Permanent Income Hypothesis

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Permanent Income Hypothesis

The permanent income hypothesis (PIH), introduced in 1957 by Milton Friedman (1912–2006), is a key concept in the economic analysis of consumer behavior. In essence, it suggests that consumers set consumption as the appropriate proportion of their perceived ability to consume in the long run. Wealth, W, is defined as the present discounted value of current and future total income receipts, inclusive of income from assets. Under the assumption that the household is infinitely lived, permanent income can be defined as that level of income which, when received in perpetuity, has a present discounted value exactly equal to the wealth of the household. Equivalently, permanent income, denoted y^P, may be regarded as the amount it is believed possible to consume while maintaining wealth intact; it is therefore expressed as equal to the “annuity value of wealth,” y^P = rw, where r is the real interest rate (assumed fixed).

More specifically, the PIH decomposes measured total disposable income, y, into a permanent component, y^P, and a transitory component, y^T. The permanent income component is deemed systematic but unobservable, reflecting factors that determine the household’s wealth, while the transitory component reflects “chance” income fluctuations. Similarly, measured consumption, c, is decomposed into a permanent component, c^P, and a transitory component, c^T. Assuming these relationships to be additive, for simplicity: y = y^P + y^T and c = c^P + c^T. It is also important to note that the PIH defines consumption in a “use sense,” through the enjoyment or destruction of consumer goods by use, rather than the expenditure upon them, so that consumption is regarded as a service flow.

In giving the hypothesis empirical substance, Friedman assumes the transitory components to be uncorrelated across consumption and income, and with their respective permanent components. The second of these assumptions follows from the definitional decomposition and the nature of transitory components. The first implies that irregular income will not result in unplanned consumption. Friedman defends this assumption by arguing that transitory income changes are likely to be reflected in changes in asset holdings. Further, since the consumption definition includes only the flow of services from goods, transitory income disbursed on durable goods may still be classified as unplanned savings. Moreover, zero correlation implies only that the average association is zero, and positive associations in some instances may well be offset by negative associations in others.

The formal relationship between consumption and income is derived from a standard intertemporal utility-maximizing framework under the assumptions of infinite life, perfect capital markets that permit borrowing and lending of unlimited amounts (subject to solvency) at the same real interest rate, and the condition that the utility function is homogeneous of positive degree in consumption for current and all future periods, such that an expansion in the feasible budget set (arising from increased income in any period) leads to an equal proportionate change in present and planned future consumption. As a consequence, at the level of the household, permanent consumption is a proportionate function of permanent income. That factor of proportionality is dependent on tastes, age, and the real interest rate (and, with allowance for uncertainty, on the ratio of financial assets to permanent income, on the basis that financial assets provide more substantial collateral than “human wealth” in the form of discounted unearned future income). The aggregate consumption function then depends on the distribution of these factors across households. If it is further assumed that the distribution of households by income is independent of their distribution by these factors, then aggregate permanent consumption obeys a simple proportionate relationship to aggregate permanent income: c^P = q y^P.

This proportionate relationship between the permanent components of consumption and income is readily reconciled with the nonproportionate aggregate relationship typically observed empirically in cross-sections and short-run aggregate data studies. This is as a consequence of low-income brackets including a greater proportion of households with negative transitory income, and high-income brackets including a greater proportion of households with positive transitory income. However, without any impact on consumption, which is still proportionate to the permanent income of those households, the observed consumption-income relationship is shallower than the underlying proportionate relationship between the permanent components (see Figure 1). More specifically, for zero mean transitory components and a random transitory income distribution, the cross-section average income group consumes cross-section average permanent income. For the above-average “high” income group, transitory income will typically be positive but not reflected in consumption, though assets will be accumulated. Similarly, below-average “low” income groups are more likely to have experienced negative transitory income, which reduces income below the permanent income level, associated with negative changes in asset holdings. Thus, the asymmetric incidence of transitory income generates an observed consumption-income relationship that is disproportional and lies away from the underlying proportionate behavioral relationship. Note that the exact shape of this observed relationship will depend on the actual distribution of transitory income in practice, while its positioning in the diagram will depend on the true cross-section average transitory income and transitory consumption values, which may not be zero as illustrated. Over time, as aggregate average permanent income grows

along trend, the cross-section consumption function shifts up, tracing out a long-run time series of aggregate average consumption and income that exhibit a constant ratio with respect to each other.

A major difficulty in attempting to test the PIH empirically is that permanent income is not observable. This necessitates the use of some proxy or means of estimating permanent income. In the empirical implementation of the permanent income hypothesis using time-series data, Friedman utilized an adaptive mechanism to relate permanent income to current and past measured income, with the greatest weight attached to current income and declining weights attached to income further in the past. That is, permanent income is represented by an exponentially weighted average of all observed measured incomes, with the weights summing to unity. This approach, with some truncation of the influence of past incomes, enabled Friedman to estimate the weight attached to current income in contributing to permanent income at around one-third (and therefore far less than unity, as would be implied by the absolute income hypothesis ) and to demonstrate the long-run proportionality of consumption and income, as implied by the PIH.

It is also of some note that the infinite distributed lag formulation of permanent income may also be expressed equivalently in terms of a finite adaptive expectations representation for permanent income, such that if current measured income exceeds the previous period’s estimate of permanent income, then the estimate of permanent income for the current period is revised upwards, the extent of the adjustment depending on the size of an adjustment parameter in the adaptive expectations mechanism. Algebraically, taking the infinite distributed lag formulation of permanent income, making use of the Koyck transformation and the definition of permanent consumption as the difference between measured and transitory consumption, it is then possible to express current measured consumption as a function of current measured income, measured consumption in the previous period, and an error term. However, this time series representation is “observationally equivalent” with the implications of alternative theories of consumption, such as the relative income hypothesis, thus weakening the distinctiveness of the permanent income approach (though it should be noted that this criticism is less damning to tests of the cross-sectional implications of the PIH noted above).

An ensuing criticism of the PIH is centered on the assumption of an adaptive relationship between permanent and measured income, which implies an underlying adaptive expectations mechanism, as discussed above. This criticism hinges on the observation that such expectations are entirely “backward-looking,” in the sense that expectations are only revised in response to past movements in income, and such revisions are in general sluggish, which suggests the possibility of systematic expectation errors. However, it is not a tenable proposition that rational economic agents, who are assumed to be optimizing subject to constraints in all other regards, would not seek to revise their expectation formation mechanism, and the information on which it draws, in such circumstances. The essence of the rational expectations hypothesis (REH) is that agents should utilize all relevant and available information in avoidance of systematic error, and the incorporation of the REH into the PIH therefore has considerable ramifications. Predominant amongst these is the implication that consumption should follow an approximate random walk, such that knowledge of previous values of any variable other than the immediately preceding level of consumption should have no predictive power for consumption, since all information available in the previous period should have been incorporated in determining the previous level of consumption. However, the available empirical evidence is not generally supportive of this proposition in its strict form, and the ensuing debate has reinforced the view that the validity of the results of tests of the PIH depend as much on the method used to represent permanent income, and in particular the relationship between current and expected future income, as on the validity of the PIH itself.

From a policy perspective, the PIH asserts that current income plays only a minor role in consumption determination, as just one element of the entire spectrum of current and expected future income, and emphasizes the assumed desire of consumers to smooth consumption flows in the face of variable income flows. In particular, conventional Keynesian demand-management policy, as might be conducted through countercyclical fiscal policy in the form of temporary income tax changes, will lead to little or no change in consumption and be relatively ineffective, since only changes perceived by households as leading to revisions in their permanent incomes will impact significantly on their consumption. Thus, transitory income movements are largely reflected in saving changes. Moreover, the economic system is consequently inherently more stable in that the income-expenditure multiplier effects of exogenous changes are reduced, so that the change in national income following a temporary change in private investment or government expenditure, for example, is correspondingly much smaller than when consumption is directly responsive to current income alone, as is the case under the Keynesian absolute income hypothesis.

However, a caveat to the preceding policy discussion is warranted in that it must be remembered that the PIH is concerned with consumption as a flow of services, as distinct from the implications for consumer expenditure, which includes expenditure on durable goods, and it is this latter concept that is important in income-expenditure analysis. Thus, while transitory income movements are reflected in savings and asset changes under the PIH, such assets include durable goods, and the potential for a sizeable multiplier effect to operate is opened through the relationship between current income and durable-good expenditures. Moreover, to the extent that capital markets are imperfect and consumers do not have good short-term lending and borrowing opportunities, the tendency toward holding transitory income in durable goods is strengthened. The issue of countercyclical policy effectiveness then becomes one of determining what form asset accumulation and associated expenditures take, and what factors influence those expenditures.

Perhaps most critically, the PIH embodies the assumption that capital markets are perfect in the sense that lenders are prepared to extend credit on the basis of repayments financed out of future income yet to be received, at a fixed rate of interest irrespective of loan size, and equivalent to the loan rate payable to deposits. However, where consumers are unable to borrow freely on perfect capital markets, possibly as a result of adverse selection and moral hazard under limited and asymmetric information, liquidity, as the ability to finance consumption, and liquidity constraints, involving limitations on the volume of borrowing as well as divergences between rates of interest on borrowing and lending, become paramount. In such circumstances, increases in current income are likely to be used to finance increased consumption, thus accentuating the observed consumption-income relationship, particularly where lenders select current income as the credit rationing device from among the observable characteristics conveying information on ability to repay debt.

SEE ALSO Absolute Income Hypothesis; Consumption Function; Life-Cycle Hypothesis; Relative Income Hypothesis