Direct questions and comments to: Glossary master
The life-cycle hypothesis presents a well-defined linkage between the consumption plans of an individual and her income and income expectations as she passes from childhood, through the work participating years, into retirement and eventual decease. Early attempts to establish such a linkage were made by Irving Fisher (1930) and again by Harrod (1948) with his notion of hump saving, but a sharply defined hypothesis which carried the argument forward both theoretically and empirically with its range of well-specified tests for cross-section and time series evidence was first advanced by Modigliani & Brumberg (1954). Both their paper and advanced copies of the permanent income theory of Milton Friedman (1957) were circulating in 1953 and led M.R. Fisher (1956) to carry out tests of the theories even preceding publication of Friedman´s work. Both the Modigliani-Brumberg and the Friedman Theories are referred to as life-cycle theories and they certainly have many similar implications, but the one that is more closely related to the life cycle with emphasis on age – Modigliani and Brumberg – is the one to which the following review concentrates.
The key which rendered the multi-period analysis tractable under subjective certainty was the specification that the life-time utility function be homothetic – this permitted planned consumption for each future period to be written as a function of expected wealth as seen at the planning date, the functional parameters being in no way dependent upon wealth, but upon age and tastes. The authors further sharpened their hypothesis. They specified that an individual would plan to consume the same amount in real discounted terms each year. Throughout, desired bequest and initial assets were set to zero. However, the authors did show that bequests could be accounted for within the homothetic utility function itself if that became necessary.
From the outset, such sharp hypothesis was desired for empirical testing. For Modigliani at least, a propelling influence had been the debate about the explanatory power of the Keynesian consumption function for forecasting postwar consumption and income. The inadequacies revealed had led already to several refined theories, notably by Duesenberry (1949) and by Modigliani (1949) himself. In the 1940s, cross-section studies had been carefully carried through at the National Bureau of Economic Research (NBER), and empirical results from these studies were promoting theoretical insights. Any new theory had to be consistent with these findings. The tighter specification of the hypothesis enabled the spelling out of the pattern of accumulating savings in the working years to finance the retirement years – hump savings. Assuming that real income of each member of the populationwide sample remained the same throughout working life, it was shown that the independent of the age and income distribution and dependent only on the proportion of retirement years to expected lifetime. This alerted economists to the fact that cross-section results do not directly translate into estimates of the marginal propensity to save of an individual planning function. This insight is of broader significance not confined to the simple hypothesis. The implications of the hypothesis for time series analysis were disseminated much more slowly as the companion paper to that on cross section interpretation was never published, accounts not being freely available until 1963 and the original text itself not until 1980.
Real consumption, including the depreciation of durable goods, is a proportion of expected real wealth, and wealth is the addition of initial assets at the planning date, current income and expected (discounted) future income. By then assuming that the proportionality factor referred to is identical across individuals, they devised an aggregate relation for each and every age group. Next they proceed to aggregate across age groups. Here the proportionality factor, depending as it does on age, is not independent of assets, and bias may be introduced, if the strictest set of assumptions used in the cross-section analysis is employed, the authors show that when aggregated real income follows an exponential growth trend the parameters of the aggregate relation remain constant over time. They are, however, sensitive to the magnitude of the growth rate of real income (a sum of growth rates in productivity and population), the saving-income ratio being larger the greater the rate of income growth.
If income and/or assets at any time move out of line with previous planning expectations, plans can be revised. Suppose income rises, yet income expectations are not revised, the change being viewed as an on-off event. Then the individual marginal propensity to save at that date would rise to finance subsequent consumption at a higher level until death. If income expectations were revised upwards permanently, then the marginal propensity to save would also rise but to a lesser degree than in the on-off case as higher consumption can more easily be provided for out of later-period incomes. Allowance for income variability is straightforward in cross section; with time series expected income, here labor income, may be set equal to a weighted average of aggregated past and expected future income, or subdivided according to whether the reference is to employed or unemployed consumers at any time (Modigliani & Ando (1963)).
Recent developments in theory and practice: Emphasizing that the young and old coexist at any time, overlapping generation models (of which Modigliani and Brumberg are now seen to be a special case) have been fruitful in depicting the equilibrium pattern of growth in an economy over time, in bringing into sharp relief the role of interest rates, and in weighing the welfare contribution of security and private market saving schemes. They have also sharpened up the treatment of bequests, both anticipated and accidental (Abel (1985)). They have lent themselves to simulation studies but have not proved rewarding for tests against empirical data. Also, models of dynamic labor supply have been developed in a life-cycle hypothesis framework; see Fisher (1971), Getz & Becker (1975) and MaCurdy (1981).
Recent applications and extensions have related to the rapid development of social security and its effects on private savings, and variation of dates of retirement (Feldstein (1974) and Kotlikoff (1984)) on the one hand and effects of switch from income or capital taxes to consumption taxes on the other (Seidman (1984)). The social security studies have necessitated the use of more carefully defined wealth and income figures. For Germany, these problems are discussed in Börsch-Supan et al. (1999).
The empirical research on the life-cycle hypothesis has raised questions as to the adequacy of the life-cycle model without much more attention to bequest issues or allowance for uncertainty as to date of death (e.g., Rodepeter & Winter, 1998). In part it is argued that the life cycle may apply to a large section of the population but the big savers and even the lowest earners may obey different criteria (Kotlikoff & Summers (1981)). Repeatedly in well-defined samples, through not in all, the decline in wealth with age was not significant; in more finely grouped data by cohorts it even rises with age.
Return to: life-cycle hypothesis
Literature: Abel (1985), Ando & Modigliani (1957), Auerbach, Kotlikoff, Hagemann & Nicoletti (1989), Attanasio (1994), Auerbach & Kotlikoff (1987), Blanchard & Mankiw (1988), Börsch-Supan, Reil-Held, Rodepeter, Schnabel & Winter (1999), Brumberg (1956), Davis (1981), Duesenberry (1949), Feldstein (1974), Fisher (1930), Fisher (1956), Fisher (1957), Fisher (1971), Fisher (1987), Friedman (1957), Ghez & Becker (1975), Hurd (1989), Kimball (1990), Kotlikoff (1984), Kotlikoff & Summers (1981), MaCurdy (1981), Modigliani (1949), Modigliani (1975), Modigliani (1963), Modigliani & Brumberg (1980), Rodepeter & Winter (1998), Skinner (1985), Summers (1981), Yaari (1965)
Entry by: Ralf Rodepeter and Joachim Winter
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June 17, 1999 Direct questions and comments to: Glossary master |
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