David A. Wise is the John F. Stambaugh Professor of Political Economy at Harvard University’s John F. Kennedy School of Government. He is also the Peter and Helen Bing Senior Fellow at the Hoover Institution, director of the NBER Program on Aging, and coeditor or editor of several volumes, including, most recently, Perspectives on the Economics of Aging.

Analyses in the Economics of Aging

The University of Chicago Press

Copyright © 2005 National Bureau of Economic Research
All right reserved.
ISBN: 978-0-226-90286-9

Contents

Preface…………………………………………………………………………………………………………………………………………………………………………..ixIntroduction David A. Wise…………………………………………………………………………………………………………………………………………………………11. Utility Evaluation of Risk in Retirement Saving Accounts James M. Poterba, Joshua Rauh, Steven F. Venti, and David A. Wise………………………………………………………………..132. Passive Decisions and Potent Defaults James J. Choi, David Laibson, Brigitte C. Madrian, and Andrew Metrick……………………………………………………………………………..593. Characterizing the Experiences of High-Cost Users in Medicare Thomas MaCurdy and Jeff Geppert………………………………………………………………………………………….794. The Efficiency of Medicare Jonathan Skinner, Elliott S. Fisher, and John E. Wennberg………………………………………………………………………………………………….1295. Intensive Medical Technology and the Reduction in Disability David M. Cutler…………………………………………………………………………………………………………1616. Broken Down by Work and Sex: How Our Health Declines Anne Case and Angus Deaton………………………………………………………………………………………………………1857. Consequences and Predictors of New Health Events James P. Smith…………………………………………………………………………………………………………………….2138. Healthy, Wealthy, and Knowing Where to Live: Trajectories of Health, Wealth, and Living Arrangements among the Oldest Old Florian Heiss, Michael D. Hurd, and Axel Brsch-Supan…………………2419. Institutions and Saving for Retirement: Comparing the United States, Italy, and the Netherlands Arie Kapteyn and Constantijn Panis…………………………………………………………28110. Household Saving in Germany: Results of the First SAVE Study Axel Brsch-Supan and Lothar Essig………………………………………………………………………………………..31711. Caste, Culture, and the Status and Well-Being of Widows in India Robert Jensen……………………………………………………………………………………………………….35712. Individual Subjective Survival Curves Li Gan, Michael D. Hurd, and Daniel McFadden……………………………………………………………………………………………………377Contributors………………………………………………………………………………………………………………………………………………………………………413Author Index………………………………………………………………………………………………………………………………………………………………………417Subject Index……………………………………………………………………………………………………………………………………………………………………..421

Chapter One

Utility Evaluation of Risk in Retirement Saving Accounts James M. Poterba, Joshua Rauh, Steven F. Venti, and David A. Wise

The last two decades have witnessed a remarkable shift in the structure of retirement saving in the United States. In 1980, most workers with pension plans participated in defined benefit plans, with benefits determined by the worker’s earnings history, years of service, and age at the time of retirement. The investment allocation of assets in defined benefit pension accounts was determined by professional money managers or corporate executives, and the worker controlled his retirement benefit only through the choice of retirement age and job change decisions.

Over the 1980s and 1990s, the U.S. pension system shifted toward a defined contribution structure, with 401(k) plans growing particularly rapidly. In the late 1990s, about 85 percent of pension plan contributions were directed to defined contribution personal retirement accounts. This shift transferred responsibility for investment decisions, contribution rates, and ultimately the draw-down of retirement assets from firms to workers. It replaced the link between retirement income, job change, and final earnings, which were important sources of worker risk, with a link between retirement account balances and the uncertain return on invested assets. The risk that workers bear as a result of fluctuations in the value of assets in retirement accounts has attracted considerable attention in the popular press, often with the claim that workers are now facing riskier retirement prospects than in the past.

This paper presents new evidence on the risk of different investment strategies when evaluated in terms of retirement wealth accumulation. We use two different approaches to describe the risk of investing 401(k) assets in a broadly diversified portfolio of common stocks, compared to a portfolio of index bonds. The first involves computing the empirical distribution of potential wealth values at retirement resulting from different investment strategies, and then making explicit comparisons of the wealth distributions. If the average return on one asset class, such as corporate stock, is substantially greater than the average return on another asset class, such as bonds, this approach shows that over long horizons, the higher-return asset class will outperform the lower-return asset class with very high probability. One criticism of this approach is that it does not adequately consider the potential cost to a retiree of the low levels of wealth at retirement that might emerge from the riskier, but higher-expected-return, strategy.

Our second evaluation approach is designed to address this issue. We assume that the value that the retiree assigns to the consumption stream after retirement can be parameterized using a simple utility function, in which utility is a function of the stock of wealth at retirement. We then use simulation methods to compute the distribution of wealth at retirement that might emerge under different portfolio investment strategies, and to evaluate the expected utility of this distribution. Comparing the expected utility, which recognizes the potential cost of a small probability of very unfavorable outcomes, provides an alternative to comparing the distributions as a method for evaluating different investment strategies.

We compare the distribution of retirement wealth and the expected utility of retirement wealth for three different investment strategies. The first involves holding only index bonds, the second holds only a portfolio of common stocks similar to the Standard & Poor 500 index (S&P 500), and the third invests in a fifty-fifty mix of index bonds and common stocks. We conduct our analysis at the household level, recognizing that retirement plan investment decisions have implications for all household members. We also treat the evaluation of risk as a collective household decision. To make the retirement wealth calculations as realistic as possible, our simulations are run through the lifetime profiles of Social Security earnings records for each of 759 Health and Retirement Survey (HRS) households. This allows for realistic variation in age-specific labor income flows. We also calculate the level of non-401(k) wealth holdings for these HRS households. We find that the expected utility of retirement wealth is very sensitive to the value of wealth held outside the defined contribution plan, including both liquid wealth and annuitized wealth such as prospective Social Security benefits or defined benefit plan payouts.

The paper is divided into seven sections. Section 1.1 describes our basic framework for evaluating the risks associated with the accumulation of retirement saving. The second section discusses our use of earnings histories for a subset of HRS households. These earnings histories are the basis for contribution flows into our hypothetical 401(k) account. Section 1.3 describes our decomposition of the wealth holdings of HRS households near retirement age. The wealth data provide the benchmark against which we evaluate the level of 401(k) assets. The fourth section describes our assumptions about the returns to both stocks and index bonds that are available for the retirement saver, and it outlines our simulation algorithm for generating the distribution of plan assets at retirement. Section 1.5 presents our results on the distribution of retirement plan balances and shows the stock of retirement wealth under different assumptions about portfolio allocation. The sixth section reports our expected utility calculations, focusing on different asset allocation strategies during the accumulation phase. A brief conclusion summarizes our findings and suggests several directions for future work, particularly the comparison between the risks of defined contribution and defined benefit retirement plans.

1.1 A Framework for Modeling Retirement Wealth Accumulation in Self-Directed Retirement Plans

To analyze the risk associated with the accumulation of retirement assets in defined contribution pension plans, we need to model the path of plan contributions over an individual’s working life and to combine these contributions with information on the potential returns to holding 401(k) assets in different investment vehicles. We need to decide whether the unit of observation is the individual or the household and to specify the age at which contributions begin and end. For the initial analysis reported in this paper, we focus our attention on married couples. We do this because we suspect that this group is more homogeneous than nonmarried individuals, some of whom are never married and some of whom have lost a spouse. Married couples represent about 70 percent of individuals reaching retirement age. We assume that a fixed fraction of the household’s earnings is contributed to a defined contribution plan. We do not address whether the contributions are due to one or both members of the couple participating in a defined contribution plan. We follow Poterba, Venti, and Wise (1998), who report that the average 401(k) contribution represents roughly 9 percent of contributing household earnings, including both employer and employee contributions.

We assume that the couple begins to participate in a 401(k) plan when the husband is twenty-eight and that they contribute in every year in which the household has Social Security earnings until the husband is sixty-three. Households do not make contributions when they are unemployed or when both members of the couple are retired or otherwise not in the labor force. When the husband is sixty-three, we assume that both members of the household retire, if they have not already, and that contributions cease.

We denote a couple’s 401(k) contribution at age a by [C.sub.i](a), where we index each couple by i. A household’s contribution [C.sub.i](a) = .09 [E.sub.i(a), where [E.sub.i](a) denotes Social Security covered earnings at age a. We express this contribution in year 2000 dollars. To find the 401(k) balance for the couple at age sixty-three (a = 63), we need to cumulate contributions over the course of the working life, with appropriate allowance for the returns on 401(k) assets at each age. Let [R.sub.i](a) denote the return earned on 401(k) assets that were held at the beginning of the year when the husband in couple i attained age a. The value of the couple’s 401(k) assets when the husband is sixty-three is then given by

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

We in turn assume that [R.sub.i](a) is determined by the returns on stocks and index bonds. The couple may hold a portfolio of all stocks, in which case [R.sub.i](a) = [R.sub.stock](a); all index bonds, in which case [R.sub.i](a) = [R.sub.bond](a); or a fifty-fifty mix of the two asset classes, in which case [R.sub.i](a) = .5 [R.sub.stock](a) + .5 [R.sub.bond](a). We discuss presently our calibration of the distribution of risky returns associated with holding stocks.

We report the distribution of [W.sub.i](63), averaged over the 759 households in our sample, for the three different investment strategies. These three distributions provide some evidence on how each investment strategy might affect the retirement resources of households that pursued them. The difficulty with this approach, however, is that it does not capture the cost of low payouts in the event of unfavorable returns. To allow for differential valuation of wealth in different states of nature, we evaluate the wealth in the 401(k) account using a utility-of-terminal-wealth approach. We assume that the household’s preferences over wealth at retirement (which we now write as W, dropping the household subscript for ease of notation) are described by a constant relative risk aversion (CRRA) utility function,

(2) U(W) = [W.sup.1-[alpha]]/1 – [alpha]

where [alpha] is the household’s coefficient of relative risk aversion. The utility of household wealth at retirement is likely to depend on both 401(k) and non-401(k) wealth, and thus we need to modify equation (2) to allow for other wealth:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The difference in the utility associated with different levels of 401(k) wealth is likely to be very sensitive to the household’s other wealth holdings, so in the empirical analysis that follows, we summarize the balance sheets of retirement-age households in the HRS.

To determine the expected utility associated with various investment strategies, we generate hypothetical thirty-five-year 401(k) return histories associated with the all index bonds, fifty-fifty bonds or stocks, and all stock investment strategies for each household in our sample. Each return history, denoted by h, generates an associated 401(k) wealth at age sixty-three, [W.sub.401(k),h] (63), and a corresponding utility level, [U.sub.h], where

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

We evaluate the expected utility of each portfolio strategy by the probability-weighted average of the utility outcomes associated with that strategy, and we denote these expected utility values [EU.sub.SP500], [EU.sub.Bonds], and [EU.sub.50-50], respectively. These utility levels can be compared directly for a given degree of risk tolerance. They can also be translated into certainty equivalent wealth levels (Z) by asking what certain wealth level would provide a utility level equal to the expected utility of the retirement wealth distribution. The certainty equivalent of an all-equity portfolio, for example, is given by

(5) [Z.sub.SP500] = [[[EU.sub.SP500](1 – [alpha])]1/(1 – [alpha]).sup.1/(1 – alpha])] – [W.sub.non-401(k)].

We present certainty equivalent calculations of this form to summarize our findings. Note that when the household has non-401(k) wealth, the certainty equivalent of the 401(k) wealth is the amount of 401(k) wealth that is needed, in addition to the non-401(k) wealth, to achieve a given utility level. We treat non-401(k) wealth as nonstochastic throughout our analysis.

1.2 Earnings Profiles for Current Retirees

Calibrating the expected utility of various 401(k) portfolio strategies requires information on both the earnings histories and the non-401(k) wealth held by these households. We obtained these data for households in the 2000 wave of the HRS. The HRS is a longitudinal study of the economic and health status of older Americans. In the first wave of the study (1992), in-home interviews were conducted for respondents in the 1931-41 birth cohorts and their spouses. Follow-up surveys were administered by telephone every two years. The fifth wave of the survey was completed in 2000, and the core final data for this wave were released in September 2002. This wave provides the most recent and complete source of information on the balance sheet of U.S. households around retirement age.

Table 1.1 shows the relationship between the number of households in various waves of the HRS and the corresponding household counts for the U.S. population. There were 7,580 households in the first wave of the HRS, but various factors, the most important of which are death or voluntary termination of survey participation, reduced the sample size in subsequent waves. By the 2000 wave, respondents from only 6,074 of the original households remained. After accounting for household splits due to divorce and excluding five observations with missing birth years, we had a sample of 6,195 households in 2000. The sampling probabilities for these households suggest that they represent 16.7 million U.S. households. Among these households, 4.3 million had a household head, which we define as the husband in the case of married couples, with less than a high school education; 8.6 million had a household head with maximum education attainment of high school or some college; and 3.8 million had a household head with a college or postgraduate education. Because lifecycle earnings profiles differ for households with different levels of education, we present separate earnings histories for these three groups.

We construct an earnings profile for each household using data from the Social Security administrative records file. These data are available for 4,233 of the 6,195 households in the 2000 wave of the HRS and contain Social Security earnings from 1951 to 1991. Appendix table 1A.1 provides a detailed breakdown of the number of sample households in the HRS that satisfy our further data requirements and are included in our sample. Throughout our analysis, we deflate historical nominal wages by the Consumer Price Index (CPI) to construct real wages at each age. For years after 1991 in which a member of the household was still working, we multiply reported HRS wage and salary earnings by a scaling factor equal to the ratio of Social Security administrative earnings in 1991 to reported HRS earnings in the same year. We thereby construct a proxy for Social Security earnings for 1993, 1995, 1997, and 1999. We assume that in even-numbered years for which we do not have a survey response, earnings remained at the same level as in the previous year.

We want to base our simulations on households who have completed their working lives, and potentially to consider their wealth at retirement relative to their final earnings. We therefore construct a measure of final earnings that we view as representative of household labor earnings near retirement. This measure is defined as household earnings in the year before the household’s reported retirement year. In dual-earner households, this is the year in which the first retirement takes place. Retirement of either the primary or the secondary earner can therefore trigger the final earnings calculation.

A number of the HRS households reported that all members of the household were still working in 2000, so that we could not define final earnings for them. Extrapolating the HRS data to the nation as a whole using HRS weights, out of 16.7 million households in the survey, 9.0 million had at least one member of the household working, and 2.6 million had two earners. Another group, 0.9 million households, contained someone who reported both working and being retired. These individuals are presumably working part-time or have partially reentered the labor force. Out of 2.1 million couples for whom we could compute final earnings, and in which the husband was aged sixty-three to sixty-seven, 1.3 million had at least one person working, 0.5 million had both working, and 0.2 million had at least one person claiming to be both retired and working.

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