Consumption and saving: theory and evidence.

• Author: Carroll, Christopher D.
• Position: Research Summaries

Consumption and saving decisions are at the heart of both short- and long-run macroeconomic analysis (as well as much of microeconomics). In the short run, spending dynamics are of central importance for business cycle analysis and the management of monetary policy. And in the long run, aggregate saving determines the size of the aggregate capital stock, with consequences for wages, interest rates, and the standard of living.

Since the pioneering work of Friedman and of Modigliani and Brumberg in the 1950s, the principal goal of the economic analysis of saving has been to formulate mathematically rigorous theories of behavior. But that goal was difficult until recently because the optimal response of saving to uncertainty was difficult to compute. Research was generally carried out under the assumption that uncertainty might boost saving somewhat, but that behavior in the presence of uncertainty was likely to be broadly similar to optimal behavior in a world in which households had perfect foresight about their future circumstances.

In two papers that grew out of my 1990 dissertation, (1) I showed that the presence of uncertainty could change the nature of optimal behavior in qualitatively and quantitatively important ways. Specifically, I examined the optimal behavior of consumers with standard attitudes toward risk (constant relative risk aversion) facing income uncertainty of the kind that appears to exist in household-level data sources. The first paper found that target or "buffer-stock" saving may be optimal under some circumstances; the second paper found that, depending on households' income profiles and their degree of impatience, it can be optimal for average household spending patterns to mirror average household income profiles over much of the life cycle. This was surprising because, in models without uncertainty, optimizing consumers spend based on their expected lifetime resources without regard to the expected timing of income. That is, spending patterns by age are not intrinsically determined by income patterns by age. (This work, and my subsequent related work, assumes that consumers have successfully solved any "self-control" problems of the type that David Laibson and others have so persuasively described).

This paper was related to two other, more abstract, papers. The more fundamental of these, (2) written with Miles Kimball, showed that in the presence of uncertainty, households with low levels of wealth will respond more to a windfall infusion of cash than households with ample resources. The other paper (3) demonstrated that the logic of precautionary saving undermines the standard "Euler equation" method of testing for optimizing consumption behavior.

Mathematical and computational aspects of optimal behavior have remained a theme in my research to the present. A recent paper provides the rigorous foundations for the mathematical methods employed in my earlier work. (4) Another paper with Miles Kimball (5) explores the theoretical implications of borrowing limitations; and, a very short new paper describes a conceptual trick that can be used to simplify and accelerate the solution of many kinds of optimal intertemporal choice models. (6) As an aid to other researchers, I have posted on my web page computer software that implements this trick to solve a variety of standard optimization problems. My web page also contains software that reproduces the computational and empirical results in most of my published papers, as well as a set of lecture notes (and associated software) that provide a comprehensive treatment of the methods for solving these models. (7)

In the end, however, mathematical models are useful only insofar as they can be related to empirical evidence about the real world. Toward the end of matching theory and data, Andrew Samwick and I wrote two papers (8,9) whose goal was to get a...