Informal Care and Formal Home Care Use in Europe and the United States

Alberto Hollya , Thomas M. Lufkina , Edward C. Nortonb , Courtney Harold Van Houtvenc Version date : July 1, 2010

This is a preliminary version. Comments are most welcome. Please do not quote without the authors’explicit consent.

a

b c

Institute of Health Economics and Management and Faculty of Business and Economics, University of Lausanne

Department of Health Management and Policy and Department of Economics, University of Michigan Center for Health Services Research in Primary Care, Durham Veterans A¤airs Medical Center and Department of Medicine, Division of General Internal Medicine, Duke University Medical Center

Correspondence: Alberto Holly [email protected] University of Lausanne, IEMS, Vidy, CH-1015 Lausanne, Switzerland Tel: +41 21 692 3482, Fax: +41 21 692 3665

Abstract The provision of informal care by adult children is an important form of longterm care for older individuals and can reduce the use of medical services if they are substitutes. We examine how informal care by all children and formal care interact, which is critically important given demographic trends and the many policies proposed to promote informal care. The purpose of this study is to compare the United States and European countries, by merging data from the U.S. Health and Retirement Study (HRS) with its European counterpart, the Survey of Health, Ageing and Retirement in Europe (SHARE). We argue that the institutional setting is di¤erent across the Atlantic, as European home care schemes are predominantly publicly run, whereas the market plays a bigger role in the United States. We use a fexible simultaneous equations approach that allows for a di¤erent relationship between informal and formal home care in the two regions, using copulas. We …nd that in Europe it is predominantly the supply of formal home care that in‡uences children’s decisions to provide informal care, while in the United States parents’decisions to use formal home care are based on the amount of informal care received and the amount of informal care provided by children is dependent on the amount of formal care.

1

Introduction

The provision of informal care by adult children is an important form of long-term care for older individuals. Informal care can reduce the use of formal health care if they are substitutes and enhance the use if they are complements. Rapid aging of populations in developed countries make this question of critical importance to health policy. Demand for informal care is growing with the ranks of the elderly, while the supply is shrinking given smaller average family size and increased labor force participation by women. Therefore, it is critically important to understand the relationship between informal and formal care to predict the likely e¤ects on future health care expenditures. We address how informal care by all children and formal home care interact, building on recent research that has highlighted the importance of informal care (Van Houtven and Norton, 2004, 2008; Bolin et al., 2008). This published work demonstrated that informal care is a substitute for formal long-term care in the United States and in Europe. The results, however, are mixed for other types of formal care. Van Houtven and Norton (2008) …nd that informal care reduces 1

inpatient expenditures in the U.S. while Bolin et al. (2008) …nd a complement relationship for Europe. Comparing the U.S. and Europe is challenging because of the large di¤erences in relevant institutions. The three published papers all modelled informal care and formal care simultaneously, and used instrumental variables to obtain consistent estimates in the face of endogeneity. Furthermore, the papers focused on how informal care a¤ects formal care, not the other way around. A close examination of the institutions in both Europe and the United States leads us to question this assumption. Therefore we propose a model that ‡exibly allows for either case and let the data decide how best to model the relationship. In Europe formal home care is mainly provided by public or not-for-pro…t institutions. In general, provision of care is only dependent on need and not on income or wealth. Therefore individuals in poorer health will use the services provided to them at low or no cost by the state or services covered by their insurance. They may turn to their children and relatives for support in the form of informal care only in cases where this formal home care is not su¢ cient. However because most European countries face budget constraints, the provision of services is limited and only a part of the needs will be met. In some cases formal care decisions are made by the authorities after explicitly accounting for the availability of informal care. Individuals who can bene…t from informal care provided by their children might not receive as much formal care as those who do not have children who can take care of them. These two e¤ects go in opposite directions. It is therefore not clear, in Europe, whether it is the amount of informal care that in‡uences formal care provision or the opposite In the United States however, publicly provided home care is much more limited, generally being available to individuals who are permanently disabled or homebound (Medicare) or meet strict asset limitations (Medicaid). These public programs do not typically account for the availability of informal care available to a parent. For this reason it may be that adult children in the U.S. wait to see if formal care will be provided publicly, and then alter their own supply decisions accordingly. In addition, given that publicly-provided home care in the U.S. is quite limited compared to Europe, the private formal home care market is much more developed there. Formal home care can be purchased privately, or, to a much smaller extent, can be …nanced through private long-term care insurance plans (10% of persons age 65 and over have long-term care insurance, Finkelstein and McGarry, 2006). Thus, the existence of a private market means that potential caregivers have more ‡exibility. In the case of parents covered under long-term care insurance, children can decide on the amount of informal care to provide, taking into account the formal home care bene…t available to the parent. Nevertheless, if there is no

2

long-term care insurance and no Medicare or Medicaid coverage, the purchase of long-term care can be very costly. Hence, it is very likely that parents will purchase formal care services only if they do not receive help from their children. Thus, informal caregivers in the U.S. will consider the potentially high cost of formal care when making their own informal care decisions, because formal care most likely will be …nanced by the parent or the parent’s family, which in turn may a¤ect a child’s bequest. In both the U.S. and European settings, the simultaneity of the care decisions between parents and children implies endogeneity in the model. We expect there to be di¤erences in the way informal care and formal care decisions are made in the two settings, but we are agnostic about the direction of causality in our estimation procedures. Using the Survey of Health, Ageing and Retirement in Europe (SHARE) and the U.S. Health and Retirement Study (HRS) we test the hypothesis that Europeans and Americans behave similarly by explicitly allowing the direction of causality to di¤er between Europe and the United States with a simultaneous equations model based on copulas. This allows to model the variables of interest, informal and formal home care, as two-part margins with generalized gamma distributions in the positive part, thus accounting for skewness and a large mass at zero, while at the same time permitting a ‡exible dependence structure between them. The results for the United States imply that informal care by the recipient’s children reduces the probability of home health use, while in Europe it is rather the formal care use of the parent that is being taken into consideration by children when deciding to provide informal care. Among users of care, we …nd that the amounts of the two types of care are much more in‡uenced by each other in the U.S. than in Europe, and that the amount of formal care more strongly in‡uences the amount of informal care than the reverse, on both sides of the Atlantic.

2 2.1

Conceptual framework The relationship between informal and formal care

Prior studies on the relationship between formal and informal care in the United States do not seem to de…nitively establish whether the two types of care are substitutes or complements. For example Langa et al. (2001) …nd that people with greater social support have a higher probability of entering a nursing home and that paid home care tends to be used predominantly by elderly living with their children, 3

while Kemper (1992) …nds that the availability of family caregivers decreased the reliance on formal care and increased the use of informal care. Most of these earlier studies do not take into account the endogeneity of formal and informal care. The few studies that control for endogeneity (Lo Sasso and Johnson, 2002; Greene, 1983) suggest that informal care and formal care are substitutes. More recently, Van Houtven and Norton (2004) analyze the e¤ect of informal care by children on formal care use. Their model is based on the parent’s optimization process given her children’s choice of informal care supply: the children …rst determine their optimal level of informal care provision, and then parents choose optimally their formal care consumption, based on the amount of informal care that they receive. They …nd that informal care reduces home health care use, using data from the HRS and the Asset and Health Dynamics Among the Oldest-Old Panel Survey (AHEAD). Furthermore they detect endogeneity and use instrumental variables to instrument for informal care. There is a growing literature on the relationship between informal care and formal care in Europe. Using SHARE, Bolin et al. (2008) apply the same model as Van Houtven and Norton (2004) to the European context. More formally, they use a probit model to analyze the probability of home care use, one measure of formal care. The quantities are then estimated using OLS, conditional on positive use. They …nd that endogeneity is detected in the model of home health care. Furthermore they show that, without correcting for endogeneity, informal care is a complement to formal home care, whereas after taking endogeneity into account they become substitutes. All of these studies have assumed the same direction of causality from informal to formal care. However, it is not clear a priori that it is the provision of informal care by children that has an impact on their parents’formal care use, since di¤erent institutional settings and markets for formal home care should imply di¤erent incentives both for informal caregivers and for care recipients.

2.2

Theoretical framework

The literature takes three directions to model informal care by children. The …rst de…nes a family utility function, as in Pezzin et al. (1996). This is rather restrictive, as it imposes that parents and children have the same objective function, which is rather unlikely, especially if they do not live in the same household. The second considers the strategic interactions between the children and treats the parent’s utility as a public good to be maximized by all children (for example Checkovich and Stern, 2002), while the third models the relationship between parents and children as two agents, either by letting only one child provide care (for example 4

Hiedemann and Stern, 1999) or by explicitly imposing only one parent and one child (for example Pezzin and Schone, 1999; Sloan et al., 1997). We will pursue in this last direction for the theoretical framework, by building on a model developed by Chiappori (1992). For simplicity we will also restrict ourselves to the case of only one parent and one child for the theoretical model, but this framework could be extended to allow for more children. The child maximizes her utility function subject to time and budget constraints. Her utility is a function of her own consumption C c , her leisure L and the amount of informal care IC provided to the parent, given her own characteristics K c , such as demographic characteristics, employment status and distance from the parent and the parent’s health status H and dependence level D. There are two justi…cations for the inclusion of informal care in the child’s utility function. An altruistic child is concerned about her parent’s well being, which is in‡uenced by the amount of informal care provided. In this case informal care has an indirect e¤ect on the child’s utility level. However informal care can also have a direct e¤ect on the child’s utility if she feels satisfaction from providing care. This e¤ect is often referred to as "process utility", as in Brouwer et al. (2005). The child must allocate her time between work W , leisure L and the provision of informal care; and her resources, that is labor income and a transfer from the parent (either positive if the parent compensates the child for her informal care provision or negative if the child substitutes informal care provision by a payment aimed at buying other types of care on the market1 ) between consumption and the costs associated with the provision of care. Her optimization problem is thus to maximize her utility U c = U c (C c ; L; IC; K c ; H; D), subject to a time constraint W + L + IC T and a budget constraint C c + pIC IC !W + S, where T is the total time endowment of the child, pIC is the opportunity cost of providing informal care (including direct costs), ! is the wage rate and S is a (non-monetary) transfer from the parent to the child. The parent maximizes her own utility function subject to a budget constraint. Her utility is a function of her own consumption C p , including insurance, and utilization of both informal and formal care F C, given K p , her demographic characteristics and health and dependence levels, H and D. In most applications the insurance status is endogenous. This e¤ect is however weakened here since the individuals considered are over 70 and are likely to have enrolled in their insurance plan before 65. The same arguments as before apply regarding the direct and indirect e¤ects of care, which could have an indirect e¤ect through the improvement of the health status or a direct e¤ect as the parent bene…ts from receiving care and attention from children. Because we are concerned with retired individuals, we can assume that the parent’s income Y is …xed. She maximizes 1

See Bonsang (2007) for a discussion on intergenerational time and …nancial transfers.

5

her utility U p = U p (C p ; IC; F C; K p ; H; D) subject to her own budget constraint C p + pF C F C Y S. The solution to this problem has the form: IC = fIC (F C; Y; C p ; C c ; T; L; K p ; K c ; H; D) F C = fF C (IC; Y; C p ; C c ; T; L; K p ; K c ; H; D) The two types of care are therefore jointly determined and will thus have to be estimated simultaneously.

2.3

Institutional setting

Institutional factors are a major determinant of informal and formal care use, but since welfare systems are more developed in Europe than in the United States (Börsch-Supan, 2007), this leads to heterogeneity on the supply side of the informal and formal care markets. In the United States, publicly provided home care is limited. The Medicare program provides treatment to the elderly in need of acute and care and short-term rehabilitation, but has no home health and nursing home care for those who are not severely impaired or homebound. For those who meet strict …nancial criteria, the Medicaid program covers the costs of care after copayments and deductibles. Therefore, there is no universal right to public services in the United States. However these public programs do not typically account for the availability of informal care available to a parent. For this reason it may be that adult children in the U.S. wait to see if formal care will be provided publicly, and then take their own supply decisions accordingly. In addition, given that publicly provided home care is quite limited, the private formal home care market is much more developed in the U.S. Formal home care can be purchased privately, or, to a much smaller extent, can be …nanced through private long-term care insurance plans (10% of persons aged 65 and over have long-term care insurance, as mentioned by Finkelstein et al., 2005). This implies that access to professional services is easier, albeit only for those who can a¤ord it. The existence of a private market means also that potential caregivers have more ‡exibility. In the case of parents covered under long-term care insurance, children can decide on the amount of informal care to provide, taking into account the formal home care bene…t available to the parent. Nevertheless, if there is no long-term care insurance and no Medicare or Medicaid coverage, the purchase of formal home care can be very costly. Hence, adult children who know their parent’s …nancial situation, insurance and disability status will know that the formal care options are limited, and will factor these limitations into their own informal care supply decisions. Clearly, a few European countries have an emerging private 6

formal home care market (such as Italy which has a large ‘grey’market for formal home care using immigrant labor, as described by Lamura et al., 2006), but in all cases these markets are not as developed as in the U.S. This also implies that in the U.S. it is more likely the use of formal care that in‡uences the amount of informal care supplied by the children. Most European countries o¤er public provision of health care, either through a national health service, a social insurance scheme or a compulsory private insurance system. All of these systems include some long-term care as part of the basic coverage, and formal home care is mainly provided by public or not-for-pro…t institutions. For example, Germany has a social insurance system covering about 90% of the population, which includes long-term care provision. Bene…ts are granted after a medical assessment of needs and are distributed in cash, in kind, or a combination of the two. Austria also has a system of long-term care allowances based on need of care and independent of income or wealth. In Spain, some autonomous regions provide home care free of charge, and so there are large disparities across regions. The Netherlands have a national insurance scheme that covers a (large) share of the costs related to formal care (Portrait et al., 2000), and in Sweden, most care for the elderly is …nanced through taxes, and provided by public organizations. For a more detailed description of the di¤erent health care systems, see OECD (2005). In general, provision of care is only dependent on need and not on income or wealth, which implies that those who need care should not worry about the …nancial consequences of receiving formal home care. This could have an in‡uence on the informal care decisions of children, as they could decide to provide care to their parents only after observing the amount of formal care provided to them, and thus this would imply that formal care that in‡uences the amount of informal care provided by children. However in most European countries, social insurance schemes are under a lot of pressure to balance their budget, and thus the provision of services is limited and only the needs of the more dependent elderly will be met. In some cases formal care provision decisions are made by the authorities after explicitly accounting for the availability of informal care, as in the Netherlands, where the needs of the elderly are assessed and the individual is generally put on a waiting list (Portrait et al., 2000). Supplementary or complementary insurance schemes provide additional coverage and allow for more use of services. This implies that individuals who can bene…t from informal care provided by their children will not receive as much formal care as those who do not have children who can take care of them. Using the European Community Household Panel (ECHP), Viitanen (2007) shows that increased subsidies to formal home care lead to a decrease in the provision of informal care outside of the carer’s household, which is

7

consistent with both hypotheses, either that in Europe children reduce their care provision if their parents receive more formal care, or that supply constraints play a role in the relationship between formal and informal care. Another key di¤erence between Europe and the U.S. is the amount of public support for informal caregivers. In some European countries informal caregivers are paid or receive pension contributions if they provide informal care in lieu of active labor force participation. Payments can be substantial, depending on the severity of the care recipient. By contrast, in the U.S. informal caregivers at most receive a modest tax credit, and very few actually do. Hence, based on di¤erences in compensation for informal caregivers, the motivations to provide informal care are also potentially very di¤erent across settings. Rather than from the state, in the U.S. any …nancial motivation to provide informal care will be due to the potential …nancial gains provided by the parent (consistent with a strategic bequest or exchange motive). Although it is illegal to divide bequests unevenly across children in most European countries, a strategic bequest or exchange motive may similarly exist (Angelini, 2007). There is however also a much higher likelihood that informal caregivers will be compensated directly. Compounding this di¤erence, is that long-term care costs in the U.S. are much more likely to be both …nanced by the parent and more likely to be substantial. Thus in the U.S. informal caregivers will consider the potentially high cost of formal care when making their own informal care decisions, since formal care most likely will be …nanced by the parent or the parent’s family, and thus will reduce the amount of eventual bequests. In conclusion, the direction of causality is not clear a priori, and we will therefore specify the most possible ‡exible model, in order to account for the di¤erent possible relations between informal and formal home care.

3

Econometric speci…cation

The variables of interest are hours of informal care and formal care. Both take only non-negative values and have skewed distributions with a large mass at zero. In order to take this into account, we model our variables of interest using use hurdle or two-part models (Duan et al., 1983). This is one of the most common approaches to deal with corner solution outcomes (Wooldridge, 2002, p. 536) in the health economics litterature. This is also the approach chosen by Van Houtven and Norton (2004) and Bolin et al. (2008), who studied the e¤ect of the number of hours of informal care on di¤erent types of formal care use. As the informal care variable was endogenous, they used used instrumental variables (IV), which did

8

not allow exploration of the reverse e¤ect of formal care on informal care. Moreover, they both only used a binary indicator of formal home care use, and were thus limited to an IV-probit estimator for this type of formal care. We extend the analysis by using a continuous variable of formal home care and simultaneous equations. This approach has two main advantages. First, it allows to study the direct e¤ects of both informal care on formal care, and vice versa, thus ensuring that the simultaneity of the parents and children’s decisions is taken into account. Second, it also accounts for potential common unobservables such as health characteristics (Charles and Sevak, 2005) or preferences for care (Bonsang, 2009) that could simultaneously a¤ect the use of formal and informal home care. This is achieved by imposing an unobserved dependence between the two types of care in order to avoid possible endogeneity biases. As we are in a simultaneous equations context, we extend the univariate hurdle model to the bivariate case. Our approach is close to the work of Yen et al. (2009), who extend the censored model (Tobit type I) model to the bivariate case, using generalized log-Burr distributions, and Deb et al. (2009), who develop another version of the bivariate hurdle model, using standard gamma distributions for the second part. The main di¤erence with our model is that theirs does not allow for a simultaneous equations speci…cation. As in the univariate case, the …rst part is a probit predicting the probability of having a positive number of hours of care. It is speci…ed as: Pi (yi > 0) = (yj

0 i

+ x0

0 i)

(1)

where yi and yj are the number of hours of informal and formal care (i; j 2 fIC; F Cg ; i 6= j), ( ) is the standard normal cumulative distribution function, x is the matrix of covariates, including an intercept, and i0 and the i0 ’s are coe¢ cients to be estimated. In the second part, we use the generalized gamma distribution in order to account for the skewness of the informal care and home care variables, in stead of the more widely used regression with a log transformed variable. Manning et al. (2005) have advocated the use of the generalized gamma distribution in health economics, because it includes the standard gamma, lognormal, exponential and Weibull distributions as special cases, and it is more robust to misspeci…cation than them. The parametrization they use is the same as Stata’s (StataCorp LP, 2009b, p. 361). It is preferred over the standard parametrization due to its numerical stability in a maximum likelihood estimation (Pentsak, 2007, p. 237). The probability density function is speci…ed as a function of the parameters i+ , i+ , i and i that are to be estimated: i

gi yi ;

+ i ;

+ i ;

i;

i jyi

> 0; x; yj =

i yi

9

p

i i

( i)

exp [zi

p

i

ui ]

if

i

6= 0 (2)

where i = j i j 2 , zi = sign( i ) ln(yi ) yj i+ x0 i+ i , and ui = i exp (j i j zi ), and with i; j 2 fIC; F Cg ; i 6= j. It simpli…es to the standard gamma distribution when = , to the Weibull when = 1, to the exponential when = = 1 and the lognormal when tends to zero, and in this case we have: gi yi ;

+ i ;

+ i ; 0;

i jyi

> 0; x; yj =

1 p

i yi

exp zi2 2

2

(3)

The cumulative density function Gi associated with gi is:

Gi yi ;

+ i ;

+ i ;

i;

i jyi > 0; x; yj =

Zyi

8
0; x)dt =

0

i i i

>0 =0 0jx; yj ) gi (yi jyi > 0; x; yj ) if yi > 0

fi (yi jx; yj ) =

(5)

For maximum likelihood analysis it is however more convenient to write this density as: fi (yi jx; yj ) = [P (yi = 0jx; yj )]1(yi =0) [P (yi > 0jx; yj ) gi (yi jyi > 0; x; yj )]1(yi >0) (6) In our case, with fi (yi ;

0 i;

6= 0, we obtain:

0 + i; i ;

or equivalently when fi (yi ;

0 i;

0 + i; i ;

+ i ;

i;

i jx; yj )

"

=

yj

0 i

x0 i

yj

0 i

+ x0

0 i

i

yj

0 i

x0

1(yi =0)

0 i

#1(yi >0) p exp zi i ui (7) p i yi i ( i)

= 0: + i ; 0;

i jx; yj )

=

yj i0

10

+

0 i

1(yi =0)

x0 i0

exp [zi2 / 2] p i yi 2

1(yi >0)

(8)

The corresponding cumulative distribution function is given by: Fi (yi ;

0 i;

0 + i; i ;

+ i ;

i;

i jx; yj )

=

= Pi (yi = 0jx) + Pi (yi > 0jx)

=

8 < :

( ( (

yj i0 yj i0 yj i0

x0 i0 ) x0 i0 ) x0 i0 )

+ + +

Zyi

1 Zyi

fi (tjx)dt

gi (tjt > 0; x)dt

0 (yj i0 (yj i0 (yj i0

+ x0 + x0 + x0

0 i ) I ( i ; ui ) 0 (zi ) i) 0 I ( i ; ui )] i ) [1

if if if

i i i

>0 =0 0)1(yjn >0)

[Ci (Fi (y1n ); Fj (0); )

fi (yi )]1(yin >0)1(yjn =0)

[Cj (Fi (0); Fj (yjn ); )

fj (yjn )]1(yin =0)1(yjn >0)

[C(Fi (0); Fj (0); )]1(yin =0)1(yjn =0)

(12)

and log likelihood: `n = 1(yin > 0)1(yjn > 0) [ln (Cij (Fi (yin ); Fj (yjn ); )) + ln (fi (yin )) + ln (fj (yjn ))] + 1(yin > 0)1(yjn = 0) [ln (Ci (Fi (y1n ); Fj (0); )) + ln (fi (yi ))] + 1(yin = 0)1(yjn > 0) [ln (Cj (Fi (0); Fj (yjn ); )) + ln (fj (yjn ))] + 1(yin = 0)1(yjn = 0) ln (C(Fi (0); Fj (0); )) (13) There are many di¤erent copula functions, each with di¤erent properties. We experimented with the Clayton, Farlie-Gumbel-Morgenstern (FGM), Frank and Gumbel copulas, which all allow di¤erent dependence structures. As discussed by Trivedi and Zimmer (2005), the Clayton copula only supports positive dependence and displays strong left tail and weak right tail dependence, the FGM copula is suitable only for limited positive or negative dependence, the Frank copula allows both negative and positive dependence and the Gumbel copula only allows positive dependence and displays strong right tail and weak left tail dependence. The distribution functions and densities of all these copulas are reported in the Appendix. The parameters i0 ; i0 ; i+ ; i+ ; i ; i ; j0 ; j0 ; j+ ; j+ ; j ; j and are all estimated together by direct maximum likelihood, using Stata 11’s modi…ed Newton-Raphson algorithm with numerical derivatives (StataCorp LP, 2009a, p. 1069).

4

Data and variables

We combine data from both SHARE and HRS. SHARE was designed to be comparable to HRS (and to the English Longitudinal Study of Ageing (ELSA)). The data from SHARE were collected in 11 European countries and Israel in 2004/2005 and cover a sample of non-institutionalized persons over 50 as well as their partners. For a more detailed description of SHARE, we refer the reader to Börsch-Supan 12

and Jürges (2005) and to Juster and Suzman (1995) for an overview of HRS. The data from Greece and Switzerland were discarded because a problem during the collection of the data made the variables on formal home care unusable. Because it is di¢ cult to assess the e¤ect of help provided by the spouse or partner for individuals living as couples and since some questions are only asked at the household level (in particular those regarding help provided by individuals living outside the household, but also …nancial questions for example), the analysis is restricted to individuals who live alone (single, divorced, widow or separated), are not institutionalized and have at least one child (o¤spring, stepchild or adopted). We further restrict the analysis to individuals aged 70 or over since people under that age are not frequent users of home care. Moreover this restriction makes the sample comparable to the one used in Van Houtven and Norton (2004). Most variables are directly comparable between the two surveys, however it is not the case of our main variables of interest. In the HRS, there is a question about the use of formal home care in the "health care utilization" section (section N). The question only asks whether the respondent has had any medically trained person at home to help them since the last interview or the last two months if it is a …rst interview. There is unfortunately no follow-up question on the amount of formal home care received. The HRS has another section on helpers (section G), and it is from there that we recover the relevant information, by considering that helpers who were paid are professionals providing formal home care. The recall period is one month in this case. The informal care variables is constructed in the same way, with one month recall, this time by using helpers who are children (natural children, stepchildren or adopted children) or grandchildren of the respondent who do not live in the same household. SHARE contains similar information on informal care. The recall period however is 12 months, so we divide the number of hours by 52 in order to have hours of care per week, which is easier to understand than hours per month or even by year. The variables from HRS are adjusted accordingly. The selection criteria are the same in both cases. The formal home care variable is the total number of hours of "professional or paid nursing or personal care" and "professional or paid home help, for domestic tasks that [the respondent] could not perform [herself] due to health problems" in the last 12 months (Survey of Health, Ageing and Retirement in Europe, 2005, question HC032). Here again, we divide the number of hours in order to account for the di¤erent recall periods. The formal care variable is thus not de…ned exactly in the same way in both samples. The explanatory variables are divided into …ve categories. The …rst is composed of demographic and socioeconomic characteristics of the respondent, such as age, the number of years of education, income and wealth categories These last to variables represent quintiles computed by country, in order to avoid cost of liv-

13

ing di¤erences. Insurance status (Medicare or Medicaid bene…ciary and long-term insurance status for the Americans; and complementary and/ or supplementary insurance for the Europeans) also belongs to this group. The insurance variables serve as exclusion restriction, since they are only included in the formal care equations. Racial variables are widely used in studies on the United States, but they are not collected in Europe, and thus were not included. The second is composed of the health variables such as the number of limitations in (instrumental) activities of daily living (I)ADLs. IADLs are activities related to independent living and include cooking, managing money, shopping for groceries or personal items, performing housework, and using a telephone. This variable ranges from 0 to 7. ADLs are activities related to personal care and include bathing or showering, dressing, getting in or out of bed, using the toilet, and eating. This variable is coded from 0 to 6. The health variables also include the number of chronic conditions and self-reported health. The number of chronic conditions is an index which takes values from 0 to 6. It includes physical conditions such as a heart attack or any other heart problem, a stroke or cerebral vascular disease, high blood pressure or hypertension, diabetes, cancer, a chronic lung disease and arthritis. Self-reported health is a subjective measure of well-being. The respondent is asked to assess her own health on a scale between 1 (excellent) and 5 (poor). We also include a binary variable taking the value 1 if there was a proxy respondent during the interview. This variable is a measure of mental health (see for example Van Houtven and Norton, 2004), because it controls for cognitive limitations. The third group is composed of behavioral variables indicating whether the respondent is a current smoker, and the frequency with which she drinks (0, never to 6 almost every day). The fourth group is made of variables concerning the children as informal caregivers, such as the number of children, the number of children living close (under 10 miles in the U.S. and under 25 kilometers away from the respondent’s house in Europe), and the number of children working. These variables also serve as exclusion restrictions, as they do not appear in the formal care equations. Finally the last group includes geographical dummies, taking the value 1 if the interview was conducted in the United States, in Northern (DK, SE), Central (AT, BE, DE, FR, NL), or Southern (ES, IT) Europe respectively and 0 otherwise. The omitted category in the analysis is the U.S. See Table 1 for a complete list of all the variables, along with descriptive statistics, Table 2 for more details of the care variables and Survey of Health, Ageing and Retirement in Europe (2005) and Survey of Health, Ageing and Retirement in Europe (2009) for a more detailed description of the variables. –Insert Tables 1 and 2 about here – 14

From Table 2 it appears that Europeans use more care on the extensive margin, while Americans have a bigger consumption of care on the intensive margin. We see that about 36% of Europeans use informal care and 28% use formal care, as opposed to 17% and 7% respectively for Americans. On the other hand, the average number of hours of care for users are smaller in Europe than in the U.S. with about 9 hours of informal care and 6 hours of formal home care per week for Europeans and 15 and 31 hours respectively for Americans.

5

Results and discussion

Since all models we have estimated have the same number of parameters, it is easy to choose the one with the best …t without the help of penalized log likelihood criteria such as the Akaike or Bayes-Schwarz information criteria (AIC and BIC, respectively). We simply choose the model with the biggest log likelihood. The preferred speci…cation is the Gumbel copula, with a log likelihood of 6698:97, as can be seen in Table 3. –Insert Table 3 about here – The bivariate Gumbel copula takes the form C(u; v; ) = exp

h

( ln (u)) + ( ln (v))

i1=

(14)

The dependence parameter is restricted to the region [1; 1), which implies that the Gumbel copula only allows positive dependence. Moreover, in this case we have C(u; v; 1) = = uv C(u; v; 1) = M = min(u; v) where is the product copula, which corresponds to stochastic independence, and M is the Fréchet-Hoe¤ding upper bound (Nelsen, 1999, p. 9). The Gumbel copula does not however attain the Fréchet lower bound W . The three copulas , M and W are important in understanding the dependence of two variables in empirical work, as it can be shown that for every copula C(u; v; ), we have W C(u; v; ) M . Therefore the ability of a given copula to represent di¤erent 15

degrees of association can be examined in terms of the extent to which it covers the interval between the lower and upper Fréchet bounds. As a consequence the Gumbel copula can only model positive dependence. This …nding was con…rmed when using copulas that allow both negative and positive dependence, like the FGM or Frank copulas. We conclude that informal and formal care have a positive association, with an estimated value of of 1:263 for the Gumbel copula. We found that this value was statistically di¤erent from 1 at the 5% level, which indicates that our copula does not reduce to a product copula, and therefore that the two variables of interest are not independent. This con…rms the presence of endogeneity, and justi…es our simultaneous estimation of the two care equations. It is not easy to compare di¤erent values of for di¤erent copulas, so other measures of association like Kendall’s tau are used in stead. It is de…ned as the probability of concordance minus the probability of discordance between two independent draws from a bivariate distribution (Nelsen, 1999, p. 126), and for the Gumbel copula we can compute it from with = 1 1= . As = 1:080 which gives = 0:074 in our case. This result could be expected, given that both types of care would be similarly in‡uenced by unobserved components of the health state and dependence level of the recipient of care. Moreover, as was mentioned earlier, the Gumbel copula displays strong right tail and weak left tail dependence, and its density is totally positive of order 2 (TP2) (Joe, 1997, p. 142). This implies that large (small) values of informal care hours are associated with large (small) values of formal home care hours. This result is consistent with the idea that the elderly with small needs use little or no formal or informal care, while those with the largest needs do not rely on only one source of care, and thus use a lot of both informal and formal care. This however does not imply that the two types of care are not substitutes, as will be seen below. Estimates for the parameters and give = 0:628 and = 1:436 for informal care and = 0:474 and = 1:412 for formal care. Tests of = 1, = 1 and = are all rejected at the 1% level, which indicates that for both informal and formal care the generalized gamma does not reduce to the standard gamma, lognormal, exponential or Weibull distributions in the continuous part. Parameter estimates ( i0 ; i0 ; i+ ; i+ ; j0 ; j0 ; j+ ; j+ ) are reported in Tables 6, 7, 8 and 9, and Tables 4 and 5 are simpli…ed versions, showing only the coe¢ cients on the care variables. –Insert Tables 4 and 5 about here – As far as the care variables are concerned, it can be seen from the hurdle part ( i0 ; j0 ) of Tables 4 and 5 that formal care and informal care are substitutes. Moreover formal care has a much larger e¤ect (approximately twice the size, depending 16

on the copula speci…cation) on the probability of informal care provision in Europe than in the U.S., with coe¢ cients ranging from 0:016 to 0:007 with the Gumbel copula. On the other hand, if we turn to the e¤ect of informal care on the probability that the parent receives formal care, we see a reverse pattern, where the e¤ect is larger in the United States than in Europe, with coe¢ cients of 0:013 and 0:021 for Europe and the U.S., respectively, in the Gumbel model. This seems to con…rm our initial intuition that European children take the amount of formal care provided to the parent into account before making their caregiving choices, while American parents seek formal care when the amount of informal care that they receive does not cover their needs. The second part of the hurdle speci…cation ( i+ ; j+ ), the continuous part, gives less striking results. First it appears that the substitution e¤ects are larger in the U.S. than in Europe, with coe¢ cients of 0:007 for both types of care in Europe, and 0:022 and 0:014 for formal and informal care respectively in the United States. The second observation is that the Clayton, FGM and Frank speci…cations give a positive, non statistically signi…cant coe¢ cient for the e¤ect of amount of formal care on the hours of informal care in Europe, while the Gumbel model gives a statistically signi…cant result (at the 10% level). The same holds for the e¤ect of formal care on informal care, still in Europe, the only di¤erence being that the Gumbel no longer gives a signi…cant result. This last result con…rms the …ndings of (Bonsang, 2009), who …nds a little or no e¤ect of the intensity of informal care on the use of formal home care by elderly Europeans, depending on the measure of formal care used. Moreover, a similar e¤ect appears in the United States, where the e¤ect of informal care on formal care disapears in the Clayton, FGM and Frank speci…cations. Trivedi and Zimmer (2009) show that the choice of a copula is important in order to capture the dependence structure, and in this is veri…ed in our case. As discussed earlier, the fact that the Gumbel copula is the preferred model shows that the informal care variables displays a strong upper tail dependence. This dependence is not properly accounted for by the other three copulas, since the Clayton copula generates dependence in the lower tail but not in the upper tail (Jondeau et al., 2007, p. 251) and the FGM and Frank copula displays no particular dependence patterns. –Insert Tables 6, 7,8 and 9 about here – Results for the other explanatory variables ( i0 ; i+ ; j0 ; j+ ) can be found in Tables 6, 7, 8 and 9. We will only comment the results from the model with the Gumbel copula, since it is the preferred speci…cation. The demographic characteristics of the parent seem to play a bigger role in the hurdle part, as the age variable is positive and signi…cant in the equation of both types of care, while gender only in‡uences the probability that children provide care. The parent’s level of 17

education has a positive impact on the amount of formal care used, which would suggest that more educated care recipients are better at "navigating the system". Income has a negative impact on the probability to receive informal care and a positive impact on formal care provision. However, amon those who receive informal care, richer parents receive more care from their children. Wealth however is not signi…cant in any equation. The health variables, having a proxy respondent, self-rated health (a larger values implies a worse health status), the number of ADL and IADL limitations and the number of conditions enter all equations signi…cantly, with a positive sign , except for our indicator of mental health, having a proxy respondent, which is not signi…cant in the …rst part of the formal care equation. Moreover Self-perceived health does not in‡uence the amount of formal care received, and the number of ADL limitations has no impact on the amount of informal care provided by children. This probably comes from the fact that personal care is mostly provided by more skilled professionals, and also from our aggregated measure of informal care which encompasses di¤erent types of interactions with the parent, ranging from personal care like bathing or getting out of bed, to help with household tasks like cleaning or preparing meals and even help with paperwork or managing bills. The number of conditions only in‡uences the probability to receive any type of care, bet not the quantities. It can be noted that our indicators of health behavior, being a smoker, and the frequency of alcohol consumption, are not signi…cant in any equation. The variables describing the children indicate that proximity is a good predictor of care provision, while for a parent, having more children has a positive impact on the amount of informal care received and on the other hand, more children working imply less hours of care. The insurance variables show that being enrolled in the Medicaid program and having a complementary or supplementary insurance has a positive impact on the probability to receive formal home care, while only Medicare has an impact on the number of hours. It is interesting to note that long-term care insurance does not statistically in‡uence the provision of formal home care. This might be due to the small number of individuals who have such an insurance coverage. Finally we see that Europeans tend to have a bigger probability than Americans to receive both informal and formal home care, but that among the recipients, the Americans tend to bene…t from more hours of care, except for individuals living in the South of Europe, who seem to have patterns of informal care provision comparable to those in the U.S.

18

6

Conclusion

In this paper we analyze the relationship between informal care and formal home care in Europe the United States, by merging two large surveys of the 50+ population, the HRS and SHARE. We show that the two types of care are substitutes, and that endogeneity is detected. Moreover we explain that institutional di¤erences must be taken into account, otherwise the direction of causality between informal care provision and formal home care use could be misspeci…ed. The main di¤erence is that European countries have predominantly public long-term-care schemes, which o¤er their services at little or no cost, and thus are used by more individuals. They are however a¤ected by supply shortages in some areas, and thus Europeans who receive care use on average less formal care than the American elderly in the same conditions. In the United States the sector of home care is more market oriented and thus allows for more ‡exibility. As Americans have to pay more for formal care, it appears that there are fewer recipients of formal care there, and that elderly Americans base their decision to use formal home care services much more on the amount of informal care that they receive than Europeans in the same situation. Moreover, public schemes have di¤erent welfare considerations than privately run services, and thus we see that there are more users of formal and informal care in Europe, while among users, it is in the U.S. that the consumption is bigger. On a more technical note, our results con…rm that using copulas with more ‡exible dependence patterns is useful, and that the speci…c choice of copula should be determined by the dependence structure of the data.

Acknowledgements The authors are listed in alphabetical order. The authors would like to thank Owen O’Donnell and participants of the Health and Labour Economics seminar of the University of Lausanne for helpful suggestions, as well as Jacques Huguenin, Florian Pelgrin, Norma B. Coe, Lucy White, Brigitte Dormont and Michel Mougeot for comments and suggestions on previous versions of this paper. This paper uses data from SHARE release 2.3.0, as of November 13th 2009. SHARE data collection in 2004-2007 was primarily funded by the European

19

Commission through its 5th and 6th framework programmes (project numbers QLK6-CT-2001- 00360; RII-CT- 2006-062193; CIT5-CT-2005-028857). Additional funding by the US National Institute on Aging (grant numbers U01 AG09740-13S2; P01 AG005842; P01 AG08291; P30 AG12815; Y1-AG4553-01; OGHA 04-064; R21 AG025169) as well as by various national sources is gratefully acknowledged (see http://www.share-project.org for a full list of funding institutions). The HRS (Health and Retirement Study) is sponsored by the National Institute on Aging (grant number NIA U01AG009740) and is conducted by the University of Michigan.

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Appendix A

Copula functions

Clayton copula C(u; v; @C(u; v; @u @C(u; v; @v 2 @ C(u; v; @u@v

1=

)= u v 1 ) =u 1 u v ) )

=v

1

1

u v

= (1 + ) (uv)

1 1

23

1 1=

1 1=

u v

1

2 1=

Farlie-Gumbel-Morgenstern (FGM) copula C(u; v; @C(u; v; @u @C(u; v; @v @ 2 C(u; v; @u@v

) = uv [1 + (1 u) (1 ) = v [1 + (1 2u) (1 ) )

= u [1 + (1 = 1 + (1

v)] v)]

u) (1 2u) (1

2v)] 2v)

Frank copula C(u; v; ) =

1

"

ln 1 +

e

u

1 e

v

e 1

e u e v 1 1) + (e u 1) (e v e v e u 1 1) + (e u 1) (e v e (u+v) e 1

@C(u; v; ) = @u (e @C(u; v; ) = @v (e 2

@ C(u; v; ) = @u@v [(e

1) + (e

u

u e + ve

1=

1

1) (e

v

#

1) 1) 1)]2

Gumbel copula C(u; v; ) = exp

h

i

with u e=

@C(u; v; ) u e 1+ 1+1= = C(u; v; ) u e + ve @u u ve 1+ @C(u; v; ) 1+1= = C(u; v; ) u e + ve @v v 2 @ C(u; v; ) (e uve) 1+ = C(u; v; ) 1+ + u e + ve @u@v uv

Appendix B

Kendall’s tau

Clayton copula (C(u; v; )) =

+2 24

ln (u) and ve =

1=

u e + ve

ln (v)

2+1=

Farlie-Gumbel-Morgenstern (FGM) copula (C(u; v; )) =

2 9

Frank copula (C(u; v; )) = 1

4

1

D1 ( )

where

Dk (x) =

8 > > < > > :

k xk

Rx 0

kjxj k 1+k jxjk

tk dt et 1

R0 x

if x

tk dt et 1

0

if x < 0

is the Debeye function. Kendall’s tau can be approximated by a Maclaurin series expansion (Nelsen, 1999, p. 150) for moderate values of : (C(u; v; )) '

1 900

1 9

3

+

1 52920

Gumbel copula (C(u; v; )) = 1

1

25

5

:::

Table 1: Descriptive statistics Mean Std. dev. Min. Max. Informal care 3.106705 12.68846 0 168 Formal care 1.968429 12.24475 0 168 Age (years) 79.21234 6.286817 70 106 Female .7712025 .420125 0 1 Education (years) 9.632753 4.190882 0 20 Income cat. (0 –4) .8018987 1.066333 0 4 Wealth cat. (0 –4) 1.362658 1.329576 0 4 Proxy respondent .078481 .2689696 0 1 Self-rated health (1=excel. –5=poor) 3.127532 1.061515 1 5 ADL limitations (n) .4139241 .9755782 0 6 IADL limitations (n) .6901899 1.280988 0 7 Conditions (n) 1.702848 1.261349 0 6 Current smoker .0924051 .2896427 0 1 Days/week drinks (n) 1.244462 2.346753 0 7 Children (n) 2.807595 1.843601 1 18 Children living close (n) 1.224051 1.286127 0 14 Children working (n) 1.909494 1.373806 0 11 LTC insurance .2126582 .4092526 0 1 Medicaid .0575949 .2330128 0 1 Compl./ suppl. insurance .2056962 .4042734 0 1 Region: –U.S. .4439873 .4969313 0 1 –Northern Europe .1335443 .3402159 0 1 –Central Europe .3490506 .4767454 0 1 –Southern Europe .0734177 .2608622 0 1 Observations 3160

26

Table 2: Descriptive statistics, care variables Mean Europe: –Informal care 3.405773 –1(Informal care > 0) .3625498 –Informal care | Informal care > 0 9.393944 –Formal care 1.737741 –1(Formal care > 0) .2868526 –Formal care | Formal care > 0 6.057959 U.S.: –Informal care 2.732177 –1(Informal care > 0) .1717748 –Informal care | Informal care > 0 15.90558 –Formal care 2.257323 –1(Formal care > 0) .0719886 –Formal care | Formal care > 0 31.35668

Table 3:

Std. dev.

Min.

Max.

n

12.24369 .4808732 18.90914 9.410107 .4524209 16.81991

0 0 .0192308 0 0 .0192308

168 1 168 168 1 168

1757 1757 637 1757 1757 504

13.21924 .3773191 28.46784 15.059 .2585612 47.51609

0 0 .2307692 0 0 .4615385

168 1 168 168 1 168

1403 1403 241 1403 1403 101

parameters and log likelihoods Copula

Clayton

FGM

parameter

Frank

Gumbel

0.148** 0.098 0.209 1.080*** (2.680) (0.757) (0.787) (33.919) Log likelihood –6699.06 –6703.39 –6703.37 –6698.97 t statistics in parentheses, * p