# **3.2 Conditional convergence**

Much of the literature has found evidence that once country characteristics are controlled for, the coefficient on initial income becomes negative and statistically significant. Tests for conditional convergence use a similar regression specification as tests for unconditional convergence but control for country characteristics: where _Xi_ is a set of country characteristics. These country characteristics include the initial levels and changes in variables relating to factors such as educational attainment, trade openness, natural resources, demographics, population health, and governance.

Controlling for the level of human capital available across economies, as measured by average years of education, has been found to result in statistically significant convergence (Barro and Lee, 1994; Mankiw et al., 1992). Other than direct inputs into the production function, a range of additional factors have also been found to be important controls for assessing convergence. These have included trade openness and export orientation (Dollar and Kraay, 2003; Frankel and Romer, 1999; Sachs and Warner, 1995), good institutions (Rodrik, 2004), natural resources and other geographical factors (Easterly and Levine, 2001, 2003; Sachs and Warner, 2001), and economic or export complexity (Hausmann et al., 2007; Hidalgo and Hausmann, 2009).

Consistent rates of convergence have also been found when controlling for country characteristics. The “rule of 2 percent” was coined after a common rate of annual income convergence across U.S. states, and separately countries, was identified when controls for factors such as educational levels and political stability were included (Barro and Sala-i Martin, 1992). Most studies have found results within a range of 1 to 3 percent per annum (Durlauf et al., 2005). An annual convergence rate of 2 percent implies that half of any initial difference in productivity levels will disappear after 35 years.

The results of a conditional convergence regression, containing typical country-characteristics used in the literature, show that lower initial incomes were associated with higher productivity growth in each decade since the 1980s.<sup>9</sup> The convergence rate is estimated to have increased over time, peaking at 1.5 percent per year over the past decade, which if sustained would halve the productivity gap in just under 50 years ( **Figure 3** ). Previous studies, including recent tests for club convergence, have documented similar rates of conditional convergence but have yet to document the acceleration in pace in recent decades (Johnson and Papageorgiou, Johnson and Papageorgiou). The panel specification, covering all decades, shows an annual convergence rate of 1.3 percent, within with the range of 1-3 percent found in surveys of the literature of growth regressions on income per capita (Annex C).<sup>10</sup> Estimates conditional on other characteristics, such as the level of education and investment,

> 9See Annex C for further details. Regression includes controls for average levels of education, trade openness, the economic complexity index of Hidalgo and Hausmann (2009), commodity exporter status, the level of investment as a share of output, and political stability.

> 10Most of these studies have performed these exercises on PPP-adjusted measures of income per capita. This alternative measure results in estimates of a convergence rate of 1.7 percent using the same specification. However, PPP-adjustment may be inappropriate for measuring output per worker. Many economies have substantially faster productivity growth measured using time-varying PPP adjustments compared to national accounts measures (Box A).

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