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(Fractional) Beta Convergence

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  • Michelacci, C.
  • Zaffaroni, P.

Abstract

Unit roots in output, an exponential 2% rate of convergence and no change in the underlying dynamics of output seem to be three stylized facts that can not go together. This paper extends the Solow-Swan growth model allowing for cross-sectional heterogeneity. In this framework, aggregate shocks might vanish at an hyperbolic rather than at an exponential rate. This implies that the level of output can exhibit long memory and that standard tests fail to reject the null of a unit root despite mean reversion. Exploiting secular time series properties of GDP, we conclude that traditional approaches to test for uniform (conditional and unconditional) convergence suit first step approximation. We show both theoretically and empirically how the uniform 2% rate of convergence repeatedly found in the empirical literature is the outcome of an underlying parameter of fractional integration strictly between 0.5 and 1. This is consistent with both time series and cross-sectional evidence recently produced.

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Bibliographic Info

Paper provided by Centro de Estudios Monetarios Y Financieros- in its series Papers with number 9803.

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Length: 36 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:fth:cemfdt:9803

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Keywords: ECONOMETRICS ; STATISTICAL ANALYSIS ; TESTING;

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References

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  1. Danny Quah, 1992. "Empirical cross-section dynamics in economic growth," Discussion Paper / Institute for Empirical Macroeconomics 75, Federal Reserve Bank of Minneapolis.
  2. Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence Across States and Regions," Papers 629, Yale - Economic Growth Center.
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  17. den Haan, Wouter J., 1995. "Convergence in stochastic growth models The importance of understanding why income levels differ," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 65-82, February.
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  19. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
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