Do Spanish informal caregivers come to the rescue of dependent people with formal care unmet needs? by 7 Sergi Jiménez-Martín * Cristina Vilaplana Prieto Documento de Trabajo 2013-21

December 2013

Universitat Pompeu Fabra, Barcelona GSE and FEDEA. ** Universidad de Murcia and FEDEA.

Los Documentos de Trabajo se distribuyen gratuitamente a las Universidades e Instituciones de Investigación que lo solicitan. No obstante están disponibles en texto completo a través de Internet: http://www.fedea.es. These Working Paper are distributed free of charge to University Department and other Research Centres. They are also available through Internet: http://www.fedea.es. ISSN:1696-750

Do Spanish informal caregivers come to the rescue of dependent people with formal care unmet needs? ^

Sergi Jiménez-Martín

Cristina Vilaplana Prieto

May 2013

Abstract

This paper analyses the effect of unmet formal care needs on informal caregiving hours in Spain using the two waves of the Informal Support Survey (1994, 2004). Testing for double sample selection from formal care receipt and the emergence of unmet needs provides evidence that the omission of either variable would causes underestimation of the number of informal caregiving hours. After controlling for these two factors the number of hours of care increases with both the degree of dependency and unmet needs. More importantly, in the presence of unmet needs, the number of informal caregiving hours increases when some formal care is received. This result refutes the substitution mode and supports complementarity or task specificity between both types of care. For a given combination of formal care and unmet needs, informal caregiving hours increased between 1994 and 2004. Finally, in the model for 2004, the selection term associated with the unmet needs equation is larger than that of the formal care equation, suggesting that using the number of formal care recipients as a quality indicator may be confounding, if we do not complete thi information with other quality indicators.

Keywords: double sample selection, unmet need, informal care, caregiver, formal care JEL Codes: H41, I10, I11

^ Financial help from project #ECO2011-30323-C03-02 is gratefully acknowledged. A previous version of the paper circulated under the title "A double sample selection model for unmet needs, formal care and informal caregiving hours of dependent people in Spain".

^ Universitat Pompeu Fabra, Barcelona GSE and FEDEA. Corresponding author. Department of Economics, Ramon Trias Fargas 25, 08005 BARCELONA (SPAIN).

^ Universidad de Murcia and FEDEA.

1. Introduction

In 2006, and still stepped in a phase of economic growth, the Spanish government enacted a new Dependency System (Act 39/2006, of 14th December, on the Promotion of Personal Autonomy and Care for Dependent persons), and long-term care expenditure with respect to GDP rose from 0.72% in 2006 to 1.02% in 2010. However, the persistent economic crisis and the increase of public deficit (8.9% at the beginning of 2012) obliged policy makers to implement control of public expenditure. In this context of budget-slashing times, funds devoted to long-term care suffered a dramatic cut in July 2012, (Royal Decree 20/2012, 13th July). This scenario runs into conflict with projections from the European Commission. The Ageing Report 2012 has revealed that due to progressive population ageing, it will be necessary to increase long-term care expenditure (EU-27) with respect to GDP in the period 2010-2060 from 1.8% to 3.6%. Given recent budget cuts observed in Spain (National Budget Act 2/2012 of 29th June and 17/2012 of 27th December), it is at least questionable that Spain will provide the necessary amount of formal care in the next decade. In this context we wonder what is going to be the “price” in terms of extra-caregiving hours that informal caregivers devote to their relatives in need of long-term care when they do not receive the required amount of formal care.

The interplay between formal and informal care has received great attention in the literature. For example, Van Houtven and Norton (2004), using data for the United States, studied the relationship between informal care provided by adult children and formal care, and concluded that informal care reduced home care use and delayed institutionalization. Charles and Sevak (2005), who also used U.S. data, found a negative and significant relationship between receiving informal care and the probability of entry into a residential home. Stabile et al. (2006) for Canada and Viitanen (2007) for the EU showed tha an increase in home care expenditure, in the first paper, and in both home care and residential homes, in the second one, led to a decrease in informal care, although for the European case, this reduction was only significant for non-co-resident informal caregivers. For the Spanish case, Jiménez-Martín and Vilaplana (2012) offer support for the complementary and task-specific models. In particular, they obtain evidence of substitution between formal and informal care for the male, young, married and unmarried subsamples. Regarding the hours of care, they found significant biases in predicted hours of care when sample selection is not taken into account.

But these results cannot be generalized. Several authors have noted the importance of the country of residence, the place where the individual receives care and the task performed by the caregiver. If we look at evidence for European countries, Bolin et al. (2008) observed that formal and informal care behaved as substitutes, although for the specific categories of “nursing care” and “in-hospital care” informal care behaved as a complement. Furthermore, informal care was more widespread in southern European countries. Regarding the nature of the aid provided, Bonsang (2009) and Mentzakis et al. (2009) found a substitution relationship for basic caregiving tasks (housekeeping tasks for the case of Bonsang), but a complementary relationship for more technological or complex tasks.

In view of this last result, the division of formal and informal tasks is of concern from a medical perspective in terms of timely and appropriate use of formal services to ensure the well-being of both caregivers and care-receivers. In fact, the Council of Europe (2003) acknowledged that in many countries most of the healthcare budget is spent on people towards the end of their lifetime. However, this does not mean that they receive the most appropriate care for their needs. The emergence of unmet personal needs with regard to daily living activities can result in a large number of negative consequences for the dependent, such as inability to drink or eat when thirsty or hungry, falls, neglected housekeeping and insufficient cleanliness due to uncontrolled urination or defecation (Allen and Mor, 1997). Unmet needs are also associated with an increase in physician visits, use of emergency departments, increase in the likelihood of home death and more frequent hospitalizations (Sands et al., 2006).

Research conducted to date has only begun to explore which factors could be related to unmet needs. The results obtained suggest that unmet needs are due to a combination of personal, social, cultural and environmental forces (Allen, 1994; Tennstedt et al., 1994). Some variables have been shown to be important predictors of unmet needs. Examples of these include dependent’s age, sex, health status and functional capacity, level of education and potential informal caregiving network (Allen, 1994; Tennstedt et al., 1994; Allen and Mor, 1997).

Although these studies provide evidence of the causes of unmet needs and knowledge of service barriers, they also present three important limitations. First, previous studies do not usually distinguish between users and non-users of services for dependent people, and in consequence, we cannot know whether the two groups suffer the same level of unmet needs. The separation of these two subsamples is fundamental because some empirical papers suggest that willingness, need and degree of service use are different (Mui and Burnette, 1994; Andersen, 1995). Second, due to the existence of great disparities between dependents’ needs and the size of their informal caregiving network, the type of unmet needs may vary among them. However, most research has not studied in depth how informal caregivers face the problem of unmet needs. Finally, many investigations are based on medical reports or non-caregivers’ statements, the primary caregiver’s perspective being widely ignored. Nevertheless, their point of view is very valuable because they act as a link between the patient and social services and constitute a fundamental factor for negotiation with service providers (Bass et al., 1999).

The literature on unmet needs in Spain is quite scarce and by no means representative of the Spanish population.¹ In this paper we avoid previous limitations by focusing on the representative subsample of dependent individuals who demand home care or day centre care while taking into account both the characteristics of the informal caregiving network and the socio-demographic characteristics of the primary informal caregiver. We use the two waves of the Informal Support Survey (IMSERSO, 1994 and 2004), which contain information about Spanish older people with disabilities (aged 60+) receiving informal care. Raw data shows that, for the same degree of dependency, there is a great variation in informal caregiving hours depending on formal care receipt and the existence of unmet needs. In this situation there may be a selection problem that may lead to inconsistent estimates of the determinants of informal caregiving hours. The selection problem arises when individuals who receive formal care (FC) are not a random sample of potential individuals with disabilities or when the occurrence of unmet needs (UNs) is not random.

Otero et al. (2003) investigated unmet needs using a sample of 1,135 elderly people living in Leganés, a large town near Madrid. Their results pointed to the existence of great social inequalities in access to home care. Tomás et al. (2002) focused on the population aged over 75 living in the city of Zaragoza, and reached similar conclusions. Finally, Orfila et al. (1997) performed a study on 1,137 elderly people living in Barcelona and observed that 10% to 25% of those interviewed suffered unmet needs and that mortality and morbidity rates over a 5-year horizon were significantly higher for the unmet needs group than for the rest of the sample.

In this regard, this research contributes to the literature by accounting for self-selection in both formal care and unmet needs. We specify an hours equation for informal caregivers and use a double selection framework to correct the likely non-random selection of dependent individuals in the receipt of formal care and the appearance of unmet needs regarding the provision of social services. The distinction from earlier work is that the two decisions are treated jointly, reflecting the various combinations of formal care and unmet needs. Clearly, specifying one of these choices as exogenous, or ignoring it, leads to biased and inconsistent estimates in the estimated hours equations. Therefore, we adopt an approach outlined by Tunali (1986) to introduce the double selection criteria into the specification. To the best of our knowledge there is no study in the international (or the Spanish) context that uses nationally representative data sets to study the response of informal caregivers’ hours to both formal care allocation and the emergence of unmet home care or day centre needs.

In this context we have the following specific objectives. First, to evaluate the incidence of unmet needs by degree of dependency, where the level of dependency (moderate, severe and high) is calculated according to the Spanish Dependency Classification introduced into the 2006 Dependency Law. Second, to analyse which factors are associated with the emergence of unmet formal care needs, paying special attention to regional characteristics of social services for dependent people. Third, given that the caregiver’s behaviour may be conditioned by his perception of the dependent’s requirements of care, we want to quantify if unmet formal care needs impinge upon the number of informal caregiving hours.

The estimation of a bivariate probit model for the variables FC and UNs reveals the existence of significant correlation between the disturbances of the two equations, thereby suggesting that the relationship between these two variables cannot be ignored in the estimation of the informal hours of care equation. In the hours equations, the interpretation of the selection terms indicates that dependent people receiving FC but having UNs get more caregiving hours than those having UNs but not receiving FC. This result implies that formal and informal care in Spain did not behave as substitutes, but rather as complements. Additionally, the selection term associated with the UNs equation is larger than that corresponding to the FC equation, implying that the inefficiencies in the allocation process are more important than the insufficient provision of some social resources for dependent people. The number of informal caregiving hours increases with the degree of dependency. Furthermore, comparing situations with UNs, the number of caregiving hours is always higher in those situations where some FC is received, which strengthens the hypothesis of complementarity or task sharing between the two types of care. Finally, the gap in caregiving hours between moderate and high dependency increased between the two waves.

The rest of the paper is structured as follows. In section 2 we describe the data, the characteristics of the sample and the determination of the degree of dependency. In section 3 we explain the double selection model. Section 4 presents the estimation results of the model. Finally, in section 5 we present some conclusions regarding long-term care policy and perspectives of the new Dependency Law.

2. Data

The data sources for the study are the two waves of the Informal Support Survey, which were carried out by IMSERSO in 1994 and 2004. The aim of the survey was to obtain information, through personal interviews at household level, from informal caregivers of dependent people. The 2004 survey contains 1,504 observations, for dependent people aged 60 or over living in Spanish households (with the exception of Ceuta, Melilla and La Rioja). The 1994 survey contains 1,702 observations for adults aged 40 or over with disabilities living in Spanish households (excluding Ceuta and Melilla). To homogenize the two samples, we dropped individuals younger than 60 years old and those living in La Rioja (37 observations) from the 1994 survey, leading to a sample with 1,665 individuals.

As the purpose of this paper is limited to the study of unmet needs among dependent people who receive informal care, the conclusions obtained cannot be applied to the fraction of institutionalized dependent people or those who only receive formal care.

These two surveys constitute the more recent available data containing information about formal care, unmet needs and number of informal caregiving hours. More importantly, given that the Spanish Dependency System started in 2007, the analysis of both surveys (referred to an earlier period) enable us to analyze the effect of formal care unmet needs over the provision of informal care, without fear of being “contaminated” by the 2007 reform and the budgetary cuts often observed since then².

2.1. Determination of the degree of dependency

Instead of proxying the degree of dependency using the traditional approach of the number of IADL and PADL, here we opt to apply the Ranking Scale mentioned in Law 39/2006, of 14^th December, for the Promotion of Personal Autonomy and Care of People in a Situation of Dependency³. The Ranking Scale distinguishes three degrees of dependency: moderate dependency when the individual needs help for daily living activities once a day; severe dependency when he needs help for daily living activities two or three times a day, and high dependency when he needs help several times per day, and due to the complete loss of physical, mental, intellectual or sensory autonomy, he requires permanent support. Moreover, the Ranking Scale identifies two levels of dependency within each of the three degrees (moderate, severe or high). The first level corresponds to those individuals who can perform the activity without the direct support of a third person, whereas the second level refers to the situation in which the dependent individual requires specific support.

Tables 1 and 2 in Appendix A compare the questionnaire for the Ranking Scale of the Dependency Law with the information from the survey. Finally, we compute the final scores and attribute the corresponding degree of dependency (Table A):

Table A. Ranking Scale for the determination of the level of dependency

2 Although we cannot asses the effect of the Spanish Dependency System (comparing the situation pre & post 2007), the budgetary cuts imposed in July 2012, have almost drown the potential benefits derived from it, and will lead our long-term care system is going to draw back to pre-reform times. Consequently, the estimations for 2004 will provide an assessment of the environment faced by informal caregivers 9 years afterwards.

³ This Ranking Scale was enacted by Delegated Legislation 504/2007, of 20^th April.

Source: http://www.dependencia.imserso.es/InterPresent2/groups/imserso/documents/binario/manualusobvd.pdf and Jiménez-Martín and Vilaplana (2012).

Comparing the two waves, we observe a slight decrease in moderate dependency (level 1) and an increase in the percentage of individuals without any degree of dependency⁴. Figures for the other degrees are approximately the same⁵.

2.2. Concept of unmet needs

With respect to the healthcare literature on unmet needs, the concept of “need” has been defined as “those requirements that enable individuals to reach, maintain or recover an acceptable level of social independence and quality of life” (Department of Health Social Services Inspectorate, 1991). A more practical definition considers that “need” is the “ability to benefit from social services” (Stevens and Gabay, 1991). However, the problem with this definition is that there is no good indicator available to measure the impact of the treatment received (Aoun et al., 2004).

One of the first definitions of “unmet need” was given by Isaacs and Neville (1976), who described an elderly person’s unmet needs as the result of one or both of the following situations: “insufficient care to fulfil his basic requirements for food, warmth, cleanliness or security at the level at which he would have provided them for himself”, and/or “when care was provided only at the cost of undue strain of relatives”.

In certain cases, an unmet need is identified with a situation in which an individual with care needs does not receive any formal aid. Alonso et al. (2007) considered that an “unmet need” appeared when mental patients had not received any formal care during the last twelve months. On the other hand, Allen and Mor (1997) designed an algorithm in which people with some difficulties for daily living activities (who did not receive formal help and did not desire to receive it) were classified as individuals with covered needs.

Some authors view the above definition as too strict. For example, Quail et al. (2007) perceived that an unmet need could arise in two situations: (1) when the individual is currently receiving help, but would like to receive more, and (2) when he does not receive any help, but has experienced some negative consequence due to the lack of it. Williams et al. (1997) also considered those unmet needs due to insufficient or inadequate formal care.

In this paper, we have considered an outcome-oriented approach because it provides a solid foundation for defining the concept of unmet needs based upon norms that may change with social standards. This definition is in consonance with Davies (1977), who described “unmet need” as the difference between the desired and the current state of well-being. The variable “formal care” takes the value 1 when the dependent individual (or his caregiver) has applied for home care and/or day centre care and actually receives it. We focus on home care and day centres because although there exist other types of social services for dependent people, demand for them was very low. For example, in 2004, applications to the laundry service accounted for only 2.49% of the total, meals-on-wheels 2.76%, and the respite service 3.32%.

⁴ This is an effect of the increase in the number of healthy life years at birth, from 67.7 in 1996 to 70.2 in 2003 (Eurostat, Health Indicators).

⁵ To validate the reliability of the estimates for the various degrees of dependency, we have compared these figures with those obtained from the White Paper on Dependency (IMSERSO, 2004; page 89). We have ascertained a grea degree of concordance between the two sources.

For the definition of the variable “unmet needs” (UN) caused by an application’s rejection we used the following two questions (i) “On this card, there is a list of social services for dependent people; could you please tell me which you have ever applied for?”, and (ii) “which of them are you receiving?”. Therefore, the variable UNs takes the value 1 when the caregiver answers Home Care and/or Day Centre to the first question, and afterwards says that he has not received the service requested. In the event of the individual having applied for both services, we are able to know if he has received both of them, only one or neither of them. For the case of UNs caused by dissatisfaction regarding the quality or the quantity of the service, we used the following question: “ Please tell me how you would evaluate the help received from social services (excellent, good, poor, bad) with respect to the following aspects: (i) provider’s training, (ii) number of hours received, (iii) provider’s attitude”. We have considered that the variable UNs takes the value 1 if, for any of the previous attributes, the informal caregiver answered “poor” or “bad”.

With respect to the question of the group of individuals who do not receive formal care and do not report unmet needs, following Allen and Mor (1997), we have classified them as individuals with covered needs. In a strict sense these individuals could suffer some certain type of unmet needs. For example, Wackerbath and Johnson (2002), Mangan et al. (2003), Aoun et al. (2005) and Orstein et al. (2009) have explored informational needs concerning community services and counselling for how to deal with disability and illness. In our case, although the survey provides information regarding other needs of caregivers (i.e., more flexible working time, possibility of receiving a caregiver allowance, tax deductions, leaves of absence), these topics are beyond the scope of this paper.

The provision of social services for dependent people in Spain, before the implementation of the new System of Autonomy and Attention to Dependent People in 2007, was conditioned to both the generosity and the requirements imposed by the different regional administrations. The White Paper on Dependency (2004) lists the variables considered for awarding social services for dependent people: (i) territoriality, that is, having lived for more than three years in the autonomous community where the application process is taking place, (ii) health status (functional dependency, mental and physical disabilities), (iii) age (most communities gave preference to individuals aged 60-65 or older), (iv) personal economic resources and (v) living conditions (living alone, dwelling conditions). Each autonomous community assigned a different weight to each of the previously mentioned factors. Therefore, the degree of generosity of each community and the prevalence of different criteria provide an invaluable source of identification of formal care in the model. Since the weights attributed to each of the requirements⁶ envisaged in the awarding process did not change between the two waves, the comparability between them is guaranteed. However, comparisons between 1994 and 2004 should be tempered by the fact that informal caregivers’ preferences may have experienced slight changes.⁷

⁶ See IMSERSO (2004), Older people in Spain. 2004 Report for detailed data of regional long-term care policies.

⁷ Between 1994 and 2004, we observe an increase in the percentage of respondents who considers that the primary caregiver should always be a woman and a decrease in the percentage who considers that care devoted by presen generations is worse than it was in the past.

2.3. Descriptive statistics

Table 3 in Appendix B shows the descriptive statistics for each of the combinations of the variables FC and UNs. Between 1994 and 2004, the percentage of individuals with unmet needs decreased by 45.23%. In particular, unmet needs caused by rejection of a previous application decreased by 46.29%, whereas unmet needs due to dissatisfaction with the quantity or quality of the formal care received decreased by 35.79%.

In aggregate terms, the level of education changed substantially because the fraction that had not even finished elementary education decreased from 95.94% in 1994 to 61.60% in 2004. As regards specific pathologies, there was an increase in respiratory problems (from 8.54% to 18.05%) and osteoarticular problems (from 24.24% to 52.65%).

The group of dependents with an income of €301-€600/month increased from 23.81% to 57.19%. In aggregate terms there was no variation according to the category of benefit received (around 40% corresponded to retirement benefit, 30% to survival benefit and 6% to disability benefit), but we find an increase in the percentage of retired individuals with FC=1&UN=1 (from 36.7% to 62.4%).

Most caregivers were women (85%) and over 50 years old⁸. There was a considerable growth in the percentage of caregivers with elementary (18.26% to 42.97%) and high school education (9.08% to 32.61%). As a consequence, there was an increase in the percentage of working caregivers (21.74% to 26.03%) and a decrease in those devoted to housekeeping (49.87% to 44.15%).

Considering now the characteristics of the different groups we observe that the fraction of permanent caregivers when rose from 70.9% to 83.3%, and the fraction of willing caregivers increased in those situations where FC=1 (from 59.8% to 68% and from 51.7% to 59%). Both facts point to a lack of perfect substitutability between formal and informal care and may indicate a caregiver’s attempt to alleviate the insufficient allocation of formal care.

For the situation FC=1&UN=1, we observe an acute increase in the percentage of dependent people who live with his/her spouse (from 27.2% to 45.5%) and a decrease in the fraction living with his/her son/daughter (from 38.7% to 28.9%). For this same category, adult children became more involved in caregiving tasks (from 42.4% to 54.7%) as opposed to the son/daughter-in-law (from 12.2% to 7.8%). We also observe an increase in the percentage of dependent people who lived in provincial capitals and suffered unmet needs (from 11.9% to 27.8% when FC=0 and from 15.8% to 31% when FC=1).

Figure 1 shows the relationship between formal care and unmet needs according to the degree of dependency. The percentage with FC=1&UN=1 increased between 1994 and 2004 for all three types of dependency, the largest increase corresponding to high dependency (from 7.12% to 11.66%). The fraction with FC=0&UN=1 shows an increasing profile with the degree of dependency, and in 2004 nearly 40% of highly dependent people did not receive any formal service although they had applied for home care or day centre care.

⁸ There was a slight increase in caregiver’s age from 51.86 in 1994 to 53.19 in 2004. We observe a higher fraction of caregivers in the intervals 50-64 and 65+ for the situation FC=1&UN=1 (from 36.1% to 41.2% between 1994 and 2004, and from 15.1% to 25.1%, respectively).

Figure 2 shows the average caregiving hours and years for those informal caregivers who provide care at least 3 hours per In the case of high dependency, caregivers devote more hours when FC=1&UN=1 (16.59 hours/day), whereas informal caregivers of moderate or severely dependent people devote more hours when FC=0&UN=1 (14.54 hours/day and 12.72 hours/day respectively). In turn, informal caregivers of severely dependent people with FC=0&UN=1 report more caregiving years (8.52) in comparison with the average of 5.64 years for the other situations.

Figure 1. Distribution of FC and UNs according to degree of dependency, 1994 and 2004 (%)

Figure 2. Average hours and years of informal caregivers who devote at least 21 hours/week, 2004

3. Econometric model with double sample selection

⁹ In this figure, we have focused on caregivers providing at least 3 hours of care per day because this level of intensity is more likely to be provided to disabled older people than care provided at lower levels of intensity (Kemper, 1992). For 2004, we have information about the number of daily caregiving hours. By fixing a threshold at 3 hours per day, we obtain the sample of caregivers with at least 21 hours per week (1,286 informal caregivers from the initial sample of 1,504 devote at least 21 hours/week).

The main aim of this study is to assess whether informal caregivers of dependent people with unmet needs and/or receiving formal care devote more caregiving hours than caregivers whose dependent relatives do not suffer any unmet need and/or do not receive any formal care. As we mentioned above, unmet needs may arise because the dependent does not receive any of the formal aid that he or she has applied for (home care and/or day centre care), or because he or she is not satisfied with either the quality or the quantity of the formal aid received.

Although we observe hours for the whole sample of informal caregivers, analysing the hours problem independently of the provision of formal care and/or unmet needs may lead to inconsistent estimates, either because the appearance of unmet needs does not follow a random process or because the dependent population who receives formal care is not a random sample of the population. Lack of control of any of these two sources of potential endogenous selection may lead to inconsistent estimates of the parameters characterizing the informal hours equation. Assuming simultaneity of all decisions, we adopt the double sample selection model proposed by Tunali (1986) to model the underlying decision process involved in receiving formal care and having unmet formal care needs and their implications for the number of informal caregiving hours.

Let us start, first, by analysing the relationship between formal care and unmet needs. The pair of decision rules may be presented in a standard bivariate framework (Heckman, 1979; Maddala, 1983), as shown in Figure 3:

Figure 3. Situation of dependent people

\[D e p e n d e n t _ {i} = \left\{ \begin{array}{l} F C _ {i} = 1 \left\{ \begin{array}{l} U N _ {i} = 1 \\ U N _ {i} = 0 \end{array} \right. \\ F C _ {i} = 0 \left\{ \begin{array}{l} U N _ {i} = 1 \\ U N _ {i} = 0 \end{array} \right. \end{array} \right.\]

where the variables and take the value 1 when the dependent individual receives formal care and suffers an unmet need respectively, and the value 0 otherwise. Consequently, there is an unmet need either if the dependent individual (or the caregiver) has applied for formal aid but does not receive it, or because the service received has fallen below expectations. These decisions may be expressed as follows:

\[\begin{array}{r} F C _ {i} ^ {*} = Z _ {1 i} ^ {\prime} \beta_ {1} + u _ {1 i} \\ U N _ {i} ^ {*} = Z _ {2 i} ^ {\prime} \beta_ {2} + u _ {2 i} \end{array}\tag{1}\]

(2)

where the variable measures the generosity level of social services for dependent people as the difference between the amount of services offered and the conditions required to be eligible for them (functional and mental disabilities, financial resources, dwelling conditions, family situation). The dependent individual receives formal care when the latent dependency level is higher than the threshold required . The variable measures the difference between the expected benefit from formal care and the current provision of services. The informal caregiver will report an unmet needs problem when the expected benefit is higher than the observed level of care, that is, when . In equations (1) and (2), the vectors and represent the set of observable characteristics that affect the receipt of formal care and the appearance of unmet needs, where and are the corresponding coefficients, and and are the residual terms, which we suppose are bivariate normally distributed with

¹⁰ To the best of our knowledge, there is no previous evidence considering the potential problem of selection in formal care or the emergence of unmet needs and their effect on informal caregiving hours.

The dependent variables are both unobservable and latent. We observed instead a binary variable that takes the value 1 if the dependent individual receives formal care ), and another binary variable that takes the value 1 if the informal caregiver perceives an unmet needs problem ). The conditional likelihood function of the bivariate probit model is given by (Greene, 2007):

\[\begin{array}{l} \ln L = \sum_ {i = 1} ^ {N} \ln \Phi_ {2} \left(q _ {1 i} \left(Z _ {1 i} ^ {\prime} \beta\right), q _ {2 i} \left(Z _ {2 i} ^ {\prime} \gamma\right); \rho^ {*}\right) \\ q _ {1 i} = \left\{ \begin{array}{l l} 1 s i F C _ {i} \neq 0 \\ - 1 o t h e r w i s e \end{array} ; q _ {2 i} = \left\{ \begin{array}{l l} 1 s i U N _ {i} \neq 0 \\ - 1 o t h e r w i s e \end{array} ; \rho^ {*} = q _ {1 i} q _ {2 i \rho} \right. \right. \end{array} \tag {3}\]

Let us now turn to the following hours equation:

\[\ln I H _ {i} = X _ {i} ^ {\prime} \gamma + \varepsilon_ {i}\tag{4}\]

where ln denotes the natural logarithm of the number of informal caregiving hours, X is a vector of exogenous variables that explain caregiving hours, and is a normally distributed error term with , which is, in general, correlated with the errors in equations (1) and (2). To illustrate the double selection problem, it might be useful to compare the number of caregiving hours of caregivers with UNs with those of caregivers without UNs. For the case in which the dependent does not receive FC, caregivers with UNs increase their caregiving hours by 33.38%, and when the dependent does receive FC, caregivers with UNs devote 60.90% additional daily hours¹¹. Is this difference indicating an extra effort by caregivers to compensate for formal care deficiencies?

Two other possible explanations have to be tested before answering this question. Firstly, caregivers with UNs may devote more caregiving hours because they are a self-selected group with regard to observable characteristics. Should this be the case, the question of extra caregiving hours would be solved by simply estimating caregiving hours which control for the relevant observable variables of each group. Secondly, if caregivers with UNs are self-selected with regard to unobservable characteristics (i.e., inadequacy of formal care for the disabilities suffered by the dependent individual), the OLS estimates are inconsistent.

Figure 4 details the possible outcomes of the selection process, where represents the set of individuals belonging to the subsample corresponds to the state in which the dependent does not receive any formal care and does not suffer any unmet need; denotes the state in which the dependent does not receive any formal care but would like , and therefore an unmet need appears; is the situation in which the dependent receives formal care and is satisfied with and denotes the situation in which the dependent individual receives formal care but considers that the amount or quality of the aid received is not what he or she expected, and consequently there is an unmet need.

¹¹ See Table 8 for mean caregiving hours in 2004.

Figure 4. Possible outcomes for the selection process Unmet needs (UN_i)

The probabilities corresponding to each subsample are expressed as follows:

\[S _ {1} = \operatorname * {P r} \left[ F C _ {i} = 0, U N _ {i} = 0 \right] = \operatorname * {P r} \left[ F C _ {i} ^ {*} \leq 0, U N _ {i} ^ {*} \leq 0 \right] =\]

\[= \operatorname * {P r} \left[ u _ {1 i} \leq - Z _ {1 i} ^ {\prime} \beta_ {1}, u _ {2 i} \leq - Z _ {2 i} ^ {\prime} \beta_ {2} \right] = \Phi_ {2} (- \Pi_ {1}, - \Pi_ {2}; \rho)\tag{6}\]

\[S _ {2} = \operatorname * {P r} \left[ F C _ {i} = 0, U N _ {i} = 1 \right] = \operatorname * {P r} \left[ F C _ {i} ^ {*} \leq 0, U N _ {i} ^ {*} > 0 \right] =\]

\[= \operatorname * {P r} \left[ u _ {1 i} \leq - Z _ {1 i} ^ {\prime} \beta_ {1}, u _ {2 i} > - Z _ {2 i} ^ {\prime} \beta_ {2} \right] = \Phi_ {2} (- \Pi_ {1}, \Pi_ {2}; - \rho)\tag{7}\]

\[S _ {3} = \operatorname * {P r} \left[ F C _ {i} = 1, U N _ {i} = 0 \right] = \operatorname * {P r} \left[ F C _ {i} ^ {*} > 0, U N _ {i} ^ {*} \leq 0 \right] =\]

\[= \operatorname * {P r} \left[ u _ {1 i} > - Z _ {1 i} ^ {\prime} \beta_ {1}, u _ {2 i} \leq - Z _ {2 i} ^ {\prime} \beta_ {2} \right] = \Phi_ {2} \left(\Pi_ {1}, - \Pi_ {2}; - \rho\right)\tag{8}\]

\[S _ {4} = \operatorname * {P r} \left[ F C _ {i} = 1, U N _ {i} = 1 \right] = \operatorname * {P r} \left[ F C _ {i} ^ {*} > 0, U N _ {i} ^ {*} > 0 \right] =\]

\[= \operatorname * {P r} \left\lfloor u _ {1 i} > - Z _ {1 i} ^ {\prime} \beta_ {1}, u _ {2 i} > - Z _ {2 i} ^ {\prime} \beta_ {2} \right\rfloor = \Phi_ {2} \left(\Pi_ {1}, \Pi_ {2}; \rho\right)\tag{9}\]

where and is the bivariate standard normal probability function. These probabilities will determine the structure of the informal caregiving hours equations. In particular, we consider a flexible specification for the logarithm of the number of informal caregiving hours for each subsample, allowing for variation in the coefficients of the regressors and the selection correction terms:

\[\ln I H _ {1 i} = X _ {i} ^ {\prime} \gamma_ {1} + \delta_ {1 1} \lambda_ {1 1 i} + \delta_ {1 2} \lambda_ {1 2 i} + \varepsilon_ {1 i}\tag{10}\]

\[\ln I H _ {2 i} = X _ {i} ^ {\prime} \gamma_ {2} + \delta_ {2 1} \lambda_ {2 1 i} + \delta_ {2 2} \lambda_ {2 2 i} + \varepsilon_ {2 i}\tag{11}\]

\[\ln I H _ {3 i} = X _ {i} ^ {\prime} \gamma_ {3} + \delta_ {3 1} \lambda_ {3 1 i} + \delta_ {3 2} \lambda_ {3 2 i} + \varepsilon_ {3 i}\tag{12}\]

\[\ln I H _ {4 i} = X _ {i} ^ {\prime} \gamma_ {4} + \delta_ {4 1} \lambda_ {4 1 i} + \delta_ {4 2} \lambda_ {4 2 i} + \varepsilon_ {4 i}\tag{13}\]

where are the coefficients associated with the selection variables , and l=1,2. which are defined as follows:

\[\lambda_ {1 1} = - \frac {\phi (\Pi_ {1}) \Phi (- \Pi_ {2} ^ {*})}{S _ {1}}; \lambda_ {1 2} = - \frac {\phi (\Pi_ {2}) \Phi (- \Pi_ {1} ^ {*})}{S _ {1}}\]

\[\lambda_ {2 1} = - \frac {\phi (\Pi_ {1}) \Phi (\Pi_ {2} ^ {*})}{S _ {2}}; \lambda_ {2 2} = \frac {\phi (\Pi_ {2}) \Phi (- \Pi_ {1} ^ {*})}{S _ {2}}\]

\[\lambda_ {3 1} = \frac {\phi (\Pi_ {1}) \Phi (- \Pi_ {2} ^ {*})}{S _ {3}}; \lambda_ {3 2} = - \frac {\phi (\Pi_ {2}) \Phi (\Pi_ {1} ^ {*})}{S _ {3}}\]

\[\lambda_ {4 1} = \frac {\phi (\Pi_ {1}) \Phi (\Pi_ {2} ^ {*})}{S _ {4}}; \quad \lambda_ {4 2} = \frac {\phi (\Pi_ {2}) \Phi (\Pi_ {1} ^ {*})}{S _ {4}}\]

\[\Pi_ {1} ^ {*} = \frac {\Pi_ {1} - \rho \Pi_ {2}}{\sqrt {1 - \rho^ {2}}}; \quad \Pi_ {2} ^ {*} = \frac {\Pi_ {2} - \rho \Pi_ {1}}{\sqrt {1 - \rho^ {2}}}\]

where (·) corresponds to the univariate standard normal density function and (·) is the cumulative standard normal distribution. It must be noted that the nature of the informal caregiving hours variable is not the same for both waves. In the first wave, it was coded as a continuous variable, so we have estimated (10)-(13) by OLS, but in the second one, it was coded as an interval variable, and therefore we have used interval regression (see section 3.1 for further details).

The sequential nature of our approach does not preclude any implication about the relationship between unmet needs, formal care and informal caregiving hours. More generally, the double sample selection model can also be estimated by maximum likelihood (ML). Full-information estimation of the double sample model via maximum likelihood is very appealing given the limited nature of the dependent variables, the need to numerically approximate multidimensional integrals to capture error correlations and the high-dimensional parameter space of the selection models (Nawata and Nagase, 1996). The likelihood for this problem is given by:

\[\begin{array}{l}L = \prod_{\substack{FC = 0\\ UN = 0}}\Phi_{2}\big(Z_{1i}^{\prime}\beta_{1},Z_{2i}^{\prime}\beta_{2},\rho \big)\cdot \phi \big(\ln IH_{1i}\big)\prod_{\substack{FC = 0\\ UN = 1}}\Phi_{2}\big(Z_{1i}^{\prime}\beta_{1}, - Z_{2i}^{\prime}\beta_{2}, - \rho \big)\cdot \phi \big(\ln IH_{2i}\big)\\ \prod_{\substack{FC = 1\\ UN = 0}}\Phi_{2}\big(-Z_{1i}^{\prime}\beta_{1},Z_{2i}^{\prime}\beta_{2}, - \rho \big)\cdot \phi \big(\ln IH_{31i}\big)\prod_{\substack{FC = 1\\ UN = 1}}\Phi_{2}\big(-Z_{1i}^{\prime}\beta_{1}, - Z_{2i}^{\prime}\beta_{2},\rho \big)\cdot \phi \big(\ln IH_{4i}\big) \end{array}\tag{14}\]

However, maximum likelihood estimation is further complicated when there is a high degree of correlation between the selection and the outcome equation (Nawata, 1994) and when the selection hurdle leads to a high degree of censoring in the first equation (Manning et al., 1997). In addition, convergence problems usually appear when it is necessary to estimate a large set of parameters (Nawata and Nagase, 1996).

Moreover, estimation via Heckman has several advantages over ML: straightforward accommodation of limited observability data to the outcome and selection equations, computational simplicity for the generation of predictions, and the possibility of avoiding multidimensional integrals. Nawata and Nagase (1996) compared the finite sample properties of the estimators obtained via ML and via Heckman’s process, and concluded that a key indicator of the likely performance of Heckman’s estimator with respect to ML is the collinearity in the systemic portion of the selection equation and the regressors in the outcome equation. We estimated the model by ML and Heckman’s method and observe a high degree of consistency between the two estimates (ML estimates are available upon request¹²). Therefore, in the following we will focus on the two-step double sample selection model.

3.1. Empirical specification and identification strategy

The variable “informal caregiving hours” (IC hours) records the number of daily caregiving hours devoted by the respondent caregiver. In case of more than one informal caregiver, we only know the number of caregiving hours of the main caregiver. In the 1994 survey, the number of caregiving hours is recorded in 4 intervals: less than 1, 1-2, 2-5 and more than 5 hours/day. In the 2004 survey, the number of informal caregiving hours was recorded in the following way: less than one hour, 1-3, 3-5, 5-8 hours/day and more than 8 hours/day. Those who answered more than 8 caregiving hours (607 observations) also report the exact number of hours (593 cases + 15 missing). For these cases we create a bracket variable, which consists of making assumptions about the intensity of caregiving (Byrne et al., 2006). Using a conservative approach, we compute the average caregiving hours assuming that the amount of care was less than or equal to 8 hours (4.06 hours per day). Nevertheless, we tested the sensitivity of the bracketing approach¹³.

¹² We performed a test of equality of coefficients between ML estimation and the double sample selection model. For both waves we cannot reject the null hypothesis: 84 (p-value: 0.9085) in 1994 and ²(43)=30.15 (p-value: 0.9306) in 2004.

To ensure the identification of the model, not only by the non-linearity of the selection correction terms, standard selection models require the existence of at least one exclusion restriction. However, for the case of double sample selection models, Tunalli (1986) states that it is necessary to impose additional restrictions to identify the selection terms. First, at least one variable of each selection equation must not be related to the unexplained hours component. Second, at least one variable included in the FC equation must not appear in the UNs equation, and vice versa. And third, these variables must not be included in the hours equations.

The three equations include age and gender of the care-receiver and also that of the caregiver¹⁴, living alone, a list of chronic pathologies, degree of dependency and size of municipality. The size of the municipality has been included in all of them because it may influence the availability of formal care (professionals and/or facilities) and consequently the emergence of unmet needs (inexistence of the service, waiting lists), but at the same time geographical dispersion could have an effect on the number of informal caregiving hours that the caregiver can devote to the dependent relative (due to transportation and time costs, Charles and Sevak, 2005)

The following variables are included in the FC and hours equations, but not in the UNs equation: marital status of the care-receiver, number of caregiving years, permanent caregiver, willing caregiver, children under 18 living at home, receiving private formal care, and whether informal caregiver receives support from other informal caregivers. The reason is that these variables may have an influence over the number of informal caregiving hours provided and/or the predisposition to apply for social services. The availability of other informal caregivers has been included in the FC and hours equation because previous research suggests that informal caregivers who do not receive help from other family members are more likely to receive assistance from formal sources (Kemper, 1992; Ettner, 1996) and consequently, primary informal caregivers behave differently if the informal caregiving network increases. In these analyses, the participation of other caregivers has been considered as exogenous, and therefore, they exclude the possible interdependence between caregiving decisions. On the other hand, the receipt of private formal care may be a consequence but not a cause of the existence of unmet needs (due to public services)¹⁵.

Variables referring to income (category of benefit, amount of monthly benefit) and to education (both caregiver and care-receiver) have only been included in the FC equation because they reflect the socio-economic status of the individual. Several authors (Kemper, 1992; Breuil-Genier, 1999; Portrait et al., 2000) have observed that more educated people have a higher probability of receiving FC or both types of care together. Several explanations are possible: (1) more educated patients tend to have more educated children to whom the opportunity cost of providing informal care tends to be higher; (2) more educated care-receivers usually prefer to remain independent of their children for as long as possible and do not feel uncomfortable paying for formal services; (3) more educated care-receivers or their children may find it easier to use information regarding services for dependent people.

¹³ We have estimated the full model excluding the 121 observations with imputed hours, and the results did not change significantly [detailed results are available from the authors on request].

¹⁴ Caregiver’s age and sex may affect the demand for social services because older caregivers may also suffer disabilities that prevent them from providing an adequate level of care to the care-receiver. With regard to gender, there is evidence that women caregivers report more unmet needs than male ones (Lima and Allen, 2001).

¹⁵ Given the information in the survey, we do not know the reason for hiring private formal care.

Both FC and UN equations share some variables which are not included in the hours equation: coverage index of home care and day centres, and the co-payment for home care and day centres (all of them by autonomous communities)¹⁶. We consider that the coverage index not only affects the probability of receiving the service but also the probability of wishing to receive it¹⁷. Additionally, the existence of a certain co-payment percentage may prevent some individuals from applying for the service or may influence the perception of the relationship between quantity and quality of the service. In fact, the difference in the variables “co-payment percentage” and “cost per hour” across autonomous communities means that the contribution made by two users who live in different regions and receive the same amount of service could be quite divergent. In this respect, Forder and Fernández (2009) consider that the existence of co-payment for formal care is an important variable regarding the appearance of unmet needs because the cost borne by the user might reduce the amount of formal care taken up by the individual with disabilities.

By contrast, in the specification of the UNs equation we have included the number of home care hours per month, the percentage of home care devoted to personal care (as opposed to housework) and the percentage of psycho-geriatric places in day centres¹⁸, all of them at the regional level. We consider that the introduction of these variables is justified by (1) the high variability of total home care hours and percentage of time devoted to personal care as opposed to housework across autonomous communities, and (2) the fact that certain mental degenerative pathologies require day centres to be adapted to specific patient needs.

Finally, the hours equation includes other caregiver characteristics: if he/she got on well with the care-receiver before the onset of the caregiving relationship, kinship between caregiver and care-receiver and kinship between primary and secondary caregivers. The importance of the kinship of the primary caregiver with respect to the care-receiver and other secondary caregivers has been widely acknowledged in the literature (Tennstedt et al., 1989; Penrod et al., 1995).

Given that the information regarding the contribution of the user to the home care service, percentage of home care devoted to personal care and coverage index of psycho-geriatric places is not available for all autonomous communities, we have defined three binary indicators referring to the observability of these variables that take the value 1 if there is information for that particular variable in the autonomous community and 0 otherwise.

¹⁶ The coverage index is the ratio between the number of users and the population over 65 years of age (source: IMSERSO (2004), Older people in Spain. 2004 Report). The co-payment borne by the user is the product of the copayment percentage and the price of the service. For 1994, the only available information accounts for the coverage index of home care and day centres.

¹⁷ For example, in 2004 the coverage index for Home Care ranges between 0.48 for Cantabria and 4.68 for Navarra. The coverage index for Day Centers varies between 0.18 for Galicia and 0.70 for Madrid.

¹⁸ In 1994, we only had information for the number of home care hours per month.

4. Empirical specification and results

4.1. The double selection process

The correlation coefficient ( ) between formal care and unmet needs is significant for both waves ( =-0.2456 (p-value=0.0000) and -0.1222 (p-value=0.0288) for 1994 and 2004, respectively), implying that the joint estimation procedure is preferable to the estimation of independent probits [detailed results of the bivariate probit are not presented but are available upon request]. More importantly, an estimation procedure based on a probit model would have left the sample selection problem unsolved. The negative sign of the estimated correlation indicates that dependent people who receive FC are less prone to suffer UNs than those who have applied for it, but do not receive any. In addition, the correlation coefficient in 1994 was twice as large as in 2004, which is a direct consequence of the increase in the coverage of social services¹⁹.

Table 4 reports the mean and median of the estimated marginal effect of each explanatory variable for the probabilities of FC=0&UN=1 and FC=1&UN=1 in 1994 and 2004. For example, to compute the effect of living alone on the probability of FC=0&UN=1, the average effect is given by:

\[\begin{array}{l} E \left[ \left(F C _ {i} = 0 \& U N _ {i} = 1\right) _ {\text {Lives alone} = 1} - \left(F C _ {i} = 0 \& U N _ {i} = 1\right) _ {\text {Lives alone} = 0} \right] = \\ = \Phi_ {2} \left(X _ {i} ^ {\prime} \beta , Z _ {i} ^ {\prime} \gamma ; \rho\right) _ {\text {Lives alone} = 1} - \Phi_ {2} \left(X _ {i} ^ {\prime} \beta , Z _ {i} ^ {\prime} \gamma ; \rho\right) _ {\text {Lives alone} = 0} \end{array}\tag{14}\]

where indicates the outcome if the dependent individual lives alone and indicates the outcome if the dependent does not live alone. This average effect has been estimated by the sample mean or the sample median as the difference across the sample. In what follows we comment on some of the key results obtained from this model.

4.1.1. Detailed results for the selection equations

Socio-demographic variables

Younger dependent individuals (under the age of 70) showed an increase in the probability of FC=0&UN=1 of 42.48% in 1994, which decreased to 22.76% in 2004, because in the 1990s many regional administrations did not allocate social services to dependent people younger than 65. In turn, those older than 90 showed an average increase in the probability of FC=1&UN=1 (25.96%) which rose to 45.43% in 2004. In this respect, the early onset of some pathologies²⁰ in conjunction with the progressive ageing of the population²¹ may exacerbate the problem of FC=0&UN=1 in the first case, and of FC=1&UN=1 in the second.

Regarding the level of education, which was used as an identification restriction, we observe that as the level of education of the dependent (caregiver) increased (from “without studies” to “college education”), the probability of FC=0&UN=1 decreased by 84.61% (87.89%) in 1994 and by 87.09% (72.66%) in 2004. This result confirms what was stated by previous studies, i.e., more educated individuals are better at navigating through the system of social services.

¹⁹ In 1994, 12.98% and 2.23% of the elderly people interviewed received home care and day centre care respectively. In 2004, these percentages were 23.38% and 6.31%.

20 According to data from Fundación Alzheimer España and Asociación Parkinson Madrid, around 2.5% of Alzheimer patients are under 55 and approximately 20% of Parkinsonism cases are diagnosed before the age of 50.

²¹ Long-term population projections (INE) for 2060 reveal that around 13.12%-14.44% of the population will be older than 80.

Individuals with no income or less than €300/month are less likely to suffer FC=0&UN=1 (- 50.79% and -14.43%) than those with more than €300 or €600/month, although the effect of income differences decreases in the second wave. With respect to the allocation system applied in 1994 and 2004 (before the Dependency Law), the dependent’s economic situation, the number of functional or cognitive disabilities and the availability of the family were taken into account for the allocation of home care and day centre care.

Dwelling arrangement

Living in a municipality with fewer than 2,000 inhabitants increased the probability of FC=0&UN=1 by 46.84% in 1994, but this effect decreased to 26.02% in 2004. The marginal effect diminishes as the size of the municipality increases (11.19% in 2004 for the case of provincial capitals).

Dependent people living alone experienced an average decrease in the probability of FC=0&UN=1 of 44.46% and an average increase in the probability of FC=1&UN=1 of 14.30% (in 1994). Between the two waves the effect on the first probability diminished, although the effect on the second one became stronger (-21.28% and 25.14% in 2004 respectively). In this case, rather than a problem of hours there may be an accounting problem regarding the aid received. When formal caregivers go to the dependent’s home they pursue a set of objectives in a limited amount of time and this situation is totally different from the environment of the dependent individual who lives with co-resident caregivers who provide the required help throughout the day.

Degree of dependency and caregiving relationship

Being highly dependent reduced the probability of FC=0&UN=1 by 47.11% on average in 1994, although this reduction decreased to 23.08% in 2004. For both waves, moderately dependent people experienced a smaller decrease in the probability of FC=0&UN=1 than highly dependent ones, and in 2004 differences between degrees of dependency narrowed. On the other hand, being severely or highly dependent increased the probability of by 12.42% and 25.24% in 1994, and this effect rose to 22.08% and 35.55% respectively in 2004. These results indicate that severely or highly dependent people have a higher probability of receiving formal care and considering that the amount of care (or the quality) is unsatisfactory.

With respect to specific pathologies, individuals suffering dementia in 1994 experienced an average increase in the probability of FC=0&UN=1 (46.72%). In 2004, we observe that the effect of dementia remained almost constant, and also that osteoarticular problems presented an increase in the probability of FC=0&UN=1 (12.72%).

Caregivers with more than 10 (12) caregiving years showed a decrease in the probability of FC=0&UN=1 (-35.18% and -23.26% in 1994 and 2004, respectively). Nevertheless, the probability of FC=1&UN=1 increased by an average of 14% when the number of caregiving years was greater than 6 (or 5 for 2004). In this respect, a longer caregiving period increases the probabilities of receiving help from the social services but also the probability that . This result is supported by the fact that in 2004 the percentage of dependent people who complemented home care with private formal care ranged from 37.50% (for less than 2 caregiving years) to 71.43% (for more than 12 caregiving years).

The effect of regional social services policies

With respect to regional policy variables, a higher coverage index for home care or day centre care decreases the probability of and . In 2004, the probability of FC=0&UN=1 decreased more with an increase in day centre coverage, whereas the probability of decreased more with an increase in home care coverage. Therefore, there is a higher probability that the receipt of day centre care completely satisfies the problem of unmet needs in comparison with home care. An additional hour of home care reduces the probability of FC=1&UN=1 by around 2% for both waves, and a 1% increase in the percentage of time devoted to personal care decreases the probability of FC=1&UN=1 by 10%. On the other hand, the cost per hour and the copayment increases the probability of significantly, and the effect of co-payment increased from 1.83% in 1994 to 7.71% in 2004. These results should be considered carefully by public authorities given the wide disparity between regions. For example, in 2004, 80% of home care time in Navarra was devoted to personal care, as opposed to only 20% in Extremadura; the average number of monthly hours was 25.14 in Navarra as opposed to 8 hours in Andalucía, and the cost per hour was highest in Navarra (€22.32) and lowest in Extremadura (€6.18).

4.2. Results for the hours equations

Tables 5 and 6 provide the estimated coefficients of the interval regressions for the number of caregiving hours. For the 1994 survey we perform an interval regression and standard errors are based on a resampling bootstrap method.²² For 2004, the hours variable is interval coded up to 8 caregiving hours/day (less than one hour, 1-3, 3-5, 5-8) and continuous from 8 hours upwards. We estimate an interval regression using the logs of the intervals or the log of the exact number of caregiving hours. We have rejected equality of coefficients test both between waves and combination of FC and UN. ²³

For the 1994 regressions, the terms and are significant, with positive and negative sign respectively. Their interpretation indicates that caregivers of dependent people with FC=0&UN=1 devote fewer caregiving hours than similar caregivers with . Therefore, in the presence of unmet needs, the provision of formal care reinforces the receipt of informal care. Comparing this result with the prevailing theories which relate formal and informal care, we could infer that the substitution model, which supports a decrease in informal care as the provision of formal care increases, does not hold for the Spanish case, at least in 1994. In this case, there could be complementarity or task specificity between the two types of care, but given that we do not know the specific functions of each type of caregiver we cannot test this hypothesis.

²²Thus, 1,000 samples of size N are drawn from the original sample with replacement. For each sample, all coefficients are re-estimated and used to derive standard errors.

²³ We have tested, first, the equality of coefficients between the various caregiving hours equations for each wave. In all cases, the chi-square statistic rejects the null hypothesis, indicating that the impact of the explanatory variables for the hours equation corresponding to each combination of the variables UNs and FC is different from that of the others. Second, we have tested the equality of coefficients between 1994 and 2004 for the same combination of UNs and FC. Once again, we reject the null hypothesis. Thereby, the adverse effects of unmet needs on informa caregiving hours do not remain constant over time and it becomes necessary to compare the estimates from the two waves to determine the magnitude of this change. Finally, we have tested (and rejected) the equality of coefficients between regressions with and without controls for sample selection.

For the 2004 regressions, there are three significant selection terms (none of the selection terms is significant in the regression for FC=0&UN=0). The selection term ₂₁ is negative, which indicates that caregivers of dependent individuals with FC=0&UN=1 have a higher probability of devoting more caregiving hours than similar caregivers with FC=0&UN=0. The selection term is positive, showing that caregivers of dependent individuals with FC=1&UN=0 devote fewer caregiving hours than caregivers with . Finally, the negative sign of the selection term suggests that caregivers of dependent people with FC=1&UN=1 devote more caregiving hours than similar caregivers with . So for the second wave we have also obtained evidence against the substitution theory (and in favour of the complementarity/task-specificity model). Moreover, the selection term is larger than and in absolute terms, indicating that the selection bias associated with the UNs equation is greater than that corresponding to the FC equation. Rather than insufficient coverage of social services, the inefficiencies associated with the allocation process constitute a more serious problem.

4.2.1. Detailed results

Socio-demographic characteristics

The regression results (see tables 5 and 6) for in 1994 show that male dependents receive fewer caregiving hours. In this situation we have observed that the percentage of sex coincidence between the caregiver and the care-receiver is lower than in the other situations (55.6% as opposed to 64.4%). Sometimes, the sex of the carer may be problematic for the receiver, because the dependent may feel uncomfortable discussing needs or receiving care from a different-sex caregiver (Cordingley and Webb, 1997).

The number of caregiving hours decreases if the dependent individual lives alone and suffers UNs, with a greater effect if some FC is received (-0.97 and -1.65 hours/week respectively in 1994, and - 1.66 and -2.03 hours/week in 2004). In fact, the data reveal that the fraction of dependent individuals living alone grew over time, from 25.0% in 1994 to 30.1% in 2004, and the percentage of caregivers who invest more than 20 minutes in displacement time rose from 29.26% to 34.29% in this period.

Degree of dependency

The number of informal caregiving hours increases with the degree of dependency and the coefficients are always higher in the regression for FC and UNs than in the situation with UNs but no FC. For example, a highly dependent person (level 2) with FC and UNs involved an increase of 4.87 hours/week in 1994 and 5.94 hours/week (exp(1.7823)) in 2004. For this same combination, the difference in caregiving hours between moderate and high dependency increased between the two waves: from 2.95 in 1994 to 3.90 in 2004. Consequently, informal caregivers face a double problem: first, they have to devote additional caregiving hours to compensate for formal care UNs, and second, their efforts show an increasing profile over time. As regards specific pathologies, mental illnesses show an increase in hours for the situation (from 2.61 to 3.31) and the coefficient for FC=0&UN=1 was significant in 2004 (1.37 hours more), although it was not in 1994.

Turning our attention to the number of caregiving years, for both waves we observe a significant increase in caregiving hours (around 1.4 hours/week) when FC=0&UN=1 and the number of caregiving years is greater than 10 (or 12 for 2004). The “career in caregiving” theory (Aneshensel et al., 1995) provides a good explanation for this result, although not all caregivers follow the same “career sequence”. The literature usually distinguishes three major stages: the acquisition role (diagnosis and transition into the role of caregiving), the enactment role (combination of in-home care and institutional care) and the disengagement role (cessation of caregiving, bereavement and social readjustment). For example, the percentage of caregivers that have been obliged to reduce leisure time or social activities is almost the same (35.19-34.36%) for the groups with less than 2 or more than 12 caregiving years (in 2004). However, the percentage of caregivers who consider caregiving as a moral obligation increases from 41.70% (less than 2 years) to 54.56% (more than 12 years). Therefore, caregivers with a long caregiving experience may be readier than others to satisfy the dependent’s demands.

Caregiving relationship

Although the type of care provided by a specific caregiver appears to be related to genderspecific roles²⁴, in this study we observe that caregiver’s gender is not significant and male and female caregivers provide similar amounts of care, which is consistent with other previous results (Stoller and Earl, 1983; McKinlay and Tennstedt, 1986). Having a good caregiver-dependent relationship (previous to the dependency relationship) increased the amount of caregiving hours in all situations in 1994. In 2004, we only observe a significant effect for FC=0&UN=1 and FC=1&UN=1, although the amount of care devoted has increased. For example, a good relationship for the case FC=0&UN=1 implied an increase of 0.84 hours/week in 1994 and 1.28 hours/week in 2004.

If the primary caregiver receives help from another family member the number of caregiving hours decreases by 3 hours/week for both waves when FC=0&UN=1 and nearly 4 hours/week when FC=1&UN=1. However, we found that one person tends to provide all informal care (59% in 1994, 51.1% in 2004), whereas secondary caregivers are few in number²⁵. This concentration of caregiving responsibilities on a nuclear family has important implications for the emergence of family/leisure problems and the possible increase in the risk of institutionalization when the primary caregiver is overloaded.

Children under 18 years old may represent an obstacle for caregiving tasks when unmet needs are present. For the situation FC=1&UN=1, having young children decreased the amount of care by 0.20 hours/day in 1994 and 1.42 hours/day in 2004.

The kinship of the caregiver with respect to the dependent reveals the existence of a gradient effect between the spouse and the son/daughter: first the spouse, and second the son or daughter. For 2004, and when FC=1, the support provided by the son/daughter-in-law is greater than for the case of the spouse and son/daughter, revealing the emergence of strong complementarities between formal care and informal caregivers.

²⁴ The percentage of men (women) who help the dependent individual is 68.74% (81.20%) for housekeeping, 68.64% (81.68%) for cooking, 72.14% (62.91%) for financial management, and 61.59% (51.01%) for transportation.

²⁵ For 2004, 20.15% of respondent caregivers received help from one other family member, 14.63% from two people and 7.71% from three.

4.3. The decomposition of the informal caregiving hours differential

The differential in the number of informal caregiving hours taking into account double sample selection can be decomposed in different parts: (i) differences in caregiver and carerecipient characteristics; (ii) differences in the estimated parameters of the caregiving hours function; (iii) differences due to the selectivity bias. Following Oaxaca (1973), we propose to analyze the difference in log IH. Given that we have estimated for equations for the number of IH we can establish four comparisons of the log IH. For example, the difference in log IH between (FC=0, UN=1) and (FC=1, UN=1) is given by:

\[\begin{array}{l} \ln I H _ {4 i} - \ln I H _ {2 i} = \left(\overline {{X}} _ {4 i} ^ {\prime} \hat {\gamma} _ {4} + \hat {\delta} _ {4 1} \overline {{\lambda}} _ {4 1 i} + \hat {\delta} _ {4 2} \overline {{\lambda}} _ {4 2 i}\right) - \left(\overline {{X}} _ {2 i} ^ {\prime} \hat {\gamma} _ {2} + \hat {\delta} _ {2 1} \overline {{\lambda}} _ {2 1 i} + \hat {\delta} _ {2 2} \overline {{\lambda}} _ {2 2 i}\right) = \\ = \left(\overline {{X}} _ {4 i} ^ {\prime} \hat {\gamma} _ {4} + \hat {\delta} _ {4 1} \overline {{\lambda}} _ {4 1 i} + \hat {\delta} _ {4 2} \overline {{\lambda}} _ {4 2 i}\right) - \left(\overline {{X}} _ {2 i} ^ {\prime} {\hat {\gamma}} _ {2} + \hat {\delta} _ {2 1} \overline {{\lambda}} _ {2 1 i} + \hat {\delta} _ {2 2} \overline {{\lambda}} _ {2 2 i}\right) + \overline {{X}} _ {2 i} ^ {\prime} {\hat {\gamma}} _ {4} - \overline {{X}} _ {2 i} ^ {\prime} {\hat {\gamma}} _ {4} = \\ = \left(\overline {{X}} _ {4 i} ^ {\prime} - \overline {{X}} _ {2 i} ^ {\prime}\right) {\hat {\gamma}} _ {4} + \overline {{X}} _ {2 i} ^ {\prime} (\hat {\gamma} _ {4} - \hat {\gamma} _ {2}) + \left(\hat {\delta} _ {4 1} \overline {{\lambda}} _ {4 1 i} - \hat {\delta} _ {2 1} \overline {{\lambda}} _ {2 1 i}\right) + \left(\hat {\delta} _ {4 2} \overline {{\lambda}} _ {4 2 i} - \hat {\delta} _ {2 2} \overline {{\lambda}} _ {2 2 i}\right) \end{array}\tag{16}\]

where are the estimated coefficients for the explanatory variables, and represent the average of the observed characteristics and and denote the average of the selectivity terms

The first term is the difference in the endowments of hours-determinant characteristics between people with or without formal care. That is, the difference in hours that a dependent with would experience if he had the same characteristics, on average, as a dependent with . The second term represents the difference in coefficients between people with and without formal care. That is, the difference in hours that dependent with (FC=0, UN=1) would experience if, given their mean characteristics, they would receive care as those with (FC=1, UN=1). The third and the fourth term represent the hours differential due to sample selectivity in formal care and in unmet needs, respectively.

To avoid the index problem, that is the instability of the decomposition depending of the choice of the reference group (with/without formal care) we follow the approach proposed by Reimers (1983) and use a weighted average of each type:

\[\begin{array}{l} \ln I H _ {4 i} - \ln I H _ {2 i} = 0. 5 \left(\overline {{X}} _ {4 i} ^ {\prime} - \overline {{X}} _ {2 i} ^ {\prime}\right) \left(\hat {\gamma} _ {4} + \hat {\gamma} _ {2}\right) \hat {\gamma} _ {4} + 0. 5 \left(\overline {{X}} _ {4 i} ^ {\prime} + \overline {{X}} _ {2 i} ^ {\prime}\right) \left(\hat {\gamma} _ {4} - \hat {\gamma} _ {2}\right) \\ + \left(\hat {\delta} _ {4 1} \overline {{\lambda}} _ {4 1 i} - \hat {\delta} _ {2 1} \overline {{\lambda}} _ {2 1 i}\right) + \left(\hat {\delta} _ {4 2} \overline {{\lambda}} _ {4 2 i} - \hat {\delta} _ {2 2} \overline {{\lambda}} _ {2 2 i}\right) \end{array}\tag{17}\]

The decomposition of the difference in informal caregiving hours, shown in Table 7, confirms some of the previous results. First, having unmet needs increases the average number of log IH (0.051 if FC=0 and 0.089 if FC=1). Second, under the existence of unmet needs, the increase in IH is higher when some FC is received. (0.108). Third, the effect of unmet needs self selection is stronger as compared to that of formal care self selection. For example, unmet needs self-selection (difference in are responsible of 50.53% of the difference in log IH when FC=0, and 48.39% of the difference in log IH when FC=1. Thus, using the number of formal care recipients as an indicator of the goodness of the longterm care system may be confounding, if we do not complete this information with other quality indicators, such as the degree of satisfaction of the carerecipients.

5. Conclusions

In this paper we have estimated the extra amount of informal caregiving hours needed when the dependent individual suffers an unmet needs problem, due to the absence, insufficiency or inadequacy of formal care. As already discussed, two potential sources of selection have to be considered when estimating models related to the provision of social services and the availability of informal caregivers. The first one is due to the self-selective nature of formal care: with regard to both observable and unobservable characteristics, formal care-receivers are not a random sample of the dependent population. The second selection issue concerns the expected well-being of the individual after his or her application for home care or day centre care or its allocation: those who are not satisfied with the quality or quantity of the care received are not randomly selected from the whole population of potential care-receivers. The estimation results show a negative correlation between both the probability of receiving formal care and the probability of having unmet needs, and a significant selection bias of formal care and unmet needs on the number of caregiving hours. Given that the unmet needs selection effect is greater than the formal care one, we may infer that the increase in the number of formal care recipients constitutes just a part of the development of a long-term care system. Thus, higher expenditure in long—term care with respect to GDP has to be accompanied by quality assessment, monitoring system and improvement in outcomes.

For both waves the number of caregiving hours increases with the presence of unmet needs, and is even greater when some formal care is received, refuting the substitution model, according to which the provision of formal care produces a decrease in the number of informal caregiving hours. For the Spanish case, it seems that formal and informal caregiving are not competing forces. Instead, informal care develops a compensatory and complementary role with respect to formal care. This result agrees with the evidence found by other authors (Van Houtven and Norton, 2004; Bolin et al., 2007; Viitanen, 2007; Bonsang, 2009) who analyzed the relationship between formal and informal care from the perspective of the caregiver and confirmed a substitution effect between home care and informal care (in the case of Bonsang, the substitution effect only prevails for paid domestic help).

In the past, policy makers should have congratulated themselves because an increase in formal care did not implied a parallel decrease in the provision of informal care At present, proceeding with caution and assuming that caregivers in 2013 will behave as those of 2004, it is clear that we face a difficult problem. We have observed that in the presence of unmet needs the informal caregiver devotes extra-care if the dependent individual is already receiving some formal care. This result implies that between 1994 and 2004, Spanish families have lead public social services come into their households and take a collaborative role in the provision of long-term care. Will informal caregivers willing go backwards to a situation where he/she was the one and only looking after the dependent individual? We would need more data to asses the trade-off between caregiver and carereceiver’s welfare. Independent of what macroeconomic figures will show, we should question any reform that casts doubts on the future of many families.

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Appendix A

Determination of the degree of dependency

The Ranking Scale considers 47 tasks grouped in 10 activities (eating and drinking, control of physical needs, washing oneself, other physical care, dressing and undressing, keeping one’s health, mobility, moving inside home, moving outside home and housekeeping). The questionnaire for people who suffer mental illness or have some kind of cognitive impairment includes six additional tasks referring to the ability to make decisions²⁶. The final score is the sum of the weights of the tasks for which the individual has difficulty, multiplied by the degree of supervision required and the weight assigned to that activity:

Score = ∑ Weight of the task performed with difficulty * Degree of supervision * Weight of the corresponding activity

The table of weights for tasks and activities distinguishes four age intervals: 3-6, 7-10, 11-17, and 18 and over. Given that our sample contains only individuals older than 60 years, we will use the weights attributed to the fourth interval. The weights assigned to each activity and task are shown in Table 1, the score in brackets corresponding to dependent people with mental illness or cognitive impairment.

We have been obliged to adapt some questions. For example, for the activity “eating and drinking”, the Ranking Scale distinguishes six different tasks, but in the survey we only have information about the ability to eat (which we assume includes the ability to drink). With respect to “control of physical needs” we have no information about the specific tasks of “dressing and undressing” and “adopting the right posture”. For this reason, we have incorporated their respective scores into the task “using the toilet”. In the activity “other personal tasks”, the survey does not include information about the abilities to comb one’s hair or cut one’s nails, so we have synthesized all these variables into one called “smartening oneself up”. The same has happened with the activity “mobility”, where we have summarized five different tasks in the ability to go to bed/stand up. With all these simplifications, we are not attempting to replace the work of the assessment professionals. The purpose of this exercise is to apply the legal benchmark and introduce a new way of classifying dependent people.

With respect to the degree of support, the Ranking Scale considers four possibilities: supervision (if the dependent only needs a third person to prepare the necessary elements to perform the activity), partial physical care (when the third person has to participate actively), maximum physical care (if the third person has to substitute the dependent individual in the execution of the activity) and special care (the dependent individual suffers behavioural disorders that hinder the provision of the task by a third person).

²⁶ With the information contained in the Informal Support Survey, we consider that an individual has cognitive impairment or intellectual disability when the informal caregiver has answered in the affirmative to the questions about memory problems, dementia, mental illness or Alzheimer.

Table 1. Comparison between the Task Table of the Ranking Scale contained in the Dependency Law and the information from the Informal Support Survey

Source: http://www.dependencia.imserso.es/InterPresent2/groups/imserso/documents/binario/manualusobvd.pdf and Jiménez-Martín and Vilaplana (2012). Variables in brackets are only applied to mental patients.

Table 2. Comparison between information about the degree of support of the Ranking Scale contained in the Dependency Law and the Informal Support Survey

Source: http://www.dependencia.imserso.es/InterPresent2/groups/imserso/documents/binario/manualusobvd.pdf and Jiménez-Martín and Vilaplana (2012). Variables in brackets are only applied to mental patients

Table 3. Descriptive statistics (using sample weights)

For the number of caregiving years, figures between brackets correspond to 2004.

Table 4. Marginal effects for the probabilities of FC=0&UN=1 and FC=1&UN=1

For the number of caregiving years, figures between brackets correspond to 2004. Marginal effects for dependent’s marital status and receiving a benefit are not shown due to space constraints, but are available upon request.

Table 5. Interval regressions for the number of informal caregiving hours, 1994

Estimated coefficients for caregiver’s age, caregiver’s marital status, permanent caregiver, willing caregiver, private formal care, size of municipality and kinship of other caregivers with respect to the primary caregiver are not shown due to space constraints, but are available upon request. Omitted variables: age 60-69 (dependent), no degree of dependency, younger than 40 (caregiver), single (caregiver), less than 2 caregiving years, municipality with less than 2,000 inhabitants. Estimates using sample weights and clusters by region.

Table 6. Interval regressions for the logarithm of the number of informal caregiving hours, 2004

Estimated coefficients for caregiver’s age, caregiver’s marital status, permanent caregiver, willing caregiver, private formal care, size of municipality and kinship of other caregivers with respect to the primary caregiver are not shown due to space constraints, but are available upon request. Omitted variables: age 60-69 (dependent), no degree of dependency, younger than 40 (caregiver), single (caregiver), less than 2 caregiving years, municipality with less than 2,000 inhabitants. Estimates using sample weights and clusters by region. (^* p<0.10; ^** p<0.05; ^*** p<0.01)

Table 7. Oaxaca decomposition of the informal caregiving diferential. 2004

Average hours per week between brackets

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