The Annals of Regional Science

, Volume 46, Issue 2, pp 369–377 | Cite as

Stochastic convergence tests for US regional per capita personal income; some further evidence: a research note

  • Ismail H. GencEmail author
  • Jon R. Miller
  • Anil Rupasingha
Original Paper


This paper contributes to the time-series literature on US regional income convergence. We apply unit root tests to metropolitan and nonmetropolitan per capita personal income series from 1969 to 2001. We show that some of the mixed results on regional income convergence in the time-series literature may be the result of using different unit root tests. We demonstrate these mixed results with our data. Then, using a test we consider the most appropriate, we generate results which reject the hypothesis that US regional incomes are nonstationary. Thus, we provide additional support for the regional convergence of US per capita regional income.

JEL Classification

C13 C21 R11 R12 


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  1. Alvi E, Rahman H (2005) US regional income and technology: a unit-root and cointegration study. Topics in Macroeconomics, 5(1), Article 11. Available at
  2. Azzoni CR (2001) Economic growth and regional income inequality in Brazil. Ann Reg Sci 35: 133–152CrossRefGoogle Scholar
  3. Barro RJ, Sali-i-Martin X (1991) Convergence across states and regions. Brook Papers Econ Activ 1991(1): 107–182CrossRefGoogle Scholar
  4. Barro RJ, Sali-i-Martin X (1992) Convergence. J Polit Econ 100: 223–251CrossRefGoogle Scholar
  5. Baumol WJ (1986) Productivity growth, convergence, and welfare: what the new evidence shows. Am Econ Rev 76: 1072–1085Google Scholar
  6. Baumol WJ, Wolfe EN (1988) Productivity growth, convergence, and welfare: reply. Am Econ Rev 78: 1155–1159Google Scholar
  7. Bernard AB, Durlauf SN (1995) Convergence in international output. J Appl Econ 10: 97–108CrossRefGoogle Scholar
  8. Bernard AB, Durlauf SN (1996) Interpreting tests of the convergence hypothesis. J Econ 71: 97–108Google Scholar
  9. Campbell JY, Mankiw NG (1989) International evidence on the persistence of economic fluctuations. J Monet Econ 23: 319–333CrossRefGoogle Scholar
  10. Carlino G, Mills L (1993) Are US regional incomes converging? A time series analysis. J Monet Econ 32: 335–346CrossRefGoogle Scholar
  11. Carlino G, Mills L (1996a) Convergence and the US states: a time series analysis. J Reg Sci 36: 597–616CrossRefGoogle Scholar
  12. Carlino GA, Mills L (1996b) Testing neoclassical convergence in regional incomes and earnings. Reg Sci Urban Econ 26: 565–590CrossRefGoogle Scholar
  13. Carvalho VM, Harvey AC (2005) Convergence in the trends and cycles of euro-zone income. J Appl Economet 20: 275–289CrossRefGoogle Scholar
  14. Cuardo-Roura JR (2001) Regional convergence in the European union: from hypothesis to the actual trends. Ann Reg Sci 35: 333–356CrossRefGoogle Scholar
  15. De Long JB (1988) Productivity growth, convergence, welfare: comment. Am Econ Rev 78: 1138–1154Google Scholar
  16. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431CrossRefGoogle Scholar
  17. Drennan M, Lobo J, Strumsky D (2004) Unit root tests for sigma income convergence across US metropolitan areas. J Econ Geogr 4: 583–595CrossRefGoogle Scholar
  18. Easterlin R (1960) Regional growth of income. In: Kuznets S, Miller A, Easterlin R(eds) Population redistribution and economic growth in the united states 1870–1950. American Philosophical Society, PhiladelphiaGoogle Scholar
  19. Enders W (2004) Applied econometric time series. Wiley, New YorkGoogle Scholar
  20. Hammond GW (2006) A time series analysis of US metropolitan and non-metropolitan income divergence. Ann Reg Sci 40: 81–94CrossRefGoogle Scholar
  21. Hobijn B, Franses PH, Ooms M (1998) Generalizations of the KPSS-test for stationarity, Econometric Institute Report, no. 9802/A, (January). Available at
  22. Ibrahim A (2004) A complementary test for the KPSS test with an application to the US Dollar/Euro Exchange Rate. Econ Bullet 3: 1–5Google Scholar
  23. Kuznets S (1955) Economic growth and income inequality. Am Econ Rev 45: 1–28Google Scholar
  24. Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationary against the alternative of a unit root. J Econ 54: 159–178Google Scholar
  25. Lall SV, Yilmaz S (2001) Regional economic convergence: do policy instruments make a difference?. Ann Reg Sci 35(1): 153–166CrossRefGoogle Scholar
  26. Loewy MB, Papell DH (1996) Are US regional incomes converging? Some further evidence. J Monet Econ 38: 587–598CrossRefGoogle Scholar
  27. MacKinnon JG (1991) Critical values for cointegration tests, Chapter 13. In: Engle RF, Granger CWJ(eds) Long-run economic relationships: readings in cointegration. Oxford University Press, OxfordGoogle Scholar
  28. MacKinnon JG (1996) Numerical distribution functions for unit root and cointegration tests. J Appl Economet 11: 601–618CrossRefGoogle Scholar
  29. Miller JR, Genc IH (2005) Alternative regional specification and convergence of US regional growth rates. Ann Reg Sci 39: 241–252CrossRefGoogle Scholar
  30. Nelson C, Plosser C (1982) Trends and random walks in macroeconomic time series: some evidence and implications. J Monet Econ 10: 139–162CrossRefGoogle Scholar
  31. Newey W, West K (1994) Automatic lag selection in covariance matrix estimation. Rev Econ Stud 61: 631–653CrossRefGoogle Scholar
  32. Ng S, Perron P (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69: 1519–1554CrossRefGoogle Scholar
  33. Said SE, Dickey DA (1984) Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71: 599–607CrossRefGoogle Scholar
  34. Sala-i-Martin X (1996) Regional cohesion: evidence and theories of regional growth and convergence. Euro Econ Rev 40: 1325–1352CrossRefGoogle Scholar
  35. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2): 461–464CrossRefGoogle Scholar
  36. Tomljanovich M, Vogelsang T (2002) Are US regions converging? Using new econometric methods to examine old issues. Empir Econ 27: 49–62CrossRefGoogle Scholar
  37. Vohra R (1998) Convergence (divergence) and the US states. Atlant Econ J 26: 372–378CrossRefGoogle Scholar
  38. Williamson J (1965) Regional inequality and the process of national development. Econ Develop Cult Change 4: 3–47Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Ismail H. Genc
    • 1
    Email author
  • Jon R. Miller
    • 2
  • Anil Rupasingha
    • 3
  1. 1.Department of EconomicsAmerican University of SharjahSharjahUAE
  2. 2.Department of Business and EconomicsUniversity of IdahoMoscowUSA
  3. 3.Department of Agricultural Economics and AgribusinessNew Mexico State UniversityLas CrucesUSA

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