Empirical Evidence for Sequential Divergence and Convergence *

Been-Lon Chen
Institute of Economics, Academia Sinica, Taiwan
Chien-fu Jeff Lin
Department of Economics, National Taiwan University
Xiaokai Yang
Department of Economics, Monash University and

This Version: February 2002

* We are grateful for comments and criticisms from the participants of the seminar at Yale University, our sessions in Far East Econometric Society Meeting, Australian Econometric Society Meeting, and International Symposium of Dynamic Models. Special thanks go to Don Snodgrass and Jong-Wha Lee for comments and suggestions. We are solely responsible for the remaining errors.

Abstract

The paper tests the hypothesis of sequential divergence and convergence of per capita income. The hypothesis states that the divergence phenomenon takes place first between each pair of economies that enter the take-off stage at different points in time and then the convergence phenomenon follows. This implies that the difference in per capita real income between the two economies is an inverted U curve. The empirical data strongly support the hypothesis.

I. Introduction
The purpose of the paper is to test the hypothesis of sequential divergence and convergence of per capita income between a country which industrializes first and other following countries. This task is motivated by inconclusive debate over convergence versus divergence in growth rates between leading and lagging economies. The new theory of endogenous growth was motivated in part by the criticism (Lucas, 1988 and Romer, 1986) of the convergence theory based on the neoclassical growth model (Solow, 1956). The absolute convergence hypothesis - per capita incomes of countries converge to one another in the long-run independently of their initial conditions - has been rejected by empirical data (Barro, 1991). Sala-i-Martin (1996) defines absolute -convergence as the case in which poor economies tend to grow faster than rich ones and defines -convergence as the case in which the dispersion of real per capita GDP levels of a group of economies tends to decrease over time. His empirical work shows that there was neither -convergence nor absolute -convergence in the cross-country distribution of world GDP between 1960 and 1990, although the sample of OECD economies displays -convergence and so do the samples of regions within a country, such as the USA, Japan, Germany, the UK, France, Italy, or Spain. More concepts have been proposed to interpret the new evidence. Conditional convergence (Sala-i-Martin, 1996) is defined as the case in which per capita incomes of countries with the same structural characteristics converge to their own steady state in the long-run independently of their initial conditions. Hence, conditional divergence may take place if their structural characteristics are not the same. Club convergence (Galor, 1996) is defined as the case that per capita incomes of countries that are identical in their structural characteristics converge to one another in the long-run provided that their initial conditions are similar as well. Club convergence relates to multiple steady states to which different groups of countries with different initial conditions converge. Hence, the divergence between clubs takes place as each club converges to a steady state different from the steady state to which the other club converges if different clubs of countries with the same structural characteristics have different initial states.

But empirical studies based on the new concepts and data of growth rates are inconclusive. In particular, a great part of recent empirical evidence is based on Barro regression of growth rates on initial per capita income. The Barro regression may miss possible sequential divergence and convergence pattern. Suppose, for instance, each of two countries experiences a decelerating growth, then an accelerating growth, and finally decelerating growth again. Then there are two inflexion points of time path of per capita income for each country. We call the first inflexion point "threshold of take-off" and the second "critical point for matured growth." Assume that country A enters the take-off stage earlier than country B, then differential of per capita income and in marginal growth rates between the two countries may increase first and then declines. If we apply Barro regression to the data set, we may see negative correlation between initial per capita income and average growth rates. Hence, the Barro aggression misses the phenomenon of sequential divergence and convergence in per capita income for this particular data set. In order to fill this gap, the paper proposes to regress per capita income differential between the leading and following economies on time. If such a differential increases first and then declines, the inverted U curve of the differential implies sequential divergence and convergence in per capita income. Since convergence in growth rates may be associated with divergence in per capita income, empirical evidence for sequential divergence and convergence in per capita income does not reject a convergence of growth rates that is generated by the Barro regression. Hence, our exercise is to pick up some information that is missed by the Barro regression rather than rejecting the conclusion generated by Barro regressions.

Many theoretical models can predict sequential divergence and convergence in per capita income between the leader and the follower. For example, the transitional dynamics of the Ramsey model, the Solow model, and other neoclassical growth models can predict such a phenomenon. Recent endogenous growth models (Kelly, 1997, Wen, 1997, Zhang, 1997, and Yang and Borland, 1991) with endogenous evolution of division of labor can predict such a phenomenon too.

In this paper, the hypothesis of sequential divergence and convergence in per capita income will be tested. We shall show that the new evidence rejects the hypothesis of monotonic convergence or divergence in per capita income, though this does not imply rejection of the convergence of growth rates generated by the Barro regression.

Two strands of previous literature relate closely to this paper. Kelly (1997) provides historical evidence from Song Dynasty China for the two patterns of growth: accelerating and decelerating growth and their connection to transaction conditions. But he does not directly test the hypothesis of sequential divergence and convergence.

Empirical evidence for catch up and many Barro regressions, relate to our paper too. However, that empirical literature focuses on data of relatively short run growth rates and do not directly test divergence and/or convergence of per capita incomes. As in Kremer (1993), the long-run growth is the focus of the current paper. We shall devise a method in this paper to test the hypothesis of sequential divergence and convergence of per capita income against a long-run empirical data over more than 120 years.

The rest of the paper is organized as follows. Section II rigorously specifies the hypotheses to test. Then the hypotheses are tested against empirical data in section III. We have found that empirical data strongly support the hypothesis of sequential divergence and convergence.

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