immigrants and natives are significant only for women; and (iv) for all subgroups, intergenerational transition matrices of natives and immigrants differ significantly. 3.2 Fertility Rates In order to calibrate the number of children that agents have, we construct total fertility rates by education level (TFR) for 3 different years: 1990, 2000 and 2005. This concept measures the expected number of children that a woman would have in her lifetime if she was subject to the current (cross-section) age-specific fertility profiles. 19 Total fertility rates can be accurately calculated with birth data from the National Center for Health Statistics (downloaded from their VitalStats system), and age-education groups from Census data (1990, 2000) and the Current Population Survey (2005). However, the available data on births doesn t detail whether the mothers are US-born, or foreign-born. In order to arrive at total fertility rates by place of births of mothers we also use information from several years of the American Community Survey (ACS). Details on the construction of these estimates are in the 17 Under the null, the statistic 2 k (q ij q n ij) I 2 im q ij m=1 j=1 is distributed chi-square with (k 1) degrees of freedom (k = 3), where n im is the number of counts of row i of sample m. The statistic for each row is to be compared with χ 2 (2), which is 5.99 (9.21) at the 5% (1%) level of significance. The statistics are 58.74 for the first row, 18.63 for the second and 10.16 for the third. 18 The null hypothesis that q ij = qij I for all i = 1, 2, 3 and j = 1, 2, 3 (matrix equality) is rejected if the statistic k 2 k (q ij q n ij) I 2 im i=1 m=1 j=1 q ij is greater than χ 2 (k(k 1)) where the degrees of freedom are in this case k (k 1) = 3 (2) = 6. The test produces a statistic of 87.52, higher than χ 2 (6) = 16.81 which is the critical value at the 1% level. For more details on this test, see Amemiya Pp. 417 and Mood-Graybill-Boes Pp. 449. 19 Total fertility rates are constructed as follows. First divide the total number of births whose mothers are in a specific age-education group (i.e. 20-24 year old mothers with 11 or less years of education) by the number of women in that age-education group. The resulting number is multiplied by 5. Finally, those quantities are added for all age-groups for a given education level. 15

appendix. Table 1. Total fertility rates by skill level. Years 1990, 2000 & 2005 US-Born Foreign-Born All Women Year Low Med High Low Med High Low Med High 2005 1.98 1.94 1.82 2.78 2.44 1.99 2.73 1.95 1.85 2000 2.24 2.00 1.59 3.04 2.50 1.76 2.26 2.00 1.84 1990 2.41 1.89 1.82 3.21 2.39 1.99 2.43 2.04 1.61 Average 2.21 1.94 1.75 3.01 2.44 1.91 2.47 2.00 1.77 The estimated fertility rates show the well-known negative relationship between education and fertility, and also display that foreign-born women have higher fertility rates than US-born women of the same skill level. 4 Calibration 4.1 Demographic Profiles A population process is described in this paper by an intergenerational transition matrix (Q), a vector of fertility rates (η) and a vector of immigration quotas. In the absence of any immigration, we denote the specific composition of the steady state native population by (x ss 1, 1, x ss 3 ) = X ss (Q, η). The model uses the matrices of intergenerational mobility Q and Q I shown in equation (15). For the fertility rates of the model, we divide by 2 the TFR s shown in table 1 in order to obtain implied model parameters. This yields η 1 = 1.1, η 2 = 0.97, η 3 = 0.87 and η I 1 = 1.5, η I 2 = 1.22 and η I 3 = 0.96. One way to assess the quantitative significance of these differences between natives and immigrants is by examining the implied composition of the population. Table 2 displays steady state ratios x ss 1 and x ss 3 implied by alternative assumptions about mobility and fertility. Table 2. Steady State Composition of Population. Different Mixed Mobility & Fertility Cases ( (Q, η) Q I, η I) ( Q, η I) ( Q I, η ) x ss 1.0978.1213.1041.1161 x ss 3.5429.7987.5010.8634 Using the data for natives (Q, η), assuming no immigration, one obtains x ss 1 = 9.78% (low to medium skilled ratio) and x ss 3 = 54.29% (high to medium skill ratio). If a population had (hypothetically) the mobility and fertility of first-generation immigrants ( Q I, η I) forever, one would obtain larger shares of the extremes in the skill distribution, with x ss 1 = 12.13% and x ss 3 = 16

79.87%. 20 Considering populations that combine the mobility of natives with the fertility of immigrants, or the fertility of natives with the mobility of immigrants (see columns 3-4), one finds that differences in mobility are far more important than difference in fertility; that is, X ss for ( Q, η I ) is close to X ss for (Q, η), and X ss for ( Q I, η ) is close to X ss for ( Q I, η I). 4.2 Production, Preferences and Taxes ( ) Production parameters are φ 1, φ 2, φ 3 and ρ. The elasticity of substitution ε = 1 between education groups has been carefully estimated in different studies that control for experience and other observables for what is traditionally defined as high-skilled versus unskilled labor inputs, as well as specifications with 4 skill types which correspond to the categories "less than high school", "high school graduates", "some college" and "college graduates". When using the two-skill specification, the empirical estimates in many studies range between 1.5 and 2.5 (see the references in Ottaviano and Peri (2012) pp. 184), which would imply 0.4 ρ.66. In specifications with more education types, the estimates range from 1.32 (Borjas (2003)) to the estimates in Borjas and Katz of 2.42 (2007), with Ottaviano and Peri s own estimates lying between those 2 extremes. These other set of estimates imply 0.24 ρ.78. Even though the definition of the skill groups is different, the intermediate value for ρ in these intervals is very close to ρ = 1, which we use as 2 baseline parameterization. We later perform sensitivity analysis. The parameters φ i are calibrated so that the model in steady state matches U.S. wage premiums for educational attainment. We normalize φ 1 + φ 2 + φ 3 = 1 and use the equations ( φi φ j ) = w i,t w j,t ( Lj,t to relate wage premiums to calibrate the ratios φ 2 /φ 1 amd φ 3 /φ 2. L i,t ) ρ 1 for i j = 1, 2, 3, (16) We use census data of the average hourly wage of workers that are between 25 and 65 years old by educational attainment; that work at least 40 hours per week, and that worked at least 40 weeks in the previous year for census years 1990, 2000 and 2005. The skill categories are defined in terms of schooling under the same { definition as for the intergenerational mobility matrices. The ( ( ) w average wage ratios obtained are 2 w w 1 ), } 3 w 2 = {1.315, 1.67}. 21 As noted above, the demographic profile of natives (Q, η) yields steady state ratios of x ss 1 = 0.0978 and x ss 3 = 0.5429. Taking into account immigration quotas of 18% for the unskilled group, 6% for the medium skilled and 13% for the high skilled group yield labor ratios given 20 We can also substitute the demographic profile of immigrants to those of natives, one skill-type at a time (i.e. substitute the demographic profile of the low-skilled immigrant for that of the low-skilled native, leaving the profile of the other natives unchanged). In all three hypothetical cases where we do this, the steady state shares of lowand high-skilled are greater than the shares implied by data on natives. 21 At a generational frequency the returns to skill have increased in the US over time. We do not attempt to formally model these changes and so we calibrate the model by using the average ratios. 17