Optimal taxation with deferred compensation.

• Author: Kim, Iltae

1. Introduction

   The traditional theory of optimal taxation assumes that wage and interest incomes are received and taxed at different times. For example, Atkinson and Sandmo [2] and King [9] derived formulae for optimal wage and interest tax rates in the standard two-period life-cycle model in which a representative consumer/taxpayer receives wage income in the first (working) period and saves out of this post-tax wage income. The net return from saving accrues and is taxed as interest income in the second (retirement) period.

   In practice, however, a substantial portion of present wage and salary compensation is paid in the form of (expected) future pension benefits and is therefore tax-deferred. Table I presents data on total civilian wages and salaries and various tax-deferred pension contributions taken from individual income tax returns for 1988 in the United States. These data show that approximately 12 percent of wage income is comprised of tax-deferred pension contributions.

   Table 1. Tax-Deferred Pension Contributions in 1988 (in millions of dollars) Wages and Salaries 2,337,984(a) Tax-Deferred Pension Contributions 276,756 Employer contributions to OASI(b) 120,813 Employer contributions to private plans(c) 75,185 Employer and government contributions to railroad retirement(d) 3,099 Employer contributions to federal, state, and local government pension funds(d) 59,152 Employee contributions to IRA and Keough plans(a) 18,509 Sources:

   (a.) U.S. Department of Treasury, Internal Revenue Service, Individual Income Tax Returns 1988, Publication 1304, September 1991, Table A.

   (b.) U.S. Department of Commerce, Bureau of the Census, Statistical Abstract of the United States 1991, Table 589, p. 361.

   (c.) U.S. Department of Commerce, Bureau of the Census, Statistical Abstract of the United States 1990, Table 677, p. 413, and Table 696, p. 429. Calculated as the ratio of employer costs for pensions to wages and salaries per hour (0.38/10.02) times total, private-industry wages and salaries (1,982,500).

   (d.) Statistical Abstract, Table 590, p. 361.

   In this paper we derive rules for optimal taxation in an alternative two-period setting in which not only interest income but also a part of wage income is deferred. As in the standard model, we assume that interest income accrues in the second period because investors bear temporal risk, so that the return to saving is received only after the resolution of uncertainty about the productivity of capital. However, we assume that incentive contracting in the form of deferred compensation is required to deal with moral hazard and adverse selection in the labor market. For example, Lazear [10] argued that deferred compensation can mitigate the moral hazard problem arising from costly monitoring of the effort and productivity of workers. Salop and Salop [17] showed that pension-type arrangements may act as a sorting device which reduces adverse selection costs when there is asymmetric information about worker productivity.(1) These imperfections dictate that some portion of the return to labor supply be deferred until the verifiable results of work effort have been observed.

   When taxes are incorporated into this framework, the returns from a portion of labor supply and all of saving are received and taxed contemporaneously. As a result, taxation distorts different margins of choice in our model and may lead to a substantially different optimal tax structure. We calculate optimal tax rates for a golden-rule economy in which government debt policy maintains the steady-state capital-labor ratio. For a plausible set of values for the compensated elasticities of consumption and labor supply, and realistic assumptions about the government's revenue requirement and the fraction of wage income that is tax-deferred, we find that optimal tax rates on interest income and on non-deferred wage income are not very sensitive to the presence or absence of deferred compensation. However, the deferred compensation is optimally taxed at a rate substantially above the rate on non-deferred wage income.

   In the following section we set out a partial equilibrium, two-period model of consumer behavior and present the marginal conditions for utility-maximizing consumption and labor supply. In section III we derive expressions for optimal, golden-rule tax rates on deferred and non-deferred wages and on interest income that maximize the welfare of a representative individual subject to the government's budget constraint. Section IV contains a comparison of our formulae for optimal taxation with those of Atkinson and Sandmo [2] and King [9]. In section V, we use empirically relevant values for the compensated own-price elasticities of consumption and labor supply, the government's revenue requirement, and the proportion of wage income that is tax-deferred to illustrate the implications of our approach for the calculation of optimal tax rates along a golden-rule path. Section VI summarizes our principal results and provides concluding remarks.

2. The Consumer's Problem

   We assume that individuals are identical and live for two periods. In the ith period (i = 1, 2), the individual consumes [c.sub.i] units of a composite consumption good, which serves as numeraire, and [l.sub.i] units of leisure (non-market) time. The consumer is endowed with M units of the numeraire good in period 1 and T units of time in each period. The individual is assumed to be retired in the second period so that [l.sub.2] = T.

   A proportion a of the return to supplying labor during the first period is received during that period and can be saved or consumed. A share 1 - [Alpha] of the return to first-period labor is deferred compensation that is received in the second period, along with the gross return to first-period saving.2 Thus, the present-value budget constraint facing a representative consumer is

   (1) [c.sub.1] + [pc.sub.2] + [wl.sub.1] = M + wT,

   where

   (2) p = 1/[1 + r(1 - [t.sub.r])]

   is the price of second-period consumption, r is the one-period interest rate, [t.sub.r] is the tax rate on interest income, and

   (3) w = [[Alpha](1 - [t.sub.w]) + (1 - [Alpha])(1 - [??.sub.w])p]w

   is the after-tax wage rate as a function of the before-tax wage rate w and the tax rates [??.sub.w] on non-deferred wages and [t.sub.w] on deferred wages.

   We assume that the consumer's utility function is continuous, increasing, and concave, and that utility depends separably on the level of government spending g, which in each period is a constant amount per person. The consumer's utility function can thus be written U([c.sub.1], [l.sub.1], [c.sub.2], T), as if it were independent of government spending.

   The government finances the exogenous expenditure level g through contemporaneous taxes on interest and wage incomes. The government's budget constraint is

   (4) g = [Alpha] [t.sub.w] wh + [(1 - [Alpha]) [??.sub.w]wh + [t.sub.r]rs]/(1 + n),

   where n is the fixed rate of population growth, h = (T - l.sub.1]) denotes labor supplied in the first period, and

   (5) s = [pc.sub.2] - (1 - [Alpha])(1 - [t.sub.w]) pwh

   denotes first-period saving. By substituting for s from (5) into (4), the government's budget constraint can be written

   (6) g = [Theta] wh + [t.sub.r] [rpc.sub.2]/(l + n),

   where

   (7) [Theta] = [Alpha] [t.sub.w] + (1 - [Alpha])[[??.sub.w] - [t.sub.r] rp (1 - [??.sub.w])]/(1 + n)

   is the effective average tax rate on wage income.

   The consumer maximizes...