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Wearing Out Your Welcome: Examining Differential Medicaid Eligibility of New Entrants and Continuing Recipients
Sarah Hamersma
Burçin Ünel
This draft: November 15, 2013
I. Introduction
While the federal government provides mandates regarding eligibility rules for public insurance
coverage of children, it provides very little regulation of coverage for their parents. Through major
welfare reforms in 1996, the Medicaid program was delinked from cash welfare and states were left
to determine their own policies, with just the minimal requirement that they not reduce income
eligibility thresholds from their 1996 nominal levels. Under the policies existing for cash assistance
and Medicaid prior to 1996, states regularly tightened income thresholds with increased spell
duration, causing long-term recipients to potentially “wear out their welcome,” losing access to the
programs if their income did not fall sufficiently over time.
Since 1996, states have made a variety of changes in income eligibility thresholds for parental
Medicaid. Some have maintained their 1996 rules, including the pattern of reduction in income
thresholds with spell duration. Others have fixed the threshold at a single level from 1996 (either
the one used for initial applicants, or the lowest one used for long-term recipients), so that there is
no longer an association between spell duration and income thresholds. The majority of states have
raised income thresholds since 1996, doing so in a variety of ways. Some have created formulas
related to the Federal Poverty Guidelines, and these are seldom tied to spell duration; others have
increased thresholds overall but still reduce them with spell duration; still others have increased
thresholds as well as making the thresholds more generous with spell duration. At this point, several
states have different “new entrant” limits relative to their “continuing recipient” limits, and the
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continuing recipient limit is sometimes higher and sometimes lower than that for new entrants. The
states with increasing or decreasing thresholds are shaded in Table 1.
The Patient Protection and Affordable Care Act (PPACA) of 2010 requires each state to expand
Medicaid coverage to all individuals with incomes up to 133% of the Federal Poverty Line by 2014.
While there were several states that had already started phasing in the (higher) Medicaid eligibility
requirements, many states were waiting for the Supreme Court to rule on the constitutionality of the
legislation before revisiting their Medicaid programs. In June 2012, the Supreme Court ruled that
the states are not required to comply with this provision. Even though this ruling allows the states
the option not to expand Medicaid coverage, many political experts believe that the states will be
under significant political and fiscal pressure to accept the federal funding that is attached to this
provision. This pressure will inevitably lead the states to revisit their current Medicaid eligibility
policies, whether they end up complying with PPACA or not.
Our goal in this paper is to consider an important feature of existing policy that is likely to be
relevant as states consider potential changes to their programs: the option to continue to use (or to
develop) parental Medicaid income thresholds that become more or less generous with duration of
participation. Our paper demonstrates that individuals’ behavior, both in obtaining eligibility for
Medicaid and maintaining that eligibility over time, is currently subject to very distinct sets of
Medicaid and employment incentives across states with differing duration-linked policies. While the
policy debate is not currently addressing duration-dependent changes in Medicaid eligibility, this
policy feature could be costly to overlook. The incentives created by different regimes may
promote systematic differences in employment choices and Medicaid participation across states for
people with otherwise similar circumstances. When deciding on the new eligibility thresholds, the
states should consider these differences, as the length of the Medicaid spell and hence the cost as
well as labor market participation may differ depending on the policy regime. In this paper, we
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develop a theoretical model in which Medicaid eligibility is endogenous (established by workers via
the number of hours they choose to work) and Medicaid thresholds may change with duration. Our
simple two-period model provides several predictions for Medicaid participation and duration, as
well as employment patterns, across individuals with varying wages in states with distinct policy
regimes. After compiling detailed program rules by state and family size, we test some of these
hypotheses with data from the Survey of Income and Program Participation (SIPP), finding some
suggestive evidence that behavior is consistent with the incentives created by this policy variation.
II. Parental Medicaid Eligibility and Spell Duration
Prior to 1996, cash assistance (Aid to Families with Dependent Children) and parental Medicaid
were tied to the same eligibility standard within each state.1 All states were subject to the same style
of eligibility formula in terms of earnings. First, each state set a “payment standard.” Then, the
initial eligibility of workers was established by comparing earnings, minus disregards, to the payment
standard, as follows: first, for initial eligibility, the disregard was $90 + $30 + 1/3 of remaining
earnings. After 4 months on assistance, the disregard was reduced to $90 + $30. Finally, after 8
additional months on assistance (12 months total), the disregard was reduced to $90. The consistent
policy across states was, thus, that people were to be encouraged to leave assistance, being allowed
to stay only if they were increasingly needy over time. While states varied in overall generosity via
choice of payment standards, the basic incentive to leave assistance over time was the same across
states.
1 In the earlier days of AFDC, there were some alternative policy parameters, but those described here were in place since 1990 (see Matsudaira and Blank (2013) for details on previous policy parameters).
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States began to make changes in both Medicaid and cash assistance (re-named Temporary
Aid to Needy Families, or TANF) earnings thresholds in the mid-1990s. In some cases, states
changed TANF and Medicaid policies in parallel, while other cases involved independent changes in
one or both programs. A detailed discussion of changes in TANF earnings disregards and their
effects is provided in Matsudaira and Blank (2013). Changes in parental Medicaid earnings
thresholds have not yet been thoroughly studied. There is evidence that increased thresholds
resulted in increased Medicaid participation (Aizer and Grogger, 2003; Busch and Duchovny, 2005;
Hamersma and Kim, 2012), and Hamersma and Kim (2009) found that increasing thresholds led to
reductions in job lock for single mothers. However, none of this literature has considered the
implications of within-state variation in thresholds conditional on spell duration. We begin our
investigation into these implications by laying out a theoretical model.
III. Modeling Medicaid Participation and Labor Supply
To analyze the effects of different policy regimes on Medicaid participation, Medicaid spell
length, and work hours, we use a simple two-period model. In the first period, an individual
chooses whether to participate in the Medicaid program, and makes labor and consumption
decisions accordingly. In the second period, in addition to choosing work hours and consumption,
a Medicaid enrollee also decides whether to continue enrollment or drop out of the program. There
may be several factors driving this decision such as changes in the need for health insurance or job
conditions. However, we would like to focus our analysis on the effects of changing eligibility
thresholds. Therefore, we assume that wages, prices, and the preferences of individuals stay the
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same in both periods. (In our empirical examination of our hypotheses, the length of such a period
will be one year.) The (two-period) utility function of an individual i is
1 1 1 1 2 2 2 2( , , ) ( , , )i i i i i i i iU c L M U c L Mδ+
where δ is the discount factor, itc is consumption, itL is hours of work, and itM is Medicaid
participation in period t, t=1,2. For simplicity, we assume that the utility function is additively
separable in the value of Medicaid participation such that for a given level of consumption and
labor,
( , ,1) ( , ,0)it it it it it it iU c L U c L− = ∆
where i∆ is a positive constant. While stigma or transactions costs may reduce the value of
Medicaid for some, it is assumed that the net (individual) value of Medicaid remains positive since it
does provide premium-free health insurance.
An individual faces two constraints in each period: the traditional budget constraint and the
Medicaid eligibility threshold. The budget constraint is:
(1) it i itpc w L≤
where p is the unit price of the consumption bundle and iw is the after-tax wage rate of the
individual.
The Medicaid eligibility threshold for an individual differs depending on their state, month, and
family size as well as (potentially) the length of their Medicaid spell. Let inI denote the “new
entrant” income threshold for Medicaid eligibility and icI denote the “continuing recipient” income
threshold for an individual i. As noted earlier, some states have Medicaid benefits that are hard to
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get initially but easier to keep (i.e. in icI I< ), while others have benefits that are not as hard to get
initially but are increasingly difficult to keep (i.e. in icI I> ).
The Medicaid eligibility constraint for a new entrant in period 1 is:
(2) 11
{0,1} if 0 otherwise
i i ini
w L IM
∈ ≤= .
The Medicaid eligibility constraint for a continuing recipient in period 2 is:
(3) 22 1
{0,1} if 0 otherwise
if 1i i ii i
cw L IM M
= =
∈ ≤
.
Note that if an individual does not participate in Medicaid in period 1, the new entrant threshold
still applies in period 2. Therefore the Medicaid eligibility constraint for such an individual in period
2 will be the same as in period 1:
(4) 22 1
{0,1} if 0 otherwise
if 0i i ii i
nw L IM M
= =
∈ ≤
.
Rewriting the utility function is helpful in analyzing how the labor supply of an individual is
influenced by the availability of the Medicaid program. For a utility-maximizing individual, the
budget constraint (1) is satisfied with equality in each period. Substituting it in to the utility function,
we get
(5) ( , ) ( , , )i itit it it it it it
w LV L M U L Mp
≡ .
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The above (one-period) utility function is concave in itL if ( , , )it it it itU c L M and is well-behaved.
Note that this model is simply a restatement of the standard labor-leisure choice model with a
Medicaid notch a la Yelowitz (1995).
To understand the behavior of an individual, we need to define two critical values, ˆiL and iL .
Let ˆ ( ) arg max ( , )it
it it it it itL
L M V L M= denote the unconstrained utility maximizing level of work hours
for individual i in period t. Although it is technically conditional on the Medicaid participation
decision, because the utility function stays the same in both periods and is additive in Medicaid
participation, ˆitL does not depend upon the period or Medicaid participation decisions:
1 1 2 2ˆ ˆ ˆ ˆ ˆ(1) (0) (1) (0)i i i i iL L L L L= = = = .
Let itL denote the number of hours that a Medicaid participant needs to work to get the same
utility that could be attained at the utility maximizing point as a non-participant, i.e.
ˆ( ,1) ( ,0)it it it itV L V L= . As Δi (the net value of Medicaid) is constant across periods, itL is the same
in both periods: 1 2i i iL L L= = .2 Because Medicaid participation provides additional utility, the
number of work hours necessary for an individual on Medicaid to attain the maximum utility level
without Medicaid participation is lower than the utility maximizing number of work hours without
Medicaid participation, so ˆi iL L< (see Figure 1). The larger the net value of Medicaid, the larger
the gap between these two values, all else equal.
2 One can imagine a model in which transaction costs for initial application and for continuing receipt could differ, driving a change in Δi across time periods. We do not extend the model to that case here, as we believe the 12 cases generated by our model, with distinct predictions, reflect a sufficiently rich model for our purposes.
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[Insert Figure 1.]
Before analyzing the two-period decision of an individual, consider the case in which the
thresholds in different periods are independent of the length of the spell. In such situations, an
individual can treat the Medicaid participation decision in each period as a single, independent utility
maximization problem. In a given period t, this decision will depend on how the maximum number
of hours an individual can work without exceeding the Medicaid income eligibility threshold,
itILw
= , compares to ˆiL and iL . Note that itL is increasing in the eligibility threshold and
decreasing in individual wage.
In Figure 2, the red highlighted curves show the piecewise utility functions conditional on the
varying eligibility requirements. For iit tL L≤ , ( ,1)it itV L is attainable, however for iit tL L> , ( ,0)it itV L
is the utility function. If the eligibility requirements are so strict that itL is less than iL , the additional
utility that a person would get from participating in Medicaid is not high enough to offset the loss in
utility from reduced income (see Figure 2A). Thus, this individual will not participate in Medicaid
and will provide utility maximizing number of work hours in that period, ˆ
iL .
[Insert Figure 2.]
If the income requirements are less strict, so that the loss in utility due to a restriction in income
is smaller than the gain in utility due to Medicaid participation, individuals will limit the number of
hours worked so that they meet the eligibility requirements. As long as itL is still binding, i.e.
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ˆit iL L≤ , an individual will restrict the number of hours worked to itL and participate in Medicaid
(see Figure 2B). For ˆit iL L> , the income threshold is not binding so the individual will participate
in Medicaid without any distortion in labor supply (see Figure 2C).
While analyzing one period independently is helpful in understanding the Medicaid participation
decision, the results do not directly generalize to a multi-period setting when the eligibility thresholds
depend on the length of the Medicaid spell. In such settings, an individual may choose to suppress
the number of hours worked in the first period to take advantage of less restrictive continuing
participant thresholds in the subsequent time periods. Alternatively, an individual may participate in
Medicaid for only one period and then drop out if the threshold is reduced. Therefore, we need to
analyze the Medicaid participation and labor supply decisions in both periods collectively.
[Insert Figure 3.]
Consider the decision tree in Figure 3. In the first period, an individual decides whether to enroll
in Medicaid or not. If an individual does not participate in the first period, the same “new entrant”
threshold will continue to apply in the second period. Because of this, if an individual does not
enroll in the first period, the second period decision will also be the same.3 The utility a non-
participating individual will get in this case is 1 1 2 2( ,0) ( ,0)i i i iV L V Lδ+ . In this scenario, the individual
will choose the number of hours worked without being subject to an eligibility constraint and
3 It is assumed that all factors other than eligibility thresholds stay constant across periods including the health needs of an individual. Because of this simplification, we do not try to use the model to directly predict participation levels (which may depend on many changing factors as well as random shocks) but instead focus on its implications for comparisons across those in differing policy regimes.
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therefore will choose the unconstrained utility maximizing level ˆiL leading to a total utility of
1 2ˆ ˆ( ,0) ( ,0)i i i iV L V Lδ+ .
If an individual chooses to participate in the first period, the decision in the second period will
be whether to continue enrollment or drop out of the program. In this case, one cannot simply say
that an individual will continue enrollment, because the second period eligibility thresholds may
differ from the first period. The individual will base the continuation decision on the new
thresholds, comparing 2 2( ,1)i iV L to 2 2( ,0)i iV L . Given this decision in the second period, the total
utility of a two-period Medicaid participant will be 1 1 2 2( ,1) ( ,1)i i i iV L V Lδ+ and the utility of a
Medicaid drop-out will be 1 1 2 2( ,1) ( ,0)i i i iV L V Lδ+ . A potential enrollee will make a participation
decision at the beginning of the first period comparing the higher of these two values to the utility
of a non-participant and choosing the number of hours worked in each period accordingly. This
decision will depend on how ˆiL and iL relate to the eligibility thresholds in each period. Let inL
denote the maximum number of hours that an individual can work without exceeding the Medicaid
“new entrant” income limit and let icL denote the maximum number of hours that an individual can
work without exceeding the Medicaid “continuing participant” income limit at the individual’s wage
rate, iw .
There are twelve different cases generated by feasible combinations of these values, which are
numbered and shown in Table 2. To illustrate the establishment of the implications for each case,
consider case 1 as an example. Solving by backward induction, an individual will first consider what
the optimal decision would be in the second period conditional on Medicaid participation in the first
period. Since i icL L> , the utility function of this individual will be similar to the one given in Figure
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2. To be eligible for Medicaid participation in the second period, this individual will have to restrict
the number of hours worked to below iL . However, the value of Medicaid to this individual is not
high enough to compensate for the utility loss incurred due to the loss in income. Therefore,
someone who chose to be a first-period-participant would choose to drop out of the program in the
second period and work ˆiL number of hours getting a utility of 2
ˆ( ,0)i iV L in the second period. This
individual would also have to restrict the number of hours worked in the first period to below iL to
be eligible as a new entrant since i inL L> . Given this, the total utility if this individual chooses to
participate in the first period will be 1 2ˆ( ,1) ( ,0)i in i iV L V Lδ+ . If instead the individual chooses not to
participate in Medicaid in the first period, then the (total) utility will be 1 2ˆ ˆ( ,0) ( ,0)i i i iV L V Lδ+ . Note
that these two expressions differ only by the first part. Since i inL L> , we can conclude that
1( ,1)i inV L < 1ˆ( ,0)i iV L and therefore the latter expression is larger than the first. This individual will
choose not to participate in Medicaid in either period and will provide the unconstrained, utility
maximizing number of hours worked.
A similar analysis of the eleven other cases leads to the predictions given in Table 2.
[Insert Table 2.]
Before discussing the implications of these cases, we think it important to note that the model
leads to definite predictions about the behavior of a potential participant in all but two cases. In
cases 8 and 10, the predictions are ambiguous. Consider Case 8 in which ˆi ic i inL L L L> > > .
Conditional on Medicaid participation in period 1, the enrollee will continue participation in period
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2 and choose the number of work hours so that the eligibility requirements are met leading to a
utility of 1 2( ,1) ( ,1)i in i icV L V Lδ+ . Comparing this to the total utility of a non-participant is not
straight forward. 2 ( ,1)i icV L > 2ˆ( ,0)i iV L since ˆ
i ic iL L L> > but 1( ,1)i inV L < 2ˆ( ,0)i iV L since i inL L> .
Thus the decision of the individual will depend on the size of these differences. If the loss in the
utility due to reducing labor supply in period 1 is not as high as the (discounted) utility gained due to
Medicaid participation in period 2, the individual will choose to enroll in Medicaid in period 1 and
restrict the number of hours worked to inL . Note that, if the individual were making independent
decisions in each period, this individual would have chosen not to enroll in period 1 since i inL L> .
But the option of taking advantage of less restrictive continuing participant thresholds in period 2
leads the individual to provide a “sub-optimal” level of labor in period 1. If, on the other hand, the
loss of income in period 1 leads to a utility loss higher than the gain in period 2, the individual will
choose not to enroll in Medicaid at all. The analysis of Case 10 is similar. Both cases illustrate the
potential incentive to make a first-period choice that may otherwise appear suboptimal, with an
artificial restriction in income, in order to obtain coverage that can then be maintained at a higher
income level due to the higher income threshold for recipients.
The variation across the 12 cases in both Medicaid participation and labor market implications is
substantial. Cases 2 and 4 are of particular interest, as they reflect the conditions under which we
would expect abbreviated Medicaid durations, due to people leaving the program when the income
threshold is tightened. All other situations imply either no Medicaid or consistent Medicaid
participation. The variation in labor market implications is even broader, as whenever there is
Medicaid participation in any period there is potential for labor market distortion due to the need to
meet eligibility thresholds. Only those who are predicted to not participate in Medicaid at all (cases
1 and 7, and possibly some in 8 or 10) and those who face non-binding thresholds due to a
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combination of a generous-enough state and/or a low-enough wage (cases 6 and 12, and possibly
some in 8 or 10) avoid distorted labor market choices. Some distortions are temporary, while others
are predicted to be ongoing.
A key contribution of this model is that it moves beyond a simple focus on the effects of
state policy parameters to a more holistic model of behavior in which people also consider their own
wages in making choices about labor force and Medicaid participation even within each state. This
means that predicted behavioral responses to duration-dependent Medicaid thresholds are not likely
to appear in some sort of simple pattern across states depending on policy regimes; they are a
function of the demographics of individuals, which may differ systematically across states and may
have substantial diversity within states. For example, the model predicts that within the same state,
an individual with one particular wage may choose not to participate in Medicaid while someone
with a lower wage may (temporarily or consistently) participate, with or without distortions in his
labor market decisions. This corresponds to what we expect to be true. However, importantly, the
model does not take “income” as given, but only hourly wage, leaving the labor supply to be
determined endogenously. Moreover, the model opens us up to thinking empirically about where
we might look to find policy effects on the margin. For instance, if a state has a “continuing
recipient” threshold that is larger than the “new” threshold (i.e. individuals are somewhere in cases
7-12), this will only affect behavior if these thresholds are high enough to attract any participants at
all (i.e. it will only matter if not everyone is in case 7). Learning whether duration-dependent
Medicaid policy affects behavior on the margin is precisely our goal, and this model provides
guidance for our empirical analysis.
IV. Testing the Implications of the Model
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A. Data and Case Classification
We examine some implications of our model using data from the Survey of Income and
Program Participation, or SIPP. The SIPP is a repeated panel survey that follows approximately
50,000 households for 3-4 years at a time (at which time a new sample is drawn); we use the panels
beginning in 2004 and 2008. Individuals in the SIPP provide detailed demographic, labor market,
and program participation information. We want to examine Medicaid durations, so the longitudinal
feature of the data is of key importance. However, we also want to be able to consider a short
enough time period that the basic assumptions of our model (such as wages and preferences that are
fixed over time) are not egregiously violated. This results in a very careful sample construction
process.
The most important variables in our analysis are the Medicaid thresholds for new and continuing
Medicaid recipients, which are unfortunately not easily available for merging into the SIPP by state
or family size. There are two key problems with existing sources of parental Medicaid thresholds:
they typically do not report thresholds separately for new and continuing recipients, and they never
report thresholds for families of any size other than three people. We address each of these issues in
turn, assembling a unique compilation of threshold data for two points in time that contains
thresholds for both new and continuing recipients in various family sizes. First, we identify a few
years in which the distinction between new-applicant and continuing-recipient thresholds has been
clearly documented– namely, 1998, 2001, and 2009 (see Guyer and Mann, 1999; Malloy, et al., 2002;
and Cohen Ross et al., 2009). In other years, only the applicant threshold is reported. We compare
the 2009 report to those from years immediately before and find that we can reasonably establish the
new- and continuing-recipient thresholds for 2008. Previous work by Hamersma and Kim (2009)
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carefully compiled continuing-recipient thresholds from 1996 through 2007, and we use their data
combined with the Kaiser reports to establish new- and continuing-recipient thresholds for 2004.
Since all of these reports provide thresholds only for families of three people, and since many
thresholds are not tied to state poverty lines, it is not straightforward to establish them for other
family sizes. This leads to our second step: while the reports do not provide them, monthly state
Medicaid thresholds for families of multiple sizes have previously been carefully compiled from
1996 through 2007 (see Hamersma and Kim, 2009) for continuing recipients. Fortunately the report
containing the 2001 data on both new and continuing-recipient thresholds (Malloy, et al., 2002)
includes detailed formulas that can be used – alongside other sources -- to help establish the
applicant value as well in a few subsequent years with a fair degree of certainty.4 Similarly, we are
able to use the 2007 thresholds from Hamersma and Kim (2009) and formulas from Malloy, et al.
(2002), to reasonably establish the other family size thresholds in 2008. Ultimately, we are able to
utilize both the 2004 and 2008 SIPP panels, linking people in families of 2, 3, 4, 5, or 6 people to
both their new and continuing-recipient thresholds in the first year of each panel.
We use the first three waves (first year) of the 2004 SIPP panel and 2008 SIPP panel to form our
base sample, identifying people who did and did not begin a Medicaid spell during that year. There
are up to three interviews for each person, and we link these together (as well as later interviews if
they have an ongoing Medicaid spell) to create one observation per person.5 We then limit our
4 Our table of thresholds for January 2004 and 2008 is provided in Table 2; detailed notes on our establishment of these thresholds (including the new-applicant thresholds by family size) are available upon request. 5 The SIPP survey is done in a staggered fashion, with four rotation groups whose first-wave interviews are in (for 2004) February 2004, March 2004, April 2004, and May 2004, and (for 2008) September through December 2008. In each interview, people are asked about the previous 4 months. This means that those in rotation group 1 will be answering questions about October 2003 through January 2004 in the first wave, group 2 will be answering questions about November 2003 through February 2004, and so on. Rather than use calendar years 2004 and 2008 (which would require us to break up some waves) we use the first 3 waves of the survey for everyone.
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sample to single parents who work for an hourly wage, since the model applies to a situation in
which a person can limit income via a choice about work hours. Admittedly, we lose a large number
of observations by restricting to hourly workers; however, salaried workers are less likely than others
to be near the margin of Medicaid participation (i.e., their iL will be high relative to the income limit
inL and close to ˆiL ), so we believe the sample remains reasonable for identifying effects of Medicaid
policy.6 Finally, we limit our sample to parents with children in the home, as we are applying
parental Medicaid rules. Descriptive statistics for this sample – which contains 9,704 people with
SIPP observations in the 2004 or 2008 panels – are provided in Table 3.
[Insert Table 3]
Upon assembling the sample and linking each family to the relevant Medicaid thresholds, we
begin the process of connecting the model with the data by assigning each worker a most likely
“case” from among the 12 produced by the model. Our model is in terms of utility, but given the
infeasibility of estimating the utility of various combinations of income and Medicaid participation
for each individual, we consider each person’s parameters in terms of cash value of income and cash
value of Medicaid.7 Assigning cases involves three main steps. First, we establish estimates of inL
and icL for each person by dividing the relevant state-by-month-by-family size Medicaid thresholds
6 Notably, by this same restriction our sample also excludes non-workers, since they do not have a reported wage. Our model does not make predictions about labor market entry or exit (the extensive margin), but rather predicts behavioral changes on the intensive margin. 7 This is similar to the assumption Moffitt and Wolfe (1992) make in order to move from their theoretical model to their empirical study. However, they have a more complex approach to the measurement of Medicaid value than we do given the different focus of their paper.
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(in $) by the person’s hourly wage (in $) to get the estimated maximum number of hours of work
this person could engage in and maintain Medicaid eligibility.
Second, we estimate a person’s value of ˆiL by applying demographic-specific average hours of
work in our sample and assuming that this is the undistorted level of work preferred by hourly
workers in that particular demographic.8 Finally, we establish an estimate of iL . To do this, we first
assign state-specific cash values of Medicaid using state-level average per-capita Medicaid spending
on adults.9 We then assess the approximate number of hours of work (at their actual wage) would
generate equivalent value to Medicaid participation, and then subtract this number of hours from ˆiL
to arrive at an estimate of iL . (In other words, we use the cash value of Medicaid as an indirect
measurement for ∆ , and use it alongside wages to back out an estimate of iL ). Based on the
ordering of these four parameter estimates, we assign each person to a case.10
8 Based on patterns identified in Pencavel (1986), and Killingsworth and Heckman (1986), we assign each observation to a cell defined by gender, age (3 categories), and education level (4 categories), and impute the average hours of work for that cell as the generally preferred work hours for a person with those characteristics. 9 While individual-specific estimates would be ideal, there is not a straightforward way to assign this variation across individuals, so we use the 2003 state expenditure levels reported by CMS as part of the 2006 edition of the Data Compendium (as they do not report for 2004). For 2008, we use the 2008 edition of the Data Compendium. See http://www.cms.gov/Research-Statistics-Data-and-Systems/Statistics-Trends-and-Reports/DataCompendium/18_2006DataCompendium.html and http://www.cms.gov/Research-Statistics-Data-and-Systems/Statistics-Trends-and-Reports/DataCompendium/16_2008DataCompendium.html. 10 As an example, consider a woman who lives in Arkansas with two children and works for a wage of $8 per hour in 2004. The number of monthly hours she could work to qualify as a Medicaid applicant would be $255/$8 = 32. That is her inL . The number of monthly hours she could work
to qualify to stay on Medicaid after 12 months would be $638/$8 = 80. That is her icL . We assign
her ˆiL based on the average work hours for her gender, age category, and education category;
suppose this is 148 hours per month. The monthly average Medicaid expenditures in Arkansas per non-elderly adult are $105 per month; this represents about 13 hours of her $8/hour work. Thus we conclude that she gets the same utility from earnings based on the 148 “optimal” hours as she would
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We cannot – nor do we desire to – argue that all of these estimated parameter values are
precisely estimated. The main purpose in developing them, however, is to assign each person to his
most likely case. Given that the assignment to cases is based on an ordering, it is fairly forgiving
with respect to noise in the estimates; we will only misclassify when the parameters are far enough
off that they become wrongly ordered. In addition, there is some built-in protection against certain
types of misclassification; for instance, regardless of their estimates of ˆiL and iL , a person in a
state with a Medicaid threshold that grows with spell duration will never be classified outside of the
cases 7-12. Similarly, a person in a state with a Medicaid threshold that tightens with spell duration
will never be classified outside of cases 1-6. (In other words, the ordering between inL and icL is not
an estimate but a policy fact, and this will result in the elimination of some cases from the set of
possible (mis)classifications.)
The distribution of individuals across cases is shown in Table 4. Note that states without a
difference in their two thresholds are categorized into the top half of the table (specifically, cases 1,
3, and 6), so there is more density there; the table displays the sample sizes separately for states with
changing and unchanging thresholds. Given that the income limits are fixed at the state level, the
individuals with relatively higher wages are likely to have low inL and icL and be classified as either
Case 1 or Case 7. This is confirmed in the table, as the mean hourly wage is highest in those two
cases. These two cases, combined, contain people who are unambiguously predicted to decline
Medicaid participation, and so the fact that these two cases make up about 65 percent of the sample
is not unreasonable (and the fact that their Medicaid participation is lower than those in any other
cases is encouraging). Density in other cells is smaller, particularly when limiting to Medicaid
working the fewer 148 – 13 hours and getting Medicaid; iL is 135. Ordering the parameters leads us to assign this observation to Case 7.
18
recipients, though in many cases our hypothesis tests will combine categories to assess model
predictions (for instance, combining cases 2 and 4 when testing Medicaid duration predictions, and
combining cases 3, 8, and 9 when testing labor distortion predictions). It is clear that there is
variation in outcomes such as Medicaid participation and length of Medicaid spells across the cases;
our goal is to assess whether this variation can be systematically linked to the distinct incentives
faced by the workers in each case.
[Insert Table 4.]
We could also assign cases at the state level, using state averages of the estimated parameters
discussion above. This moves toward a cross-state (rather than cross-individual) analysis of policy
differences, and given the heterogeneity within each state we don’t pursue this approach beyond
some basic comparisons. However, since it may be of interest, we note that there are 14 states that
are classified outside of cases 1 and 7 (the only cases with no Medicaid participation or labor market
distortion), and thus there is some variation even at the state level (though much more variation
within states across cases). Details are provided in the Appendix. We could also utilize primarily
state variation by a policy analysis that simply regresses Medicaid participation, or labor market
outcomes, against a variety of covariates including the new and continuing Medicaid thresholds.
However, this fails to take into account the way these thresholds interact with both wages and the
value of Medicaid in ways that make some people, in some states, closer to or further from the
margin of participation. We instead use our model and our empirical, individual case classification
to test hypotheses regarding Medicaid participation and duration as well as labor market outcomes.
B. Medicaid Hypothesis Tests and Results
19
The first hypothesis we test is that people for whom Medicaid is not attractive enough relative to
unconstrained earnings (cases 1 and 7) will have lower Medicaid participation rates relative to others.
This is not a test related to understanding the duration-conditional nature of some states’ Medicaid
thresholds, but rather a basic test to be sure that our classification system makes sense – i.e. that the
combination of low wages and/or high Medicaid thresholds that puts people outside cases 1 and 7 is
correlated with higher Medicaid receipt. We find that 15.1 percent of people classified as “case 1 or
case 7” participated in Medicaid sometime in the first year of their panel, while 32.4 percent of those
in other cases participated (the combined weighted mean is 21.5 percent). The theory is therefore
supported in the raw comparison of (weighted) means.11 To test the hypothesis more carefully at
the individual level, we use a linear probability model and include demographic controls (gender, age
and age-squared, race/ethnicity, marital status, and education level), an indicator for the panel year
as well as an indicator for being in case 1 or 7. Results are shown in Table 5.
[Insert Table 5]
The analysis provides strong evidence that the prediction of the model – that case 1 and case 7
are less likely to participate in Medicaid than others – is supported, with the assignment of case 1 or
case 7 indicating a 12-16 percentage point reduction in the probability of participating in Medicaid.
This is a substantial estimate given the already low participation rate in this population. The other
coefficients are of the expected signs. At least in this simple model, we see the case classification
generating the theoretically predicted results.
11 Our simple model predicts, of course, no participation at all among case 1 or 7 and a very high level of participation among other groups. However, our model only includes basic wage and (imputed) value of Medicaid as the factors in participation; we are interested in whether people’s behavior follows the relative patterns predicted in our model as it relates to those factors, rather than trying to develop a full model of Medicaid participation behavior.
20
The second hypothesis that we test is that people faced with a large enough duration-induced
reduction in the Medicaid threshold to generate an incentive to participate but then drop out (cases
2 and 4) should have shorter Medicaid durations than those in other groups. In this case, we leave
those in cases 1 and 7 out of the sample, since they are not predicted to participate in Medicaid at all
(though we try including them as an alternative specification). We then limit the sample to those
who participated in Medicaid at some point in the first year of their panel and use the duration of
that spell (in months) as our dependent variable. Because some workers may already be in a
Medicaid spell when the panel begins (or may be continuing on Medicaid when it ends, though this
is rare for spells beginning in the first year of the panel), there is a censoring issue in these data. We
run our analysis both on the full sample (knowing that spell lengths are biased downward on
average), and the sample of fresh, complete spells (knowing that measurement is more accurate but
the sample is restricted).
A basic comparison of (weighted) means indicates average spell length in the full sample among
those in cases 2 and 4 is 8.2 months while average spell length for the comparison group of all other
cases (excluding 1 and 7) is 9.8 months; for fresh, completed spells these means are 7.0 months and
7.3 months Using an otherwise similar specification to that used above, but with an indicator for
cases 2 or 4, we generate the regression estimates shown in Table 6:
[Insert Table 6]
While the much smaller sample here (only those with Medicaid spells, and outside of cases 1 and
7) reduces the power of the estimation relative to the first hypothesis test, we do find evidence that
the raw difference of 1.6 months is similar to the coefficient of interest (-1.715), which is estimated
to be different from zero with 90 percent confidence. In other words, being classified as likely to
21
take Medicaid but then dropping out is associated with shorter spell length by nearly 2 months, over
20 percent of baseline. This offers additional evidence that the incentives captured in the model
may truly affect behavior. In the second column, we add to the comparison group those Medicaid
spells among people classified in cases 1 and 7 (who are predicted not to participate at all).
Although their participation rate is low, these categories are the largest numerically so this
approximately doubles the sample size (though we still have the same small number of 79 workers in
cases 2 or 4). If we think that Medicaid participants in cases 1 and 7 might be likely to have shorter
spells (given that they weren’t predicted to participate at all), we might expect the difference between
cases 2 or 4 and the new, larger comparison group to get smaller. Indeed, the gap between groups
falls by about one month, and with almost no change in the standard error, this estimate is not
statistically significant. Finally, we run the same two sets of estimates using only people in states with
changing Medicaid thresholds (which includes the whole treatment group, since cases 2 and 4 only
arise in states with decreasing thresholds), and find a very similar pattern, with a statistically
significant effect estimated of about 2 months shorter durations for those outside cases 1 and 7
despite the much smaller sample size.
Panel B of Table 6 suggests that estimates fall in absolute value, and standard errors grow, when
we utilize only the fresh spells in the data. While using these spells eliminates the censoring problem
itself, it introduces concerns that we may be systematically dropping longer spells, and as such we
compress the level of spell-length variation in our sample (indeed, the baseline mean gap noted
earlier was only 0.3 months as compared to 1.6 months). This limited variation, combined with
smaller samples and a limited number of observations in cases 2 or 4 (there are, for example, only 33
of them in the sample used in the first column of Panel B), might partially explain the statistically
insignificant results.
22
The third hypothesis we test is that people who can participate in Medicaid without distorting
their ideal hours of work (cases 6 and 12) should have the longest Medicaid spells. This pushes the
model a bit (since the model is only two periods), but attempts to pull together the Medicaid
participation incentives and the countervailing incentives to keep earnings low; those in cases 6 and
12 are not bound by the earnings limits so do not experience what one might consider a
“compromise” in terms of labor decisions, and this may reduce pressure to leave Medicaid in the
long run. The weighted average spell length for those in cases 6 or 12 is 10.1 months compared to
9.0 months for those in other categories (not including 1 and 7, which again are left out for the
initial estimates), so the raw difference is in the expected direction. However, it makes a significant
difference if we include the spells of people in cases 1 and 7 among the comparison group; the
difference becomes 10.1 months vs. 8.4 months. Table 7 displays the individual regression results.
[Insert Table 7]
The results in Table 7 provide consistent evidence of longer spells for those who are not
predicted to experience labor distortions, with all but one of the 8 estimates obtaining statistical
significance at conventional levels. The estimates vary from one month of additional receipt to over
3 months of additional receipt. The pattern of magnitudes seems to follow some of the logic of the
model: those in cases 1 or 7 who do participate in Medicaid (against the prediction of the model)
have shorter spell durations, making the difference between the treatment (case 6 or 12) and
comparison groups larger. Results with and without censored observations are quite similar.12
12 Results are also quite similar if we restrict the sample to women, who make up over 85% of this participating subsample; this is also true for women-only estimates of the parameters in Table 6.
23
These results provide evidence of an influence of Medicaid program incentives on Medicaid
duration behavior for those whose labor supply is theoretically uncompromised.
C. Employment Hypothesis Tests and Results
The richest set of hypotheses to arise from the model relate to predicted hours of work, and in
particular predicted changes in hours of work over time when states treat Medicaid recipients
differently from applicants. We provide a brief analysis here with our current data, knowing that
with a larger data set (in particular, a data set with more Medicaid recipients), one could more
completely examine whether patterns of behavior conform to the incentives of the Medicaid
program as reflected in the model.
One can see from Table 3 that the model provides predictions about relative levels of hours of
work across cases. We provide two simple analyses here. First, consider the initial period of the
model. In this period, we see some cases predicted to be bound by the Medicaid threshold in terms
of their work hours (specifically, those in cases 2, 3, some 8, 9, some 10, and 11) while all other cases
are unconstrained. Table 8 provides the estimated effects of being “constrained” on weekly hours
worked, first defined broadly and then defined using additional features of the model.
[Insert Table 8]
The first column of Table 8 suggests 2 fewer hours of work per week for those predicted to be
constrained by the Medicaid program, and this estimate is statistically significant at the 99 percent
level. One might think of this as an “intent to treat” effect, in the sense that the predicted labor
24
reduction should only really appear among those who are indeed Medicaid participants. In other
words, some people predicted to be constrained by the model do not in fact choose to participate in
Medicaid, so their presence may dilute the estimates.13
The second column of Table 7 selects a sample – based on the model – in which we would be
more likely to find an undiluted effect of Medicaid participation itself on labor supply. We create 3
categories based on the model: those predicted to be “nonparticipants”, “unconstrained
participants” (i.e. those who participate in Medicaid but have unconstrained labor supply compared
to their utility maximizing level), and “constrained participants” (i.e. those who participate in
Medicaid and are predicted to limit their hours of work to do so). We assign people into these three
categories by case (details are provided in the table note) and leave out those whose behavior is not
aligned with the model (for example, people who chose not to participate in Medicaid despite being
in a case that is predicted to participate). The prediction is that constrained participants will have
fewer work hours than either unconstrained participants or nonparticipants (who are both predicted
to have work hours unaffected by Medicaid). Our results support lower work hours among the
constrained relative to unconstrained nonparticipants, with a difference of over 4 hours per week.
However, the unconstrained participants seem to act similarly to constrained participants as well,
indicating that they may be restricting income unnecessarily (perhaps not being sure where the
threshold is) or that we may have failed to assign them to the correct case. Thus we find that among
Medicaid recipients, hours of work per week tends to be lower than that of non-recipients regardless
of whether we predict their hours of work to be affected ex ante.
13 One might notice that the signs on the education variables indicate lower hours as education increases. We believe this is likely a result of the selection of our sample as workers who are paid an hourly wage; highly educated workers making an hourly wage may be disproportionately part-time workers (who are, for instance, in school or secondary earners).
25
The second comparison we make between work hours across cases is related to second-
period labor choices. In the context of our data, this is referring to work hours one year later than
the initial observation in the sample (or the initial observation on Medicaid, for those who
participate in it).14 The important contribution of the model here is that the assignment to cases is
not the same in the second period as the first. For example, some individuals who would have been
constrained in the initial period will be considered unconstrained in the second period since the
model predicts they will drop out of Medicaid. Therefore in the second period we define a new
“constrained” variable, defined as being in cases 3, 5, 8, or 9 (though some in 8 may be
unconstrained). Table 9 shows little evidence that those predicted to be constrained by the model
have lower labor supply, with a statistically insignificant estimate of -.940.
[Insert Table 9]
Similarly to Table 8, we also estimated a specification that restricted the sample to cases that
were aligned with the Medicaid predictions of the model. In this case there are four distinct groups
since we must condition on Medicaid choices in both the initial and later period (see table note for
details). The second column of Table 9 shows that, as predicted, those who participated only in the
first period do not show any evidence of labor market constraints in the second period. In contrast,
anyone who is a Medicaid recipient in the second period seems to act constrained, just as in Table 8.
Again, we think this brings up an interesting question (which we leave to future research) about the
14 To be clear, if someone is never on Medicaid we utilize the hours of work variable three waves (one year) after our first observation of them (where the first observation must occur in the first three waves in order for them to be included in the sample at all). If someone does participate in Medicaid in the initial three waves, we look at the hours of work variable three waves after the first Medicaid-participating wave. In both cases, then, the “three waves later” will occur in wave 4, 5, or 6.
26
behavior of people who are predicted to participate in Medicaid without any compromise in terms
of labor, as they still appear to restrict hours worked.15
The final employment hypothesis we will examine is the predicted change in labor supply
over time. Since most of the covariates in the levels models in Tables 8 and 9 would be eliminated
by looking at first differences, and since sample sizes are small, we simply take a cursory look at how
the basic predictions of the model bear out in our descriptive statistics. We classify each observation
according to whether labor supply is predicted to increase, decrease, or stay the same over time
(details of assignment are in the table note). We then provide average changes in hours for each
group in Table 10.
[Insert Table 10]
We draw two main conclusions from this table. First, none of the estimated effects are
statistically distinguishable from zero. This may be because we simply cannot precisely measure
changes in hours of work for this sample. Another possibility is that people do not make fine
adjustments on the intensive margin of labor supply even when it would be advantageous (see
Meyer, 2002 and Matsudaira and Blank, 2013). There is significant evidence from other programs
that hours of work do not move as systematically with program rules as we might expect: Saez
(2012) finds a failure of taxpayers to bunch at kink points, Hamersma (2011) shows the same with
the Work Opportunity Tax Credit, and Hamersma (2013) suggests similarly weak evidence of
bunching for Medicaid earnings limits. Our second conclusion from Table 10 is that there are very
few people in the sample facing the perverse incentive that would result in a predicted reduction in
15 Recall that they are predicted to be able to work their optimal hours either because their wages are low, the Medicaid threshold is high, or both.
27
hours worked. These are people in case 5: they face tightening Medicaid thresholds over time but
are not deterred from participating, as they are able receive Medicaid while working at their optimal
level initially and then reducing hours of work in order to maintain coverage. Since such a distortion
would be of policy concern, our evidence here that few people face that incentive is itself an
interesting finding.
V. Conclusions and Next Steps
This paper presents a basic model of behavioral responses to Medicaid income thresholds that
change based on Medicaid spell duration. States have the option of setting thresholds for
continuing recipients that are higher than, lower than, or the same as those for new applicants, and
these have important implications for Medicaid participation and labor market behavior. Our model
suggests that along with the perverse incentives created by any program with an income threshold,
there are groups in the population who may face particularly perverse incentives, such as the incentive
to temporarily reduce income to obtain Medicaid and then raise income again (which can occur in
states with higher recipient than applicant thresholds). The model ultimately defines several groups
whose Medicaid participation and hours of work are expected to be influenced differently depending
on their state’s policies as well as their own wages.
In our examination of some main predictions of the model, we find evidence that the cases
defined by the model are predictive of behavior. We find strong evidence that groups predicted to
participate in Medicaid coverage have much higher participation rates than those predicted not to
participate. Patterns in both Medicaid participation and spell length are consistent with some of the
perverse incentives illuminated by the model. We also find some evidence that the length of
Medicaid spells is responsive to the incentives created by changing thresholds that either push
28
people toward nonparticipation or provide opportunities for extended participation. Our estimates
regarding work hours provide clear evidence that individuals predicted to participate in Medicaid do
in fact have fewer weekly hours of work than those predicted to be unconstrained, though there are
some remaining questions about how to understand the behavior of individuals who are predicted to
both participate in Medicaid and also remain unconstrained in their work hours (because of low
wages and/or high Medicaid thresholds). The dynamic predictions on labor supply are not easily
tested using our data, leaving this issue open for further investigation.
Overall, we believe that the incentives described by our model are relevant to the policy
debates current taking place over implementation of PPACA. Moreover, our empirical findings
suggest these may be of real practical consequence. Further work on understanding the groups
facing the most perverse incentives – for which samples were small in our data – would help states
to predict possible changes in both Medicaid participation and the labor market in light of proposed
policy modifications.
29
References
Aizer, Anna and Jeffrey Grogger. 2003. “Parental Medicaid Expansions and Health Insurance Coverage.” NBER Working Paper 9907.
Busch, Susan H. and Noelia Duchovny. 2005. “Family Coverage Expansions: Impact on Insurance Coverage and Health Care Utilization of Parents.” Journal of Health Economics, 24, 876–890.
Cohen Ross, Donna, and Marian Jarlenski, Samantha Artiga, and Caryn Marks. “A Foundation for Health Reform: Findings of a 50 State Survey of Eligibility Rules,Enrollment and Renewal Procedures, and Cost-Sharing Practices in Medicaid and CHIP for Children and Parents During 2009” The Henry J. Kaiser Family Foundation, December 2009.
Guyer, Jocelyn and Cindy Mann. “Employed But Not Insured: A State-by-State Analysis of the Number of Low-Income Working Parents Who Lack Health Insurance” Center on Budget and Policy Priorities, February 9, 1999.
Ham, John C. and Lara D. Shore-Sheppard. “Did Expanding Medicaid Affect Welfare Participation?” Industrial and Labor Relations Review 58.3 (2005): 452-470.
Hamersma, Sarah and Matthew Kim. 2009. “The Effect of Parental Medicaid Expansions on Job Mobility.” Journal of Health Economics, 28.4 (2009): 761–770.
Hamersma, Sarah. “Why Don’t Eligible Firms Claim Hiring Subsidies? The Role of Job Duration.” Economic Inquiry 49.3 (2011):916-934.
Hamersma, Sarah. “The Effects of Medicaid Earnings Limits on Earnings Growth among Poor Workers.” The B.E. Journal of Economic Analysis & Policy, 13.2 (2013): 887-919.
Hamersma, Sarah and Matthew H. Kim. “Participation and Crowd Out: Assessing the Effects of Parental Medicaid Expansions.” Journal of Health Economics 32.1 (2013): 160-171.
Killingsworth, Mark R. and James J. Heckman. “Female labor supply: A survey”. In: Orley C. Ashenfelter and Richard Layard, Editor(s), Handbook of Labor Economics, Elsevier, 1986, Volume 1, Chapter 2, Pages 103-204.
Maloy, Kathleen A. and Kyle Anne Kenney, Julie Darnell, and Soeurette Cyprien. “Can Medicaid Work for Low-Income Working Families?” The Henry J. Kaiser Family Foundation, April 2002.
Matsudaira, Jordan D. and Rebecca M. Blank. “The Impact of Earnings Disregards on the Behavior of Low Income Families” forthcoming, Journal of Policy Analysis and Management.
30
Meyer, Bruce D. “Labor Supply at the Extensive and Intensive Margins: The EITC, Welfare, and Hours Worked.” AEA Papers and Proceedings (May, 2002)
Moffitt, Robert and Barbara Wolfe. “The Effects of Medicaid on Welfare Dependency and Work." Review of Economics and Statistics 76.4 (1992): 615-626.
Pencavel John. “Labor supply of men: A survey”. In: Orley C. Ashenfelter and Richard Layard, Editor(s), Handbook of Labor Economics, Elsevier, 1986, Volume 1, Chapter 1, Pages 3-102.
Saez, Emmanuel. “Do Taxpayers Bunch at Kink Points?” American Economic Journal: Economic
Policy 2(3), 2010: 180-212. Yelowitz, Aaron S. “The Medicaid Notch, Labor Supply, and Welfare Participation: Evidence
from Eligibility Expansions.” The Quarterly Journal of Economics 110.4 (1995): 909-39.
31
Figure 1: Utility as a function of labor supply, with and without Medicaid
32
Figure 2. Utility maximization with varying thresholds
Notes: The red highlighted curve shows the piecewise utility function conditional on the eligibility requirement. The blue circle shows the
utility-maximizing choice. Panel (A) shows the utility maximizing choice when the Medicaid threshold is very strict ( itL < iL ), panel (B)
shows the utility maximizing choice when the Medicaid threshold is somewhat strict ( iL < itL < ˆiL ), and panel (C) shows the utility
maximizing choice when the Medicaid threshold is not strict ( ˆiL < itL ).
33
Figure 3: Two-period decision tree
1st period
2nd
period
Drop out Continue
Sign up Don’t sign up
Don’t sign up
1 1 2 2( ,1) ( ,1)i i i iV L V Lδ+ 1 1 2 2( ,1) ( ,0)i i i iV L V Lδ+
1 1 2 2( ,0) ( ,0)i i i iV L V Lδ+
34
Table 1: Monthly Income Thresholds for Applicants and Continuing Medicaid Recipients
2004 2008
Applicant Recipient Applicant Recipient
Alabama 254 254 366 254
Alaska 1317 1991 1444 2181
Arizona 1362 1362 2862 1521
Arkansas 255 638 255 638
California 1362 2022 1521 2292
Colorado 511 511 949 949
Connecticut 1998 1998 2737 2737
D.C. 2612 2612 1521 1521
Delaware 1551 1362 2962 2862
Florida 806 806 806 806
Georgia 756 514 756 514
Hawaii 1463 1463 1646 1646
Idaho 407 407 595 407
Illinois 1235 1235 2737 2737
Indiana 378 378 378 378
Iowa 1065 1065 1268 1268
Kansas 493 762 493 762
Kentucky 909 616 909 616
Louisiana 280 280 280 280
Maine 1998 1998 2952 2952
Maryland 523 523 523 523
Massachusetts 1691 1691 1903 1903
Michigan 774 774 871 871
Minnesota 1272 1272 1431 1431
Mississippi 458 458 458 458
Missouri 979 979 556 382
Montana 858 858 858 858
35
Nebraska 764 764 851 851
Nevada 1728 438 1341 473
New Hampshire 781 1250 781 1250
New Jersey 533 533 1904 1904
New Mexico 903 903 903 903
New York 1959 1959 2146 2146
North Carolina 750 750 750 750
North Dakota 1395 930 905 905
Ohio 1272 1272 1288 1288
Oklahoma 591 591 711 711
Oregon 920 920 1431 942
Pennsylvania 806 806 842 806
Rhode Island 1998 1998 2737 2236
South Carolina 1270 735 1431 815
South Dakota 796 796 796 796
Tennessee 1030 1030 1143 1143
Texas 402 308 402 308
Utah 673 673 673 673
Vermont 1002 1002 2737 1003
Virginia 391 391 438 438
Washington 1092 1092 1092 1092
West Virginia 500 343 499 343
Wisconsin 1908 1908 2737 2146
Wyoming 790 790 790 790
Note: This table reflect policy rules as of January 2004 and January 2008, gathered from Kaiser Foundation reports checked against other sources. These are the income thresholds for a family of 3, accounting for earnings disregards. The “continuing recipient” threshold applies to a recipient at the 12-month mark. Some states have changing thresholds in between the 1st and 11th months as well. Shaded states are those whose thresholds are different for applicants and 12-month recipients. A detailed description of our establishment of the income thresholds is available upon request.
36
Table 2: Summary of Model Implications
Case Definition M1 M2 Medicaid pattern
L
L1
L
L2 Labor pattern
Decreasing
or equal
threshold
𝐿𝐿𝑛𝑛�
≥
𝐿𝐿𝑐𝑐�
1 ˆi i in icL L L L> > ≥ 0 0 No M 𝐿𝐿� = 𝐿𝐿� No distortion
2 ˆi in i icL L L L> > > 1 0 M drop out 𝐿𝐿𝑛𝑛� < 𝐿𝐿� Initial distortion
3 ˆi in ic iL L L L> ≥ > 1 1 M consistent 𝐿𝐿𝑛𝑛� ≥ 𝐿𝐿𝑐𝑐�
Consistent distortion
4 ˆin i i icL L L L> > > 1 0 M drop out 𝐿𝐿� = 𝐿𝐿� No distortion
5 ˆin i ic iL L L L> > > 1 1 M consistent 𝐿𝐿� > 𝐿𝐿𝑐𝑐� Later distortion
6 ˆin ic i iL L L L≥ > > 1 1 M consistent 𝐿𝐿� = 𝐿𝐿� No distortion
Increasing
threshold
𝐿𝐿𝑛𝑛�
<
𝐿𝐿𝑐𝑐�
7 ˆi i ic inL L L L> > > 0 0 No M 𝐿𝐿� = 𝐿𝐿� No distortion
8 ˆi ic i inL L L L> > >
1 1 M consistent 𝐿𝐿𝑛𝑛� < 𝐿𝐿𝑐𝑐� Consistent distortion
0 0 No M 𝐿𝐿� = 𝐿𝐿� No distortion
9 ˆi ic in iL L L L> > > 1 1 M consistent 𝐿𝐿𝑛𝑛� < 𝐿𝐿𝑐𝑐�
Consistent distortion
10 ˆic i i inL L L L> > >
1 1 M consistent 𝐿𝐿𝑛𝑛� < 𝐿𝐿� Initial distortion
0 0 No M 𝐿𝐿� = 𝐿𝐿� No distortion
11 ˆic i in iL L L L> > > 1 1 M consistent 𝐿𝐿𝑛𝑛� < 𝐿𝐿� Initial distortion
12 ˆic in i iL L L L> > > 1 1 M consistent 𝐿𝐿� = 𝐿𝐿� No distortion
37
Table 3: Descriptive Statistics
VARIABLES Female .627
(.484) Black .217
(.412) Hispanic .233
(.423) Other Race .025
(.156) High School .321
(.467) Some College .459
(.498) College Degree .065
(.246) Age 30.96
(10.48) Number of kids (18 and under) 1.63
(.869) Any Medicaid in 1st year .215
(.411) Length of Medicaid Spell* 9.01
(8.63) Hourly Wage 11.25
(4.97) Hours worked per week 34.74
(10.82)
Notes: N = 9,704. Sample includes one observation for each person who appears in the first 3 waves of their SIPP panel who is paid an hourly wage, and is a parent of a child in the home. The mean “Length of Medicaid Spell” is in months, and calculated only for those who have a spell beginning in the first 3 waves. Standard deviations are in parentheses. Omitted categories are male, white, and high school dropout. All means are weighted.
38
Table 4: Distribution of SIPP Data across Cases
Full Sample Medicaid Only Sample
Case Definition N
Mean Hourly Wage
Fraction with
Medicaid in 1st year
N Mean
Hourly Wage
Mean Length of Medicaid
spell
𝐿𝐿𝑛𝑛���
≥ 𝐿𝐿𝑐𝑐���
1 ˆ
i i in icL L L L> > = 4,301 12.47 .171 773 10.39 8.31
ˆi i in icL L L L> > >
1,519 11.72 .116 196 9.66 7.20
2 ˆi in i icL L L L> > > 147 8.33 .235 32 8.18 9.20
3 ˆ
i in ic iL L L L> = > 613 8.88 .326 204 8.67 10.11
ˆi in ic iL L L L> > >
25 7.50 .256 8 8.45 4.98
4 ˆin i i icL L L L> > > 149 9.72 .317 47 9.66 7.46
5 ˆin i ic iL L L L> > > 63 8.66 .299 20 9.59 9.73
6 ˆ
in ic i iL L L L= > > 1,382 8.89 .361 521 8.76 9.77
ˆin ic i iL L L L> > >
188 8.82 .459 89 8.79 11.96
𝐿𝐿𝑛𝑛���
< 𝐿𝐿𝑐𝑐���
7 ˆi i ic inL L L L> > > 442 16.53 .112 57 14.07 9.37
8 ˆi ic i inL L L L> > > 40 10.62 .207 11 10.67 9.59
9 ˆi ic in iL L L L> > > 0 N/A N/A 0 N/A N/A
10 ˆic i i inL L L L> > > 293 10.64 .226 74 10.82 7.51
11 ˆic i in iL L L L> > > 75 8.77 .247 21 9.81 8.62
12 ˆic in i iL L L L> > > 467 8.25 .311 163 8.23 10.29
Overall 9,704 11.26 .215 2,216 9.58 9.01
Notes: Full sample includes one observation for each person who appears in the first 3 waves of their SIPP panel who is paid an hourly wage, and is a parent of a child in the home. The sample of Medicaid recipients includes anyone in the full sample who reports any Medicaid receipt in the first 3 waves of the panel. In cases 1, 3, and 6, there are people in states with unchanging thresholds (top number) as well as people in states with changing thresholds (bottom number), and while most predictions are the same regardless, this is at times an important distinction in our later analysis. All means are weighted.
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Table 5: Testing Hypothesis of Lower Medicaid Participation for Predicted Non-participants
VARIABLES (1) (2) (3) (4) Predicted non-participant -0.157*** -0.127*** -0.161*** -0.122*** (-15.07) (-10.24) (-10.32) (-6.407) panel 0.0291*** 0.0186* 0.0638*** 0.0275 (3.226) (1.808) (4.461) (1.644) female 0.181*** 0.182*** 0.146*** 0.150*** (21.02) (21.34) (10.84) (11.19) age 0.0204*** 0.0187*** 0.0101** 0.00857** (7.454) (6.806) (2.384) (2.014) agesq -0.000300*** -0.000281*** -0.000138** -0.000122** (-7.904) (-7.410) (-2.359) (-2.088) kidslt19 0.0335*** 0.0345*** 0.0418*** 0.0417*** (6.247) (6.508) (4.839) (4.821) black 0.102*** 0.121*** 0.0956*** 0.122*** (8.860) (10.11) (4.952) (6.029) hispanic 0.000361 0.0243* 0.0217 0.0325* (0.0309) (1.904) (1.336) (1.825) otherrace -0.0342 -0.00579 0.00929 0.0174 (-1.543) (-0.246) (0.297) (0.540) highschool -0.0464*** -0.0488*** -0.0336 -0.0402* (-3.279) (-3.507) (-1.568) (-1.879) somecollege -0.0887*** -0.0909*** -0.0504** -0.0552*** (-6.392) (-6.653) (-2.355) (-2.578) college -0.160*** -0.165*** -0.117*** -0.127*** (-8.837) (-9.195) (-4.089) (-4.487) unemp 0.00484 -0.0113 -0.000583 -0.0209 (1.021) (-1.187) (-0.0681) (-1.472) Constant -0.161*** 0.461*** -0.0620 0.654*** (-3.169) (3.123) (-0.710) (3.771)
Include State Fixed Effects? N Y N Y
Include Non-Changing States? Y Y N N Observations 9,704 9,704 3,408 3,408 R-squared 0.130 0.155 0.120 0.150 Notes: Dependent variable is “any Medicaid spell beginning in first year of survey.” Omitted categories are male, white, and high school dropout. Sample contains only those with a Medicaid spell beginning in the first year of the 2004 and 2008 surveys. If “Non-Changing States” are not included, the sample contains only those in state-panels with changing Medicaid thresholds. Omitted categories are male, white, and high school dropout. * = significant at 90%, ** = significant at 95%, *** = significant at 99%.
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Table 6: Testing Hypothesis of Shorter Spells among those with Incentive to Drop Out
Panel A VARIABLES (1) (2) (3) (4) predicted Medicaid dropout -1.715* -0.723 -2.075* -0.723 (0.968) (0.924) (1.184) (1.004) Demographics? Y Y Y Y Include Non-Changing States?
Y Y N N
Include Cases 1 and 7? N Y N Y Observations 1,190 2,216 465 718 R-squared 0.063 0.052 0.085 0.083
Panel B VARIABLES (1) (2) (3) (4) predicted Medicaid dropout -0.698 -0.0489 -1.653 -0.110 (1.189) (1.100) (1.632) (1.321) Demographics? Y Y Y Y Include Non-Changing States?
Y Y N N
Include Cases 1 and 7? N Y N Y Observations 503 1,052 194 346 R-squared 0.092 0.067 0.180 0.146
Note: Dependent variable is “Length of Medicaid spell beginning in first year of survey.” The sample in Panel A contains all those with a Medicaid spell appearing in the first year of the survey, including spells in progress upon entry into the survey, as well as those that extend beyond the end date of the survey. The sample in Panel B is restricted to only those who begin their Medicaid spell within the first year of the survey (no left-censored) and end their Medicaid spell within the survey period (no right-censored). If the “Non-Changing States” are not included, the sample contains only those in state-panels with changing Medicaid thresholds. Omitted categories are male, white, and high school dropout. All specifications include quarterly dummy variables indicating the calendar quarter of the fourth month of the wave. * = significant at 90%, ** = significant at 95%, *** = significant at 99%. Full regression results are available from the authors upon request.
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Table 7: Testing Hypothesis of Longest Spells among those with No Incentives for Labor Distortion
Panel A VARIABLES (1) (2) (3) (4) predicted long- 1.149* 1.909*** 3.417*** 3.521*** term recipient (0.604) (0.448) (0.926) (0.846) Demographics? Y Y Y Y Include Non-Changing States?
Y Y N N
Include Cases 1 and 7?
N Y N Y
Observations 1,190 2,216 465 718 R-squared 0.064 0.061 0.107 0.110
Panel B
VARIABLES (1) (2) (3) (4) predicted long- 0.870 1.035** 2.651** 2.833*** term recipient (0.608) (0.468) (1.101) (0.934) Demographics? Y Y Y Y Include Non-Changing States?
Y Y N N
Include Cases 1 and 7?
N Y N Y
Observations 503 1,052 194 346 R-squared 0.095 0.072 0.200 0.173
Note: Dependent variable is “Length of Medicaid spell beginning in first year of survey.” The sample in Panel A contains all those with a Medicaid spell appearing in the first year of the survey, including spells in progress upon entry into the survey, as well as those that extend beyond the end date of the survey. The sample in Panel B is restricted to only those who begin their Medicaid spell within the first year of the survey (no left-censored) and end their Medicaid spell within the survey period (no right-censored). If the “Non-Changing States” are not included, the sample contains only those in state-panels with changing Medicaid thresholds. Omitted categories are male, white, and high school dropout. All specifications include quarterly dummy variables indicating the calendar quarter of the fourth month of the wave. * = significant at 90%, ** = significant at 95%, *** = significant at 99%.
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Table 8: Testing Hypothesis of Constrained Work Hours in First Period
(1) (2) VARIABLES those with an obs in
first 3 waves those with an obs in first 3 waves &
with Medicaid aligned with model constrained -2.014*** (0.353) unconstrained -4.024*** participant (0.446) constrained -4.788*** participant (0.671) female -2.775*** -2.161*** (0.250) (0.292) age 1.547*** 1.330*** (0.0689) (0.0804) agesq -0.0182*** -0.0157*** (0.000958) (0.00109) kidslt19 -0.295** 0.0468 (0.129) (0.157) black 1.073*** 0.422 (0.277) (0.316) hispanic 0.952*** 0.238 (0.300) (0.350) otherrace -0.883 -1.066 (0.682) (0.828) highschool 0.198 0.138 (0.337) (0.391) somecollege -1.908*** -1.703*** (0.336) (0.391) college -1.268** -1.806*** (0.548) (0.615) unemp -0.258** -0.0237 (0.126) (0.144) panel -1.102*** -0.743*** (0.239) (0.277) Constant 11.15*** 14.43*** (1.355) (1.595) Observations 9,704 6,628 R-squared 0.129 0.126
Notes: In the first column, we simply assign each person into “constrained” or “unconstrained” (the omitted category) based on their cases; “constrained” are those in cases 2, 3, 8, 9, 10, and 11 (though some in cases 8 and 10 may be unconstrained). In the second column, we use only those whose Medicaid participation is aligned with the model (since Medicaid choices should be operative in labor choices). We assign people into 3 categories: “unconstrained nonparticipants” who are not on Medicaid and fall into cases 1, 7, 8, or 10; “unconstrained participants” who are on Medicaid and fall into cases 4, 5, 6, or 12, and “constrained participants” who are on Medicaid and in cases 2, 3, 8, 9, 10, or 11.
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Table 9: Testing Hypothesis of Constrained Work Hours in Second Period
(1) (2) VARIABLES those with an obs in
first 3 waves those with an obs in first 3
waves & with Medicaid aligned with model
constrained -0.940 (0.647) unconstrained 0.370 1st-period participant (2.102) unconstrained -4.666*** both-period participant (0.754) constrained -5.599*** both-period participant (1.334) Demographics? Y Y Observations 4,539 2,820 R-squared 0.100 0.108
Notes: In the first column, we simply assign each person into “constrained” or “unconstrained” (the omitted category) based on their cases; “constrained” are those with predicted cases 3, 5, 8, and 9 (though some in case 8 may be unconstrained). In the second column, we use only the sample of those whose two-period Medicaid participation is aligned with the model’s prediction for their case (since Medicaid choices should be operative in labor choices). We assign people into four categories: the “non participants” who are not on Medicaid in either period and fall into cases 1, 7, 8, or 10, the “unconstrained first-period participants” who are on Medicaid only in the first period and fall into cases 2 or 4 (in which people receive Medicaid but still work their optimal hours), the unconstrained both-period participants” who are on Medicaid in both periods and fall into cases 6, 10, 11, and 12 (in which people again receive Medicaid but still work their optimal hours), and the “constrained both-period participants” who are on Medicaid in both periods and fall into cases 3, 5, 8, and 9.
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Table 10: Patterns in Hours of Work
Full Sample Predicted change: N
Change in Hours
Positive 221 -.174 (.793)
None 4221 .108 (.156)
Negative 36 1.121 (1.78)
Notes: The sample includes only those who appear in the first 3 waves of the SIPP and have values for “hours per week” in both their initial wave and 3 waves later. The coding of cases into predicted changes was as follows: “None” includes cases 1, 4, 6, 7, and 12. “Positive” includes cases 2, 8, 9, 10, and 11. “Negative” includes cases 3 and 5. However, we then move anyone in a state with an unchanging Medicaid threshold into the “none” category. In practice, this affects only observations in case 3 (since cases 1 and 6, which are the only others containing people in states with unchanging thresholds, were already classified as “none”). This changing categorization moves all case 3 individuals into the “none” category, leaving only the remaining case 5 people in the “negative” category. Note that cases 8 and 10 could also have potentially been put into the “none” case (as their prediction is ambiguous, and those who do not participate in Medicaid are predicted to have no change), but we wanted to include all those who might possibly face a change in predicted hours of work. Their inclusion in the “Positive” case should bias the change in hours downward if some of them do not participate in Medicaid and thus have no response to its hours-of-work incentives.
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APPENDIX
State Mean L̂ Mean L Mean ˆnL Mean ˆ
cL Case
AK 144.9 112.3 110.1 167.8 10 AL 152.5 137.7 30.9 26.6 1 AR 148.3 137.3 26.9 67.4 7 AZ 150.9 124.8 191.8 133.3 5 CA 149.1 140.5 133.7 200.6 10 CO 151.6 130.5 57.0 57.0 1 CT 149.8 131.9 191.3 191.3 6 DC 151.7 121.0 236.2 231.5 6 DE 149.7 123.6 122.7 115.9 1 FL 151.6 131.3 74.6 74.6 1 GA 150.5 119.7 75.5 52.0 1 HI 142.0 116.4 142.5 142.5 6 IA 149.2 129.1 112.2 112.2 1 ID 147.4 116.3 47.6 37.6 1 IL 147.4 124.1 195.9 195.9 6 IN 151.1 127.6 35.4 35.4 1 KS 151.9 129.3 45.5 70.2 7 KY 150.0 122.7 87.0 59.9 1 LA 150.2 123.1 28.5 28.5 1 MA 145.9 124.3 150.4 150.4 6 MD 147.8 119.2 43.3 43.3 1 ME 147.5 126.0 233.6 233.6 6 MI 149.4 127.7 77.5 77.5 1 MN 148.4 125.0 114.1 114.1 1 MO 148.9 125.2 71.0 63.1 1 MS 149.3 123.0 47.1 47.1 1 MT 147.5 117.6 83.8 83.8 1 NC 148.3 117.8 76.3 76.3 1 ND 150.6 129.9 110.6 88.3 1 NE 144.6 122.2 76.4 76.4 1 NH 144.0 119.3 62.8 105.1 7 NJ 145.7 115.4 119.5 119.5 3
NM 151.3 121.8 88.5 88.5 1 NV 152.1 135.2 126.7 38.9 1 NY 147.6 115.2 184.1 184.1 6 OH 149.3 126.4 117.2 117.2 1 OK 150.8 132.1 65.7 65.7 1 OR 153.9 132.0 98.3 85.5 1
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PA 149.1 124.2 74.7 72.8 1 RI 150.7 126.4 221.1 196.3 6 SC 151.8 132.5 127.0 73.8 1 SD 145.2 118.9 76.8 76.8 1 TN 151.0 123.4 103.4 103.4 1 TX 148.0 123.3 40.2 31.6 1 UT 143.9 125.2 61.3 61.3 1 VA 147.5 122.5 38.9 38.9 1 VT 150.1 132.9 163.4 75.6 4 WA 150.2 129.2 93.7 93.7 1 WI 149.3 130.8 213.9 186.9 6 WV 144.7 118.0 46.4 32.4 1 WY 147.7 117.1 75.9 75.9 1
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