T H E J O U R N A L O F H U M A N R E S O U R C E S • 47 • 4
Policies on the Dynamic Savings
Patterns and Medicaid Enrollment of
the Elderly
Lara Gardner
Donna B. Gilleskie
A B S T R A C T
Medicaid policies that may affect long-term care decisions vary across states and time. Using data from the 1993, 1995, 1998, and 2000 waves of the Assets and Health Dynamics Among the Oldest Old Survey, we esti-mate a dynamic empirical model of health insurance coverage, long-term care arrangement, asset and gift behavior, and health transitions over time. Long-run simulations from the estimated model reveal that most Medicaid eligibility and generosity policy variables associated with nursing home services have no effect on Medicaid enrollment and asset behavior. Those policies related to home- and community-based services, however, have a significant but small influence.
I. Introduction
The number of elderly individuals in the United States who use long-term care services in both institutional and community settings is projected to in-crease from eight million in the year 2000 to 19 million by 2050.1In 2011 an elderly
1. These projections appear in the 2003 Report to Congress entitled “The Future Supply of Long-Term Care Workers in Relation to the Aging Baby Boom Generation.” (aspe.hhs.gov/daltcp/reports/ltcwork.htm) Lara Gardner is an assistant professor of economics at Southeastern Louisiana University. Donna Gil-leskie is a professor of economics at the University of North Carolina at Chapel Hill. David Guilkey, Tom Mroz, Edward Norton, Wilbert van der Klaauw, and seminar participants at Baylor University, California State University at Fullerton, Florida Atlantic University, University at Canterbury, and West-ern Kentucky University provided invaluable comments. This work was supported by a Dissertation Fel-lowship Grant from the Centers for Medicare and Medicaid, Department of Health and Human Services. The restricted use individual data used in this paper may be obtained from the Health and Retirement Study. The authors are willing to advise scholars about the process. The state policy variables may be obtained from the authors.
[Submitted November 2009; accepted January 2012]
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person who anticipates the need for long-term care faces annual costs of $31,025 to $301,490 to live in a semiprivate room of a skilled nursing facility, and between $22,880 and $77,792 to receive home- and community-based services.2Long-term care services are likely to be the largest catastrophic expenses facing the elderly: Most long-term care services are not covered by Medicare, very few employer-provided health insurance plans cover term care, and although private long-term care insurance policies exist, they are very expensive and held by few elderly individuals.3Medicaid, which does cover nursing home stays and home- and com-munity-based services, is available only to individuals with income and assets below state-specific limits, and in some states, to those with medical expenses that reduce income below a qualifying limit.
As a means-tested health insurance program available to most low-income elderly, Medicaid is increasingly becoming a feasible financing alternative for the middle-class elderly due to the high costs of long-term care and increased longevity. The purpose of this paper is to ascertain whether Medicaid eligibility rules and benefits, which differ across states and over time, significantly affect individual decisions to become eligible for and enroll in Medicaid. A thorough answer to this question involves more than evaluating whether observed assets and insurance coverage re-spond to differences in these policies. The asset spend-down and Medicaid enroll-ment behavior of the elderly is complicated by changes in health status and care requirements over time. While Medicaid eligibility and supply policies may be in-dependent of any one individual’s health (except in the case of the medically needy criterion), her health is correlated with observed care arrangements (for example, nursing home, formal home care, informal home care, care from a spouse, and living alone with no additional sources of care) and Medicaid policies greatly affect the availability, affordability, and acceptability of these different arrangements.4 The permanent and time-varying unobserved characteristics of individuals that influence decision-making with regard to long-term care further complicate the understanding of these dynamic decisions.
Using data from the 1993, 1995, 1998, and 2000 waves of the Assets and Health Dynamics Among the Oldest Old (AHEAD) Survey, we estimate a dynamic empir-ical model that captures the simultaneity and endogeneity of health insurance cov-erage, long-term care arrangement, asset and gift behavior, and health transitions over time. In this paper we focus our discussion on the dynamic asset and Medicaid enrollment decisions, but jointly model the interrelated decisions. Having estimated
2. A more detailed description of cost estimates based on the 2011 Genworth Cost of Care Survey can be found at www.genworth.com. Nursing home median costs are lowest and highest in Texas and Alaska, respectively.
3. In 2005, private health and long-term care insurance financed 7.2 percent of total long-term care ex-penses, Medicare covered 20.4 percent, and Medicaid paid for the largest share at 48.9 percent. Over 18 percent was paid out of pocket by the individual (Komisar and Thompson 2006).
the model, we conduct simulations of behavior over time in order to explore the effects of Medicaid policy changes on the outcomes of interest. In particular, we ask (1) how Medicaid policies regarding eligibility and benefits affect asset and gifting patterns and (2) whether these policies and associated changes in assets impact take up of Medicaid.
States have considerable flexibility in determining policies that affect the attrac-tiveness of receiving Medicaid coverage for long-term care (Norton 2000; U.S. Gen-eral Accounting Office 1990). Although states must adhere to fedGen-eral guidelines when designing a Medicaid program, there are large variations in Medicaid policies across states. Additionally, states exhibit different patterns in their eligibility and generosity policies toward nursing home services versus home- and community-based services. We find that most of the Medicaid eligibility and generosity policy variables associated with nursing home services have no effect on Medicaid enroll-ment and asset behavior. Those policies related to home- and community-based services, however, have a significant but small influence. For example, a doubling of the home- and community-based services spending per eligible elderly decreases the amount of assets held slightly and increases the probability of Medicaid enroll-ment by 0.3 to 1.0 percentage points, with the largest increases among the nonmar-ried and low-asset elderly. We conclude that there is evidence of small, but modest, incentives toward spend-down behavior associated with state-level home- and com-munity-based Medicaid policy variables.
Section II reviews the relevant literature and summarizes our contributions. We hypothesize that Medicaid policy variables, such as the rules for Medicaid eligibility, reimbursement to providers, supply restrictions, and the generosity of home- and community-care programs significantly influence savings behavior and the decision to enroll in Medicaid. In Section III we present the empirical model that tests these hypotheses, while capturing the simultaneity and endogeneity of health insurance coverage, long-term care arrangement, asset and gift behavior, and health transitions over time. Data from the 1993, 1995, 1998, and 2000 waves of the AHEAD Survey are described in Section IV. We conduct simulations of behavior using the estimated parameters of the model to allow us to explore the effects of Medicaid policy changes on the choice variables. The estimation and simulation results are presented and discussed in Section V. Section VI concludes.
II. Relevant Literature and Our Contributions
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enforcement of restrictions on the transfer of assets, and, in fact, there exists a network of professionals to help the elderly successfully shield their assets from Medicaid (Moses 1990; Sloan and Shayne 1993).
Some eligible individuals, however, do not apply for Medicaid due to a lack of information on and/or understanding of the Medicaid application process, or because of a stigma associated with receiving Medicaid services. In fact, if an elderly person is welfare-averse, she may accumulate wealth instead of transferring assets, perhaps by increasing savings and lowering consumption. By accumulating wealth she can pay for future medical expenses from private savings for a longer period of time and avoid dependence on Medicaid.
The empirical evidence on the extent to which the elderly actually do transfer assets for Medicaid eligibility is mixed. The view that many elderly people become Medicaid recipients after staying in a nursing home is inconsistent with the empirical evidence that comparatively few persons switch to Medicaid after being admitted (Spence and Wiener 1990; Liu et al. 1990). Using data from two different samples of the elderly, Norton (1995) found the actual time of “spend down” was much longer than a predicted time of “spend down” absent of behavioral effects, indicating that the elderly try to avoid Medicaid eligibility. In a study of the effects of state variation in Medicaid-allowable protected assets on private long-term care insurance demand, Brown et al. (2007) estimated that a $10,000 increase in the amount of assets a household can retain while qualifying for Medicaid coverage of long-term care expenditures is associated with only a 1.1 percentage point reduction in long-term care insurance coverage. However, using AHEAD data from 1993–2002 to estimate a structural model of savings behavior, De Nardi et al. (2010) found that changes in the “consumption floor” created by Medicaid (and the Supplemental Security Income program) caused individuals to rapidly accumulate assets to self-insure. This result held for both low and high permanent income singles.
Policymakers continue to debate proposals for altering the public financing of long-term care because of its high costs and the projected large growth in the number of elderly. Over the next three decades the number of elderly is projected to more than double, rising from 40 million in 2010 to more than 80 million in 2040 (U.S. Census 2008). This growth is likely to result in a significant increase in the demand for long-term care and services despite recent declines in disability rates among the elderly. The aim of recent policy proposals is to help contain costs while still helping those in need of assistance. Traditionally, the strategies used by states to control Medicaid costs have been to tighten eligibility rules, lower payments to providers, limit supply of services, and eliminate coverage of services. Yet further reductions in eligibility, reimbursement, and service coverage could result in many elderly per-sons not receiving the care they need. An understanding of how Medicaid rules influence eligibility for and take-up of Medicaid coverage is therefore necessary for designing effective changes in the public financing of long-term care and services.
and income limits and individual- and time-specific asset and income information, we also construct variables that measure year-specific individual proximity to Med-icaid eligibility limits within the state of residence. Our variables encompass both eligibility policy and supply-side policy that affect observed demand for Medicaid coverage.
Second, we follow elderly individuals over many years in order to observe and model their asset and gifting decisions and subsequent Medicaid enrollment deci-sions. We do not restrict our analysis to insurance coverage decisions after an in-dividual has entered a nursing home. Hence, we are able to explain asset and gifting behavior while modeling and controlling for changes in health and care arrangements that may precede or follow Medicaid eligibility and enrollment decisions. The care arrangements we model include use of informal and formal care, where the elderly individual remains in the community, as well as nursing home care.
Lastly, we model health insurance, health transitions, care arrangements, and asset and gift behavior jointly in order to allow common permanent and time-varying individual unobservables to influence all observed outcomes. The survival of an elderly individual may be influenced by these behaviors and also may be correlated with the permanent and time-varying unobservables. The observed history of health and behavioral outcomes over time, together with the unobserved heterogeneity, describe expectations of future health and care requirements. Hence we do not need to rely on subjective measures of health expectations or self-reported probabilities of residing in a nursing home (Hoerger et al. 1996; Basset 2004).
III. The Dynamic Empirical Framework
A. Overview
In this section we introduce the empirical framework that allows us to explain asset and gift outcomes and Medicaid enrollment, along with care arrangements over time. These decisions affect and are affected by health and survival, and are correlated with unobservables that influence each of these outcomes differently. In the begin-ning of each period an elderly individual (age 65 or older) observes her health state and assets from the previous period. Given her Medicaid eligibility, she chooses either to be insured by Medicare health insurance only, to supplement Medicare with private insurance with or without long-term care coverage, or to dually enroll in Medicaid. Health in the current period is then realized and the individual chooses among different care arrangements and different asset and gift amounts. We make explicit below the role of endogenous previous behaviors or realizations, observed exogenous characteristics, and relevant policy variables, on current outcomes and decisions. We also describe how unobserved permanent and time-varying hetero-geneity is incorporated.
B. Set of Jointly Estimated Equations
We jointly estimate equations for health insurance(It), health(Ht), care arrangement
, Medicaid countable, or unprotected, assets u gifts g, and death .
(Ct) (At), (At) (Dt)
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by the econometrician) and unobserved (to the econometrician) variables.5The ob-served variables include, where appropriate, the endogenous previous behaviors; exogenous demographic characteristics (Xt) including age, gender, race, ethnicity, education, marital status, an indicator for a change in marital status from married to single, income, the number of children and living brothers and sisters, and interac-tions of these variables; and state-specific Medicaid policies and other measures of state generosity and prosperity(Qs). Rather than simply include the state- and
time-t
specific eligibility and allowance limits as explanatory variables in relevant equations of our jointly estimated model, we construct measures that reflect interactions of these policy limits with individual characteristics (for example, assets, income, mar-ital status, age, and state of residence and year). We also include variables that capture the supply-side characteristics of Medicaid-supported benefits in a state. The timing and use of lagged and contemporaneous variables in specific equations is detailed below.
We focus on the role of policy variables in asset, gift, and Medicaid enrollment behavior. However, the observed variation in these variables, and that of other ob-served controls, explains only part of the behavior we are trying to model. It is quite likely that unobserved individual characteristics influence some or all of these be-haviors, which over time affect subsequent decisions. For example, an individual who is highly risk averse will be more likely to buy long-term care insurance and to accumulate more assets. Or an individual may have unobserved knowledge of her genetic disposition that influences her decisions. If someone anticipates failing health, she also may expect to be unable to manage her personal finances in the future, and to need significant long-term care. Thus she may give monetary gifts to her children as a way of qualifying for Medicaid to cover long-term care expenses and/or to acquire informal care. These unobservables suggest that insurance, health, care arrangements, asset and gift levels, and survival are correlated (both within and across time).
To allow for this correlation, we model the insurance, care arrangement, assets, gifts, and health equations jointly rather than separately, and impose few restrictions on the distribution of the unobservables. More specifically, we decompose the error term of each equation e(ue)into three components: a common (across equations)
t
permanent component, a common (across equations) time-varying component, and an equation-specific serially uncorrelated component. That is, ue=ρ µe +ω υe +εe,
t t t
where µ and υt represent permanent and time-varying individual unobservables, respectively, and ρe andωe are equation- and outcome-specific factor loadings on the heterogeneity terms. We estimate the distributions ofµandυt(both the location of the mass points of each distribution and the probability of each mass point) using a discrete factor method. Also,εe is assumed to be mean zero and independent and
t
identically distributed for OLS equations (assets, gifts, and health) and independent and identically Extreme Value distributed for dichotomous or polychotomous out-comes (insurance, care arrangement, and death).
1. Health Insurance
We first consider an individual’s health insurance decision in periodt, which is made prior to realization of one’s periodthealth. All individuals are assumed to be covered
by both Part A and Part B of Medicare.6Because Medicare covers short stays in a nursing home following a hospital stay but does not provide for residence in a nursing home and only covers limited home health care, an elderly individual may choose to supplement this government-provided health insurance. Each individual has the option to hold no additional insurance (i= 0), to purchase private insurance that does not cover long-term care (i= 1), or to purchase private insurance that does cover long-term care (i= 2). Conditional on her income and assets, she also may be eligible for Medicaid (i= 3), which does cover long-term care arrangements. The individual’s health insurance coverage determines her financial out-of-pocket re-sponsibility for subsequent medical care consumption, and in particular, the long-term care arrangement.
If people are modifying their behavior to satisfy Medicaid eligibility criteria, then ignoring the endogeneity of eligibility may bias results. Putting the issue of selection aside for the moment, the notion of eligibility, in and of itself, suggests that the decision to participate in Medicaid should be estimated only on individuals who are eligible for Medicaid based on recent asset and income levels.7However, because income and assets of lastyearare not provided in the HRS/AHEAD survey waves that span two or three years, we estimate the probability of enrolling in Medicaid for all individuals and let the most recent observation of assets (that is, the previous wave) explain observed enrollment. More specifically, and expressed in log odds for notational convenience, the probability of Medicaid enrollment (i= 3) is
p(It= 3) u s 1 1
ln =α +α I +α H +α A +α Q +α X +ρ µ+ω υ
(1)
冤
冥
03 13t−1 23 t−1 33 t−1 43 t 53 t tp(It⬆3)
where I , H , and Au are endogenous lagged insurance, health, and assets
t−1 t−1 t−1
(respectively),Qsis a vector of Medicaid policy variables that influence the expected t
financial benefits (or costs) of eligibility and access to care in statesin yeart, and is a vector of exogenous demographic variables. Unobserved permanent and
time-Xt
varying individual heterogeneity is captured byµandυt.Conditional on not enrol-ling in Medicaid, the probability of selecting private insurance that does not or does cover long-term care (i= 1 or 2) relative to Medicare coverage only (i= 0) is (in log whereEtis an indicator for Medicaid eligibility attbased on assets in the previous wave.
2. Health
6. In this analysis 95 percent of the sample is enrolled in the optional Part B.
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After selecting health insurance, an individual’s health is revealed. To explain ob-served transitions in health from one wave to the other, we use a continuous measure of health (Ht), which is constructed from the data and described in the following data section. It takes on values from 0 to H, where larger values indicate worse health. Conditional on being alive in period t (Ht<H), an individual’s health in periodtis defined as
3 3 h
H =β +β I +βH +β C +βX +ρ µ+ω υ +ε
(3) t 0 1 t−1 2 t−1 3 t−1 4 t t t
where εh is a mean zero, independent and identically distributed error term. The t
previous period insurance choice (It−1), health (Ht−1), and care arrangement are endogenous explanatory variables that capture the effect of lagged health (Ct−1)
and lagged medical care intervention on current health. The probability of death at the end of periodt(that is, of not surviving to periodt+ 1) is
p(Ht+ 1=H) 4 4
ln =δ +δI +δ H +δC +δ X +ρ µ+ω υ
(4)
冤
p冥
0 1t 2 t 3 t 0 t t(Ht+ 1<H)
and depends on current period behaviors.
The equations explaining health outcomes can be thought of as structural health production functions that depend on health inputs. As such, an individual’s previous period care arrangement may impact her current period health. Similarly, the current care arrangement may influence whether she survives to the next period. If an elderly individual needs help with bathing, walking, eating, or other activities of daily living, she may do more harm to her health if she does not receive the required care (for example, if she attempts to enter/exit a bathtub alone). A care provider also can help an elderly person to properly take medications, which would influence health. The dependence of health and survival on the insurance choice is intended to capture the effect of other (omitted) endogenous medical care inputs that are affected by insurance coverage.
3. Care Arrangement and Asset and Gift Amounts
Conditional on health insurance coverage and health, the individual jointly decides among available care arrangements and savings options. In the data we observe the care arrangement outcome and the per-period level of assets and gift amounts. The mutually exclusive care outcomes of married individuals include no care (c= 0), informal home care by a spouse only (c= 1),informal home care by others (c= 2), any formal home care (c= 3),and nursing home care (c= 4). The probability that an individual has care arrangementcrelative to no care (c= 0) is (in log odds)
p(Ct=c)
Recall that previous decisions regarding assets (Au ) are part of her available in-t−1
also estimate an equation for unmarried individuals that is similar to the equation above but does not contain the “informal care by a spouse” outcome.
The equations explaining continuous values of the observed unprotected asset (Au) and gift amounts (Ag), if any, are given by
whereεuandεgare independently and identically distributed mean zero error terms.
t t
The set of jointly estimated equations includes the probabilities of any assets,
and any gifts, which are functions of the same variables as in
u g
p(At> 0), p(At> 0),
the positive amounts equations above. The endogenous amount of countable assets (theoretically) defines Medicaid eligibility but, given the two- to three-year gap be-tween survey waves, is used in our model to predict subsequent insurance status. An individual also chooses how much of her wealth to give away as “gifts.” The observed gift amounts are modeled in order to capture attempts by the individual to reimburse or elicit informal care from others or to transfer wealth to become eligible for Medicaid. Gifts are exempt from Medicaid eligibility, and cannot be liquidated by the individual for consumption expenditures. In this framework, previous assets and their return, (1 +r)Au , as well as other current period income (included in
t t−1
), are allocated in period t between consumption (including insurance, medical
Xt
care, and care arrangement), current assets(Au),and gifts(Ag).
t t
C. Method of Estimation
The likelihood function for individual n reflects the probabilities of the observed insurance choice, health state conditional on being alive, care arrangement, asset and gift behavior, and death over the four waves of the survey. Conditional on the unobserved heterogeneity, the contribution to the likelihood function of individual
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where Θ= (α,β,δ,φ,λ,ρ)is the vector of parameters to be estimated, h(•), u(•),
and g(•) are continuous density functions,Int=i if individual n selects insurance plan iat timet, and Cm=cif a married (m = 1) or unmarried (m = 0) individualn
nt
chooses care arrangementcin periodt.
Significant correlation in unobservable individual traits and preferences across the outcome variables presents itself as correlation among the errors in each equation, causing coefficients on endogenous explanatory variables to be biased if the corre-lation is unaccounted for. We approximate the unknown distributions of the per-manent and time-varying heterogeneity with discrete step functions and “integrate out” with a weighted sum of probabilities. This discrete factor random effects method, developed by Heckman and Singer (1984) and later extended to simulta-neous systems by Mroz and Guilkey (1992) and Mroz (1999), imposes no distri-butional assumptions on the unobservables. Instead, it approximates the distribution of the heterogeneity by a finite number of mass points and probability weights that are estimated jointly with the other parameters. We normalize the endpoints of the discrete mass points of each distribution to zero and one.
The ten dynamic equations described above (that is, Medicaid enrollment, sup-plemental insurance, health index, death, care arrangement if married, care arrange-ment if not married, any unprotected assets, level of unprotected assets if any, any gifts, and gift amounts if any) are jointly estimated for years 1995, 1998, and 2000. We use data from the 1993 wave to define the lagged endogenous variables that affect the 1995 outcomes. However, since 1993 was the first year the AHEAD survey was conducted, these 1993 variables cannot be explained using the dynamic equa-tions defined above, which rely on previous period behavior and outcomes. Rather, we specify reduced form equations for these lagged initial conditions. The initial condition equations are correlated with the dynamic equations through the permanent unobserved individual heterogeneity(µ). The initial condition equations are initial Medicaid enrollment, initial supplemental insurance status, initial health, initial care arrangement if married in 1993, initial care arrangement if not married in 1993, any initial assets, and level of initial assets if any.8Hence, the equation system consists of 17 correlated equations. LetI (R,,ρ0,µ)represent the probability of observing
k k k
the value of thekthinitial condition, whereR is a vector of explanatory variables, including valid exclusion restrictions that do not affect the period t> 0 decisions,
is a parameter vector, and 0 is the factor loading on for the kth equation.
k ρk µ
Thus, the likelihood function for each individualn,unconditional on the unobserved error componentsµandυt, is
K T
A n B
0
L (Θ,θ) =
∑
θ I(R, ,ρ,µ )∑
θ L (Θ⎪µ ,υ )(9) n a
{
兿
k k k a兿
冤
b nt a bt冥冧
a= 1 k= 1 t= 1 b= 1
whereθais the vector of probabilities for the A points of support of the distribution of the permanent unobservable, andθbis the vector of probabilities for the B points of support of the distribution of the time-varying unobserved heterogeneity.9
D. Identification
Identification in a system of dynamic equations such as this appears difficult to assess at first glance. However, most of the model is identified using the theoretical frame-work to derive and specify the structural demand equations for insurance, care ar-rangement, and asset and gift amounts and the structural production equations for health and death. For example, lagged values of endogenous outcomes enter almost all equations in the system (except the initial conditions). The exogenous determi-nants of these lagged values serve as exclusion restrictions (Arellano and Bond 1991). There is a great deal of variation in these lags and their determinants over the three years and 50 states that comprise our sample.
One goal of this work is to appropriately identify causal effects of Medicaid policies on Medicaid enrollment and asset and gifting behavior over time. It may appear that much of our policy variation consists of cross state differences as there is little variation in some policies within a state over time. For example, while there is very little change in state asset and income limits during our time frame, there is variation in other policy variables over time (as our policy appendix, available from the authors, demonstrates). Ultimately, however, we construct eligibility and supply-side policy variables that depend on individual characteristics that vary consupply-siderably over time (and these variables are discussed in detail in Sections IVB and IVC and Tables 4 and 5). Hence, our policy variables exhibit quite a bit of individual, state, and time variation.
Our preliminary work included a detailed assessment of the role of Medicaid income and asset limits themselves (that is, using the observed limits as the explan-atory variables) as well as our constructed policy measures (that is, using the limits and individual characteristics to construct theoretically relevant explanatory vari-ables). We found that variation in state income and asset limits did not explain variation in Medicaid enrollment or assets (any or log amount if any) regardless of specification or estimation method (that is, combinations of treating data as cross section or panel, clustering standard errors by state, and including state fixed effects). However, coefficients on the constructed eligibility policy variables, while small,
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remained statistically significant, with little to no change in the marginal effects, regardless of the model specification. Inclusion of state fixed effects reduced the significance of some supply-side policy variables (suggesting that these variables may simply reflect permanent differences across states). As an alternative to using state fixed effects that pick up permanent differences across states only, we included variables that capture the generosity of other programs in a state or simply the state of the economy in those states. These variables have considerable variation across states, but more importantly, also differ across time. In these models we again find that the constructed eligibility policy variables and some supply-side policy variables remain statistically significant. We conclude that our policy variables contain enough variation across states and time and are not correlated with unmeasured permanent and time-varying state heterogeneity.
Because the initial conditions are estimated as reduced-form equations (rather than dynamic equations with endogenous explanatory variables) that do not contain lagged values (since data before 1993 are not available), we specify them as func-tions of individual-level variables that represent sources of exogenous variation. We include variables that are significant in the initial equations and, conditional on the lagged values of the state variables, are not significant in the periodt> 0 equations.10 Additionally, the model is identified by the nonlinearities in functional form and the covariance restrictions on the permanent and time-varying heterogeneity components of the unobserved error terms.
IV. Description of Data
The data for this analysis are from the 1993, 1995, 1998, and 2000 waves of the Asset and Health Dynamics Among the Oldest Old (AHEAD). The AHEAD survey is a national panel survey composed of households in which the head of household is at least 70 years of age. AHEAD uses a national probability sample of U.S. households and sampled African Americans, Mexican-Hispanics, and residents of the state of Florida at about 1.8 times their proportion in the general population. We observe three transitions, from 1993 to 1995, 1995 to 1998, and 1998 to 2000. The initial survey data, in 1993, are treated as initial conditions.
Included in the analysis are individuals who: (1) provide a core interview all four waves; or (2) provided a core interview in periods when alive and surviving relatives answer the exit survey in the year the individual dies.11 Observations that do not meet these criteria are dropped so that a continuous panel of observations can be constructed. Of the 8,449 persons surveyed, there are 7,004 that meet these criteria.
10. Variables used for identification are spouse’s health, spouse’s education, mother attained at least 8th grade education, mother is living, mother’s age at death, father attained at least 8th grade education, father is living, father’s age at death, number of grandkids, hospitalization in the previous year, number of years employed, and indicators for six occupation categories. Descriptive statistics or coefficient estimates from the initial condition equations are available upon request.
Also dropped are the 162 persons under age 65 and 35 persons who are missing health data in all waves. After these deletions, there are 6,807 persons. Finally, we reduced the sample size by deleting those who ever had household assets greater than $2 million or gifts greater than $675,000, which resulted in a remaining 6,534 observations, for a total of 23,967 person-period observations.12
A. Individual Choice Variables and Health Outcomes
Table 1 displays summary statistics for the dependent variables of our model by year, or wave of the data. Unconditional on assets or health, 12.4 percent of the sample has Medicaid in 1995, while these numbers rise to 13.3 percent and 14.9 percent in 1998 and 2000, respectively. Among those without Medicaid, the per-centage of people with Medicare only (that is, no additional source of insurance coverage) grows over time. Individuals die with increasing frequency as the re-maining sample ages. Similarly, health deteriorates over time. The health variable used in this analysis is based on the total difficulty with Activities of Daily Living (ADLs) and Instrumental Activities of Daily Living (IADLs). We assign two points for a difficulty with an ADL and one point for a difficulty with an IADL and sum the raw scores by the equation: ((2*ADLs) + IADLs). There are six possible ADLs and five possible IADLs, leading to a health score that ranges from 0 to 17. The proportion of surviving individuals who use nursing home care increases over time.13 Among those who reside in the community, single individuals receive more care assistance than married individuals.14
The asset variables in the AHEAD are collected at the household level. However, one can distinguish assets of the elderly couple (person) in the household from the assets of other household members. Our measure of unprotected assets is the sum
12. We made considerable efforts to address concerns regarding the quality of the AHEAD data. In addition to making corrections for 1993 asset ownership and values and second home equity in 1993 as described earlier, we also addressed each of the following concerns: a) in 1995 any respondents who had not lived in their second home for at least two months out of the year were not asked about their second home equity. We used imputed values for second home equity for 1995 that were computed by Cao and Juster (2004) using data in later waves on ownership and date of purchase; b) the time series behavior of (level) assets exhibited unusual patterns when we included in the sample those individuals with reported assets above $2 million and/or reported annual gift amounts of over $675,000. Hence, we dropped from the research sample 25 persons with large (or misreported) gifts and 248 people with large nominal asset amounts.
13. In the first period of data used in this analysis, no institutionalized persons are interviewed. Although the initial conditions are estimated jointly with the structural equations in the empirical model, theoretically the fact that there are no institutionalized persons sampled in the first period could bias estimates because of selection. However, the average stay in a nursing home is quite short. Of the 374 persons who entered a nursing home between 1993 and 1995, 40 percent had died by the end of 1995; 74 percent, by the end of 1998; and 89 percent, by the end of 2000.
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Table 1
Descriptive Statistics: Dependent Variables
Notation Variable Name 1993 1995 1998 2000
It= 3 Medicaid enrolled int 10.3 12.4 13.3 14.9
It=i Supplemental insurance int
(if not enrolled on Medicaid)
i= 0 Medicare only 17.8 28.4 33.7 35.6
i= 1 Private insurance no LTC 66.7 63.1 58.6 57.1
i= 2 Private insurance with LTC 15.6 8.5 7.6 7.3
Ht Health index int 1.94
c= 1 Informal home care from
spouse
16.1 5.7 5.0 4.2
c= 2 Informal home care from
others
c= 1 Informal home care from
others
Research sample size 6,534 6,534 5,849 5,050
of stocks, bonds, savings accounts, business assets, checking and certificate of de-posit accounts, trusts, individual retirement accounts, value of secondary real estate, and other assets, minus all debts. The asset measure is designed to include only nonexempt assets, and not the value of the primary home.15In the empirical analysis, any person reporting negative assets is assigned a value of zero assets. Our gifting amounts include gifts made to children, grandchildren, friends and others in the preceding year and gifts to charity. We model both the probability of any assets (gifts) and the level of assets (gifts), if any.
Table 2 details transitions in insurance, care arrangements and health from wave
t to t+ 1. The top panel reveals movement in insurance coverage from wave to wave. While movement into private insurance with long-term care coverage is rare, movement into and out of other insurance categories is sizeable. Similarly, care arrangements change over time. No care is the most persistent state, but there is evidence of increasing probabilities of nursing home care as care needs increase as well as evidence of reduction in care needs. Finally, the bottom panel of Table 2 indicates changes in health states, with greater health limitation leading to death.
Tables 3 and 4 describe the explanatory variables used in the set of jointly esti-mated equations. Variables capturing observed permanent and time-varying individ-ual characteristics are detailed in the top two panels of Table 3. The averages or proportions of the permanent variables in the top panel of the table vary over the last three years of observation because the sample size is changing due to death. The variables summarized in the third and fourth panels of Table 3 are Medicaid policy variables and are more fully described below and in Table 4. While the supply-side policy variables capture time-varying availability and generosity of Med-icaid-covered services in each state, we also include several state- and year-specific non-Medicaid variables in order to capture unobserved aggregate conditions within a state over time. We include these variables (listed in the bottom panel of Table 3) rather than use state fixed effects in order to avoid dropping demographic variables that do not change over time and losing degrees of freedom associated with signifi-cantly more estimated parameters in our 17-equation model.
B. Eligibility Policy Variables
Table 4 describes the policy variables that explain insurance, asset and gift amounts, and living arrangement.16The constructed eligibility variables are, in many cases,
15. The data suggest that most elderly persons hold the majority of their savings in the form of housing (Venti and Wise 1991). For the purpose of this analysis, variations in housing value are taken as given. That is, the empirical model does not explicitly allow for the individual’s decision to sell (or buy) a home and, aligning with Medicaid rules, housing wealth is not included in the measurement of assets. Previous research documents that persons 65 and over simply do not move very often (Venti and Wise 1989). In the AHEAD data, 75 percent of the sample owns a home at the start of the survey (1993). Of these, less than 4 percent (who are still alive in 2000) sold their homes.
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Table 2
Transitions over Time: Insurance, Care Arrangements, and Health
Wavet−1 Wavet
Insurance Medicaid Medicare Only Private no LTC Private with LTC
Medicaid 74.85 16.48 7.71 0.96 Medicare only 12.81 58.95 26.00 2.24 Private no LTC 3.32 19.54 73.25 3.88 Private with LTC 1.60 16.02 41.19 41.19
Care Arrangement No Care
Informal Home Care from Spouse
Informal Home Care from Others
Formal Home Care
Nursing Home Care
No care 86.07 3.56 5.06 2.46 2.85 Informal home care from spouse 54.21 18.69 9.53 7.55 10.02 Informal home care from others 36.39 6.12 27.21 14.63 15.65 Formal home care 13.89 2.78 14.35 43.06 25.93 Nursing home care 15.97 0.84 8.40 9.24 65.55
Health
0 ADLs &
0 IADLs 1 IADL
1 ADL or 2 IADLs
1 ADL & 1 IADL or 3 IADLs
> 2 ADLs or
> 4 IADLs Death
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Table 3
Descriptive Statistics: Explanatory Variables
Variable 1993 1995 1998 2000
Non Time-varying Demographic Variables
Female 0.631 (0.482) 0.631 (0.482) 0.641 (0.480) 0.653 (0.476) Nonwhite 0.149 (0.356) 0.149 (0.356) 0.145 (0.352) 0.145 (0.352) Hispanic 0.058 (0.233) 0.058 (0.233) 0.058 (0.234) 0.060 (0.237) Less than high school 0.444 (0.497) 0.444 (0.497) 0.431 (0.495) 0.416 (0.493) High school degree 0.305 (0.460) 0.305 (0.460) 0.312 (0.463) 0.316 (0.465) Some college 0.144 (0.351) 0.144 (0.351) 0.147 (0.355) 0.154 (0.361) College degree 0.108 (0.310) 0.108 (0.310) 0.110 (0.313) 0.113 (0.317)
Time-varying Demographic Variables
Age–65 12.390 (6.382) 14.404 (6.465) 16.450 (6.087) 17.889 (5.784) Nonmarried 0.462 (0.499) 0.504 (0.500) 0.499 (0.500) 0.592 (0.491)
Newly single — 0.086 (0.280) 0.014 (0.117) 0.218 (0.413)
Number of children 2.633 (2.174) 2.546 (2.001) 2.842 (2.219) 2.866 (2.218) Number of living sisters 1.193 (1.333) 1.130 (1.306) 1.053 (1.287) 1.067 (1.297) Number of living brothers 0.887 (1.188) 0.827 (1.145) 0.741 (1.081) 0.759 (1.092)
Eligibility Variables
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Supply-side Variables
Bed Supply 4.115 (1.464) 4.122 (1.466) 4.672 (1.613) 4.606 (1.635) NH Revenue Loss 1.197 (1.273) 1.197 (1.273) 1.239 (1.568) 1.581 (1.942) Benefit Ratio 1.423 (1.377) 1.419 (1.373) 1.394 (1.103) 1.491 (1.080) HCBS Spending 0.260 (0.599) 0.259 (0.592) 0.392 (0.873) 0.789 (1.704)
Medicare $ Change 0 (—) 0 (—) 2.595 (0.508) 1.355 (0.738)
State Characteristics
Monthly AFDC payments for family of four (00s, $2000)
5.169 (1.878) 4.942 (1.764) 4.702 (1.632) 4.644 (1.646)
Household income (000s, $2000) 59.807 (7.913) 62.908 (8.135) 70.562 (9.774) 76.301 (11.819) Total earnings per employee (000s, $2000) 41.605 (5.837) 40.236 (5.800) 41.363 (6.374) 42.178 (6.846) Total employment per capita:
employed/population
0.542 (0.052) 0.557 (0.050) 0.576 (0.050) 0.588 (0.049)
Total retail sales per capita (000s, $2000) 8.431 (0.749) 9.057 (0.792) 9.878 (0.886) 10.833 (0.962)
Table 4
Medicaid Policy Variable Definitions
Eligibility Variables
NH Eligibility The average probability of eligibility for Medicaid coverage of nursing home care for a marital status/age/education cell within a state for a particular year.
NH Generosity The product of NH Eligibility and the average cost of nursing
home care in a state for a particular two-year period. We divide this value by 10,000 in estimation.
NH $ Loss The amount of income and assets an individual would have
to dispose of in order to obtain Medicaid coverage of nursing home care in a state for a particular year. We use the log of this value in estimation.
HCBS $ Loss The amount of income and assets an individual would have
to dispose of in order to obtain Medicaid coverage of home- and community-based services in a state for a particular year. We use the log of this value in estimation.
HCBS $ Allowable The average dollar amount of income and assets one may
retain while receiving Medicaid home- and community-based services coverage for a marital status/age/education cell within a state for a particular year.
Supply-Side Variables
Bed Supply The number of nursing home beds per 1,000 elderly in a state
for a particular year. We divide this value by 10 in estimation (that is, becomes per 10,000 elderly).
NH Revenue Loss The difference in revenue to a nursing home from accepting
the Medicaid payment rate for a patient rather than the private pay rate in a state for a particular two-year period. We divide this value by 10,000 in estimation.
Benefit Ratio The ratio of total Medicaid dollars spent on mandatory Home
Care and optional Personal Care to total dollars spent on Nursing Home care in a state for a particular year. We multiply this value by 10 in estimation.
HCBS Spending The amount of spending on optional home- and
community-based waivers per eligible elderly in a state for a particular year. We divide this value by 1,000 in estimation.
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functions of both the limits imposed by a state in a given year as well as time-varying individual characteristics (for example, assets, income, marital status, age, and state of residence) in order to capture the economic relevance of these variables. Note that the averages of these variables by year (in Table 3) reflect the composition of the sample of individuals over time and across states; alternatively, we could present the values using one observation per state per year.
We measure the generosity of Medicaid’s eligibility rules for nursing home care as in Currie and Gruber (1996) and Gruber and Yelowitz (1999). That is, we model the impact of Medicaid’s eligibility criteria for nursing home care by determining the amount of expected nursing home expenditures that would be covered by the Medicaid program for a given individual, in a given state and time period. Specifi-cally, for each person, we first determine a likelihood of being eligible for nursing home care (labeledNH Eligibility) that is a function of the legislative environment in a state and year but not related to the demographics of that state.17Then we proxy the benefits of eligibility by the average cost of nursing home care in a state and year. We calculate a measure of nursing home generosity (labeled NH Generosity) as the probability of nursing home eligibility multiplied by the expected cost of care for two years (based on the fact that there are two years between the AHEAD survey waves). This measure of the “expected dollar benefit” of Medicaid coverage of nursing home care will vary across individuals due to differences in state eligibility rules by household characteristics, as well as differences in the average costs of care in the state. These variables also vary over time as individual characteristics change and to the extent that state policy variables change over time.
We use two variables to capture the theory that persons whose asset levels are closer to the asset limit may be more willing to dispose of assets in order to become eligible for Medicaid. These constructed variables are the log amount of assets that one would have to spend, transfer, or otherwise dispose of in period t−1in order to be eligible for Medicaid nursing home coverage in period (labeledt NH $ Loss), and the log amount of assets calculated similarly for Medicaid HCBS coverage (labeledHCBS $ Loss).18
17. For each year we categorize the entire sample by the four education categories in Table 3. Then we compute the eligibility of all persons under each state’s rules in that year. The average eligibility is then measured in each marital status/education/age/state cell to get a cell-specific eligibility measure. Thus, for each year, there is an average eligibility by state, marital status, education level, and age category. The appropriate average is then assigned to each individual in the sample. There are four age categories used for this procedure: 65–75, 76–80, 81–84, and 85 and older.
If available in a state at time , Medicaid’s maintenance needs allowances (MNAs)t
and spousal protection limits define an amount of money that an individual can retain while living in the community and receiving Medicaid covered home- and community-based services. Using the state- and year-specific limits, we calculate these amounts (labeled HCBS $ Allowable) by marital status/age/education cell (in a manner similar to the calculation of NH Eligibility).
C. Supply-Side Policy Variables
Several supply-side Medicaid policies restrict the availability of Medicaid services within a state and also influence quality and pricing of care. We use the number of nursing home beds per 1000 elderly (labeled Bed Supply) within a state each year to reflect enforcement of state-specified Certificate of Need (CON) and/or morato-rium requirements that restrict the construction of nursing home beds.
To measure other supply-side policy differences within a state we define a measure of the difference between the full (or noninsured) charge for nursing home care and the Medicaid payment rate for nursing home care within a state (labeledNH Revenue Loss). This measure is individual-specific because we difference the nursing home’s projected revenue if a particular individual became eligible for Medicaid-covered nursing home care during a (two-year) stay from the revenue a nursing home would receive if a person never qualified for Medicaid coverage. The measure takes into account the timing of eligibility, predicted probabilities (from a hazard analysis) of survival in each period, and Medicaid’s nursing home reimbursement rates in the state for the particular time period.19
A state’s Medicaid expenditures on (mandatory) home health and (optional) per-sonal care services, relative to that on (mandatory) nursing home care, provides some indication of the generosity of community vs. institutional benefits within a state. We define this relative service generosity (labeledBenefit Ratio) as the ratio of total spending on home health and personal care to the total amount of spending on nursing home care. The optional HCBS Waiver program is a state’s primary mech-anism for providing Medicaid-funded, community-based, long-term care services. To approximate the availability and generosity of HCBS services for the elderly, we use the average HCBS expenditure per eligible elderly person in the state (labeled
HCBS Spending). We proxy eligibility with receipt of Supplementary Security In-come. All eligible individuals do not enroll in the Medicaid-covered HCBS program. Although Medicare only covers short stays in a nursing home and limited home health services, there is one aspect of Medicare coverage of home health that is important in the context of this study. In October 1997 there was a substantial change in Medicare’s reimbursement policy that has been associated with a decline in the provision of home care (McKnight 2006). The reimbursement policy change in-volved the imposition of average per-patient reimbursement caps to home health
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care agencies.20This policy change could give home health agencies an incentive to reduce per-patient costs. To control for the effects of this change in Medicare reimbursement to home health care agencies, we include the change in Medicare’s average payment per patient from the previous period, by state, interacted with a dummy variable indicating the post-policy period (labeled Medicare $ Change). Thus, for 1995 this variable is zero. Medicare payment information is from the National Association for Home Care and Hospice Organization.21
V. Results
We initiate discussion of the results by first demonstrating the fit of the model. Table 5 displays the observed probability of each outcome in the data and the predicted probabilities of each outcome from our estimated model. We pro-vide two different types of predictions. The first simulation involves using the values of the explanatory variables observed in the data each time period. Recognizing that some of these explanatory variables are functions of previous behavior, we then provide a second set of simulations that update the endogenous explanatory variables based on the estimated model. We believe the second simulation accurately reflects the fit of our model in both the cross-section and dynamic dimensions. Our model fits many of the outcomes very well. We tend to overestimate death and nursing home residence as the sample ages.
Table 5 also provides predictions of behavior and outcomes by permanent and time-varying mass point. The estimated distribution of the permanent heterogeneity (bottom of Table 5) reveals that most of the mass of this unobserved characteristic is to the right of the discrete distribution. The simulations suggest that these people are healthier, less likely to need care, and have larger asset and gift amounts. The time-varying heterogeneity, estimated by a three mass point distribution, places most of the mass on the middle mass point, which is almost at the center of the normalized range between zero and one. A draw from the lower tail of this distribution appears to indicate a time-varying shock that reduces health (measured by ADLs and IADLs) drastically and increases the probability of care needs. Interestingly, however, the probability of death is lower. A draw from the other side of the distribution raises death probabilities greatly. Note, in Table 5, that the factor loadings on both types of heterogeneity are most significant in the health, care needs, and death equations, suggesting that the heterogeneity that is being picked up by our discrete factor random effects procedure is most likely related to unobserved permanent and time-varying health (as opposed to unobserved economic determinants affecting insurance and assets).
We now turn to the estimated model to understand the role of Medicaid eligibility and generosity variables on behavior. The effects of the Medicaid policy variables and other exogenous variables on the outcomes of interest are not easy to derive
because they depend (importantly) on the history of the many (discrete and contin-uous) endogenous variables. To evaluate these effects, we use the estimated model to simulate and compare individuals’ per-period behaviors and outcomes under vari-ous Medicaid policy changes. By forward simulating the changes in important en-dogenous variables under various Medicaid policy scenarios, we recover the uncon-ditional impact of Medicaid policies on the outcomes of interest. We begin, however, by presenting the coefficient estimates and discussing signs and significance to pro-vide some information about the effects of variables of interest. Tables 6a–6d show selected coefficient estimates from the jointly estimated dynamic equations that ac-count for unobserved heterogeneity.22
There are many questions that could be explored with this model. In this paper, our discussion focuses on the original objectives posed in the introduction: How do Medicaid policies affect asset and gift behavior; and how do changes in asset levels and these Medicaid policies affect enrollment in Medicaid?
A. Eligibility Policy Variables
1. Medicaid Nursing Home Generosity
Conditional on lagged assets and health,NH Generositydoes not have a significant effect on the probability of Medicaid enrollment (Table 6a). However,NH Generosity
has a significant positive effect on asset levels, but does not affect the probability of holding positive assets nor gift giving (Table 6b). These results can be interpreted as follows: Higher values of NH Generosity result from a combination of more generous Medicaid eligibility rules and higher costs of nursing home care. In states with more generous eligibility rules relative to other states, people are allowed to qualify for Medicaid while holding higher asset levels. Thus, persons in states with more generous eligibility rules may choose to hold assets up to the level allowed under Medicaid coverage. In other words, these results suggest that if persons are allowed to hold more wealth under Medicaid coverage, they will choose to do so.
2. Dollar Loss Variables
The nursing home and HCBS dollar losses (NH $ Loss and HCBS $ Loss) are
constructed as the difference between lag assets and the Medicaid asset limits for nursing home care and HCBS, respectively. Our theory suggests that persons whose assets were closer to the eligibility limits in the previous period would be more likely to be enrolled in Medicaid in the current period. However, both dollar loss measures are insignificantly related to the probability of Medicaid enrollment (Table 6a). This does not suggest that spend down behavior may not be occurring, but that those persons currently enrolled in Medicaid held a wide range of assets in the previous period. This also may be a reflection of the two- to three-year gap in the data between last period’s observable assets and current period enrollment in Med-icaid.
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Table 5
Observed Data and Model Predictions by Year and by Unobserved Heterogeneity Mass Point
Medicaid
Enrolled Supplemental Health Insurance Long-Term Care Arrangementc
Any
Home Yes (Log) Yes (Log) Yes
1995
Observed 12.4 24.9 55.3 7.4 2.04 76.3 2.8 9.2 6.0 5.7 84.7 10.60 47.1 7.62 10.5
Simulateda 12.5 25.1 54.9 7.6 2.33 76.7 2.7 8.1 5.6 6.9 84.9 10.60 47.4 7.60 10.5
Simulatedb 12.5 25.1 54.9 7.6 2.33 72.1 4.1 10.8 6.6 6.3 84.9 10.60 46.7 7.63 11.0
Permanent
Observed 13.3 29.3 50.8 6.6 2.75 69.0 2.5 9.9 7.0 11.6 85.4 10.68 46.2 7.91 13.7
Simulateda 13.1 29.3 50.9 6.7 2.83 69.3 2.3 8.8 6.6 13.1 85.3 10.66 46.4 7.89 14.1
Simulatedb 14.0 28.1 47.8 10.1 2.78 59.5 3.4 12.9 10.7 13.5 80.1 10.65 43.7 7.85 16.3
Permanent
Observed 14.9 30.3 48.6 6.2 3.16 65.6 1.7 12.8 7.0 12.8 83.4 10.80 46.0 8.00 14.9
Simulateda 14.6 30.2 48.8 6.4 3.06 65.6 1.5 11.6 6.7 14.6 83.3 10.81 46.1 8.00 16.0
Simulatedb 16.1 28.0 44.8 11.1 3.16 54.2 2.2 17.8 10.4 15.3 76.5 10.80 41.6 7.92 18.4
The
Enrolled Supplemental Health Insurance Long-Term Care Arrangementc
Any
Home Yes (Log) Yes (Log) Yes
Permanent
(0.509) (0.691) (0.709) (0.214) (0.639) (0.547) (0.656) (0.657) (0.178) (0.078) (0.430) (0.126) (0.209)
Time-varying factor −1.587 0.123 −0.162 −19.57 2.387 3.075 4.062 5.016 −0.694 −0.209 −1.018 0.519 2.031
(0.313) (0.335) (0.797) (0.244) (0.936) (0.892) (0.747) (0.696) (0.679) (0.311) (0.322) (0.326) (0.398)
Estimated Heterogeneity
Mass Point 2 −1.127 (0.016) 0.245 0.243 (0.107) 0.050
Mass Point 3 1.492 (0.009) 0.816 1.468 (0.088) 0.170
Mass Point 4 — — 1.000 2.940 (0.081) 0.741
Time-varying Mass Point 1
Mass Point 2 — — 0.000 — — 0.109
Mass Point 3 −0.063 (0.022) 0.484 2.098 (0.022) 0.885
— — 1.000 −2.875 (0.095) 0.006
a. Simulated outcomes are based on the model estimates, random error draws, and observed values of all explanatory variables.
b. Simulated outcomes are based on the model estimates, random error draws, and updated values of endogenous explanatory variables using simulated results. c. Care arrangement probabilities are reported for married individuals only. The fit for nonmarried individuals (excluding the care from spouse outcome) is similar. d. Standard errors are in parentheses. Bold coefficients indicate significance at 10 percent level or smaller.
e. The factor loadings on the permanent heterogeneity factor in the care arrangements for nonmarried individuals are−0.466 (0.522),−0.357 (0.459), and 0.011 (0.550) for informal care, formal care, and nursing home care respectively. The factor loadings for the time-varying heterogeneity are2.607(0.845),3.947(0.858), and5.689
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Table 6a
Estimation Resultsafor Selected Variablesbfrom the Model with Heterogeneity Outcomes: Medicaid Enrollment and Supplemental Health Insurance
Supplemental Insurancec
Explanatory Variables
Medicaid Enrolled
Private Without LTC
Private With LTC
NH generosity −0.032 −0.032 −0.037
(0.106) (0.081) (0.095)
NH $ loss 0.012 −0.005 0.054
(0.027) (0.077) (0.077)
HCBS $ loss 0.004 −0.018 −0.048
(0.029) (0.017) (0.029)
HCBS $ allowable −0.004 0.090 0.032
(0.042) (0.183) (0.214)
Bed supply −0.003 0.136 0.130
(0.041) (0.028) (0.042)
NH revenue loss −0.032 0.030 −0.043
(0.034) (0.043) (0.052)
Benefit ratio 0.066 0.061 0.085
(0.073) (0.055) (0.096)
HCBS spending 0.084 0.019 −0.078
(0.049) (0.025) (0.067)
Medicare $ change 0.036 −0.114 −0.074
(0.238) (0.099) (0.262)
Lag assets −0.522 0.520 −1.397
(0.684) (0.757) (1.064)
Lag assets squared 0.094 −0.202 0.764
(0.359) (0.377) (0.526)
Lag health 0.063 0.017 0.001
(0.021) (0.026) (0.030)
Lag private insurance without LTC −0.856 1.875 1.259
(0.140) (0.063) (0.383)
Lag private insurance with LTC −1.343 1.488 3.748
(0.763) (0.149) (0.435)
Lag Medicaid enrolled 2.435 0.262 0.974
(0.118) (0.203) (0.556)
Medicaid eligible −0.136 −0.157
(0.886) (0.888)
a. Standard errors are in parentheses. Bold coefficients indicate significance at 10 percent level or smaller. b. Other included exogenous variables are listed in the top two panels of Table 3 and the bottom panel of Table 5.
Table 6b
Estimation Resultsafor Selected Variablesbfrom the Model with Heterogeneity Outcomes: Probability of Any Assets and Gifts, Continuous Assets and Gifts if any
Explanatory Variables Any Assets Any Gifts
ln(Assets) If Any
ln(Gifts) If Any
NH generosity −0.024 −0.020 0.020 0.000
(0.102) (0.072) (0.012) (0.038)
NH $ loss 0.018 −0.016 0.019 −0.005
(0.025) (0.016) (0.006) (0.012)
HCBS $ loss −0.039 0.038 −0.018 −0.003
(0.025) (0.012) (0.006) (0.010)
HCBS $ allowable 0.010 0.100 −0.066 −0.040
(0.172) (0.102) (0.036) (0.052)
Bed supply −0.027 0.034 −0.028 −0.025
(0.031) (0.020) (0.018) (0.017)
NH revenue loss −0.001 −0.028 −0.036 −0.001
(0.034) (0.027) (0.011) (0.021)
Benefit ratio −0.022 0.046 −0.008 −0.047
(0.066) (0.045) (0.016) (0.021)
HCBS spending −0.014 −0.004 −0.018 −0.011
(0.028) (0.019) (0.011) (0.014)
Medicare $ change 0.064 −0.166 0.010 0.028
(0.295) (0.054) (0.026) (0.035)
Lag assets 1.219 0.675 1.619 0.925
(0.604) (0.596) (0.219) (0.718)
Medicaid enrolled −0.411 −0.637 −0.718 0.138
(0.106) (0.084) (0.047) (0.085)
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Table 6c
Estimation Resultsafor Selected Variablesbfrom the Model with Heterogeneity
Outcomes: Care Arrangement If Married and Not Married
If Married If Not Married
Explanatory Variables
Spousal Care
Informal Care
Formal Care
Nursing Home
Informal Care
Formal Care
Nursing Home
NH generosity 0.031 −0.108 0.147 −0.003 0.023 0.110 0.186
(0.104) (0.085) (0.104) (0.106) (0.131) (0.135) (0.131)
NH $ loss −0.029 −0.017 −0.021 −0.015 0.057 0.105 0.067
(0.029) (0.030) (0.033) (0.032) (0.062) (0.083) (0.074)
HCBS $ loss 0.002 −0.001 0.072 0.003 −0.060 −0.079 −0.031
(0.028) (0.027) (0.032) (0.030) (0.051) (0.083) (0.073) HCBS $ allowable −0.069 −0.008 −0.105 0.435 0.066 −0.131 0.116
(0.294) (0.196) (0.272) (0.300) (0.257) (0.294) (0.277)
Bed supply 0.062 0.014 0.042 0.046 −0.037 −0.018 0.026
(0.059) (0.054) (0.068) (0.058) (0.039) (0.046) (0.041) NH revenue loss 0.006 −0.054 −0.035 −0.046 −0.013 −0.035 −0.102
(0.056) (0.062) (0.066) (0.056) (0.046) (0.052) (0.048)
Benefit ratio −0.036 −0.135 0.011 0.029 −0.096 0.220 0.001
(0.119) (0.110) (0.131) (0.137) (0.111) (0.142) (0.125)
HCBS spending −0.088 0.030 0.031 0.059 0.068 0.004 0.054
(0.078) (0.056) (0.083) (0.074) (0.053) (0.092) (0.073)
The
Medicare $ change −0.324 −0.057 0.000 0.078 −0.067 −0.043 0.066 (0.436) (0.280) (0.410) (0.387) (0.227) (0.259) (0.238) Lag assets −0.176 −1.107 −4.760 −1.821 −0.766 −0.135 −0.974
(0.874) (0.898) (1.039) (0.904) (0.780) (0.692) (0.695)
Lag assets squared 0.089 0.507 2.251 0.857 0.339 0.034 0.393
(0.433) (0.448) (0.517) (0.450) (0.395) (0.363) (0.350)
Health 0.746 0.724 0.836 0.840 0.549 0.708 0.711
(0.201) (0.200) (0.205) (0.204) (0.033) (0.035) (0.035) Health * health
improved
0.119 0.132 0.185 0.136 0.057 0.097 0.103
(0.316) (0.315) (0.323) (0.322) (0.046) (0.044) (0.044) Health * health declined
a little
−0.066 −0.109 −0.055 −0.145 0.016 −0.005 −0.005 (0.215) (0.215) (0.221) (0.223) (0.034) (0.035) (0.035) Health * health declined
a lot
−0.239 −0.209 −0.194 −0.187 −0.073 −0.087 −0.012 (0.201) (0.201) (0.205) (0.205) (0.037) (0.036) (0.036) Private insurance
without LTC
0.060 −0.091 0.383 −0.089 −0.054 0.143 −0.004 (0.464) (0.378) (0.663) (0.613) (0.226) (0.402) (0.452) Private insurance with
LTC
0.181 0.075 0.260 0.643 −0.086 −0.209 0.412
(0.904) (0.745) (0.850) (0.852) (0.540) (0.892) (0.626)
Medicaid enrolled 0.009 0.045 1.383 1.498 0.044 0.760 1.250
(0.827) (0.697) (0.794) (0.768) (0.302) (0.430) (0.406)
Gardner and Gilleskie 1111
Table 6d
Estimation Resultsafor Selected Variablesbfrom the Model with Heterogeneity Outcomes: Continuous Health Index and Probability of Death
Explanatory Variablesc Level of Health Probability Of Death
Health 0.394 0.056
(0.014) (0.025)
Private insurance without LTC −0.051 0.131
(0.041) (0.084)
Private insurance with LTC −0.123 0.235
(0.060) (0.221)
Medicaid enrolled 0.085 −0.230
(0.066) (0.174)
Spousal home care 0.491 2.203
(0.171) (0.319)
Informal home care 1.386 2.002
(0.107) (0.146)
Formal home care −0.803 2.833
(0.353) (0.212)
Nursing home care 0.580 2.772
(0.379) (0.147)
Health * spousal home care −0.175 −0.251
(0.029) (0.068)
Health * informal home care −0.226 −0.099
(0.020) (0.030)
Health * formal home care 0.425 −0.119
(0.032) (0.031)
Health * nursing home care 0.379 −0.084
(0.031) (0.026)
Health * health improved 0.049
(0.013)
Health * health declined a little −0.051
(0.015)
Health * health declined a lot −0.043
(0.015)
a. Standard errors are in parentheses. Bold coefficients indicate significance at 10 percent level or smaller. b. Other included exogenous variables are listed in the top two panels of Table 3 and the bottom panel of Table 5.
c. In the Health equation, all values of explanatory variables are lagged to explain current period health. Contemporaneous values of the explanatory variables explain Death at the end of the period.
