Correction of paper

J Popul Econ (2011) 24:317–359 DOI 10.1007/s00148-009-0286-z

O R I G I N A L P A P E R

Should the US have locked heaven’s door? Reassessing the benefits of postwar immigration

Xavier Chojnicki · Frédéric Docquier · Lionel Ragot

Received: 20 June 2008 / Accepted: 11 September 2009 / Published online: 14 October 2009 © Springer-Verlag 2009

Abstract This paper examines the economic impact of the second great immi- gration wave (1945–2000) on the US economy. Our analysis relies on a com- putable general equilibrium model combining the major interactions between immigrants and natives (labor market impact, fiscal impact, capital deepening, endogenous education, endogenous inequality). Contrary to recent studies, we show that immigration induced important net gains and small redistributive effects among natives. According to our simulations, the postwar US immi- gration is beneficial for all natives cohorts and all skill groups. Nevertheless,

Responsible editor: Alessandro Cigno

X. Chojnicki (B) EQUIPPE, University of Lille 2, 1 place Déliot, 59000, Lille, France e-mail: [email protected]

X. Chojnicki CEPII, 9 rue Georges Pitard, Paris 75015, France

F. Docquier FNRS, National Fund for Scientific Research, Brussels, Belgium

F. Docquier IRES, Catholic University of Louvain, 3, Place Montesquieu, 1348 Louvain-La-Neuve, Belgium

L. Ragot EQUIPPE, Faculté des Sciences Économiques et Sociales, University of Lille 1, 59655, Villeneuve d’Ascq Cedex, France

L. Ragot CES, University of Paris 1, Paris, France

318 X. Chojnicki et al.

the gains would have been larger if the US had conducted a more selective immigration policy.

Keywords Immigration · Welfare · Computable general equilibrium

JEL Classification J61 · I3 · D58

1 Introduction

Modern American history is characterized by two noticeable periods of free immigration. The first immigration wave started in the middle of the nine- teenth century and culminated in 1900 with almost nine million legal immi- grants. Then, between 1920 and 1950, the stock of immigrants vanished. The second wave started in 1950 and has not yet come to an end. By the late 1990s, nearly one million legal immigrants were annually entering the country. The stock of foreign-born amounted to about 10% of the population and is expected to reach 15–16% by the middle of this century. This second wave of immigration can be divided into two sub-periods. Before 1965, the immi- gration policy was ruled by a system of quotas based on national origin. Each sending country’s share in the total number of visas was determined by the representation of that ethnic group in the US population as of 1920; the UK and Germany received about 65% of the available visas. This quota- based scheme disappeared with the 1965 Amendments to the Immigration and Nationality Act, relying on new constraints (a worldwide numerical limit to the number of visas) and new objectives (family reunification, diversity in immigrants’ origin).

This new policy has considerably changed the national origin mix of immi- grants. By the 1990s, more than 80% of legal immigrants originated from less developed countries such as Asian and Latin American countries, while European immigrants only represented 16%. This change in the origin mix translated into a deep decline in the relative skills of immigrants. One should not be surprised that some US policymakers and economists are today wor- rying about the economic impact of immigration on natives’ income and well-being.

There is an extremely large literature focusing on the consequences of immigration on the labor market, on public finance, on growth and inequality... Most of these studies were conducted using partial equilibrium models.1 This induces three major shortcomings:

• Firstly, a partial equilibrium framework badly captures the interdepen- dencies between the markets, as well as natives’ responses to immigration shocks. Natives’ geographical mobility, changes in their labor supply, and

1See Section 2 for a survey of the mechanisms at work.

Should the US have locked heaven’s door? 319

saving and education decisions are very likely to affect the impact of immigration on the US economy.

• Secondly, the absence of a unified framework makes it extremely difficult to dissociate minor from major effects. Although the largest strand of literature focuses on the labor market impact of immigration, this effect is possibly less important in size than fiscal responses or growth-enhancing impacts.

• Finally, in the absence of a precise welfare criterion, partial equilibrium models fail at providing a global assessment of the effect of immigration on natives’ well-being. A fully micro-founded general equilibrium model is required to derive the immigration impact on natives’ level of utility.

Partly due to these reasons, no real consensus emerged from the theoretical and empirical literatures. Although it is commonly accepted that immigrants experience large gains as soon as they walk through heaven’s door,2 the global impact on natives remains very uncertain. Some argued that immigration induces small efficiency gains and an astonishing transfer from the poorest to the richest people (e.g., Borjas 1995). Others argue that redistributive effects are low or that immigrants provide the new blood that industrialized nations require to grow at a fast pace (e.g., Razin and Sadka 2004).

This paper aims at partly remedying these shortcomings. Focusing on the second great immigration wave (1950–2000), we use a unified general equi- librium model to examine whether some natives would have gained from (partially or totally) locking heaven’s door. Most of the ingredients of the immigration literature are included in a harmonized framework where firms, the government, and heterogenous households interact. Our framework is a computable model with overlapping generations of heterogeneous agents closely related to the works of Auerbach and Kotlikoff (1987). Two related studies are Storesletten (2000) and Fehr et al. (2004) who investigate whether a reform of immigration policies could alone attenuate the fiscal burden of aging in the coming decades. Compared to these studies, our paper has several distinctive features:

• First of all, rather than forecasting the consequences of current/future reforms, it focuses on the post-war period. We compute the hypothetical transition path of the US economy under counterfactual immigration scenarios. Although our main interest is to evaluate the global impact of immigration on natives’ utility level, our model also allows disentangling the various channels of transmission. By “exogenizing” some prices and tax rates, we can estimate the relative contribution of each mechanism at work.

• The calibration of the model deserves special attention. Some crucial parameters and exogenous unobserved processes (such as skill-biased and unbiased technical changes, the generosity of welfare programs) are

2The term heaven’s door refers here to the title of Borjas’ remarkable book (Borjas 1999b).

320 X. Chojnicki et al.

identified by letting the model match the US economic path over the post- war period. Basically, our identification process resembles Sims (1990) backsolving method for stochastic general equilibrium models. Following De la Croix and Docquier (2007) and De la Croix et al. (2007), we use a similar idea (in a deterministic framework) and artificially swap these unobserved exogenous processes for the same number of observed en- dogenous processes. Then, we solve the transformed model to identify the path of unobserved exogenous variables that exactly matches observations for the true endogenous. Finally, coming back to the calibrated “right- way” model, we can simulate counterfactual immigration variants such as a cutoff of immigration flows after 1950.

• The model relies on a complex socio-demographic block with 48 types of individual per period, distinguished by age, education level, and national origin. Calibrating this block requires historical data on education choices, fertility, mortality, in-migration, and out-migration. The calibration of the economic block will be such that our model will fit income differentials between groups and inequality measures extremely well.

• Natives and immigrants differ in terms of human capital, financial assets, and rights to receive welfare benefits. This contrasts with Fehr et al. (2004), who consider that immigrants automatically become natives (in an eco- nomic sense) after crossing the border. As in Storesletten (2000) and for tractability, we assume that the skills of second-generation immigrants are independent of the skills of their parents (second-generation immigrants behave as natives).

• The way immigrants affect wages and inequality strongly depends on the choice of a production function. An important feature of our model is that labor in efficiency units is made of three major components: raw labor, experience, and educational attainment. Our approach is highly compat- ible with the Mincerian literature on wage determination, emphasizing the contribution of these three components on labor market outcomes. Building on Ben-Porath (1967), we combine these components accord- ing to a constant elasticity of substitution technological function. These components are determined endogenously and depends on productivity changes (introduced to capture economic growth and changes in the skill premium). Card and Lemieux (2001) and Borjas (2003) use a similar approach by distinguishing workers according to their education and their experience. The supplied quantities of labor by “skill/experience” group are then combined in nested CES transformation functions (the number of embedded CES functions depends on how many groups they consider). In our model, each individual offers a quantity of experience and a quantity of education-based human capital. We consider the stocks of education and experience as homogenous. Our production function is then independent on the number of periods of life and education groups distinguished. The average experience and education level of immigrants differ from those of natives. Immigrants and native workers are thus imperfect substitutes on the US labor market.

Should the US have locked heaven’s door? 321

As Storesletten (2000) and Fehr et al. (2004), our model is based on neo- classical principles: changes in supply and demand on the labor market induce wage adjustments. Thus, in accordance with the literature, we assume that im- migration has no impact on the unemployment level of the native population. Indeed, the numerous available empirical studies from the USA fail to find that immigration has harmful effects in terms of raising unemployment in the receiving country (see, for example, Simon 1989; Borjas 1990, 1993; Friedberg and Hunt 1995). More recently, a study run by Jean and Jimenez (2007) on 18 OECD countries also demonstrates that there is no significant long-run impact of the share of immigration in the labor force on natives’ unemployment.

We evaluate the impact of immigration on natives by simulating a counter- factual scenario in which there is no immigration flow after 1950. Our simula- tion provides striking results. We find out important net economic gains from immigration but moderate redistributive implications. Hence, the postwar US immigration is beneficial for all cohorts of natives and for all skill groups. These gains result from a dominant fiscal effect and a moderate labor market impact of immigration. Although our unit of analysis is national, we obtain small wage responses and a minor effect on income inequality. Over the last 50 years, and despite the deterioration in their average education level, immigrants have significantly contributed to the American dream. Nonetheless, we also demon- strate that all generations of natives would have benefited from a stronger selection of immigrants.

The rest of this paper is organized as follows. Section 2 surveys the tra- ditional channels of transmission of immigration on the receiving economy. Section 3 describes the model. The calibration is presented in Section 4. Our two immigration variants and the simulation results are presented and commented on in Section 5. Finally, Section 6 concludes.

2 The economics of immigration

Immigrants induce many effects on the welfare of natives through the capital market, the markets for high-skill and low-skill labor, through public finance. These direct effects can be reinforced by natives’ behavioral responses. In this section, we describe these various channels, illustrating the need for a dynamic general equilibrium model to assess the global impact of immigration.

Capital dilution effect First, immigration can be seen as a supply shock on the labor market, thus impacting on the productivity of factors supplied by natives (and, hence, on wages and the return on saving). For a given stock of physical capital, an increase in labor supply reduces the capital per worker, leading to decreasing wages and increasing interest rates. It follows a redistribution from the suppliers of labor to the suppliers of capital. A vast empirical literature focuses on the wage effect of immigration and offers mitigated results. Spatial correlations between natives’ wages and immigrant stock are extremely weak. As surveyed by Friedberg and Hunt (1995), if one city has 10% more workers

322 X. Chojnicki et al.

due to immigration, the native wage decreases by 0.2–0.7% only. Borjas et al. (1997) questioned the validity of interpreting weak spatial correlation as evidence of a minor impact on the labor market. If migrants endogenously cluster in thriving economies and/or if natives respond to the local labor market changes by moving their labor or capital to other cities, the adverse impact of immigration will be diffused over the entire economy. For these reasons, the labor market impact of immigration must be measured at the national level rather than at the local level. Applying the “factor proportions approach” to national data, Borjas (2003) concluded that a 10% increase in labor supply could reduce wages by 3–4%.

The surplus of immigration The redistribution from wage earners to capital- ists is accompanied by a general rise in income of the indigenous population in the host country, the well-known immigration surplus. This surplus is captured by the fact that capitalists’ gains exceed workers’ losses. The size of the sur- plus depends on the host country’s characteristics such as the elasticity of the wage rate to labor supply, the share of labor income in total income and the proportion of migrants in the workforce. Using a static one-good model with homogenous workers, Borjas (1995) arrived at the pessimistic conclusion that a 10% increase in the workforce through immigration increases natives’ aver- age income by only 0.105%. Distinguishing high-skill and low-skill workers, immigration by workers whose skill composition differs from that of natives raises the immigration surplus, but less if immigrants are, on average, less educated than the natives. A 0.5% rise in natives’ income can be obtained if all immigrants are highly skilled.

Increased wage inequality As workers are not homogenous in skills, the skill structure of immigration also induces important redistributive effects between workers. New immigrants are competing with natives on specific segments of the labor market: high-skill immigrants compete with high-skill natives while low-skill migrants compete with low-skill natives. Many complain that US immigrants are today less educated than natives. Consequently, immigration induces downward pressures on low-skill workers’ wages and upward pressures on the skill premium, thus increasing the level of inequality. Using the “factors proportion approach,” Borjas et al. (1997) estimated that about one third of the postwar US rise in wage inequality is due to immigration.

Public finance A fourth mechanism refers to the use of social services. Low- skill immigrants are making extensive use of welfare transfers and place a substantial fiscal burden on the natives.3 This is particularly true as immigrants are likely to select their location on the basis of welfare generosity (Borjas 1999a). Welfare programs are attracting immigrants who qualify for subsidies

3See Borjas (1994), Lee and Miller (1997, 2000), Bonin et al. (2000), and Auerbach and Oreopoulos (2000) on the public finance impact of immigration.

Should the US have locked heaven’s door? 323

and are deterring out-migration. Existing studies reveal that the fiscal impact of immigration depends on whether one uses the short-run or long-run approach. Accounting for expenditures incurred and tax collected, short-run studies found out that immigrants initially create a burden for native taxpayers. As they assimilate and have children and grand-children, the immigrants’ contri- bution to the economy becomes positive: a long-run fiscal gain can be obtained.

Behavioral changes among natives Through its impact on wages, interest rates, and taxation, immigration induces indirect effects on natives’ choices of labor supply, human capital investment, and saving. These behavioral changes are largely understudied in the literature. Indirect effects on firms’ R&D expenditures and technological choices could also be expected. For example, Levine et al. (2003) analyze the consequences of immigration in a general equilibrium model with endogenous growth. They argue that the endogeneity of R&D activities and growth increases the potential surplus of immigration. Chiswick (1989) demonstrated that natives’ education choices are affected by immigration: the increasing skill premium forces them to educate more. All these induced effects involve an infinite sequence of perturbations on the demand and supply of factors, which can reinforce or attenuate the direct effect.

In the next section, we develop an intertemporal general equilibrium model of the US economy that accounts for most of the ingredients depicted above. Such a model has many advantages. It takes care of all the interdependencies between the supply/demand shocks, individual decisions, and equilibrium prices. It allows to characterize the dominant and less important effects. Given its solid microfoundatations, it also provides a synthetic measure of the global impact of immigration on natives: the change in welfare.

3 Modeling population and the economy

To compute the economic impact of immigration, we need to depict the eco- nomic environment determining how immigrants interact with natives. This requires modeling and calibrating demography, technology, individual behav- iors, and state intervention. Our model distinguishes three agents: households (natives and immigrants), firms, and the government. In- and out-migration flows are the only sources of exchanges with the rest of the world. As in Storesletten (2000), we assume that trade and financial flows are too small to make a difference. This means that we rule out any interdependencies between movements of goods, capital, and persons.

3.1 Demographics

Our population block provides a stylized but fair representation of the US population structure per age, skill level, and origin. We focus on the working age population and distinguish eight cohorts of adults, from the youngest

324 X. Chojnicki et al.

cohort (aged 15 to 24, denoted by 0) to the oldest one (aged 85 to 94, denoted by 7). One period thus represents 10 years. Individuals aged 0 at period t are forming cohort t.

There are two sources of heterogeneity within each cohort:

• The first one concerns educational attainment. We distinguish low-skill, medium-skill, and high-skill individuals. These skill levels are respectively denoted by the superscripts s = l, m, h.

• The second one refers to country of origin/birth: we distinguish natives and immigrants (first generation).4 In the spirit of Storesletten (2000), immigrants’ children are considered as natives. These categories are respectively denoted by the subscripts k = n, m.

At time t, the population aged j ( j = 0, ..., 7) of skill s (s = l, m, h), from origin k (k = n, m), is denoted by P sk, j,t . For the sake of simplicity, we assume that individuals give birth to their children at age 30, in the middle of their second adult period of life.5 Fifteen years after their birth, these children become new adults. Consequently, children born at time t (by adults of cohort t − 1) reach age 15 at time t + 2.

Fertility differs across skill and ethnic groups. At time t, the number of children per individual in a specific skill and ethnic class is denoted by nsk,t . Young agents take decisions about their level of education. At time t, the proportions of young individuals opting for low, medium, and high education are respectively denoted by π lt , π

m t , and π

h t . As explained below, π

m t and π

h t are

endogenously determined on the basis of the expected lifetime income asso- ciated to these educational levels. A change in the skill level of immigration flows then implies a change in the education choices of natives.

At each period, new immigrants are entering the country. The variable Is0,t measures the number of young immigrants entering the USA at age 0 with a skill level s. At the same time, a proportion of natives and immigrants leaves the country. The variables ξ sn, j,t and ξ

s m, j,t , respectively, measure net emigration

rates (emigrants minus immigrants compared to the previous period popula- tion size) among natives and immigrants of skill s at age j. These rates are positive for natives and they can be positive or negative for immigrants. Finally, some individuals die at each age. Mortality rates are allowed to vary between skill groups. We denote by βsj,t ( j = 1, ..., 7) the proportion of individuals of skill s dying between age j − 1 and age j.

The dynamic of population is then determined by the set of 48 equations per period (for eight age groups, three skills groups, and two origins). The number

4Immigrants are defined as individuals who were foreign-born and whose parents were non US citizens. 5Rios-Rull (1992), Storesletten (2000), or Fehr et al. (2004) use a different method. They assume that agents aged j′ to j′′ (say, 23 to 45) give birth to fractions of children at the beginning of each period.

Should the US have locked heaven’s door? 325

of young natives (aged 15 to 24) of skill s, P sn,0,t , sums up children of natives and immigrants from generation t − 2 (weighted by the probability to belong to the skill group s). The number of young new immigrants, P sm,0,t , is exogenous. The size of young cohorts (for s = l, m, h and s′ = l, m, h) is modeled as follows:

P sn,0,t = π st ∑

s′

[ P s

′ n,1,t−2n

s′ n,t−2 + P s

′ m,1,t−2n

s′ m,t−2

]

P sm,0,t = Is0,t (1)

Regarding subsequent age cohorts, we use a simple dynamic process that takes into account mortality changes, in-migration, and out-migration. The sizes of cohorts aged 1 to 7 are given by (for s = l, m, h and k = n, m):

P sk, j,t = βsj,t ( 1 − ξ sk, j,t

) P sk, j−1,t−1

3.2 Technology

The production sector plays a crucial role since it defines the way immigrants compete with native workers on the labor market. Technological assumptions govern the magnitude of the capital dilution effect, the immigration surplus, and changes in wage inequality. Instead of defining several labor markets (for low-, medium-, and high-skill workers, for young and old workers, etc.), we assume that workers belonging to different age, skill, and ethnic groups are not perfect substitutes because they have different “educational attainment/ experience” mixes. However, the stocks of education and experience are homogeneous. The interest of this approach is that the number of competing factors is independent of the number of groups considered. It slightly differs from the approach of Card and Lemieux (2001) or Borjas (2003) that aggre- gates age-specific levels of human capital in a CES function; the number of nested functions depends on the numbers of age groups considered. We are more in line with Heckman et al. (1998), who used a general equilibrium model with a sophisticated labor market. They calibrate their production function using econometric estimates of wage equations. Wasmer (2001b) uses a similar function to explain the rising returns to skill in France and the USA. De la Croix and Docquier (2007) and De la Croix et al. (2007) also use the same specification.

At each period of time, a representative national firm uses labor in efficiency unit (Qt ) and physical capital (Kt) to produce a composite good (Yt). We assume a Cobb–Douglas production function with constant returns to scale:

Yt = At K1−ϕt Qϕt , (2)

where ϕ measures the share of wage income in the national product and At is an exogenous process representing total factor productivity.

326 X. Chojnicki et al.

Building on the Mincerian studies on wage determination, Qt explicitly aggregates the attributes of native and immigrant workers. The quantity of efficiency unit of labor combines raw labor, experience, and education accord- ing to a CES nested transformation function (see Wasmer 2001b). Formally, we have

Qt = [ Lρt + μEρt + �t Hρt

]1/ρ , (3)

where Lt measures the input of manpower at time t, Et measures the input of experience, Ht is the input of education, ρ is the inverse of the constant elasticity of substitution between raw labor, experience, and education, and μ is a fixed parameter of preference for experience. Finally, �t is an exogenous skill-biased technical progress. The technological assumptions regarding the production function are highly important in determining the results. Thus, a discussion on the impact of this choice could be found in Section 5.2, as well as in Appendix A. The representative firm behaves competitively on the factor markets, which requires the equality of the marginal productivity of each factor to its rate of return.

3.3 Preferences

Individuals have an uncertain lifetime length, i.e., a probability to die at the end of each period of life. They maximize an expected life-cycle utility function that only depends on consumption expenditures. We use a time-separable logarithmic type:

E ( U sk,t

) = 7∑

j=0 �

s j,t+ j ln

( c sk, j,t+ j

) , (4)

where c sk, j,t+ j is the consumption of generation t at age j for a consumer of skill s and origin k. The term �sj,t+ j =

∏ j i=1 β

s i,t ( j = 1, ..., 7) is the probability to be

alive at age j (evaluated at age 0) and such that �s0,t+0 = 1. Following Yaari (1965), we assume that each individual has the possibility

to insure him/herself against uncertainty at the beginning of his/her life, which implies that accidental bequests are thus distributed implicitly as in a life insur- ance framework.6 Agents born at time t must select the optimal consumption plan that maximizes her expected utility subject to an Arrow–Debreu budget constraint, requiring equality between the lifetime expected income and the

6Another solution in the literature to deal with uncertainty consists in assuming, as Imrohoroglu (1998), that bequests are taxed to a 100% rate by the government and redistributed as a lump sum uniform amount to all surviving adults. As demonstrated thereafter, the approach adopted here allows for reasonable wage and wealth profiles.

Should the US have locked heaven’s door? 327

lifetime expected consumption. For a native household (k = n), the budget constraint may be written as7

7∑

j=0 R j,t+ j�sj,t+ j

[ csn, j,t+ j(1 + τ ct+ j) − T sn, j,t+ j

]

= 7∑

j=0

( w

L j,t+ j + w Ej,t+ jesn, j,t+ j + w Hj,t+ jhsn, j,t+ j

) R j,t+ j�sj,t+ j

( 1 − τ wt+ j

)

s n, j,t+ j,

(5)

where τ ct+ j and τ w t+ j are, respectively, the consumption and labor income tax

rate at period t + j; T sk, j,t+ j denotes the amount of transfers received at age j including education benefits, pensions, and other transfers (health care, family allowances, social benefits. . . ); sk, j,t+ j measures labor supply at age j; esn, j,t+ j and h

s n, j,t+ j are education and experience stocks at period t + j; and

wLj,t+ j, w E j,t+ j, and w

H j,t+ j are the marginal productivity associated respectively to

raw labor, experience, and education. The appropriate discount factor, R j,t+ j, applied to age- j income and spending is given by

R j,t+ j ≡ t+ j∏

s=t+1

( 1 + rs

( 1 − τ ks

))−1 ,

where τ ks is the capital income tax rate and rs is the marginal productivity of capital. By convention, R0,t = 1.

Maximizing expected utility with respect to the levels of consumption determines the law of motion of contingent consumption expenditures over the lifetime:

csk, j+1,t+ j+1 = (1 + rt+1)

( 1 + τ ct

) ( 1 + τ ct+1

) csk, j,t+ j ∀k; ∀s; ∀ j = 0, ..., 6 (6)

The implicit asset holdings ask, j,t+ j of each individual is defined as follows:

ask,0,t = ( w

L 0,t + w E0,tesk,0,t + w H0,t hsk,0,t

) ( 1 − τ wt+ j

)

s k,0,t

− [csk,0,t ( 1 + τ ct

) − T sk,0,t ]

(7)

R j,t+ j�sj,t+ ja j,t+ j = R j−1,t+ j−1� j−1,t+ j−1ask, j−1,t+ j−1 +

( w

L j,t+ j + w Ej,t+ jesk, j,t+ j + w Hj,t+ jhsk, j,t+s

)

×R j,t+ j�sj,t+ j ( 1 − τ wt+ j

)

s k, j,t+ j

−R j,t+ j�sj,t+ j [ csk, j,t+ j

( 1 + τ ct+ j

) − T sk, j,t+ j ]

(8)

7At each date, the composite good is taken as a numeraire. The spot price is thus normalized to one.

328 X. Chojnicki et al.

For new immigrants entering the country with age j′ = 1...7 at date t, the budget constraint is:

7∑

j= j ′ R j,t+ j− j′�sj,t+ j− j′

[ csm, j,t+ j− j ′

( 1 + τ ct+ j− j ′

) − T sm, j,t+ j− j ′ ]

= R j′−1,t−1�sj′−1,t−1asm, j ′−1,t−1

+ 7∑

j= j ′

( w

L j,t+ j− j ′ + w Ej,t+ j− j ′ esm, j,t+ j− j ′ + w Hj,t+ j− j ′ hsm, j,t+ j− j ′

)

× R j,t+ j− j′�sj,t+ j− j′ ( 1 − τ wt+ j− j′

)

s m, j,t+ j− j ′ . (9)

The variable asm, j ′−1,t−1 represents the initial asset holdings of immigrants. As in Fehr et al. (2004), we assume that migrants of each generation have the same characteristics (including implicit wealth) as a native household of the same skill levels. This means that low-skill immigrants will enter the country with a small amount of wealth whilst high-skill immigrants bring the same amount of wealth as high-skill natives. This assumption differs from that of Storesletten (2000), who assumes that immigrants bring no wealth when they arrive. However, this choice seems to play a minor part on the results, since nearly 70% of immigrants enter the country before 30, i.e., at the beginning of the wealth accumulation. Moreover, Hao (2004) demonstrates that the age– wealth profiles of immigrants and natives appear relatively similar before 35. Figure 2b below will confirm this hypothesis.

The aggregated consumption at period t then amounts to

Ct = 7∑

j=0

∑

k=n,m

∑

s=l,m,h P sk, j,t c

s k, j,t (10)

3.4 Education decisions and human capital

Through its effect on wages, interest rates, and tax rates, immigration induces behavioral changes among natives. Our model accounts for the effect on na- tives’ education decisions. This effect has been understudied in the literature.

Individuals in two distinct skill groups are differentiated by the years of schooling or, equivalently, by the time invested in education in the first period of their life. The exogenous variable 0 ≤ us ≤ 1 measures the proportion of time that an agent of skill s must devote to education between age 15 and age 24. One obviously has ul < um < uh. Hence, each young agent selects his/her optimal level of schooling by comparing the monetary gain and the

Should the US have locked heaven’s door? 329

effort required for achieving a diploma. The monetary gain is captured by the expected lifetime labor income taken from the budget constraint:

E (

AI M Est ) ≡

7∑

j=0

( w

L j,t+ j + w Ej,t+ jesk, j,t+ j + w Hj,t+ jhsk, j,t+ j

)

×R j,t+ j�sj,t+ j ( 1 − τ wt+ j

)

s k, j,t+ j

For the sake of simplicity, the effort is assumed to be proportional to the opportunity cost of education: λwL0,tus, where λ is a scale variable determining the ability to educate. Young individuals are heterogenous in the sense that λ is uniformly distributed on the segment

[ λ, λ

] .

The proportion of individuals who stopped education before reaching a high school diploma (π lt ) is exogenous. This assumption relies on the fact that the decision to stop education was mainly taken at the family level. Those who reach a high school diploma have to decide whether they pursue their educa- tion or not by comparing the gains and costs of tertiary education. The fol- lowing condition defines the interval of λ where tertiary education dominates secondary education:

E (

AI M Eht ) − λwL0,tuh ≥ E

( AI M Emt

) − λwL0,tum This condition can be rewritten as

λ < λ c t ≡

E (

AI M Eht ) − E( AI M Emt

)

wL0,t [uh − um] ,

where λct is the critical level of ability under which tertiary education dominates secondary education for the generation t members.

Consequently, the proportions of agents opting for primary, secondary, and tertiary education are given by

π l t = π lt

π m t =

( 1 − π lt

) λ − λct λ − λ + εt

π h t =

( 1 − π lt

) λct − λ λ − λ − εt,

where π lt is the exogenous share of low-skill workers and εt is a iid stochastic process.

The proportion of individuals belonging to group s is fully determined by education decisions presented above. The time invested in education influ- ences labor supply, education-related human capital, and the accumulation of experience.

330 X. Chojnicki et al.

Except for education decisions, our model assumes exogenous labor partici- pation rates. The vector of labor supply for an agent of generation t (defining labor supply at all ages) is

s k,t = (qt(1 − us), qt+1, qt+2, qt+3, qt+4(1 − αt+4), 0, 0, 0) , (11)

where qt is the exogenous activity rate at time t and αt+4 stands for the (exogenous) time spent in retirement in the fifth period of life (i.e., between age 55 and age 64). The variable qt essentially captures the rise in women’s participation rates on the labor market. Our choice to consider labor supply as exogenous (except in the first period of life) is explained by the difficulty to model and calibrate the preference for leisure in the intertemporal utility func- tion. Most dynamic models of the Auerbach–Kotlikoff type fail at matching realistic profiles of participation rates per age and/or the dynamics of average participation rates over time. Our choice should not affect the results too much since, as it will appear later, we will predict low labor market impacts of immigration.

As in Wasmer (2001a), the individual stock of experience, esk,t , sums up past participation rates on the labor market. The stock of education, h

s k,t , trans-

forms education investment when young into labor efficiency according to a decreasing return function. These vectors are written as

esk,t = ( 0, (1 − us)qtθ 1e , (1 − us)qtθ 2e + qt+1θ 1e , (1 − us)qtθ 3e + qt+1θ 2e + qt+2θ 1e , (1 − us)qtθ 4e + qt+1θ 3e + qt+2θ 2e + qt+3θ 1e , 0, 0, 0

) , (12)

where θ je ∈ (0, 1) represents one minus the depreciation of experience over the lifetime;

h s k,t =

( 0, �uψs , �u

ψ s , �u

ψ s , �u

ψ s , 0, 0, 0

) , (13)

where � > 0 and ψ ∈ (0, 1) are two parameters of the educational technology. We disregard assimilation issues and consider that experience and education

accumulated abroad are equivalent to experience and education accumu- lated in the domestic economy. The aggregate quantity for raw labor (Lt), experience (Et), and education ( Ht) are

Lt = 7∑

j=0

∑

k=n,m

∑

s=l,m,h P sk, j,t

s k, j,t

Et = 7∑

j=0

∑

k=n,m

∑

s=l,m,h P sk, j,t

s k, j,t e

s k, j,t

Ht = 7∑

j=0

∑

k=n,m

∑

s=l,m,h P sk, j,t

s k, j,t h

s k, j,t (14)

Should the US have locked heaven’s door? 331

3.5 The public sector

Immigration also impacts on the receiving economy through the public finance channel, i.e., through taxes and transfers. Due to their specific age and skill characteristics, the net contribution of immigrants to the government budget differs from that of natives. In our model, public transfers sum up education subsidies, pension benefits, and other transfers. The vector of transfers can be written as

T s k,t =

( vtqtusw

L 0,t + γ sk,0 gt, γ sk,1 gt+1, γ sk,2 gt+2, γ sk,3 gt+3, αt+4b sk,4,t+4

+ γ sk,4 gt+4, b sk,5,t+5 + γ sk,5 gt+5, b sk,6,t+6 + γ sk,6 gt+6, b sk,7,t+7 + γ sk,7 gt+7 ) ,

(15)

where vt is the rate of subsidy on the cost of education and γ sk, jgt is the amount of age-related transfers made by the government to agents of age j, skill s, and origin k. The parameters γ sk, j describe the transfers profile per age, skill, and origin; gt is a scale variable capturing the generosity of welfare programs. The endogenous variable b sk, j,t+ j measures pension benefits allocated to each full-time retiree from generation t at period t + j ( j = 4 to 7) and αt+4 the old- age participation rate. For simplicity, pension benefits are proportional to the last-period hourly earnings. We write

b sk, j,t+ j = ηtηk [ w

L 4,t+4 + w E4,t+4esk,4,t+4 + w H4,t+4hsk,4,t+4

] ( 1 − τ wt+4

) ( j = 4, ..., 7),

(16)

where ηt is a deterministic exogenous process capturing the generosity of the social security system and ηk is a pair of parameters capturing the relative pension of immigrants compared to natives (ηn is normalized to unity).

The government issues bonds and levies taxes on labor earnings (τ wt ), con- sumption expenditures (τ ct ), and capital income (τ

k t ) to finance public transfers

and general public consumption. Five types of spending are distinguished: education subsidies, social security benefits, other transfers (health care, family allowance, social benefits), non-age-specific general consumption, and the interest on public debt. The government budget constraint may be written as

τ w t

( w

L t Lt + w Et Et + w Ht Ht

) + τ ct Ct + τ kt rt Kt + Dt+1 =

∑

j

∑

k

∑

s

P sk, j,t T s k, j,t + ϑt Yt + (1 + rt)Dt, (17)

where Dt denotes the public debt at the beginning of period t; ϑt is the share of non-transfer public consumption in G D P and T sk, j,t is the amount of transfers per capita defined above. We assume in the sequel that the path of debt is given and the tax rate on consumption τ ct adjusts to balance the budget.

A competitive equilibrium is obtained when all individuals maximize their expected utility subject to the budget constraint, the representative firm max- imizes profits subject to the technology, the government budget constraint is

332 X. Chojnicki et al.

balanced, and spot prices and wages are such that the goods and labor markets are in equilibrium.

4 Calibration of the baseline

Calibration implies using data for observed exogenous variables, fixing some constant parameters, and choosing paths for the unobserved exogenous vari- ables (exogenous variables for which time series data are not available) in order to match a series of characteristics.

4.1 Identification of demographic processes

The demographic block is calibrated so as to match the structure of the US population between 1940 and 2000 and to generate demographic forecasts compatible with the recent projections of the Bureau of Census.

Between 1900 and 1930, we do not distinguish between natives and immi- grants. From 1940, we explicitly model the impact of immigration8 on the population structure by age and by education. Low-skill workers are those with less than 12 years of schooling (high school dropouts). Medium-skill workers have exactly 12 years of schooling. High-skill workers have more than 12 years of schooling (some college and college graduated). Historical data on the population structure per age are obtained from the Bureau of Census. Information about skill level and origin ( P sn, j,t and P

s m, j,t ∀ j, s) is obtained from

the Public Use Microdata Samples (PUMS) of the US Census and the General Social Survey (GSS).

To calibrate fertility (nsk,t ), mortality (β s j,t), and net emigration rates (ξ

s k, j,t ),

we use the following method. The PUMS data enable to determine the shares of low, medium, and high skill among young people (π lt, π

m t , and π

h t ). In the

baseline, these shares are set to their observed values and the educational endogenous process is calibrated so as to reproduce their historical path. Since we consider monozygotic agents, fertility rates are calibrated in order to reproduce the observed number of young people at each period. Data on fertility differential between skill groups and origins (nsk,t ) are obtained from the PUMS and the GSS. Practically, we use the average number of children ever born per women in each group to fix the ratio of fertility rate compared to low-skill natives. Then, the fertility rate in this reference group (nln,t ) is estimated so as to match the observed number of children.

Mortality rates per age and skill level (βsj,t ) are computed using life table per race (whites, blacks, and others) from the National Center for Health Statistics (NCHS). We use data on the number of deaths among whites and

8We do not explicitly model the impact of illegal immigration as in Storesletten (2000).

Should the US have locked heaven’s door? 333

blacks per age group between 1970 and 2000 (Data Warehouse on Trends in Health and Aging, NCHS) and data on the skill structure of whites and blacks per age group from the PUMS. We consider that the probability to survive of the medium skilled is a nonlinear combination of low-skill and high-skill probabilities.9

Starting from the population structure in 1940, the demographic block is then used to identify two unobserved processes, i.e., the net emigration rates of natives and immigrants (ξ sn, j,t and ξ

s m, j,t ∀ j, s) between 1950 and 2000. For future

decades, these processes are fixed so as to reproduce the US demographic forecasts of the Bureau of Census (with a projected share of immigrants cul- minating at 16% in 2050). These projections give the US structure per age and origin until 2100. The skill structure of future cohorts is estimated in the following way. For immigrants, we assume that the skill structure is stationary so that the skill structure of future immigrant cohorts gradually catches up with the skill structure of the immigrant cohort aged 15–24 in 2000. The skill structure of future native cohorts is based on the high variant of Cheeseman Day and Bauman (2000).

In sum, our baseline scenario then completely matches observations and official forecasts regarding the population structure per age, educational at- tainment, and country of birth after 1950.

4.2 Observed exogenous processes

The old age participation rate, αt+4, is computed using the effective retirement age data from Blondal and Scarpetta (1997). Overall participation rates qt are normalized to 1 in 2000 and based on Wasmer (2001a). As for public finance, three proportional taxes are introduced in our model: the labor income tax (τ wt ), the capital income tax (τ

k t ), and indirect taxes (τ

c t ). These tax rates

are calibrated in such a way that the shares of revenues in GDP correspond to the estimations of Gokhale et al. (1999), i.e., 8% for labor income, 7% for indirect taxes10 and 5% for capital income in 2000. The history of tax rates reproduces the evolution of fiscal receipts in percent of GDP. Between 1900 and 2000, the public debt/GDP ratio is exogenously set to its observed value. Observations are taken from OECD statistics for the period 1985– 2000. For previous periods, we use data from Brown (1990). We distinguish two types of government spending (net of debt charges), i.e., non-age-specific public consumption and age-specific transfers.11 For the composition of these categories, we build on Gokhale et al. (1999). The history of non-age-specific

9The log-linear process ln [ βmj,t

] = .2 × ln [βlj,t ] + .8 × ln [βhj,t

] gives a good approximation of mor-

tality differential per race and per age. 10This figure is only used as a target value since the consumption tax rate is endogenously calculated to balance the government budget constraint. 11Including medicare, medicaid, unemployment, AFDC, food stamps, and general welfare.

334 X. Chojnicki et al.

spending is based on OECD data for the period 1960–1995. For age-specific transfers, we calibrate age profiles per age, education, and country of birth. Profiles per education level are taken from Lee and Miller (1997). Differences between natives and immigrants are taken from Auerbach and Oreopoulos (2000). Within each age category, education and origin scaling factors multiply an age component. The latter is calibrated in such a way that the average level of transfers in the age class matches the estimates of Gokhale et al. (1999). We assume that the resulting age profiles are constant over time but are rescaled (through changes in gt) so as to match the share of social transfers in GDP. Social security benefits, b sk, j,t+ j, depend on the hourly earnings in the last working period: the scale process ηt is fixed so as to match the share of social security benefits in GDP. Finally, the rate of subsidy on tertiary education expenditures, vt, is taken from De la Croix and Docquier (2007).

4.3 Parameters

We use common values for calibrated models of the US economy. The labor share in output, ϕ, is set to 0.7. The depreciation rate of capital equals 0.4. This value implies an annual depreciation rate of 5%. The depreciation rate of experience follows the median hypothesis of Wasmer (2001a), i.e., an annual rate of 3%, independent of age. This yields θ 1e = 0.737, θ 2e = (θ 1e )2 etc... The parameter μ in the production function is a scale parameter of no importance given the later choice of �t; it is set to 0.5. The parameter ψ is the elasticity of education capital to investment in education. It determines the concavity of the relationship between income and education. Using ψ = 0.75, we fairly reproduce income differentials between low-, medium-, and high-skill workers. The scale parameter in the production function of human capital � is set to 1.2 so as to deliver an adequate wage profile. The parameter ηm measuring the relative pension of immigrants compared to the rest of the population is set to 0.907. Such a ratio is compatible with the generational accounting data of Auerbach and Oreopoulos (2000). The parameter ρ determines substitution between raw labor, education, and experience. In the baseline, we use ρ = 0.7, implying an elasticity of substitution (1/(1 − ρ)) of 3.33. This baseline value corresponds to the elasticity of substitution between low-skill and high-skill labor in classical production functions. Since we use a different type of tech- nology, we provide a sensitivity analysis to this parameter by setting ρ = 0.5 and ρ = 0.9 in the Appendix.

Finally, the lower and upper bounds of the ability distribution must be cali- brated to match the evolution of educational attainment in the USA. We esti- mate these parameters by a standard OLS regression. This gives λ = −1.54 and λ = 9.09. As shown in Fig. 1, this distribution provides an accurate prediction of the rise in educational attainment between 1900 and 2100. The iid deviation process εt is identified as the difference between observations and simulated values at the baseline. This identified process is used as exogenous in the alternative scenarios.

Should the US have locked heaven’s door? 335

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100

Share of highly skilled (simulations) Share of highly skilled (observations)

Fig. 1 Proportion of students opting for tertiary education (benchmark scenario)

4.4 Identification of unobserved exogenous processes

We have to identify exogenous variables for which time series data are not available. Our methodology follows two steps. In the baseline scenario (match- ing the US historical time path), we use the model to identify four unobserved exogenous variables: total factor productivity, At, the skill-biased technical progress, �t, the scale process of social security benefit, ηt, and the scale of the age-specific transfers profile, gt . These four exogenous processes are chosen so as to match available time series data for four closely related endogenous variables: the GDP growth rate, the share of social security and other transfers in GDP and the wage gap between high-skill and low-skill workers at age 45.12

Basically, our identification methodology implies swapping four exogenous variables for four endogenous variables. This resembles Sims (1990) backsolv- ing approach for stochastic general equilibrium models and is used in De la Croix and Docquier (2007) and De la Croix et al. (2007). Swapping exogenous for endogenous variables, we obtain a transformed model in which the growth rate, skill premia, shares of social security benefits, and other public transfers in GDP artificially become exogenous. We then solve the transformed model to identify the path of unobserved exogenous variables ( At, �t, ηt, and gt) that exactly matches observations for the true endogenous. Then we come back to the calibrated “right-way” model in which At, �t, ηt, and gt are identified. Back-solving is thus used, not to solve a model, but as a calibration device in a deterministic framework. This procedure allows to calibrate the model “dynamically.” This is much better and more rigorous than calibrating on

12The actual wage gap is computed from Census data.

336 X. Chojnicki et al.

a hypothetical steady state (in 1900 or in 2250) and then scaling exogenous variables to obtain reasonable outcomes at a given date, as it is usually done in computable general equilibrium tradition.

4.5 Characteristics of the benchmark scenario

Given the backsolving approach, the baseline scenario exactly matches the major “first-order” processes of the US economy (GDP growth rate, evolution of pensions and transfers, wage gap between high-skill, and low-skill workers). We have seen before that our endogenous education process gives a good approximation of human capital evolution for the post-war period. The quality of our model also depends on its ability to match individual wage and asset profiles per age. For that purpose, we compare the model’s outcome with data (PUMS for the wage profile and the Panel Study of Income Dynamics (PSID) for the asset profile). Firstly, the concave shape of the wage profile per age is fully determined by the accumulation and depreciation of experience and human capital (cf. Fig. 2a).

Contrary to Auerbach and Kotlikoff (1987), there is no need to assume an exogenous profile. This figure comforts us in the choice of the experience and human capital accumulation function parameters (θe, �, and ψ ). Secondly, it is usually argued that the standard life cycle model with selfish households does not provide a good description of wealth accumulation after retirement. It appears that our model matches the profile (cf. Fig. 2b), except for the very old people (85–94). Hence, there is no need to suppose a pure time preference parameter on top of the mortality rate.

It is also important to check whether our model reasonably reproduces the distribution characteristics (“second-order moments”). For that purpose, we focus on wages of natives aged 25 to 65 and calculate the Gini index and per- centile wage differentials based on 12 groups (four age groups and three skill groups). The Gini index summarizes the shape of the entire earnings distribution in a single statistic.

Wage profile

0

2

4

6

8

10

12

14

16

15-24 25-34 35-44 45-54 55-64

0

5000

10000

15000

20000

25000

30000

35000

simulations (left scale) observations (right scale)

(a)

Asset profile

-10

-5

0

5

10

15

20

25

15-24 25-34 35-44 45-54 55-64 65-74 75-84 85-94

0

500

1000

1500

2000

2500

3000

simulations (left scale) observations (right scale)

(b)

Fig. 2 Wage and asset profiles per age in 2000 (benchmark scenario). a Wage profile. b Asset profile

Should the US have locked heaven’s door? 337

Table 1 Index of wage inequality—baseline results and observations (1950–2000)

1950 1960 1970 1980 1990 2000

Gini index (based on Census 0.132 0.154 0.174 0.182 0.206 0.198 natives’ net wages) Baseline 0.133 0.157 0.189 0.184 0.202 0.199

P90/P10 (ratio of Census 1.983 2.151 2.797 2.853 2.628 2.638 percentiles) Baseline 1.967 1.982 2.632 2.632 2.914 2.788

P90/P50 (ratio of Census 1.444 1.546 1.929 1.634 1.289 1.412 percentiles) Baseline 1.561 1.541 1.785 1.636 1.256 1.515

P50/P10 (ratio of Census 1.374 1.391 1.450 1.746 2.039 1.868 percentiles) Baseline 1.260 1.286 1.475 1.609 2.320 1.840

Source: PUMS; authors’ calculations

As shown in Table 1, the baseline scenario gives an accurate vision of the evolution of the wage structure compared to Census data. Between 1950 and 2000, the Gini index rose from 0.132 to 0.198 (an increase of 50%), peaking at about 0.20 in 1990. Nevertheless, the Gini index is less revealing about the structure of earnings than a series of ratios of selected percentile cutoffs (P90/P10, P90/P50, and P50/P10). A useful comparison of what has happened to the upper and lower portions of the wage distribution is provided by exam- ining changes in the P90/P50 and P50/P10 ratios. The percentile differentials approach shows a similar rise in inequality; the P90/P10 census ratio rose from 1.98 to 2.64 (+33%), with a maximum at 2.85 in 1980. However, this trend is due to a pattern of wage growth in which the P50/P10 ratio increases (+36%) and the P90/P50 ratio decreases (−2.2%). Table 1 also illustrates some variations over time in the magnitude and timing of changes in wage inequality. The baseline of our model slightly overestimates this global pattern with a 41% increase in the P90/P10 ratio, a 46% increase in the P50/P10 ratio, and a 3% decrease in the P90/P50 ratio.

5 Immigration, inequality, and welfare

Once the model is calibrated so as to perfectly match the evolution of the US economy, we can simulate the impact of counterfactual immigration variants. Compared to the benchmark, our variants are based on the same parameter set and the same paths for exogenous variables, except immigration flows. We use such counterfactual experiments to assess the consequences of the US postwar immigration.

5.1 Counterfactual immigration variants

The first counterfactual scenario, no immigration (NI), assumes a cutoff of all immigration flows after the year 1950. This scenario is obtained by setting Is0,t to 0 after 1950 and considers that immigrants arrived before 1950 die and leave the country as natives (ξ sm, j,t = ξ sn, j,t for j ≥ 1). Eliminating all postwar immigration not only reduces the stock of immigrants but also affects the

338 X. Chojnicki et al.

size of future cohorts of natives since immigrants’ children are considered as natives. Comparing this scenario to the baseline provides an evaluation of the global impact of post-war immigration on the US economy.

The second scenario, selected immigration (SI), simulates the hypothetical situation of the US economy if past flows of immigrants had been more selec- tive. We start from the population structure observed in 1940. Then, between 1950 and 1960, we assume a convergence between migrants’ and natives’ characteristics. The stock of immigrants is given in the baseline. However, the skill structure of immigrants in all age groups converges towards the skill structure of natives within two decades. Practically, we model immigrants’ skill shares in all age groups as a weighted average of observed shares among immigrants and natives (the weight given to natives’ shares equals .5 in 1950 and 1.0 in 1960). Since the skill structure of migrants and natives is relatively similar until the end of 1950s,13 the selected immigration scenario gives a rough estimate of the impact of the relative immigrant skill decrease that follows the 1965 amendment act.

The impact of these alternative scenarios on US population structure is depicted in Table 2. Immigration plays a crucial role in determining the size and the structure of the US population. In the no immigration scenario, the US population grows slowly, reaching 187.8 million in 2000 compared to 220.5 in the baseline. In 2060, the US population size is 34% lower than in the baseline scenario. The immigrants’ share in the total population quickly decreases and the immigrants’ stock equals zero in 2030. Eliminating all postwar immigration also affects the age structure of the US population. The old age dependency ratio (the ratio of people aged 65 and over to people aged between 15 and 64) is much higher in the no immigration scenario, peaking at 36.8% in 2060. Moreover, this scenario strongly modifies the (endogenous) skill structure of the US population.

In the selected immigration scenario, the skill composition of the immigrant population is drastically affected but the size of annual net flows is unchanged. The population size, the share of immigrants in the population, and the age composition are thus unaffected. On the contrary, the share of low-skill immi- grants gradually declines to 8.7% in 2000 (to be compared with 28.3% in our baseline scenario) and the share of high-skill immigrants rises to 54.7% in 2000 (44% in our baseline scenario). Since the skill structures of immigrants and natives were similar before the late 1950s, the selected immigration scenario gives a rough evaluation of the impact of the decline in the relative skills of immigrants related to the 1965 Amendment Act.

13In 1960, 66% of male immigrants (against 53% for natives) were high school dropouts and 10% (against 11% for natives) were college graduates. Things had changed since the amendment act implementation. Nowadays, migrants are concentrating at the two extremities of the skill structure. For example, in 1998, 34% of male immigrants were high school dropouts against 9% for natives and 13% had validated a master’s degree against 10% for natives.

Should the US have locked heaven’s door? 339

T ab

le 2

U S

P o

p u

la ti

o n

st ru

ct u

re u

n d

er al

te rn

at iv

e sc

en ar

io

19 50

19 60

19 70

19 80

19 90

20 00

20 20

20 40

20 60

U S

P o

p u

la ti

o n

c B

as el

in e

10 9,

23 9

12 3,

13 1

14 4,

41 8

17 4,

54 6

19 4,

82 2

22 0,

53 6

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85 3

30 0,

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34 2,

73 6

(i n

th o

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n d

s) N

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% −1

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% −6

.4 %

−1 0.

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4. 8%

−2 1.

3% −2

7. 9%

−3 4.

1% S

.I .b

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

P o

p u

la ti

o n

gr o

w th

ra te

c B

as el

in e

1. 1%

1. 2%

1. 6%

1. 9%

1. 1%

1. 2%

0. 8%

0. 7%

0. 7%

(i n

% p

er ye

ar )

N .I

.a 0.

0% −0

.1 %

−0 .2

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.4 %

−0 .4

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−0 .4

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−0 .4

% S

.I .a

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

S h

ar e

o f

im m

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n ts

c B

as el

in e

9. 4%

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6. 2%

7. 2%

9. 2%

12 .1

% 14

.2 %

15 .7

% 15

.7 %

(i n

% o

f th

e p

o p

u la

ti o

n )

N .I

.a ,d

−0 .5

% −1

.3 %

−2 .5

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.2 %

−8 .2

% −1

1. 8%

−1 4.

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5. 7%

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.I .a

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

0. 0%

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H ig

h sk

il le

d im

m ig

ra n

ts B

as el

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7. 2%

12 .0

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32 .3

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% 45

.3 %

45 .5

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(i n

% o

f th

e im

m ig

ra ti

o n

st o

ck )

N .I

.a −1

.9 %

−6 .2

% −1

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3% −3

0. 7%

−2 9.

9% −2

0. 4%

− −

S .I

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2. 6%

13 .2

% 2.

0% 2.

5% 7.

9% 10

.7 %

13 .3

% 17

.7 %

22 .1

% M

ed iu

m sk

il le

d im

m ig

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ts B

as el

in e

15 .4

% 11

8. 0%

24 .8

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27 .8

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27 .8

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28 .2

% (i

n %

o f

th e

im m

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ti o

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5% −

− S

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,c 2.

3% 6.

6% 8.

7% 11

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9. 5%

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% L

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sk il

le d

im m

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B as

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70 .0

% 55

.6 %

39 .9

% 31

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28 .3

% 27

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26 .5

% 26

.5 %

(i n

% o

f th

e im

m ig

ra ti

o n

st o

ck )

N .I

.a 6.

5% 12

.3 %

23 .9

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.6 %

37 .4

% 29

.6 %

16 .9

% −

− S

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.9 %

−9 .8

% −1

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O ld

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d ep

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B as

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.7 %

14 .9

% 16

.1 %

17 .0

% 19

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18 .9

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32 .7

% 32

.8 %

(P o

p 65

+ /P

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15 –6

4 in

% )

N .I

.a 0.

3% 1.

1% 1.

3% 1.

4% 1.

8% 2.

2% 3.

2% 4.

4% 4.

0% S

.I .a

0. 0%

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f im

m ig

ra n

ts eq

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ro in

20 30

340 X. Chojnicki et al.

5.2 Results

Table 3 gives the results in deviation of the baseline. We mainly concentrate on the no immigration variant, which eliminates all postwar immigration flows. The selected variant is commented on at the end of the section.

Impact on the labor market The labor market impact of immigration has given rise to a large and controversial literature. Most attention has been paid to three explanations for rising wage inequality: demand, supply, and institutional factors. Demand factors include factor-biased technical change, trade with low-wage countries, decline of manufacturing, and rise of service jobs. Supply factors include the available quantity and quality of different types of workers: changes in educational attainment, immigration, natives’ cohort sizes, and labor force participation rates by sex and age group. Other studies have focused on the changes in labor market institutions: extent of unionization in the economy and the level of the minimum wage. In our frame- work, we disregard institutional factors but capture demand factors (through skill-biased technical changes), as well as supply factors (through a complex socio-demographic block). Although the technical change favoring high-skill workers is the main force toward rising inequality, the model determines whether changes in immigration policy mitigate or exacerbate the changes.

Our simulation reveals that the postwar immigration has reduced the stock of human capital per worker after the 1965 Amendments to the Immigration and Nationality Act. Since immigrants are less educated than natives, the average level of education increases in the no immigration variant by 4.3% in 2000 and 6.3% in 2060. Since immigrants are younger than natives, the average level of experience per worker also increases until 2020. Consequently, the skill premium (−2.3% in 2000) and the experience premium (−0.3% in 2000) are lower in the variant. These trends correspond to intuition, but their magnitude differs from recent studies in two major respects:

• First, immigration has a small impact on labor market outcomes. Accord- ing to our simulations, a 10% increase in immigration reduces the average wage of natives by 1%. Although our unit of analysis is the national level, such a magnitude is comparable to that obtained in spatial correlation studies (see Friedberg and Hunt 1995) and three or four times lower than that obtained by Borjas (2003).

• Second, all skill groups are similarly affected by immigration. On average, the wage response to a 10% increase in immigration amounts to −1.3% for low-skill, −1.2% for medium-skill, and −0.9% for high-skill workers. Given a stronger complementarity with immigrants, the highly skilled suffer less from immigration. However, the differences with the less edu- cated workers are small. Hence, contrary to expectations, the redistributive impact of immigration is quite small in our analysis. This is clearly shown in Table 3, where immigration increases by only 0.8% the wage ratio between

Should the US have locked heaven’s door? 341

T ab

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342 X. Chojnicki et al.

T ab

le 3

(c o

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Should the US have locked heaven’s door? 343

a college graduate and a high school dropout at age 45 in 2000. Demand factors and the natives’ supply of skills explain most of the drastic changes in the wage distribution over the last 50 years.

How can we explain such differences with the partial equilibrium studies by Borjas et al.14 (1997) and Borjas (2003)? These studies use the aggregate “factor proportions approach” to estimate the impact of immigration and trade on the US labor market. They found that immigration has had a marked adverse impact on the economic situation of the least-skilled US workers. Whereas immigration has modest impacts on the “college-to-high-school” wage ratio from 1980 to 1995, the effect of post-1979 immigrants on relative skill supplies explains between 27% and 55% of the actual decline in the rela- tive wages of high school dropouts over 1980–1995 (depending on the wage elasticity chosen). Although general equilibrium provides additional insights compared to partial equilibrium, the major difference resides in the way the demand side of the labor market is modeled. We show in Appendix A that nearly 80% of the redistributive effects is due to the properties of the production function and less than 20% to the general equilibrium pattern.

Indeed, when applying the production function of Borjas (2003) that com- bines native and migrant labor by skill and experience through nested CES, as well as its estimation of the different related elasticities, to our demographic data, we found that the postwar immigration explain 47% of the increase in the wage ratio between a medium-skilled and a low-skilled native aged 25 to 34 (Appendix A). With our production function that assumes that the stocks of labor, education, and experience are homogeneous, migration only accounts for less than 3% of this ratio growth. The labor market results of immigration are thus mainly explained by the specification of the production function.

However, the size and significance of the estimated relative wage effects from immigration remain highly controversial. Recently, a series of papers using strictly the same methodological framework (Borjas 2003, 2009; Borjas and Katz 2007; Borjas et al. 2008; Ottaviano and Perri 2006, 2008) fail to reach a consensus on the effect of migration on native wages. Indeed, accounting for the imperfect substitution between foreign and US workers within the same education-experience group or for reasonable speed of adjustment of physical capital (Ottaviano and Perri 2006) allows for positive effects of immi- gration on the wages of natives, even in the short run. The number of skill groups considered (and thus, the parameter restrictions on the elasticity of substitution across skill groups) also influences the results (Ottaviano and Perri 2008). Despite the lack of consensus on the wage effect of immigration, it seems, however, crucial to remind the need of a general equilibrium model to assess the global impact of immigration.

14Henceforth, BFK.

344 X. Chojnicki et al.

Impact on inequality The minor impact on wage differentials translates into a minor impact on income inequality (Table 3). By 2000, the US postwar immi- gration has increased the Gini index by 1.23%. Note that the inequality impact of immigration was negative until the 1970s. The cutoff of immigration would have increased the Gini index by 0.31% in the 1950s: the average education level of immigrants was slightly higher than the level of natives before the 1965 immigration act and became much lower in recent decades. Before 1965, a cutoff of immigration would have increased the P90/P10 ratio, mainly through the P90/P50 ratio. After 1965, the no immigration variant reduces the P50/P10 ratio. Hence, the current impact of immigration on inequality is mainly due to the large number of low-skill workers compared to the medium-skilled.

Impact on taxes Although the labor market impact is rather small, the impact of immigration on public finance is larger. Immigrants are less educated than natives and are particularly prone to using welfare programs. But they are characterized by a younger age structure and higher fertility rates. Hence, immigration has a beneficial effect on the ratio of tax payers to the beneficiaries of the welfare state. The no immigration variant predicts a sharp increase in the old age dependency ratio and a rise in public transfers. Without postwar immigration, the share of public transfers in GDP would be 0.3 point higher and the adjusted tax rate on consumption would be 1.1% higher. The fiscal gain from immigration becomes important after the 1970s and is expected to increase until 2040–2050 given the impact of immigration on the average fertility rate and the growth rate of the US population.

These results are in the line of other studies on the fiscal impact of immi- gration. Using a partial equilibrium model, Lee and Miller (2000) found that the overall present discounted value of the effect of immigration is positive, with significant variations over time. The estimated long-run fiscal impact of 100,000 more immigrants (with average characteristics) per year would be a decrease in taxes by near 1%. Razin and Sadka (1999, 2004) show evidence that, even though the immigrants may be lowly skilled and net beneficiaries of a pension system, they may nevertheless lead to a lower tax burden and less redistribution than would be the case with no immigration.

Impact on welfare Are there winners and losers from the US postwar immi- gration? We answer this question by computing the consumption-equivalent level of utility of different native cohorts by educational attainment. Figure 3a represents the welfare impact of the no immigration variant as a percentage of deviation from the baseline for the different cohorts and skill groups con- sidered. All cohorts and education groups have gained from the postwar immi- gration since welfare level are lower in the case with no migration. Cohorts born between 1950 and 1980 are the major beneficiaries, with a gain peaking at about 1%. The gains are smaller but significant (about 0.5%) for subsequent cohorts. Once again, this result is in sharp contrast with Borjas (1999b), who placed the immigration debate on redistributive ground rather than on

Should the US have locked heaven’s door? 345

-1,2

-1

-0,8

-0,6

-0,4

-0,2

0

1900 1920 1940 1960 1980 2000

Low skilled Medium skilled High skilled

(a)

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1900 1920 1940 1960 1980 2000

Low skilled Medium skilled High skilled

(b)

Fig. 3 Welfare by cohort. a “No immigration” in percent of the baseline. b “Selected immigration” in percent of the baseline

efficiency: because post-1965 immigration is disproportionately lowly skilled, he concluded on a negative impact on low-skill natives, whereas medium- and high-skill workers should win. According to our results, the redistributive impact of immigration is quite low (high-skill workers experience slightly higher gains than low-skill workers) and the net gain is strong. Such a positive welfare effect of immigration has already been obtained in Fehr et al. (2004). Assuming a doubling of immigration in the USA, they show that almost all cohorts and skill groups realize welfare gains.

Natives’ utility level is affected through three main channels: wages, taxa- tion, and interest rates. In Table 4, we disentangle welfare changes by simulat- ing alternative partial equilibrium models in which wages, tax, and interest rate responses are successively neutralized. Such a method allows us to compute the contribution of each component to welfare. Given feedback effects, the sum of all contributions does not exactly replicate the result of the full general equilibrium simulation. However, the residual term is quite low. In each skill group, the wage response is more than compensated by the fiscal and the interest rate response to immigration.

Contrary to expectation, the wage effect is always positive for the different skill groups (except for the 1900 cohorts) and eases the negative effects of the two other factors. Indeed, this wage effect could be disentangled between a “raw labor” effect (arising from the reduction of the labor/capital ratio) and a “human capital return” effect (arising from competition on the labor market between immigrants and natives of the same skill). The “raw labor” effect has a positive impact on the welfare of the different skill groups, whereas the “human capital return” effect is particularly detrimental for high-skill natives. Whatever the skill group and cohort considered, the first effect always dominates the second one.

The selected variant Our analysis suggests that the US postwar immigration is beneficial for all the parties concerned. Would the gains from immigration be larger if the US had pursued a selective immigration policy? The selected vari- ant relies on the same stocks of immigration as the baseline. It assumes that the

346 X. Chojnicki et al.

T ab

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Should the US have locked heaven’s door? 347

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348 X. Chojnicki et al.

skill distribution of immigrants converges towards the distribution of natives. In such a scenario, the average education level of immigrants increases, but the average experience decreases (immigrants have less experience but more schooling). Quantitatively, such a scenario induces similar effects on the skill premium, wage inequality, and taxes as the no immigration variant (Table 3). The magnitude of the effects is usually lower.

As appears in Fig. 3b and Table 3, all natives would have gained from a stronger selection: all determinants of the utility level are positively affected. Contrary to the no immigration variant, the distributive impact is more im- portant. A stronger selection would obviously be more profitable to low-skill workers than to medium- and high-skill workers. For recent cohorts, gains for the low-skilled are twice as large as for the highly skilled.

6 Discussion

In this paper, we develop a computable general equilibrium model to simulate the effect of the US postwar immigration on the economy. Using a backsolving calibration method, our baseline scenario matches the evolution of the US economy between 1940 and 2000. Then, we use two counterfactual variants: the no immigration variant considers a cutoff of migration flows after 1940; the selected variant assumes an identical distribution of skills for natives and immigrants. Our analysis reveals three striking results.

• First, although our unit of analysis is national (and not local), the labor market impact of immigration is very small. Distinguishing the major attri- butes of workers (raw labor, experience, education) instead of classifying workers by group reduces the relative changes induced by immigration on the labor market. A 10% increase in immigration only decreases the average wage by 1%, a figure that is compatible with spatial correlation studies.

• Second, immigration is beneficial for all. Every skill group in every cohort is gaining from the postwar immigration. Contrary to common views, immigration induces strong efficiency gains but small redistributive effects. These gains are closely related to fiscal externalities (the permanent entry of young immigrants decreases the equilibrium tax rate, although immi- grants cost more than natives in all age classes) and to a small immigration surplus (immigration increases the return on capital).

• Third, all generations would have benefited from a stronger selection of immigrants. Selection would have particularly benefited low-skill workers.

The choice of a production function has an important impact on the results. Our results suggest that (1) the efficiency impact of immigration should not be underestimated and that (2) the redistributive effects are likely to be small

Should the US have locked heaven’s door? 349

compared to skill-biased changes on the demand side. Of course, these con- clusions could be nuanced by considering various externalities associated to human capital accumulation. For example, we assume that the effect of immi- gration on the average level of education has no effect on technical changes (especially skill-biased technical changes). Assuming a relationship between the average level of education and skill biases would alter the results. By reducing the average education per worker, the US postwar immigration would have lowered the magnitude of skill-biased technical changes. This issue has been disregarded in the immigration debate and would obviously deserve more attention.

Acknowledgements We are grateful to Alan Auerbach, Tim Miller, and Philip Oreopoulos for transmitting their dataset. The second author acknowledges financial support from the ARC convention on “Geographical mobility of factors” (convention ARC 09/14-019) and from the Marie-Curie research and training network “Transnationality of Migrants” (TOM). We thank two anonymous referees for their helpful comments and suggestions on an earlier version of this paper. The usual disclaimers apply.

Appendix A: Income inequality: “factor proportions approach” vs general equilibrium

So as to correctly account for migration effects on the labor market, the tech- nological assumptions regarding the production function have to integrate the fact that workers belonging to different skill and experience groups are not perfect substitutes. So as to simplify the analysis, we assume in this paper that the stock of labor, education, and experience are homogenous so that an addi- tional year of experience to a high-skill worker contributes to the productivity the same way as an additional year of experience to a low-skill worker. Recently, numerous papers account for the effect of migration on the labor market assuming that the labor supply incorporates the contribution of workers ac- cording to their education and experience level (Borjas 2003, 2009; Borjas and Katz 2007; Borjas et al. 2008; Ottaviano and Perri 2006, 2008). These papers use the “factor proportions approach” that consists in a partial equilibrium analysis based on nested CES production functions. The aggregate production function is given by Eq. 2. The aggregate labor input Qt is defined as:

Qt = [ ∑

i

αit L ρ

it

]1/ρ , (18)

where i is an index representing the educational level and 1/(1 − ρ) is the elasticity of substitution between workers with different educational levels and with

∑ i αit = 1. Borjas, Freeman, and Katz (BFK) have used this production

function with only two inputs (high-skill labor, Lst, and low-skill labor, Lu).

350 X. Chojnicki et al.

More recently, Borjas (2003) takes into account the experience level and assumes, within each educational group, that workers with different experience are imperfect substitutes:

Lit = ⎡

⎣ ∑

j

αij L η

ijt

⎤

⎦ 1/η

, (19)

where Lijt gives the number of workers with education i and experience j at time t and 1/(1 − η) is the elasticity of substitution between workers in the same education group but with different experience levels and with

∑ j αij = 1.

Accounting for imperfect substitution between foreign and US workers within the same education-experience group is one of the main methodolog- ical contributions of Ottaviano and Perri (2006) to the “factor proportions approach.” The aggregate Lij incorporates the contributions of home-born workers (Lijn) and foreign-born workers (Lijm):

Lijt = ⎡

⎣ ∑

k=n,m αijkt L

β

ijkt

⎤

⎦ 1/β

, (20)

where 1/(1 − β) is the elasticity of substitution between US-born and foreign- born workers belonging to the same education and experience group.

BFK approach Basically, the BFK approach yields the following relationship between relative wages and relative labor supplies:

ln Wst Wut

= (1 − ρ) (

Dt − ln Lst Lut

) ,

where Dt stands for the log of relative demand shifts for high-skill workers. Denoting by Lin,t and Lim,t the labor supply of skill i = s, u of natives and

immigrants, the national supply of skill group i at time t can be written as:

Lit = Lin,t + Lim,t We have

ln Lst Lut

= ln Lsn,t Lun,t

+ ln (

1 + Lsm,t Lsn,t

) − ln

( 1 + Lum,t

Lun,t

)

so that the contribution of immigration (I MCt ) to the log of relative wages is given, in the BFK approach, by:

I MCt = (1 − ρ) [

ln

( 1 + Lsm,t

Lsn,t

) − ln

( 1 + Lum,t

Lun,t

)]

Applying such a “factor proportion” technique to our population data and using ρ = 0.7, the post-1940 immigration accounts for 33% of the 0.313 log point increase in wage differential between medium-skill and low-skill workers from 1940 to 2000. As shown in Table 5, such a contribution falls to 11%

Should the US have locked heaven’s door? 351

Table 5 Estimated contribution of immigration to wage differentials, 1940–2000

Medium vs low skilled - BFK approach

Elasticity of substitution between factors Parameter ρ 0.9 0.7 0.5 Elasticity of wage differential ρ − 1 −0.1 −0.3 −0.5 Elasticity of substitution 1/(1 − ρ) 10.0 3.3 2.0

Actual changea 0.313 0.313 0.313 Estimated contribution of immigration

Prod. function with skilled and Impact on the wage ratio 0.0344 0.1032 0.1721 unskilled labor (BFK)

Prod. function with raw labor Impact on the 0.0064 0.0192 0.0321 and education return to schooling

Percent contributionb

Prod. function with skilled and Impact on the wage ratio 11 33 55 unskilled labor (BFK)

Prod. function with raw labor Impact on the return 2 6 10 and education to schooling

Our method (general equilibrium — Impact on the wage ratio −0.7 0.5 1.5 3 inputs)

Source: Authors’ calculations Log point, except as indicated aActual changes in log wages differentials are calculated from Census data. They are expressed in log points bLog point contribution as percentage of actual log point change, 1940–2000

with ρ = 0.9 and rises to 55% with ρ = 0.5. The range of the immigration contribution is thus fully compatible with BFK results.

Our production function builds on the microeconometric wage equation (a la Mincer) and distinguishes three major wage components: raw labor, experience, and education. To simplify the exposition, let us temporarily dis- regard experience. Compared to BFK, we consider an aggregate production function F (L, H) with two inputs (raw labor, L, and education, H). The return to schooling is then given by:

ln W Ht W Lt

= (1 − ρ) (

Dt − ln Ht Lt

)

It can be reasonably assumed that the stock of human capital related to education is proportional to the number of high-skill workers ( Ht = α Lst ) and that the supply of raw labor sums up high-skill and low-skill workers (Lt = Lst + Lut ). We then have

ln Ht Lt

= ln(α) + ln (

Lst Lst + Lut

)

= ln(α) + ln (

Lsn,t Lsn,t + Lun,t

) + ln

( 1 + L

s m,t

Lsn,t

)

− ln (

1 + L s m,t

Lsn,t + Lun,t + L

u m,t

Lsn,t + Lun,t

)

352 X. Chojnicki et al.

so that the contribution of immigration (I MCt ) to the return to schooling becomes:

I MCt = (1 − ρ) [

ln

( 1 + L

s m,t

Lsn,t

) − ln

( 1 + L

s m,t

Lsn,t + Lun,t + L

u m,t

Lsn,t + Lun,t

)]

This contribution is much lower than in the BFK specification. Using the same population data as before, immigration explains only 6% of the high school premium changes between 1940 and 2000. The impact on the wage ratio

is lower since ln W s t

Wut ≈ ln

( 1 + W Ht

W Lt

) . General equilibrium effects are likely to

reduce the impact of immigration on wage differential since natives’ education choices are endogenous. However, the choice of the relevant production function has a major impact on the contribution of immigration to wage inequality. As shown in Table 5, our approach predicts a 0.5% contribution of immigration to the wage differential between medium- and low-skilled. With a lower elasticity of substitution, such a contribution could rise to 1.5%. Consequently, more than 98% of wage differential is explained by native supplies and demand changes.

Borjas (2003) approach Applying the Borjas (2003) methodology to our pop- ulation data, the net impact of immigration on the log wage of group (x, y) is:

�logWx,y = �xy,xymxy + ∑

j =y �xy,xjmxj +

∑

i =x

∑

j

�xy,ijmij, (21)

Table 6 Factor price elasticities

Education Years of Own Cross (within Cross (across experience education) education)

L (High school dropouts) 0–9 −0.313 −0.028 0.002 10–19 −0.330 −0.044 0.009 20–29 −0.341 −0.056 0.004 30–39 −0.352 −0.066 0.004 40–49 −0.358 −0.072 0.005

M (High school graduates) 0–9 −0.316 −0.030 0.012 10–19 −0.335 −0.050 0.023 20–29 −0.337 −0.051 0.019 30–39 −0.320 −0.044 0.015 40–49 −0.323 −0.037 0.015

H (some college and 0–9 −0.317 −0.031 0.017 college graduates) 10–19 −0.335 −0.049 0.026

20–29 −0.348 −0.062 0.033 30–39 −0.318 −0.032 0.017 40–49 −0.309 −0.023 0.013

Source: Borjas (2003)

Should the US have locked heaven’s door? 353

Table 7 Estimated contribution of immigration to wage differentials, 1940–2000

Medium vs low skilled — Borjas (2003) approach

Years of experience 10–19 20–29 30–39 40–49 Wage ratio M/L

2000 1.96 1.84 1.78 1.74 1940 1.58 1.51 1.47 1.45

Estimated contribution of immigration Borjas (2003) approach 0.181 0.154 0.136 0.103 Our method (general equilibrium) 0.011 0.009 0.008 0.007

Percent contribution of immigration Borjas (2003) approach 47.10% 46.47% 44.32% 35.38% Our method (general equilibrium) 2.81% 2.69% 2.60% 2.53%

Source: authors’ calculations

where mij is the percentage change in labor supply due to immigration in group (i, j), �xy,xy the own factor price elasticity, �xy,xj the (within education branch) cross-factor price elasticity, and �xy,ij the (across education branch) cross-factor price elasticity. Applying this methodology to our data, i = l, m, h and j = (0, ..., 4). The corresponding elasticities are directly taken from Borjas (2003) and adapted to our age and skill structure (Table 6).

The results of this are summarized in Table 7. The contribution of the post- Second World War immigration in wage differential between medium-skill and low-skill workers, with 10–19 years of experience, from 1940 to 2000 is evaluated to 47% with the Borjas (2003) methodology (i.e., applying elastic- ities of Table 6), while this contribution is less than 3% with our production function and general equilibrium approach. Whatever the group of experience is, we find the same order of magnitude. However, we have to keep in mind that the retained elasticities of substitution, and particularly the assumption of perfect substitution between a US-born and a foreign-born worker of the same education-experience, are highly controversial when regarding the totaly different results of Ottaviano and Perri (2006) with the same methodological approach.

Appendix B: Robustness to the elasticity of substitution

The parameter ρ determines the magnitude of wage responses (the intensity of the relationship between changes in factor proportions and changes in wages). Tables 8 and 9 give the economic consequences of immigration in alternative models. The model behind Table 8 is calibrated with a low elasticity of substitution (ρ = 0.5 and 1/(1 − ρ) = 2). The model behind Table 9 is calibrated with a high elasticity of substitution (ρ = 0.9 and 1/(1 − ρ) = 10). The conclusions are similar to the baseline simulation in Table 3 and to the magnitude of Table 4.

354 X. Chojnicki et al.

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Should the US have locked heaven’s door? 355

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b as

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Should the US have locked heaven’s door? 357

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358 X. Chojnicki et al.

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