ENDOGENOUS CYCLICAL GROWTH WITH A SIGMOIDAL DIFFUSION OF INNOVATIONS

Abstract

The model we propose in this paper is an extension of the one described in Freeman et al. [Freeman, S., Hong, D. and Peled, D. (1999) Endogenous Cycles and Growth with Indivisible Technological Developments. Review of Economics Dynamics, 2, 403–432]. In our model, we incorporate the process of diffusion of major innovations and analyze macroeconomic effects on consumption, capital and aggregate output. Following Bresnahan and Trajtenberg [Bresnahan, T. and Trajtenberg, M. (1995) General Purpose Technologies: Engines of Growth?. Journal of Econometrics, 65, 83–108.], Helpman [Helpman, E. (ed.) (1998) General Purpose Technologies and Economic Growth. MIT Press] and Lipsey et al. [Lipsey, R.G., Carlaw, K. and Bekar, C. (2005) Economic Transformations: General Purpose Technologies and Long Term Economic Growth. Oxford University Press.] we assimilate major innovations with the emergence of certain GPTs, and we suggest that the diffusion process for these technologies, at a large scale, might follow an S-shaped pattern. The proposed model presents optimum stationary solutions which are cyclical and have a wave dynamic within each cycle. The cycles are characterized by certain co-movements in consumption, R&D investment, capital accumulation and output. Consideration of the innovation diffusion process highlights new aspects of endogenous cycles and long-run growth.

Keywords:

• Endogenous growth
• Diffusion of innovations
• S-shaped dynamics
• Cycles

Acknowledgements

This paper has benefited from financial support under projects PO17-2000 of the Government of Aragon and BEC-2003-02827 of the Spanish Ministry of Science and Technology. The authors would also like to express their thanks to two anonymous referees for their helpful comments and suggestions on an earlier version of the paper.

Notes

¹Some of the cases discussed by Freeman, Hong and Peled (such as the development of the railroad system, the search for alternative energy sources, and the appearance of new information and communication systems) are examples of GPTs as defined by Lipsey et al. (1998)

²It will be clearly stated in Section 3 how this process drives productivity growth in the model.

³Normalizing the population measure to one and ignoring population growth.

⁴See e.g. Dasgupta and Heal (1979), p. 293.

⁵The representation is obtained for the same parametric values as the simulations given in Appendix 2.

⁶We can verify this for τ∈(τ*, 2τ*), if τ*<ˆ τ. Let γ (τ)=(˙ a(τ)/a(τ)) and indexed to the cycle sub-index. For ϵ>0 it holds that