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A time series analysis of U.S. metropolitan and non-metropolitan income divergence

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Abstract

This paper employs time series methods to analyze convergence across metropolitan and non-metropolitan regions during the 1969–2001 period. The results suggest that non-metropolitan regions are diverging from below the U.S. average income level, while metropolitan regions show mixed evidence of convergence. These summary results vary by geographic location and the size of the region, with medium-sized metropolitan regions showing the strongest tendencies to converge, while non-metropolitan areas with larger urban centers and small towns showed the strongest tendencies to diverge. Differences in human capital (as well as employment concentrations in farming and mining) appear to have influenced the relative performance of metropolitan and non-metropolitan regions during the last 30 years, suggesting a role for agglomeration economies in the observed trend toward divergence.

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Article 15 July 2014

Nicola Gennaioli, Rafael La Porta, … Andrei Shleifer

Notes

  1. Kane (2001) extends the time series approach using recursive parameter estimation techniques. The results suggest stronger trends toward convergence for BEA multi-state regions than those found by Carlino and Mills (1993).

  2. The estimation does not separately identify RPCPIe and υ 0. Thus, it is possible for υ0 to be large and opposite in sign from RPCPIe, as CM note, and thus for estimates of α and β to be of the same sign even though the series exhibits conditional β-convergence.

  3. This research abstracts from the issue of the relative contribution of each income source to convergence. Hammond and Thompson (2002) show that these contributions may differ. Further, the BEA income data abstracts from considerations of cost of living. It is common in the literature for the U.S. to use data unadjusted for regional costs of living, because these costs are notoriously difficult to measure. However, as Deller et al. (1996), among others, argue, cost-of-living differences may influence the results.

  4. There are 52 commuting zones that are defined as metropolitan in 1990 but were not so defined in 1969. Classifying these new metropolitan zones as non-metropolitan does not alter the qualitative results or their interpretation. Details are available from the author.

  5. The asymptotic standard error, from Campbell and Mankiw (1989), is computed as \(\frac{{{\text{VR}}(5) = 1}}{{{\sqrt {\frac{3}{4}{\left[ {\frac{T}{{N + 1}}} \right]}} }}},\) with 33 observations available, the standard error is 0.49.

  6. Results from Carlino and Mills (1993) for the 1929–1990 period using BEA state regions, and after accounting for a break in 1946, range from 0.22–0.00 for the 5-year impulse response and from 1.09–0.31 for the variance ratio. Results from Carlino and Mills (1996) using U.S. states, and after accounting for a break in 1946, range from 0.7–0.0 for the 5-year impulse response and from 1.72–0.29 for the variance ratio.

  7. I also follow Perron (1989) in this choice of an exogenously determined break point. Perron (1997), Ben-David et al. (2003) point out that allowing for endogenously determined break points (or for multiple break points) may increase the number of rejections of the null of a unit root.

  8. I summarize the results here. Full details are available from the author.

  9. Census regions are multi-state aggregates. Commuting zones are assigned to Census regions based on the location of the largest place within the zone.

  10. Small Metropolitan Center: population of the largest MSA in the commuting zone was less than 250,000 in 1990. Medium Metropolitan Center: population of the largest MSA in the commuting zone was at least than 250,000 but less than 1,000,000 in 1990. Major Metropolitan Center: population of the largest MSA in the commuting zone was 1,000,000 or greater in 1990 or the commuting zone is part of a CMSA. Small Town/Rural: population of the largest place in the commuting zone was less than 5,000 in 1990. Small Urban Center: population of the largest place in the commuting zone was at least 5,000 but less than 20,000 in 1990. Larger Urban Center: population of the largest place in the commuting zone was at least 20,000 in 1990.

  11. In contrast, Lall and Yilmaz (2001) present conditional β-convergence results suggesting that, after controlling for spatial spillovers, educational attainment no longer has a significant impact on U.S. state growth. They do find evidence that the educational attainment of first-order-contiguous states has a positive impact on state growth, probably through cross-state commuting relationships.

  12. This will not eliminate possible endogeneity problems, however. As an anonymous reviewer pointed out, industrial structure and levels of educational attainment may have been previously influenced by income levels. Crihfield and Panggabean (1995) find that educational attainment positively influences metropolitan income growth even after significant econometric attempts to control for endogeneity.

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  1. Bureau of Business and Economic Research, West Virginia University, P.O. Box 6025, Morgantown, WV, 26506-6025, USA

    George W. Hammond

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Correspondence to George W. Hammond.

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Hammond, G.W. A time series analysis of U.S. metropolitan and non-metropolitan income divergence. Ann Reg Sci 40, 81–94 (2006). https://doi.org/10.1007/s00168-005-0029-3

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