The trade-off between formal and informal care in Spain by Sergi Jiménez-Martín^* ** Cristina Vilaplana Prieto DOCUMENTO DE TRABAJO 2008-22 Serie Economía de la Salud y Hábitos de Vida CÁTEDRA Fedea – la Caixa

(version February 2009)

* Universitat Pompeu Fabra and FEDEA. ** Universidad Católica San Antonio de Murcia and FEDEA.

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Sergi Jiménez-Martín

Cristina Vilaplana Prieto

February 1, 2009

Abstract

Understanding the factors that determine the type and amount of formal care is important for predicting use in the future and developing long-term policy. In this context, we jointly analyze the choice of care (formal, informal, both together or none) as well as the number of hours of care received. In particular, we estimate and test, for the first time in this area of research, a sample selection model with the particularities that the first step is a multinomial logit model and the hours of care is an interval variable. The comparison of the confidence intervals for predicted hours of care with and without controlling for sample selection reveals significant differences between them. For the case of Spanish dependent individuals, our results support the complementary and task-specific models as opposed to the substitution model for which evidence has been found in other countries. We obtained evidence against the substitution model for the male, young and married subsamples, and only the unmarried subsample showed support for the substitution model. In a detailed analysis by population groups, we detected substantial differences by gender, age group and marital status, as well as geographical disparities in the provision of social services for dependent people.

JEL Codes: I1, J14.

Keywords: long-term care, formal care, informal care, caregivers.

^ℵWe are very grateful to Edward Norton for a helpful discussion and to David Casado, Owen O’Donnell, Pilar Garcia-Gómez, Juan Oliva, and workshop participants at the University of Barcelona, FEDEA, XXXII SAE congress, and Coimbra HEEW for helpful comments. Financial help from project SEJ2005- 08783-C04-01 is gratefully acknowledged.

^♦Universitat Pompeu Fabra and FEDEA.

^♣Universidad Católica San Antonio de Murcia and FEDEA.

1. Introduction

It is commonly accepted that family caregivers provide a vast quantity of long-term care to elderly dependent people. An important issue is the balance between what the family and the state respectively are doing for old people, and to what extent the responsibility for old people in need is a shared one.

The main purpose of this paper is to shed some light on the trade-off between formal and informal care of dependent people as well as to analyze the relationship between the choice of care and the number of hours of care provided. Formal care is defined as paid or free-ofcharge attention provided by public or private institutions and non-profit organizations, whereas informal care refers to the attention provided by family members, friends and neighbors. Some authors have considered that informal care is a source of better-quality care because of affective linkages and because it helps the patient to continue living in the community (Keating et al., 1997).

The growth of elderly population cohorts in recent decades in developed countries has entailed an increase in the proportion of people who suffer mental or physical disabilities preventing them from doing daily living activities, and Spain constitutes a paramount example. The fraction of the population aged between 65 and 80 has grown steadily since 1900, and in 2007 it represented 16.7% of the total population¹. Likewise, the fraction of the population aged 80+ had increased from 0.6% in 1900 to 4.5% by 2007. These facts are explained by the decrease in infant and elderly (70+) mortality rates and the decline in fertility rates.

The participation of age-related or ageing expenditures with respect to GDP has increased in recent years, especially since 1999 (0.15%). However, in 2004 the ageing expenditure to GDP ratio was lower in Spain than the EU-25 average² (0.32% vs. 0.53%). Spain is positioned in the group of countries with lower ageing expenditure (with Germany, 0.34%; France, 0.32%; Portugal, 0.25%; Ireland, 0.22%; Italy, 0.11% and Greece, 0.11%) and far below Austria (0.96%), United Kingdom (1.04%), Denmark (1.73%) and Sweden (2.49%).

One line in the literature has analyzed informal care from the perspective of public expenditure, praising it as a free-of-charge source of care. Nonetheless, these authors have ignored other type of costs associated with informal care, such as psychological effects, loss of leisure time, decrease in labor supply and worsening of household finances (Fast et al., 1999; Van Exel et al., 2004; Hirst, 2005). Following this line of argument, Zarit and Eggenbeen (1995) have suggested that it would be desirable to cut back public health expenditure by redirecting long-term dependent care from the public sphere to the family core. However, the family’s ability to carry most of the burden may be limited due to several sociodemographic changes, such as smaller family size, increasing female participation in the labor market and higher divorce rates.³ In future years, immigration may play an important role in the provision of formal care. In fact, between 1994 and 2004, the percentage of private household employees increased from 2.29% to 8.89%⁴, of which 30.1% (in 2004) were immigrants.

¹ Life expectancy at birth in 2005 was 83.5 (female) and 77.0 (male) in comparison with 35.7 (female) and 33.9 (male) in 1900. Life expectancy after 65 had increased from 15.3 (female) and 13.1 (male) in 1960 to 21.3 (female) and 17.3 (male) by 2005.

² Eurostat (Population and Social Conditions Database).

However, the relatively modest figures for Spanish ageing expenditure are related to “family ties”. There is solid evidence that supports the idea of strong family ties in Mediterranean countries and weak family ties in the Scandinavian ones (Bolin et al., 2007). Hence, it becomes more urgent to study the relationship between formal and informal care in Spain. If government relies on the availability of informal caregivers and chooses not to increase public ageing expenditure, then the characteristics and number of informal caregivers can affect the well-being of dependent people in Spain more than in other European countries.

In the existing economic literature on care of dependent people, there is a vexing question of whether formal caregiving hours (provided by clinical staff, nurses, physiotherapists) compensate, substitute, complement or reinforce informal caregiving hours provided by family members, friends or neighbors (Glazer, 1990; Chappell and Blandford, 1991; Mayall, 1993; Bass and Noelker, 1994; Denton, 1997). We can distinguish four models for the relationship between formal and informal care: compensatory, substitution, task-specific and complementary.

The compensatory model (Cantor, 1979) postulates the substitution of one care system by the other, but following an order of preference. The dependent individual only resorts to the use of formal care (social care services or specialized private employees) when all sources of informal care have been exhausted. However, few empirical studies have confirmed this theory (Penning and Chappell, 1990; Cantor, 1991; Chappell, 1991).

According to the substitution model (Greene, 1983), as the patient receives formal care, the family decreases the amount of informal care provided. This argument has been used by those economists who propose rationing the supply of formal care, with the aim of controlling public health expenditure. Nevertheless, applied research has revealed that, in most cases, families do not stop providing care when they receive formal aid (Archbold, 1982; Christianson, 1988; Moscovice et al., 1988; Edelman and Hughes, 1990; Tennstedt et al., 1993). In contrast,

3 All these indicators have undergone dramatic changes in recent decades. For example, the birth rate (per 1000 inhabitants) decreased from 18.8 in 1975 to 10 in 2006, with a minimum of 9.2 in 1998; the female participation rate increased from 28.8% in 1976 to 49.4% in the fourth quarter of 2007; finally, the divorce rate (per 100 marriages) increased from 4.7 in 1980 to 44.9 in 2006.

⁴ This percentage is computed as the fraction of dependent people older than 60 who have hired somebody for housework and/or company (Informal Support Survey, IMSERSO).

Liu et al. (2000) and Langa et al. (2001) found an increase in the reception of formal home care in the case of dependent people who have already lived with adult children. Viitanen (2007) analyzed the link between formal and informal care in 12 European countries and concluded that formal care substitutes informal care supplied from outside the carereceiver’s household, but does not substitute informal care by the dependent’s co-resident relatives.

The task-specific model was proposed by Litwak (1985). According to this model, formal and informal care are different, but complementary. It sustains that the informal caregiver (a woman in most cases) is more suitable for day-to-day care (washing, dressing and undressing, eating and drinking) while formal care is set aside for more technological tasks. In contrast to the compensatory model, it is the nature of the task and not the will of the patient that determines who is most appropriate for providing care (the family or the skilled professional). Several papers, such as Penning and Chappell (1990) and Fisher and Eustis (1994), have upheld this model.

Finally, the complementary model, which is a combination of the compensatory and the substitution model, was proposed by Chappell and Blandford (1991). When the dependent’s needs exceed informal care resources, formal care provides the necessary support (Bass and Noelker, 1989; Edelman and Hughes, 1990; Denton, 1997). This is the case, for example, when informal caregivers need to make use of respite services. Chappell and Blandford (1991) spelt out two circumstances in which formal care is used in conjunction with informal care: when medical requirements are very complex and when the family goes through a critical situation. In this manner, formal care becomes involved when the informal caregiver realizes that he or she cannot cope unaided.

The lack of a cohesive conclusion is due to the idiosyncrasy of informal and formal care. Both types of care may happen simultaneously, or one before and the other afterwards. In this context, the main purpose of our study is to shed some light on the trade-off between formal and informal care. In particular, we want to answer two questions: first, does the trade-off vary with the subpopulation considered? Second, and also importantly, which model of care, if any, fits the Spanish case best? Furthermore, our study extends the previous literature by analyzing the relationship between choice of care and hours of care. We want to assess whether hours of care are independent of the type of care once we condition on the choice of care.

To these ends, we consider a two-equation model for the choice of type of care and the number of caregiving hours. Following Bourguignon et al. (2007), we use a two-step model. In the first one, we estimate a multinomial logit model and use the estimates to construct expected second-stage residuals for each type of care. In the second stage, given the interval nature of the caregiving hours equation, we estimate interval regressions for each type of caregiving hours but adding, following Bourguignon et al. (2007), a set of controls (based on the expected second-stage residuals) for sample selection.

As regard specification results we have tested and not rejected the first-stage multinomial model against several alternatives: bivariate probit (FC vs. IC) and trivariate probit with space restrictions (FC vs. IC vs. FIC). We have also excluded the possibility of independence between the choice of care and the number of hours provided in the whole sample and in three alternative partitions of the sample: by gender, age group and marital status. In fact, estimation under independence implies significant biases in the estimated coefficients of several key variables of the model. More importantly, the comparison of the confidence intervals for the predicted caregiving hours by type of care reveals significant differences between the Bourguignon et al. (2007) model and a standard interval regression, indicating that the omission of sample selection bias tends to overestimate the number of caregiving hours received.

Many applied studies for various countries have found a substitution relationship between formal and informal care. For example, Van Houtven and Norton (2004) and Coyte (2001) concluded that IC reduces the amount of home care for the case of the United States and Canada respectively. Bolin et al. (2007) in a study on single-living elderly in Europe found that IC and home care were substitutes, but there was a gradient effect, which made the substitution effect stronger in southern countries. Viitanen (2007), also for the European elderly population, found that more residential care and home care services reduced the amount of IC given by middle-aged women. To our knowledge, this paper is the first attempt to study the relationship between FC and IC for the elderly Spanish population. Our results are different from previous studies for other countries, as the complementary and task-specific models are the prevailing ones. Specifically, we have obtained evidence against the substitution model for the male, young and married subsamples, and only the unmarried subsample supports the substitution model. With respect to the population groups considered, the probability of receiving IC is lower for women and the unmarried, and as regards chronic illnesses, the existence of cognitive impairments (mental illness, dementia) constitutes a determinant for the increase in IC hours for all subsamples and FC/FIC hours for the male, young, old and unmarried subsamples. We also observe that an unexpected event (for example, a hospital stay) increases the number of IC hours, but the size effect is greater for the old and unmarried subsamples.

The rest of the paper is as follows. In section 2 we describe the main data source and provide some descriptive statistics. In section 3 we propose a model of choice of care and caregiving hours, following Bourguignon et al. (2007), and validate it against several alternatives. In section 4, we present the estimation results for the whole sample and three different partitions of the sample: by gender, age group and marital status. Finally, section 5 offers some concluding remarks.

2. Data and variables

The dataset consists of information from the Disabilities, Deficiencies and Health Status Survey (DDHSS) drawn up by the National Institute of Statistics in 1999 with the objective of estimating the number of Spanish residents who suffer from a disability and identifying risk factors associated with health status.

To design the sample we followed a two-step procedure. First, using the Disabilities and Deficiencies Questionnaire we selected those individuals who answered in the affirmative to the question: “Do you suffer any kind of disability?” understanding as a disability “a limitation in performing daily living activities that is going to last more than one year”. Second, we focused on individuals over 40 years old. Although many studies have focused on the elderly population (65+) (Ettner, 1996; Carmichael and Charles, 2003), we have observed that the amount of “young” people with disabilities was not negligible⁵. The final sample (40+ years of age with any disability) contained 17,442 observations.

We consider three categories of care: “informal care” (IC), which includes those individuals who only received help from relatives (whether co-resident or not), friends or neighbors (6,216 observations); “formal care” (FC), which includes those individuals receiving help from employees, the public administration or private organizations (562 observations); and “formal-informal care” (FIC), which describes those individuals who received help from both types of care (1,002 observations). It can be inferred from these figures that there were 9,662 individuals who suffered a disability but did not need or receive any type of care. The survey indicates whether the provider of FC belonged to public social services, belonged to a private firm, or was a household employee. However, in the last case, we do not know the employee’s qualifications. Formal care recorded in this particular survey does not refer to diagnosis or medical treatment offered through hospitals. Specifically, if the patient had been admitted into hospital, formal care does not refer to attention provided by doctors (diagnosis and surgery), nurses and radiology and pharmacology services, but only to whether the family had hired somebody to alternate caregiving with other family members. The number of formal caregiving hours refers to the amount of time devoted to housework and personal care tasks. Therefore, it constitutes a good indicator of the amount of extra-family aid received by the dependent individual.

Respondents who claimed to suffer a disability were required to give more details. There was a list of 36 disabilities, which, for the purpose of this paper, were categorized into disabilities preventing personal or instrumental activities of daily living (PADL and IADL respectively)⁶, following the recommendations of the Federal Interagency Forum on Aging Related Statistics (2000). In all cases, the respondent was required to indicate the degree of severity and the prognosis associated with each disability. Preliminary analysis suggests that there is no linear relationship between the number of disabilities and the number of caregiving hours (the results of this exploration are available on request). For this reason, we have defined six binary variables (3 for PADL and 3 for IADL) that take the value 1 if the individual suffered two, three, or more than three disabilities. Apart from information about disabilities, the survey contains a list of specific pathologies, from which we have selected mental illness⁷, arthritis, muscular dystrophy, multiple sclerosis, stroke, cerebral palsy, dementia and Parkinsonism, due to the major limitations they usually involve for doing daily living activities.

⁵ There were 1,442 individuals (584 male, 838 female) aged between 40 and 64 years old who needed a caregiver to do daily living activities.

With respect to the sociodemographic characteristics of the carereceiver, we have considered those variables that may have an influence on the type of care received, either because they directly affect health status (age and sex) or because they have implications for the generation of informal networks (marital status, number of household adults). Given that some authors have documented a positive correlation between income and availability of formal care (Branch et al., 1981) we control for household income as well as for the level of education of the dependent.

From a theoretical point of view, when informal care is not available or is not enough, public social services act as a subsidiary responsible for the care of the dependent. With the aim of taking into account geographical differences in the provision of formal care, and given that the DDHSS does not include information about the price of formal care received, we have defined a set of dummy variables to denote the place of residence and the size of the municipality.

2.1. Descriptive statistics

In Figure 1 we appreciate that as people get older the percentage of non-dependent individuals decreases and at the same time the fraction of people who need some type of care increases. The number of individuals who, conditional on having a disability or a deficiency, receive IC increases from 24% at 40 years old to 70% at 90 years old. In second place, FIC represents 12.5% at the age of 90. In contrast, the trend for FC increases from 60 to 80 years old (6%) and then decreases (1.8% for the interval 96-99 years).

⁶ PADL’s include difficulties getting up and going to bed, standing up, moving indoors, washing oneself, controlling physical needs, dressing and undressing, eating and drinking. IADL’s include difficulties in carrying light objects, using utensils and tools, clutching small things with hands and fingers, moving without any mode of transport, driving one’s own vehicle, shopping, cooking, washing and ironing clothes, cleaning the house and looking after the well-being of the family.

⁷ Mental illnesses refer to bipolar disorders, depression, anxiety, stress, and schizophrenia, whereas dementia relates to all possible kinds of dementia (senile, Alzheimer, AIDS-related, brain tumor, brain damage).

Figure 1. Distribution of the population by type of care

Figure 2 illustrates the relationship between household income and type of care. It is evident that IC decreases and FIC increases with income. In fact, for the brackets €2343.95-€3906.58 and more than €3906.58, the percentage of FIC increases from 28.5% to 50%. On the other hand, low-income households [€264.5-€390.6] attain the maximum level of FC. We should clarify that the poorest and richest households do not use the same kind of FC. Wealthier families prefer (or are obliged to) to hire household employees and private sector services⁸.

Figure 2. Distribution of type of care by monthly household income brackets (€)

The rate of household employees for the whole sample is 0.7%, whereas it increases to 20% for households with an income of more than €2344/month.

Finally, Figure 3 represents the distribution of caregiving hours by type of care⁹. The mode for those that only receive FC is seven or fewer hours. However, the mode for those who receive IC or FIC is 60 hours or more.

Figure 3. Distribution of the number of weekly caregiving hours by type of care

Table 1 in the Appendix shows the fraction of individuals in the sample with a given characteristic by type of care. Of those receiving FIC, very old dependent people (aged 80-89 or 90-99) constitute the largest cohort. Unmarried dependent people (single, widowed, separated/divorced) represent 66.54% of those receiving FC. Education is a key determinant of the type of care, since non-educated individuals tend to receive IC more frequently (59.45% have not finished elementary education and only 1.48% of them have obtained a college degree). The same figures for dependent people with FC are 48.93% and 8.89% respectively. For the three types of care, more than 30% of dependent people receive a retirement benefit, and those who receive IC show the highest concentration of disability benefits, both contributive and non-contributive (30% vs. 24%).

Regarding the list of pathologies considered, dependents without any type of care show the lowest percentages for all illnesses. For the three types of care, arthritis has the highest incidence rate (around 30%). Carereceivers with FIC show the highest percentage for mental illnesses (25.88%), dementia (13.27%), moving house to receive better medical treatment or having an adapted dwelling (12.17%), and rehabilitation treatment (23.65%).

As for disabilities, carereceivers with IC mainly have difficulties in moving outdoors (86.05%), doing housework (78.81%), maintaining body postures (51.83%) and taking care of themselves (46.44%). The incidence of difficulties in relating to people (30.43%) and communicating (29.64%) is much higher among those who receive FIC. Among those who receive FC, difficulties in doing housework is the prevailing factor (91.81%). This may be explained by the fact that in many regions home care services¹⁰ emphasize home help rather than personal care.

Unfortunately, we do not know the distribution of hours between formal and informal care when the individual receives both types of care.

Dependent people with FIC suffer most PADL disabilities (3.0708), followed by those with IC (2.1476), and finally by those with FC (1.6423). A similar ranking is obtained for IADL disabilities (6.7754, 5.6134 and 5.9750 respectively).

With respect to the degree of severity, FIC carereceivers exhibit disabilities with the highest degree of severity (98.60% are very severe, 95.10% cannot do the activity), and for the three types of care, around 70% of carereceivers suffer disabilities with unfavorable prognosis. On the other hand, people who do not need a caregiver generally report the lowest percentage of disabilities with stable or unfavorable prognosis.

3. A model of choice of care and hours

The problem under consideration is by no means a simple one. On the contrary, it is a complex problem because there are multiple decision-makers involved. First, family members may or may not adjust their lifestyle to the dependent’s needs. Second, private professionals may be hired either by the family or by the patient, and finally, either the national or the regional administration may offer special services for non-institutionalized dependent people (home care, telecare, day care centers and respite services).

In this context, it seems reasonable to consider the possibility that the choice of the type of care (C) and the number of hours (H) of care provided to be jointly determined. Thus, we consider a two-equation model for estimating the decisions of type of care chosen and number of care hours received.

Following previous work by Bourguignon, Fourier and Gurgand (BFG, 2007), for each care alternative j (0=no care (omitted category), 1=formal care, 2=informal care, 3=formal & informal care), we define an “outcome equation” (1a) for the number of caregiving hours (H) received and a “selection equation” (1b) which describes the “value” (C) obtained from each type of care:

\[\begin{array}{l l} H _ {j} ^ {*} = X \beta_ {j} + \varepsilon_ {j} & j = 0, 1, 2, 3 \\ C _ {j} = Z \alpha_ {j} + u _ {j} & j = 0, 1, 2, 3 \end{array}\tag{1a}\]

(1 ) b

¹⁰ With the exceptions of País Vasco, Cataluña and La Rioja, most of the time is devoted to home help rather than to personal care activities (Observatorio de Personas Mayores, 2000).

where verifies that E[.|X, Z]=0 and . The vector represents the set of explanatory variables for the care alternatives and the vector X contains the determinants for the number of hours¹¹. Although we shall consider a very large set of explanatory variables, there are still some unobservable determinants. For example, we cannot consider (because of lack of information) family dynamics and history, caregiver’s feelings (anxiety, sadness, anger or guilt), values and beliefs about the roles of the family, the care recipient’s personality, whether the caregiver has been thrust into the role because of lack of alternatives, and the nature of the relationship between the caregiver and the dependent.

Without loss of generality, we assume for the rest of the model that the outcome variable is observed if and only if the category “formal care” has been chosen, that is, if max . The problem that we face is the estimation of and all the s taking into account that the error term ε₁ may not be independent of all the errors in the model. This situation would induce correlation between the explanatory variables and the residual term in the outcome equation. For this reason, OLS applied to the selected sample may be inconsistent. Thus, we have a selection bias model as in Heckman (1979), with the difference that the selectivity criterion is given by a multinomial logit model rather than by a univariate probit.

Several alternatives have been put forward in the econometric literature to identify the parameters of this model. Lee (1983) proposed a generalization of Heckman’s (1979) method. His approach is quite simple and only requires the estimation of one parameter in the error correction term. However, it imposes very restrictive assumptions about the structure of the covariance between and the error terms of the selection equations. To avoid this problem, Dubin and McFadden (1984) introduced a method that does not require the imposition of any constraint between and the error terms of the selection equation, but they restrict to the family of Gumbel distributions. More recently, Dahl (2002) developed a semiparametric approach, but it becomes computationally unfeasible to implement in practice as the number of alternatives increases. Finally, BFG proposed a variation to Dubin and McFadden’s method. In this paper we follow the latter approach.

11 Although it is not strictly necessary, we (over)identify the model by imposing some exclusion restrictions, that is, variables in Z that are not in X. For example: the variable “education” is included in Z but not in X because it may reflect the effect of learning externalities, that is, more education implies a higher degree of awareness about social services for dependent people (usage of internet). To check the appropriateness of this exclusion restriction in our two-stage selection model, we have included it in both stages and tested their significance in each stage. The F-test shows that this variable is significant at the 1% level in the first stage and not significant in the second stage, providing support for the exclusion restriction. On the other hand, we have included the coverage index of social services in X but not in Z, to Z, consider the possibility of substitution between formal caregiving hours at home (home care) and outside (day centers) or between personal and technical aid (home care vs. telecare), and the alleviating effect of respite services for informal care (the coverage index is the ratio between the number of users and total population ≥65 years).

BFG allow to be a linear combination of normal distributions, and as a result, also follows a normal distribution.

\[\begin{array}{l} u _ {j} ^ {*} = \Phi^ {- 1} \Big (G \Big (u _ {j} \Big) \Big) \\ \varepsilon_ {1} = \sigma_ {1} \sum_ {j} \rho_ {1} u _ {j} ^ {*} + \eta_ {1} \end{array}\tag{2}\]

(3)

where is the cumulative standard normal, is the cumulative Gumbel distribution and is the correlation coefficient between and . For each it is assumed that the expected value of and the error term are linearly related¹², where denotes a residual term orthogonal to all and such that E[ . This implies that a crucial assumption in this specification is that the Independence of Irrelevant Alternatives hypothesis holds. Substituting the error term of equation (1a) with its conditional expectation plus a residual term, we get the following expression:

\[H _ {1} ^ {*} = X \beta_ {1} + \sigma_ {1} \left[ \rho_ {1} \delta (P _ {1}) + \sum_ {j > 1} \rho_ {j} \frac {P _ {j}}{P _ {j} - 1} \delta (P _ {j}) \right] + \nu_ {1}\tag{4}\]

\[\begin{array}{l} \delta (P _ {j}) = \int u _ {j} ^ {*} g (u _ {j} + \log P _ {j}) d u \\ P _ {j} = \frac {\exp (Z _ {j} \alpha_ {j})}{\sum_ {s} \exp (Z _ {s} \alpha_ {s})} \end{array}\]

where is the Gumbel density distribution, is the probability that the alternative j is chosen, and has zero mean and is orthogonal to all other terms. Therefore, OLS may be applied in this equation to obtain a consistent estimator of (see Bourguignon et al. (2007) for details). Because of the fact that the terms need to be estimated, the standard errors from the OLS regression are incorrect, so we present bootstrapped standard errors. Note also that a joint test of significance of the coefficients of the stands for a test of the presence of relevant selection in the hours equation, and hence for the validity of the OLS estimates.

However, the “genuine” BFG model cannot be applied to our data given the interval nature of the variable “caregiving hours”. In our dataset, respondents to the DDHSS were asked to report the number of caregiving hours within a number of mutually exclusive intervals: fewer than 7, 7 to 14, 15 to 30, 31 to 40, 41 to 60 and more than 60. Thus, the dependent variable is ordinal in nature but interval coded. There are several solutions to this problem. For example, we can set caregiving hours to the mid-point of the relevant interval and then apply least squares. A more desirable approach is to follow Stewart (1983) and estimate the extended second-step equation (4) by maximum likelihood. The pseudo-likelihood function is a modification of the standard ordered probit where the unknown threshold values are replaced by a set of known thresholds that delineate the intervals.

uj

¹² The linear combination assumption is based on the fact that all u_j^* are independent of each other.

Consequently, we can consider the resulting model as a two-step procedure. In the first step, we estimate a multinomial logit model for choice of care, using as explanatory variables age, sex, marital status, main breadwinner, level of education, labor force status, monthly household income, number of children, number of adults in household, variables related to disabilities and illnesses, size of municipality and place of residence. Using the estimated coefficients we obtain the predicted probabilities and then we construct , for all . The coefficient associated with the latter term is fundamental in order to test for the validity of the joint determination hypothesis.

In the second step we estimate an augmented (with the sample selection correction terms) interval regression with known thresholds between intervals. We assume that the number of caregiving hours is explained by individual factors (age, sex, illnesses and other health variables, number, type and severity of disabilities), socioeconomic factors (main breadwinner, marital status, household income, relation with economic activity, number of children and adult members) and geographical factors (size of municipality and the coverage index of social services for dependent people).

In this context, the joint significance of the selectivity correction terms indicates that the BFG method is more consistent than OLS and therefore is the preferred estimation method for these two equations. Second, the sign of a particular selection term indicates the direction of the selection bias resulting from the choice of a particular type of care as opposed to all other types of care taken together. Therefore, it constitutes evidence in favor or against which of the proposed theories for the relationship between formal and informal care holds for each particular sample. For example: a negative selection bias term corresponding to IC care in the regression for FC hours indicates that individuals with FC receive fewer caregiving hours as opposed to all other types of care, because people with more disabilities “exit” FC and “enter” IC. We interpret this as evidence against the substitution model. Alternatively, a positive selection bias term corresponding to IC in the regression for FIC hours would reveal that individuals with FIC receive more caregiving hours as opposed to all other types of care, because fewer disabled people “exit” IC and “enter” FIC, thereby supporting the complementary and task-specific models.

Since the MNL assumption imposes strong restrictions in the error structure, we consider a few other alternatives for the first stage. For example, we may consider a bivariate probit model, in which the individual chooses IC or FC or both. We can also consider a trivariate probit with space restrictions in which the individual chooses IC, FC or FIC.

In the next section, we first test amongst these alternatives and then we move on to detailed results and interpretation.

4. Results

4.1. Specification testing and alternatives to the BFG model

There are many alternatives to the model described in the previous section, especially to the first step of the model. As stated earlier, the first-step MNL imposes a strong restriction on the correlation structure of the errors of the first-stage equation. Hence, it is advisable to test this restriction against more generalized alternatives. In this section, we first evaluate the plausibility of the IIA hypothesis and then compare the MNL with multivariate probit alternatives.

As regards the first question, an essential property of the multinomial logit model is that the odds ratios are independent of other alternatives, that is, if a subset of choices is truly irrelevant, omitting them from the model will not change the estimate assuming that we use the remaining choices systematically. However, if the remaining odds ratios are not independent of these omitted alternatives the estimated coefficients will be inconsistent. Table A presents the test of the IIA hypothesis by means of the Small-Hsiao test¹³. The results do not allow us to reject the IIA hypothesis in any of the subpopulations considered. This implies that distinguishing between FC, IC and FIC is not only analytically but also econometrically appropriate. Although, a priori, the alternative “no care” might seem irrelevant, the tests indicate that this is not the case. A dependent individual who desires formal care, but does not receive it, may prefer the option “no care” rather than “informal care” because he or she does not want to be a burden on the family¹⁴. Moreover, even when the IIA hypothesis fails, there are incentives to estimate a BFG-like model. Bourguignon et al. (2007) showed that the selection bias correction based on the multinomial logit model provides a better correction for the outcome equation (when compared to Lee (1983), Dubin and McFadden (1984) or Dahl (2002)) if we want to estimate an outcome over selected populations rather than estimating the selection process itself, even when the IIA hypothesis is violated.

With respect to the choice of the Small-Hsiao test, Cheng (2007) compared the performance of three tests for IIA: McFadden et al. (1981), Hausman and McFadden (1984) and Small and Hsiao (1985), and concluded that “IIA tests often reject the assumption when the alternatives seem distinct, and often fail to reject IIA when the alternatives can reasonably be viewed as close substitutes”. We have performed a set of Wald tests for the combination of outcome categories, where the null hypothesis is that all coefficients except intercepts associated with a given pair of outcomes are 0 (that is, categories can be collapsed). In all circumstances, we reject the null hypothesis, which means that we have appropriately categorized individuals into no care, FC, IC and FIC (results are available upon request).

¹³ See Small and Hsiao (1985) for a description of the test.

¹⁴ Our sample contained 682 (187) married women with three or more IADL’s (PADL’s) who did not receive any type of care. And according to the Survey on Living Conditions of the Elderly (IMSERSO, 2005), 77% of the respondents preferred to continue living in their own home (without adult children) and 50% considered that present generations take care of their parents worse than past generations did.

Table A. Results of the Small-Hsiao test to test the IIA hypothesis

df: degrees of freedom equal to the number of parameters in the restricted choice set.

We have also performed other specification tests comparing the goodness of fit of the multinomial logit for the first-step regression with a bivariate probit¹⁵ and a trivariate probit with space restrictions¹⁶. Our results (see Table B below) indicate that the multinomial logit model reports the lowest values for the AIC and ICOMP although the bivariate probit reports a slightly lower Bayesian Information Criterion (BIC). If we repeat the same exercise for the different subsamples (men, women, young, old, married, and unmarried), we confirm that the AIC and ICOMP are always smaller for the multinomial model.

Table B. Comparison of goodness of fit statistics for the first-step model

¹⁵ We have defined two binary variables (FC and IC) corresponding to whether the individual receives formal or informal care. For those who do not receive any type of care, both variables take the value 0. For those who receive FIC, both variables take the value 1. We have included the same explanatory variables as in the multinomial logit model. Estimation results are available upon request.

¹⁶ We have defined three binary variables (FC, IC and FIC). For those who do not receive any type of care, all three of them take the value 0. We have included the same explanatory variables as in the multinomial logit model. Estimation results are available upon request.

4.2. Trade-off between formal and informal care

Table 2 presents the predicted probabilities of receiving each type of care for the base case (male, age 80-99, married, with elementary education, household income between €390.6 and €1172 per month, suffering one PADL and one IADL and living in Cataluña) as well as the marginal effects implied by the first-step multinomial model. The probability of receiving IC for the base case is the highest (0.3056) in comparison with the probabilities of receiving some kind of formal care, whether or not it is combined with informal care (0.0374 for FC and 0.0118 for FIC). Although we have obtained the same ranking among the three types of care for other baseline cases, this cannot be interpreted as evidence in favor of the compensatory model, because in certain cases the choice of IC may be a “second best” from the point of view of both the caregiver and the carereceiver. If, for example, a dependent individual who is receiving IC applies for home care (FIC represents the “first best”) and the application is rejected, he or she would continue to receive only IC, but there would be a problem of unmet needs (which is beyond the scope of this paper).

The higher the level of education achieved, the lower the probability of receiving IC (- 4.26% for high school and -12.10% for college degree). In this regard, the education of the dependent may be a proxy for the cost of applying for social services for people with disabilities (Bass and Noelker, 1987). Alternatively, more educated potential caregivers may have a higher opportunity cost.

Married dependent people show a lower probability of receiving only FC (-3.55%). Some studies (Chappell and Blandford, 1991) have considered that the presence of a spouse guarantees the reception of informal care. However, other members of the family, for example adult children, can provide IC (Stoller and Earl, 1983; Ettner, 1995). In fact, the estimated coefficients indicate that each adult member increases the probability of receiving IC by 2.71%. The network of informal caregivers may improve the dependent’s health by listening to medical instructions, transporting the patient to appointments and noticing health problems more quickly (task-specific model).

The probability of receiving FC decreases for the two lowest-income brackets (-2.30% and -2.12%). At the same time the probability of receiving FIC increases as household income increases (1.30% for the range €1172-€1953 and 4.08% for more than €3907). It should be pointed out that FC received by individuals in lower-income brackets is usually provided by public social services (day centers, home care service), whereas individuals belonging to higherincome brackets, who do not qualify for public FC, have to rely on private FC (which may or may not be provided on a co-residency basis).

People who have benefited from rehabilitation treatment or have moved house to receive better medical treatment show a significant increase in the probability of receiving all types of care, although the probability of receiving IC increases the most (8.82% for change of residence and 2.36% for rehabilitation treatment), thereby indicating complementarity between informal and formal care.

Choice of care by age, gender and marital status

The evidence presented in Table C illustrates the appropriateness of estimating the model by gender, age group, or marital status. The whole sample (N=17,442) has been split into two subsamples according to gender (6,984 men and 10,458 women), age (7,780 up to 69 years and 9,662 individuals 70 and older) and marital status (7,154 unmarried and 10,288 married). In all cases, we clearly reject the possibility that the parameters of the model are the same.

Table C. Likelihood ratio test for the significance of different subsamples

L1 (L2) is the likelihood for the first (second) subsample. Log-likelihood for the whole sample=-10922.835.

Comparing the probabilities for the base case¹⁷ (see Tables 3, 4 and 5 in the Appendix) we observe that the probability of receiving FC is higher for women than for men (0.0052 against 0.1525), and for unmarried compared to married (0.1980 vs. 0.0211). In turn, the probability of receiving IC is much higher for older dependents (70-99 years) than it is for younger ones (40-69 years) (0.3194 against 0.1037). The lowest probability of receiving FIC corresponds to younger dependents (0.0007) whereas women and unmarried attain the highest ones (0.0233 and 0.0220). We can point to three reasons why the probability of receiving FC in the baseline is higher for women than for men. First, because women have a longer life expectancy than men, and therefore make up the majority of the very old. Second, because women play a caregiving role in the family, so that when the caregiver herself develops mental or physical limitations, the family seeks outside help (Lee et al., 1993). Third, since women tend to outlive their husbands, women are less likely than men to have a spouse to care for them in old age. The probability of receiving FC decreases by 4.00% for married men and by 1.44% for married women. On the other hand, the number of co-resident adults slightly decreases the probability of FC for men, but each additional adult increases the probability of IC for women by 5.19%. The number of children between 13 and 17 years old has a slight positive effect on the probability of FIC for the whole sample and the subsamples of women, young, old and unmarried. However, it has no effect on the number of hours, indicating that the informal caregiver is obliged to contract formal care to make parenthood and caregiving tasks compatible.

¹⁷ For men and women: individual aged 80-99, married, one PADL and one IADL, living in Cataluña. For young and old: man, married, one PADL and one IADL, living in Cataluña. For married and unmarried: man, aged 80-99, one PADL and one IADL, living in Cataluña.

Suffering three or more IADL disabilities increases the probability of receiving FC by 1.91% or 1.51% for men, and between 11.14 and 13.71% for women. Although we might think that gender differences related to IADL disabilities are connected to housework, shopping and preparing meals, we do not believe that this is the case, because the gender difference is consistently observed across other IADL disabilities such as using public transport, moving around the house and using utensils and tools. If the prognosis is that the disability can be overcome, stabilize or worsen, the probability of using IC increases for both genders.

For all subsamples, as the number of disabilities increases the probability of receiving IC increases more than the probability of receiving FC does (for PADL disabilities, the greatest increases are observed in men (7.61%), and for IADL disabilities, in women (8.59%) and unmarried (8.46%)). When the number of IADL disabilities is four or more, the probability of receiving IC increases by 18.94% and 15.12% for older and married dependents respectively.

For the subsample of young dependents, we observe a negative marginal effect corresponding to disabilities for seeing, hearing, relating, or having two or three PADL disabilities. Moreover, the highest marginal effect (in absolute value) corresponds to IC, which means that young dependents are less prone to use this type of care with respect to FC and FIC. However, for the old subsample, the probabilities of receiving all three types of care increase with the number of IADL disabilities. The explanation for these differences may be that younger dependent people seek self-control and flexibility, placing emphasis on living as meaningfully and normally as possible. Many young dependent people perceive the management of medication, catheters and ostomies as an extension of daily living activities, which can be done without the supervision of a formal caregiver, once the patient has learnt to do everything unaided. In contrast, older dependent people have accepted that certain decisions are beyond their control (for example, home care is based on schedules, which means that bath time and bedtime may be different from their wishes).

With respect to the relationship between IC and the pathologies suffered, for young dependents the greatest marginal effects are observed for mental illness and dementia (7.33% and 8.84% respectively), and for older dependents the most serious impairments are cerebral palsy and dementia (14.90 and 18.75% respectively). In this case, the difference in the social services approach between seniors with dementia and younger people with cognitive impairment suggests that ageism and not dementia is the root of the distinction. The Spanish Association of Relatives of People with Mental Illnesses claims that there is a stigma attached to mental patients and their relatives, and calls for egalitarian treatment with the rest of dependent people. There are also considerable differences according to the severity and prognosis of the disability, the effect for older dependent people, when significant, being twice the effect for younger dependents.

Living in a municipality with fewer than 10,000 inhabitants decreases the probability of receiving IC for old dependent individuals by 50%. These results cast doubt on the stereotype that seniors in rural areas are more likely than those in urban areas to have extensive, closely knit, informal networks and a stronger sense of community (Keating et al., 1997). This perspective does not take into account several hidden costs such as transportation, isolation and lack of social resources.

Finally, Table 6 presents the results dividing the sample by marital status: married and unmarried (grouping together single, divorced, and widowed). Several variables increase the probability of receiving IC for both subsamples, although the effect is always higher for married dependents (mental illness, cerebral palsy, dementia, change of residence, the number of IADL’s, severity and prognosis). The probability of receiving IC increases by 5.20% for widowed but decreases by 8.90% for divorced. Age increases the probability of receiving IC only for married, although older unmarried have a significantly higher probability of receiving FC (28.91% for 70-79 and 16.75% for 80-99).

Extremadura is the region with the smallest probability of IC for unmarried people, which may be explained by the fact that it is the third region with most elderly people living alone (21.3%). In contrast, Cantabria, Navarra and Ceuta show the highest probability of IC for women and elderly dependents. These results could be related to the characteristics of social services for dependent people in these regions. Cantabria exhibits a very low coverage index for telecare services¹⁸ (0.2 as opposed to 0.78 for Spain), whereas Navarra is the region where home care is most expensive¹⁹. Ceuta has no private or public day centers and it shows the lowest coverage index for residential centers (1.46 vs. 3.21 for Spain²⁰). It could be argued that there are other regions where the coverage index for home care is lower, but in this case 70% of the time is devoted to home help, and consequently the carereceiver does not perceive that aid as specialized or skilled. On the other hand, Ceuta is the region with the lowest percentage of elderly people living alone (14%, as opposed to 19.9% for Spain²¹), which may justify the prevalence of IC over FC.

18 Home care and telecare services depend upon local administrations, which may result in large disparities in both eligibility and generosity.

¹⁹ The cost of home care services differs greatly across regions (the most expensive being Navarra, at €19.1/hour). Moreover, the co-payment rate varies from 0% in Ceuta and Melilla (5% in Andalucía and Murcia, 10% in País Vasco) to 20% in Rioja.

²⁰ Observatorio de Personas Mayores (IMSERSO, 2000).

²¹ Population and Dwelling Census (INE, 2001).

Finally, the probability of receiving FC for elderly dependents is greatest in Cataluña. Although the coverage index is lower than the national average (1.2 as opposed to 1.8), 85% of home care time is devoted to personal care and only 15% to home help. In this respect, the estimated coefficients might reveal how useful the carereceiver perceives each type of care to be.

4.3. The hours equation

The estimation results for the caregiving hours regressions (second step of the modified BFG model) using the whole sample are shown in Table 8. The variables (k=0,1,2,3) are consistent estimators of the expected conditional residuals of the multinomial model. Each coefficient represents the covariance between the residual of the least squares regression and the corresponding residual from the multinomial logit regression. The variable σ represents the standard deviation of the error term. The significance of the selectivity correction terms individually and as a whole indicates that the appropriate method for estimating these equations is BFG. Moreover, we reject the null of equal coefficients between the corrected (BFG) and uncorrected interval regression (excluding the intercept and the selectivity terms). The results of these exercises are available upon request.

Finally, to determine how sample selection bias affects the estimated coefficient of the hours equation we have computed the 95% confidence intervals for predicted caregiving hours by type of care, subsample and illness suffered, using the BFG model and a standard interval regression (Table D). Bold figures correspond to cases where there are significant differences. The omission of the sample selection bias tends to overestimate the number of caregiving hours (for any type of care).

Table D. Comparison of the 95% confidence intervals for predicted hours, with and without control for sample selection bias

MI/D: mental illness or dementia. Others: stroke, cerebral palsy, muscular dystrophy, multiple sclerosis, Parkinsonism, arthritis.

We observe that the most significant predictor of hours of care is health status (mental illness, dementia, the number of PADL’s or IADL’s, and the number of days in hospital) and that none of the age intervals is significant for any type of care. This fact should be taken with moderate enthusiasm by policy-makers because the increase in life expectancy does not constitute a problem (in terms of health expenditure) as long as there is a parallel increase in the number of healthy years. It also reinforces the usefulness of chronic illness prevention policies as budget control instruments (since present health expenditure can “reduce” future costs).

The sign of the estimated coefficients for the variable “household income” is quite interesting because the number of FC hours decreases for households with more than €1953 per month. Regarding the provision of social services, the regional administration is responsible for both the supply of social services and the determination of what requirements are needed to apply for a place. These requirements usually include a valuation of the degree of disability, the availability of informal care and the financial situation of the applicant (Casado and López Casasnovas, 2001; Casado, 2005). Therefore, high-income households tend to be excluded from these services.

The number of FC or FIC hours increases for cerebral palsy, dementia or when the dependent has an impairment certificate, which may constitute evidence in favor of the task specific model, because professional ability is needed to perform certain exercises. On the other hand, the rise in caregiving hours as the number of IADL’s increases points to the complementary model, because the informal caregiver feels overwhelmed, or caregiving demands are excessive.

Table E (below) summarizes the interpretation of the selection bias correction terms shown in Table 6 in the Appendix. The number of the selection bias term corresponds to the alternative of care (0=no care; 1=IC; 2=FC; 3=FIC). We have found evidence in favor of the complementary and task-specific models. In fact, the number of formal or informal caregiving hours increases with the size of the household, because there are secondary caregivers that support the task of the primary one or because positive externalities related to the use of information about social services appear.

Table E. Interpretation of the bias correction terms of the BFG model: whole sample

Hours equation by age, gender and marital status

The detailed results by gender, age group and marital status are presented in Tables 7 to 9 respectively. At least one of the selectivity terms is significant in each regression. Table 7 shows the results for the second step of the modified BFG model by gender. The first thing to note is that age is a significant factor of care for the whole sample and for women (from 80 onwards). Married males tend to receive more IC hours, whereas marital status is not significant for women in any regression and main breadwinner women tend to receive fewer IC hours. Also important is that the number of co-resident adults is very significant for women (mainly daughters or daughters-in-law who act as caregivers).

Suffering dementia or mental illnesses increases the number of IC hours in all the subsamples considered. It also increases the number of FC/FIC hours for the male, young, old and unmarried subsamples. The coefficient of the variable “number of days in hospital” implies that female patients rely on their spouses less frequently than male patients do. Comparing the young and old subsamples, we observe that having been in hospital increases the number of IC hours for both, the effect being stronger for the latter group. Sometimes, an acute event that entails a hospital stay and gathering of relatives involves an urgent decision about the type of care. The initial decision may set the pattern for subsequent care. Deciding which type of care is more appropriate requires knowing the benefits, risks and costs of the alternatives.

Having received a rehabilitation treatment has a different impact because it increases the number of FC hours for the younger subsample and the number of FIC hours for the older one. This result may reflect that young people are first entitled to FC until they recover (if that is feasible), but old dependent people tend to use IC in combination with FC (for example, after a hip fracture).

As the number of co-resident adults increases, the number of FC hours for the young and the number of FC/IC/FIC hours for the old increases (with the highest coefficient corresponding to IC). We are not suggesting that the family shuns responsibility for the care of the young dependent, but that informal caregivers do not wish to interfere with patient’s daily living routines. In fact, when young dependent people decide to move to receive better attention, they experience a greater increase in the number of IC hours (6.78 vs. 3.51 for old dependent people).

Suffering dementia or mental illness and having been in hospital increase the number of IC hours for married and unmarried, but the coefficient is larger for the latter group, indicating that unmarried people are more prone to receive informal support in acute care circumstances (surgery) rather than in permanent ones (dementia). This evidence is supported by the fact that suffering disabilities with unfavorable prognosis increases the number of IC hours for married people but decreases it for unmarried.

Table F summarizes the interpretation of the selection bias terms for the models estimated. Most cases point to the complementary and task-specific models, that is, IC does not decrease when dependent people start receiving FC, and at the same time, when caregiving demands go beyond IC abilities, more complex tasks are carried out by formal caregivers. The only case in favor of the substitution model corresponds to the unmarried subsample, whereas the married, young and old subsamples clearly reject this hypothesis.

Table F. Interpretation of the bias correction terms of the BFG model

5. Conclusions

Searching for a central tendency in long-term care preferences is a worthwhile prelude to serious consideration of how to reshape policies and practices for dependent people. In this work we have explored the determinants of the choice of care as well as, conditional on the choice of care, the number of caregiving hours provided, while taking into account the potential sample selection bias induced by the type of care chosen.

On the econometric side, our study contributes to the literature by considering a joint choice of care and hours of care model. We have modeled the first-stage choice equation as a multinomial model and, more importantly, have been unable to reject this assumption against both a general (correlated alternatives) and some specific alternatives. Regarding the hours equation we have rejected the validity of the OLS estimates and, indirectly, have been unable to rule out that the choice of care and the hours of care are jointly determined.

Results from the multinomial logit for the choice of care point to the existence of differences by age, gender and marital status. Specially relevant from the point of view of policy are the results regarding the provision of social services, since the results obtained reveal large disparities among regions. The probability of receiving IC increases in those regions where social services coverage (telecare, home care) is insufficient, when the co-payment is higher than the average, or when time distribution between personal care and housework is biased towards the latter. This implies that social security programs should not be based on the assumption that dependents’ needs are about equal in all regions, since local needs vary according to the sociodemographic characteristics of the population.

Unlike Coyte (2001), Van Houtven and Norton (2004), Bolin et al. (2007) and Viitanen (2007), who confirmed a substitution effect between home care and informal care, we have obtained for the whole sample (as well as for most of the population groups considered) that an increase in the home care coverage rate implies an increase in the number of informal caregiving hours. Likewise, an increase in day center coverage rates is associated with a decrease in the provision of informal care. This points to complementarity between IC and “inside home” FC and substitution between IC and “outside home” FC. Both results are in sharp contrast with previous results obtained for other countries by Van Houtven and Norton (2004), Coyte (2001) and Bolin et al. (2007). On the other hand, we have observed the same negative correlation between residential services (day centers in our case) and IC as Viitanen (2007).

We have found a strong relationship between the number of IADL/PADL disabilities and the number of caregiving hours, which suggests that IADL/PADL disabilities should be an important criterion for determining the amount of formal care received. This is precisely the essence of the 2006 Law for the Promotion of Personal Autonomy and Care of Dependent People. According to this law, an individual is classified as being moderately, severely or highly dependent according to the number of times per day he or she requires support to perform daily living activities. The amount of services provided and the allowances received are different for the three degrees of dependency. The dependent must contribute to the cost of the service (home care) according to his or her personal income and wealth. From our point of view, this copayment should take into account the number of PADL/IADL disabilities suffered (with lower co-payment for a high dependency than a severe one, ceteris paribus).

Even after controlling for the number of PADL/IADL disabilities, mental illness, dementia and stays in hospitals are important predictors of the amount of care received. Suffering dementia and/or mental illness increases the probability of receiving FC and IC and the number of IC hours. However, it is not significant for the number of FC hours. In this regard, two factors help to clarify this situation: first, the supervision needed by those with behavioral problems may be too costly to provide with visiting staff; and second, the percentage of day center places adapted to psychogeriatric patients is quite low.

The analysis has shown that informal caregivers are not only the most usual caregivers in the community, but that they also provide the greatest amount of care. The probability of receiving IC increases with the numbers of PADL/IADL disabilities at a higher rate than the probability of receiving FC does. Results confirm that family members take part in providing the core of care: each additional co-resident adult slightly decreases the probability of FC for men and increases the probability of IC by 5% for women and unmarried.

Equity considerations dictate that long term care policies should consider the implicit costs supported by the family on an equal basis with monetary expenditure. Then, an efficient allocation of resources would be one in which informal caregivers provide care up to the point at which their opportunity costs are greater than the cost of formal care. An interesting issue for future research will be to analyze whether these changes provide a better mix between formal and informal care and whether they increase dependents’ and caregivers’ quality of life.

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Appendix.

Table 1. Descriptive Statistics by type of care received

Table 2. BFG model. First-step multinomial model. All sample. Marginal effects

Omitted category: No care. Omitted variables: age 40-49, no studies, active, missing value for household income, number of children less than 13 years old, single, size of municipality >500.000 inhabitants and Melilla. (^* p<0.10; ^** p<0.05; ^*** p<0.01). dy/dx= variation with respect to the base case. Base Case: men, age 80-99, married, elementary education, retired, household income between €390.6 and €1,171.97 per month, one PADL and one IADL disabilities, living in Cataluña

Table 3. BFG model. First-step multinomial model by gender. Marginal effects

Omitted category: No care. Omitted variables: age 40-49, single, size of municipality >500.000 inhabitants and Melilla. (^* p<0.10; p<0.05; ^*** p<0.01). Base Case: age 80-99, married, one PADL and one IADL disabilities, living in Cataluña. dy/dx= variation with respect to the base case. Results for the following variables are not shown due to space reasons: main breadwinner, level o education (elementary, high school, college), relation with economic activity (retired, contributive disability benefit, non contributive disability benefit), monthly household income (<390,6; 390,6-1.171,97; 1.171,97-1.953,27; 1.953,29-3.906,58; >3.906,58), rehabilitation treatment, impairement certificate, number of days in hospital, number of disabilities, disabilities fo (seeing, hearing, communicating, remembering/executing, relating), size of municipality (<10.000, 10.000-50.000,50.000-500.000).

Table 4. BFG model. First-step multinomial model by age group. Marginal effects

Omitted category: No care. Omitted variables: single, size of municipality >500.000 and Melilla. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Base Case: man, married, one PADL and one IADL disabilities, living in Cataluña. dy/dx= variation with respect to the base case. Results for the same variables than Table 4 are not shown due to space reasons.

Table 5. BFG model. First-step multinomial model by marital status. Marginal effects

Omitted category: No care. Omitted variables: single, size of municipality >500.000 and Melilla. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Base Case: man, one PADL and one IADL disabilities, living in Cataluña. dy/dx= variation with respect to the base case. Results for the same variables than Table 4 are not shown due to space reasons.

Table 6. BFG model & Interval Regression. Second-step hours equations. All Sample

Omitted variables: age 40-49, single, missing household income, number of children less 13 years old, size of municipality >500.000 inhabitants. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Bootstrapped standard errors. Test for all coefficients equal to zero when selection bias is not controlled: χ²(61)=291.36, p-value=0.0000; χ²(61)=1750.34, p-value=0.0000, χ²(61)=414.84, p-value=0.0000 respectively. (¶) Test equality of coefficients between models with and without controls for sample selection (second step of BFG vs. interval regression), with the exception of constant and selectivity terms.

Table 7. BFG model & Interval Regression by gender. Second-step hours equations.

Omitted variables: age 40-49, single, size of municipality >500.000 inhabitants. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Bootstrapped standard errors. Test for all coefficients equal to zero when selection bias is not controlled: χ (57)=183.22, p-value=0.0000; χ (58)=613.02, p-value=0.0000, χ (57)=123.38, p-value=0.0000 respectively for male subsample. And χ (58)=214.43, p value=0.0000; χ²(58)=1204.33, p-value=0.0000, χ²(58)=354.05, p-value=0.0000 respectively, for female subsample. Results for the following variables are not shown due to space reasons: relation with economic activity (retired, contributive disability benefit, non contributive disability benefit), monthly household income (<390,6; 390,6-1.171,97; 1.171,97-1.953,27; 1.953,29-3.906,58; >3.906,58), number of disabilities, disabilities for (seeing, hearing, communicating, remembering/executing, relating), severity (no severe/moderate severe, very severe, cannot do the activity), prognosis (recoverable with restrictions, stable, can go worse, do not know), number of PADL, PADL=2, PADL=3, PADL>=4, number of IADL, IADL=2, IADL=3, IADL>=4, size of municipality (<10.000, 10.000-50.000,50.000-500.000) (¶) Test equality of coefficients between models with and without controls for sample selection (second step of BFG vs. interval regression), with the exception of constant and selectivity terms.

Table 8. BFG model & Interval Regression by age group. Second-step hours equation.

Omitted variables: single, size of municipality >500.000 inhabitants. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Bootstrapped standard errors. Test for all coefficients equal to zero when selection bias is not controlled: χ (58)=114.58, p-value=0.0000; χ (58)=635.43, pvalue=0.0000, χ²(58)=120.75, p-value=0.0000 respectively for young subsample. And χ²(58)=243.45, p-value=0.0000; χ²(58)=1133.57, p-value=0.0000, χ²(58)=350.78, p-value=0.0000 respectively, for old subsample. Results for the same variables than Table 7 are not shown due to space reasons: (¶) Test equality of coefficients between models with and without controls fo sample selection (second step of BFG vs. interval regression), with the exception of constant and selectivity terms.

Table 9. BFG model & Interval Regression by marital status. Second-step hours equation.

Omitted variables: single, size of municipality >500.000 inhabitants. (^* p<0.10; ^** p<0.05; ^*** p<0.01). Bootstrapped standard errors. Test for all coefficients equal to zero when selection bias is not controlled: χ²(57)=132.28, p-value=0.0000; χ²(57)=919.45, pvalue=0.0000, χ (57)=194.04, p-value=0.0000 respectively for married subsample. And χ (59)=226.99, p-value=0.0000; χ (59)=929.72, p-value=0.0000, χ (59)=339.73, p-value=0.0000 respectively, for unmarried subsample. Results for the same variables than Table 7 are not shown due to space reasons: (¶) Test equality of coefficients between models with and withou controls for sample selection (second step of BFG vs. interval regression), with the exception of constant and selectivity terms.