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Aging and automation in economies with search frictions


This paper investigates the impact of an increase in life expectancy on the level and the distribution of income in the presence of skill heterogeneity and automation. It shows analytically that an increase in life expectancy induces the replacement of low-skilled workers by automation capital and high-skilled workers. Moreover, it raises the skill premium and has an ambiguous effect on total income. A simulation exercise, based on US data, shows that an increase in life expectancy raises the level as well as the inequality of income. We consider redistributive policies that can mitigate some of the adverse effects of an increase in life expectancy for low-skilled workers.

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  1. Our calculations based on data in International Federation of Robotics (2019a).

  2. See Prettner and Bloom (2020), pp. xi and xii.

  3. The advanced economies are not the only ones facing rapid population aging. Some emerging economies follow closely a similar transformation. For example, in China, the share of the population aged 65 years or over has continuously increased in recent years and reached 11.9% in 2019.

  4. For a presentation of the arguments see Chapter 6 in Prettner and Bloom (2020).

  5. The economic use of AI can be divided into five categories: Deep Learning, Robotization, Dematerialization, Gig economy, and Autonomous Driving (see Wisskirchen et al. 2017)

  6. The first industrial robot was installed in a General Motors automobile factory in New Jersey (Brynjolfsson and McAfee 2016).

  7. Other important applications of AI in health include deep learning to diagnose diseases, medical robots and AI-powered radiology assistant, to name but a few.

  8. Indeed, Gehringer and Prettner (2019) using data from the OECD find a remarkably robust positive relation between decreasing mortality and technological progress.

  9. Recent empirical studies that examine the relation between demographics and automation include Abeliansky and Prettner (2017) and Acemoglu and Restrepo (2018). The first study finds that an increase in population growth is associated with a reduction in the growth rate of automation density. The second study documents that countries that undergo faster aging—measured by an increase in the ratio of older to middle-aged workers—invest more in robots.

  10. For a summary of the stylized facts regarding the skill premium, wages, employment rates and inequality see Lankisch et al. (2019) and Prettner and Bloom (2020).

  11. This is a common way of introducing the survival probability in overlapping generations models, see, for example, Blackburn and Cipriani (2002), Chakraborty (2004), Cipriani (2014), Palivos and Varvarigos (2017) and Baldanzi et al. (2019).

  12. To simplify our analysis, we do not consider taxation and unemployment benefits.

  13. The logarithmic utility function that we use results in great analytical tractability; however, it yields a constant saving rate, βρ/(1 + βρ) (the income and substitution effect of an increase in the interest rate offset each other). Thus, one cannot distinguish the effect of an increase in patience, as captured by an increase in β, from the effect of an increase in longevity, as captured by an increase in ρ, on saving. On the contrary, the two parameters have an opposite effect on future consumption \(c_{o,t+1}^{i}.\) Whereas an increase in β raises \( c_{o,t+1}^{i},\) because the future matters more, an increase in ρ lowers it, because the opportunity cost of future consumption (= ρ/(1 + rt+ 1) increases.

  14. The working paper version of the article (Zhang et al. 2021) presents the proof of the proposition.

  15. Nevertheless, our results are robust to lower values of ϕ.

  16. Our results are also qualitatively robust to changes in σ (see Subsection A.3 in the Appendix of Zhang et al. 2021). For high values of σ the adjustment in the quantities and prices of labor are relatively small. In fact, when σ = 1, the two types of labor become perfect substitutes. In this case, the ratios of their marginal products (wages) remain constant (= λ/1 − λ) and their levels of employment cease to respond to changes in longevity.

  17. In Subsection A.4 of Zhang et al. (2021), we also present all the results in a tabular form both in levels and in percentage changes.

  18. A robot tax is often suggested as a way to mitigate the negative effects of automation (see Gasteiger and Prettner 2020 and Prettner and Bloom 2020 for details).

  19. As shown in Subsection A.5.1 of Zhang et al. (2021), our results are robust with respect to changes in τ.

  20. In Subsection A.6 of Zhang et al. (2021), we consider the case where a vacancy-maintenance subsidy at a constant rate is financed by a constant robot tax and additional lump-sum taxation. The results are qualitatively the same.

  21. As mentioned by Gasteiger and Prettner (2020), in an open-economy world, the success of a robot tax requires its coordinated implementation in many countries to avoid the reallocation of capital to jurisdictions that do not impose such a tax.

  22. This is not the first time that we observe a decrease in the life expectancy of certain groups. For example, the average life expectancy among American women without a high school diploma declined from 78.5 years in 1990 to 73.5 years in 2008 (Olshansky et al. 2012).

  23. In addition, automation capital and traditional physical capital increase as either ρh or ρl goes up (see Subsection A.2 in the Appendix of Zhang et al. 2021).

  24. Note that the income of the old high-skilled is the highest among the four groups, followed by the income of the young high-skilled, then by the income of the old low-skilled and finally by the income of the young low-skilled.

  25. As explained in detail in Prettner and Strulik (2020), these numbers are based on the empirical approximation of the ability distribution with the IQ distribution.

  26. As shown in Subsection A.5.2 of Zhang et al. (2021), our results are robust with respect to changes in τ.

  27. In Subsection A.6 of Zhang et al. (2021), we consider the case where an education subsidy at a constant rate is financed by a constant robot tax and additional lump-sum taxation. The results are qualitatively the same.


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We are indebted to Editor Oded Galor and two anonymous referees of this journal whose comments and suggestions have helped us improve the paper substantially.


Xiangbo Liu (corresponding author) acknowledges the research support by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 19XNI002).

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Zhang, X., Palivos, T. & Liu, X. Aging and automation in economies with search frictions. J Popul Econ 35, 621–642 (2022).

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  • Life expectancy
  • Automation
  • Search and matching
  • Skill heterogeneity

JEL Classification

  • J11
  • J24
  • J64
  • O33