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A Country for Old Men?
An Analysis of the Determinants of Long-Term Home Care in Europe
Abstract
This paper investigates long-term home care utilisation in Europe. We use data from SHARE on
formal (nursing care or paid domestic help) and informal care (support provided by relatives) to
study the probability and the number of hours of both types of care received. We address
endogeneity and unobservable heterogeneity in a common latent factors framework. We find that
age, disability and proximity-to-death are important joint predictors of home care utilisation. Unlike
some previous studies, we find that increasing the number of hours of informal support does not
lead to a reduction in formal care utilisation.
Keywords: long-term care, proximity to death, ageing, latent factors.
JEL: C10; I1.
This paper uses data from SHARE release 2.3.0, as of November 13th 2009. SHARE data collection in 2004-2007 was
primarily funded by the European Commission through its 5th and 6th framework programmes (project numbers
QLK6-CT-2001-00360; RII-CT-2006-062193; CIT5-CT-2005-028857). Additional funding by the US National
Institute on Aging (grant numbers U01 AG09740-13S2; P01 AG005842; P01 AG08291; P30 AG12815; Y1-AG-455301; OGHA 04-064; R21 AG025169) as well as by various national sources is gratefully acknowledged (see
http://www.share-project.org for a full list of funding institutions). We thank participants in the International
Conference on Evidence-Based Policy in Long-Term Care held in London in September 2010 and in the AIES annual
meeting in Torino (2010) for their helpful comments.
1
I. Introduction
In the last few decades, European and other developed countries have been undergoing population
ageing due to lower fertility rates and increased life expectancy and partly driven by advances in
medicine. The downside is that public and private health care expenditure (HCE) are thought to
increase with the number of elderly people and the average age of the population . This is particular
cause for concern for the sustainability of national welfare and health care systems.1 One of the
fastest growing components of HCE is long-term care (LTC).
Since the seminal paper by Zweifel et al. (1999), studies have tried to assess the role of
competing predictors of age in HCE. In particular, proximity to death (PtD) indicators have up to
now been considered the best candidates.2 PtD, in fact, appears to be able to capture individual
health deterioration and the fact that, when approaching death, the need for health care services
increases due to greater health needs rather than to age per se. In this respect, population ageing has
been claimed to be a “red herring” in the study of the evolution of HCE (see Stearns and Norton,
2004; Seshamani and Gray, 2004a,b and, for a review of the literature, Payne et al., 2007).
The same approach has been adopted for LTC expenditure. The literature provides, however,
mixed evidence about the relative contributions of age and PtD, and emphasizes the prominent role
of disability indicators. For example, using data from Switzerland, Werblow et al. (2007) break
down HCE into seven components, one of them related to LTC, and find that only for the latter
component does age seem to matter, regardless of individuals’ remaining lifespan, and PtD is
always a significant predictor of expenditure. On the contrary, based on Dutch data, De Meijer et al.
(2011) show that PtD is not a good predictor of LTC costs when disability indicators are taken into
account. In this sense, they argue that PtD itself appears to be a “red herring” to the extent that it
captures individual disability status, and conclude that both age and PtD can even become
redundant in models that appropriately control for disability. Additional insights are offered by
1
2
For an overview of issues related to ageing population, see for example European Commission (2006).
Some authors use the equivalent concept of “time-to-death”.
2
studies carried out with US data. Weaver et al. (2009) estimate the marginal effect of PtD on the
probability of receiving nursing homes and home care services using data from the Health and
Retirement Study and assess whether this is robust to the inclusion of informal care indicators
(defined as being married or living with an adult child). They find that, overall, PtD increases the
likelihood of receiving formal home health care and, to a greater extent, nursing homes. When
considering the role of informal support, however, the impact of PtD reduces.
The interest in informal support is motivated by the very nature of LTC. Unlike acute medical
care, most of the care provided to the dependent elderly does not require high level skills or capital
equipment, so that LTC is often provided by unpaid caregivers (usually relatives or friends), in
addition to, or in the place of, paid professional home care services. These services require low-tomedium skilled staff and wage variability is low, thus implying that the amount of LTC expenditure
is affected by the number of hours of care provided. This peculiarity of LTC allows, at least in
principle, for a certain degree of substitution of professional (paid) with informal (unpaid) care.
Though some economic explanations would also support complementarity, given that informal
support may consist, at least in part, in the tasks required to organize a formal care service, or in
substituting the formal caregiver on his/her day off.
The nature of the relationship between formal and informal LTC and the relative dominance of
the substitution or complementarity effect has been examined in several studies. These usually
address, in econometric modeling, the endogeneity problem that arises because of the simultaneity
bias and unobservable heterogeneity which affect the relationship between formal and informal
care. To control for endogeneity, simultaneous equations models can be used, as in Greene (1983);
Lo Sasso and Johnson (2002).3 More often, instrumental variables approaches are employed, as in
Van Houtven and Norton (2004); Charles and Sevak (2005); Van Houtven and Norton (2008);
Bonsang (2009). Most of these studies find evidence of a statistically significant substitution effect
Van Houtven and Norton (2004) provide evidence for substitutability and find that family and
3
These works look at the relationship between informal support and formal care provided within community care
programmes and nursing home utilization, respectively.
3
friends caregiving reduces nursing home admissions. They also suggest that while generally formal
and informal care may be substituted, they are complementary when considering the severely
disabled. Van Houtven and Norton (2008) show that care provided by adult children is a net
substitute for Medicare LTC expenditure of the single elderly, significantly reducing the likelihood
of incurring expenditure for home care. Such informal support is less effective among elderly
couples. Bonsang (2009) considers two types of formal home care: paid domestic help and nursing
home. He identifies a substitution effect between informal and formal care, which however
disappears for the elderly suffering from severe disabilities.4 Generally speaking, one limitation of
these studies on the relationship between formal and informal care lies in the fact that they do not
evaluate the relative importance of the causal impact of informal care vis-a-vis other determinants
of formal care (namely age, PtD and health status indicators). Moreover, the robustness of the
results relies strictly on the availability of valid instruments for informal care.
The main research issues arising from the ongoing debate on the determinants of LTC (and
which motivate this paper) can be summarized as follows: i) age, Ptd and disability indicators
should be jointly considered as the main drivers of LTC use; ii) the role of informal care and that of
the above-mentioned indicators should be studied in a unified framework; iii) any endogeneity
problems should be addressed when modeling formal LTC use, preferably using methods that do
not rely on the availability of valid (and strong) instruments for informal care.
Using data from the Survey on Health, Ageing and Retirement in Europe (SHARE), we address
the above three issues by modeling formal and informal long term home care as a system of
simultaneous equations describing the probability as well as the number of hours of both types of
care received. This is estimated within a correlated common latent factors framework, which allows
us to control for potential endogeneity of regressors and unobservable individual-specific
heterogeneity. We estimate a general model for total formal care, and two separate models for its
components, i.e. home nursing care and paid domestic help. Informal support, PtD, age, disability
4
The evidence supporting the substitution effect is found only when the model controls for endogeneity.
4
and morbidity indicators are all included in the specification for formal care equations (conditioning
also on other socioeconomic characteristics). We find that age, PtD and disability are statistically
significant predictors of long term home care utilization. The relative impact on formal LTC of
informal care, age, PtD and disability -and the interactions between these variables-are assessed by
estimating average partial effects (APEs) for different types of individuals. This leads to a
comparison between survivors and decedents, youngest and oldest old and between individuals with
different levels of LTC needs, as proxied by disability indicators.
Contrary to most previous results, we provide evidence of complementarity between formal and
informal care. The effect of informal support on formal care, however, is negligible and fairly stable
with increasing needs. We find that age, PtD and disability are statistically significant predictors of
in-home LTC utilization. Disability indicators and the oldest age category have the greatest impact
on formal care, but no prominent role for any one specific determinant emerges. Our analysis of the
indirect effect of interactions between age, PtD and disability seems to suggest that they should be
used jointly as predictors of LTC utilization.
II. Data and key variables
SHARE is the European longitudinal survey on health, ageing and retirement, which recalls the
HRS and the English Longitudinal Study of Aging (ELSA). The target population consists of noninstitutionalised individuals 50 years of age and over and the original SHARE sample consists of
28,517 individuals born before 1955. In our analysis we focus on individuals who participated in
the first wave (2004) and lived in Scandinavia (Denmark), Central Europe (Austria, France,
Germany, Switzerland, Belgium and Holland) or in the Mediterranean Area (Spain, Greece and
Italy). Following Van Houtven and Norton (2004) and Bonsang (2009), we use observations for all
respondents aged 65 or older, who have at least one child and up to 4 children, and do not live with
any of them. Additionally, we restrict the analysis to those individuals who have received LTC and
have also reported either some mobility limitation or disability, chronic disease or long-term illness.
5
This enables us to exclude from the sample those individuals who might have received any type of
LTC (particularly, paid domestic help) for reasons not strictly related with their LTC needs, giving
a target sample of 4,973 complete observations.
Formal and informal home care
SHARE provides a rich set of information about formal and informal care received at home. It is in
principle possible to distinguish between caregivers by considering that formal caregivers have an
employment contract, whereas informal caregivers are usually relatives or friends (Norton, 2000).
In the case of formal care, which can either be paid out-of-pocket or by private or public
coverage schemes, we distinguish between individuals who receive professional nursing care at
home and those who receive professional domestic help for cleaning tasks that the respondent was
unable to do because of health problems. The former is typically provided by skilled professionals
within insurance schemes, while the latter is mainly provided by unskilled workers, often
immigrants, who may be black market workers (see Lippi Bruni and Ugolini, 2006a,b). For both
types of formal care we define a dummy indicator that takes value 1 if the individual receives that
specific type of care. We also use information on the number of weeks and hours of formal care
received in the last 12 months. This allows us to define two continuous variables indicating the
average number of hours received per month in the last year (NC hours and PDH hours).5 We
aggregate information on these two types of formal care to build two general indicators (a dummy
and a continuous variable analogous to those described above) for total formal care (TFC), which is
defined as the combination of nursing care (NC) and paid domestic help (PDH) that can be received
by an individual in the same year.
An accurate quantification of informal care is problematic because this type of LTC is a nonmarket good. Although the spouse is the most common informal caregiver as they coreside with the
dependent person, in our analysis we look at children (particularly daughters), grandchildren and
sons-in-law, who are, according to the literature, the typical caregivers within the family. The
5
Given the nature of the data we use, we are unable to control for differences in quality of care delivered by
caregivers.
6
SHARE questionnaire asks respondents to describe the nature of the relationship with the caregiver,
the frequency of support received (daily, weekly, monthly or annual), and the average number of
hours (per day, week, month and year) received. We define a dummy indicator for whether the
individual has received this type of help (InfC in Table 1), and build a continuous variable for the
average number of hours received per month in the last year (InfC_hours).6
Proximity to death
New information about the living status of the first wave respondents was collected two years after
the interview (i.e., in the second wave of the survey). This covers about 71 % of our sample. We
use this information to construct a binary indicator of PtD, which takes value 1 if the respondent
died within two years of the interview and 0 otherwise. When PtD is considered, sample size
reduces to 3526.7
Individual characteristics
For each individual in our sample we observe a set of demographic variables such as gender, age
(we use age classes) and coresidence status. The latter is a dummy variable that indicates whether
respondents live alone or with their spouse or partner.8 Respondents’ socioeconomic status is
described by education and income indicators. For education we create an indicator of years of
education.9 Income is defined as equivalent total gross household income, adjusted for 2004
purchasing power parity.
The survey provides detailed information about health-related variables such as mobility
limitations (mobility), limitations in usual activities because of health problems (GALI), limitations
6
Due to poor accuracy in the responses, those individuals who reported having received more than 24 hours of care
per day, more than 168 hours per week, or more than 720 hours per month and more than 8640 in a year have been
eliminated from the sample.
7
Differences between the means of relevant variables in this sample and the initial sample of 4,973 individuals are
not statistically significant. Descriptive statistics available upon request.
8
Indicators of coresidence have been often employed in the absence of data on the availability of actual informal
care (see e.g., Van Houtven and Norton, 2004; De Meijer et al., 2011; Weaver et al., 2009).
9
This is based on the international standard classification of Education 1997 (ISCED-97) and allows for crosscountry comparisons in the presence of high intercountry heterogeneity.
7
in activities of daily living (ADL), chronic diseases (chronic) and long-term illnesses (ltillness).10
Long-term illness is represented by dichotomous variables taking value 1 for individuals with
illnesses, and 0 otherwise. The other morbidity and disability indicators are expressed in categories
that depend on the severity level of the disease or limitation.
Caregivers’ characteristics may determine the availability and the quantity of informal support
received.11 Previous studies have used indicators of
gender and residence to correct for the
endogeneity of informal care in the model for formal care by assuming that they only have an
indirect impact on formal care via informal support. In particular, SHARE provides detailed
information about children and their (physical) distance from parents. We use information about
children’s gender, marital status, employment status and age to build indicators for the proportion
of daughters, for whether the child lives with a spouse or not, the proportion of unemployed
children and the age of the youngest child.12 These are used as control variables that better specify
the informal support model. For the same purpose, we look at information about children’s place of
residence, classified according to the distance from their parents’ house. Respondents are asked
whether the child lives in his own household, in the same building, less than 1 km away, between 1
and 5 km, 5 and 25 km, 25 and 100 km, 100 and 500 km, more than 500 km away or more than 500
km away in another country. From this, we calculate a new indicator of distance from the nearest
child, assigning each observation the number of kilometers corresponding to half the bandwidth of
each possible category.13 Distance is assumed to be important because children who live farther
away may be less likely to provide informal care compared to those living closer.
-Table 1 here-
A dummy indicator for the presence of limitations in instrumental activities of daily living (IADL) was finally
excluded because of collinearity with the GALI indicators.
11
Due to the nature of the data, we cannot distinguish among adult children caregivers and non-caregivers, and this
may lead to neglecting differences in the quality of care.
12
Female children, as shown in several studies, usually provide more support to their parents compared to males
(see, e.g., Stone et al., 1987). Other works, find that sons are also becoming substantial sources of support (Carmichael
and Charles, 2003).
13
This indicator of geographical distance is also used in Bonsang (2009).
8
10
Descriptive statistics
Descriptive results are shown in Table 1. Our target sample consists of 53 % women and the
average age is about 74. The oldest old (over 85) account for 6 % of the sample and about 39 % of
respondents live alone. Around 4.4 % died between the first and the second wave of SHARE.
Roughly 50 % report having GALI limitations and 13 % ADL limitations. More than 55 % of the
sample report having chronic conditions, long-term illnesses or limitations in mobility.
LTC recipients (defined as individuals receiving either formal or informal support) represent 31 %
of the individuals. About 40 % of these receive TFC, most of which is PDH (about 70 %, against 51 %
NC). The average monthly hours of formal care received in the last year is around 21, and again most
hours refer to PDH (24, against 9 for NC). Informal support appears to be the main source of LTC in our
sample, roughly 81 % of LTC recipients receiving it. Not surprisingly, the amount of informal care
largely exceeds TFC, with about 39 hours per month.
Looking at children’s characteristics, we note that the average age of the youngest child is 42. About
a half of the children are females, while only a small proportion is unemployed (3.4 %). Children who
live with their spouse are the majority (85 %) and the average distance from parents is about 42
kilometres.
III.
The model
The distribution of formal care has a substantial number of zeros (87 % for TFC, about 91 and 93 %
for PDH and NC, respectively). In order to account for this feature of the data, we use a standard
two-part model (Cragg, 1971; Duan, 1983; Jones, 2000). This specifies the probability of receiving
care and the quantity of care received as two different processes. The first component of the model
represents a hurdle to utilization and describes the probability of observing a positive number of
hours of formal care conditional on a vector of regressors xF. This is modeled using a probit
functional form:
9
Pr(d F  1 | xF )  ( F ' xF )
(1)
where dF is a binary variable that indicates whether the individual receives formal care or not. The
second component is the conditional density for the number of hours of formal care (yF) given that
the respondent receives some care. In order to ensure positive values of the quantity of care, and
following several examples in the recent literature (e.g., Manning and Mullay, 2005; Deb et al.,
2009), this density is specified as a gamma function with two parameters:
y 
 ( 1)
exp( F )
 yF
 
f ( y F | d F  1, x F )  
;   0,   0

 ( )
(2)
where σ is the scale of the Gamma distribution parameterized as exp(βF’xF) and α is the shape
parameter. The first component of the hurdle model is estimated on the whole sample. The second
component is estimated only on the sub-sample of those individuals who receive a positive number
of hours of care. The conditional expected number of hours derived from the Gamma distribution is
simply equal to the product of the scale and shape parameters, i.e.
E( y F | d F  1)   . Thus, the (unconditional) expected number of hours of formal care yielded by
the two components of the model is:
E( y F | xF )  ( F ' xF ) exp(  F ' xF )
(3)
The demand for informal care can be specified as a two-part model as well, where the probability
of receiving informal support is Pr(d I  1 | xI )  ( I ' xI ) , the quantity of support received (in
terms of number of hours) is the f ( y I | d I  1, xI ) , dI is the binary indicator of whether the
10
individual receives informal care, yI is the number of hours of informal care. For informal care we
use the same functional forms employed in the formal care model. Therefore, the expected value of
yI is:
E( y I | xI )  ( I ' xI ) exp(  I ' xI )
(4)
In the absence of precise indications from the underlying economic theory, we specify both
components of each hurdle as identical in terms of explanatory variables. Vectors xF and xI include
exogenous covariates such as age classes, PtD, socioeconomic indicators, such as household income
(in logs) and number of years of education, disability and health indicators, gender, coresidence and
country dummy variables; xI also includes specific caregiver characteristics. The logarithm of yI is
included as predictor in the equations for formal care, as in Van Houtven and Norton (2004) and
Bonsang (2009).14 The econometric issue here is the possible endogeneity of informal care, due to
the presence of unobservable individual-specific factors influencing both hurdle models.
Formal and informal care models, described in equations (3) and (4), could be estimated as
separate univariate models. They are, however, interrelated components of the overall demand for
LTC. In order to control for simultaneity, as well as for the endogeneity of informal care, we use a
bivariate two-part model that can be estimated as a system of four equations, linked by dependence
on unobservables. This is estimated by means of a discrete latent factor model (DLFM), under the
assumption that the error process, in each equation, depends on common latent factors that
influence both the probability of having formal and informal care as well as the number of hours of
both types of care:
 ij  lij  ij , j  1,...,4
14
(5)
Note that the number of monthly hours of informal care is always greater than one in our data.
11
where εij are the unobservable terms in each equation j, ωij are the independent error components in
each equation, and the lij are the latent factors; the latent factors l1, …, l4 are associated and the
same for each individual. Unobservables are treated as random factors and integrated out of the
model (see Heckman and Singer, 1984). The DLFM offers an alternative to parametric approaches
and has the advantage of reducing the bias in identifying the distribution of the latent factors when
they are non-normal (see Mroz, 1999).15 It is based on a finite density estimator that approximates
the unknown distribution of lj using a step function based on K location mass points. Following
Balia and Jones (2011) we assume that the latent factors in equation (5) have the following factorloading specification:
l j   ju   j v
(6)
where u and v are Bernoulli random variables which take value 1 with probability p1 and p2, and
value 0 with probability (1−p1) and (1−p2), respectively. Given the factor-loading specification of
the latent factors, for each equation there are four location mass points (K = 4) because this is the
number of possible combinations of u and v. The bivariate two-part model with heterogeneity is
estimated using full-information maximum likelihood techniques.
Identification issue
Identification of all the unknown parameters of the distribution of the latent factors requires
restrictions on the support of lj (see Mroz, 1999). As in Balia and Jones (2011), we fix two mass
points to 0 and 1 and assume that u and v are Bernoulli random variables and parameterise the
15
The advantage of using this methodology is that consistent estimates can be obtained without parametric
assumptions about the distribution of the unobserved heterogeneity, while the standard maximum likelihood estimator
relies on joint normality or other parametric assumptions.
12
probabilities p1 and p2, from which πk are derived: we use a logistic distribution.16 In principle, our
mixture model does not require exclusion restrictions, being identified solely by functional form of
its components, where the mixture itself is identified by the factor-loading specification. Nonlinearity in the functional form of each equation guarantees identification of the bivariate two-part
model. Nevertheless, exclusion restrictions might be imposed when the underlying economic theory
supports the presence of covariates which directly affect one process (the demand for informal care,
in this case) and not the other (the demand for formal care). Since estimators that rely on functional
form for identification may be highly sensitive to misspecification, exclusion restrictions may be
required to achieve more reliable estimates. The specification of our model excludes a set of specific
controls for informal care, which are described in detail in section 2, from the formal care
equations. A Wald test for the joint exclusion of such control variables from the formal care model
is performed.
Endogeneity problem
The structure of the error process specified in eqs 5 and 6 allows for correlations between
equations.17 This captures both potential endogeneity and the effect of unobservable individualspecific heterogeneity: factor loadings can be interpreted, in fact, as coefficients of the omitted
variables. Therefore, the DLFM ensures that also potential endogenenity of PtD in the model is
taken into account. Previous works on HCE have revealed the importance of accounting for
potential endogeneity of PtD: the remaining life expectancy can be influenced by current total or
acute HCE (see, e.g, Zweifel et al., 2004; Felder et al., 2010). This appears to be a minor issue in
16
Thus,
pj 
j
e
j
1 e
where j =1, 2. The θj are additional parameters to estimate together with the factor-loadings
(ρj, δj), and allow the mixing probabilities πk to be recovered.
17
Correlations between latent factors are calculated as Corr(lj, lm)=Cov(lj, lm)/[sd(lj)sd(lm)] where Cov(lj, lm) and
sd(lj,m) describe, respectively, the covariance and the standard deviations of the latent factors. More details can be found
in Balia and Jones (2011).
13
the analysis of LTC, given that both formal and informal care can only have a secondary influence
on remaining lifespan compared to medical care provided in hospitals or in nursing homes.18
IV. Results
In this section we present results from the estimation of the DLFM for three models. Table 2 shows
results for the model that considers TFC as main formal care indicator; Tables 3 and 4 refer to the
models that use, instead, NC and PDH.
The number of hours of informal care (here InfC_hours is in the logs) shows a significant and
positive coefficient in both parts of our three models. Its explanatory power, however, diminishes in the
second equation of the NC and PDH models. In the latter, the coefficient is also very small. Overall,
each model shows some evidence of complementarity between the availability of informal care and the
possibility of receiving formal care. The absence of substitutability effects clearly frustrates some
simplistic views according to which informal care will significantly contribute to reducing the future
burden of LTC expenditures. In line with Sloan and Norton (1997), Mellor (2001) and Courbage and
Roudaut (2008), this result undermines a necessary condition of the so-called intra-family moral hazard
hypothesis, which is often invoked to explain the lack of systematic purchasing of LTC insurance.19
The coefficient of PtD, the first of our three main determinants of LTC utilisation, is positive and
statistically significant in both parts of the models for TFC and PDH, whereas it does not seem to
explain the demand for NC. In the case of PDH (low-skill services), in fact, out-of-pocket payments can
be more easily used to complement basic health care financed by public coverage or private insurance
when this is required by changing LTC needs of individuals. By contrast, the reason why NC (high-skill
services) appear less responsive to the changing needs of individual preferences could be related either
to the scarcity of skilled workers in the private market, or to hospitalization of those individuals who
require greater professional care.
18
See also De Meijer et al. (2011) for a discussion of this issue.
For a similar conclusion related to the application of stated preference approaches to the demand for LTC
insurance see Brau and Lippi Bruni (2008).
14
19
In each model, the coefficients of age classes indicate a positive correlation both with the
probability of receiving care and the quantity received. Coefficients are higher for the oldest old
individuals. Looking at PtD and age coefficients together, we find that they are both relevant in
explaining LTC utilisation and, consequently, the dynamics of HCEs. Our evidence with European
data, therefore, confirms previous results with HRS data by Weaver et al. (2009).
Disability and morbidity indicators should “compete with” or “dominate” age and PtD, as they
are the most genuine candidates for detecting the need for LTC. This is confirmed by the high
statistical significance of their coefficients. We find that more severe levels of disabilities (ADL,
GALI, mobility) are associated with higher probability of receiving total formal care (this result
holds particularly in the PDH model, where all coefficients are highly significant). Results are less
clear in the second part of the model, however, where only ADL detects a statistically significant
higher number of hours of formal care as severity in disability increases. GALI and mobility
indicators show a higher effect in the case of moderate and mild limitations, respectively. Overall,
in the NC and PDH models, ADLs and mobility indicators seem to capture most of the variability in
the response variables.
The indicator of coresidence status (living alone), has a positive and significant effect on both
equations of the TFC model (the size of the coefficient is comparable to PtD) and on the probability
of receiving PDH. In this case, a clear substitution effect emerges between the spouse’s help and
professional LTC services. Note that this substitution effect also holds with respect to the informal
support by children and other relatives. Only the demand for NC does not seem to be driven by
coresidence, probably because these services cannot be easily replaced by spouse’s support.
As for income and education controls, we do not find evidence of a clear socioeconomic gradient
in TFC utilisation. Household income is significant only in the second part of the PDH model,
where it always shows a positive coefficient. In fact, PDH is a relatively more marketed service,
which enables individuals to purchase the desired quantity according to their own preferences,
whereas for NC a stronger rationing on the supply side is more likely. No plain interpretation
15
emerges regarding education, which is usually not significant, apart from the second part of the NC
model; in the other equations its coefficient is nearly zero.
We conclude our comments on the results of the formal care models by highlighting that the
dummies for the presence of long-term illness and chronic diseases do not contribute to explain
formal care use, and this is also confirmed by the separate models for NC and PDH.
-Tables 2,3 and 4 about hereMoving to the equation of informal care we find that, as expected, the probability of receiving
informal support increases with age, is higher for individuals living alone and having disabilities (in
particular, the effect increases with severity of GALI and mobility limitations, and is higher for
those who have moderate ADL). Interestingly, the dummy for chronic diseases is now significant,
displaying a strong positive effect mainly for the less severe situations. A possible interpretation is
that informal support can be more useful for those individuals who do not require professional or
medical care. This would also explain the insignificance of the severe ADL category.
Estimates also show that informal support is only weakly related to PtD. Its coefficient is
significant only in the equation that describes the probability of receiving informal care in Table 2
and in the quantity equation of Table 3. This supports the idea that help by children and relatives
starts before health deterioration occurs, and being close to death at most marginally increases the
effort of those already engaged in caregiving.
Another variable with an interesting effect on informal care is household income, which for PDH
(Table 4) has a negative and significant coefficient in the quantity equation of informal care, and a
positive coefficient in the equation for the number of hours of formal care. This suggests that in the
case of PDH, highest income individuals make greater use of paid carers and, at the same time, rely
on less the support of family caregivers. This can be interpreted as evidence of an income-related
substitution effect between informal care and PDH, being the latter more easily purchased in the
market than NC services.
16
As for caregivers’ characteristics, results partially confirm their importance as predictors of
informal care. We find that the probability of receiving informal care is strongly limited by
geographical distance and to a lesser extent by children’s age, the farthest and youngest children
being less likely to be able to provide support (the other indicators do not show any significant
effect).
Analysis of the correlations between latent factors provides an insight into the role of
unobservable heterogeneity (Table 5). The correlation between the latent factors in the informal
care equations and the latent factor in the first part of the TFC model are quite strong. Corr(l3,l1)
indicates the presence of unobservables which increase the probability of receiving both informal
and formal care. This suggests that unobservable heterogeneity drives complementarity in the
availability of both types of care. By contrast, Corr(l4,l1) shows that unobservables which increase
the quantity of informal care also decrease the probability of receiving TFC, thus providing
evidence in favour of substitutability in the relationship between formal and informal care.
Corr(l3,l2)
and Corr(l4,l2) are smaller in size. The former seems to reveal the effect of
unobservables which simultaneously increase the number of hours of TFC and decrease the
probability of receiving informal support.
Uncontrolled factors such as the presence of a health or LTC insurance coverage might provide
an explanation. Interpretation of what determines Corr(l4,l2) is not straightforward. We estimate the
maximum negative correlation in Corr(l3,l4) . Unobservables that increase the probability of
receiving informal care at the same time decrease the amount of support received. This result
reinforces the idea that informal care cannot be considered comprehensive: the presence of a family
caregiver does not imply that he/she has to provide more support or all the support needed by the
disabled. Corr(l1,l2) is quite large and indicates that unobservables that increase the probability of
receiving formal care also increase the quantity demanded. This suggests, on the contrary, that
formal care is often comprehensive.
-
Table 5 about here17
The previous results largely hold in the NC model, with the exception of a weaker correlation
between latent factors l1 and l2, indicating a lower comprehensiveness of formal care when it is
provided by professional nurses (who on average provide a more professionalized service for a
lower number of hours per day), and a higher correlation between l3 and l2. This supports the idea
of substitutability between family caregivers and quantity of NC.
In the case of PDH, Corr(l3,l2) becomes positive, suggesting that the availability of a family
caregiver increases the quantity of PDH demanded. Also Corr(l4,l2) changes in sign: unobservables
that increase the amount of informal support also decrease the amount of PDH, suggesting the
presence of substitutability.
Average partial effects
A more exhaustive interpretation of the results is offered by the estimation of the average partial
effects (APEs). Partial effects are computed for each individual as the change in expected formal
care use resulting from a single unit change in the explanatory variable, as yielded by the two-part
model specified in equation 3, then averaged across the whole sample, so that they are referred to
the entire population. With the APEs, the contribution of each explanatory variable to variations in
the use of formal care (either TFC, NC or PDH) is expressed in terms of variations in the number of
hours of care received per month. In the case of informal care, income and years of education, the
partial effects are computed as the result of a single unit change from their mean value (for informal
care the mean of the predicted number of hours is used). Table 6 shows the APEs for all the
regressors included in the model.
-Table 6 about hereWe estimate quite large effects for the indicators of PtD and age. PtD is found to determine an
increase of 5.8 hours per month in expected TFC, as a combined result of an increase of 5.9 % in the
probability of receiving care, and an increase of 12 hours in amount of care. This is not, however, a
general result: the effect on the expected number of hours of NC is nearly zero, as expected from the
analysis of the model coefficients. As for age, the APE in the TFC model is comparable to that of PtD,
18
being a bit lower for those aged between 75 and 85 years (3 hours) and greater for the oldest old (7.5
hours). Looking at the NC and PDH models, we find higher effects on the probability to receive PDH,
and on the number of hours of NC. The other (statistically significant) variables which display a large
APE are the disability indicators, with an increment of nearly 22 hours of TFC associated with severe
ADL. Overall, ADL, mobility and GALI indicators seem to capture the LTC needs quite well.
We have seen that estimation results suggest the presence of complementarity between formal care
and informal support. We are now able to say that, in terms of the incremental number of hours of care,
this effect is quite small. One additional hour of informal care leads to an increase in expected TFC of
about 18 minutes (19 minutes in the case of PDH). The effect on NC is smaller (about 8 minutes). The
policy lesson which can be learned is that informal care is not likely to be considered as an effective
variable to substantially change the demand for formal care. With respect to previous studies, where
some evidence of substitutability was found, our findings call for a re-consideration of their results, on
the grounds that emphasis should be placed not only on the sign of estimation results, but also on their
size. In our view, irrespective of whether a small substitution or complementarity effect is found, the
policy implication would be that incentives for informal support are not likely to strongly modify the
European demand of at-home LTC paid services.
We improve our analysis by taking into account the indirect contribution of the interaction between
PtD and disability indicators on changes in formal care due to informal care and ageing. Table 7 shows
the APEs for different types of individuals, defined on the base of PtD and LTC needs as proxied by the
severity of disability.20 This results in calculating the partial effects, for both survivors and decedents,
for “low need” individuals (with mild ADL, mobility and GALI), “high need” individuals (with
moderate ADL and mobility and severe GALI) and “very high need” individuals (with severe ADL,
mobility and GALI). Finally, for each need category we calculate the ratio (R) between decedents and
survivors. This allows us to measure the multiplicative power of PtD on the APEs, and evaluate to what
extent it varies with disability level.
20
We only consider disability because morbidity indicators are, overall, largely statistically insignificant.
19
The APE of informal care looks quite stable to increasing needs. It is also higher for decedents in all
models, but the additional effect of PtD decreases with needs: we estimate an additional increase of
about half an hour for “low need” (the difference between 0.995 and 0.471 hours) and of about 20
minutes for “very high need” (0.714 hours minus 0.403) in the TFC model. The ratio between the APEs
of decedents and survivors is lower for individuals with “very high needs”. Interestingly, this is largely
comparable to previous results covering a large set of HCE categories and other geographical areas (see
Payne et al., 2007). We note that the APEs in the TFC model seem prominently determined by variation
in PDH, whilst NC is substantially inelastic to PtD. This again supports our conjecture, introduced when
commenting the effects of the income variable, that the provision of more professionalised paid
caregiving (NC) is strongly characterised by supply constraints, and consequently weakly responsive to
changing needs of individuals.21
The APEs of age reach very large values due to the combined effect of PtD and disability. Moving
from the group of “low need” survivors to the “very high needs” decedents in the TFC model, we
observe a variation of more than 44 hours per month in the APE of the first age group, of which nearly
18 hours (23.628 minus 5.861) attributed to variations in the disability level, and the remaining 26.4
hours (50.224 minus 23.628) attributed to PtD.
-Table 7 about hereWe further investigate the interactions between our main determinants of LTC, that is PtD, age and
disability in Table 8, which shows the APEs estimated for scenarios where these variables take
reference values. For comparison, also the APEs of informal care are estimated under these scenarios.
The ratios (R) are intended to measure the multiplicative power of PtD, age and disability separately.22
Our results show a fairly complex picture, where no prominent roles for any one of the three
determinants emerges, and significant differences can be detected depending on which APE and type of
individual is considered.
21
For example, Arnzt and Thomzen (2010) report that in Germany home care is received according to a limited
catalogue of care services provided solely by authorized agencies, usually considered rather inflexible and unsuitable to
meet individual care needs.
22
This implies calculating the ratio between the APE of the oldest and youngest old, between the APE of the “very
high need” and “low need” and, separately, that of “high need”.
20
The complementarity effect of informal care is prominently amplified by age (the ratios R range
between 2.9 and 4.8), and much less by PtD and disability, probably because the latter are more related
to the demand for more professionalized services. The APEs of age increases substantially for very high
needs, whilst the decedents category alone has a lesser effect. Interestingly, the APEs of age is amplified
by disability in the NC model (5.5 higher for “very high need” than for “low need” individuals) but
appears totally unresponsive to changes in PtD. We detect a strong multiplicative effect of age and
disability on the APE of PtD. The APE is 3.4 (PDH) up to 4.8 (TFC) times higher for the oldest old
compared to the youngest old, and 3.6 (TFC) up to 17.4 (NC) times higher for the “very high need” than
for the “low need” individuals.23 We find evidence of a strong interaction between “very high need” and
age (about 67 hours of additional TFC per month) and PtD (about 42 hours of additional TFC per
month). Conversely, combinations between age and PtD only determine much smaller effects.
The last part of Table 8 shows the APEs of the disability indicators used to define different levels of
need. Here the partial effects are calculated for specific values of PtD and age. We find that the APEs are
usually more responsive to age than to PtD. The ADL are the disability indicators associated with the
largest variations in monthly hours of formal care.
-Table 8 about here-
V. Conclusions
Within the well-established debate on the “red herrings” hypothesis in the study of HCE determinants,
according to which population ageing is unlikely to be a significant predictor of HCEs once PtD is taken
into account, LTC is usually considered an exception. The role of age should not be neglected in the
case of LTC-related expenditure (Werblow et al., 2007); or alternatively both age and PtD indicators
should be replaced by “genuine” indicators of LTC needs (De Meijer et al., 2011).
Examining this issue for the first time using the information collected by SHARE and within a
framework which also models the provision of informal care, we have found that none of the three
indicators suggested (age, PtD and disability) can be disregarded in the specification of formal home
23
This value, however, could be unreliable since the estimated coefficient for PtD in the NC model is not
statistically significant.
21
care utilisation by the European elderly. When going into detail, disability indicators and age seem to
play a more important role (and constant across all estimated models) than PtD. The effect of the latter
varies according to the type of formal care: a strong significant effect on paid domestic help, and a non
significant (and nearly null) effect on nursing care.
Through a detailed analysis based on average partial effects, we have evaluated the indirect effect of
the interactions between age, PtD and disability. We have seen that the effect of age is especially
relevant when combined with PtD and disability. For the case of severe disabilities in particular, the
estimated overall effect in terms of additional number of hours of formal care is very high (67 hours per
month of TFC, vis à vis a sample average of 8.3 hours). Even if this applies only to about one 1% of our
sample, these effects determine a overall substantial variation in formal LTC provision (about 8%, given
the previous figures). Sizeable effects emerge also when considering combinations of PtD with
disability and, alternatively, with the oldest age group. Generally speaking, though significant
differences emerge, depending on which APE and type of individual is considered, we believe that age,
PtD and disability should be used jointly as predictors of LTC use.
This paper has also modelled in a novel way the relationship between formal and informal care,
controlling for endogeneity bias with a latent factor approach and assessing the role of PtD. We have
found evidence of a significant (though small in size) complementarity between formal and informal
care, prominently amplified by age and to a lesser extent by PtD. On the whole, the effect of informal
support on formal care is negligible and unresponsive to increasing needs. From a policy point of view,
this suggests that incentives for informal support are not likely to strongly affect the European demand
for paid long-term home services. The role of informal care as an effective cost-saving alternative to
paid LTC probably needs some reconsideration.
22
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25
TABLE 1
Summary statistics
LTC
TFC (if LTC=1)
NC (if TFC=1)
PDH (if TFC=1)
TFC_hours (if LTC=1)
NC_hours (if FTC=1)
PDH_hours (if FTC=1)
InfC (if LTC=1)
InfC_hours (if LTC=1)
PtD
age 7585
age over85
female
living alone
chronic no
chronic mild
chronic moderate
chronic severe
gali no
gali mild
gali severe
adl no
adl mild
adl moderate
adl severe
mobility no
mobility mild
mobility moderate
mobility severe
ltillness
income
education (years)
children spouse
age child
unempl. children
prop. daughters
distance
Mean
0.313
0.397
0.507
0.701
21.055
9.05
23.495
0.811
38.694
0.044
0.597
0.343
0.53
0.388
0.144
0.298
0.403
0.155
0.505
0.342
0.153
0.873
0.071
0.045
0.011
0.4
0.319
0.147
0.134
0.564
101085.5
9.141
0.849
41.94
0.034
0.506
42.313
S.D.
0.464
0.490
0.501
0.458
71.785
29.294
77.584
0.392
54.760
0.206
0.491
0.475
0.499
0.487
0.351
0.457
0.491
0.362
0.500
0.474
0.360
0.333
0.257
0.208
0.103
0.490
0.466
0.354
0.341
0.496
213343.6
4.509
0.358
7.962
0.143
0.360
103.681
26
TABLE 2
Results from the total formal care model
Formal care
Probability of
receving care
Informal care
Probability of receving
care
Number of hours
Variables
Coeff.
S.E.
Coeff.
S.E.
InfC_hours
PtD
age 7585
age over85
female
living alone
chronic mild
chronic moderate
chronic severe
gali mild
gali severe
adl mild
adl moderate
adl severe
mobility mild
mobility moderate
mobility severe
ltillness
income
education (years)
children spouse
age child
unempl. children
prop. daughters
distance
country
constant
α
Latent factor
parameters
0.096*
0.320†
0.410*
0.812*
0.092
0.330*
-0.031
-0.008
0.200
0.336*
0.574*
0.246†
0.625*
0.991*
0.440*
0.334*
0.708*
0.079
0.062
0.011
0.022
0.134
0.073
0.122
0.077
0.077
0.137
0.134
0.147
0.089
0.111
0.111
0.136
0.258
0.094
0.117
0.126
0.086
0.043
0.009
0.112*
0.680*
0.548*
0.887*
-0.115
0.421*
0.533‡
0.302
0.456
0.376†
0.345
0.534†
0.811*
1.529*
0.820*
0.527†
0.724*
0.094
0.030
0.036‡
0.043
0.240
0.174
0.227
0.158
0.152
0.318
0.320
0.328
0.190
0.213
0.210
0.212
0.368
0.233
0.260
0.272
0.186
0.101
0.019
-3.915*
0.470
0.795
0.625*
1.133
0.037
logL:
N:
Notes:
Number of hours
Coeff.
S.E.
Coeff.
S.E.
0.234‡
0.201*
0.203
0.283*
0.577*
0.434*
0.300*
0.387*
0.221*
0.488*
0.107
0.628*
0.426‡
0.442*
0.598*
0.627*
0.149†
0.007
-0.006
-0.011
0.011†
0.237
0.003
-0.002*
0.135
0.075
0.147
0.068
0.069
0.115
0.115
0.131
0.077
0.104
0.11
0.138
0.248
0.078
0.100
0.119
0.074
0.025
0.008
0.084
0.005
0.198
0.082
0.000
-0.088
0.028
1.376*
0.025
-0.024
-0.075
-0.094
- 0.135‡
-0.043
-0.002
-0.082‡
0.008
0.069
-0.090†
0.033
-0.004
0.055
-0.047*
0.000
0.003
0.000
-0.032
0.023
0.000
0.065
0.039
0.076
0.036
0.036
0.066
0.067
0.070
0.045
0.051
0.046
0.054
0.089
0.045
0.050
0.055
0.041
0.016
0.004
0.044
0.002
0.099
0.040
0.000
-2.395*
0.375
1.410*
8.768*
0.222
0.470
yes
ρ1
ρ2
ρ3
ρ4
-0.074
-0.592*
0.698*
-1.531*
δ1
δ2
δ3
δ4
-0.244†
-0.328
-1.374*
2.909*
θ1
θ2
0.056
1.175*
-7690.283
3526
Significance levels.
‡: 10%
†: 5%
*: 1%
27
TABLE 3
Results from the nursing care model
Nursing care
Probability of receving
care
Coeff.
S.E.
Variables
InfC_hours
PtD
age 7585
age over85
female
living alone
chronic mild
chronic moderate
chronic severe
gali mild
gali severe
adl mild
adl moderate
adl severe
mobility mild
mobility moderate
mobility severe
ltillness
income
education (years)
children spouse
age child
unempl. children
prop. daughters
distance
country
constant
α
Latent factor
parameters
logL:
N:
Notes:
0.074*
-0.086
0.177†
0.381†
0.170‡
0.028
-0.033
0.034
0.089
0.203‡
0.565*
0.240‡
0.865*
1.186*
0.315*
0.135
0.450*
0.153
0.037
0.006
0.026
0.174
0.090
0.152
0.096
0.097
0.174
0.171
0.187
0.113
0.132
0.131
0.146
0.255
0.118
0.149
0.154
0.109
0.047
0.010
Informal care
Probability of receving
care
Coeff.
S.E.
Number of hours
Coeff.
S.E.
0.122‡
0.192
0.450†
0.897*
0.519†
0.107
-0.664
-0.584
-0.106
0.201
0.481‡
1.041*
0.799*
1.397*
0.698†
0.017
0.183
0.423
0.012
0.120*
0.067
0.356
0.222
0.328
0.251
0.253
0.450
0.440
0.446
0.288
0.283
0.312
0.300
0.439
0.323
0.394
0.406
0.270
0.129
0.024
Number of hours
Coeff.
S.E.
0.178
0.212*
0.537*
0.282*
0.575*
0.421*
0.273†
0.378*
0.211*
0.483*
0.109
0.646*
-0.018
0.433*
0.611*
0.634*
0.162†
0.003
-0.007
-0.010
0.010‡
0.225
0.002
-0.002*
0.134
0.075
0.141
0.068
0.069
0.115
0.114
0.130
0.077
0.103
0.109
0.137
0.260
0.077
0.099
0.118
0.074
0.024
0.008
0.084
0.005
0.200
0.082
0.000
0.079‡
0.002
0.065
-0.013
-0.007
-0.038
0.000
-0.079
-0.026
0.048
-0.096†
-0.010
1.423*
-0.089†
-0.014
-0.022
0.025
-0.003
0.001
0.002
0.002
0.006
0.015
0.000
0.046
0.034
0.053
0.031
0.028
0.057
0.056
0.059
0.038
0.044
0.040
0.044
0.080
0.039
0.044
0.049
0.034
0.010
0.004
0.039
0.002
0.089
0.035
0.000
-2.129*
0.372
-0.376†
8.768*
0.470
yes
-3.689*
ρ1
ρ2
ρ3
ρ4
-6295.967
3526
Significance levels.
0.526
-1.153
0.814*
-0.011
-1.809*
0.808*
-1.547*
‡: 10%
1.400
0.076
δ1
δ2
δ3
δ4
†: 5%
θ1
θ2
-0.141
-0.006
-1.330*
2.866*
-0.094
1.296*
*: 1%
28
TABLE 4
Results from the paid domestic help model
Paid domestic help
Probability of receving
care
Coeff.
S.E.
Variables
InfC_hours
PtD
age 7585
age over85
female
living alone
chronic mild
chronic moderate
chronic severe
gali mild
gali severe
adl mild
adl moderate
adl severe
mobility mild
mobility moderate
mobility severe
ltillness
income
education (years)
children spouse
age child
unempl. children
prop. daughters
distance
country
constant
α
Latent factor
parameters
logL:
N:
Notes:
Informal care
Probability of receving
care
Coeff.
S.E.
Number of hours
Coeff.
S.E.
0.024
0.140
0.087
0.128
0.089
0.088
0.167
0.164
0.175
0.104
0.127
0.122
0.143
0.254
0.115
0.137
0.147
0.099
0.055
0.011
0.072‡
0.359‡
0.163
0.448†
-0.420*
0.100
0.300
0.161
0.332
0.270
0.131
0.211
0.685*
1.685*
0.800*
0.641*
0.599†
0.056
0.317*
-0.011
0.039
0.196
0.171
0.212
0.149
0.152
0.306
0.300
0.309
0.182
0.212
0.190
0.197
0.384
0.228
0.247
0.254
0.175
0.117
0.019
-4.400*
0.593
-0.869
0.969*
1.303
0.069
ρ1
ρ2
ρ3
ρ4
-7004.196
3526
-0.074
-0.106
0.644*
-1.577*
0.076*
0.481*
0.582*
1.062*
0.124
0.513*
0.022
0.013
0.330‡
0.354*
0.467*
0.319*
0.541*
0.645†
0.458*
0.410*
0.696*
0.062
0.069
0.012
Number of hours
Coeff.
S.E.
0.185
0.204*
0.524*
0.284*
0.562*
0.425*
0.282†
0.379*
0.214*
0.477*
0.121
0.627*
0.391
0.414*
0.584*
0.610*
0.159†
0.011
-0.006
-0.006
0.009‡
0.199
0.010
-0.002*
0.131
0.074
0.138
0.067
0.067
0.114
0.113
0.129
0.075
0.102
0.108
0.135
0.240
0.076
0.097
0.116
0.073
0.025
0.008
0.083
0.005
0.196
0.080
0.000
0.062
0.002
0.042
-0.005
-0.033
-0.039
-0.014
-0.058
-0.050
-0.007
-0.069‡
0.030
0.051
-0.051
0.028
-0.004
0.034
-0.058*
0.001
-0.007
0.002
0.029
-0.006
0.000†
0.043
0.032
0.049
0.029
0.028
0.051
0.049
0.053
0.033
0.043
0.037
0.042
0.074
0.037
0.041
0.046
0.031
0.009
0.004
0.037
0.002
0.077
0.033
0.000
-2.104*
0.377
0.041
11.888*
0.144
0.594
θ1
θ2
-0.013
1.387*
yes
Significance levels.
‡: 10%
δ1
δ2
δ3
δ4
†: 5%
-0.264†
-0.163
-1.363*
2.877*
*: 1%
29
TABLE 5
Correlation coefficients –
TFC
l1
l2
l3
l4
NC
l1
l2
l3
l4
PDH
l1
l2
l3
l4
l1
1
l2
0.706
1
l3
0.636
-0.098
1
l4
-0.624
0.114
-0.999
1
1
0.096
1
0.745
-0.592
1
-0.781
0.547
-0.998
1
1
0.941
1
0.645
0.348
1
-0.592
-0.284
-0.998
1
30
TABLE 6
Average partial effects
TFC
InfC_hours
ptd
age 7585
age over85
female
living alone
chronic mild
chronic moderate
chronic severe
gali mild
gali severe
adl mild
adl moderate
adl severe
mobility mild
mobility moderate
mobility severe
ltillness
income
education (years)
NC
P(y>0)
E(y|y>0)
E(y)
0.004
0.059
0.070
0.160
0.015
0.056
-0.005
-0.001
0.035
0.055
0.103
0.044
0.127
0.222
0.070
0.051
0.126
0.013
0.008
0.002
0.338
12.017
6.667
13.058
-1.573
5.635
6.448
3.231
5.288
0.235
0.216
7.326
12.969
37.522
9.537
5.210
7.972
1.237
13.376
13.670
0.180
5.851
3.045
7.486
-0.265
2.921
2.095
1.085
2.508
0.132
0.216
2.853
6.947
21.965
3.805
2.091
4.350
0.679
4.845
4.906
P(y>0)
PDH
E(y|y>0)
E(y)
0.315
1.948
4.028
10.294
4.669
0.994
-6.922
-6.313
-1.439
0.164
0.391
13.572
9.064
22.543
6.988
0.120
1.387
3.749
9.171
10.313
0.057
0.101
0.596
1.813
0.710
0.151
-0.796
-0.660
0.000
0.033
0.119
1.394
2.887
8.147
1.143
0.122
0.629
0.563
1.082
1.208
0.002
-0.008
0.018
0.042
0.017
0.003
-0.003
0.003
0.009
0.019
0.064
0.025
0.128
0.203
0.030
0.011
0.046
0.015
0.002
0.001
P(y>0)
0.003
0.074
0.076
0.172
0.016
0.069
0.003
0.002
0.046
0.045
0.062
0.046
0.085
0.105
0.055
0.048
0.093
0.008
0.007
0.002
E(y|y>0)
E(y)
0.278
5.722
2.155
6.901
-5.896
1.388
3.826
1.914
4.309
0.262
0.127
2.709
11.327
50.541
9.955
7.297
6.659
0.762
16.488
13.291
0.106
2.868
1.659
4.781
-0.951
1.615
0.757
0.380
1.718
0.138
0.162
1.132
3.772
14.322
2.431
1.806
2.483
0.306
3.444
2.756
TABLE 7
Selected APEs for specific values of PtD and levels of need
low need
TFC
InfC_hours NC
PDH
TFC
age 7585
NC
PDH
TFC
age over85 NC
PDH
survivors
0.47
0.18
0.17
5.86
1.67
2.86
18.95
5.37
8.42
decedents
0.99
0.17
0.30
14.80
1.77
5.84
45.23
5.72
16.03
high need
R
2.1
0.9
1.8
2.5
1.1
2.0
2.4
1.1
1.9
survivors
0.39
0.15
0.15
8.45
2.51
4.34
25.03
7.46
12.24
decedents
0.78
0.15
0.26
19.64
2.78
8.14
55.54
8.31
21.65
very high need
R
2.0
1.0
1.8
2.3
1.1
1.9
2.2
1.1
1.8
survivors
0.40
0.20
0.22
23.63
9.24
13.63
63.68
25.98
36.74
decedents
0.71
0.20
0.34
50.22
10.55
23.21
130.99
29.89
59.91
R
1.8
1.0
1.6
2.1
1.1
1.7
2.1
1.2
1.6
31
TABLE 8
Selected APEs for specific values of PtD, age and levels of need
InfC_hours
ptd
age 7585
age over85
adl mild
adl moderate
adl severe
gali moderate
gali severe
mobility mild
mobility moderate
mobility severe
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
TFC
NC
PDH
survivors
decedents
R
0.16
0.06
0.10
0.36
0.05
0.17
2.3
1.0
1.8
2.68
0.59
1.51
6.69
1.79
4.42
2.53
1.39
1.05
6.26
2.87
3.49
19.94
8.08
13.19
2.08
0.30
1.36
2.76
1.17
1.27
3.25
1.13
2.13
1.79
0.12
1.58
3.79
0.62
2.23
6.54
0.64
3.09
15.72
1.97
8.56
6.30
1.48
2.17
14.87
3.15
7.24
46.16
9.00
27.71
4.99
0.33
2.76
6.40
1.29
2.44
8.02
1.23
4.64
4.41
0.13
3.45
9.01
0.69
4.58
2.4
1.1
2.0
2.3
1.1
1.9
2.5
1.1
2.1
2.4
1.1
2.1
2.3
1.1
2.1
2.4
1.1
2.0
2.3
1.1
1.9
2.5
1.1
2.2
2.5
1.1
2.2
2.4
1.1
2.1
youngest
oldest old
old
0.12
0.43
0.04
0.11
0.06
0.17
2.80
13.45
0.05
0.22
1.59
5.49
1.31
0.83
0.58
3.65
1.87
2.01
10.65
5.42
6.89
0.09
0.02
0.09
0.15
0.09
0.10
1.74
0.65
1.06
1.01
0.07
0.78
1.95
0.38
1.22
7.41
3.60
2.42
17.92
6.99
8.30
48.54
19.23
29.67
0.25
0.06
0.27
0.38
0.21
0.31
9.59
2.53
5.15
5.71
0.27
3.82
9.54
1.39
5.12
R
low need
high need
R
3.7
2.9
3.0
4.8
4.6
3.4
0.51
0.18
0.18
11.81
0.12
4.80
6.31
1.68
3.01
20.28
5.38
8.82
0.41
0.15
0.15
15.93
0.37
6.97
9.01
2.52
4.54
26.57
7.49
12.73
0.8
0.8
0.9
1.3
3.2
1.5
1.4
1.5
1.5
1.3
1.4
1.4
very high
need
0.42
0.20
0.23
42.48
2.06
21.15
24.97
9.29
14.12
67.06
26.14
37.93
R
0.8
1.1
1.3
3.6
17.4
4.4
4.0
5.5
4.7
3.3
4.9
4.3
5.7
4.3
4.2
4.9
3.7
4.1
4.6
3.5
4.3
2.6
2.4
3.2
2.5
2.2
3.0
5.5
3.9
4.9
5.6
3.7
4.9
4.9
3.7
4.2
32