See Abel (1990) and Campbell and Cochrane (1995) for more on how individuals concern about their consumption relative to others affects saving once one recognizes that saving represents future consumption.

What Is Saving?

At a more general level, the basic idea of the life-cycle/permanent-income hypothesis is a simple insight about saving: saving is future consumption. As long as an individual does not save just for the sake of saving, he or she saves to consume in the future. The saving may be used for conventional consumption later in life, or bequeathed to the individuals children for their consumption, or even used to erect monuments to the individual upon his or her death. But as long as the individual does not value saving in itself, the decision about the division of income between consumption and saving is driven by preferences between present and future consumption and information about future consumption prospects.

This observation suggests that many common statements about saving may be incorrect. For example, it is often asserted that poor individuals save a smaller fraction of their incomes than the wealthy do because their incomes are little above the level needed to provide a minimal standard of hving. But this claim overlooks the fact that individuals who have trouble obtaining even a low standard of living today may also have trouble obtaining that standard in the future. Thus their saving is likely to be determined by the time pattern of their income, just as it is for the wealthy.

To take another example, consider the common assertion that individuals concern about their consumption relative to others tends to raise then consumption as they try to "keep up with the Joneses." Again, this claim fails to recognize what saving is: since saving represents fiiture consumption, saving less imphes consuming less in the future, and thus falling further behind the Joneses. Thus one can just as well argue that concern about relative consumption causes individuals to try to catch up with the Joneses in the future, and thus lowers rather than raises current consumption.

Empirical Application: Understanding Estimated Consumption Functions

The traditional Keynesian consumption function posits that consumption is determined by current disposable income. Keynes (1936) argued that "the amount of aggregate consumption mainly depends on the amount of aggregate income," and that this relationship "is a fairly stable function." He claimed further that "it is also obvious that a higher absolute level of income ... will lead, as a rule, to a greater proportion of income being saved" (Keynes, 1936, pp. 96-97; emphasis in original).

The importance of the consumption function to Keyness analysis of fluctuations led many researchers to estimate the relationship between

(7.8)

Cov(yC) Var(y)

Cov(yP + y, yP) Var(yP + yt)

= Var(y)

" Var(y)-b Var(y)

here the second hne uses the facts that current income equals the sum of permanent and transitory income and that consumption equals permanent income, and the last line uses the assumption that permanent and temporary income are uncorrelated. In addition, the estimated constant equals the mean of the dependent variable minus the estimated slope coefficient times the mean of the independent variable. Thus,

a = C~bY

= y ~ my + y") (7.9)

= (1 ~ b)?,

consumption and current income. Contrary to Keyness claims, these studies did not demonstrate a consistent, stable relationship. Across households at a point in time, the relationship is indeed of the type that Keynes postulated; an example of such a relationship is shown in Panel (a) of Figure 7.1. But within a country over time, aggregate consumption is essentially proportional to aggregate income; that is, one sees a relationship like thai in Panel (b) of the figure. Further, the cross-section consumption function differs across groups. For example, the slope of the estimated consumption function is similar for whites and blacks, but the intercept is higher for whites. This is shown in Panel (c) of the figure.

As Friedman (1957) demonstrates, the permanent-income hypothesis provides a straightforward explanation of all of these findings. Suppose thai consumption is in fact determined by permanent income: = Y. Current income equals the sum of permanent and transitory income: = *" + . And since transitory income reflects departures of current income from permanent income, in most samples it has a mean near zero and is roughly uncorrelated with permanent income.

Now consider a regression of consumption on current income:

Ci=a + hYt+e,. {7.7)

In a univariate regression, the estimated coefficient on the independent variable is the ratio of the covariance of the independent and dependent variables to the variance of the independent variable. In this case, this imphes

Whites

FIGURE 7.1 Some different forms of the relationship between current income and consumption