Macroeconomics
Public Finance
Computational Macroeconomics

Macroeconomics
Public Finance
Undergraduate Microeconomics
Undergraduate Econometrics

1999 (Oral) Macroeconomics and Public Finance
1998 (Written) Microeconomic and Macroeconomic Theory

Defined Contribution Plan Incentives and Precautionary Savings

Professor William Brainard
Professor George Hall
Professor William Nordhaus

May 2003

Ph.D., Economics, Yale University, expected May 2003
M. Phil., Economics, Yale University, 2000
M.A., Economics, Yale University, 1998
B.A., Economics, University of Michigan, 1996

Recipient of the Raymond Powell Prize for Outstanding Teaching by a Graduate Student in the Yale Economics Department, 2000-2001
Yale University Dissertation Fellowship, Fall 2002
Yale University Fellowship, 1998-2000

Instructor, Yale University, Macroeconomic Theory and Policy (Summer 2000 and Summer 2001)
Head Teaching Assistant, Yale University, Introductory Macroeconomics (Fall 2001 and Fall 2002)
Teaching Assistant (undergraduate level), Yale University, Introductory Macroeconomics (Spring 2001), and Public Finance (Fall 2000)
Teaching Assistant (graduate level), Yale University, Macroeconomic Theory (Fall 1999 and Spring 2000)

Assistant to the Editors, Brookings Papers on Economic Activity, 2001-2002
Research Assistant for Professor Patrick Bayer, Yale University, Spring 2000

Merrill Lynch, San Francisco, CA, Financial consultant, 1996-1997

"Free Money? Vesting Rules, Unemployment Insurance, and 401(k)'s," 2002

"Do 401(k)'s Substitute for IRA's?" 1999

"401(k) Contributions and Unemployment Insurance: Substitutes or Compliments?" (work in progress)

Society for Economic Dynamics (SED) conference, New York City (June 2002)
Inter-university Graduate Student Conference, Princeton University (October 2002)

The impressive growth of defined contribution (DC) plans in the U.S. has spurred a large economics literature aimed at determining the extent to which these plans generate new national savings. This dissertation extends this research by focusing on the substitutability of DC plans for conventional savings.

The ability of DC plans to increase savings depends primarily on the extent to which individuals finance increased savings in the DC plan through a reduction in conventional savings. Any factor that influences the degree of substitution will, in turn, affect the capacity of a plan to create savings. The first essay of the dissertation constructs a life-cycle model to examine the effects of employment risk on the substitution between 401(k)'s and conventional savings. In the wake of the Enron debacle, the media have anchored much of their attention on the possibility of retirement accounts losing money in the event of job loss. One reason why this focus on employment risk might be well placed is that vesting rules explicitly link the 401(k) to employment status. Nearly two-thirds of 401(k) plans include vesting rules, which stipulate a partial or complete forfeiture of employer-matched contributions in the event of a job loss that occurs before a service requirement is met. I characterize this risk by simulating a stochastic dynamic programming model that incorporates vesting and key institutional features of the 401(k) such as withdrawal penalties, contribution limits, matching, and tax incentives. Individuals in the model maximize expected utility by choosing consumption and an allocation of savings between a conventional account and a 401(k) plan, where expectations are formed over uncertainty in returns, wages, employment, and mortality. The numerical solution to the model obtains decision rules for consumption and saving in each of 65 possible periods, which I then use to simulate an economy composed of 15,000 different life-cycle paths.

Across a broad range of parameters, several trends emerge in the simulations. First, the model predicts that the 401(k) substitutes for conventional savings both for retirement savings and, more significantly, buffer savings against employment fluctuations. This result is demonstrated by the negative correlation of unemployment insurance rates with 401(k) contributions of the young. Saving in the conventional account is done only as a buffer against wage uncertainty and when contributions to the 401(k) reach the contribution limit. The withdrawal rules on the 401(k) make the plan extremely illiquid when the individual is employed, so it is not surprising that individuals choose to save in a conventional account to smooth productivity shocks. Second, vesting rules significantly reduce participation in the 401(k). Individuals pursue a strategy of waiting until the vesting requirement is met before contributing anything to the 401(k). A commonly voiced concern about 401(k)'s is that participation is too low given the sizable benefits of contributing. Results from the simulations suggest that when one accounts for uncertainty due to the possibility of job loss, in conjunction with frequently long vesting durations, it is not clear that low participation is irrational. Third, the firm-imposed matching limit strongly influences employee contributions. The preferred tax treatment of the 401(k) does not alone serve as a sufficient inducement for individuals to contribute in early periods of life when a precautionary motive prevails. With matching, however, individuals are persuaded by the higher implicit return to build up a buffer stock in the 401(k) up to the firm matching limit.

The second essay looks at the issue of substitutability from an empirical perspective. I use an empirical model of savings to test the stronger hypothesis that DC plans substitute for one another. The Individual Retirement Account (IRA) and the 401(k) are particularly well suited for this analysis, because both plans share similar features, and they were both initiated in the late seventies. Further, the way in which the plans differ can be exploited to yield insights into their relative substitutability. For example, assets held in a 401(k) plan typically earn a higher after-tax return than they would in an IRA. This informs a prior belief that individuals will contribute to the IRA only after hitting the contribution limit to the 401(k). I use data from the Survey of Income and Program Participation (SIPP) to test this prediction and find only weak evidence in support of this strategy. A disconcerting (from a theoretical perspective) number of 401(k) contributors are infra-marginal with respect to the contribution limit, but still save a positive amount in an IRA. Further, I test the marginal substitution (i.e., saving changes with respect to an increase in the 401(k) limit) and again find little evidence of substitution between plans.

The third essay (work in progress) uses state variation in unemployment insurance to test whether 401(k)'s substitute as a buffer against employment fluctuations, which was one of the predictions of the first essay. I use data from several panels of the SIPP and unemployment data from the Bureau of Labor Statistics to estimate the elasticity of contributions with respect to a change in the unemployment insurance replacement rate. There are two advantages of focusing on the sensitivity of 401(k) contributions to unemployment insurance instead of looking directly at the substitution between 401(k)'s and conventional savings. First, data on retirement plans that include broad measures of wealth are largely unavailable, making it difficult to form inferences about substitution. The exogenous variation in unemployment insurance, on the other hand, can be used to predict the sensitivity of 401(k) contributions to a substitute for precautionary savings. Second, using unemployment insurance instead of conventional savings limits the analysis strictly to buffer-stock savings. There are many possible savings motives (e.g., for durable goods, education, or a home) that could affect an individual's willingness to substitute savings between a conventional account and a 401(k). While it would be interesting to study these other motives, focusing only on precautionary savings has the advantage that it is consistent with the simulation model, in which savings is done either as a buffer against uncertainty or for retirement.