Survey of Income and Program Part~cipation
THE EFFECT OF INCOME TAXATION ON LABOR SUPPLY WHEN DEDUCTIONS ARE ENDOGENOUS
No. 8815
b,+?-
Robert K. T r i e s t T h e Johns Hopkins U n i v e r s i t y
July 1988
T h i s paper i s based on chapter f i v e o f my d i s s e r t a t i o n a t t h e U n i v e r s i t y of Wisconsin-Madi son. I w i s h t o thank t h e members o f my d i s s e r t a t i o n committee. M a r t i n David, Robert Haveman, and A r t h u r Go1 dberger, f o r very he1 p f u l a d v i c e and comments. I have a l s o b e n e f i t t e d from comments by Joseph Cordes and Robert M o f f i t t on an e a r l i e r v e r s i o n o f t h i s paper. A l l remaining e r r o r s are, of course, my own. The views expressed i n t h i s paper a r e t h o s e o f t h e a u t h o r and do n o t n e c e s s a r i l y r e f l e c t t h o s e of t h e Bureau of t h e Census.
TABLE O CONTENTS F
I
I1
. .
.
I 1I
IV
V
. .
VI
NOTES
APPENDIX:
........................ 2 1 ...................... 22 . .......................................................... . ........................ . ...................... ...................................................................... ..................................... ............................. ................................
TABLE 3a
...................................................... 1 . S p e c i f i c a t i o n o f t h e Budget C o n s t r a i n t ............................... 2 S p e c i f i c a t i o n o f Preferences ........................................ 5 FIGURE 1 .ALTERNATIVE REPRESENTATIONS O VIRTUAL INCOME .......... 6 F TABLE 1 .1979 U.S. PERSONAL INCOME TAX ........................... 8 E s t i m a t i o n Problems .................................................. 13 E s t i m a t i o n R e s u l t s ................................................... 16 TABLE 2 .SAMPLE DESCRIPTIVE STATISTICS ........................... 18
Introduction
.LABOR
SUPPLY ESTIMATION RESULTS
TABLE 3b
LABOR SUPPLY ELASTICITY ESTIMATES
Conclusions TABLE 4a
24
LABOR SUPPLY ESTIMATION RESULTS
25
TABLE 4b
LABOR SUPPLY ELASTICITY ESTIMATES
26
28
CONSTRUCTION O THE DATASET F
31 32
C o n s t r u c t i o n of t h e p r e - t a x v a r i a b l e s C o n s t r u c t i o n of t h e t a x v a r i a b l e s
33
REFERENCES
ABSTRACT T h i s paper extends t h e standard s t a t i c model of labor supply and taxation t o t h e case where people a r e able t o legally avoid taxes through t h e use of itemized deductions. 'I'ax deductible expenditures a r e treated a s a Fiicksian composite good
with a price (for those who decide t o itemize) proportional t o one minus t h e marginal tax rate. Estimation of t h e commonly used linear labor supply model
(extended t o incorporate t h e additional composite good) on a cross-section of prime aged married men suggests t h a t tax deductible consumption i s an uncompensated s u b s t i t u t e f o r leisure (and complement with labor). T h e impact of taxes through
t h e relative price of deductible expenditures appears t o be much stronger than through t h e net wage.
I.
Introduction Previous research analyzing t h e e f f e c t of income taxation on labor supply
has largely ignored t h e role of itemized deductions.
No prior empirical work on
labor supply has modeled t h e consumption of tax deductible consumption items a s a choice variable. Hausman (1981) mentions t h e existence of itemized deductions, but
does not t r e a t them a s endogenous in his model.
A large literature has developed
on t h e e f f e c t s of taxation on t h e consumption of specific tax-deductible items, s u c h a s charitable contributions and owner-occupied housing. t r e a t s labor supply a s exogenous. This
1s
However, t h i s literature
surprising, since discussion of t h e role of
itemized deductions has been prominent In much of t h e recent debate o v e r tax reform. T h e current U.S. income tax reform combines marginal tax r a t e reductions Despite t h e importance of t h i s
with restrictions on t h e extent of deductions.
subject, we know v e r y little about t h e effect of itemized deductions and o t h e r tax preferences on t h e response of labor supply to income taxation. Deductions play an important part in the
U.S.
income
tax
system.
Approx~matelyt h i r t y f i v e percent of all U.S. personal income tax r e t u r n s filed f o r
1979 had deductions itemized (I.R.S., 1982).
T h e proportion of revenue raised from
r e t u r n s with itemized deductions i s higher than t h a t since i t i s generally t h e low income tax units who use t h e standard deduction. Of t h e 1979 r e t u r n s with
itemized deductions, aggregate deductions were twenty t h r e e percent of aggregate adjusted gross income.
If deductions a r e an increasing function of income, then t h e
tax payments of a filing unit which itemizes will increase wlth i t s income a t a r a t e lower than i t s s t a t u t o r y marginal tax rate. T h e analysis of federal income tax
r e t u r n s presented by T r i e s t (1987) indicates t h a t t h i s does occur. In this sense, t h e e f f e c t i v e marginal tax r a t e i s lower than t h e s t a t u t o r y marginal t a x rate.
1
T h e purpose of t h i s paper i s t o analyze t h e implications of t h e existence of endogenously chosen deductions f o r t h e specification and estimation of labor supply functions. Section I1 presents t h e budget constraint which a worker faces in a
s t a t i c model when some expenditures a r e deductible from taxable income. Section 1 1 1 develops t h e implications of endogenous deductions for t h e specification of labor supply functions. It i s shown t h a t when t h e commonly used linear labor supply
model is modified t o allow f o r endogenous deductions, t h e coefficients on both t h e net wage and income terms may depend on t h e marginal t a x rate. problems considered. which endogenous deductions create for empirical In section IV t h e estimation are
In t h e endogenous deductions situation, t h e complete budget constraint
estimation method proposed by Wales and Woodland (1979) and Burtless and Hausman (1978) is not feasible.
A much simpler instrumental variables estimator is suggested.
Section V contains empirical results from t h e estimation of a labor supp!y model in which deductions a r e endogenous. Section V I concludes t h e paper.
11. Specification of t h e Budget Constraint
As Heckman (1983) h a s pointed out, when expenditures on certain goods a r e tax deductible i t is no longer appropriate t o t r e a t all consumption a s a Hicksian composite commodity. Hicks' composite commodity theorem s t a t e s t h a t when t h e
relative prices of a group of commodities a r e always constant, then t h a t group of goods can be treated a s a single commodity. In t h e case of labor supply without
taxation, in a cross-section w e observe variation only in t h e price of leisure ( t h e
wage), and all o t h e r goods a r e treated a s a composite.
When t h e r e i s income
taxation with deductions f o r certain t y p e s of consumption, we observe variation in t h e price of leisure and t h e price of deductible consumption. consumption consumption commodity. can and be divided into two composite leisure commodities, is the In t h i s case, tax-deductible composite
nondeductible
consumption;
third
T h e labor supply decision determines not only t h e marginal t a x r a t e on
income, but may also a l t e r t h e relative price of deductible consumption. F o r simplicity, we will look only a t t h e case of a one-worker household in a s t a t i c setting. In t h i s case, t h e budget constraint is:
(1 1
D
+C
-t W L = Y
+ W T - R(1)
where D i s expenditure on deductible goods, C i s expenditure on non-deductible goods, L i s h o u r s of leisure, w i s t h e wage rate, Y is unearned income, T i s t h e time endowment, I i s taxable income, and R i s t h e t a x function. linear function of taxable income: T a x e s a r e a piecewise
(2)
R (I)
== R
(1,) $. tj(I
- 1,)
where j i s t h e index of t h e bracket f o r someone with taxable income I, t j is t h e marginal tax r a t e in bracket j, and I, i s t h e lower taxable income limit f o r bracket j. F o r itemizers, taxable income i s given by:
(3)
I = w(T-L) + Y
.-
D - E
For non-
where E i s t h e value of exemptions, which a r e assumed t o be exogenous. itemizers, taxable income is:
(4)
I = w(T-L)
$-
Y -- S - E
Substituting t h e t a x function into t h e budget
where S i s t h e standard deduction.
constraint yields f o r an itemizer in bracket j
(5)
(1 - t & D
=
+~
( -tj)I. 1
+C
+ t j I j - R(Ij).
(1 - t j ) ( Y -1- w T ) $- t j E
'fhe corresponding expression for a non-itemizer in bracket j is
(6)
D 4- ~ (- t j ) L l
=
4- C
(1 -tj)(Y
-t w T) + tj(E
+ S) + t j I j
- R(Ij).
Some expenditures, such as moving expenses, are tax deductible even f o r nonitemizers. Expenditures of this type are ignored in this paper. 'The primary objection to treating deductions a s a composite commodity in a static labor supply model is that i t ignores all intertemporal considerations. Interest payments, in particular, can only be properly modeled in a dynamic model. However, a dynamic model which fully accounts f o r the possibility of agents avoiding taxes through asset portfolio manipulation, use of income averaging, and use of deductions would be much more complex than t h e dynamic labor supply models developed up t o now. Modeling deductions a s a Hicksian composite good in a static setting seems t o
be a sensible first step in investigating the effect of legal tax avoidance on labor supply. Incorporation of social security taxes into t h e analysis requires some
modification of this framework. deductions.
Social security taxes apply t o labor income before
Therefore, for itemizers who are below t h e upper limit on social
security taxable earned income t h e tax rate on labor income is greater than t h e "subsidy rate" on deductions. Social security is difficult t o incorporate into a
static model since f u t u r e social security benefits are a function of present social security tax payments. Previous work has either ignored social security taxes o r -
has treated t h e employee contribution a s being equivalent t o an ordinary income tax
and ignored t h e employer contribution (as in Hausman (1981)). T h e empirical work reported in t h i s paper is based on t h e latter assumption. S t a t e and local taxes have not been incorporated Into the models estimated in this paper due to lack of data. Similarly, no attempt has been made to adjust t h e
data f o r regional differences in consumer prices (including s t a t e and local sales taxes).
111. Specification of Preferences
If a worker is a t an optimum a t a point on t h e interior of one of t h e segments of t h e budget constraint presented above, then t h e worker's behavior is locally equivalent t o utility maximi7atlon with a budget constraint which is a linear extension of t h a t segment of t h e piecewise-l~nearconstraint. If utility is a function of leisure, deductible consumption, and nondeductible consumption, then for
itemizers t h e Marshallian labor supply ( l e ~ s u r e demand) function is locally a function of t h e net wage, w(l - tj), t h e price of deductible consumption 'relative t o nondeductible consumption, (1 - tj), and "virtual" income, (1 - tj)(Y 3- w T) tJIj
-t t j E
+
- ~ ( 1 ~ 1Note . ~
t h a t t h e t a x r a t e enters t h e labor supply function through all
t h r e e arguments.
Income taxation can be viewed a s combining a lowering of t h e
prices of leisure and deductible consumption with an implicit lump sum tax equal t o tj(Y
+ w T) -
tjE
- tjIj
+
R(Ij) (see figure 1).
T h e second part of t h i s
expression, - t j E
- tjIj
+
R(Ij), is an adjustment f o r t h e f a c t t h a t t h e marginal When t h e This is the
tax r a t e times taxable income is not necessarily equal t o taxes paid. marginal r a t e increases with income, t h i s adjustment will be negative.
source of t h e claim sometimes made t h a t progressive taxation combines a lowering of
FIGURE 1 ALTERNATIVE RE:PRESENTA'TIONS OF VIRTUAL INCOME
t, t,
- marginal tax rate in income from
0 to w1 1'
-
marginal tax rate on income greater than w ti*
Y-0; E-0; D i fixed s
I I 1 i 1 I I I I 1
*
7
t h e price of leisure with an impllcit lump sum s u b s ~ d y . 'Table 1 shows the value of
R(I1)
+
t,I, corresponding t o each bracket of t h e U.S. personal income tax in 1979
( t h e year t h e data used in t h i s s t u d y was collected).
T h e appendtx t o this paper
contains an explanation of other adjustments t o v ~ r t u a lincome, such a s those for
exemptions,
t h e standard deduction, and t h e upper limit t o earnlngs subject t o t h e
social security tax. Since prevlous work a n a l y z ~ n gt h e e f f e c t of taxation on labor supply has let taxes affect labor supply only through t h e net wage and virtual income, it is lnterestlng t o consider what assumptions might justify ignoring t h e e f f e c t of T h e most
taxation on the relatlve price of deductions in labor supply estimation. obvious possibility
;
is
t o assume t h a t utility can then be
1 s
weakly separable between IL,C) and J f L , C , f D . T h e weak
the
utility
function
written
separability assumption implies t h a t t h e consumer's allocation process can be dtvided into two stages.
u
I I I 1 I I I
In t h e frrst, a declsion is made on how t o allocate income between
t h e two groups, ((L,C) and {Dl). T h e group allocations a r e functions of all prices and virtual income. In t h e second stage, a decislon i s made on how t o divide t h e The
(L,CJ group budget between leisure and total nondeductible consumption.
leisure and nondeductible consumption demands a r e functrons of w(1 - tj) and t h e group budget, (1
- t j ) ( Y + w T)
+ tjE +
t j I j - R(Ij) -- (1 - t,)D.
Since t h e group
budget is a funtion of all prices and vtrtual income, i t must be treated a s endogenous in estimation. T h e two stage budgeting which is implicit in t h e weak separability assumption
1 s
not v e r y appealing.
T h e best justification f o r i t might be t h a t some tax
deductions, s u c h as those f o r mortgage interest payments, represent t h e result of
-
TABLE 1 1979 U S . PERSONAL INCOME T A X
TAXABLE INCOME RANGE (DOLLARS)
MARGINAL TAX RATE
IMP1,ICIT LUMP SUM SUBSIDY DIJE T O THE TAX S Y S T E M
Note: The third column shows tho [t,I,
-
R(1,)I adjustment t o unearned
income which must be made in I~noarizingthe budget constraint. .In 1979 employees paid a social security t a x of 6.13% on earnings of up to $22900. For workers with earnings over thls amount, $1403 ( t h e maximum FICA payment) needs t o be subtracted from unearned income in calculating virtual income. virtual income. See t h e appendix for details on other adjustments t o
long term consumption contracts.
However, labor supply also often a t least
lmplici tl y lnvolves s u c h long term considerations. If t h e weak separability assumption holds, then one must estimate both t h e labor supply function and t h e deductions demand function in order t o make inferences concerning t h e e f f e c t of a marginal change in t h e tax r a t e on labor supply. T h e deductrons demand function must be estimated in order t o calculate T h e reason f o r t h i s i s
A
t h e e f f e c t of a tax change on t h e {C,I,) group allocation.
t h a t deductions enter into t h e virtual income term in t h e labor supply function.
change in t h e marginal tax r a t e may cause, through e i t h e r t h e net price o r virtual income arguments, a change in t h e level of deductible consumption. T h e tax-induced change in deductible consumption may cause a change in labor supply through i t s e f f e c t on t h e virtual income argument
In
t h e labor supply function.
Thus, even if
t h e weak separability assumption i s justlfied, little is gained from it.
I t is interesting t o consider t h e implications of another possible separability
assumption. If (C} is weakly separable from (L,D}, then in t h e second &age of t h e
allocation procedure labor supply i s a function of t h e price of leisure relative t o deductible rtems, w, and t h e group budget allocation, (1 - tj)(Y
+ w TI + t , E + t J I J
- I
-
.
In t h i s case, taxes enter t h e labor supply function only through t h e T h e gross wage i s used a s t h e price of leisure in t h i s case since
income argument.
i t is t h e price of leisure relative t o deductible consumption items ( t h e gross wage), r a t h e r than t h e prrce of leisure relative t o non-deductible items ( t h e net wage), which is relevant in t h e second stage of t h e budgeting process. Although t h i s
separability assumption is not especially compelling, i t illustrates t h e extreme e f f e c t s u c h assumptions can have on specification.
In many studies, labor supply has been specified a s a linear function of t h e wage and unearned income. Hausman (1981) derived the parametric form of the
underlying preferences which would result in linear labor supply when there is a single consumption good. Deaton and Muellbauer (1981) generalized this result to They showed that linear labor supply
t h e case of many consumption goods.
w
requires t h a t t h e expenditure function be of t h e form:
where u is t h e utility level, p is t h e vector of consumer prices (excluding the wage), n(u,p) is a positive decreasing function of u and is homogeneous of degree one in p, a(p) is positive and homogeneous of degree zero, b(p) i s positve and homogenous of degree one, and c(p) is homogenous of degree one. T h e various
restrictions are needed to insure t h a t the expenditure function is homogeneous of degree one in p and w, nondecreasing in p and w, increasing in u, and concave in p and w. T h e expenditure function gives t h e minimum value of "full" income
(including the value of t h e time endowment) needed t o reach a given utility level: e(u,w,p)
-
wT
+-
Y.
T h e form of t h e labor supply function can be obtained by
differentiating with respect t o w (to obtain t h e Hicksian leisure demand) and substituting for n ( u , ~ ) : ~
where
H is hours of work (H + L
s
T . This i s similar t o Hausman's specification, )
although stringent restrictions on this model a r e needed in order for i t t o be While Hausman allows t h e compatible with tlausman's stochastic a ~ s u m ~ t i o n s . ~
coefficient
on
virtual
income
to
vary
randomly
(with
a
truncated
normal
distribution) over t h e population t o incorporate heterogeneity in preferences into his model, the endogenous deductions specification allows the coefficient on virtual income t o vary systematically with the marginal tax rate (for itemizers). endogenous deductions specification, In the
b:p), the coefficient on virtual income, -- is a
function of the prices of all consumer goods (excluding leisure).
For itemizers, t h e
relative prices of these goods depends on the marginal tax rate t h a t they face. This spectfication can be adapted t o the case of endogenous deductions by making functional form assumptions about a(p), b(p), and c(p). We take a(p) = a , a special case of homogeneity of degree zero.
A simple functional form f o r b(p)
=
which is consistent with linear homogeneity is b(p) is over all consumer prices.
C b , p , , where t h e summation
t
Assume prices 1 through d-1
are t h e prices of
deductible goods and d through n are the prlces of nondeductible goods. Letting pt refer to the gross price f o r good i, and p,(l - t j ) t h e net price for an itemizer in bracket j, we can write b(p) as:
For non-itemizers, b(p) = b,
-t b,.
Assuming the same functional form for c(p):
c(p)
=,
c,(l
Cd
- tj)
$
CR
+ c,
f o r itemizers in bracket j f o r nonitemizers
Substituting t h e s e expressions into t h e labor supply function f o r itemizers yields:
where w'
= w(l
-tJ
and
Y*
. (1 -t,)Y -
$-
tJE
+ tjIj
- R(I,).
Labor s u p p l y i s
s t i l l linear in t h e net wage and v i r t u a l income, b u t i t i s nonlinear in t h e marginal tax rate. Note t h a t b,, bn, cd, and c,, a r e all dependent on t h e particular t y p e s of
deductions allowed.
Knowledge of t h e s e parameters i s not s u f f i c i e n t t o predict t h e
e f f e c t on labor supply of a change in t h e range of consumption goods which may be deducted. 'I'he labor supply of nonitemizers is:
where w* = w ( l
-tj)
and Y* = ( I
- t,)Y
+
t j ( ~
+
S) -I-
tJIJ
-
R(IJ).
Now
Y*
d i f f e r s from t h e formula f o r v i r t u a l income presented earlter since t h e p a r t of i t reflecting t h e v a l u e of t h e time endowment, w ( l wage term.
- tJ)'T,
h a s been s h i f t e d t o t h e
When t h e r e a r e n o itemizers in t h e sample used f o r estimation, only t h e
sum of bd and bn, r a t h e r t h a n t h e individual parameters, can be identified ( t h e same holds t r u e f o r c, and cn). Somewhat less obviously, r e s t r i c t i o n s on t h e functional
form presented a b o v e a r e needed f o r identification e v e n when some itemizers a r e in
t h e sample.
T h i s is due to t h e partial derivatives of H with respect to b,, b,, c, One possible restriction is t o assume t h a t b,
and c, bcing linearly dependent.5 equals zero.
With t h i s restriction, labor supply is linear in t h e variables for both Estimation can proceed with
itemizers and those who use t h e standard deduction.
c, assumed t o be a function of demographic variables and incorporating an additive stochastic term representing unobserved heterogeneity in preferences.
specification which
1 s
T h i s is t h e
used in section V below.
IV. Estimation Problems
T h e main problem in estimation is due t o t h e f a c t t h a t t h e marginal tax r a t e in not independent of either hours worked or deductions. handling estimation problems of T h e leading method f o r constraint
this type is t h e complete budget
technique described by Moffitt (1986).
Two statistical problems result from t h e First, if t h e tax r a t e is
marginal tax r a t e being a function of hours of work.
imputed based (at least in part) on hours of work times t h e wage (earnings), then measurement error in hours of work will result in measurement error *in t h e calculated marginal tax rate.
A similar problem results if actual and desired hours
of work differ due t o optimization error. parameter estimates will be inconsistent.
If no correction is made f o r this, Second, if t h e r e i s any unobserved
heterogeneity in preferences f o r hours of work, then t h e marginal tax r a t e will generally not be independent of t h e heterogeneity term. 'Those who prefer more
hours of work than average (conditional on observed characteristics) will tend t o face higher than average marginal t a x rates. Wales and Woodland (1979) considered T h e estimators used by
only t h e f i r s t of these problems (measurement error).
14
Burtless and Hausman (1978) and Hausman (1981) correct for both t h e measurement error and slmultanelty problems. However, allowing for both heterogeneity and measurement error
is
computationally very difficult when deductions are endogenous.
Due malniy t o
computat~onal constraints, there has been no work to date which has allowed for both heterogeneity and
optimization/measurement error
in
the
estimation
of
consumer demand (and labor supply) systems with nonlrnear budget constraints when t h e demands for two or more goods are simultaneously determined. Hausman and
Ruud (1984) estrmate a two good demand system (husband's leisure and wife's leisure), but they do not allow for unobserved heterogeneity of preferences. However, assuming t h a t all unexplalned variation i n hours of work is due t o optimiration or measurement error does not seem very attractive. The alternative
approach of assuming that all unexplalned varlation In hours of work is due t o unobserved preferable.
As noted by MaCurciy (1983), when observed and desired hours of work are
differences
in
preferences
for
leisure,
whlle
restrictive,
seems
equal straightforward instrumental variables estimation is consistent.
The gross
wage and unearned income can serve as instruments for t h e net wage and virtual income. However, when there is measurement error in hours of work t h e
distribution of t h e induced measurement error in t h e imputed marginal tax rate (and related variables) depends on t h e location of observed hours of work on t h e budget constraint. For example, if t h e measurement error in hours of work has a
symmetric distribution with zero expectation, t h e expected measurement error for t h e net wage will tend t o be negative for observed hours just less than t h e hours
B I I I I I I I I I I I I I I I I I I
L
a t t h e kink point of a convex constraint, and positive for observed hours slightly greater than t h e klnk hours. For this reason, t h e instrumental variables estimator T r i e s t (1987) presents monte-carlo results which v e r y sensitive t o T h i s suggests t h a t
cannot be used in this situation. suggest that the
instrumental variables estimates a r e not work.
deviations between observed and desired hours of
instrumental variables might be a useful estimation technique even when some measurement error in hours of work exists. One drawback of t h e instrumental variables approach i s t h a t it cannot handle observations where flours of work is observed exactly a t a kink point, since a t s u c h points t h e marginal tax rate is not well deflned. If t h e only source of stochastic
variation in hours of work is unobserved heterogeneity, then t h e r e is positive probability of observing observatlnns a t cech kink point (of a convex constraint). In practice, however, we never have enough Information t o determine if a sample member i s exactly a t a kink point.
In t h i s paper, I assume t h a t t h e only source of unexplained variation in labor
supply
is
due
to
an
additive
s t o c h a s t ~ c term
representing
heterogeneity
in
preferences and use t h e instrumental variables method f o r estimation.
Since t h e
marginal tax r a t e i s endogenous in this model, the right hand side variables which depend on t h e marginal tax r a t e ( t h e net wage, t h e price of deductible relative t o nondeductible consumption, and virtual income) must also be treated a s endogenous. 'The decision t o itemize i s automatically treated a s endogenous by allowing f o r t h e endogeneity of t h e relative price of deductible consumption. one for those who choose not t o itemlze. specification used and t h e choice of instruments. T h i s price is equal t o
.
Sectlon V provides details on t h e
Although measurement e r r o r in hours of work i s not allowed f o r in t h e estimation, t h e dataset used minimizes t h e problem of induced measurement e r r o r in t h e v ~ r t u a l income and net wage variables which usually plagues t h e instrumental variables estimator.
described.
'This is elaborated on in t h e next section, where t h e dataset is
V.
Estimation Results T h e data f o r estimation comes from t h e 1979 Income S u r v e y Development
Program (ISDP).
T h e main advantage of t h e ISDP data i s t h a t i t contains fairly Sample members were directly asked whether o r T h e tax data was
detailed information on taxes paid.
not t h e y itemized deductions and how much t h e y paid in taxes. collected in April, May and June of 1980.
Since t h i s information was collected a t
about t h e same time (or s h o r t l y a f t e r ) 1979 t a x r e t u r n s were filed, response e r r o r i s probably relatively low. Information on labor force behavior was collected
q u a r t e r l y during 1979.
Since t h e recall period i s much s h o r t e r than f o r most
s u r v e y s , t h e accuracy of t h e labor supply and earnings data should be v e r y good. 'The f a c t t h a t t h i s dataset allows t h e s t a t u t o r y marginal tax r a t e f o r both earnings and deductible consumption t o be determined without reference t o h o u r s of work greatly lessens t h e induced e r r o r s in variables problem. Since t h e marginal
tax r a t e is a function of tax payments, and we observe tax payments, we can impute t h e marginal tax r a t e without reference t o h o u r s of work.6 In t h e more usual case
where direct information about tax payments i s not available, taxable income must f i r s t be imputed based on reported earned and unearned income. Earned income is In t h i s
itself often imputed by multiplying reported h o u r s of work times t h e wage.
17
case, measurement e r r o r in hours of work can result in an incorrect marginal tax rate imputation. Note t h a t even when we have direct information about tax
payments, t h e r e is still a problem if actual and desired hours of work differ.
A subsample of married couples was selected f o r use in estimation.
The
selection criteria was t h a t both spouses were between 25 and 60 years old, neither spouse reported extreme disability preventing employment, neither spouse had any farm or self employment income, and t h a t data was completely reported f o r t h e variables used here. T h e fairly small sample size, 432, i s due mainly t o a high Two these
nonresponse r a t e on many of t h e questions related t o nonearned income. percent of the husbands
( 9 ' observations)
had
zero
hours
of
work;
T observations were not used f o r t h e husbands' labor supply e s t ~ m a t i o n . ~ h e wage variable was calculated in two ways. For sample members who reported a wage r a t e For sample
a t least once, an average of their reported wage r a t e s was used.
members who never reported a wage r a t e ( i f , f o r example, t h e y were paid on a s a l a r ~ e d basis), average hourly earnings was used a s t h e wage. Table.2 presents
variable definitions, means, and standard deviations f o r t h e subsample used for
estimation.
F u r t h e r details concerning c o n s t r u c t ~ o n of t h e data s e t a r e in t h e
paper. appendix t o t h ~ s To concentrate on the role of endogenous deductions, and to avoid
controversies involving t h e treatment of agents with z e r o h o u r s of work, labor supply functions were estimated only f o r husbands. 'Traditionally, t h i s group of
people was thought t o have a negative uncompensated wage elasticity and a small positive compensated wage elasticity. studies of male labor supply. Borjas and Heckman (1979) review several
After studies with particularly serious econometric
TABLE 2 SAMPLE DESCRIPTIVE S T A T I S T I C S VARIABLE HHOURS HWAC;E VIRINC HAGE HEDUC MEAN
2116.7 5.55
S T D . DEV.
519.0 2.53
DEFINITION
husband's h o u r s of work (1979) husband's net h o u r l y wage (dollars) husband's v i r t u a l income ($1000'~) husband's age husband's y e a r s of education
(-
6.88
39.5 12.29
6.05
9.95 3.13
self reported disability indicator 1 if disabled; 0 otherwise)
-
WEKN WAGE WEDUC ITEMIZER PDEDIJC IJNERN HGWAGE NCHI.DLT6 NCHILD BLACK
4572 36.9 12.3 .55 .86
4870 9.5 2.6
wife's earnings wlfe's age w ~ f e ' sy e a r s of education Itemized deducions indicator 1 if an itemizer; 0 otherwise)
(-
-
.14 1.23 4.38 .72 1.04
relattve price of deductible con. esset income ($1000'~) husband's gross wage number of children less than 6 number of children between 6 and 15 black race indicator northeast region indicator n o r t h central region indicator s o u t h e a s t region indicator s o u t h central region indicator
NE
NC
SE SC
Sample Size: 423
19
problems
are
removed
from
consideration, t h e
estimated
uncompensated
wage
elasticities range from -.I9 from -.29 t o .24. t o -.17,
t o --.07, t h e e s t ~ m a t e d"total income" elasticities range
and t h e estimated compensated wage elasticities range from .04
EIausman (1985) reviews labor supply studies which have incorporated taxes.
'The f i v e studies of prlme-age male labor supply he cites have uncompensated wage e l a s t i c i t ~ e sranglng from --0.13 to 0.09 and Income elasticities ranging from -0.17 -0.04. to
T h e linear labor supply function derived in section t h r e e was estimated:
where Fft is annual hours of work of person i, pf is t h e price of deductible relative t o non-deductible consumption faced by person i (which is equal t o one f o r nonitemizers and equal t o one minus t h e marginal tax r a t e f o r itemizers), wr is person
i's net wage, Yf is person i's virtual income, and E i is a mean z e r o random variable
which is independent across people.
Equation (11) can be derived from equations (8)
Cn
and (9) by setting b equal t o z e r o and allowing , is equal t o t h e expectation of
Cn
t o v a r y randomly o v e r people; Y
divided by b,,.
Whlle t h l s specification is a d m ~ t t e d l yad hoc, i t i s v e r y s ~ m i l a rt o t h e linear f u n c t ~ o n a lform often used in labor supply studies. T h e key difference between
thls specification and those used In previous work is t h a t t h e marginal t a x r a t e enters t h e labor supply function a s a separate argument in t h e specification used here.
Table 3a presents results of instrumental variables estimation of t h e linear labor supply specification (b, equal to zero); calculations of t h e corresponding labor supply elasticities are presented in table 3b.* included in these specifications. No demographic characteristics were
Column (1 1 contains results from estimation with
t h e price of deductions coefficient constrained to be zero, while column (2) reports results from estimation when this constraint is dropped. elasticity estimates based Table 3b presents In both
on t h e parameter estimates in table 3a.
specifications, t h e compensated
wage elasticity is of the theoretically correct
positive sign, although it is very close to zero in t h e endogenous deductions specification (col~imn(2)). When t h e relative price of deductions is added t o t h e
specification, t h e uncompensated wage elasticity changes from being positive t o negative. research. However, both estimates are well within t h e range found in previous The most price of interesting result in these tables is t h e size of the
uncompensated
deductible consumption elasticity.
This elasticity is
negative and quite large in magnitude, being nearly eight times the size of the uncompensated wage elasticity. It is surprising that deductible consumption is much more strongly substitutable for leisure than is non-deductible consumption. This result has quite interesting implications for t h e analysis of tax reform efforts. Holding virtual income constant, a decrease in t h e marginal tax rate will
decrease t h e labor supply of itemizers through two different channels: (i) by increasing the net wage, and (ii) by increasing t h e relative price of deductible consumption. Since deductible consumption has been found t o be an uncompensated
substitute for leisure, an increase in i t s price causes an increase in the consumption of leisure (decrease in t h e supply of labor). Consider t h e case of an itemizer who
TABLE 3a LABOR SUPPLY ESTIMATION RESIJLTS (standard e r r o r in parentheses') Dependent Variable: HHOURS VARIABLE --CONSTANT HWAGE VIRINC
--
(1)
(2)
-
PDEDUC
Instruments Used: UNERN, UNERN squared, HGWAGE, HGWAGE squared, FIGWAGE*UNERN, HAGE, HAGE squared, HEDUC, HEDUC squared, HAGE*HEDUC, WAGE, W A G E squared, WEDUC, WEDUC squared, WAGE*WEDUC, NCHILD, NCHLDL'r6, HDIS, BLACK, NE, NC, SE, SC all standard e r r o r reported In t h ~ s paper were calculated using t h e heteroskedasticit y consistent es tlrnator proposed b y W h i t e (1982).
TABLE 3b LABOR SUPPLY ELASTICITY ESTIMATES (standard e r r o r in parentheses) Dependent Variable: HHOURS ELASTICITY"
(1) (2)
WAGE (uncompensated)
INCOME
0.049 (0.029)
WAGE (compensated)
DEDUCTIONS (uncompensated)
0.073 (0.080)
All elasticities a r e evaluated a t t h e sample means. T h e income elasticities reported here a r e equal t o t h e mean net wage times t h e virtual income coefficient (adjusted f o r scaling); t h i s is often called t h e "total income elasticity" and differs from t h e usual definition of elasticity
.
has an initial net wage of f i v e dollars per hour.
'The estimates tn column ( 2 ) of
table 3a suggest that, holding virtual income constant, a one percentage point decrease in t h e person's marginal tax r a t e would cause approximately a one and one half hour decrease in labor supply through t h e wage effect, and approximately a fifteen and one half hour decrease i n labor supply through t h e price of deductible ~ consumption e f f e ~ t . 'The impact of the tax change through t h e price of deductions is over ten times as large a s t h e effect through t h e net wage in this case. 'I'hat t h e price of deductible relative t o nondeductible consumption has s u c h a large impact on labor supply i s v e r y surprising. Due t o t h e lack of other
evidence on this issue, t h e estimates reported here must be treated with caution. A wide v a r i e t y of f a c t o r s which a r e not considered here may be influencing t h e results. Failure t o account f o r fringe benefits, family decision making, on t h e job However, most
training, and other dynamic f a c t o r s may be causing misspecification.
of t h e existing labor supply literature i s open t o criticism f o r neglecting a t least one of these factors. T h e results do have some intuitive appeal. Mortgage payments on owner
occupied housing a r e an important component of deductions. t h a t leisure and housing might be substitutes.
I t seems reasonable
In Recker's (1965) time allocation
framework, one might think of housing expenditures as going toward t h e rental of capital goods which increase leisure (or household production) productivity. capital goods have t h e e f f e c t of increasing e f f e c t i v e leisure time. These
In t h i s context,
one might expect t h a t a decrease in t h e price of housing would result in a decrease in t h e demand f o r leisure time.
I t i s important t o remember t h a t leisure is defined
When one realizes this, i t does not seem
a s all non-market work activities.
24
unreasonable t h a t leisure and deductible consumption goods are uncompensated substitutes. 'Tables 4a and 4b a r e similar t o tables 3a and 3b, but report t h e results of estimation when c, is assumed t o be a function of demographic characteristics ( t h e demographic characteristics then enter t h e labor supply function linearly). results here a r e somewhat disappointing. The
T h e compensated wage elasticity is
negative both with and without t h e relative price of deductions in t h e specification; however, in both cases t h e associated standard e r r o r s a r e quite large. As before,
t h e uncompensated price of deductions elasticity dwarfs t h e uncompensated wage elasticity. However, t h e incorrect sign of t h e estimated compensated wage elasticity
c a s t s some doubt on t h e reliability of t h e results.
VI.
Conclusions 'This paper has extended t h e standard s t a t i c model of taxation and labor
supply t o t h e case where some consumpt~on items a r e tax deductible.
'
When t h i s
extension is made, t h e complete budget constraint estimation technique becomes impractical. Instrumental variables estimation of t h e endogenous deductions model
suggests t h a t deductible consumption items a r e uncompensated s u b s t i t u t e s f o r t h e leisure time of prime age married males. T h e e f f e c t of taxation on labor supply
through t h e impact of taxes on t h e price of deductible relative t o nondeductible consumption expenditures i s stronger than through t h e impact of taxes on t h e net wage. Although t h e empirical estimates appear t o be sensitive t o specification, and
.
LABOR
TABLE 4a SIJPPLY ES'TIMATION RESULTS (standard e r r o r in parentheses)
Dependent V a r ~ a b l e :IItIOURS VAR1ABI.L: -- -.- - - -CONSTANT HWAGE (1 1843.6 (190.5)
(2)
31 25.6 (701.6)
--
HAGE NCHILD
Instruments Used: UNERN, UNERN squared, HGWAGE, IIGWAGE squared, HGWAGEwUNERN, HAGE, HAGE squared, HEDUC, HEDUC squared, HAGE*FIEDUC, WAGE, WAGE squared, WEDUC, WEDUC squared, WAGE*WEDUC, NCHILD, NCHLDLT6, IIDIS, BLACK, NE, NC, SE, S C
TABLE 4b LABOR SUPPLY ELASTICITY ESTIMATES (standard error in parentheses)
Dependent Variable: HliOURS
W A G E (uncompensated)
INCOME
0.030 (0.030)
WAGE (compensated)
-0.100 (0.082)
DEDUCTIONS (uncompensated)
should not be taken a s definitive, t h e y do suggest t h a t t h e relative price of deductions e f f e c t may be q u i t e important. F u r t h e r research i s needed t o s e e if t h e in
r e s u l t s reported h e r e hold up when estimation is done with alternative datasets. addition, t h e r e is
i i
need t o combine t h e analysis h e r e with estimates of t h e e f f e c t s l'his additional tax
of income taxation on t h e consumption of tax deductible items.
estimation will be needed in order t o analyze t h e welfare implications of reforms.
NOTES
1.
Although t h e divergence between t h e s t a t u t o r y and e f f e c t i v e marginal t a x r a t e s does suggest t h a t deductions a r e endogenous, i t does not necessarily imply t h a t i t i s important t o t a k e t h i s endogeneity into account in estimating labor supply functions. W h e t h e r o r not treating deductions a s endogenous makes a n y difference in t h e estimated labor supply elasticities i s an empirical question which is investigated in t h i s paper.
2.
T h e term "virtual income" was c o ~ n e dby Burtless and Hausman (1978). budget constraint measured a t z e r o h o u r s of work. t h e vertical intercept a t T h o u r s of work. v a l u e of t h e time endowment.
In t h e i r
usage, however, ~t corresponds t o t h e vertical intercept of t h e linearized Here, i t i s equivalent t o T h e two measures d i f f e r b y t h e
3.
Differentiating t h e expenditure f u n c t ~ o nwith respect t o w yields t h e Hicksian leisure demand function:
Solving f o r n(u,p) from t h e e x p e n d ~ t u r efunction:
Substituting f o r n(u,p) in t h e Hicksian leisure demand r e s u l t s in t h e Marshallian leisure demand:
Applying t h e i d e n t i t y H +I. E'T yields t h e Marshallian labor supply function:
IIausman d e r i v e s his labor supply specification from t h e expenditure function
where t h e expenditure function h e r e is t h e minimum unearned income, Y, needed t o reach u t i l i t y level u. consumption llausman does not indicate how t h e price of t h e Note t h a t Hausman's good e n t e r s t h e e x p e n d ~ t u r e function.
version of t h e expenditure function is defined in terms of t h e minimum r a t h e r than Y respect function:
Y,
+ wT,
needed t o reach u t i l i t y level u. by
1
Differentiation with
t o w and
multiplication
yields t h e Hicksian labor supply
From t h e expenditure function,
Substituting f o r u in t h e Hicksian labor supply function:
T h u s , Hausman's 8 i s equivalent t o
---
1 b,
a to
=I,and b
y t o (T - a
+ %I.
Since Hausman specifies @ t o be s t o c h a s t i c and a and multiples of b.
fixed, his specification
i s consistent with Deaton and Muellbauer's only if (a - T) and c a r e b o t h fixed
6.
Since t h e sum of tax payments and tax credits is a one-to-one function of taxable income, t h e slope of t h a t function, t h e marginal tax rate, is a function of tile sum of tax payments and tax credits. T a x credits, exclusive of credits Some of t h e tax f o r personal exemptions, were approximately 3.1 percent of income tax revenue before credits on r e t u r n s filed in 1980 (IRS, 1981, p. 78). credits included in this figure, s u c h a s t h e retirement income credit, a r e not likely t o have been taken by individuals in t h e sample used for estimation. T h u s , t h e error resulting from ignoring tax credits in imputing t h e marginal tax r a t e is likely t o be v e r y small. T h e r e is some additional measurement e r r o r in t h e marginal tax r a t e resulting from categorization of t h e tax payments variable in t h e public use version of t h e ISDP data. Moreover, t h e calculation of t h e Social Security tax r a t e still depends on hours of work. Since t h e Social Security tax has a constant r a t e up to t h e maximum taxable earnings level ($22900 in 19791, one must know earned income in order t o correctly impute t h e t a x rate.
7.
'I'he small number of observation with z e r o hours of work makes i t unlikely t h a t a significant bias results from excluding these observations.
8.
Nonlinear estimation was also attempted.
However, d u e t o problems of non-
convergence t h e results a r e not reported here.
9.
As Hausman (1983) demonstrates, in actually simulating labor supply responses t o tax changes, one must allow f o r t h e possibility of agents switching from one bracket t o another. proposal.
T h e example here is meant t o be suggestive of t h e
magnitudes of t h e estimated e f f e c t s r a t h e r than a simulation of an actual policy
APPENDIX: CONSTRlJCTION O F THE DA'TASET
Data f o r estimation came from t h e version of t h e 1979 Income S u r v e y Development Program (ISDP) available in t h e SIPP
-
ACCESS database ISDPRUN.
T h e volume edited by David (1982) is a good source of general information about ISDP. T h i s appendix indicates how t h e vasiables used in t h e estimation were
constructed from this database (which is publicly available). T h e variable names in quotation marks a r e column names of tables (relations) in ISDPRUN. T h e ISDP data was collected in six waves, spaced t h r e e months apart. Interviewing occured over t h e February 1979 t o June 1980 period, while t h e data pertains t o t h e November 1978 t o May 1980 time period. into t h r e e rotation groups. T h e sample was split
One f e a t u r e of t h e sample design which makes t h e
data somewhat difficult t o use is that t h e calendar time period covered in each wave differs by rotation group. Due t o this, in order t o aggregate a variable
( f o r example, hours of work) o v e r a given span of calendar time (say, 19791, one must sum t h e values of t h e variable over a s e t of s u r v e y months t h a t v a n e s by rotation group. For example, t o compute hours worked in 1980, one sums t h e
hours of work variable o v e r {wave one, month three) t o {wave five, month two) f o r rotation group A, but sums o v e r (wave one, month one} t o {wave five, month three) f o r rotation group C. An additional complication is t h a t information was
not collected for rotation group C in wave four.
Construction of t h e pre-taxvariables: FIHOIIRS: Flours of work was f i r s t calculated f o r each month by summing ( o v e r
jobs held by a given individual) t h e product of columns "weekspald" (from table "ppmjob") and "weeklyhours" (from table "ppwjob"). T h e monthly
h o u r s figures f o r t h e twelve months of 1979 were t h e n summed t o produce annual h o u r s of work.
FIGWAGE:: 'The gross wage was calculated b y taking an a v e r a g e of t h e h o u r l y wage ("wagerate" in table "ppwjob") o v e r waves in which it was reported. If
t h e wage was not reported In any wave (if, f o r example, a sample member was paid on a salaried basis), t h e n a wage was calculated b y dividing annual labor earnings ( t h e sum of "earn~ngs" in table "ppmjob" o v e r t h e months in 1979) by annual h o u r s of work (HHOIJRS).
IINECRN: Asset Income was calculated f o r each individual b y summing dividend payments ("sc0353", "sc0343", and "sc0346" in table "ppw6div"), rental income ("sc0381", "sc0365", and "sc0376" in table "ppw6rentinc"), i n t e r e s t from
savings accounts ("sc0270", "sc0276", "sc0284", "sc0290", and "sc0293" in table "ppw6savings"), o t h e r i n t e r e s t income ("sc0315", "sc0318", and "sc0321" in
table "ppw6othint"), capital gains income ("sc2358" in table "ppw6taxes"), and o t h e r a s s e t income ("sc0471" in table "ppw6othast"). Asset income f o r e a c h Since t h e
couple was t h e n calculated b y summing o v e r t h e two spouses.
capital gains d a t a were categorized by t h e Census Bureau, t h e mid-point of t h e cell was used t o impute t h e dollar amount.
1)emographic Variables:
T h e d e m o g r a p t ~ ~ c a r ~ a b l e s were taken from tables v
"ppconstant" and "ppwave6".
Con_~tr_u-ct_!on_ _11Cthgta_x variables:
Marglnal t a x r a t e :
Slncc t h e marg~nal t a x r a t e
IS
a function of t a x e s pald
("sc2368" In table "ppwhtaxes"), i t could be Imputed based on t h i s variable. S ~ n c e tax payments were categorized by the Census Bureau, some
measurement e r r o r may be generated by t h i s imputation. Ignored In t h ~ s m p u t a t l o nd u e t o lack of data. ~
T a x c r e d i t s were
I'I'EMIZER:
T h e ltemizer dummy variable was s e t t o one if t h e couple reported
~temiz~ng deductions on t h e i r t a x r e t u r n ("sc0493" in table "ppw6taxesW).
\rIRIN(I:
Virtual income was calculated by f i r s t summing a s s e t income f o r t h e
couple ( U N E R N ) and earnings of t h e w ~ f e . T h e next s t e p was t o add t h e (t,
K(1,)) adjustment shown in table 5.1.
F o r workers with income o v e r t h e
maximum amount s u b j e c t t o social s e c u r i t y taxation, $1403 ( t h e maximum
FICA payment) was t h e n s u b t r a c t e d .
T h e marginal t a x r a t e times $2000
times two plus t h e number of chidren ( t h e imputed v a l u e of exemptions) was t h e n added ( t h i s is t h e t j E term in t h e t e x t ) . Finally, f o r t h o s e who used
t h e standard deduction, t h e marginal t a x r a t e times t h e v a l u e of t h e standard deduction ($3400) was added ( t h i s is t h e t,S term in t h e text).
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and C o n s u m e r Behavior,
9 1981, "Functional I:orrns f3r Labor Supply and Commodity Demands With and Wtthout Quantity F c s t r ~ c t ~ o n s ,E c o n o m e t r i c a , vol. 49, pp. 1521" 1532
Flausman, J., 1981, "1.abor Supply'' i n f l . J . ,Iaron and J.A. Pechman(eds.1, How T a x e s Af,fect E c o n o m i c Rch(tl iclr, U'ash~ngton,D.C.: Brookings Institution
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1983, "Stochastic Problems i n the S ~ m u l a t ~ oof Labor Supply," in M. n Feldsteln (ed .), B e h a v i o r a l S i m ululion ,%lethods i n Tax Policy 'Reseurch, Chicago: University of Chicago Prcss
, 1985, "Taxes and Labor Supply" In A.J. Auerhach and M. Feldstein, Handbook of Public Economics, vol. 1, Amsterdam: North tlolland
---and P. Ruud, 1984, "Family 1,abor Supply with Taxes," A m e r i c a n E c o n o m i c Review, vol. 74, pp. 242-248
Heckman, J. J., 1983, "Comment" on Hausman essay in M. Feldstein (ed.), Rehuvioral S i m u l a t i o n M e t h o d s i n T u x Policy R e s e a r c h , Chicago: I J n ~ v e r s i t y Chicago Press of Internal Revenue Service, 1978, S t a t i s t i c s of Income, 1975 I n d i v i d u a l I n c o m e Tax R e t u r n s , Washington, D.C.: Government Printing Office
$ 1982, S t a t i s t i c s of I n c o m e - 1979, individual I n c o m e Tax R e t u r n s , Washinkton, D.C.: Government Printing Office
liillingsworth, M. R., 1983, Labor S u p p l y , Cambridge, U.K.: Cambridge University Press Lee, L,. F. and M. M. Pitt, 1984, "Microeconomic Models of Consumer and Producer Demand with Limited Dependent Variables," unpublished (Department of Economics, University of Minnesota) MaCurdy, T. E. 1983, "A Simple Scheme f o r Estimating an lntertemporal Model :, of Labor Supply and Consumption in t h e Presence of Taxes and Ilnccrtainty," I n t e r n a t i o n a l E c o n o m i c Review, vol. 24, pp. 265-289 Mof f i t t , R., 1986, "The Econometrics of Piecewise-Linear Budget Constraints: A S u r v e y and Exposition of t h e Maximum Likelihood Method," J o u r n a l of B u s i n e s s a n d Economic S t a t i s t i c s , vol. 4, pp. 317-327 Triest, R., 1987, "'I'he Effect of Income Taxation on Labor Supply," doctoral dissertation, University of Wisconsin-Madison Wales, T. J. and A . D. Woodland, 1979, "l.abor Supply and Progressive Taxes," Review of E c o n o m i c S t u d i e s , vol. 46, pp. 83-95 White, li., "A FIeteroskedasticity-Consistent Covariance Matrix Estimator and a Direct T e s t f o r Fleteroskedasticity," t ' c o n o m e t r i c u , vol. 48, pp. 817-838
-,, 1982, "lnstrumental Variables Regression Observations," t'conumetricu, vol. 50, pp. 483-499
with
Independent