What Accounts for the Variation in Retirement Wealth Among U.S. Households? B

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9-2001 What Accounts for the Variation in Retirement Wealth Among U.S. Households? B. Douglas Bernheim Stanford University

Jonathan Skinner Dartmouth College

Steven Weinberg The Board of Governors of the Federal Reserve System

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Recommended Citation Bernheim, B. Douglas; Skinner, Jonathan; and Weinberg, Steven, "What Accounts for the Variation in Retirement Wealth Among U.S. Households?" (2001). Open Dartmouth: Faculty Open Access Articles. 2406. https://digitalcommons.dartmouth.edu/facoa/2406

This Article is brought to you for free and open access by Dartmouth Digital Commons. It has been accepted for inclusion in Open Dartmouth: Faculty Open Access Articles by an authorized administrator of Dartmouth Digital Commons. For more information, please contact [email protected]. What Accounts for the Variation in Retirement Wealth Among U.S. Households?

By B. DOUGLAS BERNHEIM,JONATHAN SKINNER, AND STEVEN WEINBERG*

Even among households with similar socioeconomic characteristics, saving and wealth vary considerably. Life-cycle models attribute this variation to differences in time preference rates, risk tolerance, exposure to uncertainty, relative tastes for work and leisure at advanced ages, and income replacement rates. These factors have testable implications concerning the relation between accumulated wealth and the shape of the consumption proﬁle. Using the Panel Study of Income Dynamics and the Consumer Expenditure Survey, we ﬁnd little support for these implications. The data are instead consistent with “rule of thumb,” “mental accounting,” or hyperbolic discounting theories of wealth accumulation. (JEL D1, D91, E21)

Wealth and saving vary considerably, even the observed variation in savings for retirement among households with similar socioeconomic within the context of standard life-cycle models characteristics (Steven Venti and David Wise, with rational, farsighted optimization. House- 1998; Annamaria Lusardi, 1999). The interpre- holds may differ with respect to patience (the tation of this variation is a pivotal issue. If rate of pure time preference), risk tolerance, saving reflects rational, farsighted optimization, exposure to uncertainty, health status, perceived then low saving is simply an expression of life expectancy, relative tastes for goods com- preferences—saying that someone saves “too plementary with leisure at advanced ages, levels little” is comparable to asserting that he or of work-related expenses, lifetime earnings, or she doesn’t listen to enough classical music income replacement rates. In this paper, we test (Edward Lazear, 1994). If, however, house- for the presence of these factors by studying holds are shortsighted, boundedly rational, data on wealth, income, and consumption dynamically inconsistent, impulsive, or prone drawn from the Panel Study of Income Dynam- to regret, then the adequacy of saving is a ics (PSID) and the Consumer Expenditure Sur- well-posed and important empirical issue (B. vey (CEX). Douglas Bernheim, 1995). Explanations for the variation in wealth that Various factors could in principle account for are based on the life-cycle framework fall into three broad categories. Each category has a dis- tinctive and testable empirical implication. Fac- * Bernheim: Department of Economics, Stanford Uni- tors in the first category create systematic versity, Stanford CA 94305, and National Bureau of Eco- correlations between the household’s wealth nomic Research (e-mail: [email protected]); Skinner: Department of Economics, Dartmouth College, and its average consumption growth rate. For Hanover NH 03755, and National Bureau of Economic example, if differences in saving result from Research (e-mail: [email protected]); Wein- differences in patience, those who save more berg: Board of Governors of the Federal Reserve System, should also exhibit higher consumption growth Washington DC 20551 (e-mail: steven.a.weinberg@ rates. Factors in the second category create sys- frb.gov). We are indebted to Richard Blundell, Martin Browning, Karen Dynan, Leora Friedberg, Alan Gustman, tematic correlations between wealth and one- Annamaria Lusardi, Jonathan Parker, Douglas Staiger, time changes in consumption at retirement. For Steven Venti, seminar participants at the NBER, MIT, example, households with higher work-related Northwestern University, SUNY Albany, and the Universi- expenses should accumulate less wealth and ties of California-Berkeley, Chicago, Georgia, Rochester, and Wisconsin, and two anonymous referees for very help- experience larger declines in measured con- ful comments. We gratefully acknowledge financial support sumption at retirement. Likewise, an unex- from the National Institute on Aging. pected early retirement prematurely terminates 832 VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 833 wealth accumulation, and should depress con- ment is larger for households with relatively sumption by forcing the retiree to revise his or less generous pension and social security bene- her expectations about lifetime resources. Fac- fits. Although our three central results challenge tors in the third category give rise to systematic the validity of standard life-cycle models, they correlations between accumulated wealth and do not rule out a variety of behavioral theories. the level of consumption. Households with We discuss these in more detail below. strong bequest motives, for example, should This paper is related to several previous stud- tend to consume less throughout the life cycle. ies. Daniel Hamermesh (1984) and Randall Our first central finding is that there is essen- Mariger (1987) find that consumption declines tially no relation between accumulated wealth sharply as households move into retirement. and consumption growth rates either prior to Hamermesh also infers that consumption at re- retirement or after retirement. This suggests that tirement is not sustainable; Laurence Kotlikoff a wide range of factors (including differences in et al. (1982) dispute this conclusion. A. Leslie patience, as measured by pure rates of time Robb and John Burbridge (1989) find that, preference) fail to provide even contributory among Canadians, consumption at retirement explanations for the observed variations in ac- falls more sharply for blue-collar workers than cumulated wealth. for white-collar workers. Jerry Hausman and Our second central finding is the existence of Lynn Paquette (1987) link the decline in (non- a correlation between wealth and the decline in medical) consumption at retirement to unex- consumption at retirement. This is superficially pected and involuntary job loss, often resulting consistent with the second category of explana- from health problems. James Banks et al. (1998) tions mentioned previously. However, these hy- track consumption and earnings of synthetic potheses do not survive closer scrutiny. The British cohorts through retirement years and impact of retirement on work-related expenses document a sharp drop in average consumption and leisure substitutes is too small to explain the at age 65. They argue that this finding is difficult decline in consumption, and other expenditures to explain with reference to conventional eco- also fall sharply. Moreover, there is little evi- nomic factors such as a reduction in anticipated dence that the decline in potentially work- labor force participation or work-related expenses. related expenses is larger for households with Eric Engen et al. (1999) maintain that it is possible less wealth. Nor is our second finding the con- to account for the observed variation in wealth sequence of unanticipated events that affect the using a life-cycle model with heterogeneous earn- timing of retirement: the pattern persists even ings chocks and pension coverage. However, their when we remove these effects statistically. model presupposes consumption smoothing at re- Taken together, our first two findings imply that tirement, which is inconsistent with the behavioral a broad range of standard life-cycle consider- patterns documented below. ations are collectively incapable of accounting for the observed variation in wealth, holding I. Theoretical Preliminaries constant income profiles. Differences in income profiles should also In discussing the potential sources of varia- contribute to variation in wealth. For instance, tion in retirement wealth, it is useful to distinguish households with relatively generous pensions between variation in income profiles and all other and social security benefits should accumulate factors. We consider these in reverse order. less wealth to smooth consumption through retirement. Yet in practice, we find that house- A. Sources of Variation in Wealth, Fixing holds with lower income replacement rates do Income Profiles not have significantly higher wealth/income ratios. One can explain this finding in the context For households with similar earnings his- of life cycle theory if pension coverage is cor- tories, pensions, inheritances, and retirement related with tastes for saving. However, it is ages, those with less wealth at retirement much more difficult to account for the observed consumed more prior to retirement, and will pattern in light of our third central finding: the consume or bequeath less after retirement. By discontinuous drop in consumption at retire- itself, the budget constraint does not tie down 834 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

the characteristics of the consumption profile where Ci is consumption in period i, Et is the more precisely. For specific models, the con- expectations operator (conditional on infor- sumption profile accommodates the budget mation available at time t), ␦ is the standard constraint in one (or more) of three ways. (constant) pure rate of time preference, and ␲ First, for those with lower wealth at retire- k is the probability of dying before period k, ment, consumption may grow less rapidly conditional upon surviving to period k Ϫ 1. over the life cycle. Second, consumption may Assume for the moment that income is poten- decline discontinuously at retirement, and this tially uncertain and independently distributed discontinuity may be larger for those with less across periods, but that the age of retirement accumulated wealth. Third, those with less is fixed. accumulated wealth at retirement may be- Maximization of (1) subject to a resource queath less, consuming more throughout their constraint yields the following first-order con- lives.1 By studying the relations between ac- dition: cumulated wealth and consumption profiles, one can therefore identify the factors that do Ј͑ ͒ ϭ ␣ E ͕UЈ͑C ϩ ͖͒, and do not contribute to the observed varia- (3) U Ct t t t 1 tion in wealth. where 1. Factors Affecting the Slope of the Con- sumption Profile.—Variation in accumulated ͑ ϩ ͒͑ Ϫ ␲ ͒ 1 r 1 t ϩ 1 wealth at retirement could in principle result (4) ␣ ϵ . from any factor that produces variation in the t 1 ϩ ␦ slope of the consumption profile. Subject to the qualifications discussed below, rising consump- Taking a second-order Taylor series expan- tion profiles correspond to high accumulation, sion of (3) yields the familiar Euler equation whereas falling consumption profiles correspond to low accumulation. E ͑C ϩ ͒ Ϫ C 1 ␺ t t 1 t Ϸ ␥ͩ Ϫ ͪ ϩ ␴2 (5) 1 ϩ , To illustrate, consider a time-separable utility C ␣ 2 t 1 function of the form t t where ␥ is the intertemporal elasticity of substitution, ␺ reflects the household’s precaution- ϱ ary inclinations, and ␴ is the standard ϭ ͑ ͒ ϩ ͸ ␭ ͑ ͒ t ϩ 1 (1) Ut U Ct Etͭ t,s U Cs ͮ , ϩ deviation of consumption in period t 1. s ϭ t ϩ 1 Equation (5) tells us that the slope of the consumption profile depends on the rate of interest, with the pure rate of time preference (patience), perceived survival probabilities, and a precaution- Ϫ s ary motive, as captured in the final term (see, 1 s t (2) ␭ ϭ ͩ ͪ ͹ ͑1 Ϫ ␲ ͒, e.g., Angus Deaton, 1991; Karen Dynan, 1993; t,s 1 ϩ ␦ k k ϭ t ϩ 1 Michael Palumbo, 1999). Variation in any of these factors can produce variation in the shape of the consumption profile and associated variation in wealth. Consider the effects of variation in patience. 1 As a matter of logic, there are obviously other possi- If the elasticity of substitution is close to zero, bilities; for example, consumption may decline discontinu- ␦ ously at some point after retirement, and this point may then variation in does not alter the consump- occur at a more advanced age for those who reach retire- tion trajectory, and therefore cannot account for ment with greater wealth. This pattern might arise in a observed variation in wealth. Early studies model with heterogeneity in finite, deterministic life spans. placed ␥ near zero (Robert Hall, 1988), but The assumption of a deterministic life span is, however, unattractive. More generally, variation in survival probabil- more recent evidence supports a small positive ities gives rise to variations in the slope of the consumption elasticity (Orazio Attanasio and Guglielmo We- profile—an example of the first pattern. ber, 1993, 1995). Consequently, one would ex- VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 835

FIGURE 1A. AGE–CONSUMPTION PROFILES FOR HIGH- AND LOW-TIME-PREFERENCE HOUSEHOLDS

FIGURE 1B. AGE–WEALTH PROFILES FOR HIGH- AND LOW-TIME-PREFERENCE HOUSEHOLDS pect the slope of the consumption profile to vary dictates the consumption growth rate (Deaton, with ␦. All else equal, impatient households 1991; Chris Carroll, 1997). Thus, consideration should consume more than patient households of liquidity constraints disrupts the clean pre- early in life, and less later in life. Patient house- diction of the basic model (a positive correlation holds should therefore accumulate more wealth between consumption growth and assets accu- for retirement (see Figure 1). This produces a mulated at retirement). However, because positive correlation between the slope of the households approaching retirement generally consumption profile and accumulated wealth at hold nontrivial assets and anticipate significant retirement. near-term declines in nonasset income (Banks et For a liquidity-constrained household or a al., 1998; Attanasio et al., 1999), we doubt that “buffer-stock” saver, the income growth rate this is a significant problem for us in practice, 836 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001 except possibly at the lowest end of the wealth understood (Laibson and Christopher Harris, distribution. 1998; Bernheim et al., 1999). Equation (5) implies that, like variations in the pure rate of time discount, variations in 2. Factors Affecting the Change in Con- perceived longevity (survival probabilities), in- sumption at Retirement.—Variation in wealth come uncertainty, and tastes for precaution ro- may also be attributable to factors that produce tate the consumption profile.2 Thus, variations downward, discontinuous jumps in consump- in wealth accumulation that result from any of tion at retirement. By the logic of the budget these factors should manifest themselves constraint, the existence of this discontinuity through a positive correlation between retire- generally implies higher consumption, and ment wealth and the growth rate of consumption therefore less wealth accumulation, before re- either before retirement, after retirement, or tirement. Figure 2 illustrates. We consider two both. The absence of such correlations would be households that are identical in all respects, inconsistent with the hypothesis that these fac- except that one prefers a flat consumption pro- tors contribute to the observed variation in file, whereas the other prefers a consumption wealth. profile with a consumption discontinuity at re- So far, we have focused exclusively on the tirement. Note that the latter household holds standard life-cycle framework. Additional con- less wealth throughout the life cycle. If such siderations emerge in alternative behavioral factors account for the observed variation in models (e.g., Richard Thaler and Hersh Shefrin, wealth, one should observe a negative correla- 1981; Shefrin and Thaler, 1988; George Aker- tion between retirement wealth and the size of lof, 1991; David Laibson, 1997). For example, the discontinuity. following Laibson, one can introduce dynamic Factors that can generate sharp changes in inconsistency by inserting a parameter, ␤ Ͻ 1, consumption at retirement include the existence measuring the extent to which individuals dis- of work-related expenses and/or preferences for count all future utility relative to today’s utility, leisure substitutes or complements (William into equation (1): Ghez and Gary Becker, 1975; Banks et al., 1998; Marianne Baxter and Urban Jermann, 1999; and ϱ Monika Butler, 2001). Variation in these factors ϭ ͑ ͒ ϩ ␤ ͸ ␭ ͑ ͒ (6) Ut U Ct ͭ t,s U Cs ͮ . may therefore provide a contributory explanation s ϭ t ϩ 1 for differences in retirement wealth. If this explanation is valid, the drop in spending at retirement Behavior then corresponds to the equilibrium should be larger for work-related expenditures of a game played by successive incarnations than that for non-work-related expenditures, and of the decision maker. As Laibson shows, larger for leisure substitutes than for leisure com- there is a tendency for dynamically inconsis- plements. One should also observe a stronger neg- tent planners to save too little, exhibiting ap- ative correlation between retirement wealth and parently high rates of time preference. If the absolute size of the discontinuity for expendi- differences in time consistency explain the ture categories that are more closely work-related observed variations in retirement wealth, one and more substitutable for leisure. In the absence would therefore still expect to find a positive of these patterns, we would infer that this expla- correlation between retirement wealth and the nation does account for a significant fraction of the consumption growth rate. However, it is im- variation in retirement wealth. portant to emphasize that the implications of these Variation in retirement wealth may also re- models for retirement saving are still imperfectly sult from unexpected events that affect the timing of retirement, such as sudden deterioration of health or loss of job (Peter Diamond and 2 These factors may change over the life cycle. For Hausman, 1984; Hausman and Paquette, 1987). example, households may have similar survival probabili- For those who retire unexpectedly early—and ties and consumption growth rates but different levels of wealth today because they expect to have different survival as a consequence retire with less than desired probabilities (and hence different consumption growth wealth—retirement coincides with “news” of a rates) in the future. negative shock to permanent income. This gives VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 837

FIGURE 2A. AGE–CONSUMPTION PROFILE WITH (AND WITHOUT) A DISCRETE SHIFT IN CONSUMPTION AT RETIREMENT

FIGURE 2B. AGE–WEALTH PROFILE WITH (AND WITHOUT) A DISCRETE SHIFT IN CONSUMPTION AT RETIREMENT rise to a negative correlation between retirement Stepping outside the life-cycle framework, wealth and the decline in consumption at retire- one can imagine other explanations for varia- ment. One can test this hypothesis by studying tions in retirement wealth that are related to residual changes in retirement consumption after differences in the size of the consumption dis- controlling for unexpected retirement shocks.3 We continuity at retirement. Suppose, for example, elaborate on this point in Section II. that saving is somewhat haphazard, but that individuals evaluate their ﬁnances upon reach- ing retirement, adjusting spending as necessary 3 Banks et al. (1998) examine changes in consumption to accommodate resources. In that case, the around age 65 for British workers. Because the retirement adequacy of savings at retirement is “news.” hazard spikes at this age, their procedure removes the idiosyncratic news from retirement events, and implicitly yields an estimate of the correlation between a predictable deter- minant of retirement (being 65) and changes in consump- that allows us to estimate the relation between consumption tion. In the same spirit, we implement a two-stage procedure and predictable changes in retirement. 838 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

Those with bad news (inadequate savings) pre- the budget constraint (Dynan et al., 2000). Fig- sumably decrease their consumption, whereas ure 3 illustrates hypothetical consumption and those with good news (excessive savings) in- wealth profiles for an individual with no bequest crease it. Alternatively, individuals may regard motive, and one who wishes to bequeath some current income as more “spendable” than assets, portion of lifetime wealth. At every age, wealth particularly those held in retirement accounts or is higher for the second household than for the converted into annuities (Thaler and Shefrin, first. Thus variation in wealth might occur if, for 1981; Shefrin and Thaler, 1988; Thaler, 1994). example, there are significant differences in the Consumption might then decline at retirement strength of bequest motives across the popula- simply because current income falls. If individ- tion [for supporting empirical evidence see Bern- uals differ in the extent to which they exercise heim (1991) and John Laitner and F. Thomas self-discipline over spendable funds, then those Juster (1996)]. Note that theories of this kind have with little self-discipline should accumulate less no implications concerning the shape of the con- wealth for retirement and experience greater sumption profile, or its relation to wealth. declines in spending than those with greater self-discipline. For both of these hypotheses, B. Variation in Wealth Resulting from the predicted patterns (a drop in spending at Differences in Income Profiles retirement and a negative correlation between wealth and the size of this discontinuity) should Survey data generally show that wealth at any cut across consumption categories, and should age rises significantly with proxies for lifetime emerge even when retirement is predictable. resources, such as household earnings. Al- Thus, in principle, it is possible to distinguish though this pattern certainly helps to account for these alternatives empirically from the standard the fact that some households accumulate more life cycle factors discussed previously.4 wealth than others, it fails to discriminate between interesting behavioral hypotheses. Varia- 3. Factors Affecting the Overall Level of tions in retirement wealth may also result from Consumption.—Variation in retirement wealth variations in the shape of the income profile. could result from factors that influence the This observation motivates a more promising overall level of consumption throughout the line of inquiry. life cycle, with bequests adjusting to satisfy One important characteristic of the income profile is the ratio of preretirement to postretirement nonasset income (the earnings replace- 4 We comment briefly on three other potential sources of ment rate). In practice, social security and correlation between wealth and predictable consumption private pension benefits account for the bulk of changes at retirement. First, R. Glenn Hubbard et al. (1995) postretirement nonasset income, and informa- suggest that asset-based means testing for welfare programs tion on the size of these benefits is readily could induce lower income households to hold very low (or zero) levels of wealth. Their model predicts a sharp con- available. Consequently, households nearing re- sumption decline at retirement, but only for the lowest tirement should be able to predict earnings re- income group; households in the upper half of the income placement rates to a high degree of accuracy. distribution smooth consumption through retirement. We Standard life-cycle models imply that, fixing nevertheless find evidence of a negative correlation between wealth and the decline in consumption at retirement even preferences, household saving should vary in- among households in the top half of the income distribution. versely with predictable differences in earnings Second, buffer-stock models imply that consumption may replacement rates. In practice, these rates are track predictable components of income (Deaton, 1991; probably correlated with unobserved household Carroll, 1997). However, these models typically predict characteristics, such as tastes for saving [pen- positive savings and consumption smoothing around retirement. Third, different households may anticipate different sions are more common among the thrifty (Wil- changes in relative prices after retirement, resulting perhaps liam G. Gale, 1998)]. However, regardless of from discount programs that target the elderly. We doubt earnings replacement rates or tastes for saving, these discounts are large enough to account for the observed the life cycle model implies that households changes in spending, particularly in expenditure categories such as groceries (see the discussion of food consumption, should still adjust saving to smooth consump- below). Also, eligibility for discounts is typically tied to tion. Consequently, even if earnings replace- age, rather than work status. ment rates are related to tastes for saving, they VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 839

FIGURE 3A. AGE–CONSUMPTION PROFILES WITH (AND WITHOUT) A BEQUEST MOTIVE

FIGURE 3B. AGE–WEALTH PROFILES WITH (AND WITHOUT) A BEQUEST MOTIVE should not be correlated with the size of the workers with tastes for leisure substitutes self- decline in consumption at retirement, at least select into jobs with poor pension coverage, or among those with nonnegligible retirement if employers offer less generous pensions to savings. workers with higher work-related expenses. As This conclusion must be modiﬁed if tastes for before, one can test these hypotheses by exam- thrift are also related to the magnitude of the ining consumption proﬁles for disaggregated consumption discontinuity at retirement. We expenditure categories. have already discussed the factors that could generate such a relation (Section I, subsection II. Empirical Models and Estimation Strategy A.2). A spurious correlation between earnings replacement rates and the size of the consump- As explained in Section I, one can distin- tion discontinuity at retirement could arise if guish between competing explanations for the 840 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

observed variation in wealth accumulation by the correlated structure of the within-household comparing aspects of consumption dynamics covariance matrix. (growth rates and discontinuities at retirement) Our primary objective is to estimate the func- ␰ across households with differing levels of assets tion (t, Xi). This function describes the aver- and rates of earnings replacement. In this sec- age consumption growth rate for a household tion, we outline our empirical strategy for mak- with characteristics Xi at age t, removing the ing these comparisons. effects of any changes in the household’s de- Our general approach is to estimate functions mographic characteristics (that is, assuming ⌬ ϭ ␰ of the following form: Zit 0). In this sense, we think of (t, Xi)as household i’s “baseline” consumption growth rate at age t. By estimating a sufficiently flex- ⌬ ͑ ͒ ϭ ␰͑t, X ͒ ϩ ⌫⌬Z ϩ ␨ . (7) ln Cit i it it ible functional form for ␰, we can determine whether consumption growth rates are system- ⌬ ϵ Ϫ In this equation, yt yt ϩ 1 yt for any atically correlated with wealth accumulation, variable y, time t is measured relative to retire- and we can ascertain the extent to which con- ment (t ϭ 0 corresponds to the year of retire- sumption discontinuities at retirement are cor- ment), Cit represents the level of consumption related with assets and income replacement in period t, ␰ is a function (discussed in greater ratios. detail below), Xi is a vector of fixed household Our specific approach is to assume that ⌫ characteristics, is a vector of parameters, Zit is a vector of demographic factors that may ␰͑t, X ͒ ϭ X ͑␤WI͑t Ͻ 0͒ change through time (such as the number of (8) i i individuals in the household), and ␨ is a dis- it ϩ ␤0I͑t ϭ 0͒ turbance term. It is natural to think of (7) as a consumption ϩ ␤1I͑t ϭ 1͒ Euler equation, augmented to allow for shifts in family composition and other demographic de- ϩ ␤RI͑t Ͼ 1͒), terminants of marginal utility (Attanasio et al., 1999). Indeed, it is possible to derive this expression from a simple model in which single- where I٪ is an indicator function that returns a ⌫ period utility is given by U(Citexp( Zit)) and value of unity when the expression is satisfied U٪ belongs to the CRRA family of utility and zero otherwise, and ␤W, ␤0, ␤1, and ␤R are functions, or more generally as an approxima- vectors of parameters. In effect, we allow tion of the Euler equation. Within this familiar households to have four different consumption ␰ framework, the function (t, Xi) captures the growth rates pertaining (respectively) to the effects of household preferences (such as the years before retirement, the first year of retire- pure rate of time preference), environmental ment, the second year of retirement, and subse- parameters (such as life expectancy, income quent years. Moreover, each of these four uncertainty, and rates of return), and aging (e.g., growth rates varies with household characteris- through its effects on survival probabilities) on tics. We estimate separate growth rates for the the slope of the consumption profile. first and second years of retirement to allow for If one adopts the Euler equation interpreta- the possibility that some adjustments to changes tion of (7), then it is natural to assume that the in work status may be delayed. ␨ consumption shock it is serially uncorrelated Though equation (7) is our primary empirical and independent of all information available to specification, in some instances we also esti- the household at time t. However, if household mate functions of the following form: consumption is subject to measurement error, ͑ ͒ ϭ ␮ ϩ ␺͑ ͒ ϩ ⍀ ϩ ␩ the estimated residuals for equation (7) may (9) ln Cit i t, Xi Zit it , exhibit negative serial correlation. Conse- ␮ ␺ quently, when we estimate equation (7), we use where i is a household fixed effect, is a clustered Huber–White standard errors (Jeffrey function (discussed in greater detail below), ⍀ ␩ Wooldridge, 2001, Chapter 10) to account for is a vector of parameters, it is a mean-zero VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 841

random variable, and all other symbols are de- every observation for each household, including fined as before. It is important to understand data from nonconsecutive years, even when in- that equations (7) and (9) are mutually consis- formation is unavailable for the intervening tent. To see this, define ␶ and T, respectively, as year(s). the first and last year in which the household is In all likelihood, the error terms in equation ϵ ¥t ␨ ␩ observed. Let vit k ϭ ␶ ϩ 1 it (the cumulative (9), it, are heteroskedastic and autocorrelated. ␶ ␨ innovation in consumption since time ) and This is certainly the case if the it are indepen- ៮ ϵ Ϫ ␶ Ϫ1 ¥T vi (T ) k ϭ ␶ ϩ 1 vik (household i’s dent, as implied by the permanent income average consumption innovation). Then (9) fol- hypothesis. As before, clustered robust Huber– ␮ ϵ ϩ ៮ lows directly from (7), with i ln(Ci␶) vi , White standard errors are used to correct for the ␩ ϵ Ϫ ៮ ␺ ϵ ¥t it vit vi , and (t, Xi) k ϭ ␶ ϩ 1 resulting nondiagonal heteroscedastic covari- ␰ (k, Xi). Notice that the individual fixed effect ance matrix. ␮ i reflects both household specific permanent To this point, we have assumed that Xi, Zit, income [as measured by ln(Ci␶)] as well as the and the timing of retirement are exogenous with household’s average consumption innovation respect to the consumption innovations. These ៮ ␩ vi. Likewise, in constructing the error term it, assumptions are potentially problematic. To the ៮ we subtract vi. These operations are necessary extent Xi measures characteristics at retirement, because, in a limited number of years, the real- it may be correlated with consumption shocks ized average of the error terms vit is not zero for occurring before retirement. Furthermore, unan- each household; particular households may on ticipated changes in Zit and in retirement plans average experience positive or negative innova- may be related to permanent per capita income ៮ 6 tions. Removing vi from the error term assures shocks, which affect consumption. We discuss ␩ 5 us that it has a mean of zero. each of these possibilities. When we estimate equation (9) rather than The potential endogeneity of Zit is least trou- equation (7), our primary interest is in the func- blesome. If unanticipated changes in these vari- tion ␺ (specifically, the manner in which this ables (e.g., the death of a family member) are function varies with household characteristics). indeed related to permanent per capita income Accordingly, we adopt the following flexible shocks, then one simply reinterprets the coeffi- functional form: cient vector ⌫ (or ⍀) as reflecting, at least in part, the impact of demographic “news” on consumption. Because we are only concerned with (10) ␺͑t, X ͒ ϭ X ␤ , i i t the properties of the function ␰ (or ␺), this reinterpretation of ⌫ (or ⍀) is innocuous for our ␤ where t is a vector of parameters. Note that purposes. this formulation permits the parameter vector to The potential endogeneity of Xi is a more vary freely with age relative to retirement t. serious concern. To test the hypotheses outlined ␺ Thus, estimates of imply an expected con- in Section II, we choose the elements of Xi to sumption trajectory for each household that de- include measures of wealth and income replace- pends on the fixed characteristics of the ment rates at retirement, which may be related household. Even though it is possible in princi- to consumption shocks that occurred prior to ␤ ple to estimate a separate t each value of t,in retirement. For the reasons discussed in Section practice this requires the estimation of a very I, subsection B, we doubt that these effects are large number of parameters. We therefore im- quantitatively important for income replace- ␤ pose the restriction that t is constant within ment rates. However, it is possible that wealth at consecutive two-year intervals. Note that equa- retirement and consumption shocks before re- tion (9), unlike equation (7), permits us to use tirement are related to common third factors. The primary candidates for these third factors

5 Normally, one should be cautious about estimating random-walk models with fixed effects. The problem is not serious in this case, however, because our primary objective 6 For these purposes, the unexpected departure (e.g., is simply to quantify average consumption relative to a death) of a nonworking household member constitutes a per benchmark year, conditioning on X and Z. capita income shock. 842 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001 are shocks to permanent income. For exam- allow for a baseline consumption trend as well ple, the receipt of a large, unanticipated in- as a discontinuity at retirement.7 It follows that heritance prior to retirement would produce a ␺͑ ͒ ϭ ␤ ϩ ͑ ␤0͒ ͑ Ն ͒ significant contemporaneous consumption (12) t, Xi t * Xi I t 0 . shock while at the same time elevating the level of wealth at retirement. This would tend Substituting (12) into (9), switching time sub- to induce a positive correlation between the scripts from age relative to retirement (t)to ϭ ϩ wealth ratio and the consumption growth rate absolute age (s ri t), and separating out prior to retirement (but not after retirement), the predictable and unpredictable components biasing our procedure in favor of the theories of retirement, we obtain that stress a connection between growth rates ϭ ␮ ϩ ␤ of consumption and wealth. Unless the esti- (13) ln Cis ˆ i s * mated relation differs markedly before and ϩ͑ ␤0͒ ͑ Ն ͉ ͒ after retirement, the magnitude of the bias is Xi Pr s ri Yis probably small. ϩ ⍀ ϩ ␷ In theory, one could remove bias created by Zis is , the potential endogeneity of retirement wealth ␮ ϵ ␮ Ϫ ␤ through the use of appropriate instrumental where ˆ i i ri *. We express the prob- Ն ͉ variables, for example, by predicting wealth at ability of being retired at age s, Pr(s ri Yis), retirement based on information obtained prior as a function of deterministic household char- to the household’s earliest consumption obser- acteristics Yis. The error term is defined as vation. In practice, the available instruments, follows: such as the value of the primary home and ␷ ϭ ͑ ␤͓͒ ͑ Ն ͒ business income are, at best, only moderately (14) is Xi I s ri good predictors of retirement wealth, so this Ϫ ͑ Ն ͉ ͔͒ ϩ ␩ procedure involves considerable loss of preci- Pr s ri Yis is . sion. Nevertheless, we use these instrumental variables to check the reliability of our main Because the probability of retirement is not findings. correlated with the transformed consump- Finally, we consider the possibility that the tion error term, we can obtain consistent es- timing of retirement is stochastic, and that pre- timates by treating (13) as a standard regres- mature retirement produces negative consump- sion equation. Identification of the baseline tion innovations. As explained in Section I, retirement effect depends on the fact that the re- subsection A.2, this would create a negative tirement hazard function is nonlinear in age (spik- correlation between retirement wealth and the ing at ages 62 and 65), so we also add a quadratic magnitude of the decline in consumption at age term. retirement. To distinguish between the various Besides substituting the probability of retire- hypotheses discussed in Section I, subsection A, ment for the retirement dummy variable, as in it is important to determine whether those with equation (13), we also modify our specification low retirement wealth experience larger de- by replacing wealth at retirement (in the vector clines in consumption at retirement, even when Xi) with a measure of wealth that is not con- the timing of retirement is properly anticipated. taminated by surprises about the timing of re- To do this, we must remove the effects of sto- tirement. Intuitively, we would like to measure chastic retirement. wealth at some standardized age that is suffi- Because data limitations force us to construct ciently advanced for individuals to have accu- predictions of retirement based on relatively mulated a significant fraction of their retirement few instruments, we must simplify our model resources, but early enough to precede retire- somewhat. In particular, assume that

7 ␰͑ ͒ ϭ ␤ ϩ ͑ ␤0͒ ͑ ϭ ͒ As we will see, the data support the simplifying as- (11) t, Xi * Xi I t 0 . sumptions that the baseline consumption trend is independent of household characteristics, and that it is the same Note that (11) is a special case of (8); here we before and after retirement. VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 843 ment for that vast majority of households. Un- the first year in which the household is retired;10 fortunately, we do not have access to this transition period data are excluded from our information. Instead, we use the data on wealth analysis. In the course of our empirical investi- that we do have, and adjust it to remove the gation, we controlled for lengthy transitions by effects of differences in age and retirement. In including a dummy variable to identify house- particular, we regress wealth on age, age- holds that spent more than two years (but fewer squared, a retirement dummy variable, and years than five years) in transition to retirement; how- retired (treating our sample as a cross section). ever, the coefficients of this variable were rarely Using the coefficients from this regression, significant and generally not large. we then adjust each household’s wealth to a The total sample used in this analysis gener- common age and work status. This is equiv- ally includes in excess of 3,500 observations on alent to using the residuals from the wealth 430 households, with the specific number de- regression as measures of “abnormal” wealth. pending on the regression specification. The By construction, this measure of wealth is or- samples are generally unbalanced because later- thogonal to information concerning retirement. retiring households are observed for fewer years However, it is still related to a wide range of after retirement, and more years before retire- idiosyncratic, unobserved characteristics that ment, than early-retiring households. This does contribute to the unexplained variation in not, however, appear to drive our findings, as wealth at retirement. similar results are obtained when the regressions are estimated using subsamples consisting III. Data of balanced panels. Unfortunately, the PSID does not contain The primary data sample for our analysis ideal data on consumption. Although many past consists of the set of all households surveyed in researchers have used food consumption to the Panel Study of Income Dynamics (PSID) proxy for total consumption, Skinner’s (1987) with a transition to retirement between the years analysis of the Consumer Expenditure Survey 1978 and 1990. We define nonretired house- (CEX) indicates that superior measures are holds to be those with at least one member available. Specifically, by using additional in- (head or spouse) working more than 1,500 formation on consumption reported in both the hours annually. We define a household to be PSID and the CEX, such as the composition of retired if no member works more than 500 hours food expenditures, utility payments, value of annually in the current year, or in any subse- the house, and car ownership, one can increase quent year for which data are available. Natu- the predictive power of the PSID consumption rally, some individuals made the transition from index threefold.11 We use this approach below nonretired status to retired status over the course with a more restricted set of consumption indi- of several years, during which time one or more cators—food at home, food away from home member worked part-time (between 1,500 and (excluding meals at work or school), and the 500 hours).8 We restricted the sample to house- imputed or actual rental value of one’s resi- holds with transition periods of less than five dence (utilities and autos were reported only years.9 For the remaining observations, the vari- sporadically)—although we also discuss regres- able t is set equal to Ϫ1 in the last year in which sion results for each component separately. In the household is nonretired, and equal to ϩ1in certain years, the PSID did not collect information

10 Note that for someone who made the transition from 8 Households may have shifted from part time back to full-time to part-time work in 1982, and from part-time to full time as well during this transition period. See Alan fully retired in 1984, the year prior to retirement would be Gustman and Thomas Steinmeier, 1984. 1981 and the year after retirement would be 1984. 9 Thirty-nine percent of households made the transition 11 In other words, using the Consumer Expenditure Sur- to retirement in one year, 73 percent took no more than two vey data, the R2 of a regression of total consumption on years, 80 percent took no more than three years, and 85 total food consumption was 0.26; with the additional com- percent took no more than four years. Thus, the restriction ponents of consumption, the R2 rose to 0.78. This is not excludes roughly 15 percent of the potential sample. Of surprising given the importance of rental or owner-occupied these, roughly half made the transition in five or six years. housing expenses in a typical budget. 844 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001 on food consumption, and we were forced to Unfortunately, since the PSID collected com- exclude these observations from the sample.12 prehensive information on the components of As mentioned previously, equations (7) and wealth only in 1984 and 1989, we typically do (9) allow the shape of the consumption profile not directly observe wealth in the year prior to to depend on the household’s earnings replace- retirement. In such cases, we extrapolate retirement rate and retirement savings, which are ment wealth by applying the intertemporal bud- summarized by the vector Xi. To provide func- get constraint. Using observed wealth in either tional flexibility, we use dummy variables that 1984 or 1989 (whichever is closer to retirement) indicate the household’s position in the sample along with estimates of consumption and mea- distribution of each variable.13 Specifically, we sures of money income, we backcast (or divide our sample into four equally sized quar- project) wealth inductively according to the tiles based on the ratio of nonasset income (total equation pension, social security, transfer, and earned income) for the first three years postretirement Ϫ ϩ Wt Yt Ϫ 1 Ct Ϫ 1 to nonasset income in the last three prior to (15) W Ϫ ϭ , retirement.14 All measures of income are after- t 1 1 ϩ r tax, where the household’s tax rate is deter- mined by taking the ratio of federal taxes paid using a real interest rate (r) of 4 percent. Alter- by the head and spouse to the total income of native approaches to imputing wealth in the the head and spouse. It is important to empha- year of retirement, such as using unadjusted size that we define earnings replacement in wealth or adjusting observed wealth to the age terms of ratios. We find, for example, that the of retirement using regression estimates on age fourth (or highest) quartile includes both high and age-squared, yielded similar results. income households with generous postretire- Equation (7) also permits the consumption ment compensation packages, as well as low profile to depend on a vector of other time- income households with high social security varying household characteristics Zit. For the replacement rates. specifications reported here, this vector includes Similarly, we also divide our sample into four demographic variables that are likely to affect equally sized quartiles based on the ratio of consumption, such as family size, disability sta- wealth in the year prior to retirement to average tus and gender of the household head, and mar- preretirement (year t ϭϪ3 through t ϭϪ1) ital status. The coefficient on female headship, nonasset after-tax income. Recognizing that for example, is thus identified by the difference there is some disagreement in the literature on between the effects on consumption of a hus- retirement saving concerning the appropriate band’s death and a wife’s death. Twenty-seven measure of wealth [compare, e.g., Eric M. En- percent of household heads report disabilities, gen et al. (1996) and James M. Poterba et al. 17 percent are female, and 68 percent are (1996)], we estimated separate specifications married. for total wealth and financial wealth; generally, Additional summary statistics for the sample the results are quite similar. appear in Table 1. There is substantial variation in income replacement rates, wealth ratios, and the level of wealth. These numbers are sugges- 12 We also dropped 28 observations for which the re- tive of the wide heterogeneity in retirement spondent reported zero food consumption, either at or away preparation among the retirement-aged popula- from home. tion. The second-to-last row of Table 1 shows 13 For the results reported in the text, we use variables the change in (log) average consumption be- that measure the household’s position in the sample distribution, rather than in the (weighted) population distribution. tween the two years prior to retirement and the We obtain similar results when we define our variables in two years postretirement. The average change terms of population distributions. As we mention later, we was Ϫ0.14, whereas the median decline was also obtain similar results for specifications involving linear Ϫ0.12. These summary statistics mask substan- and piecewise linear functions of earnings replacement rates and retirement saving. tial variation. The standard deviation of the 14 Note that we exclude asset income from the numerator change in log consumption was 0.42; the de- and denominator of the ratio. cline exceeded 30 percent for 23 percent of the VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 845

TABLE 1—SUMMARY STATISTICS

Standard Variable names Mean Median deviation Minimum Maximum Age 62.1 62 5.4 45 80 Income replacement rate 0.63 0.60 0.32 0.02 2.87 Financial wealth–income ratio 2.33 0.88 5.80 Ϫ6.24 63.51 Total wealth–income ratio 3.91 2.36 6.45 Ϫ6.10 65.86 Log consumption (1984 dollars) 9.57 9.63 5.19 5.45 11.50 Difference in log consumption Ϫ Ϫ Ϫ Ϫ (tϪ1/Ϫ2 tϩ1/ϩ2) 0.14 0.12 0.42 2.30 1.80 Family size (does not include spouse) 1.83 1 1.36 1 14

TABLE 2A—PROPORTIONAL DISTRIBUTION OF SAMPLE BY INCOME REPLACEMENT AND WEALTH QUARTILE

Income Q1 Income Q2 Income Q3 Income Q4 Total Wealth Q1 5.7 6.2 6.6 6.6 25.1 Wealth Q2 4.8 8.0 5.5 6.6 24.9 Wealth Q3 7.1 4.4 7.8 5.5 24.8 Wealth Q4 7.6 6.4 5.0 6.2 25.2 Total 25.2 25.0 24.9 24.9 100.0

TABLE 2B—AVERAGE AGE AT RETIREMENT BY INCOME REPLACEMENT AND WEALTH QUARTILE

Income Q1 Income Q2 Income Q3 Income Q4 Total Wealth Q1 59.5 60.4 60.0 61.1 60.3 Wealth Q2 59.1 61.3 61.3 60.8 60.8 Wealth Q3 60.0 61.7 61.8 60.4 61.0 Wealth Q4 59.7 61.9 61.6 61.7 61.1 Total 59.6 61.3 61.2 61.0 60.8

Note: Q1 denotes the lowest quartile and Q4 denotes the highest. sample, whereas 12 percent of households ex- each of the wealth ratio and income replacement perienced declines in excess of 40 percent. quartiles. Differences in retirement age across Table 2A shows the joint distribution of the these groups are small, and no systematic rela- sample over the wealth ratio quartiles and in- tions are apparent. This does not lend much come replacement quartiles. Under the life- credence to the view that the observed variation cycle consumption-smoothing hypothesis, we in wealth is in part attributable to unexpected would expect to observe a negative relation developments affecting the timing of retirement. between retirement income replacement rates In particular, though early retirees are most likely and retirement wealth. However, there is no to have entered retirement unexpectedly, they do evidence of this pattern. Only 24.1 percent of not appear to have accumulated less for retire- the sample falls into the Southwest/Northeast ment, relative to their incomes. diagonal, compared with 27.7 percent for the Northwest/Southeast diagonal. Both figures are IV. Basic Results close to the sample frequency (25 percent) that one would observe if the observations were Table 3 presents estimates of our first-differ- distributed randomly across the 16 cells. There enced specification [equation (7), with ␰ defined may, of course, be a variety of subtle explana- as in equation (8)]. The first row describes the tions for this pattern; taken by itself, it does not shape of the consumption profile for households justify strong inferences concerning behavior. in the lowest income replacement and wealth Table 2B shows average retirement ages for ratio quartiles (henceforth, the “benchmark” 846 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

TABLE 3—CONSUMPTION SHIFTS AND GROWTH RATES,PRE- AND POSTRETIREMENT:TOTAL CONSUMPTION

Preretirement log First-year Two-year Postretirement consumption change in log change in log log consumption growth consumption consumption growth Benchmark (quartile 1 for income and Ϫ0.024 Ϫ0.240 Ϫ0.566 0.011 wealth ratios) (0.012) (0.064) (0.078) (0.029) Wealth Ratio Quartile: Quartile 2 Ϫ0.029 Ϫ0.153 Ϫ0.291* Ϫ0.018 Quartile 3 Ϫ0.015 Ϫ0.096* Ϫ0.298* Ϫ0.026 Quartile 4 Ϫ0.017 Ϫ0.094* Ϫ0.211* Ϫ0.035 p-value for equality of coefﬁcients F(3, 435) 0.619 0.064 0.000 0.423 Income Replacement Quartile: Quartile 2 Ϫ0.027 Ϫ0.187 Ϫ0.338* Ϫ0.006 Quartile 3 Ϫ0.025 Ϫ0.168 Ϫ0.355* 0.018 Quartile 4 Ϫ0.031 Ϫ0.052* Ϫ0.199* 0.007 p-value for equality of coefﬁcients F(3, 435) 0.924 0.017 0.000 0.849

Notes: N ϭ 3,262. All significance tests use robust standard errors clustered by household (436). Additional variables are family size, marital status, disability, female widower, and a dummy variable for whether the household was working part-time for 3–4 years prior to full retirement. * Denotes hypothesis that the quartile growth rate (or jump) differs from the benchmark is rejected at the 5-percent level in a two-tailed test. group). There is a modest negative trend in Table 3 indicate that there are large differences consumption prior to retirement (Ϫ0.024). across wealth ratio quartiles in the size of the There is a substantial and significant drop consumption discontinuity at retirement. Gener- within the first two years of retirement ally, a higher wealth ratio is associated with a (Ϫ0.566), with slightly less than half of the smaller decline in consumption; in the top decline occurring in the first year. Plainly, the wealth quartile (and bottom income quartile), impact of retirement on consumption is not in- the estimated decline in consumption is stantaneous. The estimated postretirement con- Ϫ0.211, less than half the decline in the bottom sumption growth rate (0.01), though positive, is wealth quartile (Ϫ0.566). The associated coef- small and statistically insignificant. ficients are individually significant at high lev- The second section of Table 3 contains coef- els of confidence, and one rejects the hypothesis ficients that describe the consumption profiles of equal discontinuities across wealth ratio of individuals in the second, third, and fourth quartiles at the 99.9 percent level of confidence. wealth ratio quartiles. There is virtually no vari- Figure 4 depicts consumption paths for ation in the growth rate of consumption across households in each of the four total wealth ratio wealth quartiles either before retirement or after quartiles (assuming that the household falls into retirement; the significance value for the joint the first income replacement quartile), as well as hypothesis of equality across all four wealth for households in the top wealth ratio and in- quartiles is 0.619 prior to retirement and 0.423 come replacement quartiles. The horizontal axis after retirement.15 In contrast, the results in

15 As mentioned in Section III, shocks to permanent substituted predicted wealth for actual wealth; (ii) we con- income just before retirement may generate a spurious re- ﬁned attention to households for whom we observed wealth lation between wealth at retirement and preretirement con- prior to retirement, used only subsequent consumption ob- sumption growth. To examine this possibility, we servations, and substituted observed wealth for retirement implemented two alternative procedures: (i) we predicted wealth. We found no evidence of a signiﬁcant relation wealth at retirement based on information obtained before between wealth accumulation and preretirement consump- each household’s earliest consumption observation, and tion growth in either case. VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 847

FIGURE 4. CHANGE IN CONSUMPTION AT RETIREMENT, BY WEALTH QUARTILE measures years relative to retirement (e.g., sumption discontinuities at the time of Ϫ5/Ϫ6 refers to the fifth and sixth years before retirement. retirement). The vertical axis measures the log Differences in the shape of consumption pro- of normalized consumption. We define normal- files across income replacement quartiles are ized consumption as the ratio of a household’s also intriguing. In the lower portion of Table consumption during any given time period to its 3, we see large and highly significant differ- consumption during a benchmark period (by ences across these groups in the size of the arbitrary convention, the first and second years consumption discontinuity at retirement. Higher before retirement). This figure is based on the income replacement rates are associated with more flexible, less parsimonious, nonparametric smaller declines in consumption at retirement, fixed-effects specification discussed in Section and one can reject the hypothesis of an equal II [equation (9), with ␺ defined as in equation discontinuity across income replacement quar- (10)]. Appendix Table A1 contains the associ- tiles at the 99.9-percent level of confidence.17 ated parameter estimates. Once again, one sees Figure 5 depicts consumption profiles for that consumption growth rates do not differ households in each of the four income replace- systematically or significantly across wealth ra- ment quartiles (assuming that the household tio quartiles either before or after retirement. falls into the first wealth ratio quartile), as well Formally, one cannot reject the joint hypothesis as for households in the top wealth ratio and that age-specific consumption growth rates are income replacement quartiles. Like Figure the same for all wealth quartiles both before and 4, this figure is based on our more flexible, after retirement ( p ϭ 0.82).16 However, the less parsimonious, nonparametric fixed-effects figure does exhibit large differences in con-

17 Notably, these differences remain even when one re- 16 The effects of the discontinuities at retirement persist stricts attention to households that actually engage in non- for many years; we obtain similar results when we use data trivial saving (i.e., those in the top three wealth ratio including up to 10 postretirement years. quartiles). 848 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

FIGURE 5. CHANGE IN CONSUMPTION AT RETIREMENT, BY INCOME QUARTILE specification (Appendix Table A1). The figure tion problems. However, as we have noted, it is clearly shows much steeper declines in con- possible to test for the most natural version of sumption at retirement for households with this problem by examining the composition of lower income replacement rates. In combination consumption, which we do in Section V. with the data in Table 1, our nonparametric Table 3 also indicates that the slope of the estimates imply that 30.4 percent of households consumption profile does not differ much across reduce consumption by at least 35 percentage income replacement quartiles either before or points within three to four years of retirement. after retirement; the significance values of the At first, the pattern noted in the preceding F-tests for equality of the coefficients are 0.924 paragraph may appear to be reconcilable with preretirement and 0.849 postretirement. The models of consumption smoothing: because the fact that those with the lowest income replace- regression also controls for the household’s re- ment rates exhibit virtually no attempt to antic- tirement wealth ratio, it effectively rules out ipate the dramatic fall in consumption at smoothing through the endogenous adjustment retirement by scaling back on consumption of personal saving. However, recall from Table prior to retirement (Table 3 and Figure 5) casts 2A that there is virtually no correlation between doubt on conventional models of consumption a household’s positions in the wealth ratio and smoothing at retirement. Similarly, the absence income replacement distributions. Conse- of any correlation between consumption growth quently, even when wealth ratio variables are rates and income replacements rates is not gen- excluded from the regressions in Table 3, one erally consistent with models in which individ- still observes significantly larger discontinuities uals who discount the future relatively little tend in consumption for households in lower income to save more, and to self-select into jobs with replacement quartiles. (We exclude the regres- pension coverage (e.g., Gale, 1998). sion to conserve space.) As discussed in Section The preceding results are based on flexible, I, subsection B, this relation could also be at- nonparametric specifications of the relation tributable, at least in principle, to sample selec- between changes in consumption and measures VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 849 of retirement wealth and postretirement in- with leisure than restaurant meals, the decline in come replacement rates. Simple parametric spending at retirement should be less pro- specifications yield similar results.18 nounced for food consumed at home than for food consumed away from home. V. The Composition of Consumption Tables 4 and 5 contain estimates of our first- differenced specification [equation (7), with ␰ As noted in Section I, there are a number of defined as in equation (8)] for, respectively, factors that could in principle account for the food consumed away from home and food con- existence of a consumption discontinuity at re- sumed at home.19 In each case, the patterns are tirement, as well as for correlations between the broadly similar to those noted in Table 3. How- size of this discontinuity and variables such as ever, for food consumed away from home wealth or income replacement rates. In most (Table 4), the magnitude of the changes at re- cases, theory also implies that these patterns tirement are considerably less pronounced. In- should be confined to (or at least more pro- deed, one cannot reject the hypotheses that the nounced for) particular kinds of expenditure discontinuity at retirement is the same across all categories (i.e., work-related expenses and sub- wealth ratio quartiles ( p ϭ 0.256) and all stitutes for leisure). Thus, one can distinguish income replacement quartiles ( p ϭ 0.672). between theories at a more refined level by Table 5 reveals that food consumed at home examining disaggregated measures of declines by a larger amount at retirement consumption. (Ϫ0.764 for households in the lowest wealth Although the PSID is not ideally suited for and income quartiles). The magnitude of this this task, one can disaggregate somewhat by discontinuity declines monotonically with the analyzing expenditure patterns separately for household’s wealth ratio quartile, and with its food consumed at home and away from home income replacement quartile. Moreover, we (where the latter category excludes meals con- strongly reject the hypotheses that the disconti- sumed at work or school). If, as seems likely, nuity is the same across all wealth quartiles (99- home cooking is complementary with leisure percent level of confidence) and across all in- and not work-related, then spending on food come replacement quartiles (99.9-percent level consumed at home should not decline after re- of confidence). These patterns are difficult to tirement. Moreover, variation in work-related reconcile with the hypotheses that either the expenses should produce a correlation between cessation of work-related expenses or substitu- wealth and consumption only for potentially tion between market expenditures and leisure work-related spending categories, which pre- explain the sharp decline in spending at sumably excludes food consumed at home. retirement.20 Provided that home cooking is at least less Notably, in Table 5, we also reject the hy- work-related and more highly complementary pothesis that the postretirement rate of growth for food consumed at home is the same across wealth ratio quartiles. Specifically, the pattern 18 For example, we estimated specifications in which we of coefficients suggests that consumption tends replaced the wealth ratio and income replacement quartile to decline at a more rapid rate after retirement dummies with the household’s percentile rank for each of these variables. Interactions with preretirement and postre- for those who reached retirement with greater tirement dummies were jointly insignificant ( p ϭ 0.452). wealth. The same pattern was present in Table With respect to the first year retirement effect, the coefficient of the wealth ratio variable was 0.00213 (t-statistic of 2.83), and the coefficient of the income replacement ratio variable was 0.00225 (t-statistic of 2.99). With respect to 19 We obtain similar results for the fixed-effects specifi- the second year retirement effect, the coefficient of the cation. wealth ratio variable was 0.00220 (t-statistic of 2.68), and 20 There are of course some limitations of this test. At the coefficient of the income replacement ratio variable was retirement, households might switch from high-cost pre- 0.00191 (t-statistic of 2.41). We tested the implicit linearity pared food purchased at the supermarket to less expensive assumption by estimating another specification with splines basic foods prepared at home. However, the degree of at the median values of both variables. Based on the appro- substitution to low-cost items would have to be quite ex- priate F test, we failed to reject the linear specification ( p ϭ treme (and among just the low wealth and income quartiles) 0.338). to generate the pattern seen in the data. 850 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

TABLE 4—CONSUMPTION SHIFTS AND GROWTH RATES,PRE- AND POSTRETIREMENT:FOOD AWAY FROM HOME

Preretirement log First-year Two-year Postretirement consumption change in log change in log log consumption growth consumption consumption growth Benchmark (quartile 1 for income and 0.003 Ϫ0.140 Ϫ0.502 0.122 wealth ratios) (0.049) (0.198) (0.265) (0.101) Wealth Ratio Quartile: Quartile 2 0.021 Ϫ0.100 Ϫ0.300 0.018 Quartile 3 Ϫ0.042 0.170 Ϫ0.085 0.080 Quartile 4 0.014 Ϫ0.064 Ϫ0.249 0.100 p-value for equality of coefﬁcients F(3, 381) 0.297 0.144 0.256 0.564 Income Replacement Quartile: Quartile 2 Ϫ0.025 Ϫ0.153 Ϫ0.334 0.015 Quartile 3 0.036 Ϫ0.171 Ϫ0.336 0.048 Quartile 4 0.038 Ϫ0.035 Ϫ0.261 0.072 p-value for equality of coefﬁcients F(3, 381) 0.282 0.788 0.672 0.595

Notes: N ϭ 2,396. All signiﬁcance tests use robust standard errors clustered by household (382). Additional variables are family size, marital status, disability, female widower, and a dummy variable for whether the household was working part-time for 3–4 years prior to full retirement. * Denotes hypothesis that the quartile growth rate (or jump) differs from the benchmark is rejected at the 5-percent level in a two-tailed test.

TABLE 5—CONSUMPTION SHIFTS AND GROWTH RATES,PRE- AND POSTRETIREMENT:FOOD AT HOME

Preretirement log First-year Two-year Postretirement consumption change in log change in log log consumption growth consumption consumption growth Benchmark (quartile 1 for income and Ϫ0.043 Ϫ0.349 Ϫ0.764 0.022 wealth ratios) (0.018) (0.098) (0.137) (0.028) Wealth Ratio Quartile: Quartile 2 Ϫ0.054 Ϫ0.177 Ϫ0.514* Ϫ0.079* Quartile 3 Ϫ0.035 Ϫ0.156 Ϫ0.466* Ϫ0.050 Quartile 4 Ϫ0.062 Ϫ0.138 Ϫ0.380* Ϫ0.083* p-value for equality of coefﬁcients F(3, 435) 0.196 0.123 0.007 0.018 Income Replacement Quartile: Quartile 2 Ϫ0.040 Ϫ0.355 Ϫ0.482* Ϫ0.022 Quartile 3 Ϫ0.055 Ϫ0.227 Ϫ0.363* 0.037 Quartile 4 Ϫ0.057 Ϫ0.112 Ϫ0.240* 0.014 p-value for equality of coefﬁcients F(3, 435) 0.552 0.006 0.000 0.477

Notes: N ϭ 3,248. All signiﬁcance tests use robust standard errors clustered by household (436). Additional variables are family size, marital status, disability, female widower, and a dummy variable for whether the household was working part-time for 3–4 years prior to full retirement. * Denotes hypothesis that the quartile growth rate (or jump) differs from the benchmark is rejected at the 5-percent level in a two-tailed test. VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 851

TABLE 6—CONDITIONAL BUDGET SHARE REGRESSIONS,CONSUMER EXPENDITURE SURVEY, 1982–1989

Adult Food away Food at Dependent variable clothing Transportation Fuel from home home Average Budget Share (Percent) 2.50 14.85 4.39 4.22 14.63 Retired (yes ϭ 1) ϫϪ0.448 Ϫ1.665 Ϫ0.704 Ϫ0.982 1.893 Wealth quartile 1 (6.1) (4.6) (6.4) (7.0) (9.4) Retired (yes ϭ 1) ϫϪ0.539 Ϫ1.634 Ϫ0.930 Ϫ1.306 1.367 Wealth quartile 2 (6.5) (4.0) (7.5) (8.2) (6.0) Retired (yes ϭ 1) ϫϪ0.227 Ϫ1.506 Ϫ0.487 Ϫ0.534 0.040 Wealth quartile 3 (1.9) (2.6) (2.8) (2.4) (0.1) Retired (yes ϭ 1) ϫϪ0.243 Ϫ2.827 Ϫ0.665 Ϫ0.229 Ϫ0.301 Wealth quartile 4 (3.0) (7.1) (5.5) (1.5) (1.4) Married 0.418 Ϫ2.228 0.464 Ϫ3.105 3.797 (5.5) (6.1) (4.1) (21.3) (18.2) Single female head 1.110 Ϫ2.800 Ϫ1.369 Ϫ3.268 Ϫ0.734 (14.5) (7.4) (12.0) (22.4) (3.5) Any children Յ 18 Ϫ0.204 1.268 0.389 Ϫ0.627 1.685 yrs? (yes ϭ 1) (1.5) (1.9) (2.0) (2.5) (4.6) Number of children Ϫ0.229 Ϫ0.833 0.084 Ϫ0.331 1.783 (3.2) (2.4) (0.8) (2.4) (9.1) Log(total expenditures) 0.843 8.595 Ϫ0.475 1.227 Ϫ8.094 (19.0) (39.1) (7.1) (14.5) (66.4) R2 0.12 0.27 0.15 0.12 0.37

Notes: Five-year dummy variables for age and individual year dummy variables included in all regressions. The sample size is 10,260. All dependent variables are percentages of total expenditures. Absolute values of t-statistics are in parentheses.

3, but the differences across wealth ratio quar- Browning and Costas Meghir, 1991) to study tiles were statistically insignificant. Recall that the effect of retirement on relative budget the life cycle considerations discussed in Sec- shares. In effect, our object is to determine tion I, subsection A.1 predict precisely the op- whether labor market status (here, retirement) posite pattern: those with higher wealth should has independent predictive power for the budget have higher consumption growth rates. shares of particular expenditure categories Because the PSID collected data on relatively (work-related expenses and leisure comple- few expenditure categories, it is important to ments), controlling for prices and total expen- determine whether our results are more broadly ditures. In that we are not interested in representative. We therefore extend our inves- estimating the complete budget system, we tigation by analyzing Julie A. Nelson’s (1994) adopt a simplified version of the Browning– extract of the 1980–1989 Consumer Expendi- Meghir specification, wherein we simply in- ture Survey (CEX), which contains merged and clude dummy variables to allow for variation in annualized quarterly consumption data. We re- prices across years. We would expect that indi- strict our attention to 1982 through 1989 be- viduals with higher-than-average tastes for cause of concerns about poor data quality in the work might also have higher-than-average start-up years. Observations are dropped if the tastes for goods complementary with work; thus household’s data are missing for any quarter, or we would expect our ordinary least-squares if the appropriate fields indicate that income (OLS) estimates to be upper bounds on the data are of poor quality. “true” impact of retirement on commodities The CEX data are, for practical purposes, a such as transportation expenses, adult clothing, series of cross sections. The survey does not and fuel. provide a measure of each household’s wealth Table 6 contains average budget shares and at retirement, or of changes in income after parameter estimates for a simple conditional retirement. We therefore use the conditional budget share model. The model explains rela- commodity demand approach (see, e.g., Martin tive expenditures on several categories of goods 852 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001 that are plausibly complements to working (adult points for the high wealth group and a decline of clothing, transportation, fuel, and food away from 0.70 percentage points for the low wealth home including meals at work), as well as one group). Indeed, the transportation share declines non-work-related expenditure category that is pre- by more among the top wealth group than among sumably a complement to leisure (food consumed the bottom wealth group. These findings are in- at home). The model includes dummy variables consistent with the hypothesis that wealth varies for age and year (not reported) as well as the significantly across households as a result of the demographic variables listed in the table.21 anticipation of differential declines in work- A negative partial correlation between retire- related clothing, fuel, or transportation expenses. ment and potentially work-related expenses The final column of Table 6 suggests that the would not by itself indicate that such factors can budget share devoted to food consumed at home explain the variation in wealth across the pop- does increase after retirement, and that this in- ulation. To conclude that lower wealth house- crease is larger for households with less wealth. holds save less because they anticipate larger This may at first appear consistent with the declines in work-related expenses, one would hypothesis that households shift to expenditures have to find that households in lower wealth on home-production activities postretirement. quartiles experience larger declines in poten- Recall, however, that the equation explains bud- tially work-related spending at retirement. To get shares. Because retirement is, in this sam- investigate this possibility, we interact the re- ple, associated with a decline of 0.23 in the log tirement dummy variable with wealth-to- of total consumption, the equation predicts a income quartile dummies constructed from the substantial decline in spending on food con- limited wealth data (on stocks, bonds, saving sumed at home after retirement.24 Our results bonds, and checking accounts) contained in the are therefore inconsistent with the prediction Consumer Expenditure Survey.22 More than that the decline in consumption at retirement one-third of the sample has a missing value for should be confined to work-related expenses at least one wealth category; all missing wealth and leisure substitutes. values were set to zero. Thus we recognize that these wealth quartiles are measured with error. VI. Removing the “News” Associated with As is clear from the coefficients in the second Retirement through fifth rows of Table 6, retirement is indeed associated with lower budget shares for For the reasons discussed in Section I, the goods that are potentially complementary to preceding empirical patterns are difficult to rec- work.23 However, focusing on differences in the oncile with many explanations for the observed impact of retirement on budget shares across variation in wealth based on standard models of wealth groups, there is relatively little variation life-cycle optimization. The evidence presented by wealth in the share of the budget spent on so far does not, however, exclude the possibility adult clothing (a fall of 0.25 percentage points that the variation in retirement wealth and the for the high wealth group compared to a fall of associated variation in the size of the consump- 0.45 percentage points for the low wealth tion discontinuity at retirement are both attrib- group) or on fuel (a decline of 0.67 percentage utable, at least in part, to unexpected events that affect the timing of retirement. To examine this possibility, we investigate 21 We also estimated a model closer in spirit to the the manner in which consumption responds to Almost Ideal Demand System (see, e.g., Deaton and John Muellbauer, 1980 pp. 75–84); results were generally similar with interaction terms between all of the explanatory variables and the log of total consumption expenditures, but 24 The budget share for food consumed at home would much less stable. increase by 1.86 percentage points at retirement for the 22 The wealth quartile dummy variables indicate the lowest wealth group if total expenditures remained constant. household’s position within the wealth-to-income distribu- Given that food at home is income inelastic (the coefficient tion after adjusting for differences in retirement status, age, of the log of total expenditures is Ϫ8.09), the budget share and marital status. rises slightly as total expenditures decline. However, these 23 This result is consistent with similar tests in Banks et effects are much smaller, individually and collectively, than al. (1998). the overall decline in consumption. VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 853

TABLE 7—SECOND-STAGE CONSUMPTION REGRESSIONS

AB C D Total wealth, Total wealth, Financial demographics retirement Variable name Total wealth wealth excluded age Ͼ 60 Probability of retirement Ϫ0.685 Ϫ0.557 Ϫ0.627 Ϫ0.606 (4.3) (3.7) (3.6) (3.4) Wealth quartile 2 ϫ Pr(Ret) 0.287 0.280 0.261 0.235 (2.0) (1.9) (1.7) (1.5) Wealth quartile 3 ϫ Pr(Ret) 0.416 0.291 0.451 0.426 (2.9) (2.1) (2.9) (2.7) Wealth quartile 4 ϫ Pr(Ret) 0.594 0.430 0.596 0.597 (4.0) (3.0) (3.8) (3.6) Income quartile 2 ϫ Pr(Ret) 0.261 0.208 0.294 0.269 (1.8) (1.4) (1.9) (1.7) Income quartile 3 ϫ Pr(Ret) 0.298 0.266 0.341 0.286 (2.2) (2.0) (2.4) (1.9) Income quartile 4 ϫ Pr(Ret) 0.344 0.312 0.465 0.284 (2.7) (2.4) (3.4) (2.0) Family size 0.079 0.080 0.084 (5.3) (5.2) (6.8) Marital status 0.147 0.148 0.136 (6.3) (6.3) (5.1) Female head Ϫ0.231 Ϫ0.227 Ϫ0.263 (2.8) (2.7) (2.4) Age Ϫ0.092 Ϫ0.093 Ϫ0.094 Ϫ0.094 (3.7) (3.6) (3.8) (2.6) Age2/1,000 0.587 0.584 0.497 0.587 (2.8) (2.8) (2.4) (2.1) Constant 8.200 8.218 8.837 8.331 (10.2) (10.1) (11.6) (6.8) R2 0.76 0.76 0.74 0.76 (Observations) (4,817) (4,817) (4,817) (3,609)

Notes: Dependent variable is log of consumption. Household-specific fixed effects included in second-stage regression. First-stage probits are run separately for each age group; all z statistics (in parentheses) are based on bootstrapped standard errors. predictable events that affect the probability of stage consumption regression, as in equation (13). retirement. In particular, to identify the effect on For the second stage, we calculate wealth ratio consumption of predictable retirement, we ex- quartiles using a measure of “abnormal” wealth ploit the fact that the retirement hazard function instead of wealth at retirement. We bootstrap the varies sharply with age, spiking at ages 62 and two-step procedure (using 1,000 replications) to 65 (see Banks et al., 1998, for a similar identi- obtain standard errors. fication strategy). Table 7 presents estimates of the second- As explained in Section II, we remove the ef- stage regression. The results in column A, like fects of unexpected retirement through a two-step those in Table 3, control for family size, marital procedure. First, we estimate simple probit speci- status, the gender of the household head, and fications explaining retirement status as a function age.25 The estimated impact of predicted retire- of education, family size, gender of household ment for those in the lowest wealth and income head, and marital status as independent variables. quartiles is Ϫ0.685, with a z-statistic of 4.3. The We fit separate models for each integer age from magnitude of this effect declines monotonically 54 through 70, and in each instance we augment the data set to include all observations on all 25 For the regressions in Table 7, we omit disability on households, irrespective of whether they retired the grounds that it may serve as a proxy for retirement. Note between 1978 and 1990. We then introduce the also that we allow the baseline consumption trend to depend predicted probability of retirement into a second- on both age and age-squared. 854 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001 across wealth ratio quartiles: it is Ϫ0.398 in the VII. Conclusion second quartile, Ϫ0.269 in the third quartile, and Ϫ0.091 in the fourth quartile.26 Similarly, In this paper, we have found that consump- the magnitude of the effect declines monotoni- tion growth rates near retirement do not vary cally across income replacement quartiles: it is systematically with retirement wealth. Thus Ϫ0.424 in the second quartile, Ϫ0.387 in the there is no indication that heterogeneity in pure third quartile, and Ϫ0.341 in the fourth quartile. rates of time preference, subjective survival Regardless of whether one examines wealth or probabilities, income uncertainty, or tastes for income, the differences between the effects for precaution—all of which should manifest them- the lowest quartile and each of the higher quar- selves through systematic differences in con- tiles are statistically significant at conventional sumption growth rates—play a role in levels of confidence. Thus, even when we re- determining the distribution of retirement sav- move the effects of unexpected retirement, the ings. We have found a pronounced discontinu- size of the consumption discontinuity is still ity in consumption at retirement, with the size strongly related to wealth and income—if any- of the discontinuity negatively correlated with thing, the estimated patterns are even more retirement savings and income replacement striking. These estimates, combined with infor- rates. However, none of these phenomena is mation from Table 1, imply that 31 percent of confined to work-related expenses or leisure households reduce their consumption by at least substitutes. The empirical evidence therefore 35 percentage points at retirement.27 casts doubt on theories that rely on differences In columns B through D of Table 7, we in relative tastes for leisure, home production, examine the robustness of our findings with or work-related expenses to explain the varia- respect to several changes in specification. For tion in wealth at retirement. column B, we use financial wealth in place of Likewise, differences in retirement wealth for total wealth. For column C, we exclude controls households with similar income and pension for demographic characteristics on the grounds profiles (including retirement ages) could in that changes in these variables may be associ- principle result from heterogeneity in planned ated with shocks to needs and/or permanent retirement ages, provided that realized retire- income. For column D, we confine attention to ment ages are affected to some degree by un- individuals retiring after age 60 on the grounds anticipated events. Although this factor is also that shocks to permanent income are probably consistent with the negative correlation between largest for early retirees.28 In each case, we find the consumption discontinuity and retirement that our central results are highly robust. savings, it cannot account for the fact that this same pattern remains readily apparent even when we remove the effects of unpredictable 26 One obtains these numbers by adding the coefficient events that affect the timing of retirement. for the appropriate interaction term to the effect for the lowest wealth and income quartile (e.g., Ϫ0.398 ϭ Moreover, whereas variation in the strength of Ϫ0.685 ϩ 0.287). bequest motives may contribute to differences 27 Note that these figures are essentially identical to the in wealth accumulation, it fails to explain the ones reported in Section IV for our nonparametric OLS strong negative correlation between retirement estimates. The implied fraction of households suffering a substantial decline in consumption is much larger than the savings and the magnitude of the consumption figure attributed to us by Engen et al. (1999 p. 135). They discontinuity at retirement. used coefficient estimates from a two-stage specification in We are also unable to attribute differences an earlier version of this paper (NBER Working Paper No. in retirement accumulation to variation in the 6227, October 1997) that was not designed to distinguish shape of the income/pension profile. House- between age effects and the impact of a baseline retirement trend. For this reason, their interpretation of our results is holds with lower income replacement rates problematic. have larger consumption discontinuities at 28 When an individual is forced to retire unexpectedly retirement. Contrary to the central tenets before age 60, the present discounted value of lost earnings of life-cycle theory, there is little evidence may be quite large. The financial impact is even greater for those who retire early for health reasons (because of limi- that households use savings to smooth the tations on Medicare eligibility) and for those whose pension effects on consumption of predictable income plans heavily penalize early retirement. discontinuities. VOL. 91 NO. 4 BERNHEIM ET AL.: VARIATION IN RETIREMENT WEALTH 855

These findings are difficult to interpret in the their financial situation and make adjustments at context of the life-cycle model. Although it may retirement (so that the adequacy of saving is be possible to formulate some model of rational “news”), then one would expect to observe the life-cycle planning that would account for our patterns documented in this paper. A similar findings, in our view, the empirical patterns in conclusion may follow from theories of “mental this paper are more easily explained if one steps accounting,” in which individuals differ in the outside the framework of rational, farsighted extent to which they can exercise self-discipline optimization. If, for example, households fol- over the urge to spend current income, and/or low heuristic rules of thumb to determine saving from models with dynamically inconsistent de- prior to retirement, and if they take stock of cision makers.

APPENDIX

TABLE A1—REGRESSION FOR TOTAL CONSUMPTION

Interaction terms with year relative to retirement Ϫ5 and Ϫ6 Ϫ4 and Ϫ3 ϩ1 and ϩ2 ϩ3 and ϩ4 ϩ5 and ϩ6 Benchmark (1st quartile, wealth and 0.049 0.045 Ϫ0.396 Ϫ0.522 Ϫ0.444 income) (1.0) (1.2) (6.9) (7.7) (4.3) Increment—2nd wealth quartile 0.039 Ϫ0.038 0.170 0.172 0.221 (0.9) (1.1) (3.4) (2.9) (2.7) Increment—3rd wealth quartile Ϫ0.002 0.004 0.194 0.186 0.202 (0.1) (0.1) (3.5) (2.9) (2.3) Increment—4th wealth quartile Ϫ0.012 Ϫ0.031 0.286 0.246 0.261 (0.3) (0.8) (5.1) (4.0) (2.9) Increment—2nd income quartile Ϫ0.010 Ϫ0.003 0.131 0.171 0.091 (0.3) (0.1) (2.4) (2.6) (0.9) Increment—3rd income quartile 0.008 Ϫ0.026 0.141 0.275 0.096 (0.2) (0.7) (2.5) (4.2) (1.0) Increment—4th income quartile 0.053 0.032 0.265 0.363 0.256 (1.2) (0.8) (4.8) (5.8) (2.8) Part-time work Ϫ0.026 Ϫ0.061 Ϫ0.047 Ϫ0.051 Ϫ0.063 (0.5) (1.4) (0.9) (0.7) (0.9) Family size 0.044 (3.3) Female head (widowhood) Ϫ0.137 (2.1) Married 0.077 (3.2) Disabled Ϫ0.047 (2.6)

Notes: Sample size ϭ 3,980. Estimates correct for household-speciﬁc effects with robust standard errors (clustered by household). R2 ϭ 0.75. Dependent variable is log total consumption. Absolute values of t-statistics are in parentheses. The top row shows benchmark coefﬁcients for bottom wealth and income quartiles. The “increment” for each wealth ratio and income replacement quartile measures log consumption relative to the benchmark group. 856 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2001

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During the course of this project, I have benefitted from discussions with numerous friends and colleagues, and my intellectual debts are too numerous to list. However, I am especially grateful to Alan Auerbach, William Gale, and Kenneth Judd. I am also indebted to Sita Nataraj for catching a number of errors, and for suggesting a variety of expositional improvements 1173-1249. [Crossref]