Goldberger-on-Leff

Goldberger-on-Leff - Dependency Rates and Savings Rates...

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Dependency Rates and Savings Rates: Further Comment By ARTHUR S. GOLDBERGER* The empirical results on dependency rates and savings rates reported by Nathaniel Leff (1969) cannot be correct. For several cross-country samples, Leff estimates pairs of equations of the form (1) ^1 = 00-1- aiXi + CiXi -f (2) ^2 = 60 + bixi + biXi -f 63*3 -|- biXi -f- d where yi = ln S/Y = ln domestic savings ratio yi = In S/N = In per capita savings xi = ln Y/N = In per capita income a:2 = | = growth rate of per capita income X3 = ln Di = ln percentage of population aged 14 or less Xi = ln Di = ln percentage of population aged 65 or more, and a and b are least-squares regression co- efl&cients, and e\ and e^ are least-squares resid- uals. As noted by Leff, S/N^iS/Y)iY/N). Consequently, yi = yi-\-Xi. Least-squares re- gression being what it is, a proper com- putation of (2) should produce = flo + (1 + ai)xi, + 0.2*2 + (3) That is, regressing y^ on the x should give the same coefficients and the same residuals as occur when y^ is regressed on the *, except for the coefficient of Xi, which should in- crease by exactly 1.

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