Abstract
Many empirical studies try to test whether there is income convergence across metropolitan areas in the continental United States. Drennan et al. (Journal of Economic Geography 4(5), 2004) claim that income among metropolitan economies is diverging for the period 1969–2001, after applying univariate unit root tests to the time series data. This paper brings new information to this area of study by using the nonlinear panel unit root test of the Exponential Smooth Auto-Regressive Augmented Dickey–Fuller (ESTAR-ADF) unit root test on the time series data for the period 1929–2005. Our results find evidence of stationarity for time series and thereby support beta and sigma convergence among states in a nonlinear setup. However, when the non-linear test encompasses cross section dependence as advocated by Cerrato et al. (2008), the evidence is attenuated.
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References
Acemoglu, D. (2002). Technical change, inequality, and the labor market. Journal of Economic Literature, 40, 7–72.
Barro, R. J., & Sala-i-Martin, X. (1991). Convergence across states and regions. Brookings Papers on Economic Activity, 1, 107–182.
Barro, R. J., & Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100(2), 223–251.
Barro, R. J., & Sala-i-Martin, X. (1995). Economic growth. Boston: McGraw Hill.
Baumol, W. (1986). Productivity growth, convergence, and welfare: what the long-run data show. American Economic Review, 76, 116–131.
Blanchard, O. J., & Katz, L. F. (1992). Regional evolutions. Brookings Papers on Economic Activity, 1, 1–75.
Borts, G. H. (1960). The equalization of returns and regional economic growth. American Economic Review, 50, 319–334.
Borts, G. H., & Stein, J. L. (1964). Economic growth in a free market. New York: Columbia University Press.
Breitung, J., & Das, S. (2004). Panel unit root tests under cross sectional dependence. Mimeo, University of Bonn.
Browne, L. E. (1989). Shifting regional fortunes: The wheel turns. New England Economic Review, Federal Reserve Bank of Boston, May/June, 27–40.
Carlino, G. A. (1992). Are regional per capita earning diverging? Business Review, Federal Reserve Bank of Philadelphia, March/April, 3–12.
Cerrato, M., de Peretti, C., & Sarantis, N. (2008). A nonlinear panel unit root test under cross section dependence. Discussion Paper 2008–08, Department of Economics, University of Glasgow.
Choi, I. (2001). Unit root tests for panel data. Journal of International Money and Finance, 20(2), 249–272.
Crihfield, C. J., & Panggabean, M. (1995). Growth and convergence in US cities. Journal of Urban Economics, 38, 138–165.
De Long, J. (1988). Productivity growth, convergence, and welfare: comment. American Economic Review, 78, 1138–1154.
Dickey, D. A., & Fuller, W. A. (1976). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.
Drennan, M. P., & Lobo, J. (1999). A simple test for convergence of metropolitan income in the United States. Journal of Urban Economics, 46, 350–359.
Drennan, M. P., Lobo, J., Strumsky, D. (2004). Unit root tests of sigma income convergence across metropolitan areas of the U.S. Journal of Economic Geography, 4(5).
Drennan, M. P., Tobier, E., & Lewis, J. (1996). The interruption of income convergence and income growth in large cities in the 1980s. Urban Studies, 33, 63–82.
Fan, C. S. (2004). Quality, trade, and growth. Journal of Economic Behavior and Organization, 55(2), 271–291.
Friedman, M. (1992). Do old fallacies ever die? Journal of Economic Literature, 29, 2129–2132.
Glaeser, E. L., Scheinkman, J. A., Shleifer, A. (1995). Economic growth in a cross-section of cities. Journal of Monetary Economics, 36, 117–143.
Im, K. S., Pesaran, H. M., Shin, Y. (1997). Testing for unit roots in heterogeneous panels. Working paper, Department of Applied Economics, University of Cambridge.
Jones, C. (1997). Convergence revisited. Journal of Economic Growth, 2, 131–153.
Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the Nonlinear STAR Framework. Journal of Econometrics, 112, 359–379.
Levin, A., & Lin, C. (1992). Unit root tests in panel data: Asymptotic and finite sample properties. Discussion Paper No. 92–93, Department of Economics, University of California, San Diego
Levin, A., Lin, C.-F., & Chu, C.-S. J. (2002). Unit root tests in panel data: asymptotic and finite-sample properties. Journal of Econometrics, 108, 1–25.
Maddala, G. S., & Wu, S. (1999). A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics, 61, 631–652.
Mallick, R. (1993). Convergence of state per capita incomes: an examination of its sources. Growth and Change, 325–334.
Mankiw, N. G., Romer, D., & Weil, D. N. (1992). A contribution to the empirics of economic growth. Quarterly Journal of Economics, 107, 407–437.
Michael, P., Nobay, A. R., & Peel, D. A. (1997). Transaction costs and nonlinear adjustment in real exchange rates: an empirical investigation. Journal of Political Economy, 105(4), 862–879.
Perloff, H. S. (1963). How a region grows. New York: Committee for Economic Development.
Pritchett, L. (1997). Divergence, big time. Journal of Economic Perspectives, 11(3), 3–17.
Quah, D. (1993). Galton’s fallacy and tests of the convergence hypothesis. Scandinavian Journal of Economics, 93, 427–443.
Sarno, L., Taylor, M. P., & Chowdhury, I. (2004). Nonlinear dynamics in deviations from the law of one price: a broad-based empirical study. Journal of International Money and Finance, 23(1), 1–25.
Solow, R. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65–94.
Taylor, M. P., Peel, D. A., & Sarno, L. (2001). Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles. International Economics Review, 42(4), 1015–1042.
Vohra, R. (1996). How fast do we grow? Growth and Change, 47–54.
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Lau, CK.M. Convergence Across the United States: Evidence from Panel ESTAR Unit Root Test. Int Adv Econ Res 16, 52–64 (2010). https://doi.org/10.1007/s11294-009-9241-8
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DOI: https://doi.org/10.1007/s11294-009-9241-8
Keywords
- United States income convergence
- Nonlinear panel unitroottest
- ESTAR
- Cross section dependence
JEL
- C10
- F01
- J10
- O10
- O40