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Assessing the Spanish immigration policy with frequency-wise causality in Hosoya’s sense

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Abstract

We cannot ignore that anti-immigration parties are becoming essential players in present democracies. But, how concerned should we be with the effects of immigration on the host economy? According to estimates, integration is the main asset of the Spanish immigration policy: in the long term, immigrants are legally indistinguishable; hence, they produce a similar effect on employment and growth. However, employment policies could enhance the long-term contribution of immigration to economic growth and, indirectly, boost employment creation. The effectiveness of immigration policies is thus attached to employment policies. In the short term, registered unemployment seems to be further protected against economic shocks. The frequency-wise analysis makes for a deeper understanding of the role of immigration in the Spanish economy.

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Notes

  1. According to the general definition, economic growth (\(\gamma _y\)) is equal to \(\gamma _y=\gamma _Y-\gamma _P\), the difference between aggregate output growth (\(\gamma _Y\)) and population growth (\(\gamma _P\)), hence \(\gamma _Y=0\) implies \(\gamma _y=-\gamma _P\) (see, for instance, Barro and Sala-i-Martin 2004). But we need to assume \(\gamma _Y=0\) to calculate the marginal rate of technical substitution between factors i and j as the ratio of partial derivatives, \(-f_j/f_i\). Therefore, the static marginalist analysis is adequate to predict the effect of immigration on the economy during recessive phases of the cycle, but not when the economy is growing.

  2. For instance, weddings Granger cause (predict) the ringing of bells, but the ringing of bells does not Granger cause weddings. And, obviously, neither bells nor weddings explain each other.

  3. According to the Orden de 11 de marzo de 1985 del Ministerio de Trabajo y Seguridad Social.

  4. The implicit function theorem applied to the lineal function, \(a_1 x_1+a_2 x_2+a_3 x_3=0\), means that \(x_i'(x_j)=-a_j/a_i\) whenever \(a_i\ne 0\).

  5. The equivalence between frequency \(\omega \) and time t for non-periodical processes is \(t=2\pi /\omega \) years.

  6. The intersection of confidence intervals for \({\hat{\beta _g}}{ir}\) and \({\hat{\beta _g}}{ie}\) are empty, but the intersection of confidence intervals for \({\hat{\beta _g}}{rj}\) and \({\hat{\beta _g}}{ej}\) is non-empty.

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Acknowledgements

This research was supported by the University of the Basque Country Research Project; and the Escuela Politécnica Nacional in Ecuador, Grant PIS-16-18 and PIS-17-17. We acknowledge the Instituto de Economía Aplicada (IEP) of the University of the Basque Country for sharing their resources with us.

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Authors and Affiliations

  1. Department of Mathematics, Escuela Politécnica Nacional, Ladrón de Guevara E11-253, Quito, Ecuador

    Alexandra M. Espinosa

  2. Department of Public Policies and Economic History, University of the Basque Country UPV/EHU, Lehedakari Agirre, 83, 48015, Bilbao, Spain

    Alexandra M. Espinosa

  3. Department of Quantitative Methods, University of the Basque Country UPV/EHU, Lehedakari Agirre, 83, 48015, Bilbao, Spain

    Ignacio Díaz-Emparanza

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  1. Alexandra M. Espinosa
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Correspondence to Alexandra M. Espinosa.

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The authors declare that they do not have a conflict of interest. Data are officially published in the web pages of the Spanish Ministry of Labour (Mitramiss), the National Institute of Statistics (INE), the European Statistic Office (EUROSTAT), and the World Bank. Results and figures are obtained using the usual standard code and function packages of Gretl and Wolfram Mathematica software. This research was supported by the Spanish Ministry of Science and Innovation MCIN/AEI/ 10.13039/501100011033 Grant PID2019-105183GB-I00, and the Escuela Politécnica Nacional in Ecuador, Grant PIS-16-18 and PIS-17-17. We acknowledge the Instituto de Economía Aplicada (IEP) of the University of the Basque Country for sharing their resources with us.

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Appendix

Appendix

Table 8 Rewarding immigration, \(m^{ij}_t=m_t^i-\beta _u^ju_t^j\)
Full size table
Table 9 Unrewarding immigration, \(m^{ij}_t=m_t^i-\beta _g^jg_t\)
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Espinosa, A.M., Díaz-Emparanza, I. Assessing the Spanish immigration policy with frequency-wise causality in Hosoya’s sense. Empir Econ 65, 111–147 (2023). https://doi.org/10.1007/s00181-022-02328-z

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