Journal of Public Economics 91 (2007) 1920 – 1943www.elsevier.com/locate/econbaseEmployer matching and 401(k) saving: Evidence fromthe health and retirement study Gary V. Engelhardt a,⁎, Anil Kumar baDepartment of Economics, and Center for Policy Research, Syracuse University, United StatesbResearch Department at the Federal Reserve Bank of Dallas, United StatesReceived 29 July 2006; received in revised form 16 February 2007; accepted 26 February 2007Available online 6 March 2007AbstractEmployer matching of employee 401(k) contributions is often touted as a powerful incentive to save forretirement and is a key component in pension-plan design in the United States. Using detailedadministrative contribution, earnings, and pension-plan data from the Health and Retirement Study, thisanalysis formulates a life-cycle-consistent econometric specification of 401(k) saving and estimates thedeterminants of saving accounting for non-linearities in the household budget set induced by matching. Theparticipation estimates indicate that an increase in the match rate by 25 cents per dollar of employeecontribution raises 401(k) participation by 5 percentage points. The parametric and semi-parametric All research with the restricted-access data from the Health and Retirement Study was performed under agreement inthe Center for Policy Research at Syracuse University and the Federal Reserve Bank of Dallas. We thank Dan Black, DavidCard, Courtney Coile, Chris Cunningham, Bill Gale, Roger Gordon, Erik Hurst, Annamaria Lusardi, Brigitte Madrian,Costas Meghir, John Moran, Susann Rohwedder, Clemens Sialm, John Karl Scholz, two anonymous referees and seminarparticipants at Syracuse University, University of Chicago, University of Missouri, University of Virginia, Dutch CentralBank, Econometric Society World Congress, Federal Reserve Bank of Dallas, NBER Transatlantic Public EconomicsSeminar, and the NBER Universities Research Conference for helpful discussions and comments. We are especiallygrateful to Bob Peticolas and Helena Stolyarova for their efforts in helping us understand the HRS employer-providedpension-plan data. The research reported herein was supported (in part) by a grant from the TIAA-CREF Institute and (inpart) by the Center for Retirement Research at Boston College pursuant to a grant from the U.S. Social SecurityAdministration funded as part of the Retirement Research Consortium. Various portions of the underlying dataconstruction were funded by the Center for Policy Research at Syracuse University, the Economics Program, NationalScience Foundation, under grant no. SES-0078845, National Institute on Aging, under grant no. 1 R03 AG19895-01, andthe U.S. Department of Labor. The opinions and conclusions are solely those of the authors and should not be construed asrepresenting the opinions or policy of the Social Security Administration, Federal Reserve Bank of Dallas, Federal ReserveSystem, any agency of the Federal Government, Center for Retirement Research at Boston College, TIAA-CREF, UnitedStates Department of Labor, National Science Foundation, National Institute on Aging, or Syracuse University. All errorsare our own.⁎ Corresponding author.E-mail addresses: [email protected] (G.V. Engelhardt), [email protected] (A. Kumar).0047-2727/ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jpubeco.2007.02.009
G.V. Engelhardt, A. Kumar / Journal of Public Economics 91 (2007) 1920–19431921estimates for saving indicate that an increase in the match rate by 25 cents per dollar of employeecontribution raises 401(k) saving by 365 (in 1991 dollars). Overall, the analysis reveals that the 401(k)saving response to matching is quite inelastic, and, hence, matching is a rather poor policy instrument withwhich to raise retirement saving. 2007 Elsevier B.V. All rights reserved.Keywords: Employer matching; Saving; Taxation; Private pensions1. IntroductionAs 401(k)s have come to dominate the private pension landscape in the United States,researchers and policy makers have given increased attention to the impact of plan characteristicson retirement-saving decisions.1 One important characteristic is whether and to what extent theemployer matches employee contributions. A typical match might be 50 cents for each dollar ofcontribution, up to a maximum percentage of pay, say, 6%. Although much of the discussion bythe popular press and policy makers presumes employer matching raises saving, there is actuallystrikingly little consensus among researchers. Some studies have found that increases in the matchrate raise 401(k) saving (Papke and Poterba, 1995; Clark and Schieber, 1998; Vanderhei andCopeland, 2001; Choi et al., 2002). Others have found that it is not the match rate per se thatmatters, but whether the firm offers a match at all (Even and Macpherson, 1996; Bassett et al.,1998; Papke, 1995; Kusko et al., 1998). That is, providing a match raises 401(k) saving, but anincrease in the level of the match rate (conditional on providing a match) does not. Finally, stillother studies (Employee Benefit Research Institute, 1994; Andrews, 1992; Munnell et al., 2002;General Accounting Office, 1997) have suggested that, conditional on being eligible for a match,an increase in the match rate lowers 401(k) contributions, which, when interpreted in the contextof a simple two-period model of saving, suggests that the income effect dominates the substitutioneffect from the higher rate of return matching provides. Overall, this ambiguity has emerged as animportant empirical puzzle in the literature on saving behavior (Bernheim, 2003).Unfortunately, previous studies have had three important shortcomings. First, they have notcouched their analyses in formal models of intertemporal choice, even though saving involves thesubstitution of resources across time. This means that previous estimates cannot be interpreted asestimates of life-cycle-consistent determinants of 401(k) saving necessarily, because the empiricalspecifications may not have been consistent with underlying utility maximization. So, while theexisting literature has provided quite informative descriptive analyses, it has said little about how401(k) saving may respond to prospective changes in employer matching or what the optimalmatch rate should be to achieve a saving target.Second, with the exception of Choi et al. (2002), Mitchell et al. (2005), and Vanderhei andCopeland (2001), previous studies have failed to exploit the fact that multiple-match-rateschedules and caps on matching induce kinks in the budget set. As has been long recognized in thestudy of taxation on labor supply, reduced-form estimates of behavioral elasticities are biased andinconsistent unless the non-linearity is accounted for explicitly (Hausman, 1985; Moffitt, 1986,1990; Blundell and MaCurdy, 1999). Indeed, the presence of budget-set kinks may reconcile someof the findings of previous studies: for example, the provision of a match may raise 401(k) saving if1This includes work on automatic enrollment (Madrian and Shea, 2001; Choi et al., 2002, 2004), investment incompany stock (Poterba, 2003; Brown et al., 2006; Mitchell and Utkus, 2002), portfolio choice and trading in 401(k)plans (Benartzi and Thaler, 2001; Agnew et al., 2003).
1922G.V. Engelhardt, A. Kumar / Journal of Public Economics 91 (2007) 1920–1943the substitution effect dominates, but variation in match rates may not matter if employees arebunched at kinks.2Finally, previous research primarily has used nationally representative, individual-level surveydata, such as the Current Population Studies (CPS) and Surveys of Consumer Finances (SCF),which are plagued by measurement error. In particular, even though the researcher must know theentire match schedule for a plan to account for the individual's full opportunity set, as well aswhether the match is discretionary or through profit-sharing, the typical survey respondent hasgreat difficulty in accurately conveying even relatively simple pension provisions to interviewers,no less detailed matching schedules. Self-reported contribution data suffer from substantialreporting error as well.3Unlike previous studies, this paper uses the necessary conditions for optimal tax-deferredsaving to derive a life-cycle-consistent econometric specification for 401(k) participation. As analternative to the maximum-likelihood piecewise-linear-budget-set estimation summarized inHausman (1985)–and the recent, related non-parametric extensions by Blomquist and Newey(2002)–and the maximum likelihood differentiable-budget-constraint methodology of MaCurdyet al. (1990), this paper employs instrumental-variable techniques that linearize the budget set atthe observed outcome to calculate the price and virtual-income terms and then instruments tocorrect for endogeneity, which also has a long history, but a recent example of which is Ziliak andKniesner (1999). To calculate budget-set slopes and virtual income in a neighborhood aroundkink points, kernel regression is used to smooth the budget set non-parametrically. We alsoestimate a censored regression model of 401(k) saving to decompose the overall 401(k) savingresponse between the extensive and the intensive margin, where the instrumental-variable Tobitestimator of Newey (1986, 1987b) and an instrumental-variable symmetrically censored leastsquares (SCLS) estimator based on Powell (1986) and Newey (1986) are used.Empirically, the paper makes two additional contributions. First, to circumvent difficultieswith measurement error in 401(k) contributions and matching incentives that have plaguedprevious studies, administrative data from three sources are used: contributions from W-2earnings records provided by the Social Security Administration (SSA) and Internal RevenueService (IRS); detailed matching formulas from pension Summary Plan Descriptions (SPD)provided by the employers of Health and Retirement Study (HRS) respondents; and, acombination of Social Security-covered-earnings histories for 1951–1991 and W-2 earnings for1980–1991, pension SPDs, and pension-benefit calculators to construct public and privatepension entitlements and accruals. The sample consists of 1042 individuals in 1991 eligible for401(k) plans in the HRS.Second, unlike previous pension studies that have used the employer-provided SPDs in theHRS, which are available only for a non-random sub-sample of HRS respondents, the estimationuses methods laid out in Vella (1992) and Das et al. (2003) to correct for potential sampleselection bias using a set of plausible exclusion restrictions derived from Internal RevenueService (IRS) Form 5500 administrative pension-plan filings. The exclusions have substantialpredictive power for determining who is in the analysis sample. There is statistically significantevidence of selection, but the economic impact of the selection on the estimates is mixed: the bias2To compare the non-linear budget set approach with that from the previous literature, we estimated a series of ad hocreduced-form specifications similar in spirit to those in the literature, using the same estimators as used in the literature,but with the HRS data. We were able to replicate the puzzling array of results.3See Mitchell (1988), Starr-McCluer and Sunden (1999), Johnson et al. (2000), Gustman and Steinmeier (2004), andRohwedder (2003a, 2003b).
G.V. Engelhardt, A. Kumar / Journal of Public Economics 91 (2007) 1920–19431923is small in the censored regression specifications of saving, but larger in the discrete choiceparticipation specifications.The estimates from the life-cycle-consistent discrete choice regression specifications forparticipation indicate that the estimated marginal effect of an increase in the employer match rateby 25 cents per dollar of employee contribution raises 401(k) participation by 5 percentage points.In addition, the parametric and semi-parametric estimates from the two-limit censored regressionspecifications indicate that the estimated marginal effect of an increase in the employer match rateby 25 cents per dollar of employee contribution raises 401(k) contributions by 365 dollars (inconstant calendar year 1991 dollars), with just under one half of this effect on the intensive(contributions conditional on participation) margin. Comparing the Tobit and SCLS estimatesusing the Hausman-type test in Newey (1987a), the validity of the Tobit model cannot be rejected.There are three obvious limitations of these findings. First, the HRS focuses on older workers.Whether the estimates apply to younger workers is an open question. Second, this study hasnothing to say about the broader question of to what extent 401(k) saving constitutes new privatesaving, a point of substantial debate in the literature. Third, to keep the model tractable, we haveassumed full rationality in choices, perfect information, no fixed costs, and ignored otherbehavioral anomalies, such as inertia and passivity, that may be important determinants of 401(k)participation (Choi et al., 2002, 2003a,b,c, 2004a,b, 2005).The paper is organized as follows. Section 2 describes the data and sample selection, andSection 3 provides selected descriptive statistics on employer matching. Section 4 lays out theeconometric framework and construction of the key variables. The estimation results arediscussed in Section 5. There is a brief conclusion.2. Data and sample selectionThe data are drawn from the first wave of the HRS, a nationally representative random sampleof 51–61 year olds and their spouses (regardless of age), which asked detailed questions aboutwealth, demographics, and spousal characteristics in 1992, and household income, taxinformation, and IRA contributions in 1991. The HRS collected SPDs, which are legaldescriptions of pensions written in plain English, from employers of HRS respondents for allcurrent and previous jobs in which the respondent was covered by a pension. The SPDs give theemployer