Consumption Over the Life Cycle

with P. O. Gourinchas 
Econometrica, 70(1), January 2002, 47-89.

Abstract

This paper employs a synthetic cohort technique and Consumer Expenditure Survey data to construct average age-profiles of consumption and income over the working lives of typical households across different education and occupation groups. Using these profiles, we estimate a structural model of optimal life-cycle consumption expenditures in the presence of realistic labor income uncertainty. The model fits the profiles quite well. In addition to providing tight estimates of the discount rate and risk aversion, we find that consumer behavior changes strikingly over the life-cycle. Our methodology provides a natural decomposition of saving into its precautionary and retirement components.

The published paper from JSTOR

A draft from here (almost the published version).

Slightly older versions:  NBER WP 7271 (link requires access to NBER WP site)

Paper Summary

This paper answers four import questions concerning household consumption and saving behavior using a novel estimation approach. We ask, how impatient are households? Second, how willing are households to substitute consumption over time and how averse are they to risk? Third, what motivates households to save? Finally, how do these motivations and thus consumption behavior change with age? To address these issues, this paper estimates a dynamic stochastic model of household expenditure. We present a novel estimation technique that allows us to estimate structural preference parameters and characterize optimal behavior when households face uninsurable, stochastic, labor income processes.

Most recent research on consumption behavior has used a method that infers household behavior from the expected growth rate of consumption and the response of these growth rates to different real interest rates. However a growing body of empirical work rejects the fundamental assumption at the heart of these tests: that households do not completely smooth consumption over predictable movements in income. Consumption tracks income across time and across countries in ways that are not explained by variations in real interest rates or new information about household wealth. A second strand of recent research provides a candidate explanation: these observations can be explained if households face idiosyncratic risks, such as those to their own incomes, that make them unwilling to borrow against their future incomes despite expecting high income in the future on average or despite significant impatience. Theoretical and simulation work shows that such income uncertainty generates precautionary saving by households that can invalidate the use of the main empirical methodology to estimate the behavior of households.

In this paper we use household consumption data and simulation techniques to estimate a structural model of inter-temporal consumption choice with realistic levels of income uncertainty. We measure, exploit and analyze the systematic age-pattern of consumption and saving. The estimated model is then used to re-interpret life-cycle consumption and asset accumulation behavior. We find substantial age-heterogeneity in consumption behavior that results from the interaction between, and relative strengths of, retirement and precautionary motives for saving at different ages. This in turn is largely driven by the age-varying slope of the expected income profile. Further, we provide tight estimates of the key parameters of the household utility function.

Our method proceeds in two steps. We construct consumption and income profiles across the working lives of ``typical'' men of five different educational attainments and four different occupational groupings, using quality household-level data on consumption and income from a sample of roughly 40,000 households from the U.S. Consumer Expenditure Survey (CEX) from 1980 to 1993. Consumption and income profiles are both significantly hump-shaped, despite controlling for family composition and cohort effects, and consumption tracks income reasonably well early in life. We also estimation of income risk and other important factors that impact households from additional U.S. data as described in the main body of the paper.

Second, we use our estimates of the environment that households face to estimate a canonical stochastic life-cycle model of consumer behavior. For any guess of the key parameters governing household behavior, we can solve numerically and recursively for the household optimal behavior. By then simulating the behavior of a large number of households, we generate a simulated life-cycle consumption profile. By matching this simulated profile to its empirical counterpart, we estimate the parameters of the consumption problem using a Method of Simulated Moments.

Turning to our results, we find that the fitted model matches the correlation between consumption and income at young ages and the fact that most households do not save out of discretionary income until quite late in their working lives. Further, our method produces reasonable estimates of the preference parameters. The average household has a discount rate of around 4.0 to 4.5 percent and a marginal propensity to consume at retirement of 6 to 7 percent. The estimated coefficient of relative risk aversion lies between 1/2 and 1.

We find that households older than 40 save mostly for retirement and bequests. Our model explain the small amount of saving done early in life: when young, precautionary saving cancels the motive to dissave provided by the presence of high expected income later in life. We argue that observed saving patterns are quite consistent with forward-looking optimizing behavior in a life-cycle framework augmented to include income uncertainty. Finally, we find strikingly different consumption behavior for households at different ages: households behave like `buffer-stock' consumers early in their working lives and more like certainty-equivalent-lifecycle-hypothesis households as retirement nears. That is, prior to age 45, households do not smooth consumption across predictable changes in income because they face significant risk that that income will not arrive as expected. Later in life, household smooth consumption well since they hold significant amounts of wealth for retirement purposes and this wealth helps them insure their consumption levels against changes in income.