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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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