Sarah Hamersma Burçin Ünel. This draft: November 15, 2013

Transcription

1 Wearing Out Your Welcome: Examining Differential Medicaid Eligibility of New Entrants and Continuing Recipients I. Introduction Sarah Hamersma Burçin Ünel This draft: November 15, 2013 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 1

2 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 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 2

3 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). 3

4 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 4

5 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 U ( c, L, M ) + δu ( c, L, M ) i1 i1 i1 i1 i2 i2 i2 i2 where δ is the discount factor, cit is consumption, Lit is hours of work, and M it 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, where U ( c, L,1) U ( c, L,0) = it it it it it it i 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 it pc w L where p is the unit price of the consumption bundle and individual. wi is the after-tax wage rate of the 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 Iin denote the new entrant income threshold for Medicaid eligibility and Iic denote the continuing recipient income threshold for an individual i. As noted earlier, some states have Medicaid benefits that are hard to 5

6 get initially but easier to keep (i.e. Iin < Iic ), while others have benefits that are not as hard to get initially but are increasingly difficult to keep (i.e. Iin > Iic ). The Medicaid eligibility constraint for a new entrant in period 1 is: {0,1} if wl i i1 Iin (2) M i1 = 0 otherwise. The Medicaid eligibility constraint for a continuing recipient in period 2 is: {0,1} if wl i i2 Iic (3) Mi2 = if Mi 1 = 1 0 otherwise. 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: {0,1} if wl i i2 Iin (4) Mi2 = if Mi 1 = 0 0 otherwise. 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 wl i it (5) Vit ( Lit, Mit ) Uit (, Lit, Mit ). p 6

7 The above (one-period) utility function is concave in it L if U ( c, L, M ) and is well-behaved. it it it it 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, L ˆi and Let L ˆ ( M ) = arg max V ( L, M ) denote the unconstrained utility maximizing level of work hours it it it it it Lit 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, L ˆit does not depend upon the period or Medicaid participation decisions: L i. L ˆ ˆ ˆ ˆ ˆ i1(1) = Li 1(0) = Li2(1) = Li2(0) = Li. Let L it 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. V ( L,1) = V ( Lˆ,0). As Δ i (the net value of Medicaid) is constant across periods, L it it it it it is the same in both periods: L i1 = L i2 = L i. 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 L < Lˆ (see Figure 1). The larger the net value of Medicaid, the larger i i 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 Δ i 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. 7

8 [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, L it I =, compares to L w ˆi and L i. Note that L it 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 L it Lit, Vit ( L it,1) is attainable, however for L > Li, Vit ( Lit,0) it t is the utility function. If the eligibility requirements are so strict that Lit is less than L i, 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, L ˆi. [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 Lit is still binding, i.e. 8

9 L it Lˆ, an individual will restrict the number of hours worked to Lit and participate in Medicaid i (see Figure 2B). For L it > Lˆ, the income threshold is not binding so the individual will participate i 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 nonparticipating individual will get in this case is Vi 1( Li 1,0) + δvi2( Li2,0). 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. 9

10 therefore will choose the unconstrained utility maximizing level L ˆi leading to a total utility of V ˆ ˆ i1( Li,0) + δvi2( Li,0). 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 i2 i2 V ( L,1) to Vi2( L i2,0). Given this decision in the second period, the total utility of a two-period Medicaid participant will be Vi 1( Li 1,1) + δvi2( Li2,1) and the utility of a Medicaid drop-out will be Vi 1( Li 1,1) + δvi2( Li2, 0). 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 L ˆi and L i relate to the eligibility thresholds in each period. Let Lin denote the maximum number of hours that an individual can work without exceeding the Medicaid new entrant income limit and let Lic 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, w i. 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 L i > Lic, the utility function of this individual will be similar to the one given in Figure 10

11 2. To be eligible for Medicaid participation in the second period, this individual will have to restrict the number of hours worked to below L i. 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 L ˆi number of hours getting a utility of V ˆ i2( Li,0) in the second period. This individual would also have to restrict the number of hours worked in the first period to below be eligible as a new entrant since L i > L in. Given this, the total utility if this individual chooses to participate in the first period will be V ˆ i1( Lin,1) + δvi 2( Li, 0). If instead the individual chooses not to L i to participate in Medicaid in the first period, then the (total) utility will be V ˆ ˆ i1( Li,0) + δvi2( Li,0). Note that these two expressions differ only by the first part. Since L i > L in, we can conclude that V (,1) i1 L in < V ˆ i1( Li,0) 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 L ˆi > Lic > L i > Lin. Conditional on Medicaid participation in period 1, the enrollee will continue participation in period 11

12 2 and choose the number of work hours so that the eligibility requirements are met leading to a utility of Vi 1( Lin,1) + δvi 2( Lic,1). Comparing this to the total utility of a non-participant is not straight forward. V (,1) i2 L ic > V ˆ i2( Li,0) since L ˆi > Lic > L i but V (,1) i1 L in < V ˆ i2( Li,0) since L i > Lin. 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 L in. Note that, if the individual were making independent decisions in each period, this individual would have chosen not to enroll in period 1 since L i > 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 12 in.

13 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 13

14 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 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 Previous work by Hamersma and Kim (2009) 14

15 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 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 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 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. 15

16 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 L i will be high relative to the income limit L in and close to L ˆi ), 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 Lin and L ic 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. 16

17 (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 L ˆi 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 L i. 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 L ˆi to arrive at an estimate of L i. (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 ordering of these four parameter estimates, we assign each person to a case. 10 L i ). Based on the 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 Systems/Statistics-Trends-and-Reports/DataCompendium/18_2006DataCompendium.html 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 The number of monthly hours she could work to qualify as a Medicaid applicant would be $255/$8 = 32. That is her L in. 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 L ic. We assign her L ˆi 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 17

18 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 L ˆi and L i, a person in a state with a Medicaid threshold that grows with spell duration will never be classified outside of the cases 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 Lin and Lic 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 Lin and L ic 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 hours and getting Medicaid; L i is 135. Ordering the parameters leads us to assign this observation to Case 7. 18

19 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

20 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 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

21 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

22 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

23 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 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

24 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

25 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

26 The second comparison we make between work hours across cases is related to secondperiod 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 [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