Rate of Growth Effects on Aggregate Savings: Further Analysis

The basic question investigated in this paper is whether or not individual saving for retirement and (possibly) bequests can generate aggregate rates of accumulation of capital close to those which are observed. A quite understandable reaction to this question is that it was disposed of many years ago by Modigliani and Brumberg [1], [2], when they showed with a very simple model of the consumers' lifetime income process that rates of savings akin to those of the US could be generated using US demographic data. It is important to note, however, that the model which Modigliani and Brumberg use does not assume that the individual has perfect foreknowledge of his future income stream. This forces the individual annually to replan consumption, using each year whatever new information is available on the likely future income path. This " periodic replanning" assumption has a number of consequences.' From our point of view the most important of these is that it makes aggregate consumption sensitive to the procedure used to forecast future income. Modigliani and Brumberg assume that the individual forecasts future income in the following myopic fashion. At each point of time, wage income till retirement will be the current wages earned at that time. After retirement, of course, wage income will be zero. When productivity growth is taking place, this amounts to the assumption that the individual never learns that income is growing. As M. J. Farrell [3] has pointed out, this is a sufficiently unusual assumption to warrant testing the sensitivity of the model's results to it. Farrell [3], for example, keeps all the other Modigliani-Brumberg assumptions but assumes that the individual correctly foresees the growth of future income, and in this case shows that the model not only yields markedly different predictions of the savings/income ratio but, for a growth rate of 4 per cent, actually yields the prediction that the savings/income ratio will be negative. This possibility had been noted earlier by Modigliani [4]. However, in defence of the myopia assumption, Modigliani argued that even if individuals did correctly foresee a rising income, institutional capital market constraints would prevent them from borrowing against this rising income. Thus the consumption plan chosen would not differ very much from the myopia path. Institutional constraints on capital markets are one thing, however, and assumptions about expectations formation are another. To quote Farrell [3, p. 879]: " Ideally some sort of asset constraint should be included in the model, and might give Modigliani the approximation he seeks; but it is of little help to us in choosing between two expectational hypotheses." In this paper we examine the Lifetime Income model under a number of different assumptions both with regard to expectations and with regard to capital market imperfections. In particular we compare aggregate consumption and savings under three different planning regimes, utility maximisation with perfect foresight and perfect capital markets (Model 1), utility maximisation with perfect foresight but borrowing constraints (Model 2) and the original Modigliani-Brumberg case of equal planned consumption in each period but with imperfect foresight of future income (Model 3).