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Small-Time Convergence

Jamus Lim's picture

For any macroeconomist concerned about growth in nations, economic convergence---the catch-up of less developed economies with the mature industrialized ones---is the ultimate dream. The basic premise behind the notion of convergence gas been around for at least a half century, following on Robert Solow's groundbreaking work on the dynamics of economic growth. Alas, convergence, at least as commonly understood by the profession, has remained elusive for the majority of developing countries in the world. If anything, leapfrogging has only occurred when one considers a small cachet of relatively homogeneous high-income economies (an idea known as "conditional" convergence), while the bulk of the developing world has languished in various low- and middle-income traps, with the distinct possibility that convergence may in fact occur toward a bimodel< distribution (an observation that Danny Quah has termed the "twin peaks" phenomenon, or "club" convergence). At worse, the developed world has forged ahead, and we have seen divergence (big time).

Faced with the undeniable incongruence between an elegant (but evidently incomplete) theory and the harsh reality, macroeconomists have introduced a range of wrinkles to explain the apparent lack of convergence. The idea of conditional convergence has been justified theoretically, for example, by appealing to heterogeneity in factor endowments in a standard neoclassical growth model; similarly, differing distributions of human capital, or perhaps gender differences, may induce club convergence outcomes.

From a purely econometric standpoint, however, hypotheses of conditional convergence smell eerily like selecting on the dependent variable. And club convergence seems to hint at the existence of unobservables in the data, making one wonder whether such unobservables can possibly be discovered (and, more importantly from a policy point of view, whether anything can be done about them to kickstart the growth process).

The bottom line is that for several decades, both theoretically and empirically-oriented macroeconomists struggled with the seeming lack of convergence in the cross-country growth data.[*]

This result, however, appears to be changing, albeit in a tentative fashion, and by no means across the board. The academic and policy debate about the reality of decoupling between the developed and developing world echoes, to some extent, the notion that economic convergence is not entirely a pipe dream.[] Even in the professional financial market community, forecasters have increasingly built (PDF) forecasts (PDF) that embed the optimism that there will be long-run convergence.

The more recent data also appear to offer some hope. Consider, for example, data from the five-year period between 1990 and 1994 (this excludes the period of the Asian and Latin American financial crises; other 5-year periods around the start of the decade yield similar results). There is precious little evidence that there is any negative relationship between real growth and real incomes---which is what we would expect if convergence were occurring---and this is the case whether we consider the full sample (see figure below, top panel) or a subset that limits the sample to just the largest economies (see figure below, bottom panel).

Source: World Bank staff calculations, from Global Economic Monitor database.

Note: GDP and GDP per capita measured in 2004 USD. Largest economies include the largest 50 economies in the 5-year period, as measured by real GDP, and all countries include 145 economies for which data were available. Regressions of (log) growth on (log) per capita income yielded coefficients of 0.0036 (full sample) and -0.0047 (largest 50), and neither were significant at the 10 percent level.

Fast-forward about 15 years, to the period between 2003 and 2007 (this also helpfully excludes most of the anomolous data that would have resulted from the global financial crisis). Convergence remains discouragingly absent from the mess of data for the full sample (see figure below, top panel). But if we restrict the sample to just the largest 50 economies, a different picture emerges: the relationship between growth and per capita income is now unambiguously negative. For the major economies of the world, therefore, we do observe evidence of convergence, at least in recent times.

Source: World Bank staff calculations, from Global Economic Monitor database.

Note: GDP and GDP per capita measured in 2004 USD. Largest economies include the largest 50 economies in the 5-year period, as measured by real GDP, and all countries include 152 economies for which data were available. Regressions of (log) growth on (log) per capita income yielded coefficients of -0.0019 (full sample) and -0.0116 (largest 50). The former was insignificant at the 10 percent level, while the latter is significant at the 1 percent level.

Of course, this result can't be celebrated quite yet. The absence of convergence for all countries suggests that the standard assumption---that technological transfer from the frontier to the periphery occurs seamlessly, inducing convergence by virtue of catch-up from lower levels of per capita income---is not quite right. What we need to understand are the mechanisms that permit

Yet knowing that small-time convergence has undoubtedly occurred nevertheless gives development macroeconomists hope. And while there remain a host of statistical caveats to this limited convergence result---the figure above is, after all, only illustrates simple unconditional correlation at the bivariate level, and we did restrict the result to a selected subsample---the reality is that these are, after all, the largest economies---which means that, at the world stage, these economies will be the ones that ultimately drive global growth. Indeed, recognizing this fact is also the way to reconciling the seemingly inconsistent finding that emerging economies appear to be increasingly driving global growth even at the aggregate level (see figure below), while convergence may still be absent in the cross-country data.[]

Source: World Bank staff calculations, from Global Economic Monitor database.

Note: Contribution to global growth calculated from monthly industrial production data. The G7 comprise the Canada, France, Germany, Italy, Japan, the U.K., and the U.S., while the BRIICK nations comprise Brazil, Russia, India, Indonesia, China, and South Korea.

Moreover, this convergence result is not quite the same conditional convergence results obtained in the past. For one, the economies that comprise the largest economies are are relatively heterogeneous bunch in many respects (the correlation between per capita income and GDP, for example, is only 0.28, and the group includes economies as diverse as Canada, Hungary, India, Nigeria, Saudi Arabia, Singapore, South Africa, and Switzerland).

This result also comes on the back of the finding by Dani Rodrik that unconditional convergence exists at the individual manufaturing industry level (PDF). It also comes at a time when macroeconomists are slowly getting a handle on the unobservables that may be giving rise to club (and conditional) convergence: fundamentals such as institutions, as well as the important interaction effects that exist between institutions and human and social capital.

*. This is in contrast to within-country evidence. There is good reason to believe that convergence occurred between U.S. states, for example, even if the empirical evidence does not accord perfectly with the implications of a traditional neoclassical model.

. Strictly speaking, decoupling can be examined from both a cyclical and trend perspective, and convergence is generally a trend decoupling concern. Moreover, decoupling introduces additional issues such as the role of interdependence (two economies may exhibit high correlation in their business cycles and trend growth, even if one grows systematically faster than the other) as well as uncertainty (fears of the future tend to lead to sharp increases in risk correlations, which muddies the disentangling of cycle and trend effects).

. This is because cross-country regressions use countries as the ontological unit, thus weighting differently-sized economies equally; in contrast, measures of contribution to global growth measures effectively weight each country by size.

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