A Dynamic, Personal Savings Function and Its Long-Run Implications - Swamy, Subramanian (The Review of Economics and Statistics, 1968)
T HE results presented in this paper are (1) A time series of personal savings is well explained by the dynamic savings function st = ast 1 + 8z A Yt + ut. This model was previously formulated (but tested only for the United States and Canada) by Professors Houthakker and Taylor [1]. (2) The steadystate or long-run savings function implicit in the above dynamic formulation, s/y = a2 + 12 (Ay/y) fits remarkably well to international cross-section data. (3) The coefficients of the long-run savings function, as obtained by application of least squares on the function, is statistically equal to the coefficient obtained indirectly from the dynamic savings function. This implies that both dynamic and steady-state savings behavior are adequately described by st = ast+ /3Ayt + ut. (4) A few pitfalls in estimation of economic relationships when employing cross-section time series data are revealed. It will be shown that the long-run savings function implied in the Houthakker-Taylor function supplemented by some additional conditions, is precisely the long-run savings function of Modigliani [2]. Therefore, the present attempt must be regarded as a synthesis of the two theories. We shall have the benefit of more observations per country than the above mentioned authors in deriving our empirical results. II The Dynamic Savings Function Let St, yt, and at denote (personal) savings, (personal disposable) income, and non-depreciating assets at time t, in per capita terms. The Houthakker-Taylor model in terms of these variables is: St = a +at+yyt (1) dat/dt = st (2) Thus, savings is a linear function of assets and income, and the rate of change of assets at any moment of time is the savings at that moment. The long-run implication of this model has not been explored and this we shall do below. To derive the long-run effects of equations (1) and (2), we need to know something about the growth of income. Let us assume 1 that: (3) y= p, where p is a positive constant. This equation thus implies that the rate of growth (of