An alternative perspective on the stochastic convergence of incomes in the United States

Abstract

In recent years a number of studies has examined the potential stochastic convergence of incomes in the United States. This research has been based upon examination of the order of integration of the ratios of regional levels of per-capita income relative to US aggregate per-capita income, with stationary of the ratios taken as evidence of stochastic convergence. In the present article this research and its implicit assumption that the individual regional and aggregate per-capita series are I(1), are revisited. In a departure from previous research, application of a more robust testing procedure incorporating two structural breaks to the individual aggregate and regional per-capita series, rather than their ratios, is seen to result in overwhelming rejection of the unit root hypothesis for all of the series examined. The unit root hypothesis is rejected also for more disaggregated State level data. The evidence of stationarity presented for the component per-capita income series suggests that care should be exercised when both interpreting results presented previously in the literature and conducting further research.

Notes

¹Sala-i-Martin (1996) presents a formal examination to show that while β-convergence is a necessary but not sufficient condition for σ-convergence, σ-convergence is both a necessary and sufficient condition for β-convergence. A related formal analysis is provided by Furceri (2005). However, a more intuitive explanation can be presented for these results. If the spread of the distribution of per-capita incomes has decreased (σ-convergence), poorer economies must have experienced faster growth than richer economies (β-convergence). However, if poorer economies grow more rapidly than richer economies (β-convergence), it is possible that leapfrogging may occur to such an extent that the spread of the income distribution increases. This obviously corresponds to an absence of σ-convergence.

²Similar, closely related, notions of convergence are those of deterministic convergence and Bernard–Durlauf (1995) convergence. As noted by Li and Papell (1999) these are more restrictive notions than stochastic convergence. Both can be thought of in terms of the specification of the unit root test applied to the income ratio. While deterministic convergence requires the trend term to be absent from the unit root testing equation, Bernard–Durlauf convergence relates to a stationary series with a zero mean.

³Carlino and Mills (1996a) provide a similar analysis for US earnings.

⁴It should be noted that the minimum LM tests employed also have more attractive size and power properties than the two-break unit root test of Lumsdaine and Papell (1997). More precisely, while the latter tests are not robust to changes under the null, the results of Lee and Strazicich (2003) show the minimum LM tests to also possess greater power than the test of Lumsdaine and Papell (1997).

⁵All data are drawn from the Bureau of Economic Analysis (BEA). This is the source of the regional data examined by CM and LP.

⁶For example, this span of data contrasts starkly with the 17-year period covered in the empirical analysis of Evans and Karras (1996).