(Fractional) Beta Convergence
AbstractUnit roots in output, an exponential 2 per cent rate of convergence and no change in the underlying dynamics of output seem to be three stylized facts that cannot go together. This paper extends the Solow-Swan growth model allowing for cross-sectional heterogeneity. In this framework, aggregate shocks might vanish at a 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 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 per cent rate of convergence repeatedly found in the empirical literature is the outcome of an underlying parameter of fractional integration strictly between 1/2 and 1. This is consistent with both time series and cross-sectional evidence recently produced.
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Bibliographic InfoPaper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 383.
Date of creation: Oct 2000
Date of revision:
growth model; convergence; long memory; aggregation;
Other versions of this item:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
- E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
- O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bernard, Andrew B. & Durlauf, Steven N., 1996.
"Interpreting tests of the convergence hypothesis,"
Journal of Econometrics,
Elsevier, vol. 71(1-2), pages 161-173.
- Andrew B. Bernard & Steven N. Durlauf, 1994. "Interpreting Tests of the Convergence Hypothesis," NBER Technical Working Papers 0159, National Bureau of Economic Research, Inc.
- Bernard, A.B. & Durlauf, S.N., 1994. "Interpreting Tests of the Convergence Hypothesis," Working papers 9401r, Wisconsin Madison - Social Systems.
- Durlauf, Steven N & Phillips, Peter C B, 1988.
"Trends versus Random Walks in Time Series Analysis,"
Econometric Society, vol. 56(6), pages 1333-54, November.
- 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.
- Charles R. Nelson & Heejoon Kang, 1983.
"Pitfalls in the use of Time as an Explanatory Variable in Regression,"
NBER Technical Working Papers
0030, National Bureau of Economic Research, Inc.
- 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.
- John Y. Campbell & N. Gregory Mankiw, 1988.
"Are Output Fluctuations Transitory?,"
NBER Working Papers
1916, National Bureau of Economic Research, Inc.
- Diebold, Francis X. & Rudebusch, Glenn D., 1989.
"Long memory and persistence in aggregate output,"
Journal of Monetary Economics,
Elsevier, vol. 24(2), pages 189-209, September.
- Rudebusch, Glenn D, 1993.
"The Uncertain Unit Root in Real GNP,"
American Economic Review,
American Economic Association, vol. 83(1), pages 264-72, March.
- Nelson, Charles R & Kang, Heejoon, 1979.
"Spurious Periodicity in Inappropriately Detrended Time Series,"
The Warwick Economics Research Paper Series (TWERPS)
161, University of Warwick, Department of Economics.
- Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May.
- Robert J. Barro & Xavier Sala-i-Martin, 1991.
"Convergence across States and Regions,"
Brookings Papers on Economic Activity,
Economic Studies Program, The Brookings Institution, vol. 22(1), pages 107-182.
- Robert J. Barro, 2012.
"Inflation and Economic Growth,"
CEMA Working Papers
568, China Economics and Management Academy, Central University of Finance and Economics.
- Danny Quah, 1992.
"Empirical cross-section dynamics in economic growth,"
Discussion Paper / Institute for Empirical Macroeconomics
75, Federal Reserve Bank of Minneapolis.
- Quah, Danny, 1993. "Empirical cross-section dynamics in economic growth," European Economic Review, Elsevier, vol. 37(2-3), pages 426-434, April.
- Danny Quah, 1992. "Empirical Cross-Section Dynamics in Economic Growth," FMG Discussion Papers dp154, Financial Markets Group.
- Robert J. Barro, 1991.
"Economic Growth in a Cross Section of Countries,"
NBER Working Papers
3120, National Bureau of Economic Research, Inc.
- Danny Quah, 1995. "Empirics for Economic Growth and Convergence," CEP Discussion Papers dp0253, Centre for Economic Performance, LSE.
- Mankiw, N Gregory & Romer, David & Weil, David N, 1992.
"A Contribution to the Empirics of Economic Growth,"
The Quarterly Journal of Economics,
MIT Press, vol. 107(2), pages 407-37, May.
- Barro, Robert J & Sala-i-Martin, Xavier, 1992.
Journal of Political Economy,
University of Chicago Press, vol. 100(2), pages 223-51, April.
- Barro, Robert J. & Sala-i-Martin, Xavier, 1992. "Convergence," Scholarly Articles 3451299, Harvard University Department of Economics.
- Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence," Papers 645, Yale - Economic Growth Center.
- Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence Across States and Regions," Papers 629, Yale - Economic Growth Center.
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- 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.
- Quah, Danny, 1995. "Empirics for Economic Growth and Convergence," CEPR Discussion Papers 1140, C.E.P.R. Discussion Papers.
- 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.
- 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.
- 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.
- 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.
- 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.
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