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(Fractional) Beta Convergence

  • Michelacci, C.
  • Zaffaroni, P.

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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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
Contact details of provider: Postal: Centro de Estudios Monetarios Y Financieros. Casado del Alisal, 5-28014 Madrid, Spain.
Phone: 914290551
Fax: 914291056
Web page: http://www.cemfi.es/
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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. Glenn D. Rudebusch, 1992. "The uncertain unit root in real GNP," Finance and Economics Discussion Series 193, Board of Governors of the Federal Reserve System (U.S.).
  3. Robert J. Barro, 1995. "Inflation and Economic Growth," NBER Working Papers 5326, National Bureau of Economic Research, Inc.
  4. 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.
  5. John Y. Campbell & N. Gregory Mankiw, 1986. "Are Output Fluctuations Transitory?," NBER Working Papers 1916, National Bureau of Economic Research, Inc.
  6. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May.
  7. Barro, R.J., 1989. "Economic Growth In A Cross Section Of Countries," RCER Working Papers 201, University of Rochester - Center for Economic Research (RCER).
  8. Andrew B. Bernard & Steven N. Durlauf, 1994. "Interpreting Tests of the Convergence Hypothesis," NBER Technical Working Papers 0159, National Bureau of Economic Research, Inc.
  9. Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence Across States and Regions," Papers 629, Yale - Economic Growth Center.
  10. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  11. Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
  12. Jones, Charles I, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 495-525, May.
  13. N. Gregory Mankiw & David Romer & David N. Weil, 1990. "A Contribution to the Empirics of Economic Growth," NBER Working Papers 3541, National Bureau of Economic Research, Inc.
  14. Nelson, Charles R & Kang, Heejoon, 1984. "Pitfalls in the Use of Time as an Explanatory Variable in Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(1), pages 73-82, January.
  15. Danny Quah, 1995. "Empirics for Economic Growth and Convergence," CEP Discussion Papers dp0253, Centre for Economic Performance, LSE.
  16. Francis X. Diebold & Glenn D. Rudebusch, 1988. "Long memory and persistence in aggregate output," Finance and Economics Discussion Series 7, Board of Governors of the Federal Reserve System (U.S.).
  17. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  18. Bernard, Andrew B & Durlauf, Steven N, 1995. "Convergence in International Output," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 97-108, April-Jun.
  19. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  20. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  21. 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.
  22. Quah, Danny, 1995. "Empirics for Economic Growth and Convergence," CEPR Discussion Papers 1140, C.E.P.R. Discussion Papers.
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