OLS-Estimation of conditional and unconditional sigma- and beta-convergence of per capita income: Implications of Solow-Swan and Ramsey-Cass models
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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OLS-人均收入的条件和无条件 sigma 和 beta 收敛的估计：Solow-Swan 和 Ramsey-Cass 模型的含义
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发表时间：
1995
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通讯作者：
Rainer Maurer
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作者：
Rainer Maurer
在本文中，我讨论了贝塔收敛和西格玛收敛之间的一般统计关系（定义见第2节），以及索洛-斯旺和拉姆齐-卡斯模型对各国横截面上人均GDP对数的贝塔收敛和西格玛收敛的ols估计的含义。此外，我提出了条件和无条件σ和β收敛的检验。统计关系的讨论表明，基于Cauchy-Schwarz不等式，可以证明sigma-收敛必然意味着β -收敛，但β -收敛与sigma-收敛以及sigma-发散是相容的。对索洛-斯旺模型含义的讨论表明，如果横截面样本只包括具有相同稳态参数的经济体，依赖于相同的随机因素，这些模型意味着无条件的贝塔和西格玛收敛。如果经济表现出不同的稳态参数，两个模型都意味着有条件的贝塔和西格玛收敛。基于Summers/Heston（1991）和Barro/Lee（1993）数据集的众所周知的条件贝塔收敛测试结果的复制并没有拒绝条件贝塔收敛。然而，条件西格玛收敛检验的结果对于国家截面样本的轻微修改是敏感的。
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.