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We analyze the dynamic properties of the relative income of Brazilian states for the 1985-2008 period. Unit root tests suggest that shocks to relative income have permanent effects, contradicting the stochastic convergence hypothesis. On the other hand, interval estimates of the largest autoregressive root produce wide confidence intervals that include many alternatives consistent with stationarity. Additionally, the confidence interval estimate of the half-life suggests that relative income shocks die out relatively quick, within an average of 0 to 5 years. These results suggest that relative income shocks have a temporary effect, thus supporting the stochastic convergence hypothesis. Furthermore, we build a relative income series for the Brazilian states for the 1947-2008 period and redo the exercises above. Finally, all of our results remain the same when we extend the sample to the 1947-2008 period.

Unit root tests suggest that shocks to relative income across U.S. states are permanent, which contradicts the stochastic convergence hypothesis. We suggest that this finding is due to the well-known low-power problem of unit root tests in the presence of high persistence (i.e., low speed of convergence) and small samples. First, interval estimates of the largest autoregressive root for the relative income in the 48 U.S. contiguous states are quite wide, including many alternatives that are persistent but stable. Second, interval estimates of the half-life of relative income shocks that are robust to high persistence and small samples suggest that in most cases shocks die out within zero to ten years. Third, estimation of a fractionally integrated model for the relative income process suggests strong evidence of mean reversion in the data. These findings provide ample support for the stochastic convergence hypothesis.

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We assess the effects of the imperfect substitution between skilled and unskilled labor on economic growth in a model in which physical capital and skilled labor can be accumulated. It is shown that economies with higher substitutability between skilled and unskilled labor have higher levels of income per capita in the transition and in the long-run equilibrium. Furthermore, these economies have a higher level of skilled labor and a higher level of capital intensity in the long-run equilibrium. For certain parameters values, the speed of convergence depends positively on the elasticity of substitution between skilled and unskilled labor.