New ESRI Working Paper No.41

Measuring the Output of Long-Term Care Services

Shigeru Sugihara, Yasuko Ikemoto, Ikumi Imamura,
Hiroto Yoshida, Yu Taniguchi, Hiroshi Murayama, Mariko Nishi,
Yoshinori Fujiwara, Akihiko Kitamura and Shoji Shinkai

June 2017

Economic and Social Research InstituteCabinet Office
Tokyo, JapanThe views expressed in “New ESRI Working Paper” are those of the authors and not those of
the Economic and Social Research Institute, the Cabinet Office, or the Government of Japan.
(Contact us: https://form.cao.go.jp/esri/en_opinion-0002.html)

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Measuring the Output of Long-Term Care Services

Shigeru Sugihara 1
Yasuko Ikemoto1
Ikumi Imamura 2
Hiroto Yoshida 3
Yu Taniguchi4
Hiroshi Murayama4
Mariko Nishi4
Yoshinori Fujiwara4
Akihiko Kitamura4
Shoji Shinkai4June 2017

Social and Economic Research Institute, Cabinet Office.
Public Relations Office, Cabinet Office.
3 The Tohoku Bunka Gakuen University.
4 The Tokyo Metropolitan Institute of Gerontology.
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New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

1. Introduction and methods
As the number of the elderly increases rapidly in Japan, long-term care services are
increasingly needed. The growth of the consumption of long-term care services is often
taken to be the growth of reimbursements from long-term care insurance. However, thereimbursements are inputs to produce long-term care services, which are different from
outputs; that is, benefits accrued to the consumers of long-term services. In the SNA,
the output of long-term care is measured in the general framework of double deflation,
which measures real outputs by deflating nominal sales by output deflator andsubtracting nominal costs deflated by input deflator. This methodology is valid only
when suitable deflators that reflect consumers’ welfare are available, however. In
long-term care services, prices are regulated through the public insurance and are
generally not representative of consumers’ true preferences.
Recently, direct measures of output of non-market service sectors are being
actively studied and advocated. The Atkinson Review (2005) recommends measuring
output directly by counting the number of units for whom services are provided insteadof measuring output by aggregating costs of producing the services. In addition, theAtkinson Review (2005) encourages that output is adjusted for the change in quality ofservices. Eurostat (2001) also recommends direct measurement and quality adjustment.
In the United Kingdom, the Office for National Statistics calculates and publishes directand quality-adjusted output indexes for public sector activities. (Office for National
Statistics, 2007, 2008, 2015.) In the United States, pioneering research has been
conducted during the 1990s, particularly at the National Bureau of Economic Research,measuring the quality of health care and adjusting for quality change in the calculationof deflators (Cutler and Berndt, eds. 2001). The Bureau of Economic Analysis is now
developing a Health Care Satellite Account based on treatments of diseases (Dun, et al.,2015).
In this paper, we exemplify the direct method of measuring the output of long-termcare services. This method directly measures output by aggregating the volume ofservices each unit of measurement consumes and, additionally, by assigning value of theservices to each unit. We follow Dawson, et al. (2005), Castelli, et al. (2007) andCastelli, et al. (2008) in the construction of a quality-adjusted output index. Output
consists of three components: unit of measurement, quality of care, and valuation of thequality. Schematically, we can write:
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New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Output＝ ×Unit of measurement×× Quality of care×

Valuation

Output index should include not only the number of patients but also the improvementof status of the elderly attributable to long-term care. This is what a quality-adjusted
output index is intended to do. The unit of measurement is the elderly who are coveredby the long-term care insurance. All the elderly are enrolled in the insurance and arepotentially eligible for long-term care services while a little more than 10 percent of theelderly actually receive such services. Quality of care is the improvement of status of
the elderly caused by long-term care services. Valuation is the value of long-term careprovided by long-term care insurance, which will be measured by the Quality of Life ofeach elderly.
The concept of the quality of long-term care can be explained as follows（ Figure 1）.
Figure 1 The Concept of the Quality of Long-term Care

htT
htO
htC

This exposition is inspired by the discussion in Jacobs, et al. (2006). Let the original
status of an elderly at time t be htO =0.5. Suppose that when she undergoes a treatment(provision of long-term care), her status will be htT =0.7 with the apparent improvement
in her status of htT − htO =0.2. (No time lag is assumed between the intervention and its
results.) However, this is not the true improvement caused by long-term care. Supposethat when she does not undergo a treatment, her status will deteriorate to htC =0.4. The
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New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

true quality of care is htT − htC =0.3 while we can observe only htT − htO =0.2 because weusually do not know the natural history, htC .
Now suppose that in the next year we have the original status, htO+1 =0.5, the status
with a treatment, htT+1 =0.8, and the status without treatment, htC+1 =0.4. (Again, no time
lag is assumed.) Namely, the original health status and the natural history are the sameas time t. Then, the quality of health care at time t+1 is htT+1 − htC+1 =0.4 while weobserve only htT+1 − htO+1 =0.3. However, since htO+1 = htO and htC+1 = htC , we cancalculate the change in the true quality of health care as ( htT+1 − htO+1 ) − ( htT − htO ) = htT+1− htT .
It is not necessarily the case that the original statuses, htO and htO+1 , are equal.
Hence, we have to adjust the original statuses to compare outcomes, htT and htT+1 . Risk
adjustment just does this. Somewhat formally, we can model the health status of thetreated patient as a function of the original status: htT = f t ( htO ) and htT+1 = f t +1 ( htO+1 ) .
Adjusted health statuses with a common original status, h O , are htT = f t ( h O ) andhtT+1 = f t +1 ( h O ) . Then, the difference between these two outcomes is the change inquality of health care.
Now, we explain the calculation procedure. Quality-adjusted measure of long-term careis calculated by multiplying the number of the elderly by the quality of long-term carewith further adjustment made to account for the valuation of the quality. The quality oflong-term care is defined to be the improvement of the status of the elderly when theyutilize long-term care compared with the status of the elderly when they do not utilize
long-term care. The quality of long-term care services is the Quality of Life attached toeach care level category.
We take as the unit of measurement the number of the elderly at each category ofcare level. Care level is assigned to each elderly according to the amount of the careneeded and can be regarded as an indicator of the state of the elderly. (The categories ofcare level will be explained below together with institutional arrangements of thelong-term care insurance system.) The quality of care is the category of care level towhich each elderly is certified. We then attach a valuation to each care level by
estimating quality of life (QOL) of each category. In sum, quality-adjusted output index
4New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

is calculated as the number of the elderly at each category of care level multiplied by
QOL of each category.
In this calculation, we have to adjust for the change in the risks that influence thestate of the elderly. For example, as a person ages, she tends to require heavier
long-term care. Therefore, we adjust for changes in risks by statistically estimating anequation that describes the relationship between risk factors such as age andcomorbidities and the care level. The estimation will be explained below.
The calculation is summarized in Figure 2. We start with (i) the estimation of an
equation that describes the determination of probabilities of becoming in need oflong-term care for each care level. The estimated equation will be used to adjust for risk
factors, which vary from time to time, and to enable the comparison of the output
overtime.
Figure 2 The calculation procedure
(ⅱ )

(ⅲ)

Estimated probabilities
excluding quality improvement

Number of the elderly in needof long-term care excluding
quality improvement

(ⅱ)’

(ⅲ)’

Hypothetical probabilities
with quality improvement

Number of the elderly in needof long-term care with quality
improvement(ⅰ)

Estimation of probabilities
of becoming in need of long-termcare for each category

Multiply by QOL for each category(ⅳ)

Output of long-term careexcluding quality improvement

Effect of quality improvement
in long-term care(ⅳ)’

Output of long-term carewith quality improvement

After adjustment for risk factors we obtain (ii) estimated probabilities of becomingin need of care that excludes improvement of the quality of long-term care by excluding
5New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

the effect of time dummies in the estimated equation. The time dummy in the equation
represents effects specific to each year and common to all elderly people. These effects
can be regarded as technological progress, in other words, as the quality of long-termcare services. Hence, by suppressing the effects of time dummies we can calculate ahypothetical probabilities of becoming frail when no quality improvement is achieved.
Multiplying these probabilities by the number of the elderly gives (iii) the numberof the elderly in each category of care level. Finally, we obtain (iv) output of long-termcare without adjusting for quality improvement by multiplying (iii)above by QOL foreach category.
Next, we go on to adjust for the quality of care by including the effects of time
dummies in the estimated equation. We start with (i) the estimation of the equation that
determines the probabilities of frailty. Then, we go to (ii)’ instead of (ii) in Figure 2.In(ii)’ we include the effects of time dummies on the state of the elderly in addition to theeffects of risk factors. Then, (iii)’ the number of the elderly in each category of carelevel is obtained just as the case of (iii). Finally, multiplying by QOL for each category
gives (iv)’ output of long-term care for which quality of care is adjusted.

2. Institutional Description
The Japanese long-term care insurance system covers, primarily, elderly people aged
above 65 years old. People between 40 and 64 years old also enroll in the insurance. To
obtain benefits, a policyholder needs to be certified as Requiring Support or Requiring
Long-term Care by the insurer (municipality). Requiring Support is a classification for
persons whose basic activities of daily living can be performed basically independently,
but for whom some support is needed for procedural activities of daily living to prevent
becoming in need of long-term care. Requiring Long-term Care is for persons whosebasic activities of daily living cannot be performed independently and long-term care isneeded.
The certification is made for Requiring support 1 to 2 and Requiring long-termcare 1 to 5. (See Appendix) These categories are defined in terms of the time needed totake care of the elderly, not in terms of the severity of the condition of the elderly.
However, a positive correlation is observed between support/care levels and frail
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Measuring the Output of Long-Term Care Services

conditions of the elderly (Tajika and Kikuchi, 2003). The Requiring Support 1 is theleast-frail elderly for whom, in typical cases, basic activities of daily living such as
walking can be performed independently but some support is needed concerning
standing up, getting up, standing on one foot. The Requiring Long-term Care 5 is themost frail who, in typical cases, capabilities of movement have deteriorated so severelythat daily living is almost impossible without long-term care. Tajika and Kikuchi(2003)
points out that the Requiring Long-term Care 3 is the threshold between mild and severe
conditions. They classify the elderly with less than and equal to Requiring Long-term
Care 2 as mild.
The services provided to the elderly certified as Requiring Support are called"preventive benefits" while those provided to the elderly certified as Requiring
Long-term Care are called "long-term care benefits." However, those services are notmuch different across these categories. Therefore, we will not distinguish between"preventive" and "long-term care" benefits.
The Japanese long-term care insurance system provides benefits for two types of care.
One is home care, the other facility care. Home care includes home-visit care, day care,short-term admission to facilities, and rental welfare equipment.

3. Data and Descriptive Statistics
The Tokyo Metropolitan Institute of Gerontology launched a longitudinal study of aging
and health in 2002 at Kusatsu in Japan. All residents aged 65 years or older 5 have been
invited to participate in baseline and follow-up surveys and medical examinations. The
medical examination is called the Nikkori (Smile) examination and is held at a local
public health center once a year. The survey is called the Iki-iki (Lively) survey and isconducted every two years. These surveys and examinations contain detailed physicaland medical information including diseases that the elderly had suffered or is suffering.
In particular, they include information on pre-existing stroke and hypertension, which
we will use as explanatory variables in the estimation. Actually, Levine, et al. (2014)
documents that myocardial infarction and stroke hospitalizations are associated withsignificant increases in functional disability. All participants provided written informed
consent under conditions approved by the Ethics Committee at the Tokyo Metropolitan
5

Up to 2005, 70 years or older.
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New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Institute of Gerontology.
The physical and medical information is linked to the information on the long-term carebenefits approved by the long-term care insurance system. The latter information also
includes the support or care level if the elderly is certified as Requiring Support orLong-term Care.
Since the Nikkori (Smile) medical examination and the Iki-iki (Lively) healthsurvey are conducted annually and biannually, respectively, their annual data aretransformed into quarterly data. In the estimation below, pre-existing diseases of strokeand hypertension are used. If an elderly is found to suffer from a stroke in a year, she isjudged to have a pre-existing stroke after the beginning of that year and not before that.
Sample is restricted to those who are older than 70 years old because, as explained
above, the threshold of the eligibility for reimbursements in the insurance system is 70
years old up to 2005 and 65 after 2006. To secure consistency of the sample, we put
aside data of those whose ages are less than 70. Missing data of age and history of adisease (stroke) are imputed using the data, if they exist, before or after the missing data.
Specifically, a missing data of history of stroke is imputed as one if data in previous
years indicate that the person has history of stroke. Data from 2003 to 2009 are used in
the analysis below. The number of individuals is 1,482 and the number of total
observations is 6,527.
Table 1 shows basic statistics of the sample used for the estimation; from 2002 to
2009. The average age is 77.1 years old. As for the preexisting conditions, 15 percent of
the elderly has suffered from stroke, currently or in the past.
To get a feel about the overall degree of frailty of the elderly, we assign a point toeach condition; one to Independent, two to Requiring Support 1, three to Requiring
Support 2, four to Requiring Long-term Care 1, and so on. When averaged over allelderly population, the mean of the frailty points is 1.26.
The share of the elderly in each frailty condition is 89.9 percent for the elderly who
do not need support or care (Independent). As for Requiring Support/Care conditions,we aggregate categories in accordance with Tajika and Kikuchi (2003): aggregate
categories from Requiring Support 1 to Requiring Long-term Care 2 into “Mild” while
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New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

aggregating categories above Requiring Long-term Care 3 into “Severe.” The share is
7.9 percent for the mild care level and 2.2 percent for the severe care level. Below thesefigures, the ratio for each category is shown.
Table 1 Descriptive Statistics
Obs
6,527

Age

2002-2009
Mean
Std. Dev.
77.10
5.67

2002
Obs
Mean
1,001
76.94

2003
Obs
Mean
1,072
77.32

2004
Obs
Mean
996
77.15

2005
Obs
Mean
1,088
77.23

Stroke(0:No 1:Yes)

6,527

0.15

0.36

1,001

0.07

1,072

0.11

996

0.11

1,088

0.13

Sex(1:male 2:female)

6,527

1.58

0.49

1,001

1.60

1,072

1.60

996

1.59

1,088

1.58

Care level(current)

6,527

1.26

0.90

1,001

1.22

1,072

1.29

996

1.25

1,088

1.31

5,869
513
145
133
267
113
59
51
35

(share)
89.9%
7.9%
2.2%
2.0%
4.1%
1.7%
0.9%
0.8%
0.5%

909
77
15
24
34
19
11
1
3

(share)
90.8%
7.7%
1.5%
2.4%
3.4%
1.9%
1.1%
0.1%
0.3%

947
100
25
29
46
25
13
5
7

(share)
88.3%
9.3%
2.3%
2.7%
4.3%
2.3%
1.2%
0.5%
0.7%

889
89
18
25
49
15
10
5
3

(share)
89.3%
8.9%
1.8%
2.5%
4.9%
1.5%
1.0%
0.5%
0.3%

960
95
33
21
59
15
15
14
4

(share)
88.2%
8.7%
3.0%
1.9%
5.4%
1.4%
1.4%
1.3%
0.4%

Independent
Mild(～Requiring long-term care 2)
Severe(Requiring long-term care 3～)
Requiring support 1
Requiring support 2 / Requiring long-term care 1
Requiring long-term care 2
Requiring long-term care 3
Requiring long-term care 4
Requiring long-term care 5

2006
Obs
Mean
626
76.79
626
0.22
626
1.57
626
1.22

576
36
14
13
16
7
3
6
5

(share)
92.0%
5.8%
2.2%
1.3%
1.6%
0.7%
0.3%
0.6%
0.5%

2007
Obs
Mean
629
76.88
629
0.21
629
1.56
629
1.23

578
38
13
6
22
10
2
7
4

(share)
91.9%
6.0%
2.1%
0.6%
2.1%
0.9%
0.2%
0.7%
0.4%

2008
Obs
Mean
607
76.96
607
0.22
607
1.56
607
1.26

550
44
13
8
23
13
2
7
4

(share)
90.6%
7.2%
2.1%
0.8%
2.3%
1.3%
0.2%
0.7%
0.4%

2009
Obs
Mean
508
77.39
508
0.26
508
1.54
508
1.28

460
34
14
7
18
9
3
6
5

(share)
90.6%
6.7%
2.8%
0.6%
1.7%
0.8%
0.3%
0.6%
0.5%

Table 1 also provides a long-term trends of age and pre-existing diseases. The
average age followed an increasing trend from 76.9 years in 2002 to 77.2 years in 2005
before a sharp decline in 2006 to 76.8 years. From 2006 to 2009 a clear upward trend isobserved (77.4 years in 2009).The share of the elderly who suffer from stroke
continuously rose from 7 per cent in 2002 to 26 per cent in 2009 with a large jump in
2006.
The mean of the frailty points rose from 1.22 in 2002 to 1.31 in 2005. After a fallin 2006 to 1.22, it steadily rose to 1.28 in 2009. The share of the Independent category
declined from 90.8 per cent in 2002 to 88.2 per cent in 2005. After a sudden jump to92.0 per cent in 2006, it declined to 90.6 per cent in 2009. The share of the “Mild”
category showed no clear trend from 2002 to 2005. After a large drop in 2006 to 5.8 per
cent, it rose to 6.7 per cent in 2009. The share of the “Severe” category continuouslyrose from 1.5 per cent in 2002 to 3.0 per cent in 2005. After a large drop in 2006 to 2.2
per cent, it rose to 2.8 per cent in 2009.
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Measuring the Output of Long-Term Care Services

Table 2 is a matrix that shows the transition probabilities from the care level of one year
earlier to the current care level, including death. For example, 97 percent of the
independent elderly remain independent after a year, 0.7 percent of them will become
Requiring Support 1, 1.1 percent Requiring Support 2, and so on. The large percentage
figures on the diagonal indicate that people tend to find themselves in the same
categories as those in the previous year. Naturally, they often stay near the original
categories even if they make transitions and it is infrequent that they jump into far away
categories. These strongly indicate state dependence of frail conditions. In the “Mild”
categories, the elderly tend to make transitions to more severe categories than to lesssevere ones. It is a little surprising that a moderate number of the elderly in the “Severe”
categories still go back to less severe categories. People tend to die more often when
they are in more severe categories.
Table 2

Transition Matrix

Care level (t-1)

Care level (current)

independent

Requiring
Support 1

Requiring
Support 2/ Requiringlong-termcare 1Requiring
long-termcare 2Requiring
long-termcare 3Requiring
long-termcare 4

Requiring
long-termcare 5independent

97.2%

0.7%

1.1%

0.4%

0.2%

0.1%

0.1%

0.2% 100.0%

Requiring Support 1

0.0%

64.6%

31.9%

1.8%

0.9%

0.0%

0.0%

0.9% 100.0%

Requiring Support 2/ Requiring long-term care 1

0.0%

6.1%

78.1%

11.2%

3.6%

0.0%

0.5%

0.5% 100.0%

Requiring long-term care 2

0.0%

1.2%

12.9%

63.5%

11.8%

5.9%

1.2%

3.5% 100.0%

Requiring long-term care 3

0.0%

0.0%

0.0%

17.0%

59.6%

19.1%

2.1%

2.1% 100.0%

Requiring long-term care 4

0.0%

0.0%

0.0%

3.0%

0.0%

81.8%

12.1%

3.0% 100.0%

Requiring long-term care 5

0.0%

0.0%

0.0%

0.0%

0.0%

14.8%

85.2%

0.0% 100.0%

89.7%

2.0%

4.1%

1.7%

0.9%

0.8%

0.5%

0.3% 100.0%

Total

death

Total

4. The Model and Estimation
In this section, we estimate a multinomial mode that determines the care level of eachelderly people. This is the first step (i) in Figure 2.
The dependent variable is the indicator variable that shows the level of need forsupport or care. On top of the independent state, where there is need for neither support
nor care, there are two categories of Requiring Support and five categories of Requiring
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Long-term Care so that 𝑦𝑦𝑖𝑖𝑖𝑖 = {1, 2, … ,7} , with 1 indicating the independent state and7 Requiring Long-term Care 5. To model this categorical variable, an ordered logit
model is employed because there is a natural order in it.
The latent variable model is𝑦𝑦𝑡𝑡∗ = 𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 + 𝑢𝑢𝑖𝑖𝑖𝑖,

where 𝑧𝑧𝑖𝑖𝑖𝑖 is the vector of explanatory variables,𝑦𝑦𝑡𝑡−1 is the care level in the previous

year,𝜆𝜆𝑡𝑡 is a dummy variable indicating each year, t, and 𝑢𝑢𝑖𝑖𝑖𝑖 is an error term.
Cut points for respective categories are
𝛼𝛼1 < 𝛼𝛼2 < ⋯ < 𝛼𝛼𝐽𝐽 .

The actual outcome, y, realizes according as the latent variable, 𝑦𝑦 ∗ , is located below,
between or above the cut points:
y=1
y= 2

y= 3

y=7

if 𝑦𝑦 ∗ ≤ 𝛼𝛼1
if 𝛼𝛼1 < 𝑦𝑦 ∗ ≤ 𝛼𝛼2

if 𝛼𝛼2 < 𝑦𝑦 ∗ ≤ 𝛼𝛼3⋮
if 𝑦𝑦 ∗ > 𝛼𝛼𝐽𝐽

Probability distributions are specified as logit distribution, Λ(. ).

P (𝑦𝑦𝑖𝑖𝑖𝑖 = 1|𝑧𝑧𝑖𝑖𝑖𝑖 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 ) = Λ([𝛼𝛼1 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 )]P (𝑦𝑦𝑖𝑖𝑖𝑖 = 2| ∙) = 𝛬𝛬 [𝛼𝛼2 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 )] − Λ([𝛼𝛼1 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 )]⋮P (𝑦𝑦𝑖𝑖𝑖𝑖 = 𝐽𝐽|𝑧𝑧𝑖𝑖𝑖𝑖 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 ) = 1 − Λ([𝛼𝛼𝐽𝐽 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + 𝜌𝜌𝑦𝑦𝑡𝑡−1 + 𝜆𝜆𝑡𝑡 )]The time dummy, 𝜆𝜆𝑡𝑡, represents effects specific to each year and common to all elderly
people. This variable can be regarded as representing technological progress in caring of

the elderly because a lower value of 𝜆𝜆𝑡𝑡 translates into lower probability of becoming
worse long-term care status holding attributes of the elderly constant. This technologicalprogress is the quality of long-term care services. The estimates of 𝜆𝜆𝑡𝑡will play a central
role in the calculation of the quality-adjusted output index of long-term care services.
11New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Explanatory variables, 𝑧𝑧𝑖𝑖𝑖𝑖 , include age, sex and preexisting stroke. As we
mentioned previously, Levine, et al. (2014) documents that myocardial infarction andstroke hospitalizations are associated with significant increases in functional disability,
and we can use hypertension as a surrogate indicator of MI.

The care level in the previous year,𝑦𝑦𝑡𝑡−1, is included in the regression to account fora phenomenon called state-dependence. As is explained in Sugihara, et al. (2017), thisyear’s care level depends on previous year’s care level: when one year’s care level
becomes severe, next year’s care level tends to remain severe.
Prior distributions for the coefficients, 𝛾𝛾 and 𝜌𝜌 , and time dummies, 𝜆𝜆𝑡𝑡 , areassumed to be normal distributions with mean zero and variance 1000: take a genericcoefficient µ , then, µ ~ N (0,1000) . The choice of the variance of 1000 is intended torepresent a diffuse prior. Gelman and Hill (2007) give a thoughtful discussion on theappropriateness of this value in the context of the logistic models or log-transformed
regressors. They argue that in logistic and logarithmic regressions, typical changes inoutcomes are on the scale of 0.1 or 1, but not 10 or 100, so that one would not expect tosee coefficients much higher than 10 in absolute values as long as the regressors are also
on a reasonable scale. Although their choice of the value of variance is 1002 , webelieve that their argument applies to our choice, 1000.
The model is estimated by the Markov chain Monte Carlo (MCMC) method
utilizing the WinBUGS software. Convergence is checked by the Gelman-Rubin
statistics. Burn-in is 2,000 and the number of iterations used in calculation is 10,000.
Table 3 shows estimation results. Among risk factors, age strongly increases theprobability of becoming in need of long-term care while sex and history of stroke do notsignificantly influence the severity of state of the elderly. Care levels in the previous
year has a strong influence on the care levels of this year, suggesting the existence ofstate-dependence explained in Sugihara, et al. (2017).
Time dummies are negative and their magnitude is increasing over time, implyingthat quality of long-term care is steadily improving. This information will be used when
we calculate how much improvement of the quality of care contributes to long-term care
output.
12

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Table 3
node
Lagged care level
Age
Sex
StrokeTime dummy
2002
2003
2004
2005
2006
2007
2008
2009

Single Equation (for estimate the output)
mean
0.85
2.21
0.10
1.10

sd
0.12
0.22
2.70
0.81

2.5%
0.62
1.89
-6.35
-0.40

median
0.85
2.19
0.58
1.09

97.5%
1.08
2.78
4.09
2.79

-38.69-39.92-41.35-42.59-44.95-46.01-46.92-48.87

2.03
1.96
1.92
1.91
1.92
1.96
2.02
2.10

-41.83-43.04-44.51-45.79-48.25-49.44-50.48-52.68-38.87-40.10-41.52-42.75-45.09-46.11-46.99-48.91-33.88-35.55-37.45-38.92-41.37-42.33-43.01-44.76

These estimates enable us to calculate risk-adjusted probabilities of becoming frail
by substituting the mean values for each year into each explanatory variable in theestimated equation.
We calculate hypothetical probabilities of needing long-term care by suppressing
the effects of time dummies, λ, in the estimates of the multinomial model. This is doneby setting the coefficients, ρ, on time dummies equal to zero in the calculation of theestimated probabilities of needing long-term care. The resulting probabilities represent
hypothetical probabilities obtained if we assume that no improvement in the quality oflong-term care services occurred.
Table 4 shows the results. Once the risks are adjusted, the probabilities of frailty
become smaller for severe categories of frailty.
Table4 Probability of each care level status: Without quality improvement

Year

independent

2002
2003
2004
2005
2006
2007
2008
2009

90.71%
86.33%
85.99%
85.79%
87.31%
88.56%
89.79%
90.55%

Care level
Requiring
Requiring
Requiring
Requiring
Requiring
Support 2
Requiring
long-term care long-term care long-term care long-term care
/Requiring
Support 1
2
3
4
5
long-term care
1
2.65%
4.02%
1.29%
0.69%
0.32%
0.32%
2.71%
5.47%
2.31%
1.32%
1.28%
0.59%
1.95%
5.73%
2.86%
1.43%
1.33%
0.71%
0.79%
4.03%
3.12%
2.41%
2.11%
1.76%
0.26%
3.14%
2.74%
2.11%
2.13%
2.32%
0.03%
1.02%
2.63%
2.17%
2.60%
2.99%
0.00%
0.14%
0.94%
1.86%
3.00%
4.27%
0.00%
0.01%
0.11%
0.52%
2.19%
6.63%

13

Total

100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

We can also calculate probabilities including quality improvements in long-termcare services by incorporating the effects of time dummies in the estimated equation.
The results will be presented below.

6. Calculation of a Quality-Adjusted Output of Long-term CareIn this section, a quality-adjusted output index using the estimation results of theprevious section. We have calculated probabilities of becoming needy of long-term carefor each care level in the previous section. Now, we translate the estimated probabilities
into the number of elderly people in each care level category by multiplying the total
number of elderly in the population by estimated probabilities for each category of carelevel. 6 This is the step (iii) in Figure 2.
In the final step (iv), we further multiply the number of the elderly in each categoryby the quality of life for each category. The quality of life for each category is calculated
following the method of Dolan (1997). He modeled valuations for EuroQol health states
to convert EuroQol health states into quality of life. Our data contains similar questions
on health status of three of five areas of the EuroQol questionnaire. We use thisinformation and the methodology of Dolan (1997) to obtain the quality of life of eachcategory of care levels.
EuroQol consists

of

five

areas: Mobility,

Self-care,

Usual activities,

Pain/discomfort, and Anxiety/depression. Each area is comprised of three levels withthe first level no problem and the third incompetence. (Appendix Table A1)
Dolan (1997) modeled valuations for EuroQol health states to obtain a single index
of health-related quality of life. He estimated parameters that represent values for eachhealth state in EuroQol. (Appendix Table A2)
We start from the state of full health of QOL one. If a person has any problem in
mobility, self-care or usual activity, a constant 0.081 is subtracted from 1 resulting in
0.919. Next, if mobility is level 2, MO=1times0.069 is subtracted from 0.919 resulting
in0.85. Further, if self-care is level 2, SC=2 times 0.104is subtracted from 0.85 resulting
6

These numbers might be regarded as output index without quality adjustment if
numbers in each category are aggregated (possibly weighted by cost shares).
14

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

in 0.642 and so on.
Since we excluded pain/discomfort and anxiety/depression from the calculation of
QOL, the estimated QOL is upward biased. However, this is inconsequential when wewant to know the change in the quality of long-term care.
Table 5 shows the estimated QOL for each category of care level. Up to Requiring
Long-term Care 1, QOL is relatively high. QOL for Requiring Long-term Care 2 and 3
exhibits recognizable decline and decline for Requiring Long-term Care 4 and 5 issubstantial.
Table5 The QOL for each category of care level
QOL(average)
independent

0.997

Requiring Support 1

0.976

Requiring long-term care 1

0.902

Requiring long-term care 2

0.785

Requiring long-term care 3

0.623

Requiring long-term care 4

0.340

Requiring long-term care 5

0.067

To obtain the quality-adjusted output of long-term care, we further multiply the
number of the elderly in each category by the quality of life for each category. Resulting
numbers are shown in Table 6. The right-most column of Table 6 shows the resultant
quality-adjusted output index, which will be displayed in Figure 3 below along with theoutput index with quality improvements calculated below.
Table6 Output index: Without quality improvementyear

independent

2002
2003
2004
2005
2006
2007
2008
2009

1,151.5
1,125.9
1,152.4
1,181.2
1,243.1
1,303.9
1,367.0
1,425.7

Requiring
Support 1
32.9
34.6
25.6
10.6
3.6
0.5
0.0
0.0

Requiring
Support 2/Requiringlong-termcare 1
46.2
64.5
69.4
50.2
40.5
13.6
1.9
0.2

Requiring
long-termcare 2
12.9
23.7
30.2
33.8
30.7
30.5
11.3
1.3

15

Requiring
long-termcare 3
5.5
10.7
12.0
20.7
18.8
19.9
17.7
5.1

Requiring
long-termcare 4
1.4
5.7
6.1
9.9
10.4
13.0
15.6
11.7

Requiring
long-termcare 5
0.3
0.5
0.6
1.6
2.2
3.0
4.4
7.0

Total ofQOL
1,250.6
1,265.6
1,296.3
1,308.1
1,349.1
1,384.5
1,417.9
1,451.0

Outputindex（excludingyear
dummy）
1.000
1.012
1.037
1.046
1.079
1.107
1.134
1.160

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

We repeat the same procedure, but this time incorporating the contribution fromthe quality improvement. Table 7 shows the results.
Table7 Probability of each care level status: With quality improvement

Year

independent

2002
2003
2004
2005
2006
2007
2008
2009

90.71%
88.59%
89.86%
89.14%
92.13%
92.04%
91.45%
91.46%

Care level
Requiring
Requiring
Requiring
Requiring
Requiring
Support 2
Requiring
long-term care long-term care long-term care long-term care
/Requiring
Support 1
2
3
4
5
long-term care
1
2.65%
4.02%
1.29%
0.69%
0.32%
0.32%
2.58%
4.64%
1.82%
1.12%
0.85%
0.41%
2.38%
4.48%
1.55%
0.86%
0.59%
0.28%
1.84%
4.52%
1.98%
1.04%
1.05%
0.44%
1.56%
3.20%
1.10%
0.53%
0.91%
0.55%
1.60%
3.06%
1.27%
0.64%
0.68%
0.70%
1.36%
3.28%
1.65%
0.78%
0.62%
0.87%
0.91%
3.12%
1.80%
0.97%
0.84%
0.89%

Total

100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%

Now, we translate the hypothetical probabilities without quality change into thenumber of elderly people in each care level category by multiplying the total number of
elderly by estimated and hypothetical probabilities.
We further multiply the number of the elderly in each category by the quality oflife for each category. Resulting numbers are hypothetical outputs of long-term carewith quality improvements. Table 8 shows the results.
Table8 Output index: With quality improvementyear

independent

2002
2003
2004
2005
2006
2007
2008
2009

1,151.5
1,155.5
1,204.1
1,227.3
1,311.8
1,355.2
1,392.3
1,440.0

Requiring
Support 1
32.9
32.9
31.2
24.8
21.8
23.1
20.2
14.1

Requiring
Support 2/Requiringlong-termcare 1
46.2
54.7
54.3
56.3
41.3
40.8
45.1
44.4

Requiring
long-termcare 2
12.9
18.7
16.3
21.4
12.4
14.8
19.7
22.4

Requiring
long-termcare 3
5.5
9.1
7.2
9.0
4.7
5.9
7.4
9.5

Requiring
long-termcare 4
1.4
3.8
2.7
4.9
4.4
3.4
3.2
4.5

Requiring
long-termcare 5
0.3
0.4
0.3
0.4
0.5
0.7
0.9
0.9

Total ofQOL
1,250.6
1,275.0
1,316.2
1,344.1
1,396.9
1,443.8
1,488.9
1,535.9

Output
index
1.000
1.020
1.052
1.075
1.117
1.155
1.191
1.228

Figure 3 exhibits the estimated output indexes with and without quality adjustment.
Both indexes starts at 1 in 2002 as a result of normalization. The output index without
quality improvement increased to 1.16 in 2009, while the index with quality
improvement increased to 1.228 in 2009. The difference is the contribution of quality
improvement, which is substantial.

16

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Figure 3 Output index

1.28

output index(2002=1.0)

1.24

output index

1.20
output index(excluding year dummy )
1.16
1.12
1.08
1.04
1.00
0.96
2002

2003

2004

2005

2006

2007

2008

2009

The output of long-term care services increased steadily even before theadjustment of the quality of care. After the quality adjustment, the output index
increased more rapidly. The overall conclusion is that the direct method of output
measurement is a promising way for non-market service sectors and quality adjustment
is potentially very important.

7. Conclusion
The long-term care service sector is growing rapidly in Japan. However, themeasurement of its output is problematic since traditional measures adopt cost-based
approaches or double-deflation method with dubious deflators. This paper exemplified
the direct method of measuring the output of long-term care services, which directly
measures output by aggregating the volume of services each unit of measurement
consumes and, additionally, by assigning value of the services to each unit.
We started with (i) the estimation of an equation to adjust for risk factors. By
suppressing the effect of time dummies in the estimated equation, we obtained (ii)17New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

estimated probabilities of becoming in need of care when the quality of care is held
constant. Multiplying these probabilities by the number of the elderly gave (iii) the
number of the elderly in each category of care level. Finally, we obtained (iv) output of
long-term care without adjusting for quality improvement by multiplying (iii) above by
QOL for each category.
Next, we went on to adjust for the quality of care by including the effects of time
dummies in the estimated equation. We proceeded in parallel with the above steps to
obtain the quality-adjusted output index.
The output of long-term care services increased steadily even before theadjustment of the quality of care. After the quality adjustment, the output index
increased more rapidly. Overall conclusion is that the direct method of output
measurement is a promising way for non-market service sectors and quality adjustment
is potentially very important.

18

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Appendix: General Description of the Conditions of the Elderly Who Require
Support/Long-term CareFirst, the elderly are classified into three broad categories, Independent, Requiring
Support and Requiring Long-term Care. Then, Requiring Support is divided into two
subcategories and Requiring Long-term Care into five.

1. Independent (Requiring neither support nor care)
Basic activities of daily living such as walking and standing up can be performed
independently and procedural activities of daily living such as taking medicine andmaking a phone call can be done.
2. Requiring Support
Basic activities of daily living can be performed basically independently but some
support is needed for procedural activities of daily living to prevent becoming in needof long-term care.
2-1. Requiring Support 1
Basic activities of daily living can be performed basically independently but some
support is needed concerning standing up, getting up, and standing on one foot.
2-2. Requiring Support 2
Compared with the Requiring Support 1, the ability to perform basic activities of dailyliving such as walking, body washing, keeping track of finances and clipping nails has
deteriorated but possibly improved.
3. Requiring Long-term Care
Basic activities of daily living cannot be performed independently and long-term care isneeded.
3-1. Requiring Long-Term Care 1
The same as Requiring Support 2 but their conditions will remain.

19

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

3-2. Requiring Long-Term Care 2
In addition to the condition of the Requiring Long-Term Care 1, care of basic activities
of daily living is partially needed concerning wear/pull off trousers, moving and daily
decision making.
3-3. Requiring Long-Term Care 3
Compared with the Requiring Long-Term Care 2, the ability to perform both basic andprocedural activities of daily living has deteriorated significantly concerning washing
face, grooming one’s hair, oral care, urination/defecation and transferring from one
place to another and overall long-term care is needed.
3-4. Requiring Long-Term Care 4
In addition to the condition of the Requiring Long-Term Care 3, capabilities of
movement have deteriorated and dietary intake and communication become difficult sothat daily living is difficult without long-term care.
3-5. Requiring Long-Term Care 5
Capabilities of movement have deteriorated further from the Requiring Long-Term Care
4 and swallowing and memorization/understanding become difficult so that daily living
is almost impossible without long-term care.

20

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

Appendix Table A1
Area

Level

Description

Mobility123

No problems walking about
Some problems walking about
Confined to bed

Self-care1
2
3

No problems with self-care
Some problems washing or dressing self
Unable to wash or dress self

Usual activity

12
3

No problem with performing usual activities (eg. Work, study, housework, family or leisure activities)
Some problems with performing usual activities
Unable to perform usual activities

Appendix Table A2
Variable

Value of variable

Estimated coefficientaConstant any move away from full health

0.081

MO

1
2
0

If mobility is level 2
If mobility is level 3
Otherwise

0.069

SC

1
2
0

If self-care is level 2
If self-care is level 3
Otherwise

0.104

UA

1
2
0

If usual activity is level 2
If usual activity is level 3
Otherwise

0.036

M2

1
0

If mobility is level 3
Otherwise

0.176

S2

1
0

If self-care is level 3
Otherwise

0.006

U2

1
0

If self-care is level 3
Otherwise

0.022

21

New ESRI Working Paper No.41
Measuring the Output of Long-Term Care Services

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