STOCHASTIC CONVERGENCE ACROSS US STATES

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.