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Working Paper 95 19
DOES MEANS-TESTING WELFARE DISCOURAGE SAVING?
EVIDENCE FROM THE NATIONAL LONGITUDINAL SURVEY OF WOMEN
by Elizabeth T. Powers
Elizabeth T. Powers is an economist at the Federal Reserve
Bank of Cleveland. This article is based on work that
originally appeared in her doctoral dissertation. The author
thanks her dissertation committee, Alan Auerbach, David
Neumark, and especially Stephen Zeldes, who provided
many comments and suggestions. Jonathan Skinner, James
Poterba, participants in seminars at the Wharton School of
Business, the University of Pennsylvania, the University of
Colorado at Boulder, the Federal Reserve Bank of
Cleveland, Kansas State University, the University of
Illinois at Urbana-Champaign, and the University of Kansas
also made helpful suggestions and comments on the
antecedents of this work. Kristin Roberts provided research
assistance. This paper was presented at the 1995 NBER
Summer Institute's Public Economics and Social Insurance
workshop and at the 1994 Eastern Economics Association
meetings.
Working papers of the Federal Reserve Bank of Cleveland
are preliminary materials circulated to stimulate discussion
and critical comment. The views stated herein are those of
the authors and are not necessarily those of the Federal
Reserve Bank of Cleveland or of the Board of Governors of
the Federal Reserve System.
December 1995
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Abstract
This paper empirically tests whether the asset limit associated with the Aid to Families with Dependent
Children (AFDC) program discourages wealth accumulation by actual and prospective participants. Prior
to 1981, the AFDC asset test varied substantially across states, and this variation can be used to identify
the effect of the limit on wealth. Wealth holdings for female-headed households (the primary recipient
group for AFDC) for 1978 are estimated using data from the National Longitudinal Survey of Women.
A $1 difference in state limits results in an estimated $.50 difference in total net wealth holdings of
female-headed households in different states. This qualitative finding of a significantly positive effect is
reasonably robust with respect to a variety of specifications of the wealth equation and instrumenting of
the limit to correct for the potential endogeneity of policy. After instrumenting, a $1 difference in limits
implies a difference in potential AFDC recipients' wealth holdings of $.30.
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I. Introduction
Aid to Families with Dependent Children (AFDC), Supplementary Security Income, Medicaid,
and Food Stamps are the major U.S. welfare programs. Seldom-noted features of these programs are the
penalties imposed when the welfare applicant's or recipient's asset holdings exceed specified, very low
amounts. Past literature has overwhelmingly focused on the work disincentives created by welfare
programs' earnings restrictions (see Moffitt [I9921 for a survey). Recently, however, attention has begun
to be paid to the notion that asset testing may have substantial, potentially damaging, effects on behavior.
This paper presents empirical evidence on the impact of AFDC's asset-based means testing on the
savings of female-headed households.
Hubbard, Skinner, and Zeldes (1995, 1994a, 1994b) explore means testing's potential impact on
saving using a simulation model parameterized to the Michigan Panel Study of Income Dynamics
(PSID). They demonstrate that for realistic levels of welfare income and age-earnings profiles, a lowlifetime-income family would be better off (in terms of expected lifetime utility) not to undertake
significant savings, since asset holdings are heavily penalized by welfare programs, whose benefits are
high relative to their autonomous income. When income is stochastic, the inclusion of asset-based means
tests in an income maintenance program can also dramatically discourage saving by families who never
actually experience income downturns serious enough to qualify for welfare, but who are at substantial
risk of such downturns.
While Hubbard, Skinner, and Zeldes (1995) demonstrate that the pattern of asset holdings in the
PSID is consistent with strong behavioral effects of asset tests, their simulations do not constitute a
formal test of the hypothesis. If asset tests do inhibit saving in practice, this would have several
interesting implications. First, it would support Hubbard, S k i ~ e rand
, Zeldes's (1995) contention that
the presence of asset-based, means-tested income maintenance programs explains the stylized fact that
low-permanent-income families (as proxied by the household head's educational attainment) do not
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accumulate significant wealth over the life cycle. This, in turn, suggests that the life-cycle model might
be appropriate for most households once the influence of asset-based, means-tested income maintenance
programs was properly considered.'
The implication that asset tests inhibit saving would also heighten concerns that asset-based
means testing may pose a threat to the long-term economic status of welfare-dependentindividuals and
their communities (for a full discussion, see Sherraden [1991.]). There may be several transmission
mechanisms for this effect. The asset test may affect the ability to finance education and training,
contributing directly to long-term welfare dependency and even its intergenerational transmission.
Another important goal of saving is home ownership. If failure to save reduces the incidence of home or
business ownership, welfare-dependent communities may be weakened politically by a dearth of
stakeholders. Without a buffer of wealth, individuals are apt to return more quickly to welfare during
transitory income downturns. Finally, asset tests may deprive low-lifetime-income individuals of
opportunities for learning to manage their finances and to set and achieve goals (that is, to adopt a longer
planning horizon and to develop techniques appropriate to that horizon). These skills may be necessary
for achieving a permanent exit from poverty.2 If asset tests inhibit saving in practice, relaxing limits on
saving may increase the chances of a permanent exit from poverty for some families and encourage
activities with positive externalities in poor communities. However, if there is no empirical evidence of a
behavioral response to asset testing, raising limits may only increase caseloads.
This paper presents a simple test of the hypothesis that asset limits inhibit the wealth
accumulation of a welfare-prone group--families with minor children that are headed by women. I use
' Hubbard, Skinner, and Zeldes (1995) suggest that alternative models, in which some groups behave
fundamentally differently from others, are not compelling.
In contrast, many govenunent transfers directed at the middle class (e.g., the home-mortgage deduction and the
tax-free accrual of pension wealth) foster exactly such "responsible" behavior. The case of Sandra, a young New
Haven woman who spent her college savings because it threatened her family's AFDC eligibility, highlights this
alleged double standard. As her Legal Aid lawyer put it, "Here you have a situation where other children would
have been commended. They went to school full time. They worked part time. And they saved their money.
The sad part of this is Sandra wasn't able to use this money for the purpose she had intended." Allegedly at the
state's urging, the family spent their "excess" wealth on "clothes, jewelry, shoes, and perfume" (Hays [1992]).
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cross-state variation in the AFDC program's asset-testing policy to identify the effect of the asset limit in
simple, empirical wealth equations. I restrict the analysis to the AFDC program and female-headed
households for several reasons. Prior to 1981, the AFDC asset limit varied by state, while in most other
major programs, such as Food Stamps, the rules have always been federally determined and uniform.
Female-headed households are the primary users of AFDC, and the National Longitudinal Survey of
Women, a data set that tracks a group of women who were between the ages of 14 and 24 in 1968,
collects asset data at five-year intervals.
The paper is organized as follows: The next section briefly describes the mechanism by which
asset testing may discourage saving. It shows that in certain cases, wealth holdings may vary positively
with the asset limit, if that limit constrains behavior. The final portion of the section maps out an
empirical strategy. Section I11 describes the programmatic and household data used in the empirical
work. Section IV discusses the empirical implementation and presents the findings, with an emphasis on
testing the robustness of the positive relationship between the asset limit and wealth holdings. Finally, it
examines the potential endogeneity of states' asset-testing policy with the cross-state asset distribution.
Section V summarizes and discusses the limitations and potential extensions of the analysis.
XI. Theory
Several aspects of welfare policy potentially affect wealth holdings. First, the existence of the
income floor provided by welfare smooths the lifetime income path, reducing the need for life-cycle
(certainty-equivalent) saving, and for precautionary saving. By discouraging experience in the labor
market and the development of human capital, the AFDC earnings test may also cause low permanent
income and flat wage profiles. Under a life-cycle approach to saving, these factors alone can lead to low
and flat patterns of wealth holdings. The fact that income from wealth is taxed at a 100 percent rate by the
earnings test also discourages wealth accumulation. In both the theoretical discussion and the empirical
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work, I focus exclusively on the potential effect of the asset test (primarily characterized by the limit). The
basic mechanism by which asset tests depress wealth holdings can be described using a simple, twoperiod model. The results of extending the model to the multiperiod case with eamings uncertainty,
developed in Hubbard, Skinner, and Zeldes (1995), are described briefly.
A simple two-period model of consumption with certain income illustrates how means testing
discourages saving. Assume that a family's first-period earnings (YI) exceed the AFDC income eligibility
level (G) and finance first-period consumption (CI). For simplicity, assume that the gross rate of return to
savings is 1 and no assets are carried into the first period. Suppose there are no private eamings in
period 2, so that second-period consumption (C2) is financed from savings accumulated in period 1
(A2= Y1-C1),AFDC benefits (Bz), or a combination of the two. Benefits can be written as
B2 = max{O, G2 - A2).
(1)
G2is the "guarantee," or benefit payment to a zero-earning family of a given size in period 2 (for simplicity,
assumed to be the same as eligibility income). A2is assumed to be non-negative. Equation (1) indicates
that benefits are reduced dollar for dollar with available private resources (A2). Figure 1 illustrates the
budget constraint and possible consumption choices of the agent under this policy regime.
The critical feature of the agent's problem under asset-based means testing is the nonconvexity of
the budget constraint. Hence, finding the solution to the agent's problem requires evaluating the lifetime
utility of the local maximum if the agent chooses not to participate in welfare under any circumstances
(consumptionbundle A) against the utility of the local maximum given participation (here equivalent to
receiving G in period 2, or consumption bundle B). Figure 1 illustrates the case in which it is globally
optimal to consume all resources in period 1 and go on welfare in period 2 (i.e., utility at bundle B exceeds
that at bundle A).
Actual welfare policy imposes low but positive limits on the wealth holdings of applicants and
participants. Let D2 denote a binary variable set equal to one if and only if wealth at the beginning of
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period 2 (A2)exceeds L2, where L2 is the limit imposed on the wealth holdings of welfare recipients. In this
case, the benefit policy can be expressed as
B2 = max(O,G2 - Dz(A2- L2)).
(2)
As long as wealth is less than the limit, there is no reduction in the benefit payment. Once wealth reaches
the limit, "excess" wealth is taxed at a 100 percent rate until the point at which private resources exceed the
guarantee. Beyond this wealth level, the agent is ineligible for the program. Obviously, even with a
nonzero limit, today's saving choice has implications for next period's utility exceeding its usual role.
Figure 2 illustrates the budget constraint and possible consumption choices of the agent under this policy
regime, in the case in which it is marginally attractive to distort current consumption against the prospect of
future welfare participation. Notice that if the guarantee were lower than that pictured, program
participation would be suboptimal, and savings would jump up to their autonomous level. Nor would
participation be optimal, ceteris paribus, if the asset limit were smaller; this demonstrates that higher asset
limits weaken program targeting.
Blinder and Rosen (1985) investigate generic policies of the type illustrated in figure 1, where C1
and C2are two arbitrary goods. They term these "notch policies, after the shape of the budget constraint.
Using simulations, they demonstrate that small guarantees are capable of inducing substantial consumption
distortions. Thus, even if AFDC benefits are perceived as small by many female heads of families, this
does not preclude the possibility of very large associated dissavings. In fact, although low, benefits are
quite large relative to the typical income of a nonparticipating female-headed family.
Figure 3 illustrates the theory's implications for the relationship between limits and wealth
holdings. Here, optimal wealth holdings (A) are plotted against the limit (L).
denotes the level of
wealth holdings if the family relies entirely on its autonomous income. It is the level of wealth holdings that
would occur in the absence of a welfare program. A* is the level of wealth that the family would hold if
they had access to the welfare program, but it was not asset tested. Figure 3 is drawn assuming a fixed
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welfare program with a particular benefit level G, fixed autonomous income Y, and fixed preferences. The
assumptions are such that for very low levels of L, welfare participation is undesirable; hence, wealth AaUt
is chosen. As the limit is increased, participation eventually becomes desirable, and positive constrained
wealth accumulation occurs. Constrained wealth holdings grow one-for-one with the limit until the limit is
large enough so that wealth holdings are unconstrained (A*).~
Hubbard, Skinner, and Zeldes (1994a, 1994b, 1995) extend this basic model of asset-tested
welfare in two major ways. First, they extend it to include a realistic number of periods. The intuition of
the simple two-period model turns out to be relevant for the multiperiod case. If welfare payments are
sufficiently high relative to autonomous resources, the permanent-income poor find it optimal to participate
frequently in the welfare program, despite the cost of the distorted consumption induced by the asset test.
Hubbard, Skinner, and Zeldes (1995) also demonstrate that in the presence of uncertainty about future
income or expenses, means testing can depress the wealth holdings of those who never actually experience
income or consumption shocks leading to participation; this spreads the effects of means-testing to the rest
of the (expected) low-permanent-income populati~n.~
The empirical implication is that the behavioral
effects of means testing may be readily discernible for potential future welfare participants, as well as for
actual current and future participants. Although Hubbard, Skinner, and Zeldes do not explore the
implications of nonzero asset limits specifically, it seems reasonable to expect the results illustrated in
figure 3 to hold broadly in the more realistic multiperiod setting. Because of uncertainty about future
incomes and expenses, these effects may also be evident for households not currently participating in the
welfare program.
' A' may lie above or below A"', depending on preferences.
The "curse of dimensionality"when uncertainty is introduced in the nonconvex budget constraint problem is
daunting, and computing the implied wealth distributions is a major technical achievement, even with current
computing capabilities.
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Empirical Strategy
The basic empirical strategy is to estimate wealth equations for female-headed households,
including the AFDC asset limit and related policies as explanatory variables. The fact that there is crossstate variation in the AFDC asset limit prior to 1981 makes it possible to identify the limit's effect on
wealth. If female heads of families are sufficiently homogenous as a group, and if asset limits are
sufficiently low overall, one would expect to find a positive relationship between limits and wealth
holdings. That is, all else being equal, women residing in states with higher limits should typically hold
more wealth.
However, there are several reasons why a positive relationship might fail to hold in the data.
First, if limits are high relative to the desired life-cycle savings of the female heads, the limits will not
bind, and one would expect no relationship between the limits and wealth. For example, because femaleheadedness is often not a lasting condition, the typical female head may quite rationally deplete the stock
of wealth during this presumably low-income period, expecting it to be replenished upon marriage.
Similarly, if the sample includes many high-permanent-income families, prospective welfare use is not an
important consideration in determining wealth holdings.
Figure 3 illustrates a third reason for a nonpositive relationship between limits and wealth. Wide
variation in asset limits, combined with the nonconvexity of the consumer's budget constraint when
asset-tested welfare is an option, may induce a negative relationship between the limit and wealth.
Consider the case of two women with identical characteristics who face the same welfare benefit
schedule. Suppose however, that woman A's family lives in a state in which the limit is so low that
welfare participation is never optimal, given her characteristics. Woman A holds wealth A""', as shown in
figure 3. Woman B lives in a state with a higher limit and holds wealth low due to the desirability of
participation under some circumstances. If very low limits are associated with "normal" levels of wealth,
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while higher limits induce consumption distortions, this wiU be manifested in a negative cross-sectional
relationship between wealth holdings and limits.
111. Program and Household Data
Characteristics of the AFDC Program
The current AFDC program descends from the Aid to Dependent Children program, introduced
in the 1935 Social Security Act. AFDC is the largest cash welfare program in the United States and has
always clearly targeted female-headed households, defined here as a family unit with children under 18
and a mother or female guardian who does not cohabit with a husband or boyfriend. Federal AFDC
legislation sets the criteria that each state's program must meet to qualify for its share of federal funding.
These federal guidelines govern the rate at which benefits are reduced with labor earnings; determine the
relationship between a standard of need (or minimum consumption requirement) and benefits; and set a
maximum for participants' wealth holdings.
The asset test was made a requirement on states in 1955. The initial federal maximum was
$1,500 (all nominal dollars) per member of the recipient household. Five years later, the federal limit
was increased to $2,000 per recipient, with a family maximum of $8,000. States tended to choose asset
limits well below these maxima. Determination of the base to which the limits applied was also largely
controlled by the states. Consequently, nominal limits varied widely, as did their application to gross
versus net wealth; treatment of the owner-occupied home's value varied according to the interpretations
of state courts (Lurie [1977]); many states imposed multiple asset tests across different categories of
wealth (for example, savings accounts might have a lower limit than personal property). The asset limits
also depended on family size in many states. This system lasted until 1981, when the federal govemment
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imposed strict guidelines for computing testable wealth, and the federal maximum was slashed to $1,000
per family.5
To capture the effect of the asset test in the empirical implementation, four elements of policy are
included as explanatory variables: the limit on nonhome property (including financial wealth and
excluding vehicle^);^ a binary variable indicating whether the limit is applied to gross or equity value; a
binary variable indicating whether there is a housing test; and a binary variable indicating whether the
primary vehicle is tested. Appendix A contains the values for these policy variables circa 1978 for the
states in my sample. The policy variable of primary interest is the limit, which will vary positively with
wealth if the hypothesis is supported (i.e., if wealth accumulation is constrained). To isolate the effect of
the limit from that of family structure on wealth, in most specifications the limit for a family comprised
of one adult and one child is used. The other policy variables are primarily considered as control
variables, although their influences may also provide evidence of a significant effect of asset testing on
wealth. The housing (/vehicle) test is expected to reduce wealth holdings by reducing housing (/vehicle)
ownership, or the market or equity value of housing (/vehicles) held. However, in the case of certain
components of wealth (e.g., liquid wealth) one might expect a positive effect of the housing/vehicle test
via a portfolio effect. The valuation of property on a market or equity value implies a stricter asset test in
all cases.7
Sample Construction and Characteristics
The National Longitudinal Survey of Women (NLSW) is a panel survey of a group of women,
beginning in 1968 when they were between the ages of 14 and 24. Starting with that year, detailed data
The other major change was in the benefit reduction rate, or implicit tax on labor, which rose from a statutory
two-thirds tax on labor income to a 100 percent tax (after the fourth month of AFDC participation).
Because multiple limits are possible on different forms of wealth within a state, the limit can be defined in
various ways. I attempted to discern "the" limit associated with the broadest wealth definition, because states do
not consistently place separate limits on detailed categories. I have experimented with a constructed limit on
liquid wealth with mixed results.
'While this suggests interacting this variable with the limit, I did not find the coefficient for this interacted term to
be significantly different from zero, and it is not included in the presentation below.
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on assets are collected at five-year intervals. The NLSW contains a variety of financial data and data on
real property and debts. However, certain items are included in some states' asset tests for which no
NLSW data exist. These include holdings of cash, pensions, durable goods, jewelry, and life and burial
insurance. Data on whether a respondent received income from AFDC in the past survey year is also
available for 1978. In order to match the appropriate policy variables to an observation, the state of
residence must be known, but this information is not released to users of the data base. Fortunately,
states can be identified for about 60 percent of the 1978 sample by matching 1968-69 regional variables
in the NLSW (e.g., educational expenditures by locality) to their published sources and deleting 1969-78
movers.' This results in a sample of 402 female-headed families in 1978, prior to deletions for missing
values. Based on inspection of sample means, selection bias does not appear to be a problem.
Prima facie evidence from the sample suggests that asset limits should plausibly influence the
wealth holdings of most female heads, if they influence those of any female heads, either because they
are actual welfare recipients, legally bound by program rules, or because they are likely future recipients.
There is striking homogeneity in incomes in the 1978 state-matched sample used in the empirical work
below. Of all female heads, 90 percent have nominal income below $13,475 (nominal dollars) in 1978.
The small income differences between those who are on welfare at some point in the sample year and
those who are off welfare all year provide the most dramatic evidence. The ratio of mean participants' to
nonparticipants' income is nearly 0.8. Clearly, the pecuniary differences between autonomy and welfare
are not large for most of these families, which suggests that the potential for future participation among
the currently nonparticipating group is probably high. Therefore, it seems reasonable to treat all the
families in the sample similarly in the e~timation.~
' I am grateful to Jeff Gray for providing me with a list of state-respondentID matches from his state-matching
program.
In a sample of two-parent families, for example, it would be necessary to develop criteria to distinguish those
who are probably not concerned with welfare from those who are. While this is a potentially interesting issue for
further research, it can reasonably be ignored in the case of female-headed households.
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IV. Empirical Implementation and Tests
This section presents the findings from the estimation of various wealth equations, with an
emphasis on exploring the robustness of the basic finding that the limit and wealth are positively related,
as shown in the first subsection.
Parsimonious Specification
The literature contains a wide variety of empirical specifications of wealth. Wealth is often
explained as a nonlinear function of contemporaneous income and personal characteristics (for an
example in a context very similar to this one, see Feldstein [1995]). Because wealth is a state variable in
the consumer's optimization problem, it presumably reflects all static characteristics, as well as the entire
history of relevant variables for the consumer's optimization problem, including past policy. Therefore,
lagged wealth should capture the cumulative effects of these factors, as well as past welfare participation.
Because the sample is small, I begin with a "parsimonious" specification of the wealth equation which, in
theory, contains the most information using the fewest variables. The parsimonious specification includes
income terms, policy variables, and lagged wealth.''
Initially, I consider three definitions of wealth, constructed from the various components of
household assets available in the NLSW. Gross and total net wealth include the total value of
(respectively equity in) financial wealth, vehicles, housing, and other real property. Financial or "liquid"
wealth includes savings accounts, stocks, and bonds. The asset limit and other measures of asset testing
policy are constructed by state from published sources (the U.S. Department of Health and Human
Services, selected years). In states where multiple limits govern different categories of wealth, a limit
was constructed for combined real (nonhome, noncar) and financial property.
Table 1 presents the findings for the parsimonious level and log-linear models (sample means
and standard deviations of all variables are presented in Appendix B). The parsimonious wealth equations
10
Age terms were all insignificant, due to the age restriction of the NLSW sample.
11
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are estimated for all three definitions of wealth. All standard errors of the coefficient estimates are
adjusted using White's (1978) heteroskedasticity correction. The models are estimated in both level and
log versions. Simple tests (Davidson and Mackinnon [I98 11) reveal that both the log and level
specifications conveyed information distinct from the other; neither functional form emerged as clearly
superior.
For the model in levels, the level of contemporaneous income appears to exert a significantly
positive influence on all three types of wealth. The squared income term is not significantly different
from zero at standard confidence levels (all significance levels refer to two-sided t-tests unless otherwise
noted). For the net wealth equation in levels, wealth varies positively with the limit, as expected. A $1
difference in the limit results in an estimated $.48 difference in wealth holdings. The housing test also
appears to reduce total net-wealth holdings significantly. The other two policy variables, market
valuation and the vehicle restriction, have no significant effect on any of the wealth measures in the
model in levels, and the vehicle restriction has an unexpected sign in the case of net wealth. In the case
of gross wealth, only the housing-test policy variable has a significant effect (negative, as expected). Of
the policy variables, only the two-person limit has a modest effect on liquid wealth holdings (it is
significantly positive in a one-sided test at the 90 percent level). In all three level specifications, the
lagged endogenous variable is highly significant and positive, as expected.
The last three columns of table 1 present the findings for the log-log form. The elasticity of
wealth with respect to income is first negative, then turns positive at higher income levels. The limit has
a significantly positive effect in the cases of both net and gross wealth, and a marginally significant
positive effect in the case of liquid wealth. The elasticities of total net and gross wealth with respect to
the limit are both around 0.7. The elasticity of liquid wealth with respect to the limit is 0.14 and is
significantly greater than zero (in a one-sided test) at the 95 percent level. In the model in logs, the
coefficient of the housing-test variable is never significantly different from zero. The gross versus equity
valuation variable has a marginally significant positive effect in the cases of net and gross wealth,
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contrary to expectations. As in the level specification, past wealth is an important determinant of current
wealth. For the remainder of the empirical work, I focus on the total net measure of wealth.
Extended Specifications
Alternative empirical wealth equations in the literature suggest two important ways to modify the
parsimonious specification. First, since saving can be defined S,=A,-4-,,wealth can be written
A,=S,+A,,. This suggests the addition of variables expected to influence additions to wealth ('S,')
between 1973 and 1978. These might include changes in family size and the interim pattern of income,
as in Skinner (1993). Unfortunately, it is not feasible to compute a consistent family income series for
the period 1973-78 from the NLSW. Instead, factors are included which are thought to significantly
influence income over the period, along with indicators of changes in family status; binary variables
indicating a significant change in educational attainment (either high school or college graduation), and a
positive or negative change in the number of the female head's dependents. Increased educational
attainment has an ambiguous effect on final wealth via saving. While it may increase permanent income,
and thus increase consumption and reduce saving, it may also indicate a positive jump in
contemporaneous income, which would tend to increase saving. Increases or decreases in the number of
dependents also indicate a significant change in family structure. Increases in the number of dependents
raise family consumption requirements and may slow wealth accumulation, while decreases are expected
to have the opposite effect.
In addition to (or in place of) lagged wealth, variables that represent static characteristics thought
to have an important influence on 1978 wealth holdings are also included. These are binary variables
indicating whether the female head was ever mamed, whether she is a high-school graduate, and the
number of her dependents. Female heads who have been married are likely to hold more wealth, since
they had access to their husbands' earnings and assets at some time in the past. Holding a high-school
degree should also be associated with higher levels of wealth, since the individual is presumably in a
higher permanent income group.
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Table 2 reports the findings for these extended models, again in both level and log-log forms. In
the case with levels (column l), lagged wealth seems to be an "absorbing" variable. That is, the static
personal characteristics are redundant and add no explanatory power to the model. Nor are the
"updating" variables reflecting important changes between 1973 and 1978 significant at standard
confidence levels. The additional variables also have virtually no effect on the estimates of the influence
of policy, which can readily be seen by comparing the first columns of tables 1 and 2. Column 3 of
Table 2 reports the analogous findings for the log-linear case. In contrast, even when lagged (log) wealth
is included, the high-school-graduatevariable has a significant positive influence on wealth. Having
never been married marginally lowers wealth, as does an increase in the number of dependents between
1973 and 1978, as anticipated. However, as in the case of levels, the policy effects are robust with
respect to the addition of these variables.
Robustness with Respect to Lagged Wealth
Table 2 also contrasts the estimates of the extended specifications with and without lagged
wealth. While theory suggests that lagged wealth is an important state variable whose omission results in
biased estimates, use of lagged endogenous variables should be treated cautiously. For example,
autocorrelation in the errors may cause lagged wealth to be spuriously significant in the model, although
additional evidence does not support this." However, autocorrelation may still be a problem when the
true model includes lagged wealth, resulting in inefficient estimates. Unfortunately, data limitations
prevent using a Hatananka estimator." All that can be done is to investigate the sensitivity of the
findings with respect to lagged wealth.
The second column of table 2 presents the findings for the extended specification in levels when
lagged wealth is excluded from the model. The current level of income, never having been mamed, and
" The coefficients of autocorrelation when lagged wealth is excluded from the specifications (not reported) are
significantly smaller than the coefficients on lagged wealth in table 2.
'' The problem is that the required additional lag of wealth would take the sample back to 1968, when many
respondents are children living with their parent(s); alternatively, if the time-frame is shifted forward, the wealth
observations from 1983,1978, and 1973 straddle a significant change in policy regime occurring in 1981.
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being a high-school graduate are now the important determinants of wealth, although they explain little
of its total variation. The interesting result of dropping lagged wealth is that the effect of the policy
variables is no longer significant. While the estimated coefficient of the two-person limit is fairly robust
to excluding lagged wealth, its estimated standard error increases. In contrast, for the log specification,
the estimate of the effect of the limit is virtually unchanged by the inclusion or exclusion of lagged
wealth, and it remains significantly different from zero.
State Effects
An important question is whether the welfare policy variables inadvertently proxy for state-
varying characteristics that influence wealth holdings independently. For example, state-varying divorce
laws may influence settlements. A state with policies generally favorable to women may encourage
generous settlements and also set relatively generous asset limits for AFDC. The policy variables may
also inadvertently reflect interstate variation in conditions like general economic opportunity, property
values, and wages. For example, after controlling for interstate variation in welfare policy, Blank (1985)
finds that female heads still face substantially different state economic conditions.
A straightforward correction is to augment the model with state-specific binary variables to
adjust for all state-varying characteristics. Policy variables for the treatment of property, housing, and
vehicles must be dropped, since they only vary by state. Variation in the number of childrqn across
households should provide sufficient state-independent variation to identify the effect of the limit from
the state dummies. Table 3 presents the findings before and after the inclusion of state dummies. In the
absence of the other policy variables, the effect of the limit is estimated to be somewhat weaker to begin
with. However, it is still significantly different from zero at at least the 90 percent level in both log and
level specifications and is significantly greater than zero at the 95 percent level or greater in a one-sided
t-test. In both log and level versions, including state effects increases the magnitude of the estimated
coefficient on the limit, although in the log version the coefficient is no longer significantly different
from zero.
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Endogenous Policy
An important remaining concern is that the wealth distribution and asset-testing policies are
determined endogenously. To take a simplistic example, consider two states in which the income
distributions are identical, but suppose one state's wealth distribution is shifted farther to the right. In
order to generate the same number of eligible recipients in each state, the state with higher mean wealth
can set its limit higher. In this case, endogeneity biases towards a positive relationship between the limit
and wealth.
One weak test whose failure would be a strong sign that the limit "reverse causes" the findings is
to estimate the relationship between 1978 asset limits and 1983 wealth holdings. After the federal policy
change in 1981, all but a handful of states imposed an asset limit of $1,000. Suppose that the positive
relationship between 1978 wealth holdings and limits is simply due to states setting policy in response to
their wealth distributions. If there is no behavioral effect of the limit on wealth holdings, there should be
no response to the change in policy in 1981, and 1978 asset limits should continue to be a good indicator
of state-varying wealth characteristics. The lack of a significantly positive relationship between 1983
wealth and 1978 limits could result from either of two factors or from their combination. First, wealth
may actually respond to policy, and asset-testing policy changed dramatically in 1981. Second,
differences in relative state wealth distributions may have changed over the period for other reasons
(including changes in welfare policy that have nothing to do with the asset test). This last possibility
explains why the test is a weak one.
The parsimonious specification for levels in table 1 was re-estimated, substituting 1983 wealth as
the dependent variable (findings not reported). Both specifications using 1978 wealth (the new lagged
endogenous variable) and 1973 wealth (the original right-hand-side variable) as explanatory variables
were estimated. In all cases, the coefficients of the policy variables were not significantly different from
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zero at all reasonable confidence levels, indicating a lack of strong evidence of reverse causality in the
data.
An attempt is also made to correct for the possible endogeneity of policy by using a lag of the
limit as an instrument. The earliest year prior to 1978 for which there are published data on the limit is
1974. About one-half of the states have some noticeable change in their asset-testing policy between
1974 and 1978. Although ideally one would instrument the binary policy variables as well, the published
information for 1974 is less complete. The findings are presented in table 4. Without the other policy
variables, the two-person limit is significantly positive in a one-tailed test at the 95 percent level or better
in both levels and log specifications without instrumenting. The findings are quite robust with respect to
instrumenting, but the two functional forms yield contradictory interpretations of policy's role. The
corrected coefficient for the limit is smaller in the levels version, but is still significantly greater than zero
at the 90 percent level in a one-sided test. In the log specification, the limit remains highly significantly
positive and its magnitude increases somewhat, suggesting that the uninstrumented coefficient is biased
downward.
Other Robustness Issues
It is possible that the effect of welfare rules on current welfare participants generates the above
findings, and that nonparticipants do not incorporate welfare into their contingent consumption plans.
While this still supports the hypothesis that limits have an important effect on savings, the more
interesting aspect of the hypothesis raised by Hubbard Skinner, and Zeldes--that, because of uncertainty,
the effect of asset tests is to dampen wealth holdings for whole lifetime-income groups, regardless of
actual participation--should be examined in more detail. Therefore, households that reported receiving
AFDC income within the survey year were dropped, and the models were re-estimated for the remainder
of the sample. The disadvantage is that only 256 observations remain in the sample. (Sample means and
standard deviations for all variables are presented in Appendix B.)
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Table 5 presents the findings for the groups of nonparticipants in level and log versions of all
four specifications: the parsimonious specification of table 1; the extended specification of table 2; the
model with state effects of table 3; and the instrumented version of table 4. The qualitative findings are
strikingly similar to those for the entire sample, with one exception: When state effects are included, the
family-varying limit is no longer significantly positive in the log-log specification. In nearly every case,
the estimated magnitude of the limit's effect is larger in level models and smaller in log-log models when
participants are excluded. There is no obvious explanation for this pattern.
Finally, all of the specifications were investigated for sensitivity to the exclusion of outliers.
This was done by excluding observations associated with absolute standardized residuals exceeding two.
This procedure tended to result in a handful of deletions (typically fewer than 10 in the full sample), and
none of the specifications was substantively changed when re-estimated with the reduced sample.
This paper empirically tested the hypothesis that the asset-based means test affects the saving
behavior of actual and prospective AFDC recipients. The approach has been to use state variation in
asset limits prior to 1981 in order to identify the effect of the limit. In a parsimonious specification of the
empirical wealth equation, a $1 difference in two states' asset limits was estimated to result in a $.48 gap
in the total net wealth holdings of female-headed households residing in the respective states.
Alternatively, a log-log specification resulted in an estimate of the elasticity of total net wealth holdings
with respect to the limit of 0.7. The robustness of these findings was explored along several dimensions.
They were robust with respect to including additional explanatory variables. While the positive
significance of the limit in the levels version of the model was not robust with respect to replacing lagged
wealth with other characteristics, the estimated effects of policy in the log specification were quite robust
to replacing lagged wealth. The estimated effect of the limit was also reasonably robust to the inclusion
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of state effects for both functional forms. The possibility that the limits are endogenous with the asset
distribution led to the use of a lagged policy variable as an instrument for the two-person-family limit.
The findings were reasonably robust with respect to instrumenting the limit in both level and log
specifications. Finally, to estimate the impact of the limit via potential participation, the models were
reestimated using the subsample of female-headed households not participating in AFDC in the year of
the survey. The findings were quite robust with respect to this change in the sample.
Althought the findings provide support for the hypothesis, there are several potential areas for
further research that may produce still more decisive findings. Perhaps most importantly, this work relies
on the homogeneity of the female-headed household sample incomes to support the simplifying
assumption that all female heads are potential program recipients with high enough probability so that the
asset limit affects their saving behavior.I3 The inability to discern gradations of the desirability of welfare
may bias against finding a strong relationship between the asset test and wealth, if many members of the
sample have little concern about future welfare use.14 This would be of particular concern when
analyzing the effects of other welfare programs.
The treatment of the limit's potential endogeneity with wealth might also be refined. While
instrumenting using lags is a promising approach, to do this with greater precision it is desirable to
develop a model of the policy process. The various rules on housing, vehicles, and gross versus equity
valuation are probably best modeled as being determined jointly with the limit in the policy process.
Even had these other policy features not been beyond the scope of this paper, they would necessarily
have been excluded because of data limitations.
Finally, as I mentioned early on, several other ways that welfare policy potentially affects wealth
holdings might be incorporated into the analysis. The existence of the income floor provided by AFDC
13
A necessary implicit assumption is that the desirability of welfare is similar across states, which is not supported
by much of the empirical welfare literature, although the bulk of the variation may occur above a threshold
sufficient to influence saving behavior.
l4 For example, Feldstein (1995) stratifies his sample of families potentially affected by college-scholarshiprules
by income.
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reduces the need for saving in anticipation of income declines. By discouraging experience in the labor
market, the AFDC earnings test may result in low permanent income, implying lower wealth holdings at
every age. Inexperienced workers may also face flat income profiles (that is, a combination of low
earnings and AFDC), which flattens the age-wealth profile. The fact that the program taxes income from
wealth at a 100 percent rate also discourages wealth accumulation. The integration of these myriad
factors into a comprehensive analysis of welfare's influence on wealth awaits a richer treatment of the
dynamics of welfare participation than has appeared in the literature to date.
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Appendix A: Policy Variables for Selected States, 1978
State
Alabama
Arkansas
California
Connecticut
District of Columbia
Florida
Georgia
Hawaii
Idaho
I Wyoming
Limit, 2-Person Family
$1,750
2,250
6,600
250
2,000
1,200
800
575
2 000
750
Housing Test
no
Y
Y
Y
n
n
n
Y
n
Vehicle Test
yes
Y
n
n
Y
n
n
Market Valuation
yes
Y
n
n
n
n
n
Y
Y
n
Y
Y
Y
Y
Source: Author's computations using Characteristics of State Plans for AFDC (selected years) and
Research Tables Based on Characteristics of State Plans for AFDC (selected years).
I
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Appendix B : Sample Characteristics
I
I
(
I
I
L
I
I
I
Full Sample of Female-Headed Households, 1978
Variable
I Mean I Standard Deviation
Total net wealth, 1978
1 4,849.04 1
17,053.33
3,235.00
Total net wealth, 1973
12,009.00
7,911.62
Gross wealth, 1978
22,283.13
5.926.50
Gross wealth. 1973
18.5 16.00
889.77
Liquid wealth, 1978
4,9 16.37
4,059.40
622.27
Liquid wealth, 1973
Income, 1978
1 7,287.20 1
5,701.10
3,009.0 1
2,460.10
Two-person limit, 1978
Family-size-varying limit, 1978
3.477.50
2,839.00
0.44
0.27
Housing test
0.8 1
0.39
Gross valuation
0.49
Vehicle test
0.50
0.26
0.07
Change in educational attainment
0.49
0.39
Positive change in dependents, 1973-78
0.28
Negative change in dependents, 1973-78
0.09
Never married
0.30
0.46
0.49
0.61
High-school graduate
2.10
1.38
Number of de~endents.1978
I Sample Size (
391
39 1
39 1
39 1
39 1
39 1
39 1
39 1
39 1
39 1
391
39 1
386
386
386
386
386
386
1
Sample of Nonrecipient Female-Headed Households, 1978
I Mean I Standard Deviation I Sample Size
Variable
20,685.98
Total net wealth, 1978
256
6,942.16
14,577.00
Total net wealth, 1973
256
4,557.40
Income, 1978
1 7,882.80 1
5,553.70
256
2,875.90
Two-person limit, 1978
256
2,399.80
3,338.60
2,754.20
Family-size-varying limit, 1978
256
Housing test
0.24 1
0.43
256
0.39
0.8
1
256
Gross valuation
0.44
0.50
256
Vehicle test
Change in educational attainment
0.24
0.06
254
Positive change in dependents, 1973-78
0.47
0.35
254
0.29
Negative change in dependents, 1973-78
0.09
254
Never married
0.26 1
0.44
254
0.47
254
0.68
High-school graduate
1.22
1.83
254
Number of dependents, 1978
Source: Author's computations from the National Longitudinal Survey of Women.
I
I
-I
1
I
I
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References
Blank, R., "The Impact of State Economic Differentials on Household Welfare and Labor Force
Behavior." Journal of Public Economics 28,25-58, 1985.
Blinder, A., and Rosen, H., "Notches." American Economic Review 75(4), 736-747, 1985.
Davidson, R., and Mackinnon, J., "Several Tests for Model Specification in the Presence of Multiple
Alternatives," Econometrica 49,78 1-793, 1981.
Feldstein, M., "College ScholarshipRules and Private Saving," American Economic Review 84(3), 552566,1995.
Hays, C., "Welfare's Limit on Savings Foils One Bid to Break Cycle." New York Times, May 15,
1992.
Hubbard, R., Skinner, J., and Zeldes, S., "Expanding the Life-Cycle Model: Precautionary Saving and
Public Policy." American Economic Review Papers and Proceedings 84 (May), 174-179,
1994(a).
Hubbard, R., Skinner, J., and Zeldes, S., "Precautionary Saving and Social Insurance." NBER Working
Paper No. 4884, 1994(b).
Hubbard, R., Skinner, J., and Zeldes, S., "Precautionary Saving and Social Insurance." Journal of
Political Economy 103(21), 360-399, 1995.
Lurie, I., "Income, Asset, and Work Tests in Transfer Programs for Able-Bodied Nonaged Individuals,"
pp. 52-90 in The Treatment of Assets and Incomefiom Assets in Income-Conditioned
Government Benefit Programs: Technical Papers Prepared for the Federal Council on Aging.
Institute for Research on Poverty, University of Wisconsin, Madison, September 1, 1977.
Moffitt, R., Incentive Effects of the U.S. Welfare System: A Review." Journal of Economic Literature
30 (I), 1-61, 1992.
Sherraden, Michael, Assets and the Poor: A New American Welfare Policy. h o n k , NY:
Sharpe, 1991.
Skinner, J. "Is Housing Wealth a Sideshow?'NBER Working Paper No. 4552, November 1993.
U.S. Department of Health and Human Services, Characteristics of State Plans for Aid to Families with
Dependent Children, selected years.
U.S. Department of Health and Human Services, Research Tables Based on Characteristics of
State Plans for Aid to Families with Dependent Children, selected years.
White, H., "A Heteroskedasticity Consistent Covariance Matrix and a Direct Test for
Heteroskedasticity." Econometrica, 8 17-838, 1978.
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Table 1 : Basic Level and Log-Linear Models, by Type o f Wealtha
Levels
.Gross
Liquid
Variable
Constant
-1,419.20
-1,644.50
-844.90
(0.85)
Limit, two-person family, 1 97gb
House tested, 1978'
1
Market valuation for test, 1978'
Car tested, 1978'
1
-745.50
(0.49)
(
Wealth, 1973
Number of observations
0.48'
(2.21)
(1.32)
1
109.60
(0.12)
1.08'
(6.78)
391
0.34
(1.29)
/
-1,351.80
(0.56)
1
I
1,505.40
(1.21)
0.93'
(9.99)
391
-3.82'
(1.99)
0.17"'
(1.51)
-132.20
(0.28)
(
1
Gross
Liquid
-3.84"
(1.89)
-1.60
(0.94)
wealthd
-236.40
(0.93)
0.80'
(2.22)
391
Adjusted R2
61.0%
1 63.4% 1 46.4%
Notes: " Standard errors of model estimates adjustedby White's heteroskedasticity correction.
Corresponding log value implied in case of log-linear model.
Binary variable corresponds to one if statement is true.
* Negative values of net wealth are set to zero.
Significant at 95% level of confidence.
.I
Significant at 90% level of confidence.
Sisnif~cantat 85% level of confidence.
...
Source: Author's computations based on data from the National Longitudinal Survey of Women.
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Table 2: Extended Level and Log-Linear Models, with and without Lagged Endogenous Variablea
;sd
Including
(1.89)
Limit, two-person family, 1 9 7 8 ~
House tested, 1978'
1
0.47'
(2.11)
0.38
(1.1 1)
-3,905.7'
(2.94)
-436.00
156.50
(0.16)
-1,070.70
(0.76)
802.00
(0.45)
407.60
(0.17)
2,273.40
(0.82)
6,789.50
(0.95)
638.20
(0.69)
-4,248.40'
(2.85)
53 1.50
(1.39)
-101.78
(0.17)
Market valuation for test, 1978'
Car tested, 1978'
Wealth, 1973
Increased number of
dependents, 1973-78'
Decreased number of
dependents, 1973-78'
Change in education, 1973-78'
Never manied, 1978'
High-school graduate, 1978'
Number of dependents, 1978
1
Number of observations
I Adjusted RZ
I
386
60.7%
1
386
6.4%
Notes: 'Standard errors of model estimates adjusted by White's heteroskedasticity correction.
Correspondinglog value implied in case of log-linear model.
Binary variable correspondsto one if statement is true.
* Negative values of net wealth are set to zero.
Significant at 95% level of confidence.
Significant at 90% level of confidence.
Significant at 85% level of confidence.
.....
Source: Author's computations based on data from the National Longitudinal Survey of Women.
Excluding
lagged wealth
-1.74
(0.79)
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Table 3: Basic Level and Log Models. with and without State Effectsa
Levels
Excluding
Including
Variable
state dummies
state dummies
-2,181.00"'
Constant
(1.58)
NA
LogsC
Excluding
1978 Income
Family size, varying limit, 197sb
0.25"
(1.73)
0.53'
(2.04)
Wealth, 1973
1.08.
(6.49)
1.14'
(8.97)
Number of observations
I
391
I
391
Adjusted R2
60.8%
63.4%
Notes: " Standard errors of model estimates adjusted by White's heteroskedasticity correction.
Corresponding log value implied in case of log-linear model.
Negative values of net wealth are set to zero.
' Signiticant at 95% level of confidence.
Significant at 90% level of confidence.
Sigdicant at 85% level of confidence.
.....
Source: Author's computations based on data from the National Longitudinal Survey of Women.
Including
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Table 4: Instrumental Variable Estimates of Wealtha
I gsc
Excluding
Including
instrument for limit instrument for limit
-1.38
-2.04
(0.82)
(1.27)
1978 Income
0.31"
(1.6 1)
Limit, two-person family, 1978~
Wealth, 1973
Number of observations
I
1.08'
I
0.27
(1.36)
I
1
1.08'
391
391
60.8%
60.8%
Adjusted R2
Notes: " Standard errors of model estimates adjusted by White's heteroskedasticitycorrection.
Correspondinglog value implied in case of log-linear model.
Negative values of net wealth are set to zero.
' Significant at 95% level of confidence.
Significant at 90% level of confidence.
Significant at 85% level of confidence.
.....
Source: Author's computations based on data from the National Longitudinal Survey of Women.
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Table 5 : Model Findings. NonDarticiDant Subsamulea
Parsimonious Model
Extended Model
~ o g s ~
Levels
~ o g s ~ Levels
-3.71"
-3,227.70
-3.10"'
-359.80
(1.77)
(0.88)
(1.52)
(0.14)
State Effects
=9=
Variable
Constant
1978 Income
Limit, two-person family, 197Sb
0.7 1.
(2.13)
0.61'
(2.64)
0.70.
(2.07)
0.49'
(2.28)
no
no
no
no
House tested, 1978'
-43 12.00'
(2.18)
0.90***
(1.50)
-4,959.60'
(2.45)
0.82"'
(1.45)
Market valuation for test, 1978'
-1,358.10
(0.63)
1.13"
(1.75)
-1,649.90
(0.80)
1.17"
(133)
Family size, varying limit, 1 9 7 ~ ~
Car tested, 1978'
Wealth, 1973
Increased number of dependents,
1973-78'
Decreased number of
dependents, 1973-78'
Change in education, 1973-78'
Never married, 1978'
I
I
1
I
-41.13
(0.03)
1.08'
(6.78)
no
no
no
no
I
/
1
I
-0.36
(0.83)
0.53'
(8.81)
no
no
no
no
1
1
1
1
1.07'
(6.73)
-1,545.60
(0.92)
2,096.90
(0.85)
4,109.50
(0.96)
388.50
(0.28)
-0.16
(0.35)
0.46'
(7.06)
/
1
1
-1.00'
(2.31)
0.32
(0.45)
0.23
(0.32)
-0.52
(1.07)
no
1,645.80
(0.92)
1.53'
(3.21)
no
no
256
no
no
256
1,375.70'
(2.00)
no
254
0.22
(1.10)
no
254
Number of dependents, 1978
1
/
no
High-school graduate, 1978'
State effects
Number of observations
363.60
(0.25)
1
1
Adjusted R2
60.6%
38.1%
60.4%
Notes: 'Standard errors of model estimates adjusted by White's heteroskedasticitycorrection.
1
Corresponding log value implied in case of log-linear model.
Binary variable corresponds to one if statement is true.
Negative values of net wealth are set to zero.
Significant at 95% level of confidence.
Significant at 90%level of confidence.
Significant at 85% level of wnfidence.
.*...
Source: Author's computations based on data from the National Longitudinal Survey of Women.
Instrumental Variable
Estimate
Levels 1 ~ o g s ~
@FedFRASER