Reexamining the Retirement Saving Puzzle When

Grant Proposal:

“Reexamining the Retirement Saving Puzzle When

Consumption and Leisure are Partial Substitutes”

Miles Kimball, PI/PD,

April, 2002

Abstract

A number of papers have pointed to an observed drop in consumption (in the sense of expenditure on market goods and services) at retirement as evidence that people are not planning adequately for retirement and so saving too little for retirement. But theory indicates that when consumption and leisure are partial substitutes, a drop in consumption at retirement may be a perfectly rational response to the increased leisure available after retirement. The simplest calibration of the theory that leisure is a partial substitute for consumption actually suggests that consumption should drop much more at retirement than it typically does, so the puzzle becomes why consumption drops as little as it does at retirement rather than why it falls at all. This calls for further development of the theory to see if reasonable modifications of the theory can explain the more modest drop in consumption typically seen at retirement as a rational, planned response to retirement. Such a theoretical investigation is necessary if one wants to draw any valid policy conclusions from the observed drop in consumption at retirement.

Proposal

Introduction: The biggest policy question relating to Social Security in the near future is whether to shift toward a system in which private accounts play a major role. How well private accounts will work depends critically on how well households can manage their own saving and portfolio decisions in relation to retirement. An important indicator of how well households could manage these decisions under a significantly reformed Social Security system is how well they are managing these decisions now. A number of researchers have argued that the frequently observed drop in consumption (expenditures on market goods and services) upon retirement indicates that many households are undersaving for retirement.[1]

The claim that a drop in consumption at retirement indicates undersaving comes from the theoretical result that, assuming consumption and leisure are neither substitutes nor complements, a rational household will save enough to smooth consumption so that consumption in the years right after retirement is at essentially the same level as consumption in the years right before retirement. Given that assumption, the drop in consumption at retirement is, indeed, a sign of something amiss in the household’s saving for retirement. That is why the drop in consumption at retirement has been called “the retirement saving puzzle” in the literature.

However, the assumption that consumption and leisure are neither substitutes nor complements is an assumption motivated more by mathematical convenience than by reality. Those papers that have looked directly at this issue have tended to find that consumption and leisure are partial substitutes.[2] The nature of the evidence is primarily that consumption seems to move in a predictable way with differences in labor participation and labor hours, even when the difference in labor participation or hours is far removed from retirement.

Saying that consumption and leisure are partial substitutes goes far beyond saying that there are transportation, work-clothing, food at work, child-care and other work-related costs in the narrow sense that fall when someone is no longer working. Consumption and leisure can be partial substitutes in a wide variety of ways. For example, those with more time on their hands may do more fix-it jobs around their own house that they could have purchased market services for: plumbing, electrical work, yard work, home repairs, tailoring, and cooking. In addition to cooking at home instead of purchasing restaurant meals, those with more time can buy cheaper, less-prepared foods and cook more nearly from scratch. At a more subtle level, those with more time to spend can take up hobbies such as bridge that are very time-consuming but cost very little money. Also, those with the time to do comparison-shopping and shopping for second-hand items can get the same or almost the same consumption goods at a lower money price at the cost of more time spent doing the shopping.[3]

Below, I discuss how the various aspects of household production listed above can be summarized by a standard reduced-form utility function of market expenditure on goods and services C and labor hours N that is not additively separable between consumption C and labor N. In the simplest form of this utility function, the evidence on long-run labor supply and on the elasticity of intertemporal substitution for consumption implies too strong a substitutability between consumption and leisure. I propose exploring the effects on the substitutability between consumption and leisure caused by adding habit formation in consumption, durability of leisure, and job quality to this utility function, with an eye toward developing a theory of consumption-leisure substitutability realistic enough and accurate enough to be a good guide for policy. In the last section, I discuss the implications for Social Security policy of substitutability between consumption and leisure.

Summarizing the Implications of Home Production in a Standard Utility Function:

Here and in the next section, I follow a more detailed discussion in Basu and Kimball (2002). Given (1) underlying preferences over ultimate goods produced in the household, (2) a household production function that maps quantities of time and market goods devoted to various activities to the amounts of ultimate goods produced, (3) the time constraint for each individual in the household and (4) relative prices for the various market goods and services and other exogenous factors affecting the household, optimization of these preferences subject to these constraints yields a reduced form utility function: V(. . ., Ct-1, Ct, Ct+1, …;… Nt-1, Nt, Nt+1, …; … Zt-1, Zt, Zt+1, …), where at each point in time, Z is a vector of all of the relevant exogenous variables. This reduced-form utility function gives a valuable perspective because the most basic fact about long-run labor supply—namely, the cancellation of income and substitution effects on labor supply—provides important information about this reduced-form utility function.[4]

Implications of the Restriction to V=Σ βt U(Ct,Nt) for Consumption-Leisure Substitutability: Even when a utility function is not additively separable between its arguments within a time period, additive time-separability across time periods is a common assumption. But additive time-separability and the exclusion of exogenous variables from the reduced form utility function have very strong implications for the strength of consumption-leisure substitutability when combined with the evidence for cancellation of income and substitution effects on labor supply and the evidence that interest rates have at most modest effects on consumption.

Many economists have found relatively small effects of interest rates on consumption (small elasticities of intertemporal substitution in consumption)[5] which are embodied in the utility function by a marginal utility of consumption UC that declines quickly with increases in C. But the marginal utility of consumption appears as an element of labor supply decisions as well. The within-period first order condition for optimal labor supply for the household involves equating the (after-tax) real wage W/PC to the ratio of the marginal disutility of labor –UN to the marginal utility of consumption: W/PC = –UN(C,N)/UC(C, N).

The cancellation of income and substitution effects on labor supply means that when an increase in the real wage supports a proportional increase in consumption, labor N can stay approximately the same without disturbing this equation. But if the marginal utility of consumption declines quickly with increases in C, then the increase in the real wage will not be able to keep up with the rate of increase in 1/ UC. In words, as the household runs out of things it is desperate to buy, the proportional increase in the real wage will not be enough by itself to motivate the household to devote so many hours to market work. With this utility function, the only way to motivate the household to devote the same number of hours to work when UC is falling faster than W/PC rises is to have the marginal disutility of labor –UN fall with increasing consumption. In words, consumption-leisure substitutability must be strong enough for the increase in consumption to free up the time to keep desired market work up.[6]

The trouble is that the amount of consumption-leisure substitutability required to counteract the implied rate of decline in the marginal utility of consumption is very large.[7] Clearly, more degrees of freedom are needed in the utility function in order to simultaneously match facts about long-run labor supply, intertemporal substitution in consumption and the degree of consumption-leisure substitutability.

Modifying the Utility Function to Get a More Realistic Theory of Consumption-Leisure Substitutability: There are three reasonable modifications of the utility function, any one of which can help in simultaneously matching these facts. The theoretical relationships will not be fully understood without substantial research, but intuition provides strong conjectures about the likely effects of these modifications of the utility function.

Habit formation in consumption is the most obvious possibility. Habit formation in consumption makes the marginal utility of consumption drop quickly with consumption in the short-run, but not as fast in the long run, as the household gets used to the extra consumption and wants more. Habit formation can buoy up the marginal utility of consumption in the long-run whether it is the past consumption of the household itself that creates the habit (an internal habit) or the consumption of society in general that makes the household used to the idea of consuming more (an external habit). A modest amount of habit formation can substantially reduce the strength of consumption-leisure separability needed to counteract the decline in the marginal utility of consumption, but will not eliminate it. Therefore, it has a good chance of bringing the implied degree of consumption-leisure substitutability in line with the decline in consumption observed at retirement. In the literature, consumption habits have typically been modeled by a distributed lag of past consumption, but it is not clear that this is the best way to model habit formation. A principled theoretical investigation of habit formation can provide insight on this issue along with all of the other issues discussed in this proposal.

Durability of leisure is a less obvious possibility. If, in effect, new retirees have a backlog of leisure activities they are eager to pursue, it may be a while before they go through this backlog and get around to using their extra leisure to substitute for consumption expenditures. This modification is unlikely to be adequate all by itself, since by itself it implies that consumption would eventually fall by just as much as the drop in labor income predicted by the additively time-separable utility function calibrated to match long-run labor supply and intertemporal substitution in consumption evidence. But in conjunction with the other modifications, durability of leisure could help.

Finally, job quality tends to covary with the real wage and consumption in a way that helps to counteract the fall in the marginal utility of consumption. Those who work long hours despite high incomes may do so because they have challenging, meaningful jobs in pleasant work environments. Because job quality and income covary positively across time, people, and countries, job quality can potentially explain a lot of the observed long-run labor supply facts without resort to such strong consumption-leisure substitutability. My advisee, Brahima Coulibaly (2002) has recently found evidence for the view that job quality can matter in this way. But the full theoretical implications remain unexplored. One way of modeling job quality is with the modified utility function Σ βt [H(Ct,Nt) + Ω(Zt,Nt)], where Z represents the quality of jobs available to the household, H represents the part of the utility function having to do with time spent at home, while Ω represents the part of the utility function having to do with time spent at work. In this form of utility, both parts of the utility function contribute to the disutility of labor that feeds into the real wage, but all of the consumption-leisure substitutability is generated by H.

Policy Implications: The striking thing about the theory above is that it reverses the direction of the retirement-saving puzzle. Instead of the question “Why does consumption fall at retirement?” the question becomes “Why doesn’t consumption fall more at retirement?” This shift alone casts doubt on the argument that the drop in consumption observed at retirement is evidence of lack of planning or adequate preparation for retirement on the part of households. Further development of the theory is necessary in order to fully understand the observed drop in consumption at retirement.

In addition to its relevance for arguments about the sophistication of households in their retirement planning, the theory of consumption-leisure substitutability also has direct policy relevance. First, to the extent that leisure can substitute for consumption, a lower replacement ratio will be adequate for retirement. Second, both habit formation and durability of leisure would imply that consumption needs should be somewhat higher in the years immediately after retirement than later on.[8] This has obvious implications for the optimal age path of social-security benefits if some households are not adequately prepared with their own savings for retirement. Third, the theory of job quality above has important implications for the likely changes in the age of retirement over the next fifty years. To the extent that jobs become more enjoyable, while avoiding making demands that are hard for people to meet as they get older, people may choose to retire at later ages. If the typical job in the future becomes enjoyable enough that the total utility from the job itself (aside from the income it generates) becomes positive, then the theory implies that improvements in the standard of living will start to increase the willingness to keep working and delay retirement, even though it may cause people to choose shorter workweeks (since the last hour of work is likely to still have negative marginal utility simply because of the first-order condition).[9] This could have a major impact on the solvency of Social Security over the next fifty years.

REFERENCES

Attanasio, Orazio P. (1998). ``Consumption Demand,'' NBER Working Paper \# 6466 (March).

Attanasio, Orazio P., and Martin Browning (1995). ``Consumption Over the Life Cycle and over the Business Cycle,'' American Economic Review 85 (December), 1118--1137.

Attanasio, Orazio P., and Guglielmo Weber (1993). ``Consumption Growth, the Interest Rate and Aggregation,'' Review of Economic Studies 60, 631--649.

Attanasio, Orazio P., and Guglielmo Weber (1995). ``Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure

Survey,'' Journal of Political Economy 103, 1121--1157.

Banks, James, Richard Blundell, and Sarah Tanner (1998). “Is There a Retirement Saving Puzzle?” American Economic Review (September), 769-788.

Barsky, Robert, Thomas Juster, Miles Kimball and Matthew Shapiro (1997). “Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study,” Quarterly Journal of Economics 112 (May), 537-579.

Basu, Susanto and M.S. Kimball, (2002). “Long-Run Labor Supply and the Elasticity of Intertemporal Substitution for Consumption,” unpublished, University of Michigan.

Browning, Martin, and Costas Meghir (1991). ``The Effects of Male and Female Labor Supply on Commodity Demands,'' Econometrica 59 (July), 925--951.

Coulibaly, Brahima, (2002). “Changes in Job Quality and Trends in Labor Supply,” unpublished, University of Michigan.

Hall, Robert, (1988), “Intertemporal Substitution in Consumption,” Journal of Political Economy 96 (April), 339-357.

Hamermesh, Daniel (1984). “Consumption During Retirement: The Missing Link in the Life-Cycle Hypothesis.” Review of Economics and Statistics 66, 1-7.

Priority Research Areas

3 . Social Security, private saving, and other retirement income. 7. Demographic and social change.

Project Timeline

Preliminary research and Research Brief completed by April 1, 2003. Research completed by August 15, 2003. Working paper completed by September 30, 2003.

Budget

The budget requested for this project is $100,000. This covers the time of the principal investigator, which is needed to perform the analysis.

Budget Justification

The budget primarily covers the time of the PI to carry out this analysis. Because this is a theory project, that is the main cost. Amounts for materials, supplies, and duplication will cover expenses relating to writing and distributing the reports coming from this project.

Overlap and Co-funding

This project has no overlap with any other funded or proposed project. In particular, it is unconnected with the projects on the retirement elasticity that Matthew Shapiro and I are pursuing and have proposed. Without detracting from the value and relevance of this proposal, let me say that I consider the project Matthew Shapiro and I proposed (“The Retirement Elasticity: Survey Evidence”) to be the more urgent proposal both scientifically and in policy relevance, particularly since it leverages the theoretical findings of a project currently supported by the MRRC/Social Security Administration. But given funding, I will have adequate time to do both projects.

[1] See Hamermesh (1984) and Banks, Blundell and Tanner (1998).

[2] See Browning and Meghir (1991), Attanasio and Weber (1993, 1995), Attanasio and Browning (1995) and the papers cited in Attanasio (1998).

[3] There are some forms of consumption that seem complementary with leisure, such as travel. This and the question about the quantitative size of the substitutability between consumption and leisure in the examples given above means that it is important to develop a theory of the interaction between consumption and leisure that focuses on summary measures of the degree of substitutability between consumption and leisure as proposed below.

[4] By cancellation of income and substitution effects on labor supply, I mean the well-documented fact that proportionally higher real wages for all members of a household, whether over time, across households, or across countries, have relatively little effect on the total amount of labor supplied. Relevant chapters and references are easy to find in the Handbook of Labor Economics.