Conditional Convergence

We have so far documented the large differences in income per capita across nations, the slight divergence in economic fortunes over the postwar era and the much larger divergence 16

Figure 1.12.

since the early 1800s. The analysis focused on the “unconditional” distribution of income per capita (or per worker). In particular, we looked at whether the income gap between two countries increases or decreases irrespective of these countries’ “characteristics” (e.g., institutions, policies, technology or even investments). Alternatively, we can look at the “conditional” distribution (e.g., Barro and Sala-i-Martin, 1992). Here the question is whether the economic gap between two countries that are similar in observable characteristics is becoming narrower or wider over time. When we look at the conditional distribution of income per capita across countries the picture that emerges is one of conditional convergence: in the postwar period, the income gap between countries that share the same characteristics typically closes over time (though it does so quite slowly). This is important both for understanding the statistical properties of the world income distribution and also as an input into the types of theories that we would like to develop.

How do we capture conditional convergence? Consider a typical “Barro growth regres­sion”:

gt,t-ι = β ln yt-1 + X-t-ι^a + ^εt

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where gtt_-ι is the annual growth rate between dates t — 1 and t, y_t-ι is output per worker (or income per capita) at date t — 1, and X_t-ι is a vector of variables that the regression is conditioning on with coefficient vector α.

Figure 1.9 showed that the relationship between log GDP per worker in 2000 and log GDP per worker in 1960 can be approximated by the 45^o line, so that in terms of this equation, β should be approximately equal to 0. This is confirmed by Figure 1.13, which depicts the relationship between the (geometric) average growth rate between 1960 and 2000 and log GDP per worker in 1960. This figure reiterates that there is no “unconditional” convergence for the entire world over the postwar period.

Figure 1.13. Annual growth rate of GDP per worker between 1960 and 2000 versus log GDP per worker in 1960 for the entire world.

While there is no convergence for the entire world, when we look among the “OECD” nations,^[1] we see a different pattern. Figure 1.14 shows that there is a strong negative re­lationship between log GDP per worker in 1960 and the annual growth rate between 1960 and 2000 among the OECD countries. What distinguishes this sample from the entire world sample is the relative homogeneity of the OECD countries, which have much more similar institutions, policies and initial conditions than the entire world. This suggests that there might be a type of conditional convergence when we control for certain country characteristics potentially affecting economic growth.

Figure 1.14. Annual growth rate of GDP per worker between 1960 and 2000 versus log GDP per worker in 1960 for core OECD countries.

This is what the vector X_t-ι captures in equation (1.1). In particular, when this vector includes variables such as years of schooling or life expectancy, Barro and Sala-i-Martin estimate β to be approximately -0.02, indicating that the income gap between countries that have the same human capital endowment has been narrowing over the postwar period on average at about 2 percent a year.

Therefore, there is no evidence of (unconditional) convergence in the world income dis­tribution over the postwar era (in fact, the evidence suggests some amount of divergence in incomes across nations), there is some evidence for conditional convergence, meaning that the income gap between countries that are similar in observable characteristics appears to narrow over time. This last observation is relevant both for understanding among which countries the economic divergence has occurred and for determining what types of models we might want to consider for understanding the process of economic growth and differences in economic performance across nations. For example, we will see that many of the models we will study shortly, including the basic Solow and the neoclassical growth models, suggest that there should be “transitional dynamics” as economies below their steady-state (target) level of income per capita grow towards that level. Conditional convergence is consistent with this type of transitional dynamics.

1.6.