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V
THE TAXATION OF EARNINGS UNDER PUBLIC ASSISTANCE
by
N.A.Barr and R.E.Hall
Number 85
April 1972
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
MASS. INST. TECH.
MAY 9
1972
DEWEY LIBRARY
THE TAXATION OF EARNINGS UNDER PUBLIC ASSISTANCE
by
N.A.Barr and R.E.Hall
Number 85
April 1972
The research reported here was supported by a grant from the Ford Foundation
1.
INTRODUCTION
There is substantial agreement among contemporary observers that
the system of public assistance in the United States
Families with Dependent Children
—
—
especially Aid to
is thoroughtly bankrupt.
An important
link in the chain of arguments supporting this view is the belief that
public assistance discourages recipients from working by imposing a
confiscatory tax on their earnings.
Proponents of a simple negative
income tax have argued that the tax of about 50 percent on earnings implicit
in their plans is a major advance over the oppressive rates of close to
100 percent implicit in AFDC.
That is, they propose to reduce benefits under
the negative income tax by 50 cents for each dollar of additional earnings,
while they claim that AFDC reduces benefits by a full dollar for each
dollar of additional earnings.
The proponents of the Family Assistance
Plan currently under consideration in Congress have argued that the
somewhat higher implicit tax rate of 67% still represents a liberation
from
the provisions of AFDC.
This discussion revolves, or rather should
revolve, around a simple question of fact: What tax does AFDC impose on
earnings?
This question of fact does not seem to have been raised at all
in the public discussion of the defects of AFDC.
The simple belief that
AFDC is confiscatory, or nearly so, has become firmly established without
resting on any investigation of the facts about the system under indictment.
To complete the argument one must, of course, also answer the question:
are high implicit tax rates really a disincentive to labor supply?
Simple theories of labor supply are ambiguous on this point.
See,
for example, R.A. Musgrave, The Theory of Public Finance
McGraw-Hill
1959.
Chapter 11, page 232 et seq.
.
-2-
Our purpose here is to present a fairly detailed attempt to answer this
question of fact, starting from a large body of data on recipients of AFDC.
Our conclusions lend no support whatever to the critics of the system.
suggest, on the contrary,
that AFDC embodies a much more flexible and dis-
criminating resolution between the need for high tax rates
of the benefits in the hands of the poor
—
to preserve the incentive to work.
for AFDC.
They
—
—
—
to keep most
and the need for low tax rates
than does any proposed substitute
We show that AFDC benefits are decreased almost dollar for dollar
for most categories of unearned income, especially benefits received from
other programs of assistance.
for earnings are much lower.
On the other hand, the implicit tax rates
The earnings of mothers receiving AFDC are
taxed at below 40 percent in Chicago, Houston, Los Angeles, New York,
Pittsburgh and San Francisco, and at less than 75 percent in the remaining
three cities included
i,n
the study, Baltimore, Detroit and Washington, D.C.
In the seven cities where it proved possible to estimate the implicit tax
rate for the earnings of the father, it was below 40 percent for four and
below 70 percent in two more.
Statistical tests of these estimates show that
their departure from the value of 100% cannot conceivably be explained by
random variation in the data.
-3-
2.
THE DETERMINATION OF AFDC BENEFITS
AFDC provides categorical assistance to families who apply for benefits
and who are eligible for them.
The program is divided into two sections, AFDC-
FG (family group), for which a family is eligible only if the father is absent
or severely disabled
and AFDC-UP (unemployed parent), for which a family is
eligible if the father is unemployed.
AFDC-UP is optional for states.
In
December 1967 only 21 states, covering all the cities in the present study
For the United States as a
except for Houston, had instituted this program.
whole 95% of families receiving AFDC do so under AFDC-FO.
whose incomes exceed certain levels are excluded.
In addition,
families
We are concerned here with
the treatment of families who are eligible for AFDC either because of the abs-
ence or disability of the father or because of his unemployment, whose incomes
from earnings are greater than zero, but are less than the maximum permitted
by welfare regulations.
Specifically, we test the hypothesis that the benefits
of families in this group are reduced by the full amount of their earnings.
Very little information about this question is available from the federal
and state laws governing AFDC, or from the regulations of the administrators of
the program.
A great deal is left to the discretion of the case workers who are
responsible for the detailed operation of AFDC.
Consequently, we must turn to
data on the actual decisions made bv case workers in order to answer our auestions,
Our data were obtained from a detailed survey of one out of every hundred
families receiving assistance under AFDC in November 1967.
The questionnaires
were filled out by the case worker, not by the families receiving aid. Consequently, our results measure the implicit tax rates that case workers think
they are imposing, and may exceed the tax rates as perceived by family members
to the extent that they are able to conceal their true earnings
worker.
from the case
As a partial check against this, we have also computed implicit tax
-u -
rates from a body of data collected from the families themselves.
These
results tend to confirm our conclusion that the tax rates on earnings implicit
in the actual administration of AFDC are much lower than is generally thought.
Our basic data are total monthlv benefits received under AFDC in the
survey month for each of 14,224 families in the nine cities, together with income
from other sources broken down into the following categories: earnings of the
mother, earnings of the father, if present, earnings of children, earnings of
other family members, contributions of an absent father, benefits under social
security, proceeds of unemployment insurance, contribution of other persons,
other cash income, and income in kind.
The relation we wish to study has
the general form
(1)
= B
B,
1,
where B
10
- I
t.
y.
is the level of benefits received by family i, B
is the level of
benefits received by a family with no other source of income,
t
are the tax rates on the 10 different kinds of income, and y.
,
i'l
are the levels of the different kinds of income for family
This model is not in itself adequate for our study.
of benefits, B
,
through
t
through
y.
&
7
i,10
i.
The base level
varies across families as a consequence of aspects of AFDC
that are not concerned with adjusting benefits in accordance with income.
We have found it useful to take account of the race of the family head, the
presence or absence of the father, the health of the mother and father,
and the number and age of children.
Our final specification, arrived at
1
by considerable experimentation
,
10
12
1
k=l
is
k
l 'k
j-1
J
Ui
The purist should be comforted to hear that almost all experimentation
used the
data only for Los Angeles and San Francisco.
The chosen specification was then
run without change for the other seven cities, the results for
which can be
regarded as powerful confirmation of the California results.
'
where the x'sare variables defined as zero except as follows:
x,
1,1
x
= 1
for all families
= 1
if the family has a mother but no father, and
the mother is unhealthy
= 1
if the family has a healthy father but no mother
= 1
if the family has an unhealthy father and no mother
= 1
if the family has two parents and the father is healthy
= 1
if the family has two parents but the father is
unhealthy
= 1
if the head of the family is white
= 1
if there are two or more children
= 1
if there are three or more children
'
x
x.
i,4
x.
x.
'
x
1
,
x,
i,8
x
i,9
x
= 1
=2
x
i,ll
if there are five or more children
=
the number of children minus 5 if there
are 6 or more
= 1
if there is a child of pre-school age.
x
1
if there are four children
, \.£-
The ten kinds of income are the following
y
=
earned income of the mother (0 if there is no
mother)
=
earned income of the father (0 if there is no
father)
=
earned income of children
=
earned income of other family members
=
contributions from absent father
==
contributions from other persons
=
benefits from social security
=
benefits from unemployment insurance
'
y
1
»
y.
_
y.
,
y.
,.
y,
,
i,3
1,4
i,5
i,6
y
l
, /
y.
i,8
•b-
v.
-
=
other cash income
=
incomes in kind
„
i,9
y.
J
,
„
i,10
The sample consists of 12,292 one-parent families, of which all but 370
are families having mothers only.
no earnings,
Of the parents in these families 10,979 had
307 earned less than $100 per month, 560 earned between $100 and
$250 per month, and 446 earned $250 per month or more.
In addition, the
1932 families with two parents, of which 1585 had no earnings
sample contains
from either parent, 87 had joint earnings of less than $100, 127 had earnings
between $100 and $250, and 133 had earnings of $250 or more.
In the regressions,
families without earnings make no direct contribution
to estimation of the implicit tax rates on
earnings.
Rather, their role is to
make the estimates of the other determinants of benefits more precise and thus
to reduce the variance of the estimated tax rates.
Table
1
presents estimates of
t
through
t
,
,
the tax rates on earnings,
separately for each of the nine cities in the study.
enough observations to estimate
considerable accuracy.
t..
,
In every city there are
the tax on the earnings of mothers, with
Six of the nine cities have values of
below 40 per-
t
cent, and only one, Washington D.C., is above 60 percent.
In every citv,
hypothesis that
For
t
is 100 percent is rejected decisively.
t
?
,
the
the tax
rate for the father's earnings, the data are inadequate in Baltimore and Houston (the latter is in a state with no AFDC-UP)
estimates are reasonably precise.
other two are under 70 percent.
on the earnings of fathers.
,
but in the remaining cities the
Four of the seven are below 40 percent, and an-
Only Washington D.C. seems to put a confiscatory tax
Estimates of t~, the tax rate on the earnings of
the children, are of interest inasmuch as states are permitted (though not
required) to disregard in assessing benefits the monthly earnings of the children up to a maximum of $50 per child and $150 per family.
The estimates suggest
that every city except New York availed itself of this desregard provision
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Table
2
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other than earnings.
income.
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with reasonable accuracy in every city.
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or above in five of the nine cities, and below 60 percent in only one.
This component of income is probably the easiest of all to conceal from
the case worker, so the true tax rate may be much less than these estimates.
The estimated tax rates on the contribution of others seems to be somewhat
lower than those for the contribution of fathers, although many of the
standard errors are large.
The tax rates on benefits under social security are estimated with
reasonable precision in all nine cities.
is 90 percent or more,
In four of them, the estimated rate
in three it is between 65 percent and 90 percent, and
in two, Houston and San Francisco, it is below 40 percent.
Houston has very
low tax rates on all forms of income and a low overall level of benefits, but
there is no similar explanation of the low rate for San Francisco.
The benefits paid under unemployment insurance seem to be taxed at
the same rate as benefits under social security, although so few recipients
of public assistance also receive unemployment benefits that the standard
errors are large.
The estimated rates for other cash income are somewhat
lower than those for social security but are still generally higher than those
on earnings.
Finally, except in Los Angeles, it does not seem possible to
estimate the tax rates on income in kind.
Table
3
presents the estimates of the coefficients of the determinants
of benefits other than income.
The constant estimates the benefits received
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by a family with no other source of income whose characteristics are such
that all of the variables x ^ 2''*"' x i 12
are zero.
This control group
no father, and with one child
consists of families with a mother who is nonwhite,
not of pre-school age.
the
There is very substantial variation among cities in
level of benefits paid to families in this group:
Houston pays only $66 per
month, while New York pays $168, for example.
The reported health of the parents does not seem to have any systematic effect on the level of benefits that a family receives.
The estimated
effect of poor health of the mother when there is no father present is less
than $10 per month in absolute value for every city except San Francisco, where
it is paradoxically negative.
Families with fathers but no
mothers receive
substantially lower benefits than those with mothers only in every city
except New York.
have a systematic
Again, the health of the father in these families does not
effect on the level of benefits.
Families with two
parents receive higher benefits than those with only a mother in all the
cities except Chicago, Baltimore (if the father is healthy) and Detroit (if
the father is unhealthy).
Once again the health of the father has no system-
atic effect on the level of benefits.
In results not reported here we found
that the health of the mother likewise has no systematic effect.
Only Chicago seems to discriminate substantially by race.
It pays
approximately $42 per month more to families headed by whites than to those
headed by nonwhites.
In every city the benefits paid for .additional children decline as
the number of children grows.
This effect is strongest in Houston, where the
second child adds $18 per month to benefits while the sixth child adds only
$1.
Baltimore, a more generous city, drops from $41 for the second to $7 for
-11-
On the other hand, in New York benefits drop only slightly
for the sixth.
from $44 for the second to $40 for the sixth child.
Since the more generous
cities tend to reduce the incremental benefits paid for children less than
do the less generous ones, the constants in Table
3
understate the actual
variation in the benefits paid to families with large numbers of children.
Finally, in four of the cities benefits are reduced if one or more of the
children is too young for school; in the other five benefits are the same
or slightly higher.
There is thus no evidence of any substantial subsidy
to mothers who are unable to work because of the need to look after young
children
,
Table
4
presents a comparison of the benefits paid by the various
cities to a black family with no father and three children, at various
levels of the mother's earnings.
At lower levels of earnings New York is
the most generous city by a wide margin, and even at earnings of $400 per
month, only Pittsburgh with its tax rate of only 18 percent pays a higher level
of benefits than does New York.
Washington D.C. pays benefits to families
with no earnings not too far below the level of $200 per month typical of the
cities other than Houston and New York, but its tax rate is so high that it
pays almost nothing to families with earnings of $200 per month or more.
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=a4-
TABLE
4
Comparison of Benefits at Various Levels of Earnings
BENEFIT
AT
CITY
No
earnings
Earnings of
$100 per mon
Earnings of
$200 per moi
Earnings of
$400 per month
New York
253
219
185
Detroit
215
160
105
San Francisco
215
176
137
59
Chicago
207
168
129
51
Los Angeles
207
172
137
67
Pittsburgh
192
174
156
138
Baltimore
186
136
86
Washington, D.C.
162
90
18
Houston
101
81
59
Note:
117
17
Benefits are for a family with a nonwhite mother in pood health, no father,
and three children of school age.
-15-
Potential Sources of Bias
3.
In this section we consider alternative explanations of our finding
that earnings are taxed at low rates in most cities.
These explanations
are statistical in nature and our discussion will be carried out in the
context of a stylized version of our actual regression equation.
B.
(3)
where
= B
l
u.
o
- ty
'
.
1
+
u.
1
is a random disturbance.
The estimate of the tax rate,
l
t
will
11
11
be biased downward if there is a positive correlation between v. and u..
We will consider two possible sources of such a correlation: first, v. and B.
are jointly determined, so the usual problem of simultaneous equations arises,
and u. are uncorrelated in the population they may
and, second, even if y
have a positive correlation in the sample because of the peculiar way in
which it is drawn.
and y. are jointly determined, then there is an equation in
If B.
the reduced form of the system for
y.
(4)
= a
Q
We have written -
a.,
y
a lU±
u
.
rather then +
a.,
u
•
in this equation because there
seems to be a presumption that the relation between u.and y
sloped
—
is negatively
families who receive unusually high benefits (positive u.)
given their earnings ought to work less, and earn less, than families with
The regression coefficient estimating the tax
negative values of u..
rate is
(5)
^
f
^B,(y.
- y)
-.2
-16-
where V is the sample mean of the
V.
wc
,,.
plim
(6)
—
plim
o
u
,
o
the variance of u.
1
plim —
,
1
A
nlimft
plim
a
a,
1
2
a,
t+
+ a_a
J
U
o
1
=
(B
)
-
ta
u
li
.
+ u.)/v(a
i
o
+
u.
li
a,
- y)
a lUl - y)
o
ta
O
\
)
a u
= o, and plim
-1
I
J.
r
)
u
2
u.
1
=
^
t
=
v
o
so we have
,
1
2 2
(j)
W;
- ta
o
+
(a
Q
J- I
plim
We note that plim y = a
(B
7
T *
=
t
Now
.
1
'
1
2
U
2
u.
4a
i
Here the slope of the regression line is not less than
t
but, rather, is greater.
Our estimate of the tax rate ought to be overstated if the bias from simultaneity
is
a problem.
on the other hand, would cause a downward bias
Errors in observing y
in the estimate of the tax rate.
Suppose that the true level of earnings is v.
so the true relationship is
(8)
B.
l
= B
o
+
- tv.
i
Howeve r, we observe
i
which differs from y
y.
(9)
u.
y
i
= y
+ V
i
i
*
where E(y
•
y.
)
= E(v.
)
= 0.
by a random error of observation, v
:
-17-
Then the regression coefficient is
(10)
t
=
\
(y
- y)
|
N
I
|
I (y ± - y)
±
-,2
and
1
P lim v I
.
plim
(11)
plim
-
=
plim
[(B + u
B
)
-
(y
2
£ y*
+ v
+ u
" ty
2
\
P lim „ I
We let a
(
=
t
1
+ v
T)
>
and a^ = plim
-
- y)
i
=
i
and
+ v
(v
i
|
"
(y
)
[ v
±
plim ^
.
i
- v)
_
and note that
Uy* +
v.
- v) = O
2
.
+ a
Thus
2
plim
(12)
t
=
t
—^*
a
which is less than
t
if a
v
2
.
y*
+ a
2
v
> 0.
The econometric technique of two-stage least squares can, in principle,
eliminate biases due either to simultaneity or to errors in the right-hand
variable.
We applied this method using as instruments or first-stage variables
the following characteristics: the age, race, health, education and birthplace
(whether born in the south) of the mother, and separately of the father where
present, the number and ages of the children, the number of non-parental adults,
and the city in which the family lived; complete interaction was allowed between
race and the other characteristics.
those reported earlier.
Our results were very little different from
In particular, there was no definite tendency for the
tax rates estimated by two-stage least squares to exceed those estimated by
ordinary least squares.
2
-18-
Another source of bias arises from the nature of the sample.
A
family enters the regression only if it receives positive benefits.
At
higher levels of earnings it is less likely that a family will appear in
the sample than at lower levels of earnings.
Those families that have high
earnings and do appear in the sample are likely to be those who receive
unusually high benefits for their incomes.
In terms of our statistical
model, observations with high values of v. are likely to have positive
values of the disturbance, u..
would not receive
If they did not,
then it is probable
that they
positive benefits and therefore would not appear at all.
Consequently, there may be a positive correlation between y. and
u,
,
and
our estimate of the tax rate mav be biased downward on this account.
There can be no doubt that our results are contaminated by the way
the sample was chosen.
There are two reasons to believe, however, that the
bias may not be too severe.
be equally biased
—
First, all of the estimated tax rates should
unearned income should drive families out of the sample
just as surely as earned income.
Our finding that the tax rates on earned
income are substantially lower than those for unearned income cannot be
explained by the nature of the sample.
Second, the severity of the bias
depends on the dispersion of the disturbances.
If there were no disturbances,
101
all of the observed values of B. and y. would lie along6 the line B. = B
i
and our regression would estimate
•'l
t
precisely.
In fact,
- ty.,
the dispersion of the
residuals in our regressions is relatively small, as shown in Table
3,
-19-
It seems likely to us,
therefore, that our finding of relatively
low tax rates on earned income under AFDC cannot be explained purely
as a statistical artifact, and that the prevailing belief that the
system of public assistance imposes a nearly confiscatory tax on
earnings needs substantial revision.
Date Due
21
7f
«| ftN.
)EC
JUN
3
1994
2
1995
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