James Cardon and Dr. Barrett E. Kirwan, Economics
Although the theory of aggregate consumption was first addressed in 1936 by Keynes, the modern theory stems from work done in the mid 1950’s by Modigliani and Brumberg (1954) and Friedman (1957); their theory has been termed the Life Cycle/Permanent Income Hypothesis (LC/PIH). While Keynes proposed that, “the amount of aggregate consumption mainly depends on the amount of aggregate income,” 1 the modern theory proposes that consumption tracks “permanent,” or average lifetime, income rather than current income.
Although the Life Cycle/Permanent Income Hypothesis has been around since the mid-fifties only in recent decades has it become a stimulating, bewildering subject. After Lucas’ critique (1976) and Hall’s rebuttal (1978) the LC/PIH took on a form unlike it had for the previous twenty years. Hall established the baseline from which the LC/PIH is often examined today. He posited that agents seek to keep the marginal utility of consumption equal across time. This is known as consumption smoothing. If consumption responds too greatly to known innovations in income then consumption is said to be excessively sensitive.
Recent advances in prudence, precautionary savings, and liquidity constraints have further complicated the mix. These theories have attempted to account for the apparent sensitivity of consumption. Moreover, the effects of precautionary savings and liquidity constraints are not always easily discerned from each other. Carroll (1992) explains that a positive probability of having near zero income in the next period is enough to prevent consumers from borrowing in this period.2 This self imposed constraint on borrowing looks very similar to an exogenously imposed constraint of imperfect capital markets. Because of this similarity, I will refer to “borrowing” constraints in the general sense whereas previous research has specifically addressed liquidity constrained behavior.
My research begins at the traditional starting point, examining the first-order conditions relating subsequent periods. This examination yields an Euler equation, which allows me to avoid the complications and restricting assumptions involved in specifying a lifetime income path and a closed form consumption function. The Euler equation is the instrument used by Hall to develop the certainty equivalent model (CEQ model). If the Euler equation is satisfied then consumers smooth consumption across time, and the rational expectations LC/PIH model holds. However, a violation of the Euler equation indicates a deviation from the LC/PIH.
My analysis provides for a specific alternative to the CEQ model which indicates the nature of the excess sensitivity of consumption. By applying the Kuhn-Tucker conditions to the standard Bellman equation I develop a modified Euler equation that lends itself to testable hypothesis concerning the effects of borrowing constraints.3 The resulting Euler equation contains a term that should be strictly positive if the consumer is excessively sensitive to innovations in current income due to borrowing constraints. This examination, therefore, provides a specific alternative to the CEQ model.
To address the issue of borrowing constraints adequately, one must have data on individuals through time. The Panel Study of Income Dynamics (PSID), one of the most comprehensive panel surveys, lends itself to this research. The PSID is a representative panel of U.S. families interviewed annually since 1968. Although the PSID was designed to study labor market participation and labor income, it also provides information on family income, composition, and food consumption. With a few generally accepted assumptions the data can be used to examine the sensitivity issue. I use a subset of the PSID from 1975-1992.
I am formally able to test for borrowing constraints by splitting the sample into two groups, a high wealth group and a low wealth group. The low wealth group is most likely to face binding constraints while the high wealth group is unlikely to face such constraints. The first test is a test of over-identifying restrictions. If the rational expectations LC/PIH holds, then extra information should enter the log-linearized Euler equation insignificantly and should be uncorrelated with the rest of the information in the information set. That is, if borrowing constraints are the source of deviation, any extra variable in the estimated equation should be insignificant for the high wealth group and significant for the low wealth group. I test this assumption by including the log of income in the estimated equation. The second test relies on the asymmetry of borrowing constraints. Constrained consumers cannot borrow against future earnings, but they can save. This is reflected in a positive Lagrange multiplier, the extra term in the Euler equation. I estimate and test the sign of this term. Finally, I loosely estimate the correlation between the Lagrange multiplier and income. As income today increases, the multiplier should decrease, resulting in a negative partial correlation.
The results of these tests suggest that low-wealth consumers face some sort of borrowing constraint. Some consumers are excessively sensitive to innovations in income. Unfortunately, the exact reason for this excess sensitivity has not yet been determined. In order to estimate these results I assume that the component of the Euler equation indicating precautionary saving is constant, a fatal assumption that must be rectified if one is to separate the effects of liquidity constraints from precautionary savings. Although I have not solved this problem analytically, I have come closer to a solution by identifying the errors in previous research and by providing empirical evidence that borrowing constraints are a real factor in the consumption decision.
References
- Romer, David (1996): Advanced Macroeconomics, San Francisco, McGraw Hill, 312.
- Carroll, Christopher D. (1992): “The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence,” Brookings Papers on Economic Activity, 2, 61-156.
- Zeldes, Stephen P. (1989): “Consumption and Liquidity Constraints: An Empirical Investigation.” Journal of Political Economy, 97, 305-46.