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The Board of Regents of the University of Wisconsin System

Labor Supply Response Over Time

Author(s): Philip K. Robins and Richard W. West

Source:

The Journal of Human Resources,

Vol. 15, No. 4, The Seattle and Denver Income

Maintenance Experiments (Autumn, 1980), pp. 524-544

Published by: University of Wisconsin Press

Stable URL: http://www.jstor.org/stable/145400 .

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LABOR SUPPLY RESPONSE

OVER TIME*

PHILIP K. ROBINS

RICHARD W. WEST

ABSTRACT

This study uses longitudinal data from the Seattle and Denver Income

Maintenance Experiments to estimate a partial-adjustment model of labor-

supply response. It is assumed that as a result of the experimental treatments,

a person changes desired hours of work. The new desired hours of work are

estimated empirically along with the speed at which the adjustment takes

place. The results indicate that the financial treatments reduce desired hours

of

work by 9 percent for husbands, by 20 percent for wives, and by 25 percent

for single female heads of families. The estimated time periods required for

90 percent adjustment are 2.4 years for husbands, 3.6 years for wives, and 4.5

years for single female heads. Tests are performed for differences in response

by ethnicity, site, and experimental duration. The results indicate larger

reductions in desired hours of work for blacks and Chicanos (relative to

whites), for persons in Denver (relative to persons in Seattle), and for persons

on the five-year programs (relative to persons on the three-year programs).

Only in the case of husbands, however, are the ethnic, site, and duration

differences statistically significant.

The authors are economists

with SRI International.

* The research

reported

in this paper

was performed

under

contracts

with the States of

Washington

and

Colorado,

prime

contractors for the Department

of Health, Education,

and

Welfare under

contract

numbers

HEW-100-78-0005

and

HEW-100-78-0004,

respec-

tively. The opinions

expressed

in this paper

are those of the authors and should not be

construed as representing

the opinions or policies of the States of Washington

or

Colorado

or any agency

of the United States

government.

The authors

wish to acknowl-

edge valuable

discussions

with Karl

Joreskog

who-was a collaborator

during

the early

stages

of this research and whose computer program

LISREL

was used in the empirical

analysis.

Micheal

Keeley

and John Pencavel

gave

useful comments

on an earlier version

of the paper

and Paul

McElherne,

Gary Stieger,

and Richard C. Williams

provided expert

programming

assistance.

[All numbered citations

in brackets refer

to the master list of

references on pp. 707-22.]

The Journal of Human Resources * XV * 4

0022-166X/80/0004-0524 $01.00/0

? 1980 by the Regents

of the University

of Wisconsin

System

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Robins and West 1 525

I. INTRODUCTION

Other analyses of the labor-supply response to the Seattle and Denver

Income Maintenance Experiments (SIME/DIME) (Keeley et al. [113,

115], Keeley and Robins [111], and the paper by Robins and West in this

volume) focus on experimental response during a particular period of time.

However, estimated labor-supply response in the selected time period may

not be representative of the long-run response to the experiment.

For a variety of reasons, one would not expect labor-supply response

to be constant over time. In particular, one would expect families to adjust

gradually, rather than instantaneously, to the new transfer payments.

Furthermore, the experiments have a known and finite duration. Con-

sequently, one might expect families to begin adjustment to the anticipated

termination of transfer payments prior to the end of the experiment.

In this paper, our principal interest is in studying how families adjust

to the new transfer payments. We use longitudinal data from SIME/DIME

to estimate a dynamic model of the labor-supply adjustment to the

experimental negative income tax (NIT) programs. Tests are performed

for differences in response by ethnic group, site, and experimental

duration. In addition to studying the adjustment process, we also speculate

on the implications of our results for the response to a permanent national

program.

The organization of this paper is as follows: In Section II we present a

model of labor-supply response over time. In Section III we analyze the

predictive ability of the model. In Section IV, we study the effects of

ethnicity, site, and experimental duration on response. In the final section,

we summarize our results and present the conclusions of our analysis.

II. A MODEL OF LABOR-SUPPLY RESPONSE OVER TIME

Theory

Consider a person who is enrolled in an NIT experiment. Upon enroll-

ment, there is a sudden and unforeseen change in the person's budget

constraint. Both the intercept (support level) and the slope (net wage rate)

of the budget constraint are changed. As a consequence of these changes,

the person now desires to work a different number of hours. For a variety

of reasons it is unlikely that the person will immediately adjust hours of

work to correspond with these new desires. Many jobs do not have flexible

hours, and adjustment may have to wait until a new job is found.

Furthermore, the person may not even attempt to find a new job because

of the costs associated with changing jobs. However, if the job is lost for

reasons outside the person's control or the job becomes undesirable for

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526 I THE JOURNAL OF HUMAN RESOURCES

other reasons, the person may find a new job having hours consistent with

his or her desires.

One simple model of the adjustment of actual hours to desired hours is

based upon the assumption that there is a constant probability, p, of fully

adjusting in each period. Thus, in a sample of N individuals, proportion p

adjust in the first period, proportion p of the remaining (1 - p)N persons

adjust in the second period, and so on. In period t, a total of (1 - (1 - p))N

people would have adjusted to the NIT.

Another simple model allows partial adjustment and is based on the

assumption that each person adjusts hours of work by the proportion, y, of

the difference between desired and actual hours of work. Thus, if a person

starts out in period o with hours, Ho, and desired hours, H*, in period one,

hours would be Ho + (H* - Ho); in period two, hours would be:

Ho + y(H* - Ho) + y[H* - Ho - y(H* - H,)] = H,(1 - y)2 + H*(2 - y)y

and in period t hours would be:

(1) t_1y(1 - yy-lH* + (1 - y)tH = [1 - (1 - y)t]H" + (1 - y)H

It is interesting to note that expected (or average) labor supply in each

of these models is identical if p = y. That is, in the first model average

labor supply in period t is given by:

(2) Ho (1 - py + H*[1 - (1 - p)t = H* + (1 - p)t(H - H*)

which is the same as the formula for the second, or partial-adjustment

model. Since the two models have the same expected value,' it is

reasonable to choose between them on the grounds of mathematical

tractability. For this reason, we choose the second, or partial-adjustment

model, to represent the labor-supply response to the NIT experiment.

The partial-adjustment model can be written formally as:

(3) Ht = Ht_ + y(H + Ht- ) + Et

()

Co

C +Xf + ift=0

(4) H=

H(C, + Xfp + T8 + I- if t > 1

where Ht is hours of work in period t; H is desired or equilibrium hours of

work in period t; Et

is an error term; C is a constant term; X is a vector of

variables that affect desired hours of work; T is a vector of variables

representing the experimental treatments (both financial and counseling

and education/training subsidies); A is an error term representing per-

manent individual differences in desired labor supply not explained by X;

and y, 83,

and 8 are parameters to be estimated.

1 The two models have different implications for the distribution of hours of work,

however.

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Robins and West 527

Equation (3) is the formal representation of the adjustment process:

hours in period t are equal to hours in the previous period plus proportion

y of the discrepancy between actual hours in the previous period and

desired hours of work. In the preexperimental period (denoted by the

subscript o), desired hours of work are a linear function of a constant term,

a set of exogenous variables, and an error term. In the experimental

period, desired hours of work are identical to desired hours in the pre-

experimental period except for a constant term that is allowed to vary over

time and a treatment effect. It could be argued that desired hours of work

would also vary over time because of variation in the exogenous variables,

X. Apart from variation in the constant term over time, we choose to

ignore nontreatment variations in desired hours for two reasons. First, and

most important, some of the variables generating desired hours may be

changed because of effects of the experimental treatments. Because we

want to estimate the total effect of the experiment, we use preexperimental

values of the exogenous variables so that the effect of experimentally

induced changes in the exogenous variables are captured by the coef-

ficients of the treatment variables. Second, allowing the exogenous var-

iables to vary is not computationally feasible with the estimation method

chosen.

Estimation

Estimation of the model as specified above would require the assumption

that the treatment variables, T, are uncorrelated with the permanent error

in desired hours, ,u. As described in Keeley and Robins [111], this

assumption is not valid in SIME/DIME. The process used to assign

families to experimental treatments differentiated among families on the

basis of a variable called normal income. Families with different normal

income levels had different assignment probabilities to the various ex-

perimental plans. Hence, it is likely that the treatment variables are

correlated with ,u since, unless all determinants of normal income are

included in X, It will be related to "normal" income level. We deal with

this problem by adding a set of equations representing the assignment to

experimental treatment:

(5) T = ET + v

where E is the vector of normal income levels, Tr is a matrix of coefficients,

and v is a vector of freely intercorrelated error terms. Because the assign-

ment was random within normal income level, we can assume that v is

uncorrelated with the other variables in the model. However, we allow E

to be correlated with u. Other stochastic assumptions of the model are that

Et is uncorrelated with X, ,L, v, and lagged hours of work, and A is

uncorrelated with X.

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528 THE JOURNAL OF HUMAN RESOURCES

To make optimal use of observations from the preexperimental

period, we use the reduced-form equation for preexperimental hours of

work:

(6) H, = H* + eo

where E, has a different variance than Et.2 The complete model is given by

equations (3) through (6).

The stochastic assumptions of the model are:

V(E,) = 2, V(E) = Or2

E(et-) = O, E(etE) = 0 for all t, r

E(LX) = O, E(aT) 0 O, E(,E) = 0

E(vE) = O, E(vHt) = O, E(vE) = 0

E(vEt) = 0, E(Eto) = 0

The model is estimated by the method of maximum likelihood using

the LISREL program of Joreskog and Sorbom [99].3 It is assumed that the

observed variables have a multinormal distribution. While this assumption

is not likely to strictly hold,4 experience with the LISREL program

suggests that the empirical estimates are not very sensitive to the distri-

butional assumptions of the model.

Data

SIME/DIME conducts interviews three times a year in which weekly hours

of work, as well as any changes in weekly hours of work occurring since the

previous interview, are recorded. These data permit construction of a

continuous work history for each individual. For purposes of this study, we

have constructed a quarterly time series of (annualized) hours of work for

the first ten quarters of the experiment and for the four quarters prior to

the experiment.5 We believe that the partial adjustment model is ap-

2 Because of computational limitations, we do not impose the constraint that V(Eo) =

(1l/2)V(Et).

3 See Robins and West [181, App. C] for a description of how the partial-adjustment

model is set up within the LISREL program.

4 There are two reasons why the normality assumption doesn't hold. First, hours of work

are truncated at zero, and second, the treatment variables are qualitative. The former

problem seems insurmountable; multivariate tobit techniques have not yet been devel-

oped. The second problem is empirically unimportant. Estimation of the model with E in

the H* equation and omitting the T equation yields identical estimates of the experi-

mental effects.

5 For most families, less than four quarters of preexperimental data are available. We

convert the available information to an annual total, assuming that behavior in the

missing quarters is the same as behavior in the observed quarters. We thus have only one

preexperimental observation for each family.

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Robins and West 529

TABLE 1

SAMPLE SIZE BY EXPERIMENTAL

QUARTER

Experimental Sample Size

Quarter Husbands Wives Female Heads

1 2,624 2,590 1,897

2 2,573 2,559 1,878

3 2,535 2,521 1,857

4 2,496 2,492 1,820

5 2,452 2,465 1,799

6 2,408 2,432 1,779

7 2,362 2,405 1,760

8 2,305 2,362 1,731

9 2,243 2,318 1,699

10 2,171 2,252 1,656

Percent reduction

from first quarter 17.3% 13.1% 12.7%

plicable to the first ten quarters of the experiment because families are

unlikely to have begun readjusting behavior in anticipation of the end of

the experiment.6

As with any panel, observations are lost over time. Table 1 shows how

attrition in SIME/DIME affects the sample size from the first through the

tenth experimental quarters.7 During this period, the sample size is

reduced by 17 percent for husbands (1.7 percent per quarter), by 13

percent for wives (1.3 percent per quarter), and by 13 percent for female

heads of families (1.3 percent per quarter).

In this paper, we use the tenth quarter sample for the empirical

analysis. We thus ignore data for families that leave the experiment prior

to the tenth quarter. Such a sample selection procedure may lead to biased

6 The choice of time periods to analyze is, of course, somewhat arbitrary

for an experiment

of fixed length. We are unable to fully test the implications

of using more than ten

quarters

of data for two reasons.

First,

at the time this study

was undertaken,

data

for

quarters

after the 10th

experimental

quarter

were not available.

Second,

even if the data

had been available, there would have remained some problems due to the way

experimental quarters

were defined (the 12th experimental quarter

would have been

partly postexperimental

for some three-year families)

and the computational

limitations

of LISREL which forced us to aggregate quarters

into half-yearly

time periods for

purposes of analysis.

7 Virtually all of the attrition occurs because the individual either drops out of the

experiment

or cannot be found by the interviewers. A few of the observations

are lost

because of coding errors in the data. The subgroups (husbands, wives, and single female

heads) are defined as of the enrollment date. The sample

sizes differ for husbands and

wives because of selective

attrition after a marital

separation.

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530 | THE JOURNAL OF HUMAN RESOURCES

estimates of the labor-supply response to the experiment if the attrition is

systematically related to labor supply (or to the error term in the labor-

supply equation).8 In an appendix in a lengthier version of this paper

(Robins and West [181]), we present the results of a study of the effects of

attrition on the labor-supply response and conclude that our use of the

tenth quarter sample does not lead to any serious biases in the estimated

treatment effects.

The vector of treatment variables, T, includes a dummy variable for

persons receiving a financial treatment and three dummy variables for

persons eligible to receive counseling and education/training subsidies. It is

important to recognize that the estimated financial-treatment effect in this

model represents the average response to the 11 NIT programs being

tested in SIME/DIME, conditional on the assignment model used in the

experiments, and does not necessarily represent the average response that

would result from any particular nationwide NIT program applied to this

population group. Models that can be generalized to particular

nationwide

programs are presented in Keeley et al. [113, 115] and the paper by Robins

and West in this volume. Such models are difficult to integrate into the

dynamic framework presented in this paper, although we are currently

investigating methods for accomplishing such an integration.

The vector of exogenous variables, X, includes dummy variables for

site and race, number of family members, number of children under 5

years of age, years of education, a dummy variable for being a high school

graduate, age, age squared, and imputed preexperimental values for net

after-tax nonwage income and the net wage rate.9 Because of computer

8 Consider the following example: Suppose that experimental families below the break-

even level (those with relatively low labor supplies) have a smaller probability of leaving

the experiment than either control families or experimental families above the breakeven

level. Suppose further that the experimental treatments do not affect labor supply. Thus,

even though the true experimental effect is zero, we would observe an increasingly

negative difference betweeen the labor supplies of experimentals and controls because of

attrition within the experimental group that is correlated with labor supply. Adjusting the

experimental-control differential for preexperimental differences in labor supply tends to

reduce the bias, but would not eliminate it entirely unless preexperimental and

experimental labor supply were perfectly correlated.

9 Imputed values are used because the preexperimental values of net nonwage income and

net wage rate are endogenous with respect to preexperimental hours of work (because of

nonlinearity of the preexperimental tax function). The calculation of these two variables

is as follows: Imputed net wage rates are obtained by regressing the observed net wage

rate on a set of assumed exogenous variables including education, current school status,

experience, family structure, previous work history, race, net worth, and capital

income. The observed net wage rate is the product of annual earnings times one minus

the marginal tax rate divided by annual hours of work. Only data on persons working at

some time during the preexperimental year are included in the net wage rate regression

equations, although values are imputed to the entire sample. Imputed net nonwage

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Robins and West | 531

program size limitations, the experimental-hours-worked variables are

measured on an annualized half-yearly rather than quarterly basis.10

Results

Separate models are estimated for husbands, wives, and single female

heads of families. As mentioned earlier, the subgroups are defined as of

the date of enrollment so that the estimates are not conditional on

unchanged marital status. Table 2 reports the estimated speed of adjust-

ment, y, as well as the coefficients of the variables in the desired-hours

equation, 6 and 8. Also reported are the variances of/ , Et,

and H*. 1l

The results indicate statistically significant long-run financial-treat-

ment effects of -191 hours of work for husbands, -140 hours of work for

wives, and -265 hours of work for single female heads of families. The

corresponding percentage effects are -9 percent, -20 percent, and -25

percent, based on average hours worked by the control group over the

period of analysis. The speeds of adjustment are .39 for husbands, .27 for

wives, and .22 for single female heads. Thus, from 22 to 39 percent of the

deviation between actual and desired hours is removed each half year. The

estimated time periods required for 90 percent adjustment are 2.4 years for

husbands, 3.6 hours for wives, and 4.5 years for single female heads.12

The counseling and education/training subsidy treatments do not

generally have an effect on desired hours of work. The only significant

coefficient is for single female heads eligible to receive counseling and full

reimbursement of education and training expenses. Under this program,

income is obtained by regressing observed net nonwage income (linearized) on the same

set of variables. Observed net nonwage income is calculated as the sum of public

transfers (AFDC, Food Stamps bonus value, other welfare benefits, unemployment

insurance, worker's compensation, veterans benefits, training stipends, and Social

Security benefits), private transfers (alimony and child-support received), capital income

(insurance benefits, pensions, income from net worth), and earnings of family heads

times their respective marginal tax rates, less total taxes paid. Means and standard

deviations of all the variables in the model are given in the Appendix.

10 Because preexperimental hours of work are measured as an average over a year while

experimental hours of work are measured over half-yearly periods, the assumption of

equal adjustment coefficients in period one and in subsequent periods is tenuous. We

estimated a model that allows a different adjustment coefficient and a different error

variance in period one than in subsequent periods. The fit of this model is substantially

worse than the fit of the model that constrains the adjustment coefficient and the error

variance to be the same in each experimental period. Hence, we do not report the results

of the less constrained model in this paper. They are presented in Robins and West [181].

11 The variances of / and E are computed directly by the LISREL program (see Robins and

West [181, App. C] for a description). The variance of H* is calculated as l'crxx f3 + (r2,

where a is the sample variance-covariance matrix of the xs.

12 These figures are calculated as log (.1)/2log(1 - y).

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532 THE JOURNAL OF HUMAN RESOURCES

TABLE 2

MAXIMUM

LIKELIHOOD ESTIMATES OF PARTIAL

ADJUSTMENT

MODEL

(Estimated asymptotic standard errors in parentheses)

Single

Variable Husbands Wives Female Heads

Speed of adjustment per half .385*** .274*** .224***

year (y) (.013) (.011) (.012)

Experimental effects (8)

Long-run financial treatment -190.5*** -139.5*** -264.7***

effects (32.6) (37.3) (54.4)

Long-run counseling &

education/training subsidy

treatment effect

Counseling only 10.4 -99.0* 60.9

(44.5) (51.2) (72.0)

Counseling + 50% education/ -7.0 -34.4 -101.1

training subsidy (40.3) (46.2) (65.6)

Counseling + 100% -30.9 -58.3 -134.3*

education/training subsidy (47.9) (54.7) (75.4)

Nonexperimental effects (3)

1 = Denver 383.5*** 109.1*** 292.2***

(29.0) (27.7) (33.9)

Age 38.0*** 5.3 67.0***

(11.1) (11.4) (14.8)

Age2/100 -60.6*** -12.0 -69.4***

(14.6) (15.8) (19.7)

1 = Black -40.0 285.7*** 135.2***

(30.0) (29.0) (35.6)

1 = Chicano -32.2 -9.8 64.5

(40.3) (38.4) (52.0)

Number of family members 29.2* 29.7* -1.0

(15.9) (17.4) (19.1)

Number of children under -42.4** -195.2*** -125.8***

5 years of age (18.3) (18.4) (28.0)

Years of schooling -19.4** 11.8 28.9**

(7.6) (11.0) (12.5)

1 = High school diploma 154.8*** 142.0*** 263.7***

(38.1) (36.4) (45.3)

Net nonwage income -69.0** - 118.8*** -72.1***

(29.3) (43.4) (17.9)

Net wage rate 562.8*** 161.5 233.5***

(53.3) (106.7) (59.4)

'2/1000 227.1*** 176.7*** 228.4***

(17.1) (17.2) (29.2)

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Robins and West 1 533

TABLE 2 (Continued)

Single

Variable Husbands Wives Female Heads

o-2/1000 307.9*** 230.0*** 230.9***

(5.2) (3.7) (4.2)

(c*/1000 322.2 248.1 389.2

Number of observations 2171 2252 1656

* Significant at the 10 percent level. * * Significant at the 5 percent level. * *

* Significant at

the 1 percent

level.

desired hours of work are reduced by 134 hours, or by 13 percent. Of

course, these effects on desired hours of work are based on data during the

experiment and do not consider the potential long-run benefits (after the

experiment) of the additional education and training. These potential long-

run benefits would be reflected primarily in higher wage rates. As

discussed in West's paper on wage rates in this volume, there is no

evidence of an effect of the education/training subsidies on wage rates

during the experiment. We are not yet able to estimate the effects of the

counseling and education/training subsidy treatments on wage rates very

long after the experiment, and hence on future labor supply.

The estimated coefficients of the other determinants of desired hours

are also of interest. The coefficients of net nonwage income indicate a

substantial negative income effect on desired hours of work for all three

groups. The coefficients of the net wage rate variable indicate significant

and positive gross wage effects for husbands and single female heads.

These results are consistent with the predictions of economic theory;

however, the wage rate coefficients are somewhat larger in magnitude than

the coefficients typically estimated in cross-section studies.

The estimated coefficient of the site variable indicates that desired

hours of work are considerably higher in Denver than in Seattle, a result

that is probably due to greater demand for labor in Denver during the

period of analysis. The age coefficients indicate that hours of work increase

and then decrease with age. The peak age effects occur at 31 years for

husbands, 22 years for wives (not significant), and 48 years for single

female heads of families. Black women had higher desired hours of work

than either white or Chicano women.

The number of young children in the family decreases desired hours of

work for husbands, wives, and female heads, while the number of older

family members increases desired hours of work for husbands and wives.

Additional schooling increases hours worked by wives and single family

heads, but has a mixed effect for husbands.

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534 1 THE JOURNAL OF HUMAN RESOURCES

While many of the exogenous variables are significant determinants of

desired hours of work, a substantial portion of the variance of desired

hours of work is accounted for by the variance of the individual specific

error term, L. For husbands and wives, about 70 percent of the variance of

desired hours of work is accounted for by ,L, while for single female heads

the corresponding figure is about 60 percent. Thus, much of the variance of

desired hours of work is explained by unobserved individual differences

that persist over time.

III. PREDICTIVE ABILITY OF THE MODEL

The partial-adjustment model constrains the time pattern of response to

follow a geometric form. This may be a very restrictive assumption. To

determine just how restrictive the assumption is, we estimate a model that

imposes no constraints on the time pattern of response and compare the

results to estimates generated from the partial-adjustment model. The

unconstrained estimates are derived from a regression model in which

hours of work in each of the first ten experimental quarters are regressed

on a set of control variables and a set of experimental variables. The

control variables include eight dummy variables for normal income cate-

gories, preexperimental annual hours of work, dummy variables for being

black or Chicano, a dummy variable for residing in Denver, number of

family members at enrollment, number of children under 5 years of age at

enrollment, AFDC benefits in the preexperimental year, and age at

enrollment. The experimental variables are the same as in the partial-

adjustment model, namely, a dummy variable for persons receiving a

financial treatment and three dummy variables for persons eligible to

receive counseling and education/training subsidies.

The unconstrained estimates for the financial-treatment effects are

presented in Table 3.13 A comparison of the constrained and uncon-

strained estimates is presented in Figure 1. The unconstrained responses

are represented by points and the constrained responses by a dashed line. 14

As can be seen in Figure 1, the fit of the partial-adjustment model is quite

good, despite the constraint imposed on the time pattern of response.

However, it appears that the precise estimate of the long-run financial-

13 The unconstrained estimates of the counseling and education/training subsidy treatments

are not generally significant. They are reported in Robins and West [181, App. Table B-l].

14 It is important to note that in the early quarters, the unconstrained estimates for all three

groups are small in magnitude and are not statistically significant. This lack of response in

early quarters gives us confidence that we have properly accounted for the assignment

process (which led to a control sample with lower mean labor supply than the

experimental sample) and that the responses estimated in later quarters are genuine

responses to the experiment.

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Robins and West 535

TABLE 3

FINANCIAL

TREATMENT

EFFECTS ON ANNUAL

HOURS

OF WORK BY EXPERIMENTAL

QUARTER-UNCONSTRAINED

ESTIMATES

(Estimated standard errors in parentheses)

Experimental Single

Quarter Husbands Wives Female Heads

... Il,,,s ,. , , .I

1

2

3

4

5

6

7

8

9

10

Sample size

Proportion of sample

receiving financial treatment

-16.8

(31.4)

-51.5

(32.2)

-93.0***

(34.7)

-146.7***

(34.8)

-187.3***

(35.1)

-160.2***

(35.4)

-146.7***

(36.7)

-172.2***

(36.2)

-154.7***

(38.1)

-183.7***

(38.8)

2171

.57

-16.7

(26.5)

-46.3

(29.4)

-75.6**

(30.4)

-74.7**

(30.7)

-76.7**

(31.2)

--116.8***

(32.2)

- 156.9**

(33.4)

-141.0***

(33.8)

-124.9***

(34.5)

-113.4***

(34.9)

2252

.58

26.8

(34.9)

-30.6

(38.2)

-90.2**

(40.0)

-66.8*

(40.1)

-102.6**

(40.6)

-129.5***

(41.7)

-125.8***

(42.5)

-178.4***

(42.5)

-198.9***

(42.7)

-205.1***

(44.2)

1656

.63

Note: Control variables include eight dummy variables

for normal income categories,

preexperimental

annual hours of work, dummy

variables for black and Chicano,

a dummy

variable

for Denver, number

of family

members at enrollment,

number

of children under 5

years of age at enrollment,

AFDC benefits in the preexperimental

year, age at enrollment,

and three dummy

variables for the counseling

and education/training

subsidy

treatments.

* Significant

at the 10 percent

level. ** Significant

at the 5 percent

level. *** Significant

at the 1 percent

level.

treatment effect for wives may be sensitive to the time period chosen for

the analysis. For example, if only the first seven experimental quarters of

data had been used, the estimated long-run responses of wives might have

been somewhat larger. It is difficult to determine whether or not the fairly

large responses in the seventh and eighth quarters for wives are real or

whether the later responses represent readjustment to the end of the

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536 | THE JOURNAL OF HUMAN RESOURCES

200 t

, ;-

Husbands *

160 --

a _ _. - .

, - 0

--

120

- 0

120 _ _

/

80 /

40-.

0

200 _

Wives

160

i _ * * _

120

, 80 *? _

J _ _

' _

) 40 -

0

200 - Female Heads - -

160 -

120 - _

80 _ -

40

_ ! * _

40

-40

-40 I

I I .I \ 1 I ,,I-1 -.

1 2 3 4 5 6 7 8 9

Experimental Quarter 10

FIGURE 1

COMPARISON OF CONSTRAINED AND UNCONSTRAINED ESTIMATES

(Annual Rates)

.a

c

2

a

C

LL

a:

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Robins and West 537

experiment. Some evidence is provided on this issue by looking at the

unconstrained estimates separately for three- and five-year families. As

indicated in Robins and West [181, Table 14], the same pattern of response

is estimated for both three- and five-year families. Since it is unlikely that

five-year families would have begun to readjust to the end of the

experiment before the third year, we feel that the seventh and eighth

quarter estimates are statistical aberrations.

The estimated long-run financial-treatment effects produced by the

partial-adjustment model are somewhat larger than estimates provided by

the other SIME/DIME studies of labor supply, which generally focus on

the second year of the experiment. In Table 3, the average responses in the

fifth through eighth quarters are -167 hours for husbands, -123 for wives,

and -134 for single female heads. These represent 87 percent of the

estimated long-run response for husbands, 88 percent of the long-run

response of wives, and 51 percent of the estimated long-run response of

single female heads of families. Since the estimated speed of adjustment is

lowest for single female heads, it is not surprising that their long-run

response is substantially larger than the estimated response in the second

year. If the partial-adjustment model is the correct specification of the

dynamic adjustment process, analyses that focus on the second year of the

experiments will tend to underestimate the true long-run response to an

NIT. This underestimate may be especially large for single female heads of

families who take the longest to adjust to the new program.

IV. ETHNIC, SITE, AND DURATION DIFFERENCES IN RESPONSE

Having discussed the basic findings for the partial-adjustment model, we

now turn to a discussion of differences in the long-run financial treatment

effects by ethnic group, site, and experimental duration. Because of

computer program limitations on the size of the model that can be

estimated, the tests are performed in a slightly different model. The model

excludes the equations that determine treatment and allows normal income

to affect desired hours (H*) directly. For the models that constrain the

effects to be identical (so that tests of significance can be performed), the

same estimates and standard errors are obtained for the long-run financial-

treatment effects as are obtained from the previous model.

Ethnic and Site Differences

Estimates of separate responses by ethnic group and site are given in Table

4. The results indicate that there are no significant differences in response

by ethnic group or site for either wives or single female heads. But for

husbands the differences are significant in both cases. Black and Chicano

husbands have a response somewhat over twice the response of white

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538 I THE JOURNAL OF HUMAN RESOURCES

TABLE 4

ETHNIC,

SITE, AND DURATION DIFFERENCES

IN THE LONG-RUN

FINANCIAL-TREATMENT

RESPONSE

(Estimated asymptotic standard errors in parentheses)

Single

Husbands Wives Female Heads

Total -190.5*** -139.5*** -264.8***

(32.6) (37.4) (55.4)

Ethnicity

Black -270.6*** -148.8*** -284.8***

(48.1) (53.1) (66.6)

White -112.2*** -116.8*** -196.2***

(40.5) (46.4) (70.9)

Chicano -255.7*** -175.4'** -359.3***

(56.9) (62.2) (95.5)

X2 10.436*** .817 2.772

Site

Seattle -121.7*** -139.3*** -251.8***

(42.7) (48.6) (68.5)

Denver -240.9*** -139.6*** -274.4***

(38.4) (43.2) (62.4)

X2 6.181** .000 .099

Duration

3 years -159.2*** -119.5*** -250.1***

(35.7) (40.9) (58.3)

5 years -255.9*** -180.4*** -300.5***

(45.2) (51.6) (75.7)

X2 4.416** 1.338 466

Note:

The coefficients

present

the long-run

financial-treatment

effect.

The

X2

statistics

are for

the test of the null

hypotheses

of no ethnic,

site, or duration differences.

Degrees

of freedom

are two for the ethnicity

tests and one for the site and

duration

tests.

* Significant

at the 10 percent

level. ** Significant

at the 5 percent

level. *** Significant

at the 1 percent

level.

husbands, and husbands in Denver have about twice the response of

husbands in Seattle. 5

The finding of a significantly lower response for white husbands,

compared to black and Chicano husbands, is somewhat puzzling and we

15 The site difference

could be due to the fact that there are no Chicanos

in Seattle,

thus

reflecting

ethnic rather

than

site differences.

Tests for the black and

white

sample only

(Chicanos excluded) indicate that the site difference

is not due to the presence

of

Chicanos

in Denver. The site difference

is significant

at the 10 percent

level and the

Denver response

is still twice as large

as the Seattle

response.

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Robins and West | 539

have no convincing explanation for it. 6 The finding of a significantly lower

response in Seattle is more sensible. When the experiment began, the

unemployment rate in Seattle was much larger than the unemployment

rate in Denver. Average annual hours of work was about 22 percent less

for husbands and 27 percent less for single female heads (there was no

significant difference in average hours of work for wives). Over time this

difference narrowed somewhat for the control group. Since labor-supply

response is measured in terms of actual (as opposed to desired) hours of

work, it is not surprising to observe a smaller response in Seattle since

unemployed persons (with positive desired hours) cannot reduce actual

hours of work. Also, given bleak employment prospects in Seattle,

individuals may be less willing to give up a job already held and more

willing to accept a job offered.

Effects of Experimental Duration on Response

SIME/DIME is testing programs of varying length. Approximately two-

thirds of the financial-treatment sample was enrolled for three years, while

the remainder was enrolled for five years. In addition, a small sample of

families in Denver was enrolled in a 20-year program that began about two

years after the main experiment. In this subsection, we compare the

responses of three- and five-year families. We do not analyze the response

of 20-year families because only a few quarters of data were available for

them when this study was undertaken.

According to Metcalf [143], the temporary nature of the experiment

may create problems in extrapolating the results to a permanent program.

Metcalfs model implies that in a temporary experiment, the income effect

is smaller and the substitution effect is larger than in a permanent

program. 7 Thus, the labor-supply effects of a permanent program may be

16 In commenting on these findings, Garfinkel [59, p. 73] has offered an explanation that

appears plausible. He argues that blacks and Chicanos on average have worse labor

market opportunities than whites (because of discrimination) and hence respond more

to an experimental treatment that increases the attractiveness of not working.

17 If we divide up an individual's life into two unequal periods, where the first period is the

length of a temporary program, it can be shown (Keeley [108]) that under a temporary

program the substitution effect in period one is given by IH dw and the income ef-

aH,

fect is given by d (H,dw, + dYn,). Under a permanent program, the substitution

effect is given by I + 2 dw and the income effect is given by

- [(Hldw + dYn)

R(Hdw

+ dYn) where is hours

of work,

w is the net wage

rate, is net nonwage

+ R(H2dw + dYn)], where H is hours of work, w is the net wage rate, Yn is net nonwage

income, F is full wealth, and R is a constant related to the discount rate. Under a

temporary program in period one, the substitution effect is larger than under a

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540 1 THE JOURNAL OF HUMAN RESOURCES

either larger or smaller than the labor-supply effects of a temporary

experiment. The ambiguity arises because the two effects go in the

opposite direction.

SIME/DIME is the only experiment that is testing programs of

varying length. Hence, it is the only experiment that can provide evidence

on the relationship between labor-supply response and length of program.

Preliminary attempts to estimate income and substitution effects

separately for three- and five-year families have not proved too successful

(Keeley et al. [113], Burtless and Greenberg [30]). While the signs of the

income and substitution effects are consistent with Metcalf s theory, the

estimated differences are never statistically significant.

In this paper, we use the partial adjustment model as a vehicle for

attempting to distinguish effects of the three- and five-year programs. As

before, we use a single dummy variable to represent the financial treat-

ments. This parsimonious parameterization of the financial treatments,

combined with the use of longitudinal data (in a fairly constrained

economic model), provide a fairly powerful test of differences in the

responses of persons participating in these two programs. In estimating the

model, we constrain the adjustment speeds to be the same for three- and

five-year families, but do not constrain the estimates of the long-run

financial-treatment effects.18

The results are presented in Table 4. The estimated long-run res-

ponses of family heads enrolled in the five-year program are uniformly

greater than the estimated long-run responses of family heads enrolled in

the three-year program. Only in the case of the long-run response of

husbands, however, is the difference statistically significant.19

permanent program assuming leisure in periods one and two are substitutes. In other

words, leisure is "on sale" during the temporary program and individuals will be willing

to substitute future work for current work. The income effect in period one is smaller

under a temporary program because the change in lifetime wealth is smaller.

18 It is possible that the adjustment speeds are different for three- and five-year families;

however, such a test is difficult to perform within the context of the present model. For

one thing, the model could be respecified as Ht = Ht_1 + (ao + a,T)(H* - Ht_l) + et

where T is a dummy variable for five-year families. This model would allow different

adjustment speeds for three- and five-year families, but unfortunately cannot be

estimated within the LISREL framework. Second, separate equations could be estimated

for three- and five-year families (using the same control group), but such a procedure

would result in two different adjustment speeds for the control group, which isn't

theoretically appropriate.

19 Because assignment to three- and five-year programs may not have been random with

respect to household characteristics, we compared the two groups with respect to several

household characteristics. The comparisons are described in Robins and West [181] and

indicate that the estimated duration differences are real and not artifacts of the assign-

ment process.

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Robins and West 541

The finding of a significant difference in the estimated response of

three-year and five-year husbands is important because of its implications

for the effects of a permanent program. Presumably, the larger response of

five-year husbands implies that husbands in a permanent program would

have an even larger response. However, it is important to note that the

estimated difference between the three- and five-year programs are for

some average of the programs tested in SIME/DIME. Since the theoretical

biases of a short-duration experiment have opposite signs according to

whether the response is generated by the substitution effect (which is over-

estimated) or the income effect (which is underestimated), the total bias of

a particular program will vary with the support level and the tax rate of that

program. Most programs that might actually be implemented are likely to

have lower support levels than the average support level of SIME/

DIME.20 Consequently, the difference between the permanent effects of

such a program and predictions from a limited-duration experiment may be

less than the differences implied by our estimates.2

V. SUMMARY AND CONCLUSIONS

In this paper, longitudinal data from SIME/DIME are used to estimate a

partial-adjustment model of labor-supply response. Our empirical results

indicate statistically significant reductions in desired hours of work as a

result of the financial (NIT) treatments. The estimated reductions are 9

percent for husbands, 20 percent for wives, and 25 percent for single

female heads of families. Tests for differences in response across ethnic

groups and sites revealed significantly larger responses for black and

Chicano husbands (relative to white) and for husbands in Denver (relative

to Seattle). The implication of the ethnic results is that nationwide re-

sponses to an NIT may be somewhat smaller for husbands because blacks

and Chicanos comprise a smaller proportion of the U.S. population than of

20 The average support level of SIME/DIME is about 110 percent of the poverty level. The

support level of the cash assistance component of the Program for Better Jobs and

Income (PBJI), the Carter Administration's first proposal for welfare reform, was 65

percent of the poverty level, which is roughly three-fifths of the average support level of

SIME/DIME.

21 Burtless and Greenberg [30] simulated the labor-supply response to the cash assistance

component of the PBJI using three- and five-year substitution and income effects

estimated from SIME/DIME data. As indicated earlier, the estimates are consistent with

Metcalfs [143] theory but are not significantly different. Burtless and Greenberg find

that labor-supply response to the PBJI is lower when substitution and income effects for

five-year families are used. This result is due to the fact that the support level of the PBJI

is substantially lower than the average support level in SIME/DIME, while the tax rate of

the PBJI is roughly the same as the average tax rate of SIME/DIME.

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542 | THE JOURNAL OF HUMAN RESOURCES

the experimental population. On the other hand, the implication of the site

results is that nationwide responses to an NIT may be somewhat larger for

husbands because Seattle is probably unrepresentative of most cities in the

U.S. during the period of the experiment. Because of the temporary nature

of the experiments, we also tested the hypothesis that the estimated

reductions depend on the length of the experiment. For the programs in

SIME/DIME, we find the estimated reduction in desired hours of work to

be larger for persons enrolled in the longer duration (five-year) programs,

although again the difference is statistically significant only for husbands.

We argue that these findings do not necessarily imply that the reduction in

desired hours of work associated with most feasible types of permanent

nationwide NIT programs would be larger than the reductions simulated on

the basis of SIME/DIME results. This is because of the relatively generous

support levels of SIME/DIME (compared to most welfare-reform propo-

sals), and the fact that support effects are underestimated in a temporary

experiment while tax effects are overestimated.

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Robins and West 543

APPENDIX

MEANS

AND STANDARD DEVIATIONS

OF VARIABLES

Variable

Dependent variables

Hours of work (annualized)

Preexperimental period

1st experimental half-year

2nd experimental half-year

3rd experimental half-year

4th experimental half-year

5th experimental half-year

Independent variables

1 = Denver

Age (in years)

Age2/100

1 = Black

1 = Chicano

Number of family members

Number of children under

5 years of age

Years of schooling

1 = High school diploma

Net nonwage income

(in thousands of $)

Net wage rate

1 = Financial treatment

Single

Husbands Wives Female Heads

1,709

(871)

1,708

(886)

1,717

(900)

1,734

(878)

1,710

(888)

1,710

(930)

.567

(.496)

33.38

(10.04)

12.15

(7.45)

.313

(.464)

.192

(.394)

4.34

(1.41)

.839

(.874)

11.28

(2.66)

.563

(.496)

1.89

(.68)

2.27

(.34)

.568

(.496)

529

(774)

564

(819)

561

(832)

570

(819)

621

(851)

645

(861)

.575

(.495)

30.39

(9.52)

10.14

(6.67)

.326

(.469)

.197

(.398)

4.34

(1.41)

.842

(.870)

11.09

(2.20)

.536

(.499)

1.89

(.66)

1.40

(.23)

.575

(.494)

988

(933)

952

(966)

933

(962)

931

(948)

918

(958)

942

(964)

.560

(.497)

33.85

(9.95)

12.44

(7.23)

.459

(.499)

.164

(.370)

3.47

(1.36)

.545

(.744)

11.22

(2.02)

.551

(.498)

2.53

(2.34)

1.38

(.68)

.628

(.484)

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544 THE JOURNAL OF HUMAN RESOURCES

APPENDIX (Continued)

Single

Variable Husbands Wives Female Heads

1 = 3 year .386 .392 .452

(.487) (.488) (.498)

1 = 5 year .182 .183 .176

(.386) (.387) (.381)

1 = Denver .335 .345 .370

(.472) (.475) (.483)

1 = Seattle .233 .231 .258

(.423) (.421) (.438)

1 = Black .173 .182 .287

(.379) (.386) (.452)

1 = White .273 .266 .234

(.446) (.442) (.423)

1 = Chicano .121 .127 .108

(.326) (.333) (.310)

1 = Counseling only .187 .186 .190

(.390) (.389) (.392)

1 = Counseling + 50% .255 .255 .255

education/training subsidy (.436) (.436) (.436)

1 = Counseling + 100% .150 .152 .166

education/training subsidy (.357) (.359) (.372)

1 = Normal income not .019 .020 .053

determined (.136) (.140) (.223)

1 = Normal income .065 .067 .233

$1,000-3,000 (.247) (.249) (.423)

1 = Normal income .167 .171 .246

$3,000-5,000 (.375) (.377) (.431)

1 = Normal income .270 .275 .175

$5,000-7,000 (.444) (.447) (.380)

1 = Normal income .276 .265 .111

7,000-9,000 (.447) (.441) (.314)

1 = Normal income .174 .171 .015

$9,000-11,000 (.379) (.376) (.122)

1 = Normal income .119 .120

$9,000-11,000, and both (.324) (.325)

heads working in

preexperimental period

1 = Normal income .009 .010

$11,000-13,000 (.096) (.098)

Sample size 2171 2252 1656

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