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Is tightening immigration policy good for workers in the receiving economy?


Long-term effects of tightening immigration policies on native workers of a host country are analyzed using a small open overlapping-generation model. Such a policy is intended to protect native workers from losing income and possibly jobs. Results demonstrate that a stricter policy raises the unskilled wage rate as expected, but it might also raise the skilled-wage rate even if skilled and unskilled labors are (technically) complementary. Such a policy also lowers the average education level of the country. If skilled and unskilled labors are sufficiently substitutable, then the policy might instead increase immigration inflows to the host country.

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Fig. 1

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Data sharing is inapplicable to this paper, because no new data were analyzed.


  1. 1.

    Recent empirical research has been conducted actively for Syrian refugees, specifically in relation to forced migration (Tumen 2016). Especially, regarding refugees, receiving countries are forced to bear huge burdens of expenditures to provide jobs, housing, and social security. Nannestad (2007) also concludes that immigrants are rather a burden to Western welfare states because of their welfare programs. Chao and Yu (2002) theoretically demonstrate that unskilled immigrant workers can reduce welfare in the host country under imperfect competition in the goods market. Peri (2016) reports that the population shares of foreign-born residents in both Europe and the US were higher than 15% in 2015.

  2. 2.

    Djajic (1989) assumes that because a minimum skill level is necessary for immigration, the skill must be accumulated in the original country. Actually, economically developed countries such as Australia, Canada, Japan, and the US impose some regulations on potential capabilities as a floor on the level of skill that a potential immigrant must have to gain permission to work in those countries.

  3. 3.

    For example, Chao and Yu (2002) theoretically demonstrate that unskilled immigrant workers can reduce welfare in the host country under imperfect competition in the goods market.

  4. 4.

    Similar results are obtained for Europe countries, although the labor market in Europe is regarded as highly rigid (Zorlu and Hartog 2005; Brücker and Jahn 2011).

  5. 5.

    Although presuming perfect substitutability between immigrants and native workers of the same type such as Borjas (2003), the model used for the present study examines the (utility) cost of immigration, which includes costs of learning languages, and psychic costs to be highly substitutable.

  6. 6.

    Nevertheless, Peri (2016) describes that immigration policy changes aimed at opening borders have not consistently reduced barriers to entry by immigrants since about 1970.

  7. 7.

    Chassamboulli and Palivos (2013) explain an exception by which skilled and unskilled labor complementarity can be considered explicitly. For technical substitutability and complementarity, Hicks (1939, Chap. 7) provides related explanations. It is also called ‘Edgeworth complementarity’ in the literature (Chassamboulli and Palivos 2013).

  8. 8.

    Orientation of the source country’s government policies might also affect cost. For analytical purposes, we assume all particular orientations away for the analyses presented in this paper.

  9. 9.

    Beam et al. (2016) report that mere unilateral facilitation of the sending countries might not promote international labor mobility.

  10. 10.

    We do not consider the possibility that individuals are required to return to the original country. Galor and Stark (1990) show that the possibility of return migration might increase savings and economic performance.

  11. 11.

    We assume away education and skill acquisition outside the home country. Alternatively, we assume that only uneducated individuals immigrate into the host country and that they are myopic when immigrating in the sense that their immigration decisions are not entirely time consistent. Docquier et al. (2014) report that a large portion of the labor movement is from other OECD countries, although the share of college-educated immigrants is four-to-five times as large as their share among non-migrant native workers of OECD countries. Clements et al. (2008) report that the ratio of wages earned by workers in the US to those of ‘observably identical’ workers abroad is considerably high, e.g., 3.8 for a Peruvian-born worker.

  12. 12.

    This is the immigrant self-selection model described by Borjas (1994). In the present setting, immigrants are accepted as unskilled workers. Beam et al. (2016) emphasize the importance of both demand-side and supply-side factors for international labor mobility. We assume here, for simplicity, perfect substitution between low-skilled migrant and native workers. Ottaviano and Peri (2012), among others, consider imperfect substitutability.

  13. 13.

    Costs of skill acquisition can be regarded as having an inverse relation to the (innate) ability of an individual. The cost of immigration might be lower for immigrants with higher capabilities, for instance, in language.

  14. 14.

    The (semi-indirect) utility function of an immigrant indexed \(j\) can be written as \(U(j) = V(j) - \phi e(i(j)) - \theta c(j,\beta )\), where \(\phi = 0\) if the immigrant does not pursue education in the recipient country and \(\theta = 0\) if the immigrant does not immigrate.

  15. 15.

    Labor demand functions are explained in “Appendix A.1”.

  16. 16.

    For system stability, Samuelson (1983) and some other reports provide a useful explanation.

  17. 17.

    Dustmann et al. (2016) describe that the elasticity of substitution between unskilled and skilled workers is unambiguously negative. However, empirical reports describe that \(F_{{L^{{\text{s}}} L^{{\text{u}}} }}\) can be positive or negative. Bohn and Lopez-Velasco (2018) report that the estimates in the literature range between 1.5 and 2.5. “Appendix A.2” presents discussion of this issue.

  18. 18.

    Analysis of a case in which immigrant opportunities are restricted is described in the “Appendix A.3”.

  19. 19.

    By contrast, Iranzo and Peri (2009) show with simulation analysis that international skilled-labor movements and trade improve global welfare through improvements of productive efficiency, even under monopolistic competition.


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The author would like to thank three anonymous referees for their insightful comments and suggestions. He would also like to thank Yoshimasa Aoki, Kenji Kondo, Kazutoshi Miyazawa, Minoru Nakata, Hiroshige Tanaka, and seminar participants at the 2019 Spring Meeting of Japan Association for Applied Economics and Nagoya Macroeconomics Workshop for their helpful comments and suggestions on an earlier version of this paper. Financial support from the Japan Society for the Promotion of Science KAKENHI Grant nos. 16H03635 and 19H01503 is gratefully acknowledged.


The Japan Society for the Promotion of Science KAKENHI Grant nos. 16H03635 and 19H01503.

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A.1 Complementarity and substitutability between skilled and unskilled labors

In a small open economy, capital moves internationally to keep the domestic interest rate equal to the world interest rate, satisfying (1a). Therefore, we have:

$$ \begin{gathered} {\text{d}}w^{{\text{s}}} = \left[ {F_{{L^{{\text{s}}} L^{{\text{s}}} }} - F_{{KL^{{\text{s}}} }} (F_{{L^{{\text{s}}} K}} /F_{KK} )} \right]{\text{d}}L^{{\text{s}}} + \left[ {F_{{L^{{\text{u}}} L^{{\text{s}}} }} - F_{{KL^{s} }} (F_{{L^{{\text{u}}} K}} /F_{KK} )} \right]{\text{d}}L^{{\text{u}}} , \hfill \\ \end{gathered} $$


$$ {\text{d}}w^{{\text{u}}} = \left[ {F_{{L^{{\text{s}}} L^{{\text{u}}} }} - F_{{KL^{{\text{u}}} }} (F_{{L^{{\text{s}}} K}} /F_{KK} )} \right]{\text{d}}L^{{\text{s}}} + \left[ {F_{{L^{{\text{u}}} L^{{\text{u}}} }} - F_{{KL^{{\text{u}}} }} (F_{{L^{{\text{u}}} K}} /F_{KK} )} \right]{\text{d}}L^{{\text{u}}} . $$

From these equations, we obtain:

$$ \frac{{{\text{d}}L^{{\text{s}}} }}{{{\text{d}}w^{{\text{u}}} }}(: = L_{{\text{u}}}^{{\text{s}}} ) = G^{ - 1} \left[ { - \frac{{F_{{L^{{\text{u}}} L^{{\text{s}}} }} - F_{{KL^{{\text{s}}} }} (F_{{L^{{\text{u}}} K}} /F_{KK} )}}{{F_{{L^{{\text{s}}} L^{{\text{s}}} }} - F_{{KL^{{\text{s}}} }} (F_{{L^{{\text{s}}} K}} /F_{KK} )}}} \right]\;{\text{and,}} $$
$$ \frac{{{\text{d}}L^{u} }}{{{\text{d}}w^{u} }}(: = L_{{\text{u}}}^{{\text{u}}} ) = G^{ - 1} , $$

where by assumption:

$$ \begin{aligned} G \equiv & \left[ {F_{{L^{{\text{u}}} L^{{\text{u}}} }} - F_{{KL^{{\text{u}}} }} (F_{{L^{{\text{u}}} K}} /F_{KK} )} \right] \\ & \quad - \frac{{F_{{L^{{\text{s}}} L^{{\text{u}}} }} - F_{{KL^{{\text{u}}} }} (F_{{L^{{\text{s}}} K}} /F_{KK} )}}{{F_{{L^{{\text{s}}} L^{{\text{s}}} }} - F_{{KL^{{\text{s}}} }} (F_{{L^{{\text{s}}} K}} /F_{KK} )}}\left[ {F_{{L^{{\text{u}}} L^{{\text{s}}} }} - F_{{KL^{{\text{s}}} }} (F_{{L^{{\text{u}}} K}} /F_{KK} )} \right] < 0. \\ \end{aligned} $$

Therefore, if \(F_{{L^{{\text{u}}} L^{{\text{s}}} }} > 0\), i.e., if technical complementary holds, then we have \(L_{{\text{u}}}^{{\text{s}}} < 0\) from (16), where we assume for this study that \(F_{{KL^{{\text{x}}} }} > 0\) (\({\text{x}} = {\text{s}},{\text{u}}\)) and \(F_{KK} < 0\). Condition (17) implies that the demand curve of low-skilled labor is downward-sloping. A more detailed explanation is presented by Fan and Yakita (2011).

A.2 Complementarity between skilled and unskilled workers

Presuming a production function \(Y = AK^{\alpha } L^{1 - \alpha }\) in which the labor aggregate is a nested constant-elasticity-of-substitution (CES) aggregation of skilled and unskilled labors \(L = [\theta^{{\text{u}}} (L^{{\text{u}}} )^{\sigma } + \theta^{{\text{s}}} (L^{{\text{s}}} )^{\sigma } ]^{1/\sigma }\), the elasticity of substitution between skilled and unskilled labors is given as \(1/(1 - \sigma )\). From the production function, we obtain:

$$ F_{{L^{{\text{u}}} L^{{\text{s}}} }} = AK^{\alpha } (1 - \alpha )\theta^{{\text{u}}} (L^{{\text{u}}} )^{\sigma - 1} \theta^{{\text{s}}} (L^{{\text{s}}} )^{\sigma - 1} L^{(1 - \alpha ) - 2\sigma } (1 - \alpha - \sigma ). $$

Therefore, we have:

$$ F_{{L^{{\text{u}}} L^{{\text{s}}} }} \mathop = \limits_{ < }^{ > } 0\;{\text{as}}\;1 - \sigma \mathop = \limits_{ < }^{ > } \alpha . $$

The parameter of the wage change of native workers with respect to immigration shock corresponds to \(\sigma - 1\), as described by Dustmann et al. (2016). They report that the parameter estimated in various studies ranges from \(- 0.42\), as reported from a study by Card (2009) to \(- 0.04\) as reported by Card and Lewis (2007) in the Mixed Approach (presuming here that \(\sigma < 1\)). Assuming that \(\alpha = 0.33\), which is a common assumption in many reports of the literature, we have a case of \(F_{{L^{{\text{u}}} L^{{\text{s}}} }} > 0\), i.e., technical complementarity. In a small open economy with free capital mobility, skilled and unskilled labors are (gross) complements only when their technical complementarity is sufficiently strong. This paper describes that skilled native workers can benefit from immigration inflows in terms of wages only when technical complementarity between skilled and unskilled labor is sufficiently strong.

A.3 Restriction of immigrants’ opportunities for education

As explained in the text, we assume that immigrants can also acquire education and develop skills if education costs are sufficiently low. However, it might actually be difficult for immigrants to pursue education unless they are received as skilled workers by the destination country. Therefore, we briefly consider a case in which no immigrant receives education. This case is presented in Fig. 1b.

The analysis is fundamentally equivalent to that used in the preceding section. The equilibrium conditions in the labor market become:

$$ L^{{\text{u}}} (w^{{\text{s}}} ,w^{{\text{u}}} ,r) = 2\left[ {\left( {1 - \int_{0}^{{\hat{i}}} {f(i){\text{d}}i} } \right) + \alpha \int_{{\overline{j}}}^{{j_{\max } }} {h(j){\text{d}}j} } \right]\;and, $$
$$ L^{{\text{s}}} (w^{{\text{s}}} ,w^{{\text{u}}} ,r) = \int_{0}^{{\hat{i}}} {f(i){\text{d}}i} . $$

Conditions (2) and (3) are the same as those in the preceding section. Therefore, the analysis can be simplified. From these conditions, one can demonstrate that the results are qualitatively equivalent.

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Yakita, A. Is tightening immigration policy good for workers in the receiving economy?. Asia-Pac J Reg Sci 5, 975–991 (2021).

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  • Education
  • Immigration policy
  • Skilled–unskilled labor complementarity

JEL Classification

  • D15
  • F22
  • F66
  • O24