Knowledge that Transforms

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. Furthermore, if regression coefficients are guaranteed to be equal, their standard errors, and hence their ^-ratios, must be equal. If regression coefficients are guar-* Professor of economics, University of Wisconsin, Madison. anteed to differ by unity, their standard errors must be equal, and hence their t-ratios must be related by bx/si, = (ajAa.)((l-f ai)/ai) But the results Leff reports do not satisfy these arithmetic requirements. For example, consider the upper panel of his Table 1, p. 891, which refers to a sample of 47 under-developed countries. In the present notation we find:

This paper develops a approach to the theory of currency devaluation.1 The approach is monetary in several respects. The role of the real balance effect is emphasized and a distinction is drawn between the relative prices of goods, the exchange rate and the price of money in terms of goods. Furthermore, money is treated as a capital asset so that the expenditure effects induced by a change are spread out over time and depend on the preferred rate of adjustment of real balances.2 The latter aspect gives rise to the analytical distinction between impact and long-run effects of a devaluation. The first part of this paper develops a one-commodity and two-country model of devaluation. The simplicity of that structure is chosen quite deliberately to emphasize the aspect of the problem as opposed to the derivative effects that arise from induced changes in relative commodity prices. Trade is viewed as the exchange of goods for money or a means of redistributing the world supply of assets. A devaluation is shown to give rise to a change in the level of trade and the terms of trade, the price of money in terms of goods. In the second part the implications of the existence of nontraded goods are investigated, and induced changes in the relative prices of home goods enter the analysis.