مطابقت کارفرما و پس انداز 401 (k) : شواهد حاصل از مطالعه سلامت و بازنشستگی

Employer matching of employee 401(k) contributions is often touted as a powerful incentive to save for retirement and is a key component in pension-plan design in the United States. Using detailed administrative contribution, earnings, and pension-plan data from the Health and Retirement Study, this analysis formulates a life-cycle-consistent econometric specification of 401(k) saving and estimates the determinants of saving accounting for non-linearities in the household budget set induced by matching. The participation estimates indicate that an increase in the match rate by 25 cents per dollar of employee contribution raises 401(k) participation by 5 percentage points. The parametric and semi-parametric estimates for saving indicate that an increase in the match rate by 25 cents per dollar of employee contribution 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 with which to raise retirement saving.

As 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 characteristics on retirement-saving decisions.1 One important characteristic is whether and to what extent the employer matches employee contributions. A typical match might be 50 cents for each dollar of contribution, up to a maximum percentage of pay, say, 6%. Although much of the discussion by the popular press and policy makers presumes employer matching raises saving, there is actually strikingly little consensus among researchers. Some studies have found that increases in the match rate raise 401(k) saving (Papke and Poterba, 1995, Clark and Schieber, 1998, Vanderhei and Copeland, 2001 and Choi et al., 2002). Others have found that it is not the match rate per se that matters, but whether the firm offers a match at all ( Even and Macpherson, 1996, Bassett et al., 1998, Papke, 1995 and Kusko et al., 1998). That is, providing a match raises 401(k) saving, but an increase in the level of the match rate (conditional on providing a match) does not. Finally, still other studies ( Employee Benefit Research Institute, 1994, Andrews, 1992, Munnell et al., 2002 and 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 context of a simple two-period model of saving, suggests that the income effect dominates the substitution effect from the higher rate of return matching provides. Overall, this ambiguity has emerged as an important empirical puzzle in the literature on saving behavior ( Bernheim, 2003). Unfortunately, previous studies have had three important shortcomings. First, they have not couched their analyses in formal models of intertemporal choice, even though saving involves the substitution of resources across time. This means that previous estimates cannot be interpreted as estimates of life-cycle-consistent determinants of 401(k) saving necessarily, because the empirical specifications may not have been consistent with underlying utility maximization. So, while the existing literature has provided quite informative descriptive analyses, it has said little about how 401(k) saving may respond to prospective changes in employer matching or what the optimal match rate should be to achieve a saving target. Second, with the exception of Choi et al. (2002), Mitchell et al. (2005), and Vanderhei and Copeland (2001), previous studies have failed to exploit the fact that multiple-match-rate schedules and caps on matching induce kinks in the budget set. As has been long recognized in the study of taxation on labor supply, reduced-form estimates of behavioral elasticities are biased and inconsistent unless the non-linearity is accounted for explicitly (Hausman, 1985, Moffitt, 1986, Moffitt, 1990 and Blundell and MaCurdy, 1999). Indeed, the presence of budget-set kinks may reconcile some of the findings of previous studies: for example, the provision of a match may raise 401(k) saving if the substitution effect dominates, but variation in match rates may not matter if employees are bunched at kinks.2 Finally, previous research primarily has used nationally representative, individual-level survey data, 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 the entire match schedule for a plan to account for the individual's full opportunity set, as well as whether the match is discretionary or through profit-sharing, the typical survey respondent has great difficulty in accurately conveying even relatively simple pension provisions to interviewers, no less detailed matching schedules. Self-reported contribution data suffer from substantial reporting error as well.3 Unlike previous studies, this paper uses the necessary conditions for optimal tax-deferred saving to derive a life-cycle-consistent econometric specification for 401(k) participation. As an alternative to the maximum-likelihood piecewise-linear-budget-set estimation summarized in Hausman (1985)–and the recent, related non-parametric extensions by Blomquist and Newey (2002)–and the maximum likelihood differentiable-budget-constraint methodology of MaCurdy et al. (1990), this paper employs instrumental-variable techniques that linearize the budget set at the observed outcome to calculate the price and virtual-income terms and then instruments to correct for endogeneity, which also has a long history, but a recent example of which is Ziliak and Kniesner (1999). To calculate budget-set slopes and virtual income in a neighborhood around kink points, kernel regression is used to smooth the budget set non-parametrically. We also estimate a censored regression model of 401(k) saving to decompose the overall 401(k) saving response between the extensive and the intensive margin, where the instrumental-variable Tobit estimator of Newey, 1986 and Newey, 1987b and an instrumental-variable symmetrically censored least squares (SCLS) estimator based on Powell (1986) and Newey (1986) are used. Empirically, the paper makes two additional contributions. First, to circumvent difficulties with measurement error in 401(k) contributions and matching incentives that have plagued previous studies, administrative data from three sources are used: contributions from W-2 earnings records provided by the Social Security Administration (SSA) and Internal Revenue Service (IRS); detailed matching formulas from pension Summary Plan Descriptions (SPD) provided by the employers of Health and Retirement Study (HRS) respondents; and, a combination of Social Security-covered-earnings histories for 1951–1991 and W-2 earnings for 1980–1991, pension SPDs, and pension-benefit calculators to construct public and private pension entitlements and accruals. The sample consists of 1042 individuals in 1991 eligible for 401(k) plans in the HRS. Second, unlike previous pension studies that have used the employer-provided SPDs in the HRS, which are available only for a non-random sub-sample of HRS respondents, the estimation uses methods laid out in Vella (1992) and Das et al. (2003) to correct for potential sample selection bias using a set of plausible exclusion restrictions derived from Internal Revenue Service (IRS) Form 5500 administrative pension-plan filings. The exclusions have substantial predictive power for determining who is in the analysis sample. There is statistically significant evidence of selection, but the economic impact of the selection on the estimates is mixed: the bias is small in the censored regression specifications of saving, but larger in the discrete choice participation specifications. The estimates from the life-cycle-consistent discrete choice regression specifications for participation indicate that the estimated marginal effect of an increase in the employer match rate by 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 regression specifications indicate that the estimated marginal effect of an increase in the employer match rate by 25 cents per dollar of employee contribution raises 401(k) contributions by $365 dollars (in constant 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 estimates using 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 has nothing to say about the broader question of to what extent 401(k) saving constitutes new private saving, a point of substantial debate in the literature. Third, to keep the model tractable, we have assumed full rationality in choices, perfect information, no fixed costs, and ignored other behavioral anomalies, such as inertia and passivity, that may be important determinants of 401(k) participation (Choi et al., 2002, Choi et al., 2003a, Choi et al., 2003b, Choi et al., 2003c, Choi et al., 2004a, Choi et al., 2004b and Choi et al., 2005). The paper is organized as follows. Section 2 describes the data and sample selection, and Section 3 provides selected descriptive statistics on employer matching. Section 4 lays out the econometric framework and construction of the key variables. The estimation results are discussed in Section 5. There is a brief conclusion.

Previous studies have produced a puzzling array of estimates of the impact of employer matching on 401(k) saving. This probably stemmed from the use of less than ideal data and, more importantly, the failure to incorporate into estimation match-induced kinks in the budget set. In this analysis, based on the life-cycle consistent specification derived, participation and contributions are quite inelastic with respect to employer matching. Subject to the caveats stated in the Introduction, there are a number of potential implications of these findings. First, because of the estimated inelastic response, the analysis reveals that for employers and policy makers interested in promoting retirement saving by older workers through greater 401(k) participation and saving, matching is a rather poor public policy instrument. However, employers who worry about satisfying non-discrimination criteria may place greater value on these increases in participation. Second, a number of commonly advocated reforms to Social Security call for the introduction of voluntary private accounts, to which individuals could choose to contribute additional funds toward Social Security. Under some proposals, the federal government would match those contributions as an incentive. In designing such a system, it would be instrumental for policy makers to know how individual contributions would respond to the government match. Our analysis suggests that government matching of voluntary contributions to any type of Social Security personal account would be relatively ineffective in promoting personal-account contributions (Engelhardt and Kumar, 2005). Third, beyond personal accounts, there is substantial policy interest in the government provision of matching contributions designed to stimulate targeted forms of saving among lower income households, which has led researchers to evaluate the impact of Individual Development Accounts (IDA) (Mills et al., 2006), federal programs for matching IRA contributions, and the adoption of the Saver's Credit (Duflo et al., 2006). In particular, the Mills et al. and Duflo et al. analyses, which were based on randomized field experiments, have shown substantially more elastic responses from matching contributions on IDA and IRA contributions, respectively. Our reading of these two studies suggests that their findings are difficult to extrapolate to employer matching contributions in corporate 401(k) plans for three reasons. First, eligible employees in 401(k) plans are not typically lower income individuals. They are more likely to be substantially better off economically. For example, individuals in the Mills et al. analysis had incomes below 150% of the poverty line. Second, institutional features differ substantially. For example, contributions to a 401(k) plan that are matched are typically done through automatic payroll deduction, whereas contributions to IDAs and IRAs in the Mills et al. and Duflo et al. analyses were not. Third, the matching contributions in the Duflo et al. analysis were offered as part of an unannounced, take-it-or-leave-it decision, whereas employees in a 401(k) can respond to a match by contributing at any point in a given calendar year, or even a different calendar year, without foregoing the option of being eligible for a match. Overall, although these are fascinating studies that will have important implications for policy targeted to lower income households and, through randomization, have convincingly addressed important issues in the econometric identification of the causal effects of matching, these studies are of limited use in formulating policy concerning 401(k) plans. Finally, a number of prominent companies have reduced or eliminated matching contributions in the last few years due to declining profits. Although it remains to be seen if this is a long-term trend, understanding the impact of matching is critical to understanding the impact of these changes on retirement income security for a workforce increasingly dependent on 401(k) plans for retirement. The fact that the estimated response of contributions to the employer match in this paper was quite inelastic suggests that overall 401(k) activity at these firms might not be greatly affected by these changes in matching.