Valuing assets in retirement saving accounts.

INTRODUCTION

The rising importance of assets in tax-deferred accounts has changed the way U.S. households prepare for retirement. Assets in Individual Retirement Accounts and 401(k) plans, which have only been widely available since the early 1980s, exceeded four trillion dollars at the end of 2001. Projections such as those in Poterba, Venti, and Wise (2000) suggest that if current contribution patterns persist and if asset returns follow historical patterns, then assets in retirement saving accounts will grow to become an even more significant part of household wealth in the next three decades.

A substantial literature has addressed the question of whether households change their saving behavior outside tax-deferred accounts when they make 401(k) or IRA contributions. The earliest strands of this literature focused on testing whether the stock of financial assets held by households with tax-deferred accounts was lower than that held by similar households without such accounts. Studies in this tradition include Engen and Gale (2000), Engen, Gale, and Scholz (1996), and Poterba, Venti, and Wise (1996, 1998). These studies analyzed whether contributions to tax-deferred accounts reduced assets held in traditional taxable accounts dollar-for-dollar, or by a smaller amount. While many of the early discussions of retirement saving plans suggested that contributions to these plans would crowd-out a substantial amount of other private saving, most of the empirical literature points to substantial new saving associated with these plans. An implicit premise of the empirical tests that emphasize dollar-for-dollar crowd-out is that one dollar held in a tax-deferred account is equivalent to one dollar held in a taxable account.

Several previous studies have recognized the need to consider deferred tax liabilities in comparing the value of assets in tax-deferred accounts with assets held outside such accounts. Reichenstein (1998) and Reichenstein and Jennings (2003) emphasize the need to adjust the value of assets in retirement accounts when constructing a tax-inclusive measure of household net worth or evaluating preparation for retirement. They propose simple adjustments based on the marginal tax rate that a household will face after retirement. Gale (1998) develops a similar insight in his study of employer-provided pensions and household saving. He estimates the decrease in household saving outside retirement accounts that would keep a household on the same lifetime indifference curve after an increase in retirement saving as before, thereby recognizing the key differences between assets held in taxable and tax-deferred accounts. Most recently, Sibley (2002) analyzes the current, after-tax value of assets in tax-deferred accounts for various saving horizons and rates of return, although without investigating the actual distribution of tax-deferred investors across tax brackets or age groups.

Taxes generate differences in the potential value of assets inside and outside tax-deferred retirement accounts. For traditional IRAs and for 401(k) and 403(b) plans, taxes and in some cases penalties are due when assets are withdrawn from retirement accounts. When the tax rates on withdrawals from tax-deferred accounts are different from the tax rates on accumulation outside these accounts, as in the case of a capital-gain producing asset considered by Crain and Austin (1998), the incentive to save through a tax deferred account can depend on household circumstances. Gokhale and Kotlikoff (2003) note that for some households, the applicable tax rates when assets are withdrawn from a retirement account may be greater than those that applied when the funds were contributed to the account. In this case a household may actually be worse off contributing to such an account than saving in a taxable account.

The deferred taxes that can make a dollar held inside a retirement saving account worth less at retirement than a dollar held in a similar asset outside such an account are offset, particularly for long-horizon savers, by the fact that assets in retirement saving accounts can grow tax-free until the time of withdrawal. This "inside buildup" can make the retirement resources generated by a dollar held inside a tax-deferred account more valuable than those from a dollar outside such an account, particularly if the account holder has a long investment horizon. For Roth IRAs, which do not face deferred tax liabilities because contributions were made with after-tax dollars, inside buildup unambiguously makes one dollar inside such an account worth more than one dollar outside.

This paper presents simple calculations that compare the value of one dollar held inside, and outside, tax-deferred retirement accounts that were funded with pre--tax contributions. The central question underlying this analysis is how much an individual needs at various ages, outside a 401(k)-type plan, to provide the same level of retirement income support that a dollar inside a 401(k) could provide. The answer depends upon a range of assumptions, including how long the assets will be held in the retirement account, how the assets will be drawn down during retirement, what rate of return the assets will earn, how the account holder's tax rate will evolve through time, and what tax rules will apply to withdrawals. The paper notes but does not report detailed calculations about the possibility of leaving retirement account assets to future generations. With well-advised estate planning, it is possible to extend the time period over which assets can accumulate in tax-deferred accounts by deferring withdrawal well beyond the life expectancy of the original contributor.

The paper is divided into five sections. The first section presents simple calculations that illustrate how a dollar held inside a tax-deferred account can generate more, or less, retirement income support than a dollar invested in the same asset but held outside the tax-deferred account. It focuses on the case of bonds held in either location. This section develops the analytical framework that underlies the calculations throughout the paper. The second section repeats the analysis for the case of equity investments, and presents results on the relative valuation of stocks held in tax-deferred accounts and in traditional taxable accounts. The third section reports summary information on the distribution of assets held in retirement accounts by age and marginal federal income tax rate of the household head, and by asset allocation between stocks and bonds. This information is then used to develop aggregate calculations of the average relative value of the assets in tax-deferred accounts and taxable accounts. The fourth section describes the current tax rules that govern withdrawals from tax-deferred accounts and explains how they can be incorporated in the analysis. It demonstrates how households with tax-deferred accounts can increase the value of tax-deferred accumulation by delaying withdrawals until late in their own life, or by arranging to bequeath assets in their tax-deferred accounts to younger relatives. A brief conclusion sketches several directions for further work, and notes several elements of the calculations that could be improved by future empirical research.

VALUING BONDS HELD IN TAX-DEFERRED ACCOUNTS

The central element in any comparison of the value of the retirement income support that can be generated by a dollar held in a taxable account and a dollar held in a traditional tax-deferred account (TDA) such as an IRA or a 401(k) plan is the trade-off between the deferred taxes that will be due on withdrawal from the TDA, which reduce the value of assets in these accounts, and the benefits of tax-free accumulation on TDA assets. This trade-off does not exist for some classes of tax-deferred accounts, such as Roth IRAs, for which there are no future taxes due.

The present paper focuses on the tradeoff for traditional TDAs, which can be illustrated by considering an individual who is a years old and who holds interest-bearing bonds worth [D.sub.bond](a) in a tax-deferred account. Assume that the TDA was funded with pretax contributions, so that when hands are withdrawn from the account, all of the proceeds will be fully taxable at the individual's ordinary income tax rate. Assume further that there is a fixed age A at which the individual plans to withdraw all of the assets from the retirement account, so that the investment horizon is A-a.

This paper considers how much wealth the individual would need to hold in bonds outside a TDA to generate the same after-tax wealth at age A that holding [D.sub.bond](a) in bonds within the TDA will provide. Assume for simplicity that the individual's tax rate on interest income is constant through time, at least until retirement. The tax rate that applies to withdrawals from the tax-deferred account may differ from the tax rate during the accumulation phase. Let the tax rate on interest income received during the accumulation phase equal [tau], and let [[tau].sub.A] denote the marginal tax rate when the assets are withdrawn from the tax-deferred account. Let r represent the instantaneous rate of return on bonds, and assume that all of this return comes in the form of interest payments. Further assume that the return on bonds is the same, regardless of whether the bonds are held in the taxable or the tax-deferred account.

A tax-deferred account with a bond worth [D.sub.bond](a) at age a will grow to [D.sub.bond](A) at age A, where

[1] [D.sub.bond](A) = [D.sub.bond](a)*[e.sup.r(A-a)].

Since withdrawals from the TDA are fully taxable, its after-tax value is (1 - [[tau].sub.A])* [D.sub.bond](A).