A growth model with qualities, varieties, and human capital: stability and transitional dynamics

Tiago Neves Sequeira; Alexandra Ferreira-Lopes; Orlando Gomes

doi:10.1515/snde-2013-0018

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Article

A growth model with qualities, varieties, and human capital: stability and transitional dynamics

Tiago Neves Sequeira , Alexandra Ferreira-Lopes and Orlando Gomes

Published/Copyright: December 11, 2013

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From the journal Studies in Nonlinear Dynamics & Econometrics Volume 18 Issue 5

Abstract

This article analyses the stability properties of the steady-state and the transitional dynamics of an endogenous growth model with human capital, increasing-varieties R&D, and quality-ladders R&D [Strulik, H. 2005. “The Role of Human Capital and Population Growth in R&D-Based Models of Economic Growth.” Review of International Economics 13 (1): 129–145.]. We show that when spillovers within R&D sectors are higher than spillovers across the two R&D sectors, the equilibrium is unstable. However, when spillovers between sectors are higher than within, the equilibrium is a saddle-path. This result emphasizes the need for empirical research that compares quantitatively the importance of these two types of spillovers and highlights the importance of studying intersectoral effects between the two R&D sectors. We describe plausible paths of economic development after changes in crucial parameters and uncover some transitional effects that were impossible to detect in the steady-state analysis. We also show that this model’s transition dynamics can mimic the main features of the process of productivity slowdown that began in the 1970s.

Keywords: endogenous growth models; human capital; steady-state stability; transitional dynamics; vertical and horizontal R&D

JEL classification: O11; O15; O31; O33; O41

Corresponding author: Tiago Neves Sequeira, Faculdade de Ciências Sociais e Humanas, Universidade da Beira Interior, CEFAGE-UBI Research Center, Estrada do Sineiro, 6200-209 Covilhã, Portugal, Phone: +351919204088, e-mail: sequeira@ubi.pt

Acknowledgment

Tiago Neves Sequeira and Alexandra Ferreira Lopes acknowledge financial support from PTDC/EGE-ECO 102238/2008/FCT – Fundação para a Ciência e Tecnologia and Orlando Gomes acknowledges financial support from PEst-OE/EGE/UI0315/2011. The authors are also grateful to Manuel A. Gómez, for the permission to adapt some of the codes developed elsewhere to the numerical study of stability and to the transitional dynamics. The usual disclaimer applies.

Appendix

Jacobian

(14)

J=(j111−α11−α2j11vnvQξ(1−χ)(β1−α1)D−vQ(1−χ)(j11μQ+ξ(β1−α1)D)vQξ(1−χ)(β1−α1)Dj211−β11−β2j21vQvnξ(1−χ)(β2−α2)Dvnξ(1−χ)(β2−α2)Dj25j31j32ξμXj34j35j41j42j43j44j45j51j52j53j54j55), (14)

j11=−A(1−α2)(γ−1+σ−1)μQ1−χvn−1+α1vQ−1+α2;

j21=−A(1−β2)μn1−χvnβ1vQ−2+β2;

j31=AμX(1−θ)((μQ1−χVα(γ−1+σ−1)(1−α2)+μn1−χVβ(1−β2))VvQθ(σ−1);

j41=AuQ((1−α2)μQ1−χVα(μXμQ(σ−1)+(1−γ−1+σ)α2−1)−μn1−χVβ(1−β2))VvQχ;

j51=Aμn(μQ1−χVα(1−α2)(1−γ−1+σ)+μn−χVβ(((−σ)μQ+μX+μn(1−σ)β1(1−σ))(β2−1)VvQχ;

j43=μQ(ξ+μQj11χ(1−σ)(1−α2)(γ−1+σ−1));

j53=μn(ξ+AμnvQvnj21χ(1−σ)(1−β2));

j34=μX(ξ+j11μQ(γ−1+σ−1)γθ(1−σ)(1−α2));

j44=μQ(ξ+j11(Aγ(χμX−μQ(1−σ)(1−χ)+Aα2μQ(1−χ)(1−σ)(−γ+γσ))μQ2(γ−1+σ−1)γ(1−σ)(1−α2));

j54=μn(ξ+A[(j21(1−β2))+(j11vn(1−χ)(1−α2)(γ−1+σ−1))]χvnμn);

j25=−vn(1−χ)(j21V(1−β2)μn+ξ(β2−α2)D);

j35=μX(ξ−j21V(1−χ)(θ−1)θ(1−σ)(1−β2)μn);

j45=μQ(ξ−j21V(1−χ)α1χ(1−β2)μn);

j55=μn−χ[μn1+χVξ(σ−1)χ+AVβ(χ((1−σ)μQ+μX)+μn(σ−1)(1−χ)β1)]V(σ−1)χ.

where Vβ=vnβ1vQβ2; Vα=vnα1vQα2; V=vnvQ.

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Published Online: 2013-12-11

Published in Print: 2014-12-1

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Articles in the same Issue

https://doi.org/10.1515/snde-2013-0018

Keywords for this article

endogenous growth models; human capital; steady-state stability; transitional dynamics; vertical and horizontal R&D