be re

w ol CO

25 21 17 13

+ Greece

+Italy

+ Japan +Portugal

+ Austria Netherlands +Spam + + France

+ Finland

+ Belgium :f + Denmark Canada Ireland +

Australia + Sweden

USA+j.

4.5 55 65 75 85

Maximum loan-to-value ratio in the 1970s (percent)

FIGURE 7.4 The loan-to-value ratio for home purchases and the saving rate (from Jappelli and Pagano, 1994; used with permission)

In sum, their evidence suggests that Uquidity constraints are important to aggregate saving.

Empirical Application: Buffer-Stock Saving

A central prediction of the permanent-income hypothesis is that there should be no relation between the expected growth of an individuals income over his or her lifetime and the expected growth of his or her consumption: consumption growth is determined by the real interest rate and the discount rate, not by the time pattern of income.

Carroll and Summers (1991) present extensive evidence that this prediction of the permanent-income hypothesis is incorrect. For example, individuals in countries where income growth is high typically have fiigh rates of consumption growth over their lifetimes, and individuals in slowly growing countries typically have low rates of consumption growth. Similarly, typical lifetime consumption patterns of individuals in different occupations tend to match typical lifetime income patterns in those occupations. Managers and professionals, for example, generally have earnings profiles that rise steeply until middle age and then level off; their consumption profiles follow a simUar pattern.

More generally, most households have little wealth (see, for example, Deaton, 1991, and Hubbard, Skinner, and Zeldes, 1994a). Their consumption

JappeUi and Pagano go on to investigate the relationship between liquidity constraints and aggregate growth. They find that even when they control for investment, liquidity constraints are positively related to growth. Given that the way that liquidity constraints most plausibly affect growth is through their effect on saving (and hence investment), this finding is difficult to interpret.

approximately tracks their income, but they have a smaU amount of saving that they use in the event of sharp falls in income or emergency spending needs. In the terminology of Dealon (1991), most households exhibit buffer-stock saving behavior. As a result, a small fraction of households hold the vast majority of wealth.

At least three explanations of buffer-stock saving have been proposed. First, Shefrin and Thaler (1988) argue that consumption behavior is not well described by complete intertemporal optimization (see also Laibson, 1993). Instead, individuals have a set of rules of thumb that they use to guide then consumption behavior. Examples of these rules of thumb are that it is usually reasonable to spend ones current income, but that assets should be dipped into only in exceptional circumstances. Such rules of thumb max lead consumers to use saving and borrowing to smooth short-run income fluctuations, and thus cause consumption to foUow the predictions of the permanent-income hypothesis reasonably well at short horizons. But the\ may also cause consumption to track Income fairly closely over long horizons.

Second, Deaton (1991) and Carroll (1992) argue that buffer-stock saving arises from a combination of a high discount rate, a precautionary-saving motive, and some reason that households do not go heavily into debt. In Deatons analysis, the reason for the absence of debt is the presence of liquidity constraints. In CarroUs, it is that the marginal utihty of consumption approaches inflnity as consumption becomes sufficiently low; as a result, households are unwilling to risk the very low consumption that would occur if they were in debt and their future income turned out to be low. The combination of the high discount rate and the inability or unwillingness to go into debt causes households wealth to be approximately zero, and thus causes consumption to approximately track income. But even with a relatively high discount rate, the positive third derivative of the utility function causes households to view the risks of sharp falls in consumption and sharp rises as asymmetric; as a result, they typically keep a small amount of savings to use in the event of large falls in income.

Third, Hubbard, Skinner, and Zeldes (1994a, 1994b) suggest an explanation of buffer-stock saving that is close in spirit to the permanent-income hypothesis. The key elements of their explanation, aside from intertemporal optimization, are a precautionary-saving motive and the fact that welfare programs provide insurance against very low levels of consumption. For households that face a nonnegligible probability of going on welfare, the presence of welfare discourages saving in two ways: it directly provides insurance against unfavorable reahzations of income, and it imposes extremely high implicit tax rates on asset holdings. Nonetheless, the precautionary-saving motive causes these households to typically hold some assets when their consumption is above the guaranteed floor. For households whose income prospects are favorable enough that the possibility of going on welfare is negligible, on the other hand, consumption is determined by conventional intertemporal optimization; thus they ex-

Problems

7.1. The average income of farmers is less than the average income of non-farmers, but fluctuates more from year to year. Given this, how does the permanent-income hypothesis predict that estimated consumption functions for farmers and nonfarmers differ?

7.2. The time-averaging problem. (Working, 1960.) Actual data do not give consumption at a point in time, but average consumption over an extended period, such as a quarter. This problem asks you to examine the effects of this fact.

Suppose that consumption follows a random walk: Q = Q-i + e,, where e is white noise. Suppose, however, that the data provide average consumption over two-period intervals; that is, one observes (Cf + Ct+i)/2, (Ct+2 + + )/2, and so on.

(a) Find an expression for the change in measured consumption from one two-period interval to the next in terms of the es.

(b) Is the change in measured consumption uncorrelated with the previous value of the change in measured consumption? In light of this, is measured consumption a random walk?

(c) Given your result in part ( ), is the change in consumption from one two-period interval to the next necessarily uncorrelated with anything known as of the first of these two-period intervals? Is it necessarily uncorrelated with anything known as of the two-period interval immediately preceding the first of the two-period intervals?

(d) Suppose that measured consumption for a two-period interval is not the average over the interval, but consumption in the second of the two periods. That is, one observes Ct+i, Q+s, and so on. In this case, is measured consumption a random walk?

7.3. (This follows Hansen and Singleton, 1983.) Suppose instantaneous utility is of the constant-relative-risk-aversion form, uiQ) = C/(l - ), > 0. Assume that the real interest rate, r, is constant but not necessarily equal to the discount rate, p.

(a) Find the Euler equation relating C, to expectations concerning C,+i.

(b) Suppose that the log of income is distributed normally, and that as a result the log of C(+i is distributed normally; let denote its variance conditional on information available at time f. Rewrite the expression in part (a) in terms of InC,, EtllnQ+i], a, and the parameters r, p, and . (Hint: if a variable x is distributed normally with mean p and variance V, Ele"] =

hibit conventional life-cycle saving. Hubbard, Skinner, and Zeldes therefore argue that the different patterns of wealth accumulation of the poor and the rich can be explained without appealing to differences in their preferences.