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OLS-Estimation of conditional and unconditional sigma- and beta-convergence of per capita income: Implications of Solow-Swan and Ramsey-Cass models

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  • Maurer, Rainer
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    Abstract

    In this paper I discuss the general statistical relationships between beta- and sigmaconvergence (for a definition see section 2) and the implications of the Solow-Swan and Ramsey-Cass model for an OLS-estimation of beta- and sigma-convergence of the log of per capita GDP over a cross section of countries. Furthermore, I present tests of conditional and unconditional sigma- and beta-convergence. The discussion of the statistical relations exhibits that based on the Cauchy-Schwarz inequality it is possible to show that sigma-convergence implies necessarily beta-convergence but that beta-convergence is compatible with sigma-convergence as well as sigma-divergence. The discussion of the implications of the Solow-Swan model shows that - depending on identical stochastics - these models imply unconditional beta- and sigma-convergence, if the cross section sample includes only economies with identical steady state parameters. If the economies display different steady state parameters both models imply conditional beta- and sigma-convergence. A replication of the well-known test results for conditional beta-convergence based on the Summers/Heston (1991) and the Barro/Lee (1993) data sets, does not reject conditional betaconvergence. However, the results of the tests for conditional sigma-convergence are sensitive concerning slight modifications of the cross section sample of countries.

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    File URL: http://econstor.eu/bitstream/10419/47182/1/257505962.pdf
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    Bibliographic Info

    Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 698.

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    Date of creation: 1995
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    Handle: RePEc:kie:kieliw:698

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    Keywords: Beta- and sigma convergence of per capita GDP; Solow-Swan growth model; Ramsey growth model; multicollinearity; BLUE property of OLS-estimators; empirical test;

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    1. Robert J. Barro, 1989. "Economic Growth in a Cross Section of Countries," NBER Working Papers 3120, National Bureau of Economic Research, Inc.
    2. Summers, Robert & Heston, Alan, 1991. "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 327-68, May.
    3. 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.
    4. Robert J. Barro & Jong-Wha Lee, 1993. "International Comparisons of Educational Attainment," NBER Working Papers 4349, National Bureau of Economic Research, Inc.
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    Cited by:
    1. Daniela Bunea, 2012. "Is Internal Migration Relevant to Regional Convergence? Comparative Analysis Across Five European Countries," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 6(2), pages 53-72, DECEMBER.

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