Liquidity Constraints

The permanent-income hypothesis assumes that individuals can borrow at the same interest rate at which they can save as long as they eventually repay their loans. Yet the interest rates that households pay on credit-card debt, automobile loans, and other borrowing are often much higher than the rates they obtain on their saving. In addition, some individuals are unable to borrow more at any interest rate.

A large literature investigates the causes, extent, and effects of such liquidity constraints. They are potentially important for many aspects of consumption. As described in Section 7.3, they can produce excess sensitivity of consumption lo predictable changes in income. If individuals face high interest rates for borrowing, they may choose not to borrow to smooth their consumption when their current resources are low. And if they cannot borrow at all, they have no choice but to have low consumption when their current resources are low. Thus liquidity constraints can cause current income to be more important to consumption than is predicted by the permanent-income hypothesis.

This chapter will not provide a thorough treatment of liquidity con-straints. Instead, as with our discussion of precautionary saving, we will focus on the potential effects of liquidity constraints on the level of consumption.

Liquidity constraints can raise saving in two ways. First, and most obviously, whenever a liquidity constraint is binding, it causes the individual to consume less than he or she otherwise would. Second, as Zeldes (1989) emphasizes, even if the constraints are not currently binding, the fact that they may bind in the future reduces current consumption. Suppose, for example, that there is some chance of low income in the next period. If there are no liquidity constraints, and if income in fact turns out to be low, the individual can borrow to avoid a sharp fall in consumption. If there are bquidit) constraints, however, the fall in income causes a large fall in consumption unless the individual has savings. Thus the presence of liquidity constraints

See Deaton (1992, pp. 194-213) for a general introduction to liquidity constraints. In addition. Section 8.7 presents a model of capital-market imperfections in the context of loans to firms rather than to households.

more of tliose resources are expected to come in the future. As a resuh, precautionary saving can help to account for the fact that when income is expected to rise, consumption is also expected to rise. Finally, Dynan (1993) and Carroll (1994) investigate the empirical relationship between households uncertainty about their future income and consumption growth; they reach conflicting conclusions, however.

. Al -H 2 + ez[yi] cz = mid ~--~--,Ai -t- 2

(7.45)

Thus the liquidity constraint reduces current consumption if it is binding.

Now consider the first period. If the liquidity constraint is not binding that period, the individual has the option of marginally raising Ci and paying for this by reducing cz. Thus if the individuals assets are not literally zero, the usual Euler equation holds. With the specific assumptions we are making here, this means thai Ci equals the expectation of cz-

But the fact that the Euler equation holds does not mean that the liquidity constraints do not affect consumption. Equation (7.45) implies that if the probability that the liquidity constraint will bind in the second period is strictly positive, the expectation of cz as of period I is strictly less than the expectatton of (Ai -i- 2 -1- £2[ :;])/2. Ai is given by Aq + yi - Q, and the law of iterated projections implies that Ei[£2[l3]] equals £1[ ]. Thus,

„ Aq+ 1+£1[ 2]+£1[ ]- 1 „

Cl <----. (7.4b)

causes individuals to save as insurance against the effects of future falls in income.

These points can be seen in a three-period model. To distinguish the effects of liquidity constraints from precautionary saving, assimie that the instantaneous utility function is quadratic. In addition, continue to assume that the real interest rate and the discount rate are zero.

Begin by considering the individuals behavior in period 2. Let a, denote assets at the end of period f. Since the individual lives for only three periods, d equals 2 + is, which in turn equals a\ + Yz + y3 - c. The individuals expected utility over the last two periods of life as a function of his or her choice of cz is therefore

u = {cz- ) + ezkai + YZ + Y3- cz) - fl(Ai + 2 + i3 - cz)]. (7.43)

The derivative of this expression with respect to cz is

= 1 - flC2 - (1 - aez[ar + YZ + Y3- cz])

cz (7.44)

= fl(Ai + yz + Ezm] - 2Cz).

This expression is positive for cz < (Ai + yz + ez[y])/2, and negative thereafter. Thus, as we know from our earlier analysis, if the liquidity constraint does not bind, the individual chooses cz = (Ai + yz + ez[yi])/2. But if it does bind, he or she sets consumption to the maximum attainable level, which is Al -I- l2- Thus,

Empirical Application: Liquidity Constraints and Aggregate Saving

As we have just seen, liquidity constraints can raise saving. Jappelli and Pagano (1994) invesHgate empirically whether cross-country differences in liquidity constraints are important to cross-country differences in aggregate saving.

Jappelli and Pagano begin by arguing that there are important differences in the extent of liquidity constraints across countries. In Spain and Japan, for example, home purchases generally require down payments of 40% of the purchase price, whereas in the United States and France they requhe 20% or less. Similarly, Korea strongly restricts the availabihty of consumer credit, but the Scandinavian countries do not. Bankruptcy and foreclosure laws also vary greatly. In Belgium and Spain, for example, it takes two years or more to foreclose on a mortgage, whereas in Denmark and the Netherlands it takes less than six months. Greater legal barriers to foreclosure are likely to discourage lending.

Jappelh and Pagano then ask whether these differences in credit availability are associated with differences in saving rates. They first examine the relationship between the loan-to-value ratio for home purchases (that is, one minus the required down payment) and the saving rate. As Figure 7.4 shows, there is a clear negative association. They then add the loan-to-value ratio to a regression of saving rates on measures of government saving, the demographic composition of the population, and income growth. The loan-to-value ratio enters negatively and significantiy. In a typical specification, the point estimates imply that an increase in the required down payment of 10 percent of the purchase price is associated with a rise in the saving rate of 2 percent of NNP. They also find that using a measure of the availability of consumer credit in place of the loan-to-value ratio yields similar results.

Because both present and future liquidity constraints potentially affect behavior, complete solutions of models with liquidity constraints usually require the use of numerical methods (see, for example, Deaton, 1992, pp. 180-189).

Adding Ci / 2 to both sides of this expression and then dividing by 3/2 yields

Ci <----. (7.47)

Thus even when the hquidity constraint does not bind currently, the possibility that it will bind in the future reduces consumption.

Finally, if the value of Ci that satisfies Ci = E1IC2] (given that C2 is determined by [7.45]) is greater than the individuals period-1 resources, Ao + Fi, the first-period Uquidity constraint is binding; in this case the individual consumes Aq + Yi?