Pay less, consume more? Estimating the price elasticity of
demand for home care services of the disabled elderly∗
Quitterie Roquebert† and Marianne Tenand‡
March 6th , 2016
Preliminary version. All comments are welcomed.
Abstract
Although the demand for home care is increasing with population ageing, little is
known about the price sensitivity of the consumption of these services. This paper estimates the price elasticity of the demand for home care of the disabled elderly, using the
features of the French home care subsidy program (“APA”). We use an original dataset
collected from a French District Council with administrative records of out-of-pocket
payments and home care consumption of APA beneficiaries. We exploit inter-individual
variations in producer prices to identify the out-of-pocket price elasticity and explore the
potential nonrandom producer selection. We fit a censored regression model to deal with
observational issues. Our baseline estimations yield a price elasticity estimate around -0.7.
This estimate, however, should be seen as an upper bound as we find evidence of endogenous producer selection. Overall, our results point to a price elasticity much lower than
unity, around -0.5: a 10% increase in out-of-pocket price is predicted to lower consumption by 5%, or about 45 minutes per month for the median sample consumer. It implies
that home care subsidy policies should be analyzed primarily in terms of redistribution
rather than in terms of allocative efficiency.
JEL Classification: C24; D12; I18; J14.
Keywords: long-term care, price elasticity, public policy.
∗
This research project was supported by a research grant from ANR (ANR-14-CE30-0008), and benefitted from the joint support of Direction Générale de la Santé (DGS), of Mission recherche de la Direction de
la recherche, des études, de l’évaluation et des statistiques (MiRe-DREES), of Caisse Nationale d’Assurance
Maladie des Travailleurs Salariés (CNAMTS), of Régime Social des Indépendants (RSI) and of Caisse Nationale de Solidarité pour l’Autonomie (CNSA), within the call for projets launched by IRESP in 2013. We
are grateful to an anonymous French District Council (Conseil départemental ) for granting the access to its
data. We are also grateful to the MODAPA research team for the fruitful discussions and suggestions, and
especially to Agnès Gramain for her patient supervision and many comments. We are grateful to Pierre-Yves
Geoffard, to the participants of the WIP Seminar (PSE), of the LIRAES “Young researchers” seminar and to
the Hospinnomics group (PSE) for their useful remarks. All remaining errors are ours.
†
Corresponding author. Paris School of Economics – Université Paris 1, Centre d’économie de la Sorbonne.
106-112 Bd de l’Hôpital, 75013 Paris. Tel: +33 1 43 13 62 14. E-mail: [email protected]
‡
Paris School of Economics – Ecole normale supérieure, Paris-Jourdan Sciences économiques.
1
1
Introduction
Like most developed countries, France is facing the ageing of its population:
due to the increase in life expectancy and the advance in age of baby-boomers, the
share of the population above 60 is predicted to grow from 21.5% in 2011 to 32.1%
in 2060 (Blanpain & Chardon 2010). As the rise in disability-free life expectancy
does not match the increase in life expectancy (Sieurin et al. 2011), the number of
the elderly needing assistance to perform the activities of daily living is expected to
grow substantially. Most disabled elderly keep on living in the community rather
than entering specialized institutions (Colombo et al. 2011). Besides medical
and nursing care, community-dwelling disabled elderly are often provided basic
domestic help such as meal preparation, assistance with personal hygiene or house
chores. Domestic assistance may be provided by relatives (informal care), but
also by professional services (formal care), whose utilization is increasing. In most
countries, public policies tend to foster the utilization of formal home care by
granting the disabled elderly with subsidies to finance home care consumption.
However, these public programs only partially cover the cost of professional home
care, such that the disabled elderly often bear non-negligible out-of-pocket cost. In
France, the average monthly out-of-pocket payment on domestic help utilization
was estimated to amount, at least, to 160e in 2007 (Bérardier 2011), or about
14% of the average monthly pension benefit1 .
The existence of substantial out-of-pocket payments leads to an immediate
concern: how sensitive to price are the disabled elderly when consuming home care
services? This paper sheds a new light on this question by estimating the price
elasticity of the demand for non-medical home care services of the disabled elderly.
It specifically addresses the effect of price on consumption at the intensive margin.
This effect is a priori unclear, but it has direct implications for the design of public
policies. If price elasticity is found to be small, home care subsidies work as pure
redistributive transfers (from taxpayers to disabled elderly). If the consumption of
home care services is assumed to be notably elastic, home care support programs
have efficiency implications: as in the health care context, generous subsidies
may induce over-consumption and a welfare loss, while insufficient coverage could
undermine the preventive effects home care was found to have on the health of
the elderly (Stabile et al. 2006, Barnay & Juin 2015, Rapp et al. 2015).
Previous literature has studied the impact of out-of-pocket payments on the
consumption of medical services. But despite the growing concern about the
financing of long-term care, the price effect of professional domestic help has been
little investigated. Some papers have tested for the effect of benefiting from home
1
The average pension benefit in 2007 is provided in Deloffre (2009).
2
care subsidies on the utilization of paid domestic help; but because of a lack
of detailed information on out-of-pocket payments, they have not been able to
quantify the price elasticity of demand.
Our paper addresses this shortcoming by making use of the French home care
scheme targeted to the disabled elderly, the APA policy (Allocation personnalisée
d’autonomie). With more than 710,000 beneficiaries in 2013, the APA policy
for the elderly living in the community amounted to a spending of 3.1 billion
euros in 20132 , or 0.15% of GDP. APA works as an hourly subsidy on professional
domestic help. Administrative records of the scheme provide detailed information
on home care consumption and out-of-pocket payments of APA beneficiaries, but
they are available only at the local level. We use an original dataset, made of the
individual records that we collected for the beneficiaries of a given District Council
(Conseil départemental ). To identify home care price elasticity, we exploit interindividual variations in producer prices. We first assume the producer prices to
be exogenous, and then relax this assumption to assess whether APA beneficiaries
endogenously select into a given producer. We control for disposable income
and other individual characteristics (disability levels, socio-demographic variables)
that affect the consumption of home care. As the volume of care recorded in the
administrative dataset is censored to the maximum number of subsidized hours,
we fit a censored regression model with individual-specific censoring points.
Our baseline results indicate a significant, negative price elasticity of -0.7. However, this estimator seems to be inflated by nonrandom producer selection. Given
this selection effect, the true price elasticity seems to be closer to -0.5. On average,
an increase of 10% of the hourly out-of-pocket payment is predicted to reduce the
(uncensored) care hours consumed by 5%, or 45 minutes per month for a beneficiary consuming the median monthly volume of 15.5 hours. Although precision is
low, our results point to a price elasticity lower than unity.
Our paper contributes to the literature by providing further evidence that
the consumption of home care services is price-sensitive. Positive out-of-pocket
payments can partly explain why many APA beneficiaries do not consume the
full amount of care hours for which they are entitled to a subsidy. Contrary to
most previous works on home care consumption, our empirical strategy allows to
quantify its price elasticity, whose magnitude turns out to be low. In that respect,
this makes home care services closer to acute care than to elective health care
services. We can expect that increases in the generosity of public subsidies, as the
ones planned by a 2016 French reform, would cause a small increase in home care
consumption, and above all a decrease in total out-of-pocket payments borne by
2
Drees, Enquête annuelle Aide sociale, 2013. The APA programme has also a component devoted to the
elderly living in nursing homes, but we focus here on the home care part of the scheme.
3
the disabled elderly.
The outline of the paper is as follows: Section 2 reviews the literature that
focused on the elasticity of the demand for medical services and domestic help.
Section 3 gives more details on the APA policy. Section 4 presents the original
administrative dataset that is used. Section 5 presents the theoretical model and
Section 6 the empirical strategy. Section 7 presents and discusses the estimation
results. Section 8 concludes with directions for extensions.
2
Related literature
Although home care services are, in many countries, not regarded as health
care services strictly speaking, our paper directly relates to the large empirical
literature that has investigated the question of the price sensitivity of health care
spending. Following the conceptual works that have put forward the notion of ex
post moral hazard in the context of insurance, many papers have attempted to
estimate the price elasticity of health care consumption3 . Following the seminal
RAND experiment, Manning et al. (1987) and Keeler & Rolph (1988) estimated
the price elasticity of total health care spending to be -0.2. Although this figure
must be taken with caution (Aron-Dine et al. 2013), subsequent works, making
use of ingenious instruments to exploit exogenous variation in copayments and
deductibles associated with individual health care plans, have found similar values
(Eichner 1998). More recent works have highlighted the heterogeneity of the price
sensitivity of health care consumption, which is lower at older ages and varies with
the types of medical services (Duarte 2012, Fukushima et al. 2015).
Home care provision being a more recent political and lesser budgetary concern, the literature on the price sensitivity of formal home care consumption is
not prolific. The economic literature on long-term care has focused on the relationship between informal and formal care, wondering if they should be regarded
as complementary or substitute goods for the elderly living the community. Some
papers have focused on the potential “crowding-out effect” of informal care by
privately- or publicly-funded formal care, (Christianson 1988, Ettner 1994, Pezzin
et al. 1996, Hoerger et al. 1996, Motel-Klingebiel et al. 2005, Stabile et al. 2006,
Byrne et al. 2009, Rapp et al. 2011, Fontaine 2012) while another strand has investigated the impact of informal care on professional care utilization (Greene 1983,
Kemper 1992, Lo Sasso & Johnson 2002, Van Houtven & Norton 2004, Bolin et al.
3
In the field of health care, ex post moral hazard is defined as the propensity to consume more medical care
in the presence of an insurance scheme relative to the situation of no insurance. It can thus be quantified by
measuring the price elasticity of the uncompensated or compensated demand for health care (Pauly (1968),
Nyman (1999); see Bardey et al. (2003) for a survey).
4
2008, Bonsang 2009, Holly et al. 2010). The other determinants of the demand for
formal care, such as its price, have been much less investigated. Using American
data (Coughlin et al. 1992, Ettner 1994), but also European datasets (de Meijer et al. 2009, Kalwij et al. 2009, Fontaine 2012), the existing contributions have
nonetheless highlighted several determinants of home care consumption, like sociodemographic characteristics (age, sex, marital status, children’s characteristics),
geographical variables (area of residence, local market constraints) and health and
disability measures. In addition, a few papers have made use of variables indicating whether the individual benefits from -or is eligible to- a public program
subsidizing formal home care. Using Medicaid and Medicare eligibility or actual
benefits (Coughlin et al. 1992, Ettner 1994, Pezzin et al. 1996), inter-regional
differences in home care subsidies in Canada (Stabile et al. 2006) or the fact of
receiving APA subsidies in France (Rapp et al. 2011, Fontaine 2012), they capture
the qualitative effect of receiving subsidies on home care consumption. Overall,
the results show a small but statistically significant positive effect of subsidies on
formal home care consumption. Individuals are then found to be sensitive to the
price they pay out-of-pocket on home care services4 .
However, these estimations do not allow a direct quantification the consumerprice elasticity and to evaluate precisely the effect of a change in consumer price
on consumption. This shortcoming is mainly explained by the lack of available
relevant data. Contrary to the health care sectors, in which claims addressed to
public or private health insurances contain information about the price charged
by practitioners, producer prices of home care services are seldom observed, because both price regulation and coverage by private insurance are low (Brown &
Finkelstein 2009). Moreover, in France as in many other countries, public programs financing home care services are decentralized at the local level. Such an
organization of public policies has two consequences. Firstly, there is no unified
information system that would provide an administrative national dataset. Secondly, the price that individuals have to pay out-of-pocket on their home care
consumption depends on local policies. As a consequence, it is extremely difficult
to obtain information on individuals’ real home care consumption and consumerprice.
As far as we know, only two studies provide a direct estimation of consumerprice elasticity for home care services. They both find a negative price elasticity
but with a somewhat different magnitude. Using the 2008 French Disability and
Health Survey on Households (Handicap Santé Ménages, or HSM) supplemented
4
Some recent papers, based on cross-countries comparisons, provide additional though indirect evidence,
by underlining the effects of long-term care institutional settings on home care utilization (Motel-Klingebiel
et al. 2005, Viitanen 2007, Holly et al. 2010, Bakx et al. 2015).
5
with another dataset on the implementation of local policies, Hege (2016) estimates the price elasticity of professional home care utilization computing an
expected value of consumer price of each individual. This expected value depends
both on the district in which the individual lives and her expected copayment
rate. Hege (2016) concludes to an average point estimate at -0.15, significantly
different from zero.
Given the lack of data, estimating the price elasticity at the national level
leads to use proxies or to make strong assumptions on the consumption and outof-pocket characteristics. Bourreau-Dubois et al. (2014) have chosen to work at
the local level in order to avoid these approximations, at the cost of reduced
external validity. Using administrative data on APA beneficiaries from a given
District Council, they can observe the real value of the out-of-pocket payment.
They find that a 10% increase in the price reduces the number of hours of care by
5.5%.
In this paper, we use a methodology similar to Bourreau-Dubois et al. (2014)5 .
Our data are obtained from another local district with different socio-demographic
characteristics. Thanks to the comparison of results, the robustness of the empirical strategy and the external validity of the conclusions will be discussed.
Compared to Bourreau-Dubois and coauthors’ study, we address explicitly the
concern that individuals may select into a given home care producer, which may
cause individual out-of-pocket price paid on home care to be endogenous.
3
Home care subsidies to the elderly in France
The APA program
The objective of the French APA program is to help financing the cost of
professional care services for the elderly persons who require assistance in the
activities of daily living (household chores, meal preparation, personal hygiene,
grocery shopping,...). This policy is defined at the national level and implemented
at the district level (Département).
There are three eligibility conditions to the APA program. First, as the policy
is targeted to the elderly, an individual must be at least 60 years-old to be eligible.
Secondly, the individual must have been living in France for at least three months.
Finally, the individual must have been assessed as disabled. This last condition
5
Our paper can be seen as a companion work to both Hege (2016) and Bourreau-Dubois et al. (2014) as
these authors and we are part of a same research team. The “MODAPA” research project aims at studying
the determinants of long-term care utilization in France, and especially the effect of out-of-pocket payments
on professional home care utilization, by the means of different empirical strategies. More information on the
project can be found at: www.modapa.cnrs.fr.
6
requires a specific evaluation from a team managed by the District Council, that
we will call here the evaluation team, which is composed of medical professionals
(nurses, doctors) and/or social workers. The evaluation team visits each APA
applicant in order to evaluate her needs in terms of assistance in the activities
of daily living. To do so, they use a scale established at the national level, the
“AGGIR” scale (Autonomie Gérontologie Groupe Iso-Ressources), which allows
an assessment of the individual’s degree of autonomy with seventeen measures of
physical and cognitive capacities together with measures of abilities to perform the
basic activities of daily living (corresponding to some Activities of Daily Living, or
ADL, and Instrumental Activities of Daily Living, or IADL). This scale enables
the evaluation team to define the disability group of the individual (“GIR”, or
Groupe Iso-Ressources): six disability groups exist, going from the group of nondisabled individuals (GIR 6) to the group of extremely disabled individuals (GIR
1). Only individuals who are found to be moderately to extremely disabled (GIR
4 to GIR 1) are eligible to APA6 .
For eligible individuals, the team establishes a “personalized care plan”: this
document lists the activities for which the individual needs some assistance and
computes the hours necessary to their realization. This gives the maximum number of hours that are eligible to APA subsidies, which is called the care plan
volume. The monetary valuation of the care plan volume must not exceed a given
legal ceiling which depends on the individual’s disability group. For instance, in
October 2014, the expenses associated with the care plan volume for an individual
in disability group GIR 1 can not exceed 1,313e per month, whereas it can not
exceed 563e per month for individuals in GIR 47 .
Up to the care plan volume, the consumer price of each hour of care is reduced
by the APA scheme, which works as an hourly subsidy. For hours beyond the care
plan volume, there is no more subsidy from the District Council: the consumer
bears the full price of home care services.
Computation rules of APA out-of-pocket payments
Up to the care plan volume, for each hour consumed, the APA beneficiary is
charged an hourly out-of-pocket payment which depends on the producer price
and a copayment rate increasing with her disposable income. The scheme of the
copayment rate is as follows. For individuals with low income (below 739e in
6
Compared to the more classical scales built with information on the restrictions in ADL and IADL,
such as Katz or Lawton scales, AGGIR scale does not include all conventional ADL and IADL, but uses
additional cognitive and physical disability criteria. It is also a more complex tool as it works as an algorithm.
More information on AGGIR scale can be found on the official website of French public administration:
https://www.service-public.fr/particuliers/vosdroits/F1229.
7
These amounts must be related to the average pension benefit, which was of 1,419e in 2012 (Solard 2015).
7
December 20148 ), the copayment rate is zero: the APA beneficiary has no outof-pocket payments if she consumes no more than the care plan volume. For the
individuals with high income (higher than 2,945e), the copayment rate is set at
90%. For individuals with income between these two thresholds, the copayment
rate is an increasing linear function of disposable income.
The copayment rate is usually applied to the producer price to obtain the
hourly out-of-pocket payment. An individual whose copayment rate is equal to
0.5 and who receives an home care hour priced at 22e would pay 11e. In that
case, out-of-pocket payment depends directly and linearly on both the individual
disposable income and the producer price.
More precisely, this computation rule is applied by most District councils when
the producer chosen by the beneficiary is a regulated structure (service autorisé),
whose price is generally directly administrated by the District Council. If the producer chosen by the individual is not regulated (unregulated home care structure
or over-the-counter worker), the copayment rate is applied to a lump-sum price,
which does not depend on the producer price. This difference in the computation
of the consumer’s participation has important implications on what can be known
of APA beneficiaries’ out-of-pocket payments: we are going to focus only on APA
beneficiaries that are served by a regulated home care structure.
4
Data
Administrative data from a District Council
In order to quantify the price elasticity of the demand for home care services,
we need precise information on out-of-pocket payments and home care consumption. As of today, in France, there is no national survey providing directly the
out-of-pocket payments borne by the disabled elderly. The 2008 French Disability and Health Survey on Households only indicates whether participants benefit
from the APA policy. Given that the APA programme is implemented at the district level, there is no centralized administrative dataset that provides individual
information on producer prices, copayment rate and participation computation
rules. The central administration only releases aggregate information on APA
recipients (distribution of disability levels, average cost of personalized care plans,
average monthly payment made by District Councils, etc.) that are not sufficient
to compute individual out-of-pocket payments. Thus, the only way to quantify
8
This threshold depends on the value of a national disability allowance (Majoration pour Tierce-Personne),
which is re-evaluated in April each year to take into account the inflation rate.
8
the effect of out-of-pocket payments on home care consumption is to collect and
use the administrative files on the APA recipients of a given district.
We choose to collect data from a District council in which computation rules
of out-of-pocket payments (see Section 3) are similar to the rules applied in the
majority of French districts: when home care is provided by a regulated service,
the actual producer price is used to compute the out-of-pocket payment, while
a lump-sum price is used when the producer is not regulated. In this district,
in 2013, the majority (81%) of APA beneficiaries receive domestic help through
regulated structures. 17% are employing over-the-counter workers and 6% receive
services from unregulated structures9 .
We also paid attention to selecting a District council whose demographic characteristics are close to the average national ones. In this district, in 2013, the
population aged 60 years and older represented almost 1/4 of the total district
population, which is equivalent to the national rate10 . The population living in
the community and benefiting from the APA program represents around 5% of
the elderly aged 60 and older in the district, while this share is a little lower at
the national level (4.6%). This proportion increases to more than 11% for the
elderly beyond age 80 at the district level, while only 9.3% of the overall French
population living in the community and aged 80 or more receives APA11 .
However, in terms of income, the district indicators are slightly higher than
national averages: in 2012, almost 70% of households are subject to the income
tax, whereas it is the case for 64% of households nationwide. The poverty rate is
lower in this district, both on average (less than 10%, for a 15% rate at the national
level) and for each age group (among the population aged 75 and older, the poverty
rate is 8% in the district whereas the national rate is 10%)12 . As the copayment
rate on home care expenditures depends on income, APA beneficiaries of this
district are then more likely to support non-negligible out-of-pocket payments.
The individual data were collected for every month for the years 2012 to 2014.
Given that infra-yearly variation in out-of-pocket prices is very low, we picked up
a single month for each of the three years. We retained the month of October,
when home care consumption is less likely to be affected by temporary shocks on
households (like holidays and visits from children). Given that our identification
strategy will draw on cross-sectional variations, results obtained on October 2014
are presented as the baseline results; the Appendices provide the results obtained
on the other years (and on the pooled sample) as robustness checks.
9
The total slightly exceeds 100%, since a small share of APA recipients are provided subsidized home care
by different producers.
10
Insee, estimations de population, 2012
11
Drees, Enquête annuelle “aide sociale”, 2013
12
Insee-DGFiP-Cnaf-Cnav-Ccmsa, Fichier localisé social et fiscal, 2012
9
Sample selection
Due to the difference in computation rules according to producer status, our
District Council has direct information on out-of-pocket payments of APA beneficiaries only for those buying services from a regulated structure. Beneficiaries
that receive home care exclusively from over-the-counter employees (15% of the
initial sample) and non-regulated services (5% of the initial sample) are thus not
retained in the sample we use to estimate the price elasticity of home care demand.
We also drop the individuals that receive home care from more than one producer: adding as control a dummy indicating whether the individual receives home
care from another producer would not adequately take into account the simultaneity of consumption decisions and would be likely to bias our estimators. As a last
step, we keep only beneficiaries whose copayment rate is strictly greater than zero
and strictly smaller than 90%. As explained in Section
Table A.1 in Appendix A.1 provides a summary of the different selection steps,
while Table A.2 (same Appendix) assesses the selection on observable characteristics into a regulated producer using a Probit model. We end up with a sample
of 2,862 individuals.
Figure 1: Sample selection on copayment rate: APA schedule in 2014.
10
Descriptive statistics
Table 1: Descriptive statistics - October 2014
Variable
Care plan volume [a]
Care plan monetary value [b]
Hours effectively subsidized [c]
Underconsumption of care plan volume
Amount of effective subsidies [d]
Ratio [c]/[a]
Ratio [d]/[b]
Individualized income
Copayment rate
Producer price
Hourly out-of-pocket price
Total out-of-pocket payments
on subsidized hours
Age
Men
Disability level 1 (most severe)
Disability level 2
Disability level 3
Disability level 4 (least severe)
Living with a spouse
Living alone
Spouse in institution
Number of individuals
Number of households
Note: “pp.” stands for percentage points.
Average
20.6
455.5e
17.7
59.8%
300.7e
85.6%
67.4%
1,314e
23.7%
22.2e
5.2e
91.3e
84.2
26.0%
1.2%
12.5%
19.6%
66.7%
100%
33.8%
66.6%
0.6%
100%
Standard-dev.
10.7
238.3e
10.9
49.0 pp.
201.4e
20.3%
23.8%
422e
17.3%
1.6e
3.8e
98.6e
7.5
43.9 pp.
2,862
2,785
Table 1 presents the descriptive statistics of the sample that will be used for the
estimation. The socio-demographic composition can be compared with national
data on APA recipients. The composition of the sample is similar to the national
one regarding sex: it counts 74.0% of women while it is 73% at the national
level (Borderies & Trespeux 2015). Strongly disabled individual are slightly less
represented: respectively 1.2% and 12.5% of the sample are GIR1 and GIR2, the
least two severe disability levels, whereas these rates are respectively 2% and 17%
at the national level. The average copayment rate on APA is slightly higher than
the national one (23.7%, against 20% at the national level), reflecting the fact
that individuals in our district tend to be richer than the national average. The
average income displayed in the table takes is the “individualized income”. For
individuals that have a spouse alive, it is equal to the household income divided
11
by a factor of economies of scale of 1.713 . The large majority (almost 2/3) of the
individuals in our sample lives alone, which is consistent with the high proportion
of women and the average age of 84 years: given that the life-expectancy of men
is shorter than the one of women, many disabled elderly are widowed women.
Very few individuals have their spouse living in an institution (nursing home or
specialized hospital unit), while 18.6% of those who live with a spouse have a
partner who is also receiving APA.
The average personalized care plan volume is 20.6 hours per month, with a monetary equivalent of 456e: this is slightly less than the national average amount,
of 489e in 2011 (Drees 2012). On average 17.7 subsidized hours are effectively
consumed by the individuals in our sample. 59.8% of APA beneficiaries do not
consume the maximum number of hours for which they are entitled to a subsidy;
out-of-pocket price sensitivity of the disabled elderly is a natural candidate to
explain part of this high figure.
5
Theoretical model
Let us write the marshallian (uncompensated) demand for home care services
under the general form:
h∗i = g(CPi , Iˆi ; Xi )
(1)
With:
h∗i effective hours of home care services consumed by individual i;
g(.) demand function for home care services;
CPi individual’s i consumer price for one hour of home care services;
Iˆi the individual total disposable income available for consumption;
Xi a set of individual socio-demographic characteristics.
In the case there are no public subsidies, the consumer price is equal to the
price charged by the producer of home care services and the income corresponds
directly to the disposable income of the individual: CPi = pi and Iˆi = Ii , where
pi is the market price charged by the producer chosen by individual i for one hour
of home care service, and Ii is individual i’s (monetary) disposable income.
With APA policy, the beneficiary receives an hourly subsidy, which reduces the
amount she has to pay out-of-pocket: the consumer price is now equal to home care
market price times a copayment rate, which depends on her individual disposable
income Ii . Denoting ci the copayment rate of individual i, we have: ci = ci (Ii ),
and thus: CPi = ci (Ii )pi . But this is true only up to the care plan volume, i.e
the maximum number of hours that are eligible to APA subsidies that is defined
13
It is the individualized income that is used by the District Council to compute the copayment rate.
12
in the personalized care plan (see Section 3). For hours consumed beyond that
threshold, the consumer price goes back to the full producer price; but note that
the total disposable income available to consumption now integrates subsidies on
the first h̄i hours consumed.
Figure 2: Demand for home care services with APA: a kinked-budget constraint
ܻ
݄‫ כ‬is observed
‫ ܫ‬൅ ሺͳ െ ܿሻ‫݄݌‬ത
‫ܫ‬
݄‫ כ‬is censored
െܿ‫݌‬
െ
ܿ‫݌‬
Budget set
െ‫݌‬
‫ܫ‬
൅ ሺͳ െ ܿሻ݄ത
‫݌‬
݄ത
IȀሺܿ‫݌‬ሻ
݄‫כ‬
Let us denote h̄i the care plan volume of individual i; with APA, the budget
constraint can be written as:
(
Ii = ci pi h∗i + Yi
Ii = ci pi h̄i + pi (h∗i − h̄i ) + Yi
if h∗i ≤ h̄i
⇐⇒ Ii + (1 − ci )pi h̄i = pi h∗i + Yi if h∗i > h̄i
where Y denotes the composite good, whose price is set to 1. In other words,
the APA programme creates a kink in the budget constraint of the beneficiary,
as illustrated by Figure 2. Denoting I˜i = Ii + (1 − ci )pi h̄i the virtual income of
individual i (Moffitt 1986, 1990), we can rewrite the demand function specified in
Equation (1) as follows:

∗

 hi = g(ci .pi , Ii ; Xi )
h∗i = h̄i

 ∗
hi = g(pi , I˜i ; Xi )
if h∗i < h̄i
if h∗i = h̄i ,
with g(pi , I˜i ; Xi ) < h̄i < g(ci pi , Ii ; Xi )
if h∗i > h̄i
13
The objective of the paper is thus to get an empirical estimate of the following
quantity, which is simply the point price elasticity (at the sample average):
˜ X)
dg(CP, I;
CP
˜ X)
dCP
g(CP, I;
6
Empirical strategy
Econometric specification
As explained in Section 4, our data come from administrative sources: they
are produced by a given District Council, in charge of subsidizing home care for
the elderly eligible to APA. For each APA recipient of the district, the dataset
contains the number of home care hours that are charged by the producer to
the District Council or, equivalently, the consumption of subsidized hours of home
care. However, we do not observe directly the total volume of home care consumed
by each APA beneficiary, who are free to consume home care beyond h̄i .
Let us denote hi the number of hours of service billed to the District Council
for beneficiary i. Only effectively-consumed hours can be billed and this within
the limit of the care plan volume. Thus, hi ≤ h∗i and hi ≤ h̄i . This implies that
our measure of effective home care consumption is possibly right-censored. If the
individual consumes less than the care plan volume, the consumption registered
by the District Council is equal to her effective consumption (hi = h∗i if h∗i < h̄i ):
in such a case, there is no censoring issue. But if the individual consumes more
than the care plan volume, the consumption registered by the District Council
will systematically be equal to her individual ceiling (hi = h̄i if h∗i ≥ h̄i ).
Consequently, when hi = h̄i is observed, we either have h∗i = h̄i (when no
censoring) or h∗i > h̄i (right-censored consumption, as shown by Figure 2). Thus,
the observed consumption of home care is the following:
(
hi = g(ci .pi , Ii ; Xi ) if
hi = h̄i
g(ci pi , Ii ; Xi ) < h̄i
if g(ci pi , Ii ; Xi ) ≥ h̄i
(2)
System (2) makes clear that the estimation of the parameters of the demand
function g(.) will need to rely on information relating to the first segment of the
budget constraint. Given that the distribution of home care consumption is highly
skewed, we assume a log-linear specification of g(ci pi , Ii ; Xi ), which is standard in
14
the literature on health care expenditures:
ln(h∗i ) = β0 + β1 .ln(CPi ) + β2 .ln(Ii ) + Xi0 .θ + i
(3)
β1 represents the consumer price elasticity and β2 represents the incomeelasticity of the uncompensated demand for home care service.
On the observable segment of the budget constraint, the consumer price equals
the out-of-pocket price after the subdisidy: ci pi . In the data, the observed value of
the disposable income is not the current value of income, but the value of income
when the copayment rate was computed or last revised, denoted IiD . We can
express current disposable income as: Ii = IiD .γiD , with γiD the rate of increase of
individual disposable income since i’s first personalized plan was set. As the rate
of increase in disposable income γiD is not directly observable, we write:
ln(h∗i ) = β0 + β1 .ln(CPi ) + β2 .ln(IiD ) +
2014
X
λd 1di + Xi0 .θ + i
(4)
d=2009
where 1di is a dummy equal to one when i’s copayment rate was last revised
in year d (1d , d = 2009, ..., 2014) and coefficients λd should capture the rate of
increase in income14 since year d.
Together with the observational scheme summed up by System (2), Equation
(4) corresponds to a Type-1 Tobit model. Estimation of parameters β and θ
can be done by Maximum Likelihood15 , after making the following parametric
assumption:
|
pi , I D , X, 1 ∼ N (0, σ 2 ).
(5)
We are then able to estimate the parameters of interests16 .
Identification
As explained earlier, the copayment rate ci depends linearly on disposable
income. Thus, variation in the consumer price, CP , may come either from a
variation in the producer price p or from a variation in the disposable income,
14
We implicitly assume that the rates of increase in disposable income are identical for two individuals whose
personalized plans were decided upon the same year d. Retirees’ income is mostly made of pension benefits,
which are reevaluated every year following the inflation rate. See for example Deloffre (2009) who documents
that in 2007, pension benefits amounted to 87% of gross income in households with at least one retired
individual, living alone or with a partner. Nonetheless, we make a strong assumption given the heterogeneity
in income composition according to income level and the higher increase in financial and housing income
relative to pension income in the past decade.
15
The likelihood function is provided in Appendix A.3.
16
We actually estimate an equivalent but more refined equation that is less sensitive to measurement errors
than Equation (3). For the sake of simplicity, we do not present this equation here. See Appendix A.2 for
details.
15
I D . Given that our specification directly includes disposable income I D as a
control, any variation in the consumer price (all other things – including income
– being equal) arises because of a variation in the producer price. In other words,
the consumer-price elasticity of demand (coefficient β1 ) is identified by the crosssectional variation in producer prices 17 .
In the district, in 2014, we have 28 different producers. Some producers happening to be priced by at the same level, we end up with 23 different prices. The
minimum price is set to 19.7e and the maximum to 23.5e, for an average value
22.2e and a standard-deviation of 1.3e.
For our estimation to give unbiased coefficients, the producer price for an individual i must not be correlated with the unobserved factors, i , that affect home
care consumption. Price endogeneity, however, may arise for different reasons
(Zhen et al. 2013). First, supply-demand simultaneity may bias the estimation of
demand parameters if supply determinants are not properly (jointly) taken into
account. Zhen et al. (2013) argue that this is not likely to be a major issue in
micro data. Supply-demand simultaneity could nonetheless be a concern with our
data as APA beneficiaries in our sample may represent a high proportion of the
customers of the home care services whose prices are used for identification here.
Second, price exogeneity may be undermined by omitted variable biases. Think
about the classical trade-off between quality and quantity: with a given disability level and budget constraint, one individual may prefer to consume a smaller
volume of home care but resorting to a more expensive, possibly better quality,
service. On the contrary, an individual who expects or plans to buy a high volume of care may choose on purpose a relatively cheap producer, inducing some
reverse causality in the relationship between out-of-pocket payment and consumption we are interested in. More generally, unobserved health and disability state,
unobserved informal care provision and heterogeneity in individual preferences
may induce non-random selection into home care producers, which would make
between-producer variations improper to use for price elasticity identification.
There are reasons to consider that the price endogeneity caused by supplydemand simultaneity must be negligible when studying APA beneficiaries’ demand
for home care services. As explained in Section 3, the market for home care services
provided to the disabled elderly is regulated by local authorities: the producer
price cannot be seen as an equilibrium value jointly determined with equalization
of supply and demand. First, for each regulated producer, the price is set each
year considering the average production cost of two years earlier. The current
producer price depends on the current average cost only insofar as current and
17
See Appendix A.2 for a formal proof and more details.
16
past average costs are correlated. Second, and more essentially, the computation
of the average cost by the District Council is not done following an economic
approach. Indeed, the pricing does not only take into account the average cost of
production, but also administrative and political considerations (Gramain & Xing
2012).
Concerns about endogenous producer selection are more difficult to dismiss a
priori. They will be further argued in the following section.
7
Results
Baseline results
As we estimate a censored regression model, the coefficients displayed in the
results tables give the predicted impact of a marginal (or 0/1) change in a given
explaining variable on the total, uncensored home care consumption. The predicted impact is thus the sum of the impact on the volume of care subsidized by
the District Council and of the effect on the volume of care consumed beyond the
care plan volume (with individuals paying the full hourly price of care).
Table 2 presents our baseline results, obtained running our estimation on
the data from October 2014. Specifications (1) and (2) do not include sociodemographic controls, while Specifications (3) and (4) do. Standard errors in
Specifications (1) to (3) are clustered at the household level, while they are clustered at the producer level in Specification (4).
With no controls whatsoever, a 1% increase in the consumer price is associated with a very small increase of -0.05% in the hours of home care consumed.
Comparison of Specifications (1) and (2) shows that there is a negative correlation between income and producer prices. The estimated coefficient increases (in
absolute value) to -0.707 when we add disposable income and socio-demographic
controls. The price elasticity coefficient is significantly negative in Specifications
(3) and (4), suggesting that the disabled elderly are indeed sensitive to the consumer price of home care services. It means that a 10% increase in the hourly
consumer price would increase consumption by about 7%, or 65 minutes a month
for an APA beneficiary consuming the median consumption of home care of 15.5
hours a month.
Turning to the effects of control variables, specifications (3) and (4) show that
an increase of 10% in disposable income (or about 60 e more per month) is
predicted to increase home care consumption less than proportionnally, by 6.6%.
Note that any marginal increase in disposable income entails two effects: (i) a true
income effect, through which the increase in the individual’s budget set would
17
Table 2: Consumer price elasticity estimation - baseline (2014)
Consumer price (log)
Dependent variable: hours consumed (log)
(1)
(2)
(3)
(4)
-0.050∗∗
-0.254
-0.697∗∗∗
-0.697∗∗
(0.019)
(0.310)
(0.256)
(0.291)
0.649∗∗
(0.255)
0.649∗∗
(0.292)
-0.265∗∗∗
(0.069)
-0.070∗
(0.039)
Ref.
-0.265∗∗∗
(0.078)
-0.070∗∗
(0.031)
Ref.
Age: 90 or older
0.072∗
(0.040)
0.072∗∗
(0.032)
Woman
0.065∗
(0.036)
0.065∗∗
(0.026)
Living with no spouse
0.317∗∗∗
(0.034)
0.031
(0.083)
0.570∗∗∗
(0.216)
Ref.
0.317∗∗∗
(0.032)
0.031
(0.059)
0.570∗∗∗
(0.127)
Ref.
1.253∗∗∗
(0.134)
0.956∗∗∗
(0.050)
0.523∗∗∗
(0.039)
Ref.
1.253∗∗∗
(0.141)
0.956∗∗∗
(0.049)
0.523∗∗∗
(0.024)
Ref.
4.761∗∗∗
(0.820)
0.725∗∗∗
(0.016)
Yes
Yes
2862
40.2%
2785
4.761∗∗∗
(0.898)
0.725∗∗∗
(0.015)
Yes
Yes
2862
40.2%
27
Disposable income (log)
0.206
(0.309)
Age: 60-69
Age: 70-79
Age: 80-89
Spouse receives APA
Spouse in institution
Living with non-APA spouse
Disability group: 1
Disability group: 2
Disability group: 3
Disability group: 4
Constant
Sigma
Dummies for year of MTP
Dummies for latest plan
Observations
Censored observations
Number of clusters
3.046∗∗∗
(0.031)
0.871∗∗∗
(0.016)
No
No
2862
40.2%
2785
3.911∗∗∗
(0.984)
0.870∗∗∗
(0.016)
Yes
No
2862
40.2%
2785
AIC
5946.576 5951.604 5355.254 5355.254
BIC
5964.454 5993.319 5468.480 5468.480
Standard errors in parentheses; ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Clustering of standard errors is done at the household level in
specifications (1) to (3) and at the producer level in specification (4).
18
make the consumption of all normal goods increase, and (ii) an offsetting price
effect, due to the fact that an increase in income will induce APA copayment rate
to rise, increasing therefore the out-of-pocket payment borne on each subsidized
hour consumed. The presented coefficient captures the effect of an increase in
income when the copayment rate is fixed (only effect (i) is playing), which is likely
in the short-run. Given that we find a negative price elasticity, the estimated
coefficient of 0.66 provides a lower bound for the overall income effect on demand
for home care services.
As expected, disability level is found to have a very significant effect: the
heavier the disability level (as recorded by its administrative measure), the higher
the predicted consumption, all other factors being equal. Even when controlling
for disability level, age still has a significant effect on the consumption on home
care services. In particular, the youngest APA beneficiaries (between 60 and 69
years old) are predicted to consume substantially less home care on average than
the other recipients. This echoes de Meijer et al. (2011) who have studied the
determinants of long-term care spending using Dutch data; they found that, once
disability and chronic conditions were taken into account, age retains a significant
though small positive effect on home care expenditures (at the intensive margin).
To deepen the analysis on the disability effect, we estimated the model on three
sub-samples corresponding respectively to individuals of disability levels 1 or 2,
disability level 3 and disability level 4 (Table A.3, Appendix A.4). APA beneficiaries of disability group 4 (the least severely disabled) appear to be the more
sensitive to price. Conversely, most severely disabled individuals (disability groups
1 and 2) seem much less sensitive to out-of-pocket price in their consumption of
home care. This finding is consistent with previous works showing that poorer
health status is associated with a lower price elasticity (Fukushima et al. 2015),
receiving medical services being more discretionary for the relatively-more healthy
patient. The precision on the subsample of more disabled individuals is however
very low. This is both because the sample is small and the rate of censored observations is higher than in the other subsamples (44% vers 39%). Lower precision
in one subsample could also have arisen if some home care services were “specializing” into most or least severely disabled individuals, but this does not appear
to be the case as the variation in producer prices is similar in the 3 subsamples.
Being a woman, rather than a man, increases the consumption of professional
home care by a small but statistically significant amount. Compared to having a
co-residing spouse not receiving APA, having a co-residing spouse receiving APA
does not affect own home care consumption (but only 6% of our sample has an
APA recipient spouse). On the contrary, having a spouse in institution increases
19
significantly the amount of professional assistance received; this effect does not
depend on sex (as was tested with an interacted term, not included in the baseline
regression). Finally, having no spouse alive is associated with a higher professional
home care consumption. Overall, the results on the effects of household structure
are consistent with the literature on home care utilization, which has shown the
importance of co-residing spouse in providing informal care that partly substitutes
for formal home care services. Finally, the dummies signaling the year when the
most recent personalized care plan was established by the evaluation team of the
District Council are jointly significant (at the 5% level), but their interpretation is
hard to make. Even an alternative specification using the time elapsed since the
latest care plan was set does not show support for the assumption that the more
time since the most recent evaluation and the further away the actual disability
relative to the “official” disability level.
Going back to our main coefficient of interest, we observe by comparing Specifications (3) and (4) of Table 2 that the price elasticity is significant at the 1%
level when clustering at the household level, but only at the 5% level when we
cluster at the producer level. As some producers are priced at the same level, we
could have clustered at the price level. It would mean we expect some correlation
in the error term of observations with same price but different producers. We
assume such correlation to be negligible relative to intra-producer correlation of
errors. Thus, we cluster at the producer level18 .
Table A.5 in Appendix A.4 give the results of the same estimation using data
from October 2012 and October 2013, as well as the results obtained pooling
observations from 2012, 2013 and 2014. Results for 2013 are very similar, while
results obtained on 2012 data give a point estimate for the price elasticity of 1.0%. However, given the low precision of our estimators, we cannot reject the
assumption that the price elasticity was the same for the three years.
Dealing with the selection into a producer
As explained in Section 6, our cross-sectional identification strategy relies on
the assumption that individuals do not select into a given producer based on unobserved factors affecting home care consumption. How credible is this assumption?
Officially, APA legislation states that APA recipients are free to choose the
producer they want to receive their subsidized home care hours from. When the
evaluation team elaborates the personalized care plan, the team should communicate a list of the regulated producers operating in the area. This list should
18
Standard error of the price elasticity estimator goes from 0.287 when we cluster at the producer level to
0.291 when clustering at the price level. The coefficient remains statistically significant at the 5% level.
20
include both public and non-profit home care providers (CCAS, CIAS and Associations d’aide à la personne) together with for-profit providers. Selection into
for-profit providers is likely to be nonrandom: for-profit providers are likely to
target specific customers segments (either quite rich APA recipients with high
quality expectations or, on the contrary, financially-constrained beneficiaries who
look for relatively cheap services). However, for-profit producers still represent
a small share of regulated home care providers in France. In the district we got
our data from, there are only 3 for-profit services, providing home care to 3.4%
of our sample. Thus, the potential endogenous selection into these producers is
likely to have negligible impact on our estimators. Regarding non-profit home
care providers (5 such structures operating in the district, which provide care to
exactly 50% of our sample), it would be naive to assume they have no commercial
strategies whatsoever. The selection is all the more likely that we know from
ethnographic field observations that, in some District Councils, the evaluation
teams greatly influences the choice of a given producer (Billaud et al. 2012). The
evaluation team probably allocate APA beneficiaries into a given producer rather
than another taking into account health conditions and potential recipient’s own
and family desires, which are not recorded in our data.
Overall, it is hard to assume a priori that there is no endogenous selection into
home care services. Therefore, we need to assess whether our results are empirically robust to such selection. For this purpose, we decompose our sample into two
sub-populations: on the one side, the individuals that live in a municipality where
a single producer is found to operate; on the other hand, the individuals living in a
municipality where two or more regulated producers have customers. The idea is
that selection into a producer should be negligible in the first sub-sample, while it
may arise in the second sub-sample. We thus estimate our identification equation
on the two sub-populations. Table 3 presents the results of these estimations,
reporting in addition the price elasticity estimator found on the entire sample
(column (1), same as column (3) of Table 219 ). When we restrict our sample to
individuals have no producer choice, the point estimate of the price elasticity is
reduced to -0.445. Given the smaller sample size and reduced identifying variation
in prices, precision is much lower compared to the baseline regression. Thus, we
cannot formally reject that the the price elasticity is zero at conventional statistical significance levels. The point estimate of the price elasticity is higher when we
run the estimation on the sub-population of individuals who can choose between
different providers. Despite the low precision, the estimator is significantly differ19
The difference with Table 2 is that we cluster here at the producer price level rather than at the producer
level. It makes it possible to take into account the fact that the construction of the two subsamples artificially
increases the empirical variance in prices and thus the precision of our estimates.
21
ent from zero at the 1% level, with a point value of -1.097. This figure captures
two effects: first, the price elasticity we are interested in; second, a selection effect
that we may interpret as a form of price-sensitivity: as the selection effect induces
an inflating effect, it means that, on average, individuals choosing relatively cheap
services consume more hours.
Table 3: Testing for selection into a producer - October 2014
Dependent variable: hours consumed (log)
(1)
(2)
(3)
Consumer price (log)
-0.697∗∗
-0.445
-1.097∗∗
(standard error)
(0.295)
(0.472)
(0.432)
p-value
0.016
0.345
0.010
Socio-demographic controls
Yes
Yes
Yes
Dummies for year of MTP
Yes
Yes
Yes
Dummies for latest plan
Yes
Yes
Yes
Sample
All
Single
Multiple
producer producers
Observations
2862
1142
1720
Censored observations
40.2%
42.6%
37.4%
Number of clusters
23
14
21
Standard errors in parentheses, clustered at the producer price level.
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Table A.5 in Appendix A.4 shows that results obtained on years 2012 and
2013 are similar: the point estimates obtained on the restricted sample of APA
beneficiaries who have different producers providing care in their municipality
of residence (columns (1), (2) and (3)) are systematically higher (in absolute
value) than those obtained on the sample of individuals with no apparent producer
choice. A unit price elasticity seems clearly to be a upper bound, while the low
precision does not make it possible to reject formally that APA recipients’ demand
is insensitive to the consumer price they pay on home care services.
Discussion of results
Given our limited sample sizes and the limited variation in producer prices,
our identification strategy does not allow us to end up with a precise estimate of
the price elasticity of demand for home care of APA recipients. Still, we are able
to draw some interesting conclusions that shed a new light on the disabled elderly
behaviour in terms of demand for home care services.
First, in line with the results obtained by previous literature (Coughlin et al.
1992, Ettner 1994, Fontaine 2012), our results suggest that the disabled elderly are
indeed sensitive to their hourly out-of-pocket payment when choosing their level
of home care consumption. Thus, home care consumption of the disabled elderly
can not be fully understood using the socio-medical notion of “needs” captured by
22
the personalized care plan. Despite the prescriptive nature of the care plan (and
its potential nudging effect), actual home care consumption seems to be influenced
by a trade-off between the out-of-pocket cost of an extra hour and its marginal
value.
Our results also provide evidence that the price-sensitivity of the demand for
domestic help is seemingly lower than unity. This result is in line with what has
been found by the companion works of Bourreau-Dubois et al. (2014) and Hege
(2016), which estimated the average price elasticity of demand to be respectively 0.5 and -0.15. Then, home care services can be regarded as necessary goods, in the
sense that any increase in price will not be fully compensated by the decrease in
consumption. It goes against the idea according to which, for some beneficiaries,
the APA scheme subsidizes mainly comfort services. To compare these values
with parameter estimated by the literature on the demand for medical services,
it is better to retrieve the price elasticity of home care expenditures 20 . As our
estimations suggest that the price elasticity of the demand for home care is lower
than -0.5, we can infer that the price elasticity of home care expenditures will
be positive: an increase in the unit out-of-pocket payment of formal care will
lead to a less than proportional decrease in consumption, and thus to an increase
in expenditures21 . Manning et al. (1987), Keeler & Rolph (1988) found a price
elasticity of overall medical care spending of -0.2; although its magnitude is subject
to discussion (Aron-Dine et al. 2013), its negative sign was found to be robust.
Subsequent works have found values in the same line (Eichner 1998, Fukushima
et al. 2015). Some recent studies have provided evidence that price elasticity
varies with the type of care considered: Duarte (2012) find acute care services
to have a zero price elasticity of expenditures, and Fukushima et al. (2015), in a
study on the medical spending of the elderly, similarly find elective care to have
a high price sensitivity while generic drugs consumption reacts little to price.
Our paper provides interesting evidence that, at the intensive margin, home care
consumption is closer to acute care in terms of price-sensitivity than to elective
care.
One limitation of our cross-sectional identification strategy is that the consistency of our estimates relies on the classical assumption that there is no omitted
20
A unit price elasticity of demand corresponds to a price elasticity for expenditures equal to zero (since
the variation in consumption exactly offsets the variation in the unit price), and an inelastic demand implies
a price elasticity of expenditures of exactly +1 (any price increase inflates proportionally expenditures on the
good).
21
This holds both for out-of-pocket expenditures and for total expenditures when the individual consumes
no more than the hours prescribed in her personalized care plan. Things get somewhat trickier for individuals
consuming unsubsidized hours, given the nonlinear budget constraint of individuals, but unless the income
elasticity of home care demand is very high, we should also observe an increase in out-of-pocket and total
expenditures.
23
variable bias. Given the administrative nature of our data, the information we
have on the health status and on family characteristics is poor. This is a serious
limitation given that the economic literature has provided empirical evidence that
informal care and formal care tend to substitute to one another: in particular,
receiving more informal care from relatives was found to decrease formal care use
by the disabled elderly, both at the extensive and intensive margins (Van Houtven
& Norton 2004, Bonsang 2009). For example, individuals with no spouse alive are
more prone to receiving informal care from their children (Fontaine et al. 2007).
Then, omitting information on informal care provision may bias the estimates of
our entire set of coefficients. As a robustness check, we include as control whether
the individual receives formal home care during the week-end and public holidays22 . For a given level of disability, individuals that do not receive care over the
weekend are more likely to receive assistance from their relatives. As shown in
Table A.5, in Appendix A.4, the fact of receiving home care during the weekend is
associated with more hours consumed during the labor days of the week. But controlling for home care utilization during the weekend does not affect significantly
the estimate of the price-elasticity23 .
Regarding our out-of-pocket price measure, we have not taken into account
tax reductions on home care services. In France, expenditures on home care of a
given year can be reduced by income tax reductions granted the following year.
We do not observe the tax reductions which the individuals in our sample may be
benefit from. Using the reported income and information about family structure,
we could attempt to simulate individual tax reductions on home care spending and
thus reconstruct a “net” out-of-pocket payments. However, this would necessarily
lead to measurement errors, as the income used to compute APA is not exactly
the taxable income. Our estimations rely on the implicit assumption that APA
beneficiaries are sensitive to the “spot” or ex ante price (Geoffard 2000).
Furthermore, our estimation strategy implicitly assumes that the individualspecific censoring point is uncorrelated with the unobserved determinants of professional home care consumption. Some recent developments semiparametric estimation methods may allow us to relax the assumption that the individual censoring point is uncorrelated with unobserved factors.
Some refinements of the analysis could be conducted using the same data and
22
In our estimations, the dependent variable is the number of hours consumed between Monday and Saturday,
except for holy days. But APA beneficiaries may also receive a subsidy for a few hours of care to be received
during weekends and holy days, which are set separately in the personalized care plan. We did not include
the home care hours received on weekends as a control in our baseline specifications because of a simultaneity
concern. Note that only 7.5% of our sample has weekend hours included in her personalized care plan.
23
We are currently exploring possibilities for panel estimation, which would make it possible to address
more directly the concern of unobserved individual heterogeneity while providing another source of variations
in prices (intra-producer variations over time).
24
empirical strategy. We could allow the price elasticity to vary across observable
characteristics, such as income. Indeed, past literature on health care consumption has shown that high-income individuals tend to be more price-sensitive than
low-income individuals (Duarte 2012), notably because richer individuals tend to
score higher at financial literacy, which is associated with greater price-sensitivity
(Hastings & Tejeda-Ashton 2008). Similar mechanisms may play a role in home
care consumption, although the important role assumed by the District Council’s
evaluation team in the choice of a provider may blur those effects.
In the same vein, we could want to break down formal home care in different
categories of intervention. The APA scheme is meant to subsidize the provision of
human assistance in the various activities of daily living: in practice, home care
services include house chores, grocery shopping, assistance with personal hygiene
or with transfers (from bed to a chair or from a chair to the bathroom), etc. If
the demand for home care services follows a pattern similar to the demand for
medical care services, we would expect the demand for some home care services
to be less price-sensitive than the demand for others. However, our data are not
precise enough to allow such a refined analysis. Thus, the implicit assumption we
make is that hours of care are homogeneous, both in terms of their nature and
quality.
8
Conclusion
This paper estimates the consumer price elasticity of the demand for home care
services of the disabled elderly living in the community. The empirical strategy
draws on the French APA program, which works as a partial hourly subsidy on
professional domestic help. We extracted data from local administrative records
providing unique information on home care consumption and copayments. Our
censored-regression model exploits inter-individual variation in producer prices to
identify the consumer-price elasticity.
Our baseline results show a point estimate of -0.7 at the average. The consumption of home care services by the disabled elderly is thus sensitive to their
hourly out-of-pocket payment; but this sensitivity is limited, as any increase in the
consumer price would induce a less than proportional decrease in consumption.
The baseline estimator, however, seems to be inflated by nonrandom producer
selection. Indeed, the disabled elderly intending to consume more might choose ex
ante a cheaper producer. We test this hypothesis by estimating the model on two
different subsamples. When restricting the sample to individuals who receive care
from the only provider operating in their municipality, the point estimate is lower
25
(-0.4), and, because of a loss in statistical power, no more significantly different
from zero. Conversely, the estimation on the subsample of individuals who can
choose between different producers yields a statistically significant coefficient of
-1.1. This coefficient captures both some endogenous selection into a producer
and the actual price elasticity.
Our baseline empirical strategy thus captures what we may call the overall
price sensitivity of consumption, which includes both an ex ante selection into a
producer on the basis of expected consumption (“pay less to consume more”), and
the real price elasticity (“consuming more when paying less”). The value of (real)
price elasticity is partially identified: it seems to be, in absolute value, inferior to
one. The point estimate of -0.4 we obtain when producer selection is shut down
is stable across our three years of observation. In order to assess the robustness
of this estimate, we intend to match our sample with rich information on the
geographical distribution of home care services. Hopefully such information will
provide a way to find a instrument for producer prices, thus enabling to identify the
price elasticity parameter with exogenous variations in out-of-pocket payments.
In addition, this supply-side information will probably permit us to control for
potential rationing effects.
The external validity of our results should obviously be qualified: our dataset
is not nationally representative, and our study focuses on APA recipients who
consume home care from regulated services. Yet there are several reasons to
think that general policy implications can be drawn from our results. Indeed, our
district was selected to be “average” in terms of economic and socio-demographic
characteristics. In addition, our estimates are in line with what was obtained by
Bourreau-Dubois et al. (2014) on data from another French district.
As expected, public policy implications flowing from our study first relate to
the effect of the out-of-pocket payment on consumption. Given the very low
price elasticity found on APA recipients, the decrease of copayment rates planned
by a recent APA reform24 can be predicted to reduce beneficiaries’ overall outof-pocket expenses on professional home care, while having little volume effect.
In such a context, the degree of generosity of home care subsidies essentially
reflects the extent of redistribution between taxpayers and the disabled elderly.
Our study pointed out another policy issue relative to the unequal access to home
care producers among territories. Indeed, individuals living in municipalities with
a unique producer cannot select their producer, on the basis of price or other
characteristics such as quality or weekend service. It evidences the need for further
development on spatial equity in access to home care services.
24
Loi no 2015-1776 du 28 décembre 2015, Journal officiel no 0301 du 29 décembre 2015.
26
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30
A
Appendices
A.1
Sample selection
This Appendix aims at documenting the various selection steps our initial
dataset has gone through. For our baseline month (October 2014), the administrative records indicate that 5,575 beneficiaries were receiving APA; but for 86
individuals, essential information on the hours subsidized, on copayment or on covariates was missing. These individuals are presumably former APA recipients not
yet erased from the files, so we dropped them. The total number of beneficiaries
is thus considered to be 5,489. Table A.1 sums up the selection steps.
Table A.1: Sample selection steps
Recipients consuming from a regulated producer at least
All APA
recipients
All
“Stable” APA recipients
Recipients consuming only from
one regulated producer
All
Recipients with
0 < ci < 90%
(1)
(2)
(3)
(4)
(5)
5,489
4,202
3,530
3,327
Number
2,862
76.5%
83.9%
94.2%
% of previous step
86.0 %
100%
76.5%
64.2%
60.5%
% of initial sample
52.1%
Notes: (i) “Stable” APA recipients in October 2014 are defined as those for which information is available
also for the months of September and November 2014. (ii) For additional 86 individuals (not in the
numbers here above), the administrative files contained no information on the copayment rate or or the
consumption of home care hours. These individuals are presumably former APA recipients not yet erased
from the files.
All
In order to observe precisely both out-of-pocket payments and the number of
hours that are effectively consumed and subsidized, we retain only the beneficiaries that receive care from a regulated producer. We estimate a Probit model to
assess the impact of observable characteristics on the probability to choose a regulated producer. Results are displayed in Table A.2 (p. 33). The results show that
individuals with more severe disability level, or those without a spouse at home
are more likely to receive care from a regulated producer, while richer individuals
are more likely to receive care from unregulated services or over-the-counter employees. Older individuals are less likely to receive care from a regulated producer.
Beneficiaries receiving care from a regulated producer represent the majority
of APA recipients in the district (more than 4/5). We then dropped the observations who have missing information for the current month, the preceding
31
month or the next month to avoid potential unobservable shocks to bias our estimations. Indeed, missing information could be related to temporary absences
(like hospitalizations) or temporary disruptions (e.g. visits from relatives, who
replace temporarily professional home care services by providing informal care).
The remaining individuals can be regarded as “stable”.
Some individuals receive home care from several producers at the same time.
Taking into account the simultaneity of home care consumption decisions of one
individual consuming care from different producers would complexify considerably
our empirical strategy: we drop these individuals. In addition, so as to make the
relationship between the consumer price and the producer price fully linear in
disposable income (see Appendix A.2), we retain only those individuals with a
copayment rate strictly between 0 and 90%.
Finally, we go from column (5) to our final sample by dropping the 5 individuals
for which information on some covariates is not available. We end up with a sample
that represents 52% of total APA recipients of the district.
32
Table A.2: Selection on observable characteristics into a regulated producer
Dependent variable:
Probability to choose a regulated producer
(probit model)
-0.027∗∗∗
(0.003)
Reported income
0.144∗∗
(0.049)
0.117
(0.120)
0.708∗∗
(0.236)
Ref.
Living with no spouse
Spouse receives APA
Spouse in institution
Living with non-APA spouse
Woman
-0.002
(0.046)
Disability level: 1
-0.308∗∗
(0.157)
-0.093
(0.058)
-0.038
(0.051)
Ref.
Disability level: 2
Disability level: 3
Disability level: 4
Age: 60-69
0.037
(0.099)
-0.073
(0.059)
Ref.
Age: 70-79
Age: 80-89
-0.705∗∗∗
(0.048)
Age: 90 or older
1.437∗∗∗
(0.076)
Observations
5489
Number of clusters
5329
Probit coefficients - and not marginal effects - are displayed.
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.
Standard errors are clustered at the household level.
Reported income is expressed in hundred euros per month.
Constant
33
A.2
Identification
In Section 6, we presented the equation we want to estimate:
ln(h∗i )
= β0 + β1 .ln(CPi ) +
β2 .ln(IiD )
+
2014
X
λd 1di + Xi0 .θ + i
(6)
d=2009
As the copayment rate is set to be strictly proportional to disposable income,
the consumer price on subsidized hours is a linear function of the disposable income:
CPi = ci pi =
0.9
I D pi
2M T PiD i
where M T PiD is the value of a particular disability allowance (M T P , see Section
3) the year individual i’s copayment rate was last computed. Equation (6) is thus
equivalent to:
h
ln(h∗i ) = β0 + β1 . ln(pi ) + ln(IiD ) + ln
2014
X d d
0.9 i
D
λ .1i + Xi0 .θ + i
+
β
.ln(I
)
+
2
i
2M T PiD
d=2009
Given that the disability allowance M T P D will take the same value for two individuals whose copayment rate was last revised in the same year, dummies 1di in
Equation (6) will control for inter-individual variation in this parameter. Rearranging terms and introducing a new set of parameters µdd=2009,...,2014 , we obtain25 :
ln(h∗i ) = β0 + β1 .ln(pi ) + (β1 + β2 ).ln(IiD ) +
2014
X
µd 1di + Xi0 .θ + i
(7)
d=2009
Equation (7) exhibits two interesting features of our econometric specification.
First, it shows that inter-individual variations in producer prices of home care
unambiguously identifies the consumer price-elasticity of home care, β1 . Second, it
indicates that any hypothetical variation in the disposable income that individual
i had when her copayment rate was last computed would have had two distinct
effects on the current volume of home care consumed:
• An income effect, which captures the additional home care consumption induced by a marginal increase in the current disposable income (since we
assume current disposable income and past disposable income are mechanically related);
• A price effect, that arises because any change in the disposable income at the
time the personalized plan was set induces a change in the current individual
25
Given that the dummies 1di are also meant to capture the unobservable increase in disposable income since
the time the observed income was registered in the District Council, the implicit assumption we have to make
is that M T P and income have evolved at the same rate for a given individual. This assumption is reasonable
since both pension benefits and the disability benefit MTP are set to follow the inflation rate.
34
consumer price.
In order to obtain directly the standard errors associated with the estimator of
coefficient β2 , (7) can be written alternatively as:
2014
X
ln(h∗i ) = β0 + β1 . ln(pi ) + ln(IiD ) + β2 .ln(IiD ) +
µd 1di + Xi0 .θ + i
(8)
d=2009
Compared to Equation (6), Equations (7) or (8) are less sensitive to the measurement errors on the relationship between income and consumer price. Indeed,
for 2% of our sample, the relationship between the income and the copayment
rate does not verify the legal formula used to compute the copayment rate, from
the disposable income and the value of the M T P disability allowance26 . After a
careful examination of the data, we hypothesize that most of these errors occurred
when the copayment rate was computed, while the values of income and of the
copayment rate are assumed to be the real ones. It is then worthy -in terms of
precision gained - to include the corresponding observations in the estimation. We
add a dummy variable 1ei signaling whether the individual is affected by such a
calculation error.
To sum it up, in order to take into account the various subtleties of the APA
policy and the measurement errors, the true estimated equation is thus:
ln(h∗i )
2014
X
D
D
= β0 + β1 . ln(pi ) + ln(Ii ) + β2 .ln(Ii ) +
µd 1di + ζ.1ei + Xi0 .θ + i (9)
d=2009
26
In practical terms, this means that we are not able to retrieve the year in which the copayment rate was
officially computed; as a consequence, for those individuals, all dummies 1d take the value of zero.
35
A.3
Maximum likelihood estimation of the model
Based on Equation (9), we derive the conditional likelihood function for our
sample, that is to say the probability we observe the sample values of hours consumed, hi , given the consumer price CPi , disposable income at the time the personalized care plan was set, IiD and other individual characteristics Xi . To make
notations more tractable, we denote: Zi = (1, CPi , IiD ); β the (3,1) vector of parameters β0 , β1 and β2 ; 1i = (12000
, ..., 12014
, 1ei ) is the vector of year dummies,
i
i
and λ is the (15,1) vector of parameters λ2000 , ..., λ2014 . Then:
ln(h∗i ) = Zi0 β + 10 λ + Xi0 θ + i
We consider hi as a random draw from the distribution of random variable h.
Given parameters β, λ and θ, the contribution to the likelihood of an individual
i whose number of hours consumed is censored (hi = hi ≤ h∗i ) is:
P(ln(h) = ln(hi ) |Zi , 1i , Xi ) = P(Zi0 β + 10 λ + Xi0 θ + ≥ ln(hi ))
= 1 − P( < ln(hi ) − Zi0 β − 10 λ − Xi0 θ)
ln(hi ) − Zi0 β − 10 λ − Xi0 θ <
σ
σ
ln(hi ) − Zi0 β − 10 λ − Xi0 θ =1−Φ
σ
=1−Φ
given that /σ ∼ N (0, 1).
Similarly, the contribution to the likelihood of an individual i whose number
of hours consumed is accurately observed in the data (hi = h∗i < hi ) is:
f (ln(hi ) | Zi , 1i , Xi ) =
∂P(ln(h) ≤ ln(hi ) | Zi , 1i , Xi )
∂ln(hi )
where f is the conditional density of random variable ln(h). We have:
P ln(h) ≤ ln(hi ) | Zi , 1i , Xi ) = P(ln(h) − Zi0 β − Xi0 θ ≥ ln(hi ) − Zi0 β − Xi0 θ | Zi0 , Xi
= P( ≥ ln(hi ) − Zi0 β − Xi0 θ)
=Φ
ln(hi ) − Zi0 β − 10i λ − Xi0 θ σ
Taking the partial derivative, we get:
f (ln(hi ) | Zi , 1i , Xi ) =
1 ln(hi ) − Zi0 β−, 10i λ − Xi0 θ φ
σ
σ
Assuming that (hi , Zi , 1i , Xi ) : i = 1, ..., n are i.i.d, the conditional likelihood
36
function writes:
L(ln(h) | Z, 1, X, β, θ, σ) = P(h1 , ..., hn | Z1 , ..., Zn , , 11 , ..., , 1n , X1 , ..., Xn , β, θ, σ)
=
=
n
Y
P(ln(hi ) | Zi , 1i , Xi , β, θ, σ)
i=1
n h
Y
1−Φ
i=1
ln(hi ) − Zi0 β − 10 λ − Xi0 θ 1[hi =hi ] 1 ln(hi ) − Zi0 β − 10 λ − Xi0 θ 1[hi <hi ] i
+
φ
σ
σ
σ
Taking the log, we obtain the following log-likelihood function:
L(β, λ, θ) = logL(ln(h) | Z, 1, X, β, θ, σ)
n h
X
ln(hi ) − Zi0 β − 10 λ − Xi0 θ 1 ln(hi ) − Zi0 β − 10 λ − Xi0 θ i
+ 1[hi <hi ] φ
=
1[hi =hi ] 1 − Φ
σ
σ
σ
i=1
Consistent estimators of β and θ in Equation (4) can be derived as the arguments of the maximization of the log-likelihood function, provided it is concave.
Note that in order to derive this expression of the likelihood function, we must assume that the censoring point h̄i does not depend on the error term, i . In other
words, we must assume here the exogeneity of the individual censoring points,
conditional on the observable variables Xi , Z.
A.4
Robustness checks
(see page below)
37
Table A.3: Disability level and price-elasticity - estimations using 2012, 2013 and 2014
Dependent variable: hours consumed (log)
Disability group: 1 & 2
(1)
0.166
(0.645)
Disability group: 3
(2)
-0.710∗∗∗
(0.002)
Disability group: 4
(3)
-1.045∗∗∗
(0.250)
Disposable income (log)
-0.138
(0.642)
0.691∗∗∗
(0.003)
0.982∗∗∗
(0.249)
Age: 60-69
0.053
(0.146)
-0.005
(0.075)
Ref.
-0.075∗∗∗
(0.011)
0.053∗∗∗
(0.012)
Ref.
-0.176∗∗∗
(0.051)
-0.109∗∗∗
(0.033)
Ref.
Age: 90 or older
0.028
(0.085)
0.014
(0.011)
0.152∗∗∗
(0.022)
Woman
0.215∗∗∗
(0.077)
0.118∗∗∗
(0.016)
0.061∗∗
(0.024)
Living with no spouse
0.616∗∗∗
(0.081)
0.266∗
(0.137)
1.060∗∗
(0.529)
Ref.
0.403∗∗∗
(0.015)
0.088∗∗∗
(0.013)
0.475∗∗∗
(0.013)
Ref.
0.242∗∗∗
(0.028)
-0.081
(0.049)
0.378∗∗
(0.174)
Ref.
Consumer price (log)
Age: 70-79
Age: 80-89
Spouse receives APA
Spouse in institution
Living with non-APA spouse
2.186
1.517∗∗∗
5.975∗∗∗
(2.081)
(0.018)
(0.788)
Sigma
0.787∗∗∗
0.729∗∗∗
0.663∗∗∗
(0.043)
(0.003)
(0.014)
Observations
1145
1656
5391
Censored observations
44.4%
39.4%
38.6%
Number of clusters
27
28
28
Standard errors in parentheses; ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.
Standard errors are clustered at the producer price level.
All specifications include the year the latest plan was decided upon s well as the year in which
the copayment rate was computed (“year of MTP”).
Estimations used pooled data from October 2012, October 2013 and October 2014.
Constant
38
Table A.4: Robustness check: estimations on October 2012, 2013 and 2014
Dependent variable: hours consumed (log)
2012
(1)
-0.984∗∗∗
(0.259)
2013
(2)
-0.723∗∗
(0.298)
2014
(3)
-0.697∗∗
(0.291)
2012-14
(4)
-0.827∗∗∗
(0.248)
Disposable income (log)
0.944∗∗∗
(0.261)
0.685∗∗
(0.295)
0.649∗∗
(0.292)
0.785∗∗∗
(0.246)
Age: 60-69
-0.124∗
(0.066)
-0.048
(0.045)
Ref.
-0.030
(0.052)
-0.062∗∗
(0.030)
Ref.
-0.265∗∗∗
(0.078)
-0.070∗∗
(0.031)
Ref.
-0.140∗∗
(0.057)
-0.063∗∗
(0.029)
Ref.
Age: 90 or older
0.141∗∗∗
(0.032)
0.128∗∗∗
(0.032)
0.072∗∗
(0.032)
0.109∗∗∗
(0.023)
Woman
0.102∗∗∗
(0.030)
0.129∗∗∗
(0.031)
0.065∗∗
(0.026)
0.100∗∗∗
(0.018)
Living with no spouse
0.341∗∗∗
(0.034)
-0.082
(0.081)
0.553∗∗∗
(0.154)
Ref.
0.335∗∗∗
(0.034)
0.044
(0.058)
0.459
(0.301)
Ref.
0.317∗∗∗
(0.032)
0.031
(0.059)
0.570∗∗∗
(0.127)
Ref.
0.332∗∗∗
(0.025)
0.010
(0.042)
0.523∗∗∗
(0.163)
Ref.
1.318∗∗∗
(0.210)
0.798∗∗∗
(0.041)
0.533∗∗∗
(0.039)
Ref.
0.873∗∗∗
(0.195)
0.890∗∗∗
(0.047)
0.513∗∗∗
(0.040)
Ref.
1.253∗∗∗
(0.141)
0.956∗∗∗
(0.049)
0.523∗∗∗
(0.024)
Ref.
1.136∗∗∗
(0.104)
0.889∗∗∗
(0.037)
0.527∗∗∗
(0.021)
Ref.
Consumer price (log)
Age: 70-79
Age: 80-89
Spouse receives APA
Spouse in institution
Living with non APA-spouse
Disability group: 1
Disability group: 2
Disability group: 3
Disability group: 4
5.375∗∗∗
4.162∗∗∗
4.761∗∗∗
4.851∗∗∗
(0.804)
(0.874)
(0.898)
(0.770)
Sigma
0.690∗∗∗
0.668∗∗∗
0.725∗∗∗
0.698∗∗∗
(0.020)
(0.026)
(0.015)
(0.018)
Observations
2571
2758
2862
8191
Censored observations
44.8%
38.2%
40.2%
39.6%
Number of clusters
28
28
27
28
Standard errors in parentheses; ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.
Standard errors are clustered at the producer level.
All specifications include the year the latest plan was decided upon as well
as the year in which the copayment rate was computed (“year of MTP”).
Estimations used data from October 2012, October 2013 or October 2014.
Constant
39
Table A.5: Robustness checks: Selection into a producer - estimations (2012-2014)
Dependent variable: hours consumed (log)
Consumer price (log)
(standard error)
p-value
Socio-demographic controls
Dummies for year of MTP
Dummies for latest plan
Sample
—2012—
(1)
(2)
-0.643
-1.209∗∗∗
(0.418)
(0.433)
0.124
0.005
Yes
Yes
Yes
Yes
Yes
Yes
Single
Multiple
producer producers
—2013—
(3)
(4)
-0.418
-0.785∗∗
(0.884)
(0.355)
0.636
0.028
Yes
Yes
Yes
Yes
Yes
Yes
Single
Multiple
producer producers
Observations
799
1772
812
Censored observations
319
720
314
Number of clusters
16
28
15
∗
∗∗
∗∗∗
Standard errors in parentheses; p < 0.10,
p < 0.05,
p < 0.01.
Standard errors are clustered at the producer price level.
Estimations used data from October 2012, October 2013 or October
1946
740
25
—2012-14—
(5)
(6)
-0.479
-1.061∗∗∗
(0.355)
(0.263)
0.177
0.000
Yes
Yes
Yes
Yes
Yes
Yes
Single
Multiple
producer producers
2753
1120
37
5438
2124
59
2014.
Table A.6: Robustness chek: Inclusion of home care received on weekends (2012-2014)
Dependent variable:
hours consumed (log)
(1)
(2)
(3)
-0.832∗∗∗ -0.956∗∗∗ -0.903∗∗∗
(0.247)
(0.252)
(0.259)
Consumer price (log)
Consumes care on weekends
0.491∗∗∗
(0.055)
0.077
(0.107)
Yes
Yes
Yes
8191
39.6%
28
0.118∗∗∗
(0.031)
Yes
Yes
Yes
8191
39.6%
28
Number of hours received on weekends
Socio-demographic controls
Dummies for year of MTP
Dummies for latest plan
Observations
Censored observations
Number of clusters
Yes
Yes
Yes
8191
39.6%
28
AIC
14894
14718
14673
BIC
15063
14908
14863
Standard errors in parentheses; ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.
Standard errors are clustered at the producer level.
Estimations used data from October 2012, 2013 and 2014.
40