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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