Should the US have locked heaven’s door?

Reassessing the benefits of postwar immigration


This paper examines the economic impact of the second great immigration wave (1945–2000) on the US economy. Our analysis relies on a computable 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 immigration is beneficial for all natives cohorts and all skill groups. Nevertheless, the gains would have been larger if the US had conducted a more selective immigration policy.

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  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

    Immigrants are defined as individuals who were foreign-born and whose parents were non US citizens.

  5. 5.

    RiosRull (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.

  6. 6.

    Another 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.

  7. 7.

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

  8. 8.

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

  9. 9.

    The log-linear process \(\ln \big[ \beta _{j,t}^{m}\big] =.2\times \ln \big[ \beta _{j,t}^{l}\big] +.8\times \ln \big[ \beta _{j,t}^{h}\big]\) gives a good approximation of mortality differential per race and per age.

  10. 10.

    This figure is only used as a target value since the consumption tax rate is endogenously calculated to balance the government budget constraint.

  11. 11.

    Including medicare, medicaid, unemployment, AFDC, food stamps, and general welfare.

  12. 12.

    The actual wage gap is computed from Census data.

  13. 13.

    In 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.

  14. 14.

    Henceforth, BFK.


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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.

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Correspondence to Xavier Chojnicki.

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

So as to correctly account for migration effects on the labor market, the technological 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 additional 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 according 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 Q t is defined as:

$$ Q_{t}=\left[ \sum_{i}\alpha _{it}L_{it}^{\rho }\right] ^{1/\rho}, \label{aeq1} $$

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 α it  = 1. Borjas, Freeman, and Katz (BFK) have used this production function with only two inputs (high-skill labor, L st , and low-skill labor, L u ).

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

$$ L_{it}=\left[ \sum_j \alpha_{ij} L_{ijt}^{\eta } \right] ^{1/\eta}, \label{aeq2} $$

where L ijt 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 α ij  = 1.

Accounting for imperfect substitution between foreign and US workers within the same education-experience group is one of the main methodological contributions of Ottaviano and Perri (2006) to the “factor proportions approach.” The aggregate L ij incorporates the contributions of home-born workers (L ijn ) and foreign-born workers (L ijm ):

$$ L_{ijt}=\left[ \sum_{k=n,m} \alpha_{ijkt} L_{ijkt}^{\beta } \right] ^{1/\beta}, \label{aeq3} $$

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:

$$ \ln \frac{W_{st}}{W_{ut}}=(1-\rho )\left( D_{t}-\ln \frac{L_{st}}{L_{ut}} \right), $$

where D t stands for the log of relative demand shifts for high-skill workers.

Denoting by L in,t and L im,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:

$$ L_{it}=L_{in,t}+L_{im,t} $$

We have

$$ \ln \frac{L_{st}}{L_{ut}}=\ln \frac{L_{sn,t}}{L_{un,t}}+\ln \left( 1+\frac{ L_{sm,t}}{L_{sn,t}}\right) -\ln \left( 1+\frac{L_{um,t}}{L_{un,t}}\right) $$

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

$$ IMC_{t}=(1-\rho )\left[ \ln \left( 1+\frac{L_{sm,t}}{L_{sn,t}}\right) -\ln \left( 1+\frac{L_{um,t}}{L_{un,t}}\right) \right] $$

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% 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.

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

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 disregard experience. Compared to BFK, we consider an aggregate production function \(F\left( L,H\right) \) with two inputs (raw labor, L, and education, H). The return to schooling is then given by:

$$ \ln \frac{W_{t}^{H}}{W_{t}^{L}}=(1-\rho )\left( D_{t}-\ln \frac{H_{t}}{L_{t}} \right) $$

It can be reasonably assumed that the stock of human capital related to education is proportional to the number of high-skill workers \((H_{t}=\alpha L_{t}^{s})\) and that the supply of raw labor sums up high-skill and low-skill workers \((L_{t}=L_{t}^{s}+L_{t}^{u})\). We then have

$$ \begin{array}{rcl} \ln \frac{H_{t}}{L_{t}} &=&\ln (\alpha )+\ln \left( \frac{L_{t}^{s}}{ L_{t}^{s}+L_{t}^{u}}\right) \\ &=&\ln (\alpha )+\ln \left( \frac{L_{n,t}^{s}}{L_{n,t}^{s}+L_{n,t}^{u}} \right) +\ln \left( 1+\frac{L_{m,t}^{s}}{L_{n,t}^{s}}\right) \\ &&-\,\ln \left( 1+ \frac{L_{m,t}^{s}}{L_{n,t}^{s}+L_{n,t}^{u}}+\frac{L_{m,t}^{u}}{ L_{n,t}^{s}+L_{n,t}^{u}}\right) \end{array} $$

so that the contribution of immigration (IMC t ) to the return to schooling becomes:

$$ IMC_{t}=(1-\rho )\left[ \ln \left( 1+\frac{L_{m,t}^{s}}{L_{n,t}^{s}}\right) -\ln \left( 1+\frac{L_{m,t}^{s}}{L_{n,t}^{s}+L_{n,t}^{u}}+\frac{L_{m,t}^{u}}{ L_{n,t}^{s}+L_{n,t}^{u}}\right) \right] $$

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 \(\ln \frac{W_{t}^{s}}{W_{t}^{u}}\approx \ln \left(1+ \frac{W_{t}^{H}}{W_{t}^{L}}\right) \). 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 population data, the net impact of immigration on the log wage of group (x,y) is:

$$ \Delta log W_{x,y}= \epsilon_{xy,xy} m_{xy} + \sum_{j \neq y} \epsilon_{xy,xj} m_{xj} + \sum_{i \neq x} \sum_{j} \epsilon_{xy,ij} m_{ij}, \label{aeq4} $$

where m ij is the percentage change in labor supply due to immigration in group (i,j), ε xy,xy the own factor price elasticity, ε xy,xj the (within education branch) cross-factor price elasticity, and ε 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).

Table 6 Factor price elasticities

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 elasticities 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.

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

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.

Table 8 Economic consequences of the US immigration (lower elasticity of substitution, ρ = .5)
Table 9 Economic consequences of the US immigration (higher elasticity of substitution, ρ = .9)

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Chojnicki, X., Docquier, F. & Ragot, L. Should the US have locked heaven’s door?. J Popul Econ 24, 317–359 (2011).

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  • Immigration
  • Welfare
  • Computable general equilibrium

JEL Classification

  • J61
  • I3
  • D58