OSIPP Discussion Paper : DP-2013-E-006
Exploring the causal relationship between length of stay in hospitals and treatment outcome: Evidence
from Japanese AMI patients*
September 26, 2013
Satoshi Shimizutani†
Research Fellow, Gender Equality Bureau, Cabinet Office

Hiroyuki Yamada††
Associate Professor, Osaka School of International Public Policy (OSIPP)Haruko Noguchi†††
Professor, Faculty of Political Science and Economics, Waseda University

Yuichiro Masuda††††MD, Director of Medicine, Gifu Health Management Center

Masafumi Kuzuya†††††
MD, Professor, Graduate School of Medicine, Nagoya University【Keywords】Japan, Rokuyo, Length of stay, Hospitals, Rehospitalization, Health expenditure【Abstract】In this study, we explore the causal relationship between length of stay (LOS) in hospitals and the treatment
outcome for Acute Myocardial Infarction (AMI) patients in Japan, where the average LOS (ALOS) is the longest among OECD
countries. Using chart-based data, we address the endogeneity between LOS and treatment outcome by using an exogenous
variation based on Rokuyo (the six basic labels allocated to each weekday), which is found to be irrelevant to admission day
but relevant to discharge day. While we do find a significant association between LOS and rehospitalization probability in theordinary least squares (OLS) estimation, we do not find a significant relationship once LOS is instrumented by the six basic
labels in various instrumental variable estimations. This implies that additional stay that was induced owing to patient’s
choice of preferred Rokuyo at discharge has no effect on rehospitalization probability.
* We would like to express our appreciation to the medical facilities collaborated with the Tokai Acute Myocardial Infarction
Study (TAMIS) project. TAMIS is funded by the Pfizer Health Research Foundation, the Japan Foundation Center for Global
Partnership, and the Economic and Social Research Institute, Government of Japan. Our research project has been approvedby the Ethics Committee of the Department of Geriatrics, Nagoya University, and the medical facilities involved. We also
thank Hirofumi Kurokawa for his excellent research assistant work and the Seimeikai Foundation. The views expressed inthis paper are ours and not of the institutions to which we belong. All remaining errors are our own.
† Corresponding author. Postal Address: Nagatacho 1-6-1, Chiyoda-ku, Tokyo 100-8914, Japan;
E-mail:satoshi.shimizutani@cao.go.jp and sshimizutani@gmail.com.
†† Co-lead author. E-mail: hyamada@osipp.osaka-u.ac.jp.
††† E-mail: h.noguchi@waseda.jp.
†††† E-mail: masuda@med.nagoya-u.ac.jp.
††††† E-mail: kuzuya@med.nagoya-u.ac.jp.

1. Introduction
In this study, we carefully explore the causal relationship between length of stay (LOS) in
hospitals and treatment outcome for acute myocardial infarction (AMI) patients in Japan. This isa controversial topic stemming from a serious concern regarding the rapidly expanding medicalcare expenditure in Japan. We focus on a unique Japanese feature to provide new quantitative
evidence on the causal effect of LOS on treatment outcome, which is relevant to healtheconomists and policymakers within and outside Japan.
Internationally, the health/medical aspects in Japan are considered to have efficientfeatures. First, the general health status of the Japanese is well shaped, which is evident from thehigh life expectancy and the very low infant mortality (WHO, 2013).1 Second, healthexpenditure is relatively low in Japan. Both the relative proportion of total health expenditure to
GDP and per capita expenditure in Japan are close to the average of OECD countries. Third,
Japan established a mandatory health care system in 1961, providing universal medical coverage
linked to jobs or regions of residency through employers or municipalities, where thegovernment determines the national fee schedule (including drug fees) that is applicable to allproviders. These characteristics illustrate that the Japanese population enjoys better health andlonger life expectancy at a relatively lower cost of access to medical care for those who are
insured.
In contrast to these aspects, the average length of stay in hospitals (ALOS)—which isoften used as an indicator of health efficiency—is much longer in Japan as compared to otherOECD countries (OECD, 2011). Figure 1 illustrates the cross-country comparison among
OECD countries in terms of ALOS and curative (acute) care beds per 1,000 people (OECD,2013). The ALOS, for all causes, is 18.2 days in Japan, which is substantially higher than that in1

By causes of mortality, the number of deaths per 100,000 people owing to AMI, cancer, or diabetes mellitus
is much lower in Japan than the OECD average (OECD, 2013). In addition, risk factors related to daily
smoking, overweight or obese population, and adult alcohol consumption is lower in the total Japanese
population.

OECD countries (7.5 days) and close to four times that in the US (4.8 days).2 On the other hand,the number of curative care beds per 1,000 people is 8.0 in Japan, which is much higher than theOECD average of 3.4; moreover, the ratio of practicing physicians per 1,000 people is 2.2,
which is lower than the OECD average of 3.2.3
Owing to rapid aging in Japanese society, health expenditure has also been steadily
increasing both in terms of the absolute and relative amounts to GDP; this is expected to expand
further in the future with a larger proportion of the elderly having higher per capita expenditures(National Council on Social Security, 2006). The Japanese government considers the longer
ALOS compared with other developed countries as one of the causes of the increasing medical
expenditure in Japan, based on the observed positive correlation between per capita inpatient
medical expenditure for the elderly and the ALOS among prefectures. Under the uniform
fee-for-service system prevalent in hospitals, a longer hospitalization term appears justified
since the “price” for hospitalization does not change. Indeed, according to OECD (2011), “[t]heabundant supply of beds and the structure of hospital payments in Japan provide hospitals withincentives to keep patients longer. Financial incentives inherent in hospital payment methods
can also influence length of stay in other countries.”
The Japanese government has revised the fee-for-service schedule for either acute or
chronic hospitals in order to encourage hospitals to discharge patients earlier. In 1991–92, thegovernment increased a patient’s out-of-pocket hospitalization fee4, established a reward fee forshorter hospitalization, and introduced convalescent wards in a general hospital for long-term
hospitalized patients. Moreover, in 1998, the government began to lower the hospitalization fee
of general hospitals offering acute medical care if a patient aged 75 or over is hospitalized forover 90 days (Izumida, 2004; Yamamoto, 2004) and introduced the public long-term careinsurance program in 2000. During this period, the ALOS—excluding that in chronic2

For Japan, the ALOS data refers to ALOS for acute care, excluding long-term care beds in hospitals (OECD,2013).
3 In contrast, the density of nurses is higher in Japan than the OECD average.
4 The reform is legislated by the Revision of Law of Health and Medical Services for the Elderly (Rojin
Hoken Hou).

hospitals—substantially declined from 34.4 days in 1994 to 17.9 days in 2012, although it is still
the longest in Japan among OECD countries.5
Further, the government and each prefecture was required to establish a “Plan for
Effective Medical Expenditure” (Iryohi Tekiseika Keikaku) for the 2008–2013 period; the main
objective of this plan is to reduce the ALOS so that the gap between the ALOS among
prefectures and the shortest LOS among prefectures (Nagano Prefecture) is halved by 2015.6 In
parallel with the change in incentives for hospitals, in 2003, the Diagnostic Procedure
Combination (DPC)—an inpatient prospective payment system—was introduced for “special
function hospitals”; this was considered the Japanese counterpart of the Medicare Prospective
Payment System (PPS) in the US (Anderson and Ikegami, 2011), which aimed to reduce thevariation in health expenditure and LOS across hospitals.7
While a reduction in the LOS in hospitals has been a focal point in medical reform inJapan, it is important to consider the effect of shorter LOS on treatment outcome, but not merely
by relying on a simple “the shorter, the better” discussion that assumes that all other things areequal. A shorter LOS may reduce the cost per discharge and shift care from inpatient to lessexpensive post-acute settings (OECD, 2011). On the other hand, if a longer LOS contributes to abetter treatment outcome, a shorter LOS may have an adverse effect on treatment outcome.
Moreover, shorter LOS may need more intensive and costly services per day and could lower
the comfort and recovery of the patient and increase the readmission rate, thereby resulting in ahigher cost per episode of illness.8
Thus, when exploring the causal effect of LOS on treatment outcome, we need to consider
5

Izumida (2004) examined the effect of change in fee for hospital services on LOS in 1997, 1998, and 2000,
and found that the 1997 and 1998 reforms affected the LOS in hospitals.
6 The plan has a legal basis in the Act on Assurance of Medical Care for Elderly People (Koreisha no Iryo no
Kakuho ni kansuru Horitsu), which has been effective from April 2008.
7 Anderson and Ikegami (2011) summarized the following concerns on Japan’s DPC acute hospital payment
system: (1) a hospital-specific conversion factor that adjusts payments made by the DPC system, (2) asignificant proportion of payments that are made outside the DPC system, (3) the number of cases for which
payment is made outside the DPC system, (4) the per day payment system, (5) specific adjustments based on
hospital behavior, and (6) the auditing mechanisms.
8 Tokunaga and Imanaka (2002) argue that aspects that determine patient satisfaction depend on the LOS in
Japanese hospitals.

the endogenous relationship. One direction for addressing this endogeneity is to focus on a“natural experiment,” which is represented by any policy or institutional changes. Evans et al.
(2008) carefully examined the impact of state and federal laws designed to increase the length of
postpartum hospital stay that substantially reduced the proportion of newborns discharged early.
A simple OLS estimation revealed that a shorter postpartum hospital stay is correlated with
better health since healthier babies are discharged sooner. In contrast, a 2SLS estimation using aseries of laws changed in the late 1990s as instrumental variables revealed that an increase in thelength of postpartum hospital stay is unrelated to the baby’s health. They concluded that the
average effect of longer postpartum LOS on the probability of readmission is small, but it can behighly cost effective for high-risk babies.
To the best of our knowledge, no existing research in Japan explores the causal effect of
LOS on treatment outcome. Extending the scope to recent studies outside Japan, Kociol et al.
(2012) examined data on AMI patients from 17 countries and found a substantial variation in the
30-day readmission rate and LOS across the countries (not including data from Japan); the30-day readmission rates were higher for the US than other countries, while the median LOS
was shortest for US patients (3 days) and longest for Germany (8 days). Then, they found thatthe difference in the 30-day post-discharge readmission rate after ST-segment elevation
myocardial infarction (STEMI) treatment across countries is greatly attenuated after adjustment
for LOS. On the other hand, Saczynski et al. (2010) observed that LOS after AMI treatment
significantly declined from 7.2 days to 5.0 days between 1995 and 2005 in the US; however,they found that a declining LOS is not associated with an increased risk for early readmission or
all-cause mortality.9
In this study, we adopt an alternative approach to address the endogeneity issue to provide
new persuasive evidence. Rokuyo is a label on Japanese calendars and pocket diaries thatindicates one’s good or bad luck, direction, or fortune for each day. Rokuyo comprises six basic
9

The sample was 4,184 patients hospitalized with AMI in a central New England metropolitan area during 6
annual periods (1995, 1997, 1999, 2001, 2003, 2005). The findings are not changed across year under study.

labels that include Sensho, Tomobiki, Senbu, Butsumetsu, Taian, and Shakkou to indicate how
auspicious a given day is.10 Rokuyo is a rather popular and prevalent superstition in Japan wheremost people know the statements on formal (ceremonial) occasions such as “a marriage party
should not made on a Butsumetsu day” and “a funeral day should not take place on a Tomobiki
day,” regardless of whether they believe this. Since AMI is an acute disease, a patient usuallycannot choose a Rokuyo day on admission, but can do so for discharge. In other words, a patient
who is going to be discharged can avoid a Butsumetsu (unlucky) day and even wait for the next
Taian (lucky) day.
Indeed, subsequent sections show that the days of admission for AMI patients are random
across Rokuyo, but those of discharge are clearly more concentrated on a Taian day and less on a
Butsumetsu day. Thus, the Rokuyo day at the time of discharge is a valid instrument since it isrelated to LOS, but not related to treatment outcome. One might argue that a patient who
suffered a serious heart attack is more likely to choose a good day for discharge, and thus, theRokuyo day is not purely unrelated to treatment outcome. However, our data—whichcorresponds to the Cooperative Cardiovascular Project (CCP) in the US—provides a variety ofindicators of the severity levels of AMI, which enable us to control for the seriousness of the
AMI that a patient has undergone. Moreover, as we discuss below, the correlation coefficients
between the discharge Rokuyo and explanatory variables are low—less than 0.1.
The remainder of this manuscript is organized in the following manner. In Section 2, we
describe the data used in the estimation and provide evidence of the Rokuyo day on

The Japanese “roku” means “six”. The origin of Rokuyo is unclear but was imported from China to Japanin the 14th century. Interestingly, Rokuyo gained the popularity after the World War Second. The definition foreach label is as follows (Takano et al. (2011) except Shakko).
Butsumetsu: (the) Buddha's death; a very unlucky day according to traditional almanacs.
Taian: a lucky [an auspicious] day (on the Japanese calendar).
Senshou: a day on which bold actions are supposed to turn out well; a day supposed to be lucky in themorning and unlucky in the afternoon.
Senbu: a day on which it is supposed to be better to avoid disputes and hurried actions; a day supposed to be
unlucky in the morning and lucky in the afternoon.
Tomobiki: a day on which one's bad luck is thought to affect one's friends, and which is therefore avoided
when scheduling funerals
Shakko: a day which is lucky during the hour of the horse (11 am–1 pm) but the luck is bad for the rest.
10admission/discharge. In Section 3, we conduct a regression analysis to explore the relationshipbetween LOS and treatment outcome with alternative specifications. In Section 4, we provide
various robustness checks on our main results. In Section 5, we present the conclusion.

2. Data description and Rokuyo at admission and discharge
In Japan, it is fair to say that large-scale patient-level data that is internationallycomparable is scarce. An exception is the Tokai Acute Myocardial Infarction Study (TAMIS),
whose objective is to create a database comparable to the Cooperative Cardiovascular Project(CCP). The CCP is designed to improve the quality of care for Medicare beneficiaries with AMI.
TAMIS aims to investigate the variation in the quality of healthcare with respect to treatments
and outcomes between the US and Japan, controlling for chart-based detailed clinicalinformation on AMI patients.11 In addition to rich information on individual characteristics,
comorbidity and severity at admission, TAMIS provides data that is essential to thisanalysis—the dates of admission to and discharge from a hospital for each episode of illness,
which enables us to identify on which Rokuyo day a patient was admitted and discharged.
The data collection enabled us to obtain abstracted charts pertaining to 3,274 heart attack
patients who were newly hospitalized in 15 municipal or non-profit high-tech and high-volume
general hospitals located in the Tokai area of Japan that provide coronary angiography (CAG)
and percutaneous coronary intervention (PCI) between January 2001 and December 2003, theperiod when stent technology prevailed (called TAMIS-II Data)12. In the process of datacollection, charts were carefully reviewed by research nurses and physicians in the standardized
11

The CCP is undertaken by the Health Care Financing Administration (HCFA, currently called Center for
Medicare and Medicaid Services: CMS). See the detailed description of the TAMIS project in Noguchi et al.
(2008).
12 See Hirakawa et al. (2005), Hirakawa et al. (2006), and Kimata et al. (2008). The TAMIS project alsocollected data on AMI patients during the period 1995–1997 in the same manner. Noguchi et al. (2008) useddata for the period 1995–1997 to explore factors for the extraordinarily frequent use of percutaneoustransluminal coronary angioplasty (PTCA) for the treatment of AMI and found that the probability ofreceiving PTCA is affected by the density of medical resources in a region; moreover, they found that medical
expenditure was higher for treated patients but that there are no significant differences in hospitalization days
between those who were treated and those who were not, thereby implying that the frequent use of PTCA is
economically motivated.

manner of abstraction of medical records as done by the HCFA/CMS for the CCP. The record
abstracts contain over 100 comorbid diseases and severity measures that collectively summarize
all the major associated diseases and functional status impairments. Moreover, the abstracts
include AMI severity measures following the CCP’s expert advisory panel, which influence theappropriateness of major AMI treatment decisions and health outcomes (Noguchi et al., 2008).
Table 1 presents the frequency of Rokuyo days at admission and discharge as well as
ALOS. The data demonstrates that Rokuyo days are random at admission (Column 1) and the
ALOS is comparable regardless on which Rokuyo day a patient was admitted (Column 2). Table
2 presents the test statistics from the Kolmogorov–Smirnov test for equality of distribution of
LOS by Rokuyo on admission and discharge days. As the table clearly shows, there is no
significant difference in the distribution of LOS across Rokuyo on admission. On the contrary,
the Rokuyo day of discharge is concentrated more on Taian, (21.9 percent) and less on
Butsumetsu (13.2 percent) (Column (3) in Table 1). The pattern follows the ALOS by Rokuyo on
discharge days (Column 4). The gap in the ALOS between Taian and Butsumetsu is 2.3 days.
Further, Table 2 reveals that the distribution of LOS differs among some Rokuyo. In particular,
the distribution of LOS on Taian is statistically different from that on Butsumetsu, Sensho, andSenpu. Further, that of Senpu is statistically different from Tomobiki in addition to Taian.
These observations demonstrate that the Rokuyo day of admission and the subsequent
LOS are random. This is natural because a patient who has a heart attack needs to behospitalized immediately and cannot wait to choose a suitable Rokuyo day for admission.13 In
contrast, it is evident that discharge is more frequent on Taian and less so on Butsumetsu. The
non-random variation stems from the fact that a patient can choose (or wait for) a good Rokuyo
day for discharge even if he/she no longer requires hospitalization. According to modern science,
Rokuyo is a superstition and the choice of Rokuyo does not affect the treatment outcome for13

According to the guideline for AMI treatments, a doctor must make a diagnosis within 10 minutes after apatient arrives at the hospital, describe the treatment with the risks and benefits to the patient and family
members, and begin treatment within 30 minutes (Uematsuse, 2002).

AMI patients.
Table 3 reports the descriptive statistics of individual demographics. We excluded theobservations with missing variables among the listed ones. Further, we also excluded theobservations of those patients who passed away during hospitalization. The probability ofrehospitalization within one year, which is the treatment outcome variable in this study, is 39.3
percent. In this study, the definition of “rehospitalization” is the case in which a patient who
received AMI treatment is readmitted within one year after discharge in the same hospital where
the patient received the initial AMI treatment. If a patient passed away within one year after
discharge, we considered this rehospitalization. It must be noted that we faced several issues
related to the definition of rehospitalization. First, a patient may be re-hospitalized in a different
hospital than the hospital where he/she received the initial treatment. In this case, we cannot
trace the patient’s rehospitalization. However, as discussed subsequently, the average age of thepatients in the data is 65. Hence, it is not very realistic to imagine that elderly patients who haveundergone an episode of AMI frequently move away from the place where they used to stay.
Therefore, the bias arising from this concern could be minimal, if any. Second, the data wascollected at 15 high-tech and high-volume medical facilities located in the Tokai area of Japan.
Thus, we do not have information on potential patients admitted to more small-scale facilities
that may be characterized as low-tech and/or low-volume; this may create a sample selection
bias. However, generally speaking, an AMI patient is admitted to a health facility that is
equipped with a certain high level of technology. Hence, the issue of sample selection caused bythis problem may not be very serious. Third, the one-year time window of rehospitalization isarbitrarily determined by the authors, although this time-window appears to be a standard length
for research purposes. In robustness checks, we change the time-window of rehospitalization to
six months, nine months, and two years to ascertain whether our main results are affected.
Fourth, while we can trace the death of patients after discharge if that happens, information on
the cause of the death was not collected.

The average age of patients is 65 years and males account for over three-fourths of thesample. By type of medical insurance, over 60 percent of the patients in the sample arebeneficiaries of National Health Insurance (NHI), followed by Employee Health Insurance andMutual Assistance Insurance. The number of family members living with a patient is more than
two and more than three-fourths of the sample has a spouse. The ALOS is 19.63 days. As
mentioned in the previous section, the Rokuyo day at discharge is concentrated on Taian (22.1
percent), while that at admission is comparable across Rokuyo.
Table 4 reports the descriptive statistics of variables representing comorbidity and severity
at admission. We converted all the information on comorbidity and severity at admission into
dummy variables. The main reason for this is that in emergency cases such as AMI, it is difficult
to collect all the detailed information on the patient, which may create many missing variablesin the dataset. This would have forced us to exclude the observations on all such patients owing
to missing data. To avoid this problem, we included “missing” as one category of dummy
variables. Taking height as an example, approximately 20 percent (variable name: hei_y) of thepatients’ height is “unknown,” which also makes it impossible to compute their Body Mass
Index (BMI). Here, we use the word “unknown” and “missing” as synonyms. We face thechoice of either excluding these observations or using a dummy variable for the missing variable,
and adopt the latter method. As discussed earlier, one justification of using this method is rooted
in practical reasoning. In emergency cases, collecting detailed information on patients is very
difficult or occasionally even impossible. Thus, we interpreted the dummy variable representing
missing data as information indicating the severity of a patient’s condition. We use these createddummies in the econometric analyses presented in the next section (McClellan and Noguchi,1997).
Examining comorbidity variables at admission, most patients in the sample are totallycontinent (98.3 percent) and are able to walk independently (96.7 percent). By incidence of typeof disease, the most prevalent is current cigarette smoker (over 50 percent), followed by

hypertension (43.2 percent), and diabetes (any type, 27.8 percent). Moreover, 12.6 percent of thepatients in the sample had CAG history and the proportion of PTCA history or CABG history
was smaller. With regard to severity variables at admission, there is a non-negligible amount of
missing data in temperature, mean arterial pressure (MAP), height, BMI, Albumin, EKG trace:transmural (new qwave), etc., thereby justifying using our dummy variable approach. Needlessto say, myocardial infarction (MI) (excluding old MI) was detected by using EKG trace for 90
percent of the patients; 17.4 percent of the patients had transmural q wave, while 22 percent ofthem had congestive heart failure. The proportion of patients whose highest creatinine level is
25 or more was very small and the blood urea nitrogen level was normal for approximately 70
percent of the patients (variable name: bunsun1).

3. Estimation and results
In this section, we conduct a regression analysis to link LOS with treatment outcome. The
specification is described in the following manner:yi   0   1k xi    2l zi   i ,
k

(1)

l

where yi is the dependent variable and refers to the dummy variable that takes the value of one ifa patient is re-hospitalized within one year after discharge, and zero otherwise. The explanatory
variables can be divided into two categories: xi refers to the variables that indicate individual
characteristics and health facility dummies (the variables shown in Table 3) and zi refers tocomorbidity and severity variables on admission. The last term,  i , is an error term.
Table 5 presents the estimation results based on a linear probability model using the OLS
method.14 The model includes fixed effects at the health facility level and the standard errors
are also clustered at the health facility level. Column (1) reports the coefficients on xi s,
14

The results reported in the section are not altered if we employ a probit estimation.

excluding zi s from the explanatory variables. The coefficient on LOS is positive and significant,thereby indicating that the longer a patient is hospitalized, the higher the probability ofrehospitalization. Column (2) shows the estimated coefficients on both xi s and zi s, including
comorbidity and severity variables at admission in the explanatory variables. Again, thecoefficient on LOS is positive and significant, thereby implying that the longer a patient is
hospitalized, the higher the probability of rehospitalization is. No individual characteristics are
significant once comorbidity and severity variables at admission are included. Some
comorbidity variables at admission such as hypertension, angina, family medical history ofischemic heart disease, renal failure, and CABG history are found to be positively statisticallysignificant, thereby implying that these comorbidities have a positive correlation with theprobability of rehospitalization. Similarly, some severity variables at admission such as high
MAP, low weight, high level of white blood cells, and congestive heart failure are positive andstatistically significant, thereby implying that these comorbidities have a positive correlation
with the probability of rehospitalization.
In sum, the OLS estimation shows a positive and significant relationship between LOS
and rehospitalization probability. However, we cannot interpret these findings as the causal
association between LOS and rehospitalization. The positive association may simply show that apatient with a higher rehospitalization probability is more likely to be discharged later15.
Another case is that there might be an unobservable factor that affects both LOS and probabilityof rehospitalization simultaneously (i.e., omitted variable bias), while it appears that there isalmost no possibility of bias caused by measurement error because the variable we areconcerned about for this bias is LOS, which is accurately measured in the data. In any case, wehave to address this reverse causality or a possible bias caused by unobservable factors in
capturing the causal effect of LOS on treatment outcome.
Thus, we conduct the estimation using instrumental variables in order to address the15

See Evans et al. (2008) for a similar positive relationship in the case of postpartum hospital days and healthstatus of newborn babies.

endogeneity issue between LOS and the readmission probability. The instrumental variables are
Rokuyo days at admission and discharge, which was reviewed in Section 2. Conceptually, thedischarge Rokuyo is a valid instrument that is related with LOS but not related with treatment
outcome. Moreover, the correlation coefficients between the discharge Rokuyo (IV) and
explanatory variables are low—less than 0.1 in absolute value (results are omitted to save space
but available upon request). We include Rokuyo day at admission as an instrumental variable too
because the discharge day is partially affected by the day of admission, and the Rokuyo day atadmission might affect the choice if discharge day given the order of the Rokuyo days.16
We implement two-stage least squares (2SLS), two-step generalized method of moments(GMM), and limited information maximum likelihood (LIML) estimations. Before we discuss
the results, it is important to note the following aspects. First, as our OLS results show, omitting
comorbidity and severity variables at admission from the specification of the outcome equation
may cause a severe omitted variable bias. Thus, we applied the three aforementioned estimation
methods to the specifications that include these variables. Second, because we cluster theobservations at health facility level, the number of clusters is much smaller than the sum of thenumber of exogenous regressors and that of excluded instruments. In such a circumstance, thecovariance matrix of orthogonality conditions is not full rank and GMM and overidentification
tests are infeasible since the weighting matrix cannot be calculated. To solve this problem, asufficient number of exogenous regressors is “partialled out” from all the other variables in theestimation for the weighting matrix to have full rank. Further, according to the Frisch–Waugh–
Lovell (FWL) theorem (Frisch and Waugh, 1933; Lovell, 1963), in the two-step GMM
estimation, the coefficients for the remaining regressors are the same as those that would beobtained if the variables were not partialled out when the coefficients of the partialled variables
are not calculated. As a result of this procedure, in the results of the GMM estimation, we report
16

The order of the Rokuyo days is fixed in the following manner: Sensho, Tomobiki, Senbu, Butsumetsu,
Taian, and Shakko. However, the first day of January and July is set to be Sensho, that of February and Augustis Tomobiki, that of March and September is Senbu, that of April and August is Butsumetsu, that of May andNovember is Taian, and that of June and December is Shakko (all months are included in the old (lunar)calendar). In other words, the Rokuyo day begins in each lunar month with the first day in the same order.

only the coefficients of LOS—age, gender, number of family members living with a patient, andpresence of spouse. This does not compromise the value of our approach because what we areinterested in is the coefficient of LOS. Third, because there are numerous comorbidity andseverity variables at admission, we do not report the coefficients of these variables. Althoughhealth facility dummies are included in the specification, they are omitted from the table.17
Table 6 reports the estimation results of the 2SLS, two-step GMM, and LIML as well as
the result of the first stage of 2SLS. The dependent variable in the first stage is LOS, which is an
endogenous variable in the second stage. The dummy for rehospitalization within one year is thedependent variable in the second stage. The result of the first stage of specification (1) indicatesthat the coefficient of Taian at discharge is positive and significant (base case is Butsumetsu).
This implies that LOS on Taian discharge is longer than that on Butsumetsu discharge by 1.5
days. We also notice that the coefficients on admission are not significant for any Rokuyo except
Sensho, which is marginally and negatively significant at the 10 percent level. However, as we
discussed in detail earlier, the Rokuyo at admission is conceptually random because a patientcannot choose when he/she is affected by AMI and cannot wait to be hospitalized once anepisode occurs. Elderly and male patients are more likely to have longer LOS, while LOS tends
to be shorter if the patient has a spouse.
The F-value of the first stage is 12, which implies that the relevance of the instrument isstill satisfied according to the Staiger–Stock rule of thumb (F > 10; Staiger and Stock, 1997).
The reported Kleibergen–Paap Wald rank F statistic is 12.36, which again implies that weakidentification is not to be considered a problem. Further, the Sargan–Hansen J statistic is 4.490
and its p-value is 0.8763. Thus, the joint null hypothesis that the instruments are valid and thatthe excluded instruments are correctly excluded from the estimated equation cannot be rejected.
Examining the coefficients in the second stage of the estimation, the coefficient on LOS is
not statistically significant. In contrast to the results in Table 5 using OLS, this observation

17

The full results are available on request from the authors.

indicates that the difference in LOS across discharge Rokuyo does not affect rehospitalization
probability. While the gap in LOS between Butsumetsu (base case) and Taian is 1.5 days in thefirst stage, the coefficient on LOS in the second stage is not statistically significant. This result is
not altered even in specification using two-step GMM or LIML.
In sum, while the association between LOS and rehospitalization is statistically significant
in the OLS estimation, the coefficient of LOS is no longer significant once the endogeneity iscorrected by using Rokuyo as an instrumental variable. In other words, additional stay caused by
the choice of preferable Rokuyo at discharge (by patients) does not have a causal effect on
treatment outcome.

4. Robustness checks
We conducted two types of robustness checks. The first one was using a different time
window for rehospitalization. In the main specification, we specified that a patient is consideredrehospitalized if he/she was rehospitalized (or passed away) within one year after discharge.
However, this one-year time window is slightly arbitrary. We re-estimate the same model bychanging this time window for rehospitalization to six months, nine months, and two years. In
the second robustness check, we use the log of LOS. As depicted in Figure 2, the distribution of
LOS is skewed to the right; thus, in alternative specifications, we use log(LOS) instead of LOS.
Figure 3 illustrates the distribution of log(LOS), which is closer to a normal distribution than
LOS itself.
Table 7 presents the results of these two robustness checks. The table reports thecoefficient of LOS or log(LOS) in the second stage of the estimation. When log(LOS) is used,
the results from the first stage of the estimation (not shown) are similar to those using LOS. In
particular, the coefficient of Taian is positive and statistically significant. If the Rokuyo atdischarge is Taian, the LOS is longer by 1.2 days than the LOS at discharge on Butsumetsu.
Further, the F-value and Sargan–Hansen J statistic are 14.04 and 4.332 (P-value = 0.8882),

respectively, thereby implying that the instruments are valid.
The table shows that the OLS estimation consistently indicates a positive relationshipbetween LOS (or log(LOS)) and probability of rehospitalization, regardless of the time windowof rehospitalization. On the other hand, once instrumented, such a positive relationship loses its
significance. There is only one case—time window of six months for rehospitalization estimatedby two-step GMM using LOS—where the relationship is negative and very marginallysignificant at the 10 percent level. However, in all other cases in 2SLS, two-step GMM, and
LIML, the coefficient of LOS or log(LOS) are insignificant. Therefore, these robustness checks
broadly support our main results.

5. Conclusion
A long ALOS is one of the distinct characteristics of the Japanese medical care program.
In this study, we carefully explored the causal relationship between LOS in hospitals andtreatment outcome for AMI patients in Japan. We addressed the endogeneity between LOS andtreatment outcome by using an exogenous variation in the Rokuyo days, which are found to beirrelevant to admission day but relevant to discharge day. While we did find a significant
association between LOS and rehospitalization probability in the OLS estimation, we did not
find a significant relationship once LOS is instrumented by the six basic labels in 2SLS,
two-step GMM, and LIML estimations.
This implies that additional stay because of patient’s choice of preferred Rokuyo atdischarge has no effect on rehospitalization probability. In particular, our result shows that the
gap in the ALOS for a patient discharged on a Taian day and for a patient discharged on a
Butsumetsu day is 1.5 days and the difference has no effect on rehospitalization probability.
Our results suggest that there is room for improving efficiency in the use of medical
resources. Whether a reduction in LOS contributes to reducing total medical costs depends not
only on LOS but also on the supply of medical care services, including the number of beds aswell as density of physicians and nurses. A subject for further research could be theconsideration of any possible change in hospital behavior to maintain the revenue specified
under the fee-for-service program.

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Figure 1 Average length of stay, curative care beds, and physician density among OECD
countries(Note) Data is taken from OECD Health Data 2013. The timing is 2011 or the closest year.

.03
.02
0

.01

Frequency

.04

.05

Figure 2: Length of Stay

0

50

100
Length of stay

150

200

Patients hospitalized for more than 180 days were excluded.

.4
0

.2

Frequency.6.8

Figure 3: log(Length of Stay)

0

1

2
3
log(length of stay)

Patients hospitalized for more than 180 days were excluded.

4

5

Table 1: Rokuyo on admission and discharge days and the length of stay
(1) Admission(2) Length of stay(3) Discharge(4) Length of stay

Frequenc(%)

Average

S.D.

Frequency(%)

AverageS.D.

yButsumetsu

545

16.87

20.31

16.99

390

13.26

18.85

15.54

Taian

549

16.99

20.77

18.29

646

21.96

21.18

15.88

Shakko

560

17.33

19.00

14.04

449

15.26

19.12

13.90

Sensho

516

15.97

18.85

14.13

518

17.61

18.87

14.20

Tomobiki

521

16.13

19.61

14.74

497

16.89

20.58

16.62

Senpu

540

16.71

20.16

15.45

442

15.02

18.46

13.18

Total

3231

2942

(Note) The sample used to compute length of stay excludes patients hospitalized for more than 180 days.

Table2: Kolmogorov-Smirnov test for equality of distribution of length ofstay by Rokuyo on admission and discharge days
Admission
Taian
ShakkoButsumetsu
0.862
0.446

Taian

Shakko0.837

SenshoTomobikiSensho

0.296

0.733

0.997

Tomobiki
Senpu

0.802
0.470

0.984
0.865

0.940
0.676

Discharge

Butsumetsu

TaianShakkoSenshoTomobiki
Senpu

0.009***
0.772
0.969
0.113
0.627

Taian
0.139
0.041**
0.638
0.000***

Shakko

0.797
0.600
0.244

0.843
0.534
Sensho

0.307
0.313

0.528
Tomobiki

0.029**(Note)
1. The sample to compute length of stay excludes a patient who is hospitalized
more than 180 days.
2. *** significant at 1 percent level, ** significant at 5 percent levelTable 3 Descriptive statistics (Individual demographics)
Variablesdum1: re-hospitalization dummy (within 1 year, =1 if re-hospitalized)
Age
P_1: Sex (=1 if male)iins1: type of medical insurance (National Health Insurance)
iins2: type of medical insurance (Employees Health / Mutual Assistance Insurance)
iins3: type of medical insurance (no insurance, 100% OOP)
iins4: type of medical insurance (Government-managed insurance)
iins5: type of medical insurance (Public assistance)
iins6: type of medical insurance (Health Insurance Society)fam: Number of family members living with a patient
spouse: Presence of spouse (=1 if yes)days_h: LOS
rok1_d: Rokuyo at discharge (Butsumetsu )rok2_d: Rokuyo at discharge (Taian )rok3_d: Rokuyo at discharge (Shakko )rok4_d: Rokuyo at discharge (Sensho )rok5_d: Rokuyo at discharge (Tomobiki )rok6_d: Rokuyo at discharge (Senbu )rok1_h: Rokuyo at admission (Butsumetsu )rok2_h: Rokuyo at admission (Taian )rok3_h: Rokuyo at admission (Shakko )rok4_h: Rokuyo at admission (Sensho )rok5_h: Rokuyo at admission (Tomobiki )rok6_h: Rokuyo at admission (Senbu )_IFA_1_2 : hospital 2 dummy_IFA_1_3 : hospital 3 dummy_IFA_1_4 : hospital 4 dummy_IFA_1_5 : hospital 5 dummy_IFA_1_6 : hospital 6 dummy_IFA_1_7 : hospital 7 dummy_IFA_1_8 : hospital 8 dummy_IFA_1_9 : hospital 9 dummy_IFA_1_10 : hospital 10 dummy_IFA_1_11 : hospital 11 dummy_IFA_1_12 : hospital 12 dummy_IFA_1_13 : hospital 13 dummy_IFA_1_14 : hospital 14 dummy_IFA_1_15 : hospital 15 dummy# obs Mean
S.D.
2690 0.393 0.488
2690 65.090 11.327
2690 0.784 0.411
2690 0.639 0.480
2690 0.161 0.367
2690 0.013 0.112
2690 0.096 0.294
2690 0.010 0.098
2690 0.083 0.276
2690 2.152 1.605
2690 0.775 0.417
2690 19.631 15.418
2690 0.135 0.341
2690 0.221 0.415
2690 0.152 0.359
2690 0.172 0.377
2690 0.170 0.375
2690 0.151 0.358
2690 0.170 0.376
2690 0.173 0.379
2690 0.171 0.377
2690 0.161 0.368
2690 0.161 0.368
2690 0.163 0.370
2690 0.041 0.197
2690 0.095 0.293
2690 0.113 0.316
2690 0.089 0.285
2690 0.025 0.157
2690 0.011 0.103
2690 0.032 0.177
2690 0.095 0.293
2690 0.038 0.192
2690 0.085 0.279
2690 0.036 0.186
2690 0.151 0.358
2690 0.024 0.154
2690 0.126 0.332

Table 4: Descriptive statistics (Comorbidity variables and severity variables at admission)
Variables(1) Comorbidity variables at admission
uri1: Continence: totally continenturi2: Continence: occasionally incontinenturi3: Continence: no urine output
uri4: Continence: unknown
walk1: Mobility: Walks Independently
walk2: Mobility: Walks with assistancewalk3: Mobility: Unable to walk
walk4: Mobility: unknown
X_1y: Hypertension
X_1d: Hypertension: unknown
Y_1y: Hyperlipemia
Y_1d: Hyperlipemia: unknown
Z_1y: Diabetes （any type）
Z_1d: Diabetes （any type）: unknown
AA_1y: Diabetes treated by insulin
AA_1d: Diabetes treated by insulin: unknown
AB_1y: Angina
AB_1d: Angina: unknown
AD_1y: Cardiac heart failure or pulmonary edema
AD_1d: Cardiac heart failure or pulmonary edema: unknown
AF_1y: Old myocadial infarction
AF_1d: Old myocadial infarction: unknown
AH_1y: Current cigarette smoker
AH_1d: Current cigarette smoker: unknown
AJ_1y: Arrhythmia
AJ_1d: Arrhythmia: unknown
AK_1y: Family medical history of schemic heart disease
AK_1d: Family medical history of schemic heart disease: unknown
AL_1y: Renal failure
AL_1d: Renal failure: unknown
AM_1y: Cirrhosis
AM_1d: Cirrhosis: unknown
AN_1y: Cerebrovascular accident: Cerebral infarction
AN_1d: Cerebrovascular accident: Cerebral infarction: unknown
AO_1y: Cerebrovascular accident: Brain hemorrhage
AO_1d: Cerebrovascular accident: Brain hemorrhage: unknown
AP_1y: Cerebrovascular accident: Subarachnoid hemorrhage
AP_1d: Cerebrovascular accident: Subarachnoid hemorrhage: unknown
AQ_1y: COPD
AQ_1d: COPD: unknown
AR_1y: Aneurysm of aorta
AR_1d: Aneurysm of aorta: unknown
AS_1y: Ulcus pepticum
AS_1d: Ulcus pepticum: unknown
AT_1y: Cancer
AT_1d: Cancer: unknown
AU_1y: Autoimmune disease
AU_1d: Autoimmune disease: unknown
AV_1y: Drug allergy/med reaction
AV_1d: Drug allergy/med reaction: unknown
AW_1y: Dementia/alzheimer's disease
AW_1d: Dementia/alzheimer's disease: unknown
AX_1y: Terminal illness
AX_1d: Terminal illness: unknown
AY_1y: CAG history
AY_1d: CAG history: unknown
AZ_1y: PTCA history
AZ_1d: PTCA history:unknown
BA_1y: CABG history
BA_1d: CABG history: unknown(2) Severerity variables at admission
Heart rate
admspls0: =1 if heart rate < 60admspls1: =1 if 60 <= heart rate < 80admspls2: =1 if 80 <= heart rate < 100admspls3: =1 if 100 <= heart rate < 120admspls4: =1 if 120 <= heart rate < 150admspls5: =1 if 150 <= heart rate
admspls_y: =1 if heart rate unknown
Temperatureadmtmp1: =1 if temperature > 38.3
admtmp2: =1 if 35.8 <= temperature < 38.3
admtmp3: =1 if temperature < 35.8
admtmp_y: =1 if temperature unknown

# obs

Mean

S.D.

Min

Max

2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960
2960

0.983
0.010
0.001
0.005
0.966
0.022
0.008
0.004
0.432
0.000
0.175
0.000
0.278
0.000
0.038
0.728
0.123
0.000
0.030
0.000
0.098
0.000
0.533
0.001
0.054
0.000
0.087
0.000
0.019
0.000
0.004
0.000
0.090
0.000
0.012
0.007
0.006
0.007
0.010
0.000
0.012
0.000
0.094
0.000
0.044
0.000
0.017
0.000
0.053
0.000
0.017
0.000
0.001
0.000
0.126
0.000
0.086
0.000
0.010
0.000

0.130
0.102
0.039
0.072
0.181
0.146
0.090
0.061
0.495
0.000
0.380
0.019
0.448
0.000
0.191
0.445
0.329
0.019
0.172
0.019
0.297
0.000
0.499
0.033
0.225
0.019
0.282
0.019
0.136
0.000
0.061
0.019
0.286
0.000
0.108
0.086
0.074
0.084
0.102
0.000
0.107
0.000
0.292
0.000
0.206
0.000
0.130
0.000
0.224
0.000
0.128
0.000
0.039
0.019
0.332
0.019
0.280
0.019
0.102
0.019

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1

2960
2960
2960
2960
2960
2960
2960

0.102
0.417
0.351
0.094
0.023
0.002
0.010

0.303
0.493
0.477
0.292
0.151
0.047
0.098

0
0
0
0
0
0
0

1
1
1
1
1
1
1

2960
2960
2960
2960

0.002
0.726
0.191
0.081

0.047
0.446
0.394
0.272

0
0
0
0

1
1
1
1

Table 4 (continued): Descriptive statistics (Comorbidity variables and severity variables at admission)
Variables# obs
MAP(mean arterial pressure)
map0: =1 if MAP < 60
2960
map1: =1 if 60 <= MAP < 802960
map2: =1 if 80 <= MAP < 1002960
map3: =1 if 100 <= MAP < 1202960
map4: =1 if 120 <= MAP < 1502960
map5: =1 if 150 <= MAP
2960
map_y: =1 if MAP unknown
2960
Height (cm)
hei0: =1 if hei < 1402960
hei1: =1 if 140 <= hei < 1502960
hei2: =1 if 150 <= hei < 1602960
hei3: =1 if 160 <= hei < 1702960
hei4: =1 if 170 <= hei < 1802960
hei5: =1 if 180 <= hei
2960
hei_y: =1 if height unknown
2960
Weight (kg)
wei0: =1 if wei < 402960
wei1: =1 if 40 <= wei < 50
2960
wei2: =1 if 50 <= wei < 60
2960
wei3: =1 if 60 <= wei < 702960
wei4: =1 if 70 <= wei < 802960
wei5: =1 if 80 <= wei < 902960
wei6: =1 if 90 <= wei2960
wei_y: =1 if weight unknown
2960
BMI
bmi0: =1 if bmi < 18.5
2960
bmi1: =1 if 18.5 <= bmi < 252960
bmi2: =1 if 25 <= bmi < 302960
bmi3: =1 if 30 <= bmi2960
bmi_y: =1 if BMI unknown
2960
Glucoseadmglu0: =1 if admglu < 502960
admglu1: =1 if 50 <= admglu < 250
2960
admglu2: =1 if 250 <= admglu < 4002960
admglu3: =1 if 400 <= admglu < 600
2960
admglu4: =1 if 600 <= admglu
2960
admglu_y: =1 if Glucose unknown
2960
Albuminadmalb0: =1 if admalb < 22960
admalb1: =1 if 2 <= admalb < 52960
admalb2: =1 if 5 <= admalb
2960
admalb_y: =1 if Albumin unknown
2960
Highest creatinine
admlcre9_1y: =1 if Highest creatinine >= 25
2960
admlcre9_1d: Highest creatinine unknown
2960
Hematocrit
admhemac0: =1 if admhemac < 202960
admhemac1: =1 if 20 <= admhemac < 25
2960
admhemac2: =1 if 25 <= admhemac < 302960
admhemac3: =1 if 30 <= admhemac < 352960
admhemac4: =1 if 35 <= admhemac < 55
2960
admhemac5: =1 if 55<= admhemac
2960
admhemac_y: =1 if Hematocrit unknown
2960
White blood cells (unit:000)
admwbc0: =1 if admwbc < 10002960
admwbc1: =1 if 1000 <= admwbc < 15000
2960
admwbc2: =1 if 15000 <= admwbc
2960
admwbc_y: =1 if White blood cells unknown
2960
Platelets (unit:0000)
admlplt0: =1 if admlplt < 202960
admlplt1: =1 if 20 <= admlplt < 1002960
admlplt2: =1 if 100 <= admlplt < 500
2960
admlplt3: =1 if 500 <= admlplt
2960
admlplt_y: =1 if Platelets unknown
2960
Blood urea nitrogenbunsun0: =1 if bunsun < 102960
bunsun1: =1 if 10 <= bunsun < 20
2960
bunsun2: =1 if 20 <= bunsun < 30
2960
bunsun3: =1 if 30 <= bunsun
2960
bunsun_y: =1 if Blood urea nitrogen unknown
2960
CH_1y: EKG trace: MI /injury (excluding old MI)
2960
CH_1d: EKG trace: MI /injury (excluding old MI): unknown
2960
CJ_1y: EKG trace: transmural (new qwave) MI2960
CJ_1d: EKG trace: transmural (new qwave) MI: unknown
2960
CK_1y: EKG trace: old/remote MI2960
CK_1d: EKG trace: old/remote MI: unknown
2960
CL_1y: EKG trace: ventricular tachycardia/flutter
2960
CL_1d: EKG trace: ventricular tachycardia/flutter: unknown
2960
CM_1y: EKG trace: atrial fibrillation/flutter
2960
CM_1d: EKG trace: atrial fibrillation/flutter: unknown
2960
CN_1y: EKG trace: LBBB
2960
CN_1d: EKG trace: LBBB: unknown
2960
CO_1y: EKG trace: RBBB
2960
CO_1d: EKG trace: RBBB: unknown
2960
CP_1y: EKG trace: left fascicular blocks
2960
CP_1d: EKG trace: left fascicular blocks: unknown
2960
CQ_1y: EKG trace: heart block, 2nd/3rd degree2960
CQ_1d: EKG trace: heart block, 2nd/3rd degree: unknown
2960
CS_1y: CHF (congestive heart failure) /pulmonary edema on chest X rays
2960
CS_1d: CHF (congestive heart failure) /pulmonary edema on chest X rays: unknown
2960
CW_1y: Stress test suggests ischemia
2960
CW_1d: Stress test suggests ischemia: unknown
2960

Mean

S.D.

Min

Max

0.019
0.205
0.411
0.236
0.062
0.003
0.063

0.138
0.404
0.492
0.425
0.241
0.058
0.243

0
0
0
0
0
0
0

1
1
1
1
1
1
1

0.007
0.076
0.200
0.374
0.142
0.006
0.195

0.082
0.265
0.400
0.484
0.350
0.074
0.396

0
0
0
0
0
0
0

1
1
1
1
1
1
1

0.019
0.100
0.230
0.261
0.138
0.045
0.017
0.000

0.136
0.301
0.421
0.439
0.345
0.206
0.131
0.000

0
0
0
0
0
0
0
0

1
1
1
1
1
1
1
0

0.047
0.500
0.213
0.030
0.211

0.212
0.500
0.409
0.170
0.408

0
0
0
0
0

1
1
1
1
1

0.002
0.833
0.104
0.014
0.001
0.046

0.043
0.373
0.305
0.120
0.033
0.209

0
0
0
0
0
0

1
1
1
1
1
1

0.003
0.845
0.016
0.136

0.058
0.362
0.124
0.343

0
0
0
0

1
1
1
1

0.001
0.034

0.027
0.182

0
0

1
1

0.006
0.010
0.035
0.151
0.776
0.003
0.019

0.074
0.098
0.185
0.358
0.417
0.058
0.136

0
0
0
0
0
0
0

1
1
1
1
1
1
1

0.000
0.899
0.094
0.006

0.019
0.301
0.292
0.079

0
0
0
0

1
1
1
1

0.425
0.557
0.012
0.000
0.006

0.494
0.497
0.108
0.000
0.079

0
0
0
0
0

1
1
1
0
1

0.069
0.681
0.182
0.058
0.010
0.896
0.000
0.174
0.271
0.041
0.000
0.154
0.001
0.089
0.001
0.014
0.001
0.059
0.001
0.010
0.001
0.055
0.001
0.220
0.002
0.011
0.846

0.254
0.466
0.386
0.234
0.100
0.305
0.000
0.379
0.445
0.198
0.019
0.361
0.027
0.285
0.027
0.120
0.027
0.235
0.027
0.098
0.033
0.229
0.027
0.414
0.043
0.105
0.361

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Table 5: OLS estimation using Rokuyo
Dependent variable: Rehospitalization dummy (within 1 year, =1 if rehospitalized)(A) Individual demograraphics
days_h: LOS
Age
P_1: Sex (=1 if male)iins1: type of medical insurance (National Health Insurance) [base case]iins2: type of medical insurance (Employees Health / Mutual Assistance Insurance)
iins3: type of medical insurance (no insurance, 100% OOP)
iins4: type of medical insurance (Government-managed insurance)
iins5: type of medical insurance (Public assistance)
iins6: type of medical insurance (Health Insurance Society)fam: Number of family members living with a patient
spouse: Presence of spouse (=1 if yes)
_IFA_1_1 : hospital 1 dummy [base sase]_IFA_1_2 : hospital 2 dummy_IFA_1_3 : hospital 3 dummy_IFA_1_4 : hospital 4 dummy_IFA_1_5 : hospital 5 dummy_IFA_1_6 : hospital 6 dummy_IFA_1_7 : hospital 7 dummy_IFA_1_8 : hospital 8 dummy_IFA_1_9 : hospital 9 dummy_IFA_1_10 : hospital 10 dummy_IFA_1_11 : hospital 11 dummy_IFA_1_12 : hospital 12 dummy_IFA_1_13 : hospital 13 dummy_IFA_1_14 : hospital 14 dummy_IFA_1_15 : hospital 15 dummy(B) Cormobidity variables at admission
uri1: Continence: totally continenturi2: Continence: occasionally incontinenturi3: Continence: no urine output
uri4: Continence: unknown
walk1: Mobility: Walks Independently
walk2: Mobility: Walks with assistancewalk3: Mobility: Unable to walk
walk4: Mobility: unknown
X_1y: Hypertension
X_1d: Hypertension: unknown
Y_1y: Hyperlipemia
Y_1d: Hyperlipemia: unknown
Z_1y: Diabetes （any type）
Z_1d: Diabetes （any type）: unknown
AA_1y: Diabetes treated by insulin
AA_1d: Diabetes treated by insulin: unknown
AB_1y: Angina
AB_1d: Angina: unknown
AD_1y: Cardiac heart failure or pulmonary edema
AD_1d: Cardiac heart failure or pulmonary edema: unknown
AF_1y: Old myocadial infarction
AF_1d: Old myocadial infarction: unknown
AH_1y: Current cigarette smoker
AH_1d: Current cigarette smoker: unknown
AJ_1y: Arrhythmia
AJ_1d: Arrhythmia: unknown
AK_1y: Family medical history of schemic heart disease
AK_1d: Family medical history of schemic heart disease: unknown
AL_1y: Renal failure
AL_1d: Renal failure: unknown
AM_1y: Cirrhosis
AM_1d: Cirrhosis: unknown
AN_1y: Cerebrovascular accident: Cerebral infarction
AN_1d: Cerebrovascular accident: Cerebral infarction: unknown
AO_1y: Cerebrovascular accident: Brain hemorrhage
AO_1d: Cerebrovascular accident: Brain hemorrhage: unknown
AP_1y: Cerebrovascular accident: Subarachnoid hemorrhage
AP_1d: Cerebrovascular accident: Subarachnoid hemorrhage: unknown
AQ_1y: COPD
AQ_1d: COPD: unknown
AR_1y: Aneurysm of aorta
AR_1d: Aneurysm of aorta: unknown
AS_1y: Ulcus pepticum
AS_1d: Ulcus pepticum: unknown
AT_1y: Cancer
AT_1d: Cancer: unknown
AU_1y: Autoimmune disease
AU_1d: Autoimmune disease: unknown
AV_1y: Drug allergy/med reaction
AV_1d: Drug allergy/med reaction: unknown
AW_1y: Dementia/alzheimer's disease
AW_1d: Dementia/alzheimer's disease: unknown
AX_1y: Terminal illness
AX_1d: Terminal illness: unknown
AY_1y: CAG history
AY_1d: CAG history: unknown
AZ_1y: PTCA history
AZ_1d: PTCA history:unknown
BA_1y: CABG history
BA_1d: CABG history: unknown

Column (1)coefficient
S.E.
0.00310.0014-0.0267-0.0003-0.0771-0.0357
0.0344-0.02160.00470.0272-0.3799-0.2107-0.0256-0.5599-0.0637-0.0750-0.3816-0.4539-0.3025-0.6407-0.3498-0.5702-0.6730-0.50340.0009 ***0.0011
0.02200.02120.08710.0400 **0.09540.0303 ***0.00320.01880.0113 ***0.0123 ***0.0122 **0.0129 ***0.0088 ***0.0130 ***0.0099 ***0.0128 ***0.0068 ***0.0104 ***0.0097 ***0.0113 ***0.0165 ***0.0085 ***Column (2)coefficient
S.E.
0.00240.0012-0.0158

0.0008 ***0.00120.0272-0.0022-0.0425-0.0260
0.0508-0.02070.00480.0199-0.3308-0.1671-0.0388-0.4836-0.0508-0.0708-0.4089-0.4244-0.3085-0.6033-0.2941-0.5765-0.6687-0.5023

0.02610.09010.04030.08070.03380.00340.01960.0250 ***0.0217 ***0.0167 **0.0413 ***0.0200 **0.0252 ***0.0294 ***0.0266 ***0.0291 ***0.0281 ***0.0264 ***0.0174 ***0.0272 ***0.0191 ***0.08850.09130.12070.13000.03100.02820.0496
0.0371-0.3261-0.0635-0.0011-0.0957
0.06250.95950.0697-0.31110.0203-0.0174
0.0612-0.0320
0.40610.0456-0.2400-0.1552-0.0044-0.26240.00730.1708-0.2373-0.11220.3670-0.0051
0.0465-0.28710.33620.31670.0726 *0.07830.14900.0129 ***0.02620.1013 ***0.06580.06560.07270.0263 **0.0702 ***0.08230.1178 ***0.04230.01120.08800.03530.0781 ***0.0264 *0.0620 ***0.0714 **0.14900.0904 ***0.03270.1136
0.0994 **0.0436 **0.0971 ***0.0746
0.07160.02800.0586
0.09330.04440.0601 ***0.0722 ***0.15440.0379 ***0.0509 *0.0769 **-0.00730.07460.04280.0154-0.16090.3441-0.1664-0.1071
0.09190.1637-

Table 5 (continued): OLS estimation using Rokuyo
Dependent variable: Rehospitalization dummy (within 1 year, =1 if rehospitalized)(C ) Sererity variables on admission
Heart rate
admspls0: =1 if heart rate<60admspls1: =1 if 60<=heart rate<80admspls2: =1 if 80<=heart rate<100admspls3: =1 if 100<=heart rate<120admspls4: =1 if 120<=heart rate<150admspls5: =1 if 150<=heart rate
admspls_y: =1 if heart rate unknown
Temperatureadmtmp1: =1 if temperature>38.3
admtmp2: =1 if 35.8<=temperature<38.3
admtmp3: =1 if temperature<35.8
admtmp_y: =1 if temperature unknown
MAP(mean arterial pressure)
map0: =1 if MAP<60map1: =1 if 60<=MAP<80map2: =1 if 80<=MAP<100
map3: =1 if 100<=MAP<120
map4: =1 if 120<=MAP<150
map5: =1 if 150<=MAP
map_y: =1 if MAP unknown
Hight (cm)
hei0: =1 if hei<140
hei1: =1 if 140<=hei<150
hei2: =1 if 150<=hei<160
hei3: =1 if 160<=hei<170
hei4: =1 if 170<=hei<180
hei5: =1 if 180<=hei
hei_y: =1 if height unknown
Weight (kg)
wei0: =1 if wei<40
wei1: =1 if 40<=wei<50
wei2: =1 if 50<=wei<60
wei3: =1 if 60<=wei<70
wei4: =1 if 70<=wei<80
wei5: =1 if 80<=wei<90
wei6: =1 if 90<=wei
wei_y: =1 if weight unknown
BMI
bmi0: =1 if bmi<18.5
bmi1: =1 if 18.5<=bmi<25
bmi2: =1 if 25<=bmi<30
bmi3: =1 if 30<=bmi
bmi_y: =1 if BMI unknown
Glucoseadmglu0: =1 if admglu<50admglu1: =1 if 50<=admglu<250admglu2: =1 if 250<=admglu<400admglu3: =1 if 400<=admglu<600admglu4: =1 if 600<=admglu
admglu_y: =1 if Glucose unknown
Albuminadmalb0: =1 if admalb<2admalb1: =1 if 2<=admalb<5admalb2: =1 if 5<=admalb
admalb_y: =1 if Albumin unknown
Highest creatinine
admlcre9_1y: =1 if Highest creatinine>=25
admlcre9_1d: Highest creatinine unknown
Hematocrit
admhemac0: =1 if admhemac<20admhemac1: =1 if 20<=admhemac<25admhemac2: =1 if 25<=admhemac<30admhemac3: =1 if 30<=admhemac<35admhemac4: =1 if 35<=admhemac<55admhemac5: =1 if 55<=admhemac
admhemac_y: =1 if Hematocrit unknown
White blood cells (unit:000)
admwbc0: =1 if admwbc<1000admwbc1: =1 if 1000<=admwbc<15000
admwbc2: =1 if 15000<=admwbc
admwbc_y: =1 if White blood cells unknown
Platelets (unit:0000)
admlplt0: =1 if admlplt<20admlplt1: =1 if 20<=admlplt<100
admlplt2: =1 if 100<=admlplt<500
admlplt3: =1 if 500<=admlplt
admlplt_y: =1 if Platelets unknown
Blood urea nitrogenbunsun0: =1 if bunsun<10bunsun1: =1 if 10<=bunsun<20bunsun2: =1 if 20<=bunsun<30
bunsun3: =1 if 30<=bunsun
bunsun_y: =1 if Blood urea nitrogen unknown
CH_1y: EKG trace: MI /injury (excluding old MI)
CH_1d: EKG trace: MI /injury (excluding old MI): unknown
CJ_1y: EKG trace: transmural (new qwave) MI
CJ_1d: EKG trace: transmural (new qwave) MI: unknown
CK_1y: EKG trace: old/remote MI
CK_1d: EKG trace: old/remote MI: unknown
CL_1y: EKG trace: ventricular tachycardia/flutter
CL_1d: EKG trace: ventricular tachycardia/flutter: unknown
CM_1y: EKG trace: atrial fibrillation/flutter
CM_1d: EKG trace: atrial fibrillation/flutter: unknown
CN_1y: EKG trace: LBBB
CN_1d: EKG trace: LBBB: unknown
CO_1y: EKG trace: RBBB
CO_1d: EKG trace: RBBB: unknown
CP_1y: EKG trace: left fascicular blocks
CP_1d: EKG trace: left fascicular blocks: unknown
CQ_1y: EKG trace: heart block, 2nd/3rd degree
CQ_1d: EKG trace: heart block, 2nd/3rd degree: unknown
CS_1y: CHF (congestive heart failure) /pulmonary edema on chest X rays
CS_1d: CHF (congestive heart failure) /pulmonary edema on chest X rays: unknown
CW_1y: Stress test suggests ischemia
CW_1d: Stress test suggests ischemia: unknown
Constant
R-squared

Number of observations(Note) ***, **, and * indicate significance at the 1%, 5% and 10% levels.

coefficient

S.E.

coefficient-0.0835-0.1111-0.1305-0.1242-0.07990.62230.20292690

0.0752 ***S.E.

0.0504 *0.0355 ***0.0361 ***0.0450 ***0.05740.08040.2813---0.0521-0.0557-0.0046

0.1536
0.15380.14850.12860.14480.11790.12180.40190.05440.08370.0887
0.09500.07870.1611
0.09260.01040.12470.15180.13990.12900.06990.1946
0.09620.07100.07390.07980.07020.18000.14120.13040.12130.11340.07250.0946-

0.09630.06640.06380.07340.08620.11510.1294--0.1220-0.0758-0.0674
0.07130.13500.07500.06250.1483-0.1164-0.0513-0.1816
0.2967-0.13180.15490.14650.1586
0.24770.1571

0.05220.03170.10070.19060.18780.19400.0462-0.0262

0.32650.0585-0.0134-0.1672-0.0720-0.0797-0.05230.01550.18130.10370.11930.1047
0.09100.14220.4536
0.48190.29520.1118 ***0.1237 ***0.1116 ***0.15140.14700.0127-0.11380.1086
0.1130-0.05650.02330.03230.02350.11190.07540.05690.0866
0.03820.0305-0.00400.02450.02890.03730.00170.0558-0.4338
0.09400.01510.02570.9343
0.0988-0.05900.03450.02300.06200.04170.03400.0000 (omitted)-0.07120.0744-0.2730
0.0796-0.02020.03180.06190.0248-0.45120.02290.01290.04890.06150.0308-0.3276
0.50900.2520
2690

**

**
*

*
**
**
*

**

***
***
*

***

**
***
**

Table 6: 2SLS, 2-Step GMM, and LIML estimation using RokuyoSpecification (1)2SLS

days_h: LOS
Age
P_1: Sex (=1 if male)iins1: type of medical insurance (National Health Insurance) [base case]iins2: type of medical insurance (Employees Health / Mutual Assistance Insurance)
iins3: type of medical insurance (no insurance, 100% OOP)
iins4: type of medical insurance (Government-managed insurance)
iins5: type of medical insurance (Public assistance)
iins6: type of medical insurance (Health Insurance Society)fam: Number of family members living with a patient
spouse: Presence of spouse (=1 if yes)rok1_d: Rokuyo at discharge (Butsumetsu )rok2_d: Rokuyo at discharge (Taian )rok3_d: Rokuyo at discharge (Shakko )rok4_d: Rokuyo at discharge (Sensho )rok5_d: Rokuyo at discharge (Tomobiki )rok6_d: Rokuyo at discharge (Senbu )rok1_h: Rokuyo at admission (Butsumetsu )rok2_h: Rokuyo at admission (Taian )rok3_h: Rokuyo at admission (Shakko )rok4_h: Rokuyo at admission (Sensho )rok5_h: Rokuyo at admission (Tomobiki )rok6_h: Rokuyo at admission (Senbu )Constant
R-squared
F value
Kleibergen-Paap Wald rk F statistic
Sargan-Hansen J statistic [P-value]

Number of observations(Note)First stage
Second stage
Coefficient
S.E.
Coefficient
S.E.
0.00580.00800.05500.0274 **0.00090.0017 ***2.3516
0.5277 ***-0.0286
0.0236
0.03380.59790.00250.0170-2.7166
2.3065-0.0730
0.0819-2.2318
1.1688-0.0267
0.0361 **4.96942.3074 **0.01490.0922-0.7949
1.2016-0.01890.0271 ***-0.2399
0.15320.00530.0034-2.30470.8644 ***0.03500.02771.54770.7480 **-0.0844
1.19070.86701.14580.3916
0.77170.30950.67790.05201.1098-1.8235
1.0951-1.4883
0.7869 *-1.15540.8582-0.50310.870419.2471 11.1911
0.750
0.213 ***
0.3041
12.00
12.36
4.490 [0.8763]
2690
2690

1: Standard errors are clustered at health facility level. ***, **, and * indicate significance of the 1%, 5%, and 10% levels.
2: In all the specifications, comorbidity variables at admission, severity variables at admission, and health facility level fixed effect are included.

Specification (2)Two step GMM
Second stage
Coefficient
S.E.
0.004
0.015
0.001
0.001
-0.020
0.056
0.005
0.004
0.024
0.032
-

-

2690

Sprcification (3)LIMLSecond stage
Coefficient
S.E.
0.00230.01310.00120.0013-0.0155
0.0470-0.00220.0248-0.0428
0.0927-0.02620.03980.0515
0.0966-0.02080.02980.00470.00520.0196
0.03440.35140.36622690

Table 7: Robustness checks
OLS
Length of stayTime-window ofrehospitalization
6 months
9 months
1 year
2 years

Coefficient
0.00210.00190.00240.0020S.E.
0.0007 ***0.0008 **0.0008 ***0.0009 **2SLSCoefficientS.E.

Two step GMM
Coefficient

S.E.

LIML
Coefficient

S.E.

-0.0008-0.00130.00580.00630.00760.00810.00800.0086-0.0083-0.0030
0.00430.01110.0048 *0.00460.01540.0069-0.0036-0.0025
0.00230.00790.01450.01120.01310.0120

6 months
0.06990.0179 ***0.07679 months
0.07050.0208 ***0.0082log(LOS)
1 year
0.07610.0202 ***0.07392 years
0.06890.0228 ***0.1414(Note) ***, **, and * indicate significance of the 1%, 5%, and 10% levels.

0.19320.16890.18310.21370.1331-0.0166-0.0176
0.10900.12000.12180.12830.16150.0808-0.0094
0.07330.16140.30910.21710.23820.2707

LOS