Incentive effects of alternative negative income tax plans

Journal of Public Economics 3 (1974) 237-249. 0 North-Holland

INCENTIVE

EFFECTS OF ALTERNATIVE LNCOME TAX PLANS Samuel

A. REA,

Publishing Company

NEGATIVE

Jr.*

University of Toronto, Toronto, Canada

Received January 1973, revised version received February 1974

1. Introduction There have been many proposals to replace the current welfare system with some form of negative income tax. In order to choose among .alternative programs, one must consider several conflicting objectives. One of the primary public concerns is the effect of transfer programs on work incentives. However, attempts to design programs with superior incentives may conflict with other objectives such as minimizing the budget cost and the real cost and concentrating the funds on the poorest members of society. In this study labor supply functions are estimated from cross section data, and the effects of alternative programs on labor supply and costs are simulated. The results enable one to observe the trade-offs between the various goals of a negative income tax. Information on the labor supply effects of transfer programs is relatively scarce. Several experiments are underway which will allow one to directly observe the effects of a negative income tax. i However, these experiments share the problem that the recipient may view his benefit as transitory. In addition the Hawthorne effect may be present. Cross-section estimates of the labor supply function can provide an additional basis for predicting the incentive effects of transfer programs. It is necessary to assume that the observed cross-section function will hold when changes in net wages and unearned income are made at one point in time, and once a supply function is estimated, one must assume that individuals are fully rational in their response to the parameters of the negative income tax. *The author is grateful to Martin S. Feldstein for helpful comments during the course of this research and to William J. Raduchel for his programming talents. The projects was supported by Grant No. 91-23-70-24 from the Manpower Administration, U.S. Department of Labor. However, the content of the paper is the responsibility of the author. %ee Watts (1971).

238

S.A. Rea, Jr,, Incentive effects of negative income tax

2. The labor supply function 2.1. The model It was hypothesized that the supply decision is based on a family utility function. In a family in which only the husband and wife work the family maximizes U(T- L,, T-L,, I) subject to I = LMWM+LFWF+ Y, where L is annual hours of labor, Z is total family income, W is the wage rate, Y is family unearned income, and T is the number of hours in a year. Subscripts M and F indicate the male and female worker, respectively. It can easily be shown that a change in hours supplied can be divided into income and substitution effects,2 AL,

= [($$+L@j]A

+[($$++)]A

AL,

W,

W,,+[f$]A

Y,

(1)

= [($$+LF@)]AWF

+[($-)u+L@]AW~+[$jAY.

(2)

The substitution effects, (aL,/a W,,), and (a&/a W,), must be positive if the second-order conditions hold. The cross-substitution effects, (aL,/a WF), and (aL,/a W,); are positive (and equal) if the leisure of the husband and the leisure of the wife are complementary. The income effects (aL,/a Y) and (&,/a Y) will be negative if leisure is a normal good. The analysis is similar for single individuals and families with one wage earner. 2.2. Estimation

Eqs. (1) and (2) were estimated for men and women over age 25 in the U.S. with the March 1967 Current Population Survey, a sample of approximately 100,000 persons. 3 This survey covers income and work experience in 1966. The dependent variable, hours worked per year, had to be constructed from weeks worked during 1966 and the number of hours worked during the March 1967 survey week.4 The wage rate in the regression equals earnings during 1966 divided by hours worked during 1966. For those working less than 14 weeks the ZKosters (1966). %ain and Watts (1973) highlight the problems in estimating labor supply functions. They are particularly critical of those who truncate their samples by income. 41n cases where the individual reported that he was part time for economic reasons or was part time in March and full time during 1966 the hours were adjusted upward to reflect the underemployment. See Cohen et al. (1970) and Rea (1971).

.A. Rea, Jr., Incentive eflects of negative income tax

239

average wage in the individual’s occupation was substituted. The error in the wage estimates is negatively correlated with the error in the hours worked. This could negatively bias the wage coefficients. One alternative is to estimate the wage from variables such as age and education. 5 The problem with this approach is that education has a positive effect on labor supply, and if education is omitted from the supply equation, the wage coefficient is positively biased. In most studies eqs. (1) and (2) are integrated so that labor supply is a function of wages and nonwage income.6 This is appropriate only if the coefficients are assumed constant, but there is no a priori reason to believe that this is true. Therefore, the equations were estimated using dummy variables for the wage rates and unearned income. All interactions between the dummy variables representing the husband’s wage, the wife’s wage, and family unearned income were included to allow a free functional form.’ The coefficients of eqs. (1) and (2) are assumed constant between steps in the resulting step function. Although the wage and income variables are of primary importance in this study, many other variables were hypothesized to have an influence on labor supply: age, sex, race, marital status, number of children, education, area employment conditions, region, occupation, health, unemployment,s and receipt of public assistance benefits. The working population ‘over 25 was divided into male and female, married and not married, and age less than or over 63.9 In addition, separate regressions were run for married men and women whose spouses were not in the labor force. 2.3. The results The summary regression results are shown in table 1.” Because of the large number of dummy variables, wage and income interactions as well as control variables, only average responses to wage and income changes are shown.” The complete results are available from the author. The wage and income variables were significant as a group, but many of the differences between interaction terms were not significantly different from zero. The average coefficients indicate that the supply of labor responds negatively to an increase in unearned income, %SeeKalachek and Raines (1970). 6For example, Kosters (1966) and Kalachek and Raines (1970). Rosen and Welch (1971) use a quadratic form but point out that the estimates are sensitive to the form chosen. 7For example the equation estimated for the husband is LM = f ( WM , Wr , Y) + aX,+ bX, , where XM and XF are control variables (such as education and age) which apply to the husband and wife respectively. sThe model which leads to the inclusion of hours of unemployment as an independent variable is presented in Rea (1974). gThe age is that reported in March 1967. The income and supply data are for 1966. “The labor supply estimates in Cain and Watts (1973) are not directly comparable because of differences in the sample chosen and the dependent variable. The cross substitution effect is not estimated in any previous study. “The average responses were produced by simulations in which the response to wage and income changes was predicted.

240

S.A. Rea, Jr., Incentive

effects of negative

income tax

as expected if leisure is a normal good. The supply also declines with an increased wage rate because the income effect outweighs the substitution effect. The substitution effect was calculated from the average wage and income responses. As required by the second-order conditions it was positive in all but one case. The cross-substitution effect in families in which both husband and wife work was positive, indicating that their leisure is complementary. The cross-substitution effects should be equal for husband and wife, but for those over 63, the null hypothesis that the two were equal could be rejected. Table 1 Average wage and income responses. Regression number Age 25 to 62 Age 63 and over

Group”

1 2 3 4 5 6

M,MSP,SW F,MSP,HW M,MSP,SNW F,MSP,HNW M,NMSP F,NMSP

7 8 9 10 11 12

M,MSP,SW F,MSP,HW M,MSP,SNW F,MSP,HNW M,NMSP F,NMSP

Number of observations 12605 12605 12278 344 3611 5348 -~ 876 876 1505 412 559 1072

Cross effectsC gi

RZ

AY

0.33 0.18 0.30 0.27 0.33 0.30

- 0.065 -0.039 -0.014 -0.117 -0.145 -0.137

-115 -16 -98 40 -83 -62

32 72 -66 129 201 173

-16 -55

72 33

0.46 0.30 0.40 0.32 0.37 0.30

-0.251 - 0.076 - 0.268 -0.117 -0.197 -0.275

-185 -67 -118 40 -106 -194

243 35 298 83 164 149

-75 -67

261 79

a M = male, F = female, MSP = married spouse present, NMSP = not married spouse present, SW = wife in labor force, SNW = wife not in labor force, HW = husband in labor force, HNW = husband not in labor force. b Calculated at the mean hours. c The effect of changes in the wife’s wage on the husband’s hodrs worked and vice versa.

3. Effects of a negative income tax 3.1. Theory A negative income tax m its simplest form has three important parameters. Every family receives an income guarantee, G, which varies with family size and composition. If the family has other income, benefits are reduced. The income is in effect taxed at a rate r. The point where benefits are reduced to zero is called the break-even point, B, which equals G/r. Consider a family in which there is only one wage earner. For someone initially earning less than the break-even point [( WL + Ye) < G/r, where Y,, is family unearned income] the effect of the negative income tax on labor supply is the same as the effect of an increase in unearned income equal to G-r Y, and

S.A. Rea, Jr., Incentive effects of negative income tax

241

a reduction in the wage equal to r W: AL = [(&)I_CL(g)j-rW)+[g](G-rYJ. The person receiving benefits acts just as if he had total unearned income equal to G-t- (1 -r) Y,, and a wage equal to (I -r) W.” Below the break-even point, G is greater than LrW+r Yo. Therefore, the total response must be negative. The analysis is similar for a family in which both the husband and wife work. No previous study has correctly taken account of the disincentives for those initially earning above the break-even income.13 In fig. 1 the leisure-income constraint for a negative income tax is FCE. The individual at point D reaches a higher indifference curve if he reduces his earnings in order to qualify for the negative income tax. Using the same technique as for those earning less than B, one can predict that if the person reduces his earnings, he will be at point A. Further calculations are necessary in order to predict whether A is preferred to D. For a finite change in the wage rate the usual compensating change in income, (L&d W), will overcompensate the individual as shown in fig. 1. Hicks has shown that if the compensating variation in income equals (L,)(d W)+(Z/8W),(d W)’ the individual will be just compensated for a finite change in the wage rate.’ 4 It follows that if the wage rate equals (1 - r) Wand total unearned income equals Y,,+ (L,)r W- $(dL/dW),(r W)‘, the individual will be just as well off as in his initial position. In fig. 1, this puts the individual at point J. In general, earnings will be reduced in order to qualify for benefits if a point such as A is preferred to J. This will be the case if (G-r Y,,) > Lor W$(lJL/dW),(r W)“. This can be extended to a family in which both husband and wife work. Both will reduce hours worked in order to qualify the family for benefits if 15 (G-rY,J

>

LMorWM+LForWF-$(rWd2

Since the substitution effects have been estimated from the regression coefficients,’ 6 this test enables one to predict the response of a family with income greater than B. lZThe effect of the current income tax is ignored. r3For example, see Green and Tella (1969) and Greenberg and Kosters (1970). r4Hicks (1946, p. 331). 1 5Ibid. 16For this purpose the substitution effect is calculated between steps of the step function, but is not calculated at the mean hours as is customary:

(&).= (~-$3)/(W2W&) which follow from Hicks’ compensating

s

variation described above.

242

S.A. Rea,

Jr., Incentiveeffects of negative income tax

Y

LorW

0

n. 1 i

I I

I I

G

+

Cl-r)Y

I I

cl

I

\P

1

I

LEISURE

T-I

INCOME

Fig. 1 3.2.

Simulation of alternative negative income tax plans

The U.S. President’s Income Maintenance Commission suggested a guarantee of $750 for each adult and $450 for each child.’ ’ All income would be taxed at a 50 % rate. Seven variations of this plan were simulated, each with the same ratio between the guarantees for adults and children. Guarantees for a family of four ranging from $1600 to $4000 and tax rates of 33 %, 50 % and 67 % were specified. The filing unit was defined as an individual over 18 or a married couple together with their children under 18.l’ Incentive effects for those age 25 and over l9 were predicted using eq. (3) and the supply equations estimated above. All of the wage and income inter“The Income Maintenance Commission (1969) suggested that the adult rate apply only to the first two adults in a family. ISThe supply effects would not differ significantly if a family filing unit had been chosen because relatively few of those affected by the filing unit definition are in the labor force. The total cost of a program is significantly affected by the definition of the filing unit. 19Working wives of men age 25 and over are included regardless of age.

S.A. Rea, Jr., Incentive effects of negative income tux

243

action terms were used, not just the average response. The predictions were made on a person by person (or couple) basis using the March 1967 CPS. All individual responses are weighted by the sample weights. Unmarried women with children who reported unearned income from public assistance” were assumed to be receiving AFDC payments. Since the plans examined here would replace AFDC and other current programs, all of their unearned income was set equal to zero at the beginning of the simulation. ” Other public assistance programs are not as easily identified with the data available, but they are less likely to give benefits to those in the labor force. The dummy variable in the supply function representing public assistance income was also set equal to zero for the group losing AFDC payments. This partially offsets the hours reduction resulting from the new program.

3.3. Predicted incentive eflects The aggregate results of the simulations are summ..rized in table 2. The results indicate that the reduction in hours is not large for the least generous programs. A $2400 guarantee for a family of four and a 50 % tax rate reduces hours worked by 12 %. In comparing the incentive effects it should be remembered that there is a different group of recipients for each plan. For a given tax rate the percentage hours reduction rises with the guarantee level. The hours reduction also increases with the tax rate. The tax rate seems to have a greater impact on the percentage reduction than the guarantee. However, when one looks at a group who are recipients regardless of the tax rate, those with incomes less than the guarantee, the hours reduce by only 1% as the tax rate increases from 50 % to 67 %. This may indicate that the estimated supply curve is vertical at these low income levels. However, since many of those who qualify have net wages in the lowest bracket, their supply cannot respond further to tax rate changes. This is probably realistic given that the wages are already extremely low. The greatest change in the hours response occurs for working couples. The hours reduction for the husband is only 2% for the plan offering $1600 for a family of four and a 50 % tax rate, With a $4000 guarantee the hours reduce by 32%. The unmarried individuals have the least responsiveness to the changing plans. This is partly because the change in guarantee level is small in absolute terms for a small family or single individual. Another interesting way of examining the results is to look at the income and supply changes for the average person or couple. In table 3 the effects are shown for the plan recommended by the Income Maintenance Commission. The table illustrates how the average family substitutes leisure for part of its new income. Instead of receiving an additional $625 in income, the average family (or 9ome other types of income such as alimony and annuities were also included because these items were not reported separately. 21This process removed $704 million.

$ 2573 15009 7451 4600 16185 9856 17645

$ 300 450 450 450 600 600 750

$ 500

750 750 750 1000 1000 1250

0.5

0.33 0.5 0.67 0.5 0.67 0.67

$ 2882 15799 8596 5916 18391 13349 23854

Hours reduction 9 6 12 17 13 21 22

Zhours reduction

95 29 56 78 35 54 38

Before 93 16 39 71 13 26 10

After

‘A of recipients below poverty line

a Those over age 25 and in the labor force who qualify after hours adjustment. b Applies only to families with one or more persons over age 25 and in the labor force. c Percentage reduction for those who qualify.

4788 18655 9707 6094 15596 10102 14571

No hours reduction

Child

Guarantee

Gross budget cost” (millions)

Adult

Tax rate

Thousands” of filing units

Table 2 Aggregate incentive effects.

57 33 55 71 54 67 69

42 66 44 25 45 28 27

Below G GtoB

1 1 1 4 1 5 4

Above B

% of benefits to those initially

$ 210 745 722 654 1400 1516 2530

Welfare cost (millions)

M,MSP SW F,MSP HW M,MSP SNW F.MSP tiNW M, NMSP F NMSP

:MSP

2306

3072

1811

1188

403

11785

1188

166

1544

544

1342

1138

213

178

1697

1506

2223

213

1841

844

1311

1225

1865

199

2377

1865

1595

1079

1080

12

9

9

8

18

1259 1231

13

14

10

23

17

10

14

10

% hours reduction

988

1467

1348

1425

1161

2069

1056

2143

Number Hours per year of recipients Before After (000)

2132

553

831

903

1392

464

1072

1332

1290

1474

3991

766

2848

Earnings

206

579

691

1448

1023

736

81

64

984

147

116

2338

1132

1522

2351

2415

2272

1419

1354

2458

4138

3730

Unearned Total income income

Before hours reduction

1923

456

104

808

1056

406

832

1201

1025

1239

3707

745

2585

Earnings

2129

1035

1395

2256

2079

1974

729

374

498

531

533

710

888

1288

2858

1409

1843

2787

2612

2684

2176

1616

527

1089

4864

4574

3257

1010

1128

1034

2223

3854

3446

Total own Total income Benefits income

After hours reduction

1794

892

1196

1659

1573

1697

1532

1072

2146

2937

2851

1.18

0.47

0.70

0.67

0.90

0.41

0.63

0.88

0.70

1.06

1.73

0.63

1.20

Guarantee Wage

’ M = male, F = female, MSP = married spouse present, NMSP = not married spouse -esent, SW = wife in labor force, SNW = wife not in labor force, HW = husband in labor force, HNW = husband not in labor force. b Average per member of labor force.

TotaP

Age 63 and over

:

Age 25

M,MSP SW F,MSP HW M.MSP SNW F,MSP HNW M NMSP

Group”

Table 3 Response of the average recipient to guarantee of $750 per adult, $450 per child and a 50% tax rate.

246

S.A. Rea, Jr., Incentive effects of negative income tax

individual) preferred to lower earnings by $209 (216 hours) and receive only $520 in additional income. A technique was presented above which enables one to find which individuals with income above the break-even point (B) will reduce their earnings in order to receive benefits. These recipients have not been included or have been included inaccurately in other estimates of the cost of a negative income tax. The results of this aspect of the simulations are shown in table 4. Only a small proportion of the recipients fall into this category, but the absolute number is rather large. The percentage rises with the tax rate as expected. The higher the tax rate, the less income must be given up in order to qualify. The relative number is about constant as the guarantee is increased. The average income of those who reduced their incomes from above B is presented in table 4. The excess of income over B rises with the guarantee. The change in income divided by the change in hours is an average of the marginal rates of substitution of leisure for income. This must be less than the wage rate if there is a diminishing marginal rate of substitution. The ratio should also decrease with the tax rate. Both of these properties were observed. The reduction in labor supply is not a real cost. The recipients simply buy some leisure as well as market goods with their added income. The real cost occurs because of the distortion of the marginal rate of substitution of income for leisure. That is, a transfer of the same amount of income without altering the net wage would make all recipients better off. The dollar value of the real cost NW W,(r VI z 2 is shown in table 2. The aggregate welfare cost remains about constant or declines as the tax rate increases with the guarantee held constant. This is the result of offsetting influences. The reduction in the number of recipients lowers the welfare cost, but the increasing tax rate increases the cost. The welfare cost as a per cent of the amount transferred rises with the tax rate but never exceeds 11% of the amount transferred. The distributional effects of the plans are shown in table 2 using as reference points the government’s poverty line, 23 the guarantee level, and the break-even income. The percentage of benefits going to the poor is greatest for plans with high tax rates, which are also the programs with the greatest disincentives. 3.4. Further considerations An income maintenance program could have a number of other possible effects such as an alteration in job search and other investment in human 2ZHarberger (1964). If there are two workers in the family the cost equals

No attempt is made to include the real cost of the additional taxation that is required. 23The poverty line was converted to 1966 prices.

$300 450 450 450 600 600 750

Children

0.50 0.33 0.50 0.67 0.50 0.67 0.67

Tax rate

* Hours per filing unit.

$500 750 750 750 1000 1000 1250

Adults

Guarantee filing units 6 3 7 11 5 11 10

293 652 643 683 857 1124 1412

zto[

Number of filing units (000) $201 309 315 296 350 394 417

Before g-153 -334 -193 -177 -305 -352 -354

After

Total income in relation to B

1703 2095 1679 1644 1731 1705 1761

2052 2451 2074 2160 2218 2411 2547

$507 810 701 833 960 1461 1490

$153 167 193 360 305 715 719

After

Before

Hours per year”

Reduction in earnings

Benefits received

Table 4 Hours response of average filing unit initially above break-even income.

1.01 1.81 I .29 0.92 1.34 1.06 0.98

A income A hours

$1.45 2.28 1.77 1.61 1.97 2.07 1.90

Wage rate

$ 2 % 2 09 f? 5(P S 6 2

* K 2 =: w

:, “g +

2

248

S.A. Rea, .Jr., Incentive effects of negative income tax

capital, improved wages because of the decreased supply of unskilled labor, and increases in illegal or unreported work because of the tax on earnings. For various reasons the existing cross-section data do not allow reliable estimates of participation responses. 24 Omission of the participation rate changes could account for the relatively small disincentives. A more fundamental problem is that one can never be certain that cross-section evidence on hours worked can be applied directly to predicting the response to income maintenance programs. The desirability of the negative income tax over the current welfare system is based largely on its improved work incentives. However, the proliferation of government programs with implicit tax rates on income, particularly in housing and medical care, negates the incentives offered by the negative income tax. These programs were ignored in the simulations.

4. Conclusion Cross-section estimates of the labor supply function were used to simulate the incentive effects and costs of various negative income tax programs. Although the cost estimates will be altered by changes in prices, employment conditions, and the income distribution, the general conclusions will be unaffected. It was found that the reduction in hours of work that would follow a negative income tax is not large for a modest program, 12 % for a $2400 guarantee (family of four) and a 50 % tax rate. The number of recipients initially above the break-even income is also relatively small. By reducing the tax rate improved work incentives can be obtained at the expense of a substantial increase in the budget cost and the payment of a much larger percentage of the benefits to higher income groups. An increase in the guarantee, which is necessary if those out of the labor force are to have adequate incomes, also raises the budget cost substantially. There is no dominant negative income tax plan given the objectives of transferring income to the poorest individuals, minimizing the budget cost and real cost, and improving work incentives. The choice of plan will depend on the nature of one’s objective function. 24The chief problem is imputing a wage rate for those who are not in the labor force. There are also estimation problems associated with the dichotomous dependent variable.

References Cain, G.G. and H.W. Watts, 1973, Income maintenance and labor supply (Rand McNally, Chicago). Cohen, M.S., S.A. Rea, Jr. and R.I. Lerman, 1970, A micro model of labor supply, U.S. Bureau of Labor Statistics Staff Paper 4 (U.S. Government Printing Office, Washington, D.C.). Green, C. and A. Tella, 1969, Effect of nonemployment income and wage rates on the work incentives of the poor, Review of Economics and Statistics LI, 399-408.

. S.A. Rea, Jr., Incentive effects of negative income tax

249

Greenberg, D.H. and M. Kosters, 1970, Income guarantees and the working poor: The effect of income maintenance programs on the hours of work of male family heads, Rand Publication R-579-OEO (Rand Corp., Santa Monica). Harberger, A.C., 1964, Taxation, resource allocation and welfare, in: National Bureau of Economic Research, The role of direct and indirect taxes in the federal revenue system (Princeton University Press, Princeton) 25-70. Hicks, J.R., 1946, Value and capital, 2nd ed. (Clarendon Press, Oxford). Kalachek, E.D. and F.Q. Raines, 1970, Labor supply of lower income workers, in: President’s Commission on Income Maintenance Programs, Technical studies (U.S. Government Printing Office, Washington, D.C.) 159-186. Kosters, M., 1966, Income and substitution effects in a family labor supply model, Rand Publication P-3339 (Rand Corp., Santa Monica). Rea, S.A., Jr., 1971, The supply of labor and the incentive effects of income maintenance programs, unpublished Ph.D. dissertation (Department of Economics, Harvard University, Cambridge, Mass.). Rea, S.A., Jr., 1974, Unemployment and the supply of labor, Journal of Human Resources IX, 279-289 Rosen, S. and F. Welch, 1971, Labor supply and income distribution, Review of Economics and Statistics LB, 278-282. U.S. President’s Income Maintenance Commission, 1969, Poverty amid plenty: The American paradox (U.S. Government Printing Office, Washington, D.C:). Watts, H.W., 1971, The graduated work incentive experiments: Current progress, American Economic Review LXI, 15-22.