OLS-Estimation of conditional and unconditional sigma- and beta-convergence of per capita income: Implications of Solow-Swan and Ramsey-Cass models - Rainer Maurer (Kiel Institute of World Economics (IfW); ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften, Leibniz-Informationszentrum Wirtschaft, 1995)
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.
Keywords: C12; C21; F43; O11; 330; Beta- and sigma convergence of per capita GDP; Solow-Swan growth model; Ramsey growth model; multicollinearity; BLUE property of OLS-estimators; empirical test; Entwicklungskonvergenz; Schätztheorie; Wachstumstheorie; Offene Volkswirtschaft; Schätzung; Theorie