tail (revealing the presence of few very unequal countries in the sample). Regarding changes in the (log) Gini, the average annual change between two five-year periods would be .1 percent, indicating that on average inequality changes little over time. However, there is considerable dispersion: the 2 standard deviation interval would range from about –6.8 percent to 6.8 percent. The changes in the Gini coefficient also present a skewed distribution but in this case it is toward the lower tail. As for the income data, average annual growth rates between two five-year periods would be about 2 percent, but dispersion is also high (very similar to that found in the changes in the Gini coefficient). The variables that aim to represent the various aspects of economic development tend to be skewed toward the lower tail, something that would reveal the presence of a few very underdeveloped countries in the sample. The inflation rate also presents a skewed distribution but in this case is likely to reflect a few instances of extreme macroeconomic mismanagement.

# **V. Empirical results**

We start this section by presenting results for equations (10) and (11) under the restriction that β=ω=0. Thus equation (11) is basically reduced to a test of convergence for inequality considering the potential impact of income levels, whereas in equation (10) we explore, in addition to the speed of convergence for per capita income levels, the potential impact of inequality on growth. We estimate the equations with four different methods: OLS, fixed effects, 2SLS<sup>14</sup> , and the Arellano and Bond (1991) GMM estimator. In turn, we present the results of the Arellano and Bond estimator treating the nonlagged-dependent-variable regressor both as an exogenous variable and as a predetermined variable.

Inspection of table 3 suggests convergence in inequality levels, with the estimators that take into account the possibility of fixed effects resulting in a faster speed of convergence. For example, while the pooled estimator suggests a half-life of about 20 years, the other estimators suggest a half-life of between 1 and 5 years. These results are consistent with the findings of Benabou (1996) and Ravallion (2002)<sup>15</sup> who also find inequality convergence. Further, their estimated coefficients for the speed of convergence are of a similar order of magnitude to our pooled estimator. Two possible interpretations behind the inequality convergence given by Ravallion are related to (i) the implications of the neoclassical growth model (which in addition to predicting income convergence across countries would also predict inequality convergence), or more pragmatically to (ii) the widespread convergence of economic policy during the 1990s. This second argument is likely to weigh less, however, when we take into account the fact that we also find inequality convergence when we control for policy changes, and therefore for policy convergence. As for the impact of initial income on the changes in inequality, table 3 does not find any significant effect, although admittedly, given how parsimonious the models are, this could be due to omitted variables bias.

> 14  In equation 10 the instruments are 3 lagged growth observations and inequality with 3 lagged values of inequality. In equation (11) lagged inequality is instrumented with lagged changes  in inequality and initial per capita income in equation (10) is instrumented with 3 lagged growth observations.  These instruments would be valid even in the presence of fixed effects.

> 15 Ravallion uses a different estimation technique. Rather than relying on the relation between initial Gini and the subsequent change in the index, Ravallion (2002) measures the speed of convergence by comparing estimated trends in inequality with predicted initial levels of inequality.

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