New ESRI Working Paper No.42

State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

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.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

State Dependence of Long-Term CareandPreventive Effects of Care Expenditures

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.
121

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Abstract
How to provide long-term nursing care to the elderly is a major policy issue worldwide.
Japan, with its highly aged society, is a nice laboratory of long-term care policies. The
Japanese long-term care insurance system has emphasized prevention of progression offrailty of the elderly who have the risk of falling into the conditions of being in need ofcare. The notion of preventive effects of long-term care is potentially important not only
for individuals but also for the society through reduced costs. Preventive effects take on
more importance when deteriorated conditions tend to entail further deterioration (state
dependence).
This paper investigates the preventive effects of long-term care expenditures aswell as the degree of state dependence. Long-term care expenditures are found to
significantly ameliorate care needs. We also confirmed state dependence of frailty.
When the sample is restricted to the elderly with less severe conditions, preventive
effect is stronger than for all the elderly. This result confirms our hypothesis: the earlier,the better.

2

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

1. Introduction
How to provide long-term nursing care to the elderly is a major policy issue worldwide.
In Japan, in particular, thanks to its already highly aged society, the burden of long-termcare is immense both for the households and for the society as a whole. Long-term carepolicies have tried to mitigate the severity and costs of long-term care without muchsuccess. The quantity and quality of care are perceived inadequate while costs areinexorably increasing. Rigorous analysis with detailed data is lacking to remedy thissituation. Decision makers in Japan require much better information on the effect andefficiency of long-term care expenditures. The Japanese experience is valuable also forother countries because they, too, are experiencing or will experience the same
quagmire.
The Japanese long-term care insurance system has emphasized prevention ofdeterioration of the conditions of the elderly who have the risk of being in need of care.
In fact, the insurance provides not only for long-term care expenditures but also forpreventive expenditures. The former is expenditures to provide long-term care and thelatter is those to prevent the elderly from falling into the condition where long-term careis needed. In the system, a category, “Requiring Support,” is created for those who havethe risk of deteriorating but not yet in need of long-term care. Strictly speaking, theelderly in this category already suffer from a slight physical and/or mental disorder. In
general, therefore, long-term care expenditures are expected to prevent the conditions of
the elderly from deteriorating further when such care is provided in early stages offrailty stemming from old age. Here, “prevention” can conceptually include services for
those who are already in need of long-term care.
The emphasis on prevention is unique to the Japanese system. The German system,
for example, covers relatively severe conditions only. In the case of health care,prevention of diseases is considered very important. In contrast, long-term care tends tobe regarded only as taking care of the elderly who have already suffered from severe
frailty and who have no hope of redeeming more favorable conditions. However, by
preventing bedsore or bed-ridden inactivity, for example, long-term care can avoid
deterioration of frailty and can ameliorate the condition of the elderly. The notion of
preventive effects of long-term care is potentially important not only for individuals but
also for the society through reduced costs.

3

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Preventive effects take on more importance when deteriorated conditions tend toentail further deterioration: once an elderly’s condition deteriorates, she tend to remainfrail or even to become worse on top of the initial deterioration. This phenomenon,
called state-dependence, is one of the key hypotheses this paper is going to investigate.
The other hypothesis we focus on is that long-term care has preventive effects. A
difficult question is that it is not easy to pin down the preventive effects in the presenceof endogeneity of care expenditures. Long-term care may prevent deterioration of theelderly’s conditions and, hence, may contribute to the reduction of care expenditures.
Here, however, comes a problem of reverse causality. An elderly who has a severe
frailty will consume a lot of long-term care, which induces a positive relationshipbetween care expenditures and deteriorated conditions. The problem is that careexpenditures correlate with unobserved heterogeneity in the error term due toendogeneity. Note that lagged care levels in the dynamic panel model also give rise tothis kind of correlation. As we will see later, empirical studies in Japan have obtained
mixed results although they make great efforts to statistically estimate causal effects.
This paper investigates some preventive effects of long-term care in the Japanesecare insurance system. We take into account state dependence of care needs by utilizing
dynamic panel data. We adopt the estimation method proposed by Wooldridge (2005) tocontrol endogeneity, or correlation between unobserved heterogeneity and explanatory
variables. We further try to adjust for attrition bias following Albert andFollmann(2003).
The paper is organized as follows. Section 2 introduces our conceptual frameworkand hypotheses. Section 3 reviews existing literature and 4 describes the institutionalfeatures of the Japanese long-term care insurance system. Section 5 explains the data
sources and Section 6 provides descriptive statistics. Section 7 presents the model andSection 8 gives the results. Section 9 concludes.

2. Conceptual Framework and Hypotheses
Figure 1 depicts our conceptual framework. An elderly i with a long-term care level j attime t-1 will transit to a care level j’ at time t. Various factors affect this transition
including age and pre-existing illness. Long-term care is expected to moderate the4New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditurestransition to higher care level through preventive effects.
Figure 1 Conceptual Frameworkｔｔ－１[State dependence]

Frailty in theprevious period

Long-term careexpenditures

Frailty in thecurrent period

Age
Disease[Preventive effect]

Our main hypotheses are as follows. First, effects of shocks to physical and/or
mental conditions are persistent. Once an elderly’s condition deteriorates, she tends toremain feeble or even to become worse after that. This phenomenon is called state
dependence.
Second, long-term care expenditures have preventive effects against worsening
care level. As will be explained below, the Japanese long-term care insurance systemcovers both long-term care proper and care for prevention. The idea is that if preventive
care can prevent the elderly from requiring more and more heavy long-term care, such
expenditures would be cost effective and worth spending. Two sub-hypothesis are: onthe one hand, such preventive effects are stronger for home care than for facility care.
On the other, preventive care is more effective when implemented in early stages offrailty than when the person is already in an advanced stage.

3. Literature Review
State Dependence
Literature on state dependence of health is vast. Jones, et al. (2006a) provides a survey.
Most closely related to our paper is Contoyannis, et al. (2004), which investigates the5New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

dynamics of self-assessed health. The paper utilizes dynamic panel ordered probit
models, which include lagged health status as an explanatory variable to capture state
dependence. To allow for the possibility that the observed regressors may be correlatedwith the individual random effect, the individual random effects are parameterized as inMundlak (1978), Chamberlain (1984) and Wooldridge (2005). They found substantial
positive state dependence. Another example which explores state dependence is Heiss,
et al. (2009). They analyze transition matrix for self-reported health, which is assumed
to depend on a latent health variable, and find that future paths of health and disability
are very strongly related to health and disability at age 50.
Care Expenditures and Outcomes
We are unaware of any English literature that examines the effect of long-term careexpenditures and outcomes. A few papers study the relationship between health careexpenditures and health outcomes. Martina, et al. (2007), for example, examines
whether health spending improves health outcomes employing instrumental variables
methods and finds that the cost of a life year saved in cancer is about ￡13,100 and incirculation about ￡8,000, which challenges the traditional view that health care has
little marginal impact on health.
The relationship between long-term care expenditures and outcomes is studied in
the context of the Japanese long-term care insurance system. Tajika and Kikuchi(2003)
analyzes effectiveness of the long-term care utilization to sustain or improve elderly’s
long-term care levels in early stages of frailty. They do not adjust for selection bias bystatistical techniques such as propensity score matching or instrumental variables. They
did not observe preventive effects of care utilization. Yuda, et al. (2013) investigates theeffects of the introduction of preventive long-term care benefits on the care level of theelderly in the very early stage of frailty. They utilize the propensity score matching
method to control for selection. It should be noted, however, this method is valid only
for selection on observables. They find that some of the preventive long-term caresignificantly sustain or improve the conditions of the elderly requiring help.
Attrition
Jones, et al. (2006b) documents health-related non-response in the British Household
Panel Survey and utilizes an inverse probability weighted estimator as is proposed by
Wooldridge (2005). They find evidence for non-response bias, which, however, turns
out to be inconsequential.
6New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

4. Institutional Description
The Japanese long-term care insurance system covers, primarily, elderly people aged
above 65 years old and above. People of age between 40 and 64 years old also enroll in
the insurance. To obtain benefits a policyholder need to be certified as Requiringsupport or Requiring Long-term care by the insurer (municipality). Requiring Support isthe 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 whose basic activities of daily living cannot be performed
independently and long-term care is needed.
The certification is made for Requiring support levels 1 to 2 5 and Requiring
Long-term care levels 1 to 5 6. (See Appendix) These categories are defined in terms ofthe time needed to take care of the elderly, not in terms of the severity of the conditionof the elderly. However, a positive correlation is observed between Support/Care Levels
and frail conditions of the elderly (Tajika and Kikuchi, 2003). The Support level 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 Care level 5 is the most frail who, in
typical cases, capabilities of movement have deteriorated so severely that daily living isalmost impossible without long-term care. Tajika and Kikuchi (2003) points out that theCare level 3 is the threshold between mild and severe conditions. They classify theelderly with less than and equal to Care level 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 ofcare. One is home care, the other facility care. Home care includes home-visit care, daycare, short-term admission to facilities and rental welfare equipment.
5
6

Sometimes referred to as “Support Level 1(2)”.
In the following, sometimes referred to as “Care Level 1(-5)”.
7

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

5. Data
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 7 have been
invited to participate in baseline studies and follow-up surveys and medical
examinations. The medical examination is called the Nikkori (Smile) examination and isheld at a local public health center once a year. The survey is called the Iki-iki (Lively)
survey and is conducted every two years. These surveys and examinations containdetailed physical and medical information including diseases that the elderly had
suffered or is suffering from currently. In particular, they include information on
pre-existing stroke and hypertension, which we will use as explanatory variables in theestimation. Actually, Levine, et al. (2014) documents that myocardial infarction andstroke hospitalizations are associated with significant increases in functional disability.
All participants provided written informed consent under conditions approved by the
Ethics Committee at the Tokyo Metropolitan Institute of Gerontology.
The physical and medical information is linked to the information on the long-termcare benefits approved by the long-term care insurance system. The latter information
also includes the Support Level or Care Level if the elderly is certified as Requiring
Support or Requiring Long-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 suffered a stroke in a year, she isjudged to have a pre-existing stroke after the beginning of that year and not before that.

6. Descriptive Statistics
Table 1 shows basic statistics of the sample used for the estimation; from 2006 to 2009.
The average age is 76.4 years old. As for the preexisting conditions, 11 per cent of theelderly has suffered from stroke, currently or in the past, and 46 per cent fromhypertension.

7

Up to 2005, 70 years or older.
8New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table 1 Descriptive Statistics
2006Q3-2009Q4
Age
Sex (1:male 2:female)
Stroke (0:No 1:Yes)
Hypertension (0:No 1:Yes)
Care level(current)

Obs
Mean Std. Dev.
19,30376.38
6.96
19,3031.57
0.49
19,3030.11
0.31
19,3030.46
0.50
19,303
1.40
1.28

2006
Obs

2007
Mean

Obs

2008
Mean

Obs

2009
Mean

Obs

Mean

1,354
1,354
1,354
1,354
1,354

76.49
1.58
0.11
0.40
1.31

1,423
1,423
1,423
1,423
1,423

76.37
1.58
0.11
0.44
1.33

1,448
1,448
1,448
1,448
1,448

76.50
1.58
0.11
0.47
1.31

1,421
1,421
1,421
1,421
1,421

76.88
1.58
0.11
0.47
1.33

17,136
1,509
658(share)
88.8%
7.8%
3.4%

1,188
126
40

87.7%
9.3%
3.0%

1,249
128
46

87.8%
9.0%
3.2%

1,279
129
40

88.3%
8.9%
2.8%

1,251
121
49

88.0%
8.5%
3.4%

Requiring support 1

336

1.7%

42

3.1%

43

3.0%

43

3.0%

39

2.7%

Requiring support 2/ Requiring long-term care 1

760

3.9%

59

4.4%

49

3.4%

47

3.2%

47

3.3%

Requiring long-term care 2

413

2.1%

25

1.8%

36

2.5%

39

2.7%

35

2.5%

Requiring long-term care 3

251

1.3%

22

1.6%

18

1.3%

17

1.2%

19

1.3%

Requiring long-term care 4

280

1.5%

11

0.8%

19

1.3%

18

1.2%

20

1.4%

Requiring long-term care 5

127

0.7%

7

0.5%

9

0.6%

5

0.3%

10

0.7%

Long-term care expenditure 1)2)
in which
Home care expenditure
Faciliy care expenditure

2,167

14.21

10.73

166

13.59

174

13.64

169

14.39

170

14.31

2,167
2,167

8.95
5.26

9.40
10.66

166
166

8.32
6.29

174
174

8.69
5.72

169
169

9.47
5.72

170
170

9.39
5.47

Independent
Mild(～Requiring Care 2)
Severe(Requiring Care 3～)1) Care expenditure : not includes "Independent"
2) 10 thousand yen

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 1.40.
The share of the elderly in each frailty condition is 88.8 per cent for the elderlies
who do not need support or care (Independent). As for Requiring Support/Careconditions, we aggregate categories in accordance with Tajika and Kikuchi (2003):
aggregate categories from the Support Level 1 to the Care Level 2 into “Mild” while
aggregating categories above the Care Level 3 into “Severe.” The share is 7.8 per centfor the mild care level and 3.4 per cent for the severe care level. Below these figures, theratio for each category is shown.
Care expenditures 8 per elderly who are authorized as Requiring Support orLong-term Care are 142,100 yen for the whole period. When divided into two
categories, home care expenditures are 89,500 yen and facility care expenditures are
52,600 yen.

8

In this paper, “long-term care expenditures” include the expenditures spent by theelderly in the category Requiring Support.
9New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

To provide a long-term perspective, we show the data from 2002 to 2009 in Figure
2. For the whole data period, the average age is 76.3 years. The average age has
increased rapidly from 75.6 years in 2002 to 76.5 years in 2006. This trend continues inthe estimation period, from 2006 to 2009, although at a slightly decelerated rate (76.9
years in 2009).
Figure 2 Age and Pre-existing diseases: Stroke and Hypertension
77

0.5

76.5

0.4

76

0.3

75.5

0.2

75

0.1

74.5

0
2002
2003
Age(left scale)

2004
2005
Stroke(right scale)

2006

2007
2008
Hypertension(right scale)2009

Ten per cent of the elderly has suffered from stroke, currently or in the past, and 41
per cent from hypertension for the whole data period. From 2002 to 2006, the ratios forstroke rose from 5 per cent to 11 per cent and that for hypertension from 34 per cent to40 percent. After 2006, these ratios are stable for stroke (11 per cent in 2009) andincreasing for hypertension (47 per cent in 2009).
The mean of the frailty points, the overall degree of frailty of the elderly which is
calculated as above, is 1.29 (not shown). This index rose from 1.17 in 2002 to 1.31 in
2009. After 2006, its movement is a little erratic, but it seems that the rising trend
continued (1.33 in 2009).
Figure 3 shows the trend in the share of the elderly in each frailty condition. The
trends suggest an increasing frailty during the period. The elderly who do not needsupport or care (Independent) account for 88.3 per cent in the whole period. The shareof the Independent category declined from 91.4 per cent in 2002 to 86.9 per cent in2005 before slightly increased after 2006 (88.0 per cent in 2009). The share of the “Mild”
10New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

category is 9.2 per cent over the whole period with a rise from 7.8 per cent in 2002 to
9.3 per cent in 2006 and a decline thereafter (8.5 per cent in 2009). On the other hand,the share of the “Severe” category is 2.5 percent over the whole period with acontinuously rising trend throughout the period from 0.9 percent in 2002 to 3.4 percent
in 2009 although the trend slightly decelerated after 2006.
Figure 3 Distribution of Care Levels: Independent, Mild and Severe
0.12

0.92

0.1

0.9

0.08

0.88

0.06

0.86

0.04

0.84

0.02

0.82

0

0.8
2002

2003

2004

2005

2006

Mild(~Requiring long-term care 2)(left scale)

2007

2008

2009

Severe(Requiring long-term care 3~)(left scale)

Independent (right scale)Care expenditures per elderly who are authorized as Requiring Support orLong-term Care are 130,000 yen for the whole period. Figure 4 shows the trend of careexpenditures. They increased from 110,000 yen in 2002 to 136,000 yen in 2006
although the increase after 2006 is slightly subdued (143,000 yen in 2009). Whendecomposed into home care and facility care expenditures, the former is 82,000 yen
while the latter is 57,000 yen for the period as a whole. Home care expenditures
increased steadily from 65,000 yen in 2003 9 to 83,000 yen in 2006 (939,000 yen in2009). On the other hand, facility care expenditures, first, increased from 55,000 yen in
2002 to 63,000 yen in 2006 and, then, decreased to 55,000 yen in 2009.

9

A sharp drop from 2002 to 2003 is likely to be an anomaly.
11

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Figure 4 Care Expenditures: Total, Home Care and Facility Care
16

(10 thousand yen)

14
12
10
8
6
4
2
0
2002

2003

2004

2005

Care expenditure Home care expenditure

2006

2007

2008

Care expenditure Faciliy care expenditure

2009

Care expenditure

Table 2 is a matrix which 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 level 1, 0.5 percent the support level 2, and so on. The large
percentage figures on the diagonal indicate that people tend to find themselves in thesame 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. 10 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 (current)

Care level (t-4)

independent

Requiring
Support 1

Requiring
Support 2

Requiring
long-termcare 1Requiring
long-termcare 2Requiring
long-termcare 3Requiring
long-termcare 4

Requiring
long-termcare 5

Total
death

independent

97.0%

0.7%

0.5%

0.4%

0.3%

0.2%

0.2%

0.1%

0.6%

100.0%

Requiring Support 1

2.2%

57.0%

21.9%

9.6%

5.6%

1.5%

0.4%

0.0%

1.9%

100.0%

Requiring Support 2

0.0%

13.5%

45.1%

21.1%

7.6%

4.2%

3.4%

2.1%

3.0%

100.0%

Requiring long-term care 1

0.0%

4.2%

15.8%

41.0%

24.8%

7.9%

2.2%

0.7%

3.5%

100.0%

Requiring long-term care 2

0.0%

2.1%

3.3%

16.6%

51.7%

13.6%

9.1%

0.9%

2.7%

100.0%

Requiring long-term care 3

0.0%

1.3%

2.6%

5.7%

8.8%

43.6%

25.1%

7.5%

5.3%

100.0%

Requiring long-term care 4

0.0%

0.0%

0.5%

0.0%

10.1%

11.6%

61.1%

11.6%

5.1%

100.0%

Requiring long-term care 5

0.0%

0.0%

2.8%

0.0%

0.0%

8.3%

13.8%

67.9%

7.3%

100.0%

88.6%

1.6%

1.7%

1.9%

2.0%

1.2%

1.4%

0.7%

0.9%

100.0%Total

The transition from Care Level 5 to Support Level 2 is an amazing exception. (It israre, to be sure.) This case is an anomaly due to a small sample size.

10

12New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

7. The Model
The dependent variable is the indicator variable which shows the level of need forsupport or care. On top of the independent state where there is no need for support nor
care, there are two categories of Requiring support and five categories of Requiring
Long-term Care so that 𝑦𝑦𝑖𝑖𝑖𝑖 = {1, 2, … ,8} with 1 indicating the independent state and 8
Requiring Long-term care 5. To model this categorical variable, an ordered probit model

is employed because there is a natural order in it. To incorporate state dependence,
lagged dependent dummy variables (𝑦𝑦𝑖𝑖2𝑡𝑡 through 𝑦𝑦𝑖𝑖8𝑡𝑡) are included as an explanatory
variable.
The latent variable model is𝑦𝑦𝑡𝑡∗ = 𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖 ,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 + 𝑢𝑢𝑖𝑖𝑖𝑖.
𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1(1)

𝑗𝑗 = 2, ･･･, 8

Cut points for respective categories are

𝛼𝛼1 < 𝛼𝛼2 < ⋯ < 𝛼𝛼𝐽𝐽 .

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

y=2
y=3

y=8

if 𝑦𝑦 ∗ ≤ 𝛼𝛼1

if 𝛼𝛼1 < 𝑦𝑦 ∗ ≤ 𝛼𝛼2
if 𝛼𝛼2 < 𝑦𝑦 ∗ ≤ 𝛼𝛼3⋮
if 𝑦𝑦 ∗ > 𝛼𝛼𝐽𝐽

Probability distributions are specified as normal distribution, Φ(. ).

P�𝑦𝑦𝑖𝑖𝑖𝑖 = 1|𝑧𝑧𝑖𝑖𝑖𝑖 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 � = Φ([𝛼𝛼1 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 )]P(𝑦𝑦𝑖𝑖𝑖𝑖 = 2| ∙)= Φ�𝛼𝛼2 − �𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 �� − Φ([𝛼𝛼1 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 )]⋮P�𝑦𝑦𝑖𝑖𝑖𝑖 = 𝐽𝐽|𝑧𝑧𝑖𝑖𝑖𝑖 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 � = 1 − Φ([𝛼𝛼𝐽𝐽 − (𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾 + ∑8𝑗𝑗=2 𝜌𝜌𝑗𝑗 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐𝑖𝑖 )]13(2)New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Explanatory variables include age, sex and preexisting conditions such as strokeand hypertension. As we mentioned previously, Levine, et al. (2014) documents thatmyocardial infarction and stroke hospitalizations are associated with significant
increases in functional disability and we can use hypertension as a surrogate indicator ofMI.
A dummy for each quarter is included to control for factors which are specific toeach period, for example, quality of care in the long-term care insurance system. To
mitigate wild variations of quarter dummies, autoregressive restriction is imposed.
Specifically, the dummy, 𝜆𝜆𝑡𝑡, for each period is distributed as normal whose mean, 𝑚𝑚𝜆𝜆𝑡𝑡 ,depends on the realized value of the dummy for the previous period.
2

𝜆𝜆𝑡𝑡 ~ 𝑁𝑁(𝑚𝑚𝜆𝜆𝑡𝑡 , 𝜎𝜎𝑡𝑡𝜆𝜆 )𝑚𝑚𝜆𝜆𝑡𝑡 = 𝛿𝛿𝑡𝑡 ∙ 𝜆𝜆𝑡𝑡−1

(3)
(4)

Contoyannis, et al. (2004) adopts the method proposed by Wooldridge(2005) also
to control for the initial value problem. The initial value problem occurs when the
regression equation includes the lagged dependent variable as an independent variable,
in which case the dependent variable at time zero, 𝑦𝑦0 , is out of the model and how tomodel the correlation between 𝑦𝑦0 and the unobserved heterogeneity is problematic. Of
course, the correlation between the dependent variable and the lagged dependent
variable through the unobserved heterogeneity is a more general problem in the
dynamic panel data model. In the likelihood or Bayesian framework, the unobserved

heterogeneity is given a distribution and multiplied out as is described in Wooldridge(2002). The correlation between the initial value, 𝑦𝑦0 , and the unobserved heterogeneity
is not modeled, however. Hence, we have to worry about that correlation.
Wooldridge (2005) proposes that the unobserved heterogeneity be modeled as
dependent on the initial value, 𝑦𝑦0 , in addition to strictly exogenous variables in themodel, 𝑧𝑧𝑖𝑖 = {𝑧𝑧𝑖𝑖1 , … , 𝑧𝑧𝑖𝑖𝑖𝑖 }. 11 In actual implementation, as described in Wooldridge(2005), we can estimate the mode by including 𝑧𝑧̅𝑖𝑖 in explanatory variables at each time

period, where 𝑧𝑧̅𝑖𝑖 is the average over the sample period of explanatory variables for anindividual i.
Wooldridge’s method is an extension of the method proposed by Chamberlain (1980),
which in turn adopts an idea contained in Mundlak (1978) to the case of the initialvalue problem.

11

14

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expendituresor𝑐𝑐𝑖𝑖 |𝑧𝑧𝑖𝑖, 𝑦𝑦𝑖𝑖0 ~𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁(𝜆𝜆1 + 𝑧𝑧̅𝜆𝜆2 + ∑8𝑗𝑗=2 𝜆𝜆3𝑗𝑗 ∙ 𝑦𝑦𝑖𝑖,𝑗𝑗,0 , 𝜎𝜎𝑎𝑎2 )(5)𝑐𝑐𝑖𝑖 = 𝜆𝜆1 + 𝑧𝑧̅𝜆𝜆2 + ∑8𝑗𝑗=2 𝜆𝜆3𝑗𝑗 ∙ 𝑦𝑦𝑖𝑖,𝑗𝑗,0 + 𝑎𝑎 𝑖𝑖 , 𝑎𝑎 𝑖𝑖 ~𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁(0, 𝜎𝜎𝑎𝑎2 ).

(6)

Substituting equation (6) into equation (1) gives the equation to be estimated.
Wooldridge (2005) points out that these explanatory variables, 𝑧𝑧𝑖𝑖 = {𝑧𝑧𝑖𝑖1 , … , 𝑧𝑧𝑖𝑖𝑖𝑖 },included in the modeling of the unobserved effect must be strictly exogenous
conditional on 𝑐𝑐𝑖𝑖 in the following sense: for t = 1, 2, ．．．，T,

E (𝑦𝑦𝑖𝑖𝑖𝑖│𝑧𝑧𝑖𝑖1 , … , 𝑧𝑧𝑖𝑖𝑖𝑖, 𝑐𝑐𝑖𝑖) = E (𝑦𝑦𝑖𝑖𝑖𝑖│𝑧𝑧𝑖𝑖𝑖𝑖, 𝑐𝑐𝑖𝑖 ).

(7)

Strict exogeneity requires that the explanatory variable not correlate with thedependent variable for all leads and lags conditional on the unobserved heterogeneity. In
our case, explanatory variables include lagged long-term care expenditures. We have tocheck the exogeneity of lagged expenditures in two respects. On the one hand, lagged
long-term care expenditures share the unobserved heterogeneity with the dependent
variable. On the other hand, care expenditures without lags are simultaneously
determined with the care level, 𝑦𝑦𝑖𝑖𝑖𝑖 so that, analogously to simultaneous equation bias,
past and future expenditures are correlated with the care levels. Concerning the first
aspect, as is explained in Wooldridge (2002) using an example of production function,
lagged long-term care expenditures can be assumed to be exogenous once conditionedon the unobserved effect although they are not exogenous when not conditioned on theunobserved effect. As for the second aspect, we use lagged expenditures in the
regression model so that simultaneity is eliminated.
Prior distributions for the coefficient, 𝜌𝜌𝑗𝑗 , on the lagged care level, 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 , and thecoefficients, 𝛾𝛾, on explanatory variables, 𝑧𝑧𝑖𝑖𝑖𝑖 , including the lagged long-term careexpenditures together with the unobserved heterogeneity, 𝑎𝑎 𝑖𝑖, are assumed to be normal
distributions with mean zero and variance 1000: take a generic coefficient µ , then,µ ~ N (0,1000) . The choice of the variance of 1000 is intended to represent a diffuse
prior. Gelman and Hill (2007) give a thoughtful discussion on the appropriateness of
this value in the context of the logistic models or log-transformed regressors. They
argue that in logistic and logarithmic regressions, typical changes in outcomes are on
15

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

the scale of 0.1 or 1, but not 10 or 100, so that one would not expect to see coefficientsmuch higher than 10 in absolute values as long as the regressors are also on areasonable scale. Although their choice of the value of variance is 1002 , we believe that
their argument applies to our choice, 1000.
2

Prior distribution on the variance, 𝜎𝜎𝑡𝑡𝜆𝜆 , of the time dummy, 𝜆𝜆𝑡𝑡, is specified so as toits standard deviation , 𝜎𝜎𝑡𝑡𝜆𝜆 , is uniformly distributed over the domain (0, 100). Prior
distribution for the unobserved heterogeneity, 𝑎𝑎 𝑖𝑖, is also specified so as to its standard
deviation , 𝜎𝜎𝑎𝑎2, is uniformly distributed over the domain(0,100). The range of 0 to 100
is chosen, again, in view of the argument made by Gelman and Hill (2007). Uniform
prior on standard deviation is generally the preferred prior by practitioners. 12 While we

could have also applied uniform priors to the coefficients on the lagged care level andother explanatory variables, we adopted more conventional and slightly more
informative priors for these variables as was explained above. Prior distribution on thecoefficient, 𝛿𝛿𝑡𝑡, of the AR process of time dummies, 𝜆𝜆𝑡𝑡, are more stringent N (0,10)
because we would like to tighten the variation of time dummies.

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.
The Missing data mechanism is modeled as the shared random effect model, in
which the observation mechanism is independent of the missing data mechanism
conditional on the unobserved random effect (Daniels and Hogan, 2008). Dropping thesuffixes, the decomposition of the joint probability of the dependent variable, y, and theindicator of missing data, r, conditional on the explanatory variables, x, can be
represented as𝑝𝑝(𝑦𝑦, 𝑟𝑟 | 𝑥𝑥) = ∫ 𝑝𝑝(𝑦𝑦, 𝑟𝑟 | 𝑏𝑏, 𝑥𝑥)𝑝𝑝(𝑏𝑏) 𝑑𝑑𝑑𝑑.

(8)

The missing data mechanism is molded à la Albert and Follmann (2003). Missing
data are categorized into two patterns: missing intermittently and dropped out. In theformer case, an individual is sometimes missing and sometimes observed. In the latter
case, an individual will never be observed after her observation is first missed. The drop
Spiegelhalter, et al. (2004) contains a detailed discussion on the prior for the
standard deviation of the random effects.

1216New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expendituresout category includes the cases of death, moving out of the town and cause unknown. 87
percent of the elderly did not drop out, while 0.9 percent experienced intermittent
sassing and 12 percent dropped out.
𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜0
𝑅𝑅 𝑖𝑖𝑖𝑖 = � 1 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
2𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑜𝑜𝑜𝑜𝑜𝑜
The probability of observed/intermittently missing/dropped out is assumed tofollow a logit distribution starting from the status other than dropped out.
12∑
1+ 𝑙𝑙=1 exp(𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙𝜂𝜂+𝛾𝛾𝑙𝑙 𝑏𝑏 𝑖𝑖)
𝑝𝑝�𝑅𝑅𝑖𝑖𝑖𝑖 = 𝑙𝑙�𝑏𝑏𝑖𝑖 , 𝑅𝑅𝑖𝑖,𝑡𝑡−1 ≠ 2 � = � 𝑒𝑒𝑒𝑒𝑒𝑒(𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙𝜂𝜂+𝛾𝛾𝑙𝑙𝑏𝑏 𝑖𝑖)
1+∑2𝑙𝑙=1 𝑒𝑒𝑒𝑒𝑒𝑒(𝑥𝑥𝑙𝑙𝑙𝑙𝑙𝑙𝜂𝜂+𝛾𝛾𝑙𝑙 𝑏𝑏 𝑖𝑖)

𝑙𝑙 = 0𝑙𝑙 = 1, 2(9)Since l=2 is an absorbing state, the transition probability starting the status ofdropped out is
𝑝𝑝�𝑅𝑅𝑖𝑖𝑖𝑖 = 2�𝑅𝑅 𝑖𝑖,𝑡𝑡−1 = 2� = 1(10)Correlation between random effects, 𝑏𝑏 𝑜𝑜 and 𝑏𝑏 𝑑𝑑, in the shared parameter model is
specified as a multivariate normal distribution with a mean vector M and avariance-covariance matrix Ω. The prior distribution of the diagonal elements, 𝜔𝜔𝑘𝑘𝑘𝑘,

k=1,2, of Ω is assumed to be uniform. The off-diagonal elements, 𝜔𝜔21 = 𝜔𝜔12 , arelinked to the diagonal elements through the definition of the correlation coefficient,which is also assumed to follow a uniform distribution.
𝐵𝐵 ~ 𝑀𝑀𝑀𝑀𝑀𝑀(𝑀𝑀, Ω)𝑏𝑏 𝑜𝑜
𝐵𝐵 ≡ � 𝑑𝑑 � ,𝑏𝑏𝜔𝜔2Ω ≡ � 11𝜔𝜔21

𝑚𝑚𝑜𝑜
𝑀𝑀 ≡ � 𝑑𝑑 �
𝑚𝑚
𝜔𝜔12
�
𝜔𝜔222

𝜔𝜔11 ~ 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(0,100 ), 𝜔𝜔22 ~ 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(0,100 )𝜔𝜔12 ~ 𝜌𝜌 ∙ 𝜔𝜔11 ∙ 𝜔𝜔22, 𝜔𝜔21 = 𝜔𝜔12 ,𝜌𝜌~ 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑( −1,1 )
17

(11)

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Other prior distributions are as follows. The vector of coefficients 𝛽𝛽𝑘𝑘 follows an
independent multivariate normal distribution, whose generic component is

𝛽𝛽𝑘𝑘𝑘𝑘 ~ 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁(0, 0.1). Priors for 𝛿𝛿𝑘𝑘 ,𝜃𝜃𝑘𝑘 , 𝛿𝛿𝑑𝑑 , 𝜃𝜃𝑑𝑑 , 𝜙𝜙𝑎𝑎𝑎𝑎 and 𝜙𝜙𝑑𝑑𝑑𝑑 are normal distribution,
one of which is generically 𝛿𝛿𝑘𝑘 ~ 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁(0, 0.1).

8. Estimation Results
The estimation period is from the third quarter of 2006 to the fourth quarter of 2009. In
total 2,053 elderly are included in the sample.
Results of 6 estimations are presented below. In the first estimation, Requiring
Long-term Care level is regressed on lagged care level dummies 13 , age, sex,
pre-existing stroke and hypertension, lagged care expenditures, quarter dummies,
averages of explanatory variables and the first observed care level dummies. The
averages of explanatory variables are averages of an individual’s care expenditures andpre-existing diseases (stroke and hypertension).
The second estimation adjusts for drop out by simultaneous estimation of the carelevel equation and the drop out equation with shared parameter. The explanatory
variables in both equations are the same as the first estimation. The third estimation
decomposes care expenditures into home care and facility care expenditures, while thefirst and second estimations used total care expenditures.
The fourth estimation restricted sample to the elderly who are in relatively mild
categories, Requiring Support 1 and 2 using total expenditures. These constitute tests of
the hypothesis: the earlier the better. The fifth and sixth estimations restricted thesample to slightly more severe categories, Requiring Long-term Care 1 and 2.
(1) Single equation; Total expenditures
Table 3 shows the results for the estimation of the care level equation. In this firstestimation, we did not adjust for attrition. The lagged care expenditures are total
expenditures without being decomposed into home and facility care expenditures.

In this chapter and Table 1-9,”care level” includes Requiring Support level (1-2) andRequiring Lon-term Care level (1-5).

13

18

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table 3Single Equation (Total long-term care expenditures)
mean

Lagged care level dummy
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
Lagged long-term care expenditures
Age
Sex
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4sd

2.5%

median

97.5%

1.49
2.24
2.97
3.64
4.51
5.27
6.83
-0.04
0.24
-0.07
0.59
-0.14

0.10
0.09
0.09
0.11
0.14
0.20
0.23
0.00
0.17
0.06
0.32
0.15

1.31
2.07
2.78
3.41
4.23
4.90
6.37
-0.04
-0.06
-0.19
-0.04
-0.45

1.49
2.24
2.96
3.64
4.51
5.28
6.83
-0.04
0.23
-0.07
0.59
-0.14

1.69
2.42
3.15
3.86
4.79
5.64
7.27
-0.03
0.61
0.05
1.25
0.16

-1.11
-1.29
-1.13
-1.09
-1.09
-1.20
-1.32
-1.22
-2.35
-0.40
-1.31
-1.14
-1.34
-1.27

1.57
1.56
1.55
1.53
1.52
1.52
1.51
1.50
1.49
1.48
1.50
1.50
1.50
1.50

-4.00
-4.15
-3.98
-3.92
-3.92
-4.02
-4.14
-4.03
-5.14
-3.18
-4.12
-3.95
-4.16
-4.10

-0.22
-0.38
-0.21
-0.18
-0.20
-0.34
-0.50
-0.45
-1.63
0.28
-0.64
-0.50
-0.75
-0.74

0.76
0.53
0.65
0.66
0.62
0.48
0.35
0.44
-0.69
1.26
0.39
0.58
0.41
0.49

The estimated coefficients on the care level in the previous quarter are large andhighly statistically significant. With a significant negative coefficient, care expenditures
have preventive effects against worsening care conditions.
Sex 14 and hypertension tend to be negative, but insignificant. Time dummies arenegative over time which indicates the existence of common factors affecting theindividuals at each period. We may interpret such tendency as representing the qualityof long-term care services.
To provide an indication of the magnitude of the association between current carelevel and lagged care level, we can compute the average treatment effects (ATEs) ofeach category on lagged care level. Wooldridge (2002) computes the partial effect withrespect to a binary data. We extend this idea to ordered probit model as Jones, etal.(2006).

14

1 : Male, 2 : Female
19New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

To obtain the ATEs of each lagged care level, j, on current care level, k, we
compare the probability of being care level, k, including the effects of the lagged, j, withthe probability excluding the effects of the lagged, j.
Specifically, let 𝑞𝑞𝑖𝑖𝑖𝑖 be the probability below k including the effects of thelagged, j, similar, 𝑞𝑞𝑞𝑞𝑖𝑖𝑖𝑖 excluding the effects of the lagged, j. Then the ATEs arecomputed by taking differences of 𝑞𝑞𝑖𝑖𝑖𝑖 and 𝑞𝑞𝑞𝑞𝑖𝑖𝑖𝑖 averaged on individuals. Following
Wooldridge (2002), to account for individual effects, we adjust the original parameters15
�2 )-1/2.
by multiplied by (1 + 𝜎𝜎𝑎𝑎𝑞𝑞𝑖𝑖𝑖𝑖 ≡ 𝜙𝜙� 𝑎𝑎�𝚥𝚥 − �𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾�𝑎𝑎 + 𝜌𝜌�𝑎𝑎 ,𝚥𝚥 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐�
𝑎𝑎𝑎𝑎��
𝑞𝑞𝑞𝑞𝑖𝑖𝑖𝑖 ≡ 𝜙𝜙� 𝑎𝑎�𝚥𝚥 − �𝑧𝑧𝑖𝑖𝑖𝑖 𝛾𝛾�𝑎𝑎 + 𝜌𝜌�𝑎𝑎 ,𝚥𝚥 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 + 𝑐𝑐�
𝑎𝑎𝑎𝑎 − 𝜌𝜌�𝑎𝑎 ,𝚥𝚥 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑡𝑡−1 ��(12)∆𝑗𝑗𝑘𝑘 denotes the ATEs of lagged care level, j, and current care level, k.
if k = 1

1

1

𝑁𝑁∆𝑗𝑗𝑘𝑘 = ∑𝑁𝑁
𝑖𝑖=1 𝑞𝑞𝑖𝑖𝑖𝑖 − ∑ 𝑖𝑖=1 𝑞𝑞𝑞𝑞𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁

if k = 2, … ,7
1

1

1

1

𝑁𝑁
𝑁𝑁
𝑁𝑁
∆𝑗𝑗𝑘𝑘 = ∑𝑁𝑁
𝑖𝑖=1 𝑞𝑞𝑖𝑖𝑖𝑖 − ∑ 𝑖𝑖=1 𝑞𝑞𝑖𝑖,𝑘𝑘−1 − � ∑ 𝑖𝑖=1 𝑞𝑞𝑞𝑞𝑖𝑖𝑖𝑖 − ∑ 𝑖𝑖=1 𝑞𝑞𝑞𝑞𝑖𝑖,𝑘𝑘−1 �𝑁𝑁

if k = 8

𝑁𝑁

1

𝑁𝑁

𝑁𝑁

1

𝑁𝑁
∆𝑗𝑗8 = 1 − ∑𝑁𝑁
𝑖𝑖=1 𝑞𝑞𝑖𝑖7 − �1 − ∑ 𝑖𝑖=1 𝑞𝑞𝑞𝑞𝑖𝑖7 �
𝑁𝑁

𝑁𝑁

(13)

Table 4 shows the ATEs of lagged care level state on the probability of current carelevels. A positive sign implies a positive association with current care level. In general,
the ATEs on the diagonal are higher than the ATEs off the diagonal, which means
current care levels tends to be the same as the previous care levels.
For example, Requiring Long-term Care 2 in previous quarter, the ATE of reported
Requiring Long-term Care 2 (0.327), is higher than other levels.

15

Subscript “a” below denotes the original parameters, and “ � ̂” denotes estimates.
20

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table4

ATE(Average Treatment Effect）on probability of reporting Care level

Care levels (t-1)

Independent

Requiringsupport 1

Requiringsupport 2

Care levels (t)Requiring
Requiring
long-term
long-termcare 1care 2Requiring
long-termcare 3Requiring
long-termcare 4

Requiring
long-termcare 5Requiringsupport 1-0.395-0.088

0.172

0.212

0.088

0.010

0.001

0.000

Requiringsupport 2-0.427-0.227

0.065

0.290

0.237

0.053

0.009

0.000

Requiring
long-termcare 1-0.393-0.297-0.095

0.198

0.364

0.162

0.059

0.003

Requiring
long-termcare 2-0.322-0.320-0.209

0.027

0.327

0.290

0.189

0.019

Requiring
long-termcare 3-0.288-0.325-0.252-0.081

0.149

0.294

0.410

0.094

Requiring
long-termcare 4-0.249-0.310-0.278-0.128

0.026

0.158

0.481

0.300

Requiring
long-termcare 5-0.271-0.320-0.268-0.118-0.019

0.019

0.212

0.765

This confirms the existence of state dependence. This indicates that long-term carelevel has a kind of self-magnifying effects in that once a person gets into a situation
where she needs nursing care; her care level tends to worsen cumulatively. It is likelythat a person below Requiring Long-term Care 2 in the previous quarter tends toRequiring Long-term Care 2 or 3, while it is less likely that she requires no Long-term
Care.
(2) Simultaneous equations; Total expenditures
In Table 5, a drop-out equation is simultaneously estimated with the care level equation.
Results on care expenditures are similar to the case of the single equation estimation.
The lagged care level estimate is also robust to the adjustment for attrition bias. Thus,
the preventive effects of care expenditures and state dependence are confirmed evenwhen dropping out is controlled for. Moreover, age and stroke affect it significantly.
And coefficients on care levels in the drop-out equation are not easy to interpret. Hence,
we will report only the results of the single equation estimation below because we haveconfirmed the robustness of the results on lagged expenditures and lagged care levels.

21

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table 5

Simultaneous Equations (Total long-term care expenditures)
mean

Care level equation
Lagged care level dummy
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
Lagged long-term care expenditures
Age
Sex
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4Drop-out equationAge(1)not drop-out(2)temporary drop-out(3)drop-out
Sex(1)not drop-out(2)temporary drop-out(3)drop-out
care level (current)(1)not drop-out
Independent
Requiring help 1
Requiring help 2Care level 1
Care level 2
Care level 3
Care level 4
Care level 5(2)temporary drop-out
Independent
Requiring help 1
Requiring help 2Care level 1
Care level 2
Care level 3
Care level 4
Care level 5(3)drop-out
Independent
Requiring help 1
Requiring help 2Care level 1
Care level 2
Care level 3
Care level 4
Care level 5

sd

2.5%

1.49
2.25
2.98
3.65
4.54
5.30
6.82
-0.04
0.22
-0.06
0.71
-0.08

0.10
0.09
0.09
0.11
0.13
0.19
0.24
0.00
0.07
0.06
0.23
0.15

1.32
2.08
2.81
3.44
4.30
4.99
6.41
-0.05
0.15
-0.16
0.22
-0.38

1.49
2.24
2.99
3.65
4.52
5.27
6.79
-0.04
0.18
-0.06
0.72
-0.08

1.69
2.41
3.15
3.86
4.79
5.69
7.32
-0.03
0.32
0.07
1.13
0.21

-2.26
-2.43
-2.27
-2.22
-2.23
-2.32
-2.43
-2.34
-3.46
-1.49
-2.39
-2.21
-2.41
-2.34

2.55
2.55
2.54
2.54
2.54
2.54
2.53
2.53
2.53
2.53
2.53
2.52
2.52
2.51

-5.97
-6.12
-5.94
-5.87
-5.91
-6.00
-6.09
-6.03
-7.10
-5.17
-6.04
-5.85
-6.07
-5.99

-0.94
-1.14
-0.99
-0.97
-1.00
-1.12
-1.28
-1.19
-2.31
-0.37
-1.35
-1.18
-1.41
-1.37

0.20
0.06
0.24
0.29
0.31
0.24
0.16
0.24
-0.82
1.13
0.25
0.44
0.28
0.35

-0.62
-0.49
-0.44

0.05
0.05
0.05

-0.67
-0.56
-0.49

-0.64
-0.51
-0.46

-0.54
-0.41
-0.36

0.40
0.31
0.31

1.17
1.16
1.16

-1.30
-1.48
-1.38

0.61
0.51
0.52

1.87
1.90
1.80

2.27
3.63
-3.49
15.45
10.54
-0.44
20.68
9.33

1.78
8.23
14.46
11.45
16.37
19.87
15.35
7.58

0.55
-7.33
-18.200.09-4.06-29.61
-2.21
-2.54

1.42
4.50
-11.15
16.23
0.07
8.12
21.10
8.19

4.83
14.34
18.01
30.53
35.25
21.38
40.83
24.67

-3.03
0.24
-7.78
10.58
4.49
-6.12
-18.78
2.65

1.81
8.22
14.49
11.50
16.37
19.88
22.71
7.58

-4.90
-10.84-22.44-4.91-10.37-35.59-64.90
-9.51

-3.90
1.05
-15.48
11.24
-5.85
2.19
-18.26
1.61

-0.34
11.01
13.89
25.43
29.37
15.53
21.29
17.71

0.65
0.76
-7.16
10.17
4.56
-5.61
14.51
3.67

1.78
8.24
14.48
11.45
16.37
19.87
15.34
7.61

-1.08
-10.20-21.76-5.30-10.06-34.72
-8.25
-7.99

-0.20
1.59
-14.87
11.02
-5.91
2.98
14.94
2.75

3.22
11.53
14.49
25.33
29.07
16.18
34.66
19.09

22

median97.5%

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures(3) Single equation; Separated expenditures
Table 6 shows the results when care expenditures are separated into two categories:
home care expenditures and facility care expenditures.
The effects of two categories are the same; both are significantly ameliorate carelevels. This result is contrary to our hypothesis: home care and facility care is effective
in preventing aggravating frailty. However, this may be because in this estimation we do
not distinguish between early and late stages of frailty. We will explore this distinction
next.
Table 6

Single Equation (Separated long-term care expenditures)

Lagged care level dummy
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
Lagged long-term care expenditures(home care)
Lagged long-term care expenditures(facility care)
Age
Sex
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4

mean

sd

2.5%

median

97.5%

1.50
2.26
2.99
3.65
4.51
5.25
6.80
-0.03
-0.04
0.20
-0.07
0.67
-0.12

0.10
0.09
0.10
0.12
0.15
0.20
0.24
0.01
0.01
0.11
0.06
0.35
0.16

1.31
2.08
2.80
3.43
4.22
4.87
6.34
-0.04
-0.05
-0.02
-0.19
-0.02
-0.42

1.50
2.26
2.99
3.66
4.52
5.25
6.80
-0.03
-0.04
0.20
-0.07
0.66
-0.12

1.70
2.44
3.19
3.88
4.79
5.63
7.25
-0.02
-0.03
0.38
0.06
1.36
0.20

-0.03
-0.20
-0.03
0.02
0.02
-0.07
-0.17
-0.06
-1.18
0.78
-0.11
0.07
-0.12
-0.05

0.44
0.43
0.42
0.41
0.40
0.40
0.40
0.40
0.40
0.40
0.41
0.41
0.42
0.44

-1.33
-1.51
-1.30
-1.24
-1.26
-1.32
-1.42
-1.30
-2.41
-0.42
-1.34
-1.16
-1.36
-1.29

0.03
-0.13
0.03
0.07
0.07
-0.01
-0.11
-0.01
-1.13
0.83
-0.06
0.11
-0.07
-0.00

0.64
0.46
0.60
0.64
0.62
0.51
0.39
0.50
-0.62
1.34
0.48
0.67
0.50
0.61

(4) Requiring Support 1 and 2; Single equation; Total expenditures
Estimation results for persons requiring support are dramatic. In Tables 7, we restrict the
sample to the least severe categories: Requiring Support 1 and 2.
23

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table 7

Requiring Support 1 and 2 ; Single Equation(Total long-term care expenditures)

Lagged care level
Age
Sex
Lagged long-term care expenditures
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4

mean
0.92
0.42
-0.32
-0.10
2.18
-0.75

sd
0.15
0.28
0.28
0.02
1.80
0.44

2.5%
0.61
-0.09
-0.86
-0.14
-0.71
-1.62

median
0.92
0.41
-0.31
-0.10
2.02
-0.74

97.5%
1.21
0.94
0.20
-0.05
6.09
0.09

0.47
-0.44
0.33
0.02
0.15
-0.15
-0.02
0.01
-1.70
0.56
-0.54
0.03
-0.42
-0.73

0.70
0.66
0.62
0.59
0.56
0.54
0.54
0.56
0.59
0.58
0.62
0.64
0.69
0.75

-0.97
-1.88
-1.02
-1.35
-1.18
-1.47
-1.35
-1.33
-3.13
-0.86
-2.01
-1.49
-1.99
-2.39

0.44
-0.45
0.31
0.01
0.13
-0.14
-0.01
0.02
-1.66
0.62
-0.47
0.11
-0.32
-0.64

1.95
0.93
1.66
1.28
1.31
0.93
1.05
1.08
-0.62
1.59
0.51
1.12
0.76
0.55

Table 7 shows the results for the estimation using total care expenditures as an
explanatory variable. Even total expenditures exert favorable effects on care levels. This
result confirms our hypothesis: the earlier, the better.
(5) Requiring Long-term Care 1 and 2; Single equation; Total expenditures andseparated expenditures
As shown in Tables 8 and 9, we picked up slightly more severe categories: Requiring
Long-term Care 1 and 2. The coefficient on total expenditures is smaller than that in thecase of Requiring Support and virtually the same as the results for the case of all
samples. When expenditures are decomposed into two categories, the results for the
early stages of frailty are similar to the results for the whole sample including laterstages, home care and facility care is effective in preventing aggravating frailty.

24

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Table 8Requiring Long-term Care 1 and 2 ; Single Equation(Total long-term care expenditures)

Lagged care level
Age
Sex
Lagged long-term care expenditures
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4

Table 9

mean
1.39
-0.07
-0.23
-0.05
-0.60
0.00

sd
0.13
0.38
0.15
0.01
0.87
0.48

2.5%
1.14
-0.75
-0.54
-0.07
-2.33
-0.96

median
1.39
-0.04
-0.23
-0.05
-0.60
-0.01

97.5%
1.66
0.61
0.07
-0.03
1.09
0.99

-0.32
-0.39
-0.47
0.14
-0.01
0.21
-0.09
0.23
-1.71
2.54
0.49
0.55
0.33
0.50

0.82
0.79
0.77
0.76
0.75
0.77
0.79
0.83
0.87
0.92
0.97
1.04
1.10
1.18

-2.24
-2.20
-2.22
-1.53
-1.61
-1.35
-1.67
-1.33
-3.33
0.92
-1.16
-1.15
-1.46
-1.41

-0.23
-0.32
-0.42
0.16
-0.00
0.19
-0.11
0.17
-1.79
2.44
0.34
0.37
0.13
0.29

1.30
1.27
1.27
1.98
1.96
2.34
2.18
2.66
0.84
5.33
3.37
3.58
3.50
3.84

Requiring Long-term Care 1 and 2 ; Single Equation(Separated long-term care expenditures)

Lagged care level
Age
Sex
Lagged long-term care expenditures(home care)
Lagged long-term care expenditures(facility care)
StrokeHypertension
Time dummy
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4

25

mean
1.41
0.30
-0.18
-0.04
-0.06
-0.73
0.12

sd
0.12
0.33
0.16
0.01
0.01
0.87
0.48

2.5%
1.18
-0.41
-0.50
-0.07
-0.08
-2.35
-0.79

median
1.41
0.38
-0.18
-0.04
-0.06
-0.76
0.11

97.5%
1.66
0.81
0.12
-0.02
-0.03
1.07
1.07

0.07
-0.08
-0.24
0.30
0.03
0.17
-0.22
0.01
-2.03
2.13
0.01
-0.01
-0.34
-0.25

0.77
0.73
0.71
0.68
0.66
0.66
0.67
0.69
0.72
0.78
0.79
0.84
0.89
0.96

-1.26
-1.32
-1.46
-0.91
-1.19
-1.07
-1.55
-1.36
-3.49
0.59
-1.57
-1.65
-2.09
-2.09

0.03
-0.11
-0.27
0.24
-0.00
0.13
-0.22
-0.00
-2.03
2.14
0.02
-0.01
-0.30
-0.23

2.06
1.84
1.63
2.15
1.82
1.95
1.49
1.69
-0.43
3.78
1.66
1.70
1.41
1.62

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

9. Conclusion
This paper investigated the preventive effects of long-term care expenditures. The
notion that long-term care can avoid deterioration of frailty or can ameliorate thecondition of the elderly is unique to the Japanese long-term care insurance system, but
is potentially important not only for individuals but also for the society through reduced
costs. Preventive effects take on more importance when deteriorated conditions tend toentail further deterioration. With the existence of state dependence, preventive care may
stave off an avalanche of deteriorated frailty.
State dependence is incorporated into the model by utilizing dynamic panel data.
To control endogeneity, or correlation between unobserved heterogeneity andexplanatory variables we adopt the estimation method proposed by Wooldridge (2205).
We further try to adjust for attrition bias following Albert and Follmann(2003).
Long-term care expenditures are estimated to significantly ameliorate care levels
although their magnitude is rather modest. We also confirmed state dependence of carelevels. These findings are confirmed even when attrition bias is adjusted for. When
expenditures are divided into home and facility care, both categories is effective inprevention of care.
When the sample is restricted to the least severe categories, Requiring Support 1
and 2, preventive effect is stronger than for all the elderly. This result confirms our
hypothesis: the earlier, the better.
For slightly more severe categories, Requiring Long-term Care 1 and 2, preventive
effect is less marked and virtually the same as the case of all sample.

26

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Appendix: General Description of the Conditions of the Elderly Who Requires
Support/Long-term CareFirst, “the elderly” is 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, 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.

27

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

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.

28

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

References
Albert, Paul and Dean Follmann. (2003) A Random Effects Transition Model for
Longitudinal Binary Data With Informative Missingness. Statistica Neerlandica.
vol. 57, no. 1, pp. 100–111.
Chamberlain, Gary. (1980) Analysis of Covariance with Qualitative Data. Review of
Economic Studies. vol.47, pp.225-238.
Contoyannis, Paul, Jones Andrew and Nigel Rice. (2004) The Dynamics of Health in
the British Household Panel Survey. Journal of Applied Econometrics, J. Appl.
Econ. vol. 19, PP. 473–503.
Daniels, Michael and Joseph Hogan. (2008) Missing Data in Longitudinal Studies:
Strategies for Bayesian Modeling and Sensitivity Analysis. Chapman andHall/CRC.
Gelman, Andrew, and Jennifer Hill. (2007) Data Analysis Using Regression andMultilevel/Hierarchical Models. Cambridge University Press.
Heiss, Florian, Axel Borsch-Supan, Michael Hurd and David Wise. (2009) Pathways toDisability: Prediting Health Trajectories. In David Cutler and David Wise (eds.)
Health at Older Ages: The Causes and Consequences of Declining Disability
among the Elderly. University of Chicago Press.
Heiss, Florian, Steven Venti and David Wise. (2014)
The Persistence andHeterogeneity of Health Among Older Americans. NBER Working Paper. No.
20306.
Jones, A.M., Rice, N., Contoyannis, P., & Jones, A.M. (ed) (2006a) The Dynamics ofHealth. In Andrew Jones, ed. The Elgar Companion to Health Economics. pp.
17-25. Edward Elgar.
Jones, Andrew, Xander Koolman and Nigel Rice. (2006b) Health-Related
Non-Response in the British Household Panel Survey and European Community
Household Panel: Using Inverse-Probability-Weighted Estimators in Non-Linear
29

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Models. J. R. Statist. Soc. A. vol.169, Part3, pp.543-569.
Levine, Deborah, et al. (2014) Functional Disability and Cognitive Impairment after
Hospitalization for Myocardial Infarction and Stroke. Circulation CardiovascularQuality and Outcomes. vol. 7. pp. 863-871.
Martina, Stephen, Nigel Riceb and Peter Smith. (2008) Does Health Care Spending
Improve Health Outcomes? Evidence from English Programme Budgeting Data.
Journal of Health Economics. vol. 27, pp.826–842.
Mundlak, Yair. (1978) On the Pooling of Time Series and Cross Section Data.
Econometrica. vol. 46, issue 1, pp. 69-85.
Shinkai, shouji, Hiroto Yoshida, Yoshinori Fujiwara, Hidenori Amano, Tarou Fukaya,
Sanyun Ri, Naoki Watanabe, Shuuichirou Watanabe, Osamu Kumagai, Mariko
Nishi, Hiroshi Murayama, Yuu Taniguchi,
YumikoShimizu,
Yuu
Taniguchi,

Youko Kousa, Hiromi Ooba,
TaduruOkabe and Natsumi

Hoshikawa, Yumiko Tsuchiya. (2013) Experience and Accomplishments of the Ten
Years of Preventive Long-Term Care Activity in Kusatsu-cho. Journal of theJapanese Society of Public Health. vol. 60, no.9, pp.596-605.
Spiegelhalter, David, Keith Abrams and Jonathan Myles. (2004) Bayesian Approaches
to Clinical Trials and Health-Care Evaluation. John Wiley & Sons.
Tajika, Eiji, and Jun Kikuchi. (2005) Effects of the Long-Term Care Insurance to
Sustain or Improve Elderly’s Long-term Care Level. The Quarterly of Social
Security Research. vol.41, no.3, pp.248-262. (In Japanese)
Wooldridge, Jeffrey. (2000) A Framework for Estimating Dynamic, Unobserved Effects
Panel Data Models with Possible Feedback to Future Explanatory Variables.
Economics Letters. vol.68, pp.245-250.
Wooldridge, Jeffrey. (2002) Econometric Analysis of Cross Section and Panel Data.
MIT Press.
Wooldridge, Jeffrey. (2005) Simple Solutions to the Initial Conditions Problem in
30

New ESRI Working Paper No.42
State Dependence of Long-Term Care andPreventive Effects of Care Expenditures

Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity.
Journal of Applied Econometrics. vol. 20, Issue 1, pp. 39–54.
Yuda, Michio, Wataru Suzuki, Ryouko Morozumi and Yasushi Iwamoto. (2013) Effectsof the Introduction of Preventive Long-Term Care Benefits on the Care Level ofthe Requiring Help. The Quarterly of Social Security Research. vol.49, no.3, pp.
310-325. (In Japanese)31