Income tax policy and lifetime labor supply

Journal

of Public

Economics

INCOME

26 (1985) 327-347.

TAX POLICY

AND

Richard U.S. Department Received

August

of Labor,

North-Holland

LIFETIME

LABOR

SUPPLY

A. IPPOLITO* Washington,

1983, revised version

DC 20210,

recilved

USA

February

1984

A progressive income tax structure provides incentives for individuals to alter their rate of work and their age of retirement. Compared to a zero tax or proportional tax equilibrium, progressive taxation induces individuals to take less leisure in the form of retirement in exchange for more leisure during the worklife, especially at high wage levels. The imposition of a special pension tax provision on top of a progressive tax structure offsets the distortion on leisure alternatives imposed by progressivity. Indeed, the pension tax deferral provision can neutralize the impact of tax progressivity on the work profile over life. The magnitude of these tax inducements in the U.S. tax structure are non-trivial and therefore are expected to alter labor supply decisions over the lifetime. The model finds empirical support using data from the Social Security Newly Entitled Beneficiaries Survey.

1. Introduction A substantial literature has arisen to explain the precipitous decline in labor force paticipation rates of older workers in the United States since World War II.’ These studies concentrate on the labor supply effects of social security or private pension rules that may involve actuarially unfair pension formulas, forced savings or restraints on minimum or maximum retirement ages. The presumably actuarially unfair social security formula, in particular, has been treated as an implicit tax on work at older ages.2 At the same time, another tax policy that may signiticantly affect the retirement age has been almost completely ignored. It is well known that by saving for retirement through pensions, individuals can reduce their lifetime tax liability.3 Contributions to pension plans made directly by the firm are *The views expressed in this paper are those of the author and therefore do not necessarily reflect the position of the U.S. Department of Labor. I am indebted to Pauline Ippolito for her help in setting-up and solving the model described below and for her extensive comments. The comments of Gary Fields, Alan Gustman, Donald Parsons, Olivia Mitchell, John Turner and anonymous referees are also gratefully acknowledged. ‘For example, participation rates of males aged 65 or older are now less than half of their 1947 level. ‘Most of these studies are reviewed in Mitchell and Fields (1982), but also see Gustman and Steinmeier (1983), Mitchell and Fields (1984), Parsons (1980), and Ward (1983). 3Since 1974, income saved through IRA and Keogh Plans is also subject to this tax policy, and hence, results developed below for pensions operated by firms can be extended to these new plans. 0047-2727/85/$3.30

0

1985, Elsevier Science Publishers

B.V. (North-Holland)

R.A. Ippolito,

328

Income tax policy

not taxable to the worker until he actually receives the pension. Pensions, when taxed late in life, are usually subject to lower marginal tax rates than would be applied if the income were taxed at the time it was actually earned. While this tax advantage is recognized as a potentially important determinant of the growth in pension coverage, it has not itself been treated as a determinant of the retirement age. The implications of taxation on labor supply have been considered in the context of work-leisure choices during prime working years [see, for example, Kosters (1969) and Rosen (1976)]. Heckman (1976) has considered the role of income taxation in a lifetime variable hours model without retirement, and Kotlikoff and Summers (1979) have considered taxes in a lifetime model that fixes the rate of work but allows variable retirement4 In this paper, a lifetime labor supply model is developed which allows the individual to choose his retirement age and his hours worked in response to tax structure. It is shown that the structure of income taxation and, in particular, tax progressivity and the special tax provision afforded to pensions can generate price incentives that significantly affect an individual’s lifetime labor allocation, especially the decision to retire. The implications of these effects for efficient resource allocation are considered and the sensitivity of labor supply behavior to tax structure is estimated using data from the Survey of Newly Entitled Beneficiaries.

2. A lifetime

model of retirement

In this section, a model is described that captures the main implications of tax structure for optimal lifetime behavior. Consider an individual who wishes to find the consumption path c and hours path h that maximize discounted lifetime utility:

ieppi

[u(c) - V(h)]&,

where i is age, IV is the (certain) age of death, p is the individual’s discount rate, and U and I’ denote the instantaneous utility from consumption and disutility from work. Utility from consumption increases at a diminishing rate, and disutility from work increases at an increasing rate: U’(c) >O, U”(c) ~0, V’(h) >O and V”(h) >O. The specification of lifetime utility in (1) assumes separability in consumption and leisure and independence of utility from age. The utility function in (1) could be generalized to incorporate an uncertain age of death, a bequest motive and interdependencies among 41n a related paper Burkhauser and Turner (1978) develop a model of social security taxation on work at older ages in which workers are permitted to alter their hours of work during their prime working years.

R.A. lppolito, Income tax policy

329

compensation, leisure and age. But these alternatives would merely add to the complexity of the model without affecting the main qualitative results. The individual’s choices are also assumed to be subject to the following wealth and behavioral constraints: P=wh+rY-c-T(I)=s,

(14

Y,=O

(lb)

c>O

and and

Y,=O, Oshsh,

(Ic)

where Y is wealth, Y, and Y, are beginning and ending wealth (which are arbitrarily set to zero), T is the (instantaneous) tax which depends on taxable income I, and w is the wage rate which may depend on the work rate h. Hours worked h are assumed to be non-negative but less than the total hours h available for work and leisure. The rate of savings in the model is denoted by s( = Y). There are several alternative ways to introduce a rationale for retirement into the model. A popular and intuitive way is to specify a wage function that depends on the individual’s age [see, for example, Heckman and MaCurdy (1980)]. As workers age, their productivity falls, reflecting degenerating health or other factors, and hence full-time leisure becomes optimal at some point in the career. But this method forces us into an optimal control framework: while it does not affect the nature of the results, it does obscure them. A simpler alternative, and the one used below, is to specify a wage function that depends on the rate of hours worked. In this model, it is easy to show that full-time leisure at the end of life can be superior to taking leisure evenly over the lifetime because too much leisure during work periods can impose significant wage penalties on the worker. This method provides us with a clean model to generate retirement and to exhibit the sensitivity of lifetime labor supply choices to the selection of income tax structure. The wage rate is assumed to depend on the work rate in the following way: w = w(h),

w’(h)$O

and

as hzh” (ld)

w”(h)<0

for O
Note that if there are sufficiently high fixed costs to employment, the wage rate would be negative at low work rates. Thus, we will assume w(0) ~0. The wage function in (Id) reflects the common-sense notion that while the

330

R.A. Ippolito,

Income

tax policy

individual is free to choose his work rate h in the model, he cannot choose any rate of work without consequence. In particular, it is assumed that there is a work rate ho at which the wage rate is highest and that the wage rate falls as the individual deviates from this maximizing rate. Such a relationship would be the result, for instance, of a tradeoff between the gains of learning by doing or the amortization of fixed costs of employment and the losses due to fatigue or boredom.5 The model does not formally constrain the no-work periods to occur consecutively or at the end of life. Thus, we add the extraneous restriction that the firm precludes intermittent furloughs during the worklife, allowing the individual to enjoy full-time leisure only by retiring at the end of his worklife. The retirement age will be denoted by R. In this model, the only function of savings is to support consumption during the retirement period. The only function of pensions is to provide a vehicle to accommodate this savings motive. Finally, the exposition is facilitated if a specific tax function is used. In particular, assume that the tax function takes the form

T(I)=al

+(b/2)P,

a>O,bzO,

(14

where T(I) denotes instantaneous taxes and I is intantaneous taxable income. The marginal and average tax rates will be denoted by t and t, respectively. The function in (le) leads to a good approximation of the tax schedule that has characterized the post-World War II period in the United States.6 This simple model provides the basis for our evaluation of the labor supply implications of two basic attributes of a comprehensive income tax structure. First, the impact of progressivity in the tax structure is considered. Second, the effect of the tax deferral provision for pension savings is examined within the context of a progressive tax structure. The choice of the retirement age and the rate of work during the worklife are of primary interest in the analysis, but lifetime effects of taxation naturally lead to implications for the rate of savings and consumption. For the sake of clarity, the basic attributes of alternative tax structures are illustrated in the case where the discount and interest rates are zero. The implications of positive ‘For example, in a simple human capital model, investment in firm-specific capital together with learning-by-doing will easily generate a positive wage-hours locus. Fatigue must ultimately offset the efficiency efforts of working higher work rates, especially if labor is significantly specialized. These issues are discussed in Ippolito (1977). ‘Using the data described in footnote 9, the marginal tax rate in the United States is found to be related to the hourly wage rate in the following way:

t = 0.092 + 0.024 wage rate, RZ = 0.96 (148.2) (215.2) where the numbers in parentheses are t-statistics.

R.A. Ippolito, Income tax policy

interest and discount rates for the solution briefly discussed below.

are straightforward

331

and will be

3. Optimal lifetime labor supply with different tax structures 3.1. Simple income tax ~ no pension provision In this section, the individual’s optimal labor allocation is determined within a tax structure that reflects a simple progressive system [like the one defined in (le)]. No pension tax deferral is allowed. Because the discount and interest rates have been set equal to zero, it is straightforward to show that the solution to the model is piecewise constant. That is to say, the optimal consumption path is constant throughout life and the hours path and the savings rate are constant during the worklife. As such, the problem is reduced to that of finding the rate of consumption c, the rate of hours worked h during work periods and the age of retirement R that maximize lifetime utility: U=NU(c)-RV(h) subject

(24

to Rwh=Nc+RT(wh).

The following

first-order

(W conditions

characterize

the solution:

(34

U’(c) = %, V’(h)=I1A(h)[l V(h)s%wh[l

-t(wh)], -f(wh)],

(3W with equality

when R
(34

where .4(h)= w(h)+ w’(h)h is the marginal wage rate earned by working more per period and 2 is the Lagrange multiplier. Recall that t is the marginal tax rate and f is the average tax rate. At any level of consumption, disutility from work is minimized in this model by working as few hours per period and working every period in the life. Retirement is optimal when the wage penalty from working fewer hours per period is sufficient to offset the reduction in disutility generated by a noretirement policy. Since the only interesting case occurs when retirement is optimal. for the remainder of the analysis it is assumed that R
R.A. Ippolito,

332

Income

tax policy

form the condition:

W4

V’(h) A(h)(l-t)

V(h) P(h) = h.

=w(h)(l-f)’

(34

Condition (3d) requires that the ratio of the marginal disutility from an increase in the rate of work during work periods relative to the marginal disutility from an additional period of work must equal the increase in income from increasing the rate of work compared to postponing the age of retirement. The optimal hours worked per period h* is determined completely by condition (3d). Using condition (3a) in condition (3b), the optimal consumption path c* is determined by h *. The age of retirement is solved directly from the budget constraint given, h* and c*. These conditions give us the main implication of tax progressivity for labor supply allocation and efficiency. In particular, it is apparent from (3d) that the existence of progressivity in the tax structure leads the individual to attain any given level of lifetime consumption by exchanging a lower rate of work for postponed retirement. More precisely, recall that the degree of progressivity in the tax function is determined by the parameter b in (le). Differentiating (3d) with respect to b yields: d h*/db ~0.~ Given any level of consumption, it is immediately apparent from the budget constraint that d Rldh 0. Thus, an important feature of tax progressivity is that it distorts the worker’s optimal distribution of work over his lifetime and may have significant implications for his optimal retirement age. Intuitively, the distortion occurs because a progressive tax system taxes higher rates of work more than more periods of work. The individual can reduce his tax burden by reducing his rate of work (the income from which he pays marginal tax rates) and increasing the number of periods worked instead (the income from which he pays average tax rates). Given this labor allocation distortion, it is interesting to note that the effective marginal tax rate on work is measured by the marginal rate t regardless of whether the individual increases work through a higher rate of work or through later retirement. That is to say, it is apparent from (3b) and (3~) that tax progressivity imposes a wedge between the individual’s disutility-price ratios. Representing this wedge by A, it is easily shown that A=[P(h)/iw]-[V’(h)/kl(h)]=(t-f)>O. ‘More particularly, we obtain:

recalling

the tax function

in (le) and differentiating

(3d) with respect

to h,

order condition

for a

dh/db=A1[0.5(1-Q-‘-(1--r)-‘]/[+]
in brackets

[ +] is the negative

of the second

R.A. Ippolito, Income tax policy

333

If the individual increases his rate of work, he pays the tax rate t. If he works more periods, he pays the tax rate f but he also incurs the welfare loss A, and thus, in equilibrium, the individual still bears the implicit tax burden t+A=t.

(4)

3.2. Income taxed over life: Tax deferral for pension savings In a simple income tax structure without a pension provision, the individual’s income is taxed during the period in which it is earned. The pension tax provision allows the individual to defer taxation on that portion of earnings saved through a pension until the individual actually draws on his pension to support consumption during retirement. In essence, the pension tax provision works to convert the income tax into a consumption tax. Since savings occurs only to support retirement in the model, the conversion to a consumption tax is complete.8 Under this tax provision, the individual’s budget constraint is written as: Rwh=Nc+RT(wh-s,)+(N-R)T(-s,),

(54

where si (>O) is the individual’s pension savings rate during each of R work periods, and s2 (CO) is the individual’s pension withdrawal (negative savings) during each of (N-R) retirement periods. Withdrawals from the pension fund must equal contributions: (N-R)s,+Rs,

=O.

Maximizing (2a) subject straightforward to derive optimal solution:

(W to the budget the first-order

constraints conditions

U’(c) = A, V’(h)=iA(h)[l

in (5a) and (5b), it is that characterize the

(64 -t(wh-s,)],

(6b)

V(h) = A[wh - T(wh - sl) + T( - sJ] + r/(s, - sJ,

(64

y = - E,t(wh - SJ

(64

*In a more general model, where savings takes place for reasons other than supporting retirement, the special pension tax provision works in the direction of creating a consumption tax but the conversion is incomplete.

JPE

(‘

334

R.A. Ippolito, Income tax policy

and y= -At(-s,),

(64

where A and y are the Lagrange multipliers. Combining (6d) and (6e) it follows that marginal tax rates during work and retirement periods are equal, t( -s2) = t(wh-s,), and hence consumption gross-of-tax is equal during work and retirement periods: -s2 = w&s,. Using these results and (6d), the condition in (6~) can be rewritten as V(h)=Awh[l-t(wh-Si)]. Finally,

combining V’(h) ---=--A(h)

(64

(6~‘) and (6b), we have the condition:

V(h) w(h).

(60

Condition (6f) completely determines the optimal work rate during work years. The condition holds the main implication of the pension tax deferral for efficient allocation of resources. In particular, note that the hours solution in the case of the pension tax deferral described in (6f) is identical to the solution to (3d) when taxes are proportional (i.e. when t= f). That is to say, the switch towards lower work rates in exchange for postponement of retirement caused by tax progressivity is eliminated by the pension tax deferral provision. The offset occurs because a tax rule characterized by progressivity combined with a pension savings deferral does not discriminate according to the timing of lifetime earnings. Incremental earnings generated from either postponing retirement or increasing the rate of work are in effect spread out as additional taxable income over the lifetime, and therefore are taxed according to a marginal tax rate evaluated at the gross-of-tax consumption rate (wh - si = - sZ). In the U.S. tax structure, the magnitude of the hours-retirement distortion caused by tax progressivity is directly related to the size of the tax wedge t -?, which in turn is directly related to the wage level. The magnitude of these wedges has been calculated for a sample of workers in the United States for the year 1970. The results are shown in table 1. The average tax wedge (t-f) turns out to be approximately 7.6 percent and, furthermore, more than 12 percent of the workforce faces wedges higher than 10 percent.’ %ross income, deductions, exemptions and taxes paid as a function of income level are available from the Internal Revenue Service, Statistics of Income. From this data, a function relating taxes to gross income can be estimated. Tax rates were calculated for the year 1970 but similar results were found for other years. To obtain a realistic estimate of tax rates paid by a representative cross-section of workers, the tax rates were applied to a sample taken from the Newly Entitled Beneficiaries Survey in 1970 (considered in more detail below). It was assumed

R.A. Ippolito, Income tax policy

335

Table1 Tax

wedge,

male

workers 1970.

A=t--i

Proportion workforce

As 5% 5”,,15%

0.4% 87.2% 9.2% 3.2%

in

of

.

Mean: 7.6%,

United

States.

Average wage rate $2.16 4.0 I 8.19 14.58 $6.35

Note: Individuals are assumed to tile a joint return where spouse earnings or outside income equals 50 percent of the worker’s wage earnings. The sample is comprised of 1908 recently retired wage earners from the Newly Entitled Beneficiaries Survey, 1970. A description of income tax calculations is found in footnote 9.

Thus, the impact of the pension tax deferral on labor allocation can be sizeable and perhaps dramatic for high-wage workers. The pension tax deferral also increases the individual’s net wage and therefore generates an income effect and a leisureconsumption price effect. If the government reacts to revenue lost through pension tax deferrals by raising the tax schedule in a compensating manner, these wage effects will be short-lived. In addition, even comparing workers covered and uncovered by pensions, the impact of the tax deferral provision on the absolute wage rate will be smal1.l’ For these reasons, the direct impact of the pension tax provision on the net wage will be ignored for the remainder of the paper.

that each worker filed a joint return and that his wage income comprised income declared. Wages for pension-covered workers are adjusted upward implicit pension savings rate (see below). Applying the tax rate structure relation In (t-i)

= -3.08+0.097 (654.2)( 115.1)

wage rate.

two-thirds of gross to account for their to this sample, the

R* =0.874

was found, where the numbers in the parentheses are r-statistics. “‘The tax rate paid by non-covered workers is t(n$h*)h*). The tax rate paid by covered workers is t(~?(h**)h**), where w(/i**),** > w(h*)h*. Using the Newly Entitled Beneficiaries Survey, which is discussed below, it is evident that pension savings represents only about 15 percent of the gross wage (s, =O.l5wh). Since the median tax rate is approximately 0.25, it follows that pensions could reduce the marginal tax rate for the average worker by approximately 3.75 percentage points. But since ~(h**)h**>w(h*)h*, even this difference is exaggerated. Combining the small implied tax reduction with the pervasive low estimates of labor supply elasticities in the literature [see Borjas and Heckman (1979)], it is evident that lifetime labor supply effects from the pension tax deferral will be nil.

336

3.3. Extensions

R.A. Ippolito, Income tax policy

of the model

If the model is generalized to allow either positive interest and discount rates, or age-dependent utility and wage functions, the solutions would no longer be piecewise constant, but rather would be expressed in terms of continuous consumption and hours paths. The qualitative nature of the results, however, would be the same: progressive taxation artificially flattens hours paths; the pension tax deferral removes the distortion. But one novel problem is encountered. If the optimal consumption path is non-constant, the pension tax deferral scheme itself will induce the individual to artificially flatten his consumption pattern: this is because the pension tax deferral imposes a progressive tax on consumption. The consumption distortion created by the pension tax provision, however, is easily eliminated if the deferral provision in the tax code is written in a way that permits workers to choose the timing of their pension tax deductions, and to borrow from their pension fund.’ ’ These provisions require minor modifications to the U.S. Tax Code. l2

4. Empirical 4.1. Empirical

estimates model

In this section, a simple empirical model is specified for the purpose of generating preliminary estimates of the parameters in the model. Towards this end, the simplifying assumption is made that pension coverage is exogenously given to the worker. If pension tax deferral status in the tax “In this way, if an individual prefers to consume more later in life, he can contribute more heavily to his pension fund early in his career but declare a portion of his contributions as taxable income at the time he makes his contributions. In exchange, these contributions (plus interest) are exempt from taxation at the time he uses the pension to support retirement consumption. Conversely, if the individual prefers to consume more early in life, he can contribute sufficient income to the pension plan to smooth taxable income but borrow back a portion of the contribution for immediate consumption. The individual would then be required to pay back the loan (with interest) to the pension fund and withdraw the proceeds as retirement income for purposes of calculating taxable income during retirement. In a world in which a perfect capital market existed, these rules could lead to an arbitrage problem. That is, if interest on loans is deductible, the individual has an incentive to borrow funds from the market and deposit the proceeds into the tax-preferred pension plan. If the individual can control the timing of his pension deductions, the arbitrage opportunity is limited only by imperfections in the capital market. If these imperfections are not important, the modifications to the U.S. tax code discussed above must be accompanied by elimination of the tax deductibility of interest on borrowed funds. “In the U.S. tax code, the individual is free to declare a portion of his pension savings at the time he makes the contribution (technically known as employee contributions) but only the actual contributions, not the accumulated interest are exempt from later taxation during retirement. In addition, prior to 1982, the U.S. tax code permitted borrowing from the pension fund. But in the Tax Equity and Fiscal Responsibility Act of 1982, limits were imposed on participants’ ability to borrow from their pension plan.

R.A. Ippolito,

income

331

tax policy

code were made available on an individual basis, this assumption would be untenable. But prior to 1974 in the United States, workers could qualify for the deferral only if they worked for a firm that offered a pension plan as a form of compensation. To be sure, in the long run, workers could select themselves into the optimal pension firm. But for the sample considered below (1970 retirees) this assumption has some justification because many if not most retirees who collected pensions upon retirement were already employed by the firm when coverage spread rapidly after the dramatic increase in tax rates during World War II.13 The assumption nevertheless represents a clear (and perhaps important) simplification of reality. In addition, for the purposes of estimation, it is necessary to assume specific functional forms for the utility and wage functions used in the model. For our purposes the following forms are chosen: U(c) = D In c,

(7a)

V(h) = Beuh,

(7’4

and w(h) =

Qh",

(7c)

where D, B, Q, u and a are positive constants. It is easy to show that retirement is optimal only when h
where z=(l is a convenient is a constant.

-t)/(l

-t)

measure

‘-‘Tax rates and pension

(ga) of progressivity

coverage

in the tax structure

and k ( = (1 + a)/u))

data over time can be found in Ippolito

(1983)

R.A. Ippolito,

338

Income tax policy

The variable P in eq. (8) assumes a unit value for workers who are covered by a pension, and zero otherwise. Thus, for workers not covered by pensions, the hours choice is affected by the relative tax term. For pension-covered workers, hours are equal to the constant k: the tax term disappears. Since the tax parameter r is less than unity in a progressive tax system, uncovered workers work fewer hours per period than similarly-paid pension-covered workers. At progressively higher wage levels, the parameter r becomes smaller and therefore the hours wedge becomes even greater. The tax term in eq. (8) reflects the fundamental distortion caused by tax progressivity when pensions are not availed to workers. It is noted that in a proportional tax system the parameter r equals unity and hence hours h are determined strictly by the value of the parameter k for all workers. Thus, in the absence of tax progressivity, wages would not explicitly determine the rate of hours worked in this model. Given the simple structure of the model, the retirement age is found sequentially, given a solution for hours h. More particularly, log-linearizing the function V(h) around equilibrium so that V’(h)=PV(h)/h, it is straightforward to derive the periods equation as14 R=k’th-“,

(9)

where k’ (= N(l +a)D/P) is a constant. The tax parameter r enters the periods equation because in a progressive tax system, while the price effect of a higher wage is determined by the net wage evaluated at the marginal tax rate, the income effect of a higher wage is determined by the net wage evaluated at the average tax rate. Higher wages lead to lower values of r and therefore earlier retirement, reflecting a greater impact of a wage increase on income relative to marginal net wage. In this model the price and income effects of wages on periods are each equal to unity, leaving the power of r also equal to unity. If the tax is proportional (z= l), periods worked are determined directly by the utility and wage function parameters, the rate of hours worked and the (assumed known) age of death. The pension tax provision affects the retirement age R only indirectly through its influence on the rate of work h. 4.2. Econometric

specjfication

A few econometric and (9) are estimated.

issues must be addressed before the equations First, the tax rate calculation for each individual

in (8) in the

14Because pension savings are tax-deferred, tax rates will be evaluated at somewhat lower levels for pension-covered workers. But the impact of this nuance on the value of 7 is trivial. For the average-wage worker in the sample, s=O.87 for a non-pension worker and 0.887 for a pension worker characterized by the average pension savings rate (s=O.lS). Thus. for practical purposes, the impact of pensions on z can be safely ignored.

R.A. Ippolito,

Income tax policy

339

sample is influenced by his rate of work and his wage rate which itself is influenced by his rate of work. While not explicitly recognized above, the wage rate may also be related to age. In addition, pension-covered workers who wish to retire early will exhibit higher pension savings rates which also will affect hours h and periods R. To purge the estimates of the simultaneity bias, the tax term z is calculated at the income rate I =( 1 + sP)hw(h, R), where S is the average pension savings rate (approximately 0.15), h=40 hours per week and 17= 58 years old. l5 The observed wage rate during the last year of full-time work in the last job is adjusted to w(h, R) using the wage-age and wageehours relationships estimated in Gordon and Blinder (1980) and Rosen ( 1976).lh Second, since the model is characterized by a sequential solution, hours enters the periods equation as an independent variable. A statistical problem, however, remains. In particular, hours h and periods R may be related through unmeasured personal characteristics (workaholics have higher h’s and higher R’s, while loafers have lower h’s and lower R’s).” Therefore, rather than entering observed hours directly in (9) the predicted hours generated by the estimation of (8) is used Third, the factors k and k’ in (8) and (9) must be specified in more detail. The two factors are similar except that the individual’s age of death N and the consumption utility parameter D are components of the constant k’ in eq. (9); otherwise they depend upon the leisure utility and wage function parameters. It is assumed that the values of these parameters are related to industry, occupation and personal characteristics, including the worker’s sex, race, education and spouse work status. Other factors besides the age of death will also affect the retirement age without also affecting the rate of hours worked. For example, if tenure levels 15The implicit pension savings rate s is solved directly from the data base used below. The variable s is the proportion of the gross-of-pension savings wage rate implicitly contributed to the pension fund. Assuming that workers receive pensions that are equal to their implicit pension savings. the following relation must be (approximately) true: e~“‘~H’dl, !m( R) J”e’4 rJ(I K’di=Pj B R where h represents annual hours worked, rc(R) is the observed wage rate at age R, B is the age the individual begins his last job. R IS the age the individual retires, r is the real interest rate, g is the rate of growth of wages (which incorporates experience and overall productivity improvements over time), N is the age of death (set equal to the expected age of death), and P is the annual pension. The calculation assumes that workers will earn the real rate of interest on their contributions and that pension payments are indexed to inflation (which approximates reality prior to 1970). Service levels and pension amounts are observed. Thus, assuming that r=0.02 and g=O.O5, the savings rate s was solved for each individual in the survey. lhFor an extended discussion of the role of the worker-loafer distinction in retirement studies, see Ward (1983). “This method of neutralizing the simultaneity bias typically found when confronting tax progressivity is similar to techniques used by Hausman and Wise (1976) and Rosen (1976). More eloquent methods are found in Burtless and Hausman (1978) and Nakamura and Nakamura (198 1) blso see Hausman ( 19X4)]. [s/( 1 -s)]

R.A. Ippolito,

340

Income tax policy

at retirement are expected to fit within a predetermined distribution in the firm, individuals who take longer to find a long-term job match will, other things constant, retire at older ages. In addition, factors may arise late in life that are unexpected and that may affect the immediate choice of retirement age. Health and marital status at older ages, and a last job that was not the longest job may each provide some indication of unexpected events late in life. In the same vein, the individual’s particular retirement date may be affected by the pension and social security formulas in place at the time of his retirement which may have changed in unpredictable ways over his work tenure.‘* In addition, pensions themselves may reflect individual or firm characteristics. If so, the coefficient on the no-pension-tax interaction variables will be biased. To accommodate this potential problem, pension dummy variables will be included in both equations. Unlike the tax effects, pension rules are not related to the wage level either in the firm or across firms, and thus the inclusion of pension dummy variables is expected to measure the influence of either pension rules or pensions-covered workers’ or pension-sponsoring firms characteristics separate from the tax effects.” A social security pension term will also be included to measure the differential impact of public versus private pension formula effects on retirement age. Fourth, and finally, because the tax term z is related to the wage level, the presence of the interaction term between pensions and the tax term z in (8) could measure the influence of the wage rate which does not itself enter the “That is to say, contrary to the assumption made in the model, pension plans are not necessarily neutral in the incentives they provide workers to retire at particular ages. Like the social security system, the present value of pension payments may depend upon the age the individual chooses to retire. If individuals do not select themselves into the perfect plan, or if workers were caught in pension plans that were created in their firms after their employment, non-age-neutrality of the pension plan rules could themselves affect the age of retirement, independent of the effects of the special tax deferral afforded to pension-covered workers. ‘“First, the Internal Revenue Service enforces a set of a discrimination rules that denies taxexempt status to pension plans (or a set of pension plans) that treat employees differently based on their wage level. In addition, available evidence suggests that the implicit optimal retirement ages favored across pension plans (through unfair actuarial formulas) are not systematically related to the average wage level across firms. If pension plan rules were systematically related to the average wage level across firms, retirement ages would be systematically related to the firm’s average wage. To test this hypothesis, a random sample of 3142 individuals were drawn from a Department of Labor data base that includes information about retirees in 1977 and 1978 from 350 pension plans. Using age of retirement as a dependent variable, the following regression results were found: age retirement

: 54.9 + 9.2E-06 wage(95.9) (1.15)

6.94 avg. wage-plan (0.30)

- 0.23 union ( I .26)

+ 0.72 male - 0.88 white + 0.002 plan size + 0.17 age started (3.28) (24.47) (3.97) (3.79) + lirm size + industry

dummy

variables,

with firm

R’ = 0.22,

where numbers in parenthesis are t-values. The l-value on the average wage in the plan variable is only 0.30, suggesting that pension rules that may affect retirement are unrelated to the average wage level in the plan.

R.A. Ippolito,

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341

model. If its exclusion represents a mis-specification, the coefficient on the pension-tax interaction term will be biased. To accommodate this problem, the tax term z is entered into the equation separately. In sum, the two equations which will be estimated sequentially are lnh=a,lnz+a,(l-P)+a,(l-P)ln+AK+error,

(10)

lnR=b,lnh^+b,(l-P)+b,Ins+B(K+H)+error,

(11)

where K and H are vectors of other variables discussed above. The following signs are predicted by the model: a2 > 0, 6, ~0 and b, > 0. Recalling that the tax term is less than unity (r< 1, In z CO), the expected result, a2 >O, implies that workers not covered by pensions work fewer hours than similarly paid workers covered by pensions. Moreover, since the tax term becomes smaller at higher wage rates [z’(w) CO], the prediction a,>0 also implies that the hours distortion for uncovered workers is greater the higher the wage rate. The hypothesis b, 0 merely says that in a model where the substitution and income effects from a wage increase exactly cancel, the income effect must dominate in a progressive tax framework because the income stimulus from higher wage is greater than the price stimulus [i.e. (1 - f) > (1 - t)]. More specifically, the model predicts that a2 and b, will be insignificantly different from unity. Also, recall that -b, is a direct estimate of the utility function parameter j3 = E V/E/z, where E is the dln operator. 4.3. Description of data base Data from the Survey of Newly Entitled Beneficiaries conducted by the Social Security Administration was used to estimate the equations. The survey includes a sample of individuals who applied for social security payments in the United States in 1970. A cross-section of retirees who worked at least a portion of their lives under social security covered employment are included in the survey.20 “‘The survey does not incorporate a simple cross-section of retirees in a given year, nor does it follow a given cohort’s retirement pattern over several years. The Survey of Newly Entitled Beneficiaries is a mixture of these kinds of samples. The survey includes information about the retirement patterns of up-to-age-62 retirees for the 1908 birth cohort. That is, most of the individuals from this cohort who retired at or prior to age 62 applied for social security at age 62 in 1970. Individuals who applied at age 63 in 1970 typically represent individuals from the 1907 birth cohort who retired at age 63. Those who applied at age 64 typically represent individuals from the 1906 birth cohort who retired at age 64, and so on. For our purposes, it is assumed that the cohort effects are small, and hence that the sample can be considered exactly like a cross section sample.

342

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Each individual in the survey reports the year in which he left his last fulltime job which, for our purposes, is taken as an empirical approximation to the age of retirement. If the respondent’s last job was not his longest, additional data are available in the survey that pertain to the individual’s longest job. The number of periods the individual worked in his lifetime is assumed to equal his age of retirement less his age of entry into the workforce. The latter age is assumed to be 18 years old for a high school graduate and is adjusted upwards or downwards, depending upon the individual’s reported years of education. Hours per period worked during the lifetime are measured by the annual hours worked in the last job. Approximately half of the sample respondents were entitled to private pensions when they retired. 4.4. Empirical

results

The results are listed in table 2. First, consider the hours equation in column 1 in the table. While the wage rate per se does not appear explicitly, Table 2 Estimates

of labor

supply

equations Dependent

Independent

variables

Intercept

In h (I)

In R (2)

3.76 (201.5)

9.79 (14.10) - 1.58 (X.67) 0.549 (8.02)

In h^ 0.263 (6.94) 0.192 (3.38) 0.036 (4.57)

In7 (1-P).lnr 1-P Health Retired

for health

reasons

Health

worse than others

Health

problems

during

_ worklife

variable

-0.079 (9.02) 0.0022 (0.58) -0.021 (5.78)

- 0.004 (0.54)

Individual characteristics Female Non-white Years education Spouse

was employed

-0.071 (14.32) - 0.024 (2.70) 0.0026 (3.70) -0.007 (1.87)

-0.148 (11.34) -0.039 (5.41) -0.019 (28.81) -0.013 (4.08)

343

R.A. Ippolito, Income tax policy Table 2 (continued) Dependent

Independent

In h (1)

variables

Marital ,status at retirement Widowed

In R (2)

0.025 (5.26) 0.0013 (0.24) 0.011 (1.95)

Divorced Never married Social security Portion of retirement (included for pension only)”

variable

-0.110 (8.68)

annuity recipients

Last job characteristics Last job was longest

~ 0.078 (11.81) 0.0017 (12.14)

Age started last job (if last job was longest job) Other pension characteristics If last job was not longest: Had pension on longest but not last job Had pension on longest and last job

0.002 (0.21) -0.004 (0.33)

Other variables (not reported) Industry dummy variables” Occupation dummy variables’ Geographical location variablesd R2 Number

of observations

0.15 2719

0.63 2719

“The numerator of this variable is the monthly social security income. The denominator includes this income plus the monthly pension payment. The latter payment is actuarially adjusted to the same age that social security payments started. bDummy variables for each of nine two-digit SIC industry codes were included. ‘Dummy variables for each of ten two-digit BLS occupation codes were included. dDummy variables denoting Central United States, Northeast and South and a dummy variable denoting residence in an urban area were included.

the consistency of the results with other labor supply studies can be readily determined. In particular, since the tax term z is directly related to the wage rate, the relation Eh/Ew=(Eh/Ez)(Ez/Ew) (where Ei denotes dlni) can be used to compute the elasticity of hours with respect to a change in the wage rate Eh/Ew. In particular, it is easy to determine the tax-wage relation in the

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R.A. Ippolito, Income tax policy

United States: Er/Ew = -0.1 1.21 The value of E/I/ET is given as 0.263 in table 2. Therefore, the hours-wage elasticity Eh/Ew equals -0.029, which is consistent with other estimates in the literature [see Borjas and Heckman (1979)]. The results are also consistent with the main implication of the tax model considered above. That is, the coefficient on the interaction term between the no-pension variable 1 -P and the tax variable z is significantly greater than zero. This result is consistent with the predictions of the tax theory, except that the coefficient is somewhat smaller than the unit coefficient portrayed in eq. (10). Recalling that lnz ~0, the results suggest that workers who are not covered by pensions work fewer hours per period. Since the wage rate and the tax term are negatively related (Ew/ET CO), the results also imply that the impact of pension coverage is greater the greater the individual’s wage rate. Workers not covered by pensions who earn the mean hourly wage rate (~1=$6.35, z=O.87) work 2.6 percent fewer hours compared to similarly paid covered workers. Non-covered workers at the 95percentile wage (w=$15.10, r = 0.75) work 5.5 percent fewer hours than similarly paid covered workers. Consider next the periods equation estimates reported in column 2 of table 2. The results support the hypothesis that hours and retirement are substitutes in producing lifetime income. The coefficient on the (predicted) hours variable is negative and significant, suggesting that periods worked over the lifetime are indeed negatively related with the rate of hours worked: the (absolute) elasticity is significantly greater than unity, implying that higher rates of work during the worklife are more than completely offset by fewer periods worked. Recalling the construction of the equation, the (negative of the) estimated coefficient on h is equal to the elasticity of disutility with respect to hours, and thus, the utility parameter /I’= E V/Eh is estimated to be 1.58. The coefficient on the tax ratio variable In z is 0.549, which is significantly greater than zero as expected but lower than the unit coefficient predicted in (11). The estimated coeficient implies a negative relation between periods worked and the wage rate equal to -0.06 [i.e. ER/Ew=(ER/Er)(Ez/Ew)= (0.549)( -0.1 l)= -0.06). Neither the sign nor the magnitude of this relationship is inconsistent with past studies of retirement behavior [Mitchell and Fields (1982)]. The coefficients on the pension dummy variables, while not directly incorporated in the model, are also interesting. First, the coefficient on the no-pension dummy variable in the hours equation is 0.036, suggesting that, 21This result is found from the following Inr=0.067-0.11 lnwage, (55.7) (167.1) where t is constructed /-statistics.

regression

R2 =0.91,

from data described

in footnote

for this data set: n=2719, 9 and where numbers

in parentheses

are

R.A. Ippolito,

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345

holding tax effects constant, pensions are associated with workers and firms that exhibit slightly lower annual work rates. Since pension rules do not explicitly regulate hours worked, it can be presumed that this coefficient owes its significance to some unmeasured characteristics of either firms that offer pensions or individuals who are covered by pensions. In contrast, the coefficient on the no-pension dummy variable in the periods equation is significantly negative. Accounting for hours worked and pension tax effects, the results suggest that pensions themselves are affiliated with later retirement. Since the impact of pensions on the longest but not last job (reported elsewhere in the table) was found to be insignificant, it is reasonable to infer from the result that the measured positive impact of pensions themselves is attributable to actuarial rules that may influence the retirement age, not to the affiliation of pensions with either firms or individuals.22 The impact of pensions on periods worked can also be compared to the impact exerted by social security. Presumably, the impact of social security rules will more likely affect pension-covered workers’ retirement decisions relative to the impact of private pension rules, the greater is the social security annuity relative to the pension annuity. Actuarially adjusting these annuities to an age-65 equivalent, the results show that the more important the social security annuity, the fewer periods are worked by the individual, thereby suggesting that social security rules may induce earlier retirement than pension rules. 5. Concluding remarks The introduction of progressivity into an income tax code creates distortions in lifetime labor allocation. Tax progressivity stimulates workers to take less leisure in the form of retirement in exchange for more leisure during the worklife. The special tax deferral afforded pension savings allows the individual to spread his income over life for tax purposes. All income from work, whether derived from higher rates of work or more periods, are taxed in the same way. Hence, the incentive created by progressivity for the individual to rearrange his labor allocation over life is eliminated. The result holds regardless of the levels of the interest rate and the discount rate. Recognizing the tentative nature of the empirical estimates, the thrust of the results may have important implications for studies of retirement behavior and efficient tax structure. Most empirical retirement studies do not accommodate lifetime behavior, especially in regard to the potential tradeoff between hours and periods worked. 23 The results reported above suggest 22Pensions earned in previous jobs cannot directly influence the age of retirement in the last job. Since these coefficients are insignificant, the significant pension intercept variable for last-job pension suggests that pension rules themselves affect the choice of retirement age. 23An important exception is found in Burkhauser and Turner (1978) who recognize the potential impact of the social security earnings test on retirement age and, through substitution, on hours worked during prime working ages.

346

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tax policy

that this tradeoff might be quite dramatic. If so, the measured impact of social security (or private pension) rules on retirement age could significantly overstate their impact on lifetime (and therefore national) income. Similarly, these same studies tend to assume that workers are conversant with, and sensitive to, social security rules that implicitly tax work at older ages, yet ignore the possibility that these same workers will incorporate the implications of the income tax structure itself for optimal lifetime allocation of work. The results found above strongly suggest that workers do account for these tax rules and that the implication for hours worked (and indirectly for retirement age) can be quite important, even dramatic for high wage earners. The model and results certainly support the lifetime approach to calculating the true nature and magnitude of tax distortion [Levhari and Sheshinski (1972)]. The paper also has implications for the perennial debate about the merits of income versus consumption taxation. The special tax deferral provisions for pension savings does not yield a strict consumption tax solution: among motivation for other things, it only addresses one, albeit an important savings. Nevertheless, recognizing the usual second-best caveats, the provision does have some endearing qualities from a strict efficiency viewpoint: it eliminates the labor allocation distortion inherent in progressive taxation schemes, and it is easy to show that the usual intertemporal neutrality is preserved when positive interest rates are incorporated. The results are attained without affecting the basic underlying progressive tax structure.24 Finally, until recently, the U.S. tax code required individuals to join firmsponsored pensions to qualify for the tax deferral provision for pension savings. This requirement, together with U.S. Internal Revenue Service regulations requiring firms to offer homogeneous pension plans to all its employees, imply that many individuals would be constrained from taking optimal advantage of the law. Recently, the availability of Individual Retirement Accounts (IRAs) has become part of the U.S. tax code (subject to The results of this paper strongly suggest that, from a strict constraints).2s efficiency viewpoint, the availability of unlimited IRAs would represent an attractive alteration to the current U.S. tax code.26

“‘While the pension tax provision eliminates temporal work distortions, it can induce artificial flattening of consumption over the lifetime if the optimal path is not constant. This problem is eliminated if the pension tax code permits flexibility in the timing of pension savings deductions and allows borrowing from the pension plan at market interest rates. At present, the U.S. tax code only partially fulfills these requirements. See footnote 12. *?Since the passage of the Employee Retirement Income Security Act of 1974, individuals not covered by lirm-sponsored pensions have been allowed limited access to IRAs. Since 1981, individuals already covered by a firm-sponsored pension plan can also qualify for IRA savings limits. Under current law these limits are $2000 per worker. 26More discussion about the inefftciencies of IRS rules that favor firm-sponsored pensions and the attractive features of allowing unlimited IRA access is found in Ippolito (1983).

R.A. Ippolito,

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tax policy

341

References Borjas, George J. and James J. Heckman, 1979, Labor supply estimates for public policy evaluation, in: Proceedings of the thirty-first annual meetings (Industrial Relations Research Association, Madison). Burkhauser, Richard V. and John A. Turner, 1978, A time series analysis of social security and its effect on the market work of men at younger ages, Journal of Political Economy 86, 701& 715. Burtless, Gary and Jerry A. Hausman, 1978, The effect of taxation on labor supply: Evaluating the Gary negative income tax experiment, Journal of Political Economy 86, 1103-l 130. Gordon, Roger H. and Alan S. Blinder, 1980, Market wages, reservation wages, and retirement decisions, Journal of Public Economics 14, 431442. Gustman, Alan L. and Thomas L. Steinmeier, 1983, A structural retirement model, mimeo. Hausman, Jerry A., 1984, Taxes and labor supply, in: Alan Auerbach and Martin Feldstein, eds., Handbook of public finance (North-Holland, Amsterdam), forthcoming. Hausman, Jerry A. and David A. Wise, 1976, The evaluation of results from truncated samples: The New Jersey income maintenance experiment, Annals of Economic and Social Measurement 5, 421-445. Heckman, James J., 1976, A life cycle model of earnings, learning and consumption, Journal of Political Economy 84, Sl l-S44. Heckman, James J. and Thomas E. MaCurdy, 1980, A life cycle model of female labor supply, Review of Economic Studies 47, 47774. Ippolito, Richard A., 1977, The division of labor in the firm, Economic Inquiry 15, 4699492. Ippolito, Richard A., 1983, Public policy towards private pensions, Contemporary Policy Issues, a supplement to Economic Inquiry 21, 53-76. Kosters, Marvin, 1969, Effects of an income tax on labor supply, in: Arnold C. Harberger, ed., The taxation of income from capital (The Brookings Institution, Washington, D.C.) 304324. Kotlikoff, Larry J. and Larry H. Summers, 1979, Tax incidence in a life cycle model with variable labor, Quarterly Journal of Economics 93, 7055718. Levhari, David and Eytan Sheshinski, 1972, Lifetime excess tax burden of a tax, Journal of Political Economy 80, 139-147. Mitchell, Olivia and Gary Fields, 1982, The effect of pensions and earnings on retirement: A review essay, Research in Labor Economics 5, 115-156. Mitchell, Olivia and Gary Fields, 1984, The economics of retirement behavior, Journal of Labor Economics (forthcoming). Nakamura, Alice and Masao Nakamura, 1981, A comparison of the labor force behavior of married women in the U.S. and Canada, with special attention to the impact of taxes, Econometrica 49, 451489. Parsons, Donald O., 1980, The decline in male labor force participation, Journal of Political Economy 88, 117-134. Rosen, Harvey S., 1976, Taxes in a labor supply model with joint wage-hours determination, Econometrica 44, 485-507. Ward, Michael, P., 1983, The effect of social security on male retirement behavior, mimeo.