What have we learned from the convergence debate Nazrul Islam Economic growth Spring semester, 2009 David Tønners

Why is the convergence issue so important? It could in principle be a way of testing different theoretical models empirically. As an example neo-classical growth models (e.g. Solow (1956) and Ramsey (1928)) imply conditional convergence. Important for policy recommendations. E.g. should we give foreign aid to poor countries?

The purpose of the article To survey the litteature on convergence; in particular the different concepts of convergence, the methods of determining whether there is convergence and the actual results

Within / between countries In terms of growth rates / income levels In terms of β- / σ convergence Absolute / conditional Income / Total Factor Productivity (technological catching up) Global / club Deterministic / stochastic Different convergence concepts

With global convergence, the economy will reach a unique steady state (determined by structural characteristics) as in the Ramsey or Solow-model. A different approach is to introduce multiple steady-states (Club-convergence). Therefore a country may be poor only because it starts out with a income level below a certain treshold. Global versus club-convergence

Deterministic versus stochastic convergence One way of studying convergence between countries is by using a time-series approach. If a deterministic trend is allowed when testing for unit roots, convergence is called deterministic. If a stochastic trend is allowed, convergence is stochastic.

The different approaches to determining whether convergence occurs: Cross-section approach: convergence between countries Panel approach Time series approach Distribution approach (focuses on sigma convergence)

Convergence or not? The cross-section approach: Baumol (1986) looked at 16 OECD-countries. In this sample growth is negatively related to the initial income level. Evidence of unconditional (or maybe conditional) convergence. However, this study suffers from a selection bias: DeLong (1988) In larger samples no unconditional convergence is present.

The missing convergence in larger samples could reflect that we should test for conditional convergence instead. When variables mesuring the amount of labor and capital is included some researchers were able to find covergence. Indicates that convergence is at best conditional (as the neoclassical growth models predicts). Barro (1991) includes human capital and. He also finds conditional beta-convergence. Convergence or not? The cross-section approach:

Next step is to use regressions derived from a formal economic model, instead of ad-hoc specifications (such as Baumol (1986) and Barro (1991)). Mankiw, Romer and Weil (1992) is one of the most influential studies of this kind. They estimate the Solow (1956)-model augmented with human capital. Convergence or not? The cross-section approach:

Mankiw, Romer and Weil (1992) Test for unconditional convergence:

Mankiw, Romer and Weil (1992) Test for conditional convergence:

Mankiw, Romer and Weil (1992) Test for conditional convergence:

Problems with MRW (1992) Treats the technological level and the rate of technological growth as part of the error term. This is a problem if these are correlated with the explanatory variables (savings, population growth or human capital). This is the problem of Omitted Variable Bias, and results in a biased OLS-estimator.

Correlation between the rate of technological growth and the savings rate (investment rate)

How to solve the problem of Omitted Variable Bias? One way to solve this problem is by using panel data. This approach also produces a estimate of the technological level for each country. Islam (1995) finds that the highest technological level is about forty times as high as the lowest. Important to explain what causes differences in the technological level across countries. Some complications arise in using panel data (small sample bias, short frequency etc.)

The time series approach Can be used to sudy both convergence across and within countries. Test for convergence within a country corresponds to a Dickey-Fuller test. The null is no-convergence (corresponds to a unit root). Across countries: testing for unit-roots in the deviations. Either the deviation from a reference economy (e.g. USA) or the average. Notice: even if two economies does not converge within (there is a unit root) there could still be convergence between, if the time series co-integrate (the unit root cancels in the deviation).

The distribution approach Focuses on sigma-convergence, by looking at the actual income distributions. For the OECD-area and the USA-regions sigma-convergence seems to be present. But not for larger samples. Corresponds the findings of absolute / conditional beta- convergence.

The distribution approach: results Persistence: most countries remian in the same position of the distribution A tendency towards a more ’bi-modal’ structure: supports the concept of club-convergence

Further research on convergence: Incorporation of open-economy aspects in the estimation of convergence regressions (including spill-overs between countries). E.g. the question of how international trade is related to growth A better theoretical fundament for explaining club-convergence (why do multiple steady-states occur?)