Keynes (1936) introduced the consumption function as the relationship between consumption and income. Although Keynes (pp. 95–6) believed this relationship ‘a fairly stable function’, substantial shifts in the function were soon observed by empirical workers. Much work in the post-World War II era achieved functional forms by the 1970s which admirers and critics alike could agree were relatively shiftless. Most recent work has considered not functional form but whether or not observed changes in consumption are consistent with models of efficient markets.

The Keynesian Conception

Keynes conceived of the consumption function as relating consumption to disposable income as these are now conventionally measured in the national income accounts. These concepts were basic to the model of The General Theory and Keynes was doubtless pedagogically correct to posit a simple relationship which could be refined by future research.

The need for refinement became apparent shortly. In longer time series, consumption seemed to vary around a constant fraction of disposable income. In contrast, consumption functions fitted to depression-era or cross-section data seemed to indicate that this ratio (which Keynes called the average propensity to consume or APC) declined as disposable income rose. In other words, these studies estimated that the derivative of consumption with respect to disposable income (the marginal propensity to consume or MPC) was less than the APC.

Alvin Hansen (1939) among others predicted that a secular stagnation would result unless government spending filled this growing gap between output and consumption. When the gap failed to appear, the time was ripe for more sophisticated theories of the relationship between consumption and income. These theories were the earliest and perhaps still most successful resorts to microeconomic foundations for macroeconomics.

Permanent Life-Cycles

In the early 1950s our two dominant models of consumption developed: the permanent-income and life-cycle hypotheses. While these models were once viewed as competing, they can now be seen as complementary with differences in emphasis which serve to illuminate different significant problems. Both models emphasized the distinction between consumer expenditures measured by the national income accounts and pure consumption which was to be explained by optimal allocation of present and future resources over time. The permanent income hypothesis (PIH) stressed stochastic variations in income (and consumption) over time and viewed saving in terms of a bequest motive. The life-cycle hypothesis (LCH) stressed predictable variations in income (and consumption) over the life cycle and viewed saving as resulting from the greater wealth and numbers of younger savers in comparison to older dissavers.

The original published references are to Friedman (1957) for the PIH and Modigliani and Brumberg (1954) for the LCH. Given the delays in NBER publication of Friedman’s work which was widely circulated in manuscript form, the two hypotheses are generally regarded as distinct, contemporaneous responses to the described conflict between earlier studies and Simon Kuznets’ data on the national income accounts for the 20th century. From the perspective of the monumental careers of the two principal proponents, priority does not seem an issue that need be resolved here.

The PIH relates (pure) consumption to the perpetuity stream that could be consumed forever. The agent is typically regarded as an infinitely lived individual. This represents the underlying notion of a family whose generations are linked by operative transfers from parent to child or vice-versa. Saving arises to equate the ratio of marginal utility of present and future consumption to the marginal rate of transformation implicit in market (real) interest rates. In this way the PIH is said to emphasize the bequest motive for saving.

In contrast, the strict LCH had individuals consuming their entire endowments over their lifetime. Saving was supposed to arise because young workers were more numerous and wealthy (due to technological progress) than the older generation who were dissaving to finance retirement. This provides an avenue by which faster growth can increase saving. Alternatively, as discussed below, factors such as social security which change the extent of mismatch between lifetime consumption and income patterns are predicted to have profound effects on aggregate saving.

These approaches – and their synthesis with inter-generationally linked utility functions – have led to a rich literature quite apart from the consumption function, but those developments are beyond the scope of this essay.

From the point of view of the consumption function per se, the PIH and LCH imply that pure consumption is a fraction (variable in principle but rarely in practice) of wealth or permanent income. Here wealth is inclusive of human as well as non-human capital and permanent income is a (conventionally constant) long-term ex ante real interest rate times this wealth. (Note that, contrary to Sargent (1978) and others this wealth is not the discounted present value of expected future income to the extent, as in the PIH, that future income is expected to rise through planned saving.) The empirical estimation of wealth or permanent income became a central issue in the specification of the consumption function.

Friedman proposed a computationally simple estimator of permanent income as a geometrically weighted average of past income. Since on this scheme, permanent income changes – besides normal growth – by a fraction, say β, of the difference between current income and permanent income, Friedman related this scheme to the adaptive-expectations approach recently introduced by his student Phillip Cagan (1956).

Modigliani and his associates proxied normal labour income by current income and the product of this variable and the unemployment rate and attempted to measure non-human wealth by collecting estimates of the national balance sheet at market values. In principle, this method seemed more clearly related to the underlying framework than Friedman’s permanent-income proxy, but in practice it suffered several comparative disadvantages: (1) major components of non-human wealth had no market valuation; (2) the wealth estimates were not part of the national income accounts and competing variants were available with substantial delay and at irregular intervals; (3) for forecasting purposes, substantial additional equations were required to forecast (often poorly) future movements in wealth.

Darby (1974) reconciled these empirical measures of wealth by demonstrating that under the PIH, Friedman’s geometrically weighted measure could be derived as the constant real interest rate β times a (backward-looking) perpetual inventory of wealth. This β value was estimated as about 0.10 per annum in contrast to higher values such as Friedman’s 0.35 per annum. These higher values were explained by biases that arise as data deviate from pure consumption toward expenditures by consumers.

Empirical work on consumption functions has frequently floundered on the use of theories of pure consumption to explain data which are in whole or part consumer expenditures. Both the PIH and LCH were theories of pure consumption. Modigliani and Ando provided one link to consumer expenditures in their MPC model by modelling household investment in durable goods analogously to firm’s investment behaviour. Operating in the PIH tradition, Darby (1972, 1974) argued that aggregate transitory income represented a change in wealth, part of which change would be invested in consumers’ durable goods. (Darby (1972) in particular argued that because transitory income is received in non-human form, a disproportionate effect on durable-goods purchases may arise during the adjustment process, a result which explains the results of Hayashi 1982.) Darby (1975, 1977–8) later combined pure consumption and durable investment equations to obtain a unified consumer expenditure function which avoided some of the inherent difficulties in dividing consumer expenditures into durable and nondurable portions.

The PIH and LCH thus evolved to explain aggregate consumer expenditures by wealth as a determinant of pure consumption and by changes in wealth and other variables which determine household investment in durable goods. The correlation of the determinants of this household investment with short-run (transitory) fluctuations in income explain a MPC which is substantial in magnitude even though substantially below the APC.

This brief development has omitted discussion of alternative views of the consumption function. Perhaps the most notable of these is the view that the substantial value of the MPC reflects liquidity constraints which prevent a substantial share of consumers (measured by wealth and consumption) from following their optimal intertemporal consumption plan. The author of this essay regards these alternative views as providing qualification of the dominant wealthbased view.

Efficient-Market Approaches

Hall (1978) proposed to sidestep Friedman’s backward-looking measure of wealth as well as the substantial empirical problems involved in measuring the market value of wealth. Instead, he posed the question of whether or not changes in consumption can be modelled empirically as determined by ‘news’. Specifically, the assertion is that if wealth estimates and hence consumption are based on rational expectations, no past information including past changes in consumption or income should affect current changes in consumption.

Hall (1978) answered his question affirmatively, Flavin (1981) dissented, but Hayashi (1982) showed that excess sensitivity of spending to changes in wealth appeared to be confined to consumers’ durable goods purchases. Taken as a whole, these studies seem to confirm the basic Friedman–Modigliani conceptions that aggregate consumption as determined by wealth but that it is important to distinguish between consumer expenditures and consumption.

Bequest Versus Life-Cycle Saving

Saying that consumers optimally allocate wealth leaves several important questions unanswered: Do consumers have operative linkages in utility functions across generations? Are consumers able to see through the veil of government to the ultimate production possibilities faced by society? If the first of these questions is answered affirmatively, transfer programmes such as social security which change the life-cycle pattern of income receipts will not affect aggregate consumption and saving. (The representative infinitely lived individual does not care whether he or she pays social security taxes which are refunded as equal benefits. Intergenerational transfers can be adjusted so that this representation is acceptable where utility functions are linked across generations.) If the second question is also answered affirmatively, then Ricardian equivalence holds (it is irrelevant whether government taxes or borrows) and the relevant income concept for the aggregate consumption function is net national product less government spending for goods and services.

Feldstein (1974) claimed that aggregate saving had been significantly reduced by the US social security programme. As pointed out by Barro (1978), this effect would not arise with intergenerationally linked utility functions. Using different methodology, White (1978) and Darby (1979) concluded that life-cycle motives accounted for an at most small fraction of aggregate saving and wealth. Kotlikoff and Summers (1981) relaxed Darby’s assumptions on smooth growth of population and labour income without substantially changing the estimates on the range of assets attributable to life-cycle motives. These estimates seem to suggest that intergenerational linkages are indeed very important, as assumed by the PIH. The life-cycle effects highlighted in the LCH would appear more important for analysing cross-sectional data than as determinants of aggregate consumption.

The Ricardian equivalence idea was urged by Barro (1974) and Kochin (1974). It requires a certain suspension of disbelief to assume that bonds and taxes have equivalent effects on consumer behaviour, but the data are not very inconsistent with that notion. Indeed recent studies by Seater (1982) and Kormendi (1983) provide some evidence that Ricardian equivalence is a better working hypothesis than its denial.

Conclusions

The consumption function suggested by Keynes provided a useful challenge to theoretical and empirical economists. The relationship between changes in consumer expenditures and current income has been explained generally in a way which is consistent with microeconomic foundations and which is adequate in a multitude of specifications for most forecasting purposes. (Technical differences among empirical specifications are as large in number as they are uninteresting to the nonspecialist.) For policy analytic purposes, two key questions are outstanding: are life-cycle effects significant in the aggregate, and do individuals effectively see through government? This author’s reading of the evidence suggests answers of no and maybe, but it is hard to put much certainty in any answer unless one starts with dogmatic priors.

The consumption function has faded as a topic of intense research largely because of the success of previous work in achieving a workable consensus. The unsettled issues, however, have crucial policy implications and there is much value yet to be added.

See Also