Academic journal article Journal of Money, Credit & Banking

Is the Asymptotic Speed of Convergence a Good Proxy for the Transitional Growth Path?

Academic journal article Journal of Money, Credit & Banking

Is the Asymptotic Speed of Convergence a Good Proxy for the Transitional Growth Path?

Article excerpt

THE GROWTH LITERATURE has devoted considerable time and effort in analyzing the asymptotic speed of convergence predicted by alternative growth models. (1) An important reason for this analysis is its role in establishing stability of the model's long-run equilibrium. Perhaps a more important reason is that, as argued by Ortigueira and Santos (1997) and Eicher and Turnovsky (2001) among many others, a desirable property for growth models is to deliver an asymptotic speed of convergence that is consistent with cross-country empirical studies. (2)

In this paper, we show that the asymptotic speed of convergence in itself maybe a misleading representation of the transitional growth path. For this reason, a careful examination of the entire adjustment path predicted by transitional dynamics is needed to successfully discriminate among alternative growth theories.

More specifically, we study convergence speeds in two versions of the type of hybrid non-scale R&D-based growth framework studied by Eicher and Turnovsky (1999a, 1999b, 2001), one without and another with endogenous human capital accumulation. (3) We first compute the asymptotic speeds of convergence predicted by the system of equations that characterize the models' equilibrium dynamics. We find that both the non-scale R&D-based growth model with human capital and the one without human capital predict empirically supported values.

We discover, however, that this result alone is not very informative about the overall capacity of these two models for reproducing convergence episodes. The reason is that small variations in the asymptotic speed can be related to substantial changes in the initial periods of the adjustment path. More specifically, when we simulate the whole transitional path, we find that, even though both frameworks deliver similar asymptotic speeds of convergence, the dynamics of the model with human capital are able to reproduce important output-convergence experiences such as those of Japan and South Korea much more accurately than the ones of the model without human capital.

We also show that the introduction of human capital makes the asymptotic speed of convergence much less sensitive to changes in some underlying parameter that can be influenced by policy actions. This finding can offer theoretical support to Barro and Sala-i-Martin's (1995) result that convergence-speed estimates do not vary substantially across different countries or regions.

The remainder of the paper is organized as follows. In Section 1, we present the R&D-based model with human capital and study its steady-state predictions. In Section 2, we derive the equations used in the transitional dynamics analysis. Sections 3 and 4 obtain numerical results for the asymptotic speed of convergence and examine the entire adjustment path, respectively. Section 5 discusses the findings in more depth, relating them to the existing literature. Section 6 concludes.


The models studied in this paper are extensions of the type of non-scale R&D-based framework studied in Eicher and Turnovsky (1999a, 1999b, 2001). As shown by Jones (1995), this type of framework succeeds in reconciling important properties of the data, such as increasing R&D intensity, with constant output growth rates. We incorporate two modifications: first, we allow for human capital stock to accumulate endogenously over time, and second, technology imitation is costly. As suggested by Bils and Klenow (2000), these modifications make the R&D-based growth model more appropriate for analyzing countries at different levels of economic development.

In this section, we first outline the economic environment under which households and firms operate when human capital accumulation is possible. Then we solve the socially optimal problem. Our exposition is focused on aggregate technologies. …

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