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Endogenous fertility and human capital in a Schumpeterian growth model

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Abstract

This study develops a scale-invariant Schumpeterian growth model with endogenous fertility and human capital accumulation. The model features two engines of long-run economic growth: R&D-based innovation and human capital accumulation. One novelty of this study is endogenous fertility, which negatively affects the growth rate of human capital. Given this growth-theoretic framework, we characterize the dynamics of the model and derive comparative statics of the equilibrium growth rates with respect to structural parameters. As for policy implications, we analyze how patent policy affects economic growth through technological progress, human capital accumulation, and endogenous fertility. In summary, we find that strengthening patent protection has (a) a positive effect on technological progress, (b) a negative effect on human capital accumulation through a higher rate of fertility, and (c) an ambiguous overall effect on economic growth.

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Notes

  1. See Jones (1999) for an excellent review of these subsequent generations of R&D-based growth models.

  2. See, for example, Strulik (2005) for a discussion.

  3. See also Barro and Becker (1989) for a seminal study on endogenous fertility in an overlapping-generation model with exogenous growth.

  4. See also Jones (2003), who analyzes the effects of an exogenous increase in the R&D share of labor chosen by the government. He finds that this policy change increases growth in the short run but decreases growth in the long run through a lower rate of fertility due to a crowding-out effect on labor supply. In contrast, our result of a negative effect of patent breadth on economic growth is based on a higher rate of fertility through an opportunity-cost effect of lower foregone wages.

  5. See Scotchmer (2004) for a comprehensive review of this patent-design literature.

  6. See also Horowitz and Lai (1996).

  7. Early studies on the R&D-based semi-endogenous growth model include Jones (1995), Kortum (1997), and Segerstrom (1998).

  8. Early studies on the second-generation R&D-based endogenous growth model include Young (1998), Dinopoulos and Thompson (1998), and Peretto (1998).

  9. See Laincz and Peretto (2006) and Ha and Howitt (2007) for empirical evidence that supports the second-generation R&D-based growth model.

  10. See Growiec (2006) for an interesting discussion on alternative ways of modeling endogenous fertility in the growth literature.

  11. We follow a common approach in the literature to assume that θ is independent of capital accumulation or technological progress; see also Yip and Zhang (1997) and Connolly and Peretto (2003). Otherwise, as technology or human capital accumulates, θ increases causing a lower time cost of fertility, which in turn leads to a rising fertility rate instead of a constant fertility rate (i.e., ruling out a balanced growth path). However, we think it is reasonable that parental human capital contributes to the health and education of children, and this positive effect is captured by the law of motion for human capital per capita in Eq. 4.

  12. This is known as the Arrow replacement effect in the literature. See Cozzi (2007) for a discussion on the Arrow effect.

  13. We follow the standard approach in the literature to focus on the symmetric equilibrium. See Cozzi et al. (2007) for a theoretical justification for the symmetric equilibrium to be the unique rational-expectation equilibrium in the quality-ladder growth model.

  14. In an earlier version of this study, see Chu and Cozzi (2011), we consider a semi-endogenous-growth version of the model by specifying \(\overline{\varphi }_{t}\) to be decreasing in aggregate technology. In that model, we find that patent breadth has the same effects on fertility as in the current framework. However, the current framework is more general because long-run growth depends also on the R&D share of human capital whereas this R&D share only plays a role on short-run growth, but not on long-run growth in the semi-endogenous growth model.

  15. We assume constant returns to scale at the firm level in order to be consistent with free entry and zero expected profit.

  16. It is useful to recall that a t  = v t /N t .

  17. See Appendix B (available online) for derivations.

  18. See footnote 20 for a discussion.

  19. To see this, differentiating Eq. 23 with respect to ξ yields \(\partial g_{h}/\partial \xi =(1-n/\theta )-(1+\xi /\theta )\partial n/\partial \xi >0\) . Recall that 1 − n/θ > 0 and \(\partial n/\partial \xi <0\).

  20. In the special case of ϕ = 1, it can be shown that patent breadth μ has no effect on the fertility rate n  ∗  leaving only the positive effect on \(s_{r}^{\ast }\).

  21. In an extension of their model with human capital, Futagami and Iwaisako (2007) find that increasing patent length has a negative effect on the wage rate and human capital accumulation via an alternative mechanism other than endogenous fertility.

  22. Jones and Williams (2000) consider a lower bound for ϕ to be about 0.5 based on empirical estimates for the social rate of return to R&D. In this study, we intentionally choose a small value for ϕ in order for TFP growth g z not to be overly responsive to the R&D share of GDP. In our calibration, the elasticity of TFP growth with respect to the R&D share of GDP is about 0.2. If we set ϕ to a higher value of 0.5, the elasticity increases to about 0.5. However, while R&D share of GDP in the USA has been steadily rising, TFP growth shows no significant upward trend.

  23. Persons in households with older children spend even less time for child caring.

  24. We would like to thank a referee for suggesting this interesting extension.

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Acknowledgements

The authors would like to thank Silvia Galli, Oded Galor, and the anonymous referees for their insightful comments and helpful suggestions. The usual disclaimer applies.

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Authors and Affiliations

  1. Durham Business School, Durham University, Durham, UK

    Angus C. Chu & Guido Cozzi

  2. Institute of Economics, Academia Sinica, Taipei, Taiwan

    Chih-Hsing Liao

  3. Department of Economics, National Chengchi University, Taipei, Taiwan

    Chih-Hsing Liao

  4. School of Economics, Shanghai University of Finance and Economics, Shanghai, China

    Angus C. Chu

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  1. Angus C. Chu
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  2. Guido Cozzi
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  3. Chih-Hsing Liao
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Correspondence to Angus C. Chu.

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Chu, A.C., Cozzi, G. & Liao, CH. Endogenous fertility and human capital in a Schumpeterian growth model. J Popul Econ 26, 181–202 (2013). https://doi.org/10.1007/s00148-012-0433-9

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