the welfare cost of uncertain tax policy

Journal of Public Economics 37 (1988) 129-145. North-Holland

THE WELFARE COST OF UNCERTAIN TAX POLICY

Jonathan SKINNER* Uniwrsity of Virginia, Charlottesville, VA 22901, USA

National Bureau of Economic Research, Cambridge, MA 02138, USA

Received April 1987, revised version received June 1988

Frequent shifts in tax policy can increase uncertainty about future tax rates. This paper measures the impact of uncertain tax policy on savings, labor supply, and welfare in the United States. A vector autoregression model is used to measure the uncertain component of wage and capital income taxation during 1929-75. These parameters are implemented in a two-period model of consumption and labor supply. Removing all uncertainty about future tax policy can lead to an annual welfare gain of 0.4 percent of national income, or about 15 billion dollars in 1986.

It is as inevitable as death and taxes that Congress will tinker with the tax code.

J. Danforth Quayle’

1. Introduction

Traditional studies that measure the excess burden of taxation assume that tax rates are certain and unchanging, at least until the government decides to change them. Recent experience in the United States has emphasized that taxpayers are justified in treating taxes as another unpredictable factor in an uncertain world. For example, following the passage of the Economic Recovery Act of 1981, a number of provisions, such as the controversial rule allowing the trading of corporate tax credits, immediately came under attack. The threat of repeal discouraged many firms from taking advantage of the tax cuts; the chairman of one corporation, able to sell benefits for less than half their estimated value, attributed the low price to the ‘risk of losing the tax benefits through a change in the tax law or other contingencies’ [Clark (1981)]. It is only recently that the top marginal rate in the newly revamped tax bill has been set at 33 percent; prior proposals specified rates ranging

*I am grateful to Jonathan Eaton, Maxim Engers, T. Wake Epps, Don Fullerton, Donald Kiefer, William R. Johnson, Edgar Olsen, Steven Stern, two anonymous referees, and seminar participants at the University of Washington for helpful suggestions.

‘Quoted in Clark (1983).

0047-2727/88/$3.50 1988, Elsevier Science Publishers B.V. (North-Holland)

130 J. Skinner, Uncertain tax policy

from 27 to 38 percent. Even the current U.S. tax revision promises to be further evised; according to one senator, ‘there will be tax bills coming down the pike for the rest of our lives’ [Birnbaum (1986)].

The potential dangers of uncertain taxes have been recognized since Adam Smith, who observed that, ‘The certainty of what each individual ought to pay is, in taxation, a matter of so great importance, that a very considerable degree of inequality,. . . is not near so great an evil as a very small degree of uncertainty’ [Smith (1976, II, p. 351)].2 This view suggests that the proper role for the government is to reduce uncertainty about future tax rates. However, there are two reasons why unexpected variations in tax rates may increase, rather than decrease, economic welfare. First, if the income fluctu- ation is positively correlated with the tax rate, the variance of net-of-tax income may be reduced, thereby benefiting the risk-averse taxpayer. In a progressive tax system, for example, a rise in income is partially offset by a rise in tax rates, while a fall in income is cushioned by a decline in tax rates. The second reason was suggested by Stiglitz (1982) and Weiss (1976), who argued that random taxation can increase social welfare in the presence of existing taxes. The idea is that the tax uncertainty can cause consumers to work more and save more, thereby increasing revenues and partly offsetting the distortion caused by the initial labor and capital income taxation.3

This paper measures the uncertain component of wage and interest income taxes during the period 1929-75. Marginal tax rates calculated by Joines (1981) are used in a vector autoregression (VAR) model which includes government expenditure and debt, interest rates, and earnings. The estimated coefficients indicate that the one-year-ahead forecast error of the wage tax is 1.8 percentage points, and for the capital income tax 3.0 percent. While unexpected shifts in the wage rate are positively correlated with the wage tax, unexpected shifts in the interest income tax are negatively correlated with the interest rate. One reason for this negative correlation is the implicit ‘tinkering’ that occurs when capital income taxes are not indexed to inflation; unexpected jumps in the inflation rate both increase the real tax rate, and decrease the real ex post interest rate. The interest income tax therefore can accentuate interest rate uncertainty. Using empirical parameters in a two- period model, the annual cost of uncertain taxes is estimated to be 0.4 percent of national income, or 15 billion dollars in 1986. Alternatively, the marginal efficiency cost of increasing the standard error of interest income

*Smith’s concern was that the uncertainty of taxation ‘encourages the insolence and favors the corruption’ of the tax collection agents. Currently, those who write the code, rather than those who collect taxes, might be more subject to lobbying efforts. See also the 1982 Economic Report of the President, p. 111.

3Even if labor supply and savings increase, the consumer may still be worse off owing to the additional uncertainty introduced by the random taxes. The Stiglitz result can be applied either to the case of uncertain future tax rates, or to the case of randomness across individuals at a point in time [Chang and Wildasin (1987)].

J. Skinner, Uncertain tax policy 131

tax uncertainty by one percentage point is estimated to be 0.25 percent of national income.

The remainder of the paper is organized as follows. Section 2 discusses recent studies of tax uncertainty and presents a simple general-equilibrium model of consumer, government, and production sectors which jointly determine labor supply, savings, taxes, government expenditures, and debt. In section 3, a VAR corresponding to the reduced form of this model is estimated. Section 4 provides a numerically computable model of individual consumption and labor supply decisions solved subject to the VAR estimates, while section 5 concludes.

2. A model of uncertain taxation

There has been recent interest in the welfare implications of uncertain or unpredictable tax policy. Bizer and Judd (1988) have developed a general- equilibrium model of capital accumulation with risky taxation, and found that for plausible parameters, (certain) investment tax credits induced more investment than the prospect of future (uncertain) tax rate reductions. Fullerton, Lyon and Rosen (1984) used a disaggregated model of corporate capital to show that uncertain inflation rates affect the capital income tax nonlinearity; the expected welfare cost of capital income taxation exceeds the welfare cost given the expected rate of inflation.

Auerbach and Hines (1987) documented the dramatic variation in investment tax incentives during the postwar period; for example, the effective tax on equipment for a myopic investor ranged from 104 percent in 1975 to -2 percent in 1982. Finally, Kaplow (1986a, 1986b) has argued that the government should not compensate taxpayers when the tax code is changed unexpectedly. The tax changes he considers are efficient responses to a changing environment; by the government withholding any compensation, taxpayers are discouraged from activities which may become inefficient in the future. This paper takes a different view of unexpected tax changes, and focuses instead on the randomness in tax rates caused by an imperfect tax code and government tinkering.

The model presented below allows for a general equilibrium determination of government expenditure and debt, taxes, interest rates, and wages. The purpose of developing this model is to outline the framework used by consumers to form expectations about future factor prices and tax policy. There are three sectors in the economy. The first is composed of consumers who make labor supply and savings choices contingent upon expectations about future net wage and interest rates. The second is the production sector, which relates the supply of labor and capital to gross wages and interest rates. The third sector is the government, which simultaneously determines expenditures, debt, and tax rates.

132 J. Skinner, Uncertnin tax policy

Turning first to the choice facing consumers, written:

f~= U(C,,I,,G,)+E{U(C,,l,,G,)},

I assume that utility is

(1)

where Ci, li and Gi represent consumption, leisure, and the per capita provision of a government output (which can be either a public or private good), and E is the expectations operator conditional on information at period 1. The timing of the model is that individuals choose labor supply at the outset of the period. At the end of the period, wages and interest rates are realized, taxes are paid, Gi is determined by the government, and the consumption decision is made. Labor supply decisions are determined before the net wage is realized to reflect human capital investments and occu- pational choices made early in the life cycle which affect subsequent work effort.4 Although there is no specific bequest function, C, can be thought of as combining second-period consumption and any bequests or assets retained for a later period.

The individual’s budget constraint is written:

hzw;-Rz =S,(l+r:)+h,w:-R,+p---,

1+r; (2)

where w: and r: are the gross-of-tax wage and interest rates in period i, hi is hours of work (hi = 8 -Ii, where f3 is the full endowment of time), Ri measures tax revenue collection in year i, and So savings from the previous period, which is accumulated at the interest rate r:.

The actual tax code in the United States is complex and nonlinear, but it can be approximated by a negative income tax with a guaranteed lump-sum subsidy of p >O in each period, and marginal tax rates ti on wage, and ?i on interest, income. The present value of revenue is:

i?=t,w~h,+~,Sor~-p+(l+rf)-‘[tzw~hz+z,S,r~-p], (3)

and S,-S,(l+r:)+h,w:--RI--C, is defined to be net savings in period 1. Substituting (3) into (2) and rearranging yields:

cl+l”,: hw2 ~=X+h,w,+---,

2 1 +r2

4Alternatively, labor supply could be chosen after the wage is realized. In such a model there would be less lifetime uncertainty since consumers could adjust labor supply to reflect the information conveyed by the realized wage.


where ri =rF( 1 -ri) is the net-of-tax interest rate, wi= wt( 1 - ti) is the net wage, and ‘virtual’ nonwage income X is S,( I+ I~) +,u[l +( 1 + rJ_i]. Note that the two-period utility function may also be expressed in its indirect form J=J=E{V(X, Wl, w2, I,)>.

In the second, production, sector, a linear homogeneous production function is specified of the form:

Yi = _Uki9 hi),

where y,, output, depends on capital ki and labor hi, and all variables are expressed in per capita terms. The production function fi is allowed to vary randomly over time, leading to unpredictable shifts in the marginal product of capital 3jJaki or the marginal product of labor af;:/ahi, holding ki and hi constant. This degree of randomness ensures uncertainty about final factor prices, wt = djJahi and r: = cYf;,/ak,.

For the third sector, I specify a government or political ‘utility’ function:

Zi = Zi(gi, ti, Si, di, EU).

The government objective function Zi is assumed to be (i) positively affected by increased government spending gi, where gi is defined to be the ratio of government spending to GNP (SO Gi=givi); (ii) negatively related to (possibly random) tax rates ti and ri; (iii) negatively related to increased debt di, where di is the ratio of debt to GNP; and (iv) positively related to individual utility EU.

While EU enters the government objective function, it is not necessary that the government maximize it. If the government’s objective include goals that benefit government leaders at the expense of consumer utility, then the changing short-term priorities of a new administration can lead to clear efficiency costs. An alternative view of the government is that it maximizes consumer utility EU by adjusting tax rates in an optimal way to changes in the economic environment. In the empirical section, an econometric model is estimated which allows for optimal tax variation in response to observable factors. To the extent that the component of the tax rate deemed ‘random’ by the econometrician is in fact an optimal government response to some unobservable factor, the model presented here will overstate the true degree of tax uncertainty.

The three sectors of the model have been described to suggest the relevant set of information that the consumer uses to form expectations about future uncertainty in net-of-tax wages, interest rates, and government behavior, and thereby make current consumption and labor supply decisions. From eqs. (1) and (4), the optimal choice of consumption C, can be written as a function of current and expected future variables;


CI =C(Q,,P,,E(Q,),E(P,),S1),

where government choices are Qi = {g,, di, ti, ti>, factor prices are Pi = { wt, r:}, and D is the variancecovariance matrix of the joint distribution of Qz and P, (higher moments of the distribution are ignored). Since labor supply is determined before wages are realized, information from the previous period is used:

(54

(W

Assume that consumers are rational, so they form optimal predictions at period 1 of E(P,) and E(Q,). The set of information available at the end of period 1 is summarized by T1-{g,, dl, E,, z~, 17, ~7)‘; it is straightforward to show that r1 is relevant to forming optimal predictions of E(P,) and E(Q1).5 If the structural model is assumed to be linear, the optimal linear prediction of Tz (a 6 x 1 vector) is given by:

l-2 = Y’r, + 02, (6)

where Y, a 6 x 6 matrix, is estimated using vector-autoregression methods, and v2 depends both on production shocks and shifts in tax policy. The variance-covariance matrix s2, an estimate of E{u,v;}, is then calculated from the residuals. Note that Y is simply a reduced-form matrix with no structural interpretation, since the structural model is unidentified.

The two-period formulation has often been used to characterize ‘working’ and ‘retirement’ stages of the life cycle. Since second-period labor supply is endogenous, it seems reasonable to assume that the representative consumer in the second period is still working; hence the relevant age category is XL 59, planned from the perspective of age 35. These ages are chosen arbitrarily for the purposes of calibrating the appropriate levels of consumption and labor supply; the results are not sensitive to this choice of age groups. The essential feature of the prediction problem faced by consumers, however, is that they must make current savings (and human capital) decisions which will subsequently be affected by tax policy for a number of years in the future.

The horizon relevant to the 35-year-old is not simply the value (and variance) of a tax rate in some future year, but the average tax during the time the individual is between 50 and 59.6 In the derivation below, it is shown how the VAR model using annual data (which we observe) translates into the optimal prediction of average tax rates and factor prices 15-25 years in the future. Using q to denote the year, Y, the 6 x 1 vector of (annual)

5Since P, is a function of lirst-period saving (which in turn depends on C,) and QZ is jointly determined with P,, all variables in the lirst period provide information about P, and Q2.

6The arithmetic mean approximates the (geometric) effective tax rate on interest income.


dependent variables (which corresponds to f in the two-period model), and fl the corresponding 6 x 6 matrix of VAR coefficients (which corresponds to Y in the two-period model), the annual reduced-form equation is:

r,=nu,_, +F,, (7)

where eq is assumed to be distributed normally, and E(E,+Q) =O, 4 #q’. Let the forecast period stretch from j to j’ years in the future (in the example above, from 15 to 25 years). Then the optimal forecast of TZ given information at period 1, averaged over N =f -j+ 1 years in the future, is:

f2= i Y,IN=YZ-,, (8) m=j

where

Y+E{Y,)=nmY,.

The optimal prediction of any (yearly) vector Y at a future year m is Y,, while the average of Ym over the N years is simply P. The error of a single year’s prediction can be written:

Y,-Y~=nj-'&1+nj-2&2+...+&,. (9)

After some rearrangement, the variance of the prediction is expressed as:’

i flmZ(nm)‘], k=O m=O

(IO)

where 4 = ~~=F~ nk, C = E(EE’), and ZI” = I, the identity matrix. In section 3, l7 and C are estimated using annual U.S. data; these matrices

are then transformed into Y and Sz, and used to solve for optimal consumption and labor supply characterized by the functions C, = C,(T,, YyT,,Q) and h,=h,(T,, YT,,Q). By changing characteristics of 52, one may measure how individuals respond to differing degrees of tax risk.

‘For example, let j= 1 and j’= 3. Then:

r,-i-,=n2&,+rl&,+E3,

r,-r,=ne,+EZ.

rl --rl =El.

The variance of r is therefore:

{(I + n + nqq~ + n + n 2)’ +(I + np(r + ny + q/9.


3. A VAR model of expenditure, debt, income, and taxes

The estimation of eq. (7) uses yearly U.S. data between 1929 and 1975. The measure of privately held government debt is from Barro (1979), while combined federal and state government expenditures are calculated from the National Income and Product Accounts. Owing to difficulty in measuring wages since 1929, earnings are estimated in the VAR model and subsequently converted to wage rates for the numerical calculations. Earnings are defined as the ratio of employee compensation to total nonagricultural employees. All variables defined above are adjusted by the GNP deflator to real 1972 dollars, and real ex post interest rates are measured as the Moody Aaa rate minus the change in the GNP deflator (Economic Report of the President, 1985).

Joines (1981) calculated effective marginal tax rates on capital income and labor income during 1929-75. The labor income tax is the marginal tax on labor income, weighted by the share of labor income in each marginal bracket. Taxes on labor income are defined as state and local (proportional) taxes plus federal wage, salary and social security taxes, plus taxes on miscellaneous income (which is included as earned income).8 Capital income includes interest and dividend income plus taxable capital gains,9 while the capital income tax is composed of state and local proportional taxes, corporate, dividend, interest, and other unearned income taxation.

There are two general methods for measuring ex post marginal tax rates. The first takes an average of the statutory marginal rates, weighted by taxable income [Barro and Sahasakul (1983a, 1983b)]. This paper uses the second measure of marginal taxes [Joines (1981), Seater (1985)lj which calculates the actual (weighted) change in tax payments as income grows. That is, the marginal tax is defined as (T- T*)/(AGZ -AGZ*), where T and T* are actual taxes paid, and AGI and AGZ* adjusted gross income, in adjacent brackets.lO

Estimates of the VAR model are presented in table 1. These are reduced- form coefficients, and should therefore be interpreted cautiously to avoid confusion with the (unidentified) structural coefficients. The coefficient of lagged expenditures on current debt, 0.992 (t-statistic of 6.20), and the

6Attributing miscellaneous income (partnership, business, and farm) to capital income generally made less than 1 percentage point difference in the tax rate [Joines (1981)]. Browning (1985) argues that the present value of benefits rises by only 12 cents per marginal dollar paid in social security taxes. For this reason social security has been included as a payroll tax [for an opposing view, see Burkhauser and Turner (1985)].

There might have been greater variability in tax rates if the ‘inflation premium’ for interest and dividend income had been excluded from the tax base.

loThe measure used in this paper accounts for available deductions and exemptions available to higher income taxpayers that make the effective marginal rate less than the statutory rate. In many respects a more fundamental divergence in the measurement of taxes comes between what Fullerton (1984) refers to as average effective tax rates (which correspond to both the Barro and Seater measures of taxation) and marginal effective tax rates, which are forward-looking tax rates on investment decisions now under consideration.

Tab

le

1

Coe

ffic

ient

m

atri

x of

th

e V

AR

m

odel

an

d co

rrel

atio

n co

effi

cien

ts

of

the

resi

dual

s.

~___

_ __

____

_ __

~ E

quat

ion:

(1

) (2

) __

__~~

- (3

) (4

) (5

) (6

) L

agge

d:

Exp

endi

ture

s D

ebt

Ear

ning

s In

tere

st

rate

W

age

tax

Inte

rest

ta

x __

___

___~

-

Exp

endi

ture

s 1.

023

0.99

2 3.

729

0.24

9 -0

.014

0.

001

(7.8

7)

(6.2

0)

(3.8

0)

(2.0

5)

(0.3

3)

(0.0

1)

Deb

t -0

.261

0.

753

- 1.

773

- 0.

079

- 0.

025

0.03

9 (6

.15)

(1

4.44

) (5

.53)

(1

.99)

(1

.83)

(0

.96)

Ear

ning

s -0

.033

-

0.04

8 0.

443

-0.0

51

0.00

9 0.

012

(1.9

5)

(2.3

2)

(3.4

6)

(3.2

4)

(1.6

2)

(0.7

3)

Inte

rest

ra

te

- 0.

286

-0.1

21

- 1.

228

0.27

0.

036

0.23

9 I-

(1.8

7)

(0.6

4)

(1.0

6)

(1.8

9)

(0.7

4)

(1.6

1)

2 3 W

age

lax

0.25

6 -

0.07

9 9.

923

1.33

6 0.

631

-0.4

13

z (0

.62)

(0

.15)

(2

.94)

(3

.44)

(4

.71)

(1

.02)

*w

Inte

rest

in

com

e ta

x 0.

303

0.04

9 -

0.59

4 -0

.611

0.

181

0.98

7 s

(1.5

2)

(0.2

0)

(0.4

0)

(3.2

9)

(2.8

2)

(5.1

4)

w

a C

onst

ant

0.15

8 0.

177

2.57

8 0.

42 1

-0

.071

-0

.023

7 $.

(1.5

1)

(1.4

0)

(3.2

3)

(4.2

8)

(2.0

9)

(0.2

3)

RZ

0.

816

0.96

4 0.

975

0.57

6 0.

973

0.82

1 i b

Stan

dard

er

ror

0.03

4 0.

041

0.25

4 0.

03 1

0.

018

0.03

3 S

___

2 C

orre

latio

n co

efft

cien

ts

of

resi

dual

s

~_._

_ E

xpen

ditu

res

Deb

t E

arni

ngs

Inte

rest

ra

te

Wag

e ta

x In

tere

st

tax

Exp

endi

ture

s D

ebt

Ear

ning

s In

tere

st

rate

W

age

tax

Inte

rest

ta

x

____

_--

1.00

0 0.

759

1.00

0 0.

679

0.33

3 1.

000

0.18

6 0.

438

0.41

9 1.

000

0.53

3 0.

234

0.45

7 -

0.06

2 1.

000

0.41

6 0.

026

0.44

3 -0

.248

0.

766

1.00

0

Not

e:

Ear

ning

s ar

e m

easu

red

in

units

of

10

00.

Abs

olut

e va

lues

of

t-

stat

istic

s ar

e in

pa

rent

hese

s.


insignificance of lagged debt on wage taxes or interest income taxes lends support to Barro’s (1979) hypothesis that governments meet shifts in expenditures primarily by issuing debt rather than raising taxes. However, the negative and significance effect of lagged debt on current expenditures also suggests that increasing levels of debt tend to reduce expenditures. Aside from the interest rate regression, variables lagged beyond one year were not significant.

The correlation coefficients for the contemporaneous residuals are also presented in table 1. The interpretation of the covariance structure is more relevant to the study of how uncertain taxes interact with other factors. For example, the positive correlation (0.457) between earnings and wage taxes means that an unexpected drop in earnings (or wages) will lead to a lower than expected wage tax. Thus, the worker is partially ‘insured’ by the knowledge that net wages will not drop by the full proportional amount of the gross wage decrease. The negative covariance between the interest income tax and real interest rates leads to even more uncertainty in the net-of-tax rate of return; unexpectedly low gross interest rates are associated with high taxes, and conversely. This negative correlation may be caused by unexpected inflation, which tends to reduce ex post real interest rates and increase effective tax rates. The standard error of the one-year forecast is 1.8 percent for the wage tax and 3.0 percent for the interest income tax.

The Joines data stop at 1975, so that measures of effective tax rates from King and Fullerton (1984) are used for 1980. Weighted effective tax rates for capital income, including insurance companies and nonprofit institutions, were 37.2 percent, and the tax on labor income plus the measure of social security taxes [Barro and Sahasakul (1983a, b)] yields 37.1 percent. The average wage and interest rates were $5.02 and 2.7 percent, respectively. The coefficient of Y, and ?, are presented in table 2, along with the initial 1980 variables (r,). Assuming stationarity of the model, the optimal prediction is that earnings will rise from $10,040 to $12,160 in real terms, the government will erase its debt, the wage tax will fall to 31.7 percent (3.5 percent standard error) and the interest income tax will rise to 44.2 percent (4.4 percent standard error).

Correlation coeflicients of the variance-covariance matrix r are also presented in table 2. The positive covariance between earnings and wage taxes (0.932) and the negative covariance between interest taxes and the interest rate (-0.744) become more pronounced in the 20-year forecasts. The next step is to measure how this uncertainty affects consumers’ consumption, labor supply, and utility.

4. A model of consumption and labor supply

The utility function in eq. (1) is specified to be:

Tab

le

2

Mat

rix

of

coef

fici

ents

an

d re

sidu

al

corr

elat

ion

coef

kien

ts

for

pred

ictio

ns

1995

-200

5.

___~

__

(1)

(2)

(3)

(4)

(5)

(6)

Lag

ged

vari

able

s E

xpen

ditu

res

Deb

t E

arni

ngs

Inte

rest

ra

te

Wag

e ta

x In

tere

st

tax

Exp

endi

ture

s -

0.04

0 0.

350

~ 2.

299

-0.0

40

- 0.

562

0.55

7 D

ebt

- 0.

034

0.21

4 -

1.52

0 -

0.02

6 -0

.370

0.

318

5 E

arni

ngs

0.00

7 -

0.04

9 0.

341

0.00

5 0.

008

-0.0

08

2 In

tere

st

rate

0.

036

- 0.

262

1.85

2 0.

032

0.05

1

-0.0

32

Wag

e ta

x 0.

219

2 -

1.65

1 11

.898

0.

175

0.30

4 -0

.244

F

Inte

rest

in

com

e ta

x 0.

057

- 0.

265

2.14

4 0.

035

0.06

1 -

0.02

2 C

onst

ant

0.22

2 2

0.87

0 4.

667

~ 0.

034

0.12

7 0.

592

1980

ba

selin

e 0.

364

0.23

4 10

.04

0.02

7 0.

371

0.37

2 9

Est

imat

e 19

95-2

004

0.37

2 -0

.160

12

.16

0.07

7 g.

0.

317

0.44

2 S.

E.

of

estim

ate

3 0.

039

0.11

7 0.

875

0.02

3 0.

035

0.04

4 E

C

orre

latio

n co

effi

cien

ts

of

resi

dual

s w

E

Exp

endi

ture

s D

ebt

Ear

ning

s In

tere

st

rate

W

age

tax

Inte

rest

ta

x 2

Exp

endi

ture

s -_

1.

000

Deb

t 0.

152

l.OC

O

Ear

ning

s 0.

740

-0.3

88

1.00

0 In

tere

st

rate

-0

.502

-

0.73

0 -

0.00

3 l.C

QO

W

age

tax

0.77

0 -0

.112

0.

932

- 0.

226

1.00

0 In

tere

st

inco

me

tax

0.72

1 0.

625

0.36

5 -0

.744

0.

622

1.00

0


EU=((a& +C$)““+p(G,)+(l +S)-‘E{(al$+ C$yip+p(Gz))/y, (11)

where 6 is the time preference rate, and a is a parameter reflecting the relative tradeoff between leisure and consumption in a particular year. The leisureconsumption elasticity of substitution is g, = l/( 1 - p), while a, = 1/(1-y) is the elasticity of substitution between household ‘output’ in year 1 and in year 2.

There is little evidence on how G, and G, enter lifetime utility functions. To simplify the problem, G, and G2 are specified to enter the utility function additively. This assumption has two strong implications. The first is that G, and Gz will have no effect on the leisure+onsumption choice in either year, since neither enters the leisure or consumption first-order conditions. The second is that the distribution of Gi will not affect estimates of the welfare cost of uncertain taxation, so that p need not be specified.” For this reason, government spending does not enter in the calculations of labour supply and consumption choices described below. Debt may also be excluded from the calculations, since it is assumed not to be an argument in the utility function.

Using the budget constraint from eq. (4), the first-order conditions for C, and I, are:

l+r, ___

[ 1 l+S (124

E{H ;lP-1[aIp2-1 -w,C$-l]}=O, (W

where12

and

Hi = alp + Cf.

Eqs. (12a) and (12b) are highly nonlinear, and can be solved using

‘t That is, the measure of the excess burden of uncertain taxation will be independent of whether government spending is positively or negatively correlated with unexpected shifts in taxes. To see this, note that the utility function can be expressed as EV =E{V,(C1,1,,C2,12)+ V,(G,, G,)}, where V, and Us are concave functions. The expected value of utility will be the sum of the expected values of V, and V,, regardless of the covariance between the two. Any comparison of uncertain and certain tax regimes involves changes in U, but leaves the distribution of Vb unaffected; hence E{V,} is a constant term.

121n general, I, is predetermined, since it was chosen at time 0. Assuming that it is freely chosen, as is done here, will tend to understate the true welfare cost of tax uncertainty.


numerical methods. Writing wages as earnings divided by 1830 hours (see below), denoting the LHS of (12a) as M, and the LHS of (12b) as M,, and assuming normal error terms, the first-order conditions take the form:

wz,r,,t,,Tz)MjdW,dr,dttdz,=O, j=c,l, (13)

where i(. , . , , .) is the truncated density function of normally distributed random variables with mean I- and variance-covariance matrix given by the corresponding 4 x 4 submatrix of Q [Johnson and Kotz (1972, p. 40); corrected for the transformation of earnings to wages]. The limits of integration given by a, prevent explosive solutions (e.g. if r2 -=z - 1) and reduce computational costs.

The parameters of the utility function were chosen to be consistent with life cycle consumption and labor choices for a representative individual between ages 30 and 39 making decisions about labor supply and consumption for ages 5&59. The Consumer Expenditure Survey of 1972-73 was used to measure household consumption and work hours for both the 30-39-year- olds and the 5O-59-year-olds. Average consumption for the 30-39-year-old families was $9400, while gross-of-tax earnings were $12,400 and assets (which includes the market value of the house) were $19,000, or the potential for consuming an additional $1900 per year over the lo-year period. Using information from the Survey on actual taxes paid, ‘virtual’ income given the linear marginal tax rates was calculated to be $6500. Labor supply was assigned by multiplying the number of weeks worked during the past year times 40 hours (if a full-time worker), 20 hours (if part time) or 0 hours (if reported not working). Average hours for the 3&39-year-old were approximately 1830 yearly hours, while 50-59-year-olds worked an average 1680 hours.

There is substantial evidence about the value of y. Friend and Blume (1975) in their study of financial portfolio decisions suggested that (T, was less than 0.5, while Ghez and Becker (1975) placed on o’c an upper bound of 0.28. Skinner (1985) found estimates between 0.25 and 0.5, although Hansen and Singleton (1983) and Weber (1970, 1975) found values generally exceeding 0.5. I assume that a,=0.35, although the model is tested for higher and lower elasticities.

The evidence on the uncompensated labor supply elasticity in static models suggests an average elasticity of approximately 0.3.13 The link between the elasticity of substitution cI and the conventional labor supply elasticity is complex, since changes in the wage rate will also have an impact

t3This elasticity represents a weighted average for men’s and women’s labor supply elasticities; see Killingsworth (1983) for a summary of past studies.


Table 3

Savings, labor supply, and the excess burden of certain and uncertain tax policies. __- ___

(1) (2) Inter- Leisure- (3) (4) temporal consumption Change in Change in (5) (6) elasticity elasticity first-period second-period Change in Welfare

(0,) (a,) hours of work hours of work savings gain __-

1 0.35 0.50 0.1 - 1.8 0.8 0.4 2 1.35 0.50 0.8 -2.3 3.5 0.2 3 0.35 1.50 0.1 - 1.0 0.6 0.4 4 0.15 0.50 -0.1 -0.4 -0.4 0.5 5 0.35 0.15 0.5 -2.5 1.8 0.8 6” 0.35 0.50 0.1 -3.6 0.2 0.6

Notes: The utility parameters are adjusted so that first-period consumption is $9400 and tirst- period labor supply is 1830 annual hours in the perfect foresight case for each numerical simulation. All changes are in percentage terms. Welfare gain is expressed as a percentage of lifetime income.

“Nonwage income is $8500 rather than $6500.

on the dynamic path of labor supply. If we assume that the wage change is foreseen, it can be shown the implied 6, corresponding to the 0.3 labor supply response will be approximately 0.5. The time preference rate 6 was chosen to replicate the observed level of consumption in the first period ($9400), total time endowment 0 was set to 4000 hours, and the leisure preference parameter c1 was adjusted to insure 1830 hours were spent working in the first period.14

Comparing a regime with taxes that have a random component and taxes that can be forecast with complete certainty is problematic, since switching to certain taxes will have general equilibrium effects on the distribution of gross wage and interest rates. However, we can pose the following conceptual experiment: What are the benefits of certain taxation to an individual in an economy in which the estimated variance-covariance structure of wages and interest rates prevails? Under the status quo of uncertain taxation, consumption and labor supply are chosen which satisfy (12a) and (12b) integrated over uncertain wl, rt, t2, and r2. This outcome is compared to certain taxation, in which savings and labor supply are chosen subject to (12a) and (12b) integrated over uncertain wz and rr, holding t2 and T? constant (i.e. perfectly foreseeable) at their means values.

The first row of table 3 presents the results of the model for the baseline

t4The distribution of D was truncated by a rectangle 2.5 standard deviations above and below the mean for all four variables, encompassing 96.3 percent of the normal distribution. Optimal consumption and labor supply were determined iteratively by the numerical integration of (13). The mean value of r’ (the random interest rate), was adjusted to ensure that its expected value E{(l +r’)19} was equal to the perfect certainty interest rate (1.077)‘9. For the baseline parameters, the annualized value of 6 was -0.0099, and x=0.184.


parameters of ee and el. When certain taxes are imposed, hours of work rise by 0.1 percent in the first period, and fall by 1.8 percent in the second period. The explanation for these changes is that the certain tax regime reduces the variance in net interest rates. Thus, providing for C, is more easily achieved by saving in the first period, rather than working extra hours in the second period; overall savings rises by a total of 0.8 percent.

The measure of the welfare change is the dollar amount necessary to compensate the consumer ex ante for the utility loss imposed by tax uncertainty (i.e. compensating variation), plus the expected value of the difference in tax revenue collected by the government, all expressed as a proportion of lifetime income. The government is assumed to be risk neutral; if it were risk averse, any reduction in revenue uncertainty would lead to even higher welfare gains. Column 6 indicates that for the parameters a,=0.35 and CJ~= 0.50, the welfare gain of certain tax rates is 0.4 percent of lifetime income. Conversely, the annual loss of uncertain taxation, expressed as a proportion of 1986 U.S. national income, is $15 billion.

This finding is not particularly sensitive to alternative specifications of the utility function. Rows 2-5 present results from the numerically computable model for different values of oc and el. Row 2 uses an intertemporal elasticity of 1.35; while savings and labor supply are more responsive to certain tax policy, the welfare gain is only 0.2 percent. A high intertemporal elasticity of substitution is equivalent to a low degree of risk aversion in this model; hence the reduction in income variation is less valuable. Neither increasing the labor supply elasticity (row 3), nor reducing 6, to 0.15 (row 4), has a large effect on the efhciency gain, while lowering the labor supply elasticity to 0.15 (row 5) doubles the advantages of certain taxation. Finally, row 6, by allowing a larger endowment of virtual income ($8500 rather than $6500), yields an efficiency gain estimate of 0.6 percent. This calculation supports the view that the greater variability of the interest income tax, combined with its negative correlation with real interest rates, causes the greatest harm to risk- averse taxpayers.

The marginal impact of increased tax uncertainty is substantial. For example, increasing the standard deviation of the (reduced-form) residual of the interest income tax Zi from 3 to 4 percent leads to a decline in ex ante utility equivalent to 0.25 percent of national income. This estimate suggests that the increased variance of inflation rates during the late 1970s and 1980s by increasing uncertainty about the net-of-tax return on capital income, could have imposed a substantial, but unmeasured, cost on taxpayers. Finally, the calculation suggests that a succession of tax changes which fuel taxpayers’ suspicions of future tax shifts can, at the margin, offset much of the perceived efficiency gains from tax reform.

There are at least two potential sources of error in these calculations. The first is that the elements of Y, the prediction matrix, are assumed to be


known with certainty. If taxpayers are unsure about the true parameters of the model (i.e. there is a chance that future trends in debt, spending, and taxes will change), then the calculations understate the true degree of uncertainty. The second source of error comes in the assumption that government expenditure Gi is additively separable. If Gi were a substitute for consumption and leisure, then the welfare cost calculations would overstate the true cost, since unexpected jumps in tax rates would be compensated for by unexpected increases in government spending.

5. Conclusion

The traditional analysis of uncertainty and taxation focused on the beneficial effects of a certain tax on the return from a risky asset [Stiglitz (1969), Eaton and Rosen (1980), Kanbur (1983)]. The government, by collecting a fixed proportion of the return, or subsidizing a fixed proportion of the loss, shares the risk of the investment. This paper has shown that tax rates in the United States have displayed considerable variability during the period 1929-75, thereby eroding the potential benefits of taxes in reducing risk. The additional excess burden of uncertain rather than certain tax policy is estimated impose an annual cost equal to 0.4 percent of GNP, or $15 billion in 1986. The random components of the wage and its tax rate are positively correlated, but the random components of the real interest rate and its tax rate are negatively correlated, suggesting that capital income taxation increases the variability of net interest rates.

Uncertain tax policy may also be harmful if ‘permanent’ tax cuts are perceived by taxpayers as random shifts in tax policy, and unlikely to persist in the future. The government might then find substantial erosion in tax revenue from existing capital, with only a minor increase in long-term investment [Skinner (1984)].

Tax policy is often unpredictable because of factors beyond the control of the government. However, the cost of extensive tinkering with the tax code should be recognized. Furthermore, the value of tax provisions that are flexible to future economic conditions, such as the indexing of capital gains to inflation, are substantial in an uncertain environment. Neither the government nor the taxpayer gains from tax codes which must constantly be adjusted in light of differing rates of inflation or economic activity. While taxes may be inevitable, they need not be as unpredictable.

References

Auerbach, Alan 1. and James R. Hines, 1987, Anticipated tax changes and the timing of investment, in: Martin Feldstein, ed., The effect of taxation on capital accumulation (University of Chicago Press, Chicago, IL).

Barro, Robert J., 1979, On the determination of public debt, Journal of Political Economy 87, 94G97 1.


Barro, Robert J. and Chaipat Sahasakul, 1983a, Measuring the average marginal tax rate from the individual income tax, Journal of Business 56,419452.

Barro, Robert J. and Chaipat Sahasakul, 1983b, Average marginal tax rates from social security and the individual income tax, NBER Working paper no. 1214.

Birnbaum, Jeffrey H., 1986, In turning to deficit, congress may tinker with the taxes again, The Wall Street Journal.

Bizer, David and Kenneth L. Judd, 1988, Capital accumulation, risk and uncertain taxation, Mimeo.

Browning, Edgar K., 1985, The marginal social security tax on labor, Public Finance Quarterly 13, 227-251.

Burkhauser, Richard V. and John A. Turner, 1985, Is the social security payroll tax a tax?, Public Finance Quarterly 13, 253-267.

Clark, Timothy, 1981, Selling tax breaks - if both parties benefit, then why is congress unhappy?, National Journal 13,2238-2241.

Clark, Timothy, 1983, Tinkering with the tax code, National Journal 15, 387. Chang, F.R. and D.E. Wildasin, 1987, Randomization of commodity taxes: An expenditure

minimization approach, Journal of Public Economics 31, 3299346. Eaton, Jonathan and Harvey Rosen, 1980, Labor supply, uncertainty, and efficient taxation,

Journal of Public Economics 14, 365-374. Fullerton, Don, 1984, Which effective tax rate?, National Tax Journal 37, 2341. Fullerton, Don, Andrew B. Lyon and Richard J. Rosen, 1984, Uncertainty, welfare cost and the

‘adaptability’ of U.S. corporate taxes, Scandinavian Journal of Economics 86, 229-243. Friend, Irwin and Marshall E. Blume, 1975, The demand for risky assets, American Economic

Review 65, 90&922. Ghez, Gilbert and Gary S. Becker, 1975, The allocation of time and goods over the life cycle

(Columbia University Press, New York). Hansen, Lars Peter and Kenneth J. Singleton, 1983, Stochastic consumption, risk aversion, and

the temporal behavior of asset returns, Journal of Political Economics 91, 249-265. Johnson, Norman J. and Samuel Kotz, 1972, Distributions in statistics: Continuous multivariate

distributions (Wiley, New York). Joines, Douglas, 1981, Estimates of effective marginal tax rates on factor income, Journal of

Business 54, 191-226. Kanbur, S.M. Ravi, 1983, Labour supply under uncertainty with piecewise linear tax regimes,

Economics 50, 3799394. Kaplow, Louis, 1986a, An economic analysis of legal transitions, Harvard Law Review 99,

509-6 17. Kaplow, Louis, 1986b, Optimal government policy toward risk imposed by uncertainty

concerning future government action, Mimeo. Killingsworth, Mark, 1983, Labor supply (Cambridge University Press, Cambridge). King, Mervyn A. and Don Fullerton, 1984, The taxation of income from capital (The University

of Chicago Press, Chicago). Seater, John, 1985, On the construction of marginal federal personal and social security tax rates

in the United States, Journal of Monetary Economics 15, 121-136. Skinner, Jonathan, 1984, Uncertain tax policy and economic efficiency, Mimeo. Skinner, Jonathan, 1985, Variable lifespan and the interest sensitivity of consumption, Review of

Economics and Statistics 67, 616623. Smith, Adam, 1976, The wealth of nations (The University of Chicago Press, Chicago). Stiglitz, Joseph E., 1969, The effects of income, wealth, and capital gains taxation on risk-taking,

Quarterly Journal of Economics 82, 2633283. Stiglitz, Joseph E., 1982, Utilitarianism and horizontal equity: The case for random taxation,

Journal of Public Economics 18, 1-33. Weber, Warren E., 1970, The effect of interest rates on aggregate consumption, American

Economic Review 60, 591-600. Weber, Warren E., 1975, Interest rates, inflation, and consumer expenditures, American

Economic Review 65, 843-858. Weiss, Laurence, 1976, The desirability of cheating incentive and randomness in the optimal

income tax, Journal of Political Economy 84, 1343-1352.

the welfare cost of uncertain tax policy

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