GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.149

Economic and Behavioral Factors in an Individual’s Decision to Take
the Influenza Vaccination in Japan

Yoshiro Tsutsui, Uri Benzion, and Shosh Shahrabani

August 2010; revised February 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

ECONOMIC AND BEHAVIORAL FACTORS IN AN INDIVIDUAL’SDECISION TO TAKE THE INFLUENZA VACCINATION IN JAPAN†

YOSHIRO TSUTSUI*a, URI BENZIONb, and SHOSH SHAHRABANIc
a

Graduate School of Economics, Osaka University, Japan; CREED, FEB, University of
Amsterdam, Netherlandsb

Department of Economics, Ben Gurion University; Interdisciplinary Department of Social
Sciences, Western Galilee College, Israelc*Economics and Management Department, Max Stern Academic College of Emek Yezreel, Israel

Corresponding address: CREED, FEB, University of Amsterdam, Roetersstraat 11, 1018WB

Amsterdam, Netherlands; Phone: +31 20 525 4295; Fax: +31 20 525 5283; E-mail:tsutsui@econ.osaka-u.ac.jp† The authors gratefully acknowledge financial support from Center of Excellent (COE) andGlobal COE projects of Osaka University.
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ABSTRACTIn this paper, we investigate what people in Japan consider when deciding to take the influenza
vaccination. We develop an economic model to explain the mechanism by which people decide to
take the influenza vaccination. Using our model and the data obtained from a large-scale survey
we conducted in Japan, we demonstrated that people make rational decisions about vaccinations
after considering its cost and benefits. People consider the probability of infection, severity of thedisease, and the vaccination’s effectiveness and side effects. The time discount rate is anotherconsideration because the timing of costs and benefits of the vaccination differ. Risk aversion(fearing the contraction of the flu and vaccination’s side effects) also affects the decision. People
also deviate from rationality—altruism and status quo bias play important roles in thedecision-making. Overconfidence indirectly affects the decision via perception variables such as
the subjective probability of infection and assessment of influenza’s severity. The decision also
depends on attributes such as gender, age, and marital status. If the general perception of flu andvaccination is inaccurate, supplying accurate information regarding those may increase or
decrease the vaccination rate, depending on whether this perception is, respectively, higher orlower than the objective rates. Thus, we examine whether the general perception is biased. Our
survey suggests that disseminating information on the vaccination’s effectiveness may increase therate of vaccination, whereas that on the probability of infection may have the opposite effect.

KEY WORDS: influenza; inoculation; survey; time preference; JapanJEL Classification Numbers: I19

Running head: Decision to take influenza vaccination in Japan2

1. INTRODUCTION
Influenza can be a serious disease in modern societies. As a serious pandemic, it can cause
morbidity and mortality, as in 2009 with the swine flu. Since vaccination against flu canpotentially prevent it, a study of the factors that are considered when making the decision to takeor not to take the influenza vaccine can help prevent outbreaks of the disease. The objective of thecurrent study is to examine how willingness to take the influenza vaccination depends on
economic aspects such as costs and benefits as well as behavioral aspects including perceptions ofinfluenza and the vaccination against it, preference parameters, and personal attributes. To achieve
this aim, we use the behavioral economic model and results of a large data survey in Japan.
The study takes an economic approach and determines the relationship between vaccine
taking and the costs/benefits of vaccination from utility-maximizing behavior. Based on the classic
expected utility framework, we assume that people compare the benefits and costs of taking thevaccine, and choose to be vaccinated if the benefits exceed the costs. Our model predicts that thedecision to be vaccinated depends on the perceived probability of infection, severity of the disease,side effects of vaccination, and inoculation costs.
The economic approach has been used to examine individual decisions regarding whether or
not to take the vaccine [4, 9, 11]. Nevertheless, the theoretical framework of Shahrabani et al. [11]show that the decision to take the vaccine based on objective factors can differ from that based on
subjective or psychological factors. Their results show that values of objective factors predict avery high vaccination rate, implying that an individual’s perceptions and beliefs do not accuratelyreflect actual values; further, it predicts that behavioral factors may be important in the decision.
For example, perceived risks of infection may affect an individual’s propensity to be immunized [9].
Thus, psychological factors, in addition to economic variables, should be considered to fully
understand the reasons for the vaccination rate.
The Health Belief Model (HBM) developed by Rosenstock et al. [10] is a traditional
psychological approach to explaining and predicting preventive health behavior. HBM has beenused to explore a variety of health behaviors, including vaccination [3, 6, 8, 12, 14]. According to
the HBM, the acceptance of an influenza vaccine depends on the following predictors: perceptionof susceptibility to influenza, beliefs about the severity of influenza, perceived benefits of the3

vaccine in preventing influenza, and perceived barriers to accepting a vaccine [3, 5].
The factors that explain vaccination behavior according to utility-maximizing behavior arevery similar to those of the HBM. However, our theory predicts that an individual’s time discountand risk aversion also play important roles in the decision to take a vaccination or not. We
hypothesize that people choose to take a flu vaccination when the benefits exceed the costs(specified as benchmark equations in section 2.1), but introduce an extended model that takes into
account behavioral aspects which may affect the decision to be vaccinated. In particular, we
examine whether psychological factors such as altruism, overconfidence, and the status quo effectplay an important role in the decision.
We designed questions concerned with a respondent’s beliefs and preferences with regard to
influenza and vaccination, and conducted a large-scale survey in Japan to test our theoretical
hypothesis. Thus, although we rely on the economic approach, we actually use perception or belief
variables, as does the HBM, so that our results are immune to the critique of [11].
The current study contributes to existing literature by (a) theoretically and empiricallyelucidating the important role of time discounting and risk aversion in the decision to take avaccination, (b) expanding the behavioral economic model to include the impact of altruism on thewillingness to be vaccinated; (c) presenting empirical results of the model using a large-scale
survey in Japan; (d) applying the results to derive policy implications with regard to disseminationof information on influenza and the vaccination against it; and (e) comparing factors affecting thewillingness among Japanese people to be vaccinated to factors affecting the population in the USA
as reported in previous studies [14].
The paper is organized as follows. In section 2, we explain the analytical framework including
the basic model and extended model. In subsections 2.1 and 2.2, we develop a model based onrationality, while in subsection 2.3, we introduce behavioral variables to the basic model. Section
3 explains the methods and describes the survey in Japan. Section 4 is devoted to the results.
Section 5 summarizes the study and concludes by showing how the inoculation rate can beincreased.

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2. ANALYTICAL FRAMEWORK
2.1. Model
Benefits: The benefits of vaccination are (a) improving current and future health and (b) reducing
the degree of inconvenience to one’s family and friends when one is infected with flu. Thesebenefits are realized a couple of months after being vaccinated. Thus, the magnitude of thebenefits depends on how one perceives (1) the seriousness of the disease, (2) how the vaccination
relieves the condition, and (3) the probability of infection, as well as his/her time discount rate,
and risk aversion. Time discounting matters because the benefits of vaccination are received in the
future, while the costs are paid earlier. Risk aversion involves assessing the risk of contracting flu
and the side effects of the vaccination.
We denote the probability of contracting flu by PROB, the effectiveness of the vaccination by
EFFECT, and the damage of contracting flu by DAMAGE. Thus, the damage of contracting flu isreduced to (1  EFFECT )  DAMAGE , where EFFECT is assumed to take on a value between
zero and one.
Costs: The cost of vaccination (COST) consists of the fee for inoculation (FEE), opportunity,and psychological costs of taking the vaccination, and perceived side effects of vaccination(SIDEEFFECT). We assume that people suffer these costs at the time of vaccination.
Decision to be vaccinated: The utility of the individual in our model is defined overconsumption in two periods, x1 and x2 . In period 1, the individual decides whether he/shewants to take the vaccine, and in period 2, the individual may be infected by influenza. Thus, theexpected utility in the case of taking vaccination is:u ( x1  COST )   (1  PROB )  u ( x2 )  PROB  u ( x2  (1  EFFECT )  DAMAGE ) (1)while the expected utility of not taking vaccination is:u ( x1 )   (1  PROB)  u ( x2 )  PROB  u ( x2  DAMAGE )

(2)

where  is the discount factor. A person will take the vaccination if the value of Equation (1) islarger than the value of Equation (2).
Assuming that x1  x2  COST and DAMAGE, and expanding the utility function to the5second order, we find that people take the vaccination, if:

 COST  PROB  EFFECT  DAMAGE1  COST 2    PROB  EFFECT  (2  EFFECT )  DAMAGE2  0
2where  stands for the absolute risk aversion, (3)u". This inequality implies that people areu'more likely to take the vaccination when (a) PROB, (b) EFFECT, or (c) DAMAGE is greater, (d)COST or (e) time discount rate (1 1 ) is smaller, or (f) risk aversion (  ) is higher (lower,

respectively), in the case where the fear of getting the flu is greater (smaller) than the fear of side
effects, i.e., COST 2  ()   PROB  EFFECT  (2  EFFECT )  DAMAGE 2 (see Appendix 1).
Conditions (a) to (d) conform to the results of the HBM.
Assuming a linear function, (a) to (f) are described in Equation (4), which is the basic
equation for estimating willingness to take the vaccination (WTVACCIN).

WTVACCINi  a0  a1 PROBi  a2 EFFECTi  a3 DAMAGEi  a5 COSTi a6 i  a7 i  ui

(4)

where the subscript i stands for the individual i. It is straightforward to prove that a1 , a2  0 and

a3 , a5 , a6  0 , and a7 will be positive when DAMAGE dominates SIDEEFFECT.
To identify the channels through which risk aversion affects WTVACCIN, we adopt crossterms of risk aversion and COST, and risk aversion and DAMAGE, using the following equation.

WTVACCINi  a0  a1 PROBi  a2 EFFECTi  a3 DAMAGEi  a5COSTi  a6 i a8 i DAMAGE  a9 i COSTi  ui

(5)where it is demonstrated that a8  0 and a9  0 .

2.2. Variables in the basic equation
Willingness to get the vaccination: WTVACCIN is the respondent’s intention to take thevaccination within 12 months.
Probability of infection: PROB is the respondent’s assessment of the probability of being
infected with flu within 12 months, expressed as a percentage.

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Damage of flu: DAMAGE is the respondent’s assessment of the damage suffered if he/she
contracts flu. It consists of two elements: SEVERITY, the respondent’s assessment of the potential
severity of the disease; and BOTHER, the respondent’s assessment of the degree to which his/herfamily and friends would be inconvenienced if the respondent were infected.
Effectiveness of vaccination is denoted as EFFECT.
Cost of vaccination: We examine COST using the following: (a) the respondent’s assessmentof the seriousness of the side effects of a flu shot, SIDEEFFECT, (b) the monetary cost of the shot,and (c) the psychological costs. Variables relating to the monetary cost include the inoculation fee,
FEE, and per capita income, INCOME, used to normalize the FEE. Variables associated with theopportunity costs of taking the injection include wage and regional dummies, which include
factors such as the cost of transportation to the administering hospital.
Preferences: Preferences include time discount rate, TDR, and absolute risk aversion, ARA.
To determine TDR, we ask respondents which option they prefer: an earlier receipt with a smaller
reward or a later receipt with a larger reward. To determine ARA, we ask respondents which
option they prefer: lower wage with lower risk or higher wage with higher risk, following themethod of Barsky et al. [2]. Definitions of all the variables we used are presented in Appendix 2.
Using these notations of the variables, our basic Equation (4) is now described as

WTVACCIN i  b0  b1 PROBi  b2 EFFECTi  b3 SEVERITYi  b4 BOTHER
 b5 FEE  b6 SIDEEFFECT  b7 INCOMEi  b8TDR  b9 ARA i  u i(6)

2.3. Extension of the model considering behavioral variables
Our basic model assumes that rational individuals decide whether they want to take thevaccination based only on the costs and benefits of vaccination. However, other variables
representing behavioral preferences and attributes may also affect the decision. In this subsection,
we present an extended model that incorporates behavioral preferences and socio-economic
variables into the basic Equation (6).
Our extended model takes into consideration an individual’s altruism, overconfidence, anxiety
regarding his/her health, and experiences of vaccination and flu, i.e., behavioral preferences thatare often disregarded in traditional economics.
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Altruism: Those who are more altruistic and caring may be more likely to take a vaccine
because they want to avoid troubling other people. If so, the degree of altruism, ALTRUISM, has apositive

effectontakingavaccination.

To

examinethis,weinsert(b4  b22 ALTRUISM) BOTHER or b10 ALTRUISM b4 BOTHER instead of b4 BOTHER
in the regression, where b4 and b22 represent concern for family and friends, and b10 for the public.
We expect b4 and b22>0. In addition, b10>0 if a respondent believes that vaccination will mitigate
flu epidemics and improve social welfare.
Overconfidence: Overconfidence may lower a respondent’s assessment of the potential levelof PROB, SEVERITY, SIDEEFFECT, or BOTHER. However, these variables are already includedin the regression. To examine whether or not overconfidence affects vaccination behavior throughsome other channel not already specified in the regression, we add a variable for overconfidence,
OVERCON.
Anxiety over health condition: Those who are concerned about their health will tend to takethe vaccination. Thus, we take into account three variables: the degree of their health anxiety,
UNHEALTH, and whether they undergo blood tests periodically, TESTP, or when disease issuspected, TESTS.
Psychological costs: Status quo bias means that people are reluctant to try new things [7].
Accordingly, people who have never been vaccinated may resist taking the vaccination while
those who are accustomed to being vaccinated every year may be reluctant to stop being
vaccinated. We measure this psychological cost of taking the vaccination by the respondent’s
experience with flu vaccination, EXVACCIN. Those vaccinated in recent years are more likely to
be vaccinated again.
Past experience of catching flu: Past experience of being ill with the flu, EXFLU, is also
expected to influence WTVACCIN. Those seriously affected in the past will tend to take thevaccination, while those who experienced a mild infection may think that inoculation is
unnecessary. Those seriously affected would have clearer memories of their illness and EXFLU is
expected to be positive.
Attributes: We include gender, age, marital status, whether or not the respondent has children,and level of education in our extended regression Equation (7):8

WTVACCIN i  b0  b1 PROBi  b2 EFFECTi  b3 SEVERITYi  b4 BOTHERi  b5 FEEi
 b6 SIDEEFFECTi  b7 INCOMEi  b8TDRi ( HOMEWORKi )  b9 ARAi (UMBRELLAi ) b10 ALTRUISM i  b11OVERCON i  b12 HEALTH i  b13TESTPi  b14TESTS i(7) b15 EXVACCIN i  b16 EXFLU i  b17 MALEi  b18 AGEi  b19UNMARRYi  b20 NOCHILDi b21 SCHOOLi  b22 ALTRUISM i  BOTHERi  u i

3. DATA AND THE ESTIMATION METHOD
3.1. Data
Data used in this paper were obtained from a survey conducted by the COE (Center of Excellence)
project of Osaka University in February 2005 with 4300 people from throughout Japan, randomly
selected by the double stratified random sampling method.1 The selected participants were visitedin their homes and given a questionnaire. Several days later, the filled-out questionnaires were
picked up from their homes; 2987 questionnaires (70%) were returned. The range, means, andstandard deviations of the main variables used for the analysis are presented in Table 1.

Place Table 1 here

3.2. Estimation method
Since willingness to get the vaccination, WTVACCIN, is an ordered variable from 1 to 5, weestimate Equation (6) by ordered probit. A problem with this estimation is that those who decide to
take the vaccination usually assess PROB to be lower than those who choose not to be vaccinateddo. Thus, a reverse causality between WTVACCIN and PROB exists, making PROB an
endogenous variable.
This conjecture has some support. WTVACCIN among 60--70-year-old respondents issignificantly higher than among 20--50-year-olds. 2 In contrast, PROB decreases with age,probably because elderly people are more likely to take the flu vaccination than younger people
and believe that they are protected against the flu.
1

The questionnaire (in Japanese) is found at
http://www2.econ.osaka-u.ac.jp/coe/project/survey-0502.pdf.
2
The t statistic of the difference of means test between over- and under-60 groups is 10.2, rejecting the
hypothesis of equal means at very low probability. Thus, those over 60 are more willing to be
vaccinated than those under 60. Experience of vaccination, EXVACCIN, is also higher for over- 60s.

9

Since all the subjective variables, including WTVACCIN, may be endogenous, we check to see
if results that do not correct the endogeneity biases are robust. We eliminate this endogeneity byregressing each subjective variable over the exogenous variables to estimate a reduced form. In
the case of PROB, we construct the fitted value, FITTTED_PROB, as in regression Equation (8).
Using FITTED_PROB instead of PROB in Equation (7) will correct the endogeneity biases.3

PROBi  c 0  c 7 INCOME i  c 9 TDRi ( HOMEWORK i )  c10 ARA i (UMBRELLAi ) c11 ALTRUISM i  c12 OVERCON i  c13 HEALTH i  c14 TESTPi  c15 TESTS i
 c 8 EXVACCIN i  c16 EXFLU i  c17 MALE i  c18 AGE  c19UNMARRYi(8) c 20 NOCHILD i  c 21 SCHOOLi  u i
By the same token, SEVERITY and BOTHER may be affected by WTVACCIN. Thus, we estimate
Equation (8) for these two variables and construct the fitted values, FITTED_SEVERITY andFITTED_BOTHER.

4. RESULTS
4.1. Results of basic Equation (6)Estimates of basic Equation (6) are presented in the left-hand columns of Table 2. Because thedependent variable, WTVACCIN, is denoted in integers from 1 to 5, and larger values indicate
stronger willingness, we estimate the equation with ordered probit. However, we do not try tocorrect endogeneity biases here. Pseudo R

2

is around 0.11, high for a cross-sectional regression

with a large number of samples. Most of the estimates are significant and show the expected sign,
suggesting that basic Equation (6), assuming rational choice, explains vaccination behavior well.

Place Table 2 here

PROB, EFFECT, SEVERITY, BOTHER, and SIDEEFFECT are highly significant, showing a
positive sign as expected. FEE is not significant, implying that monetary cost is not important inJapan. However, per capita household income has a positive sign and is significant at the 5% level,
suggesting that higher income promotes WTVACCIN. This may be because the fee is of less3

Equation (8) is identified by the absence of the insignificant variables present in Equation (7).

10

importance to households with a higher income.
To save space, we do not show the results associated with opportunity costs in this regressionin Table 2. Therefore, the following is a brief report on the effect of opportunity costs. Important
opportunity costs include those for transportation and lost revenue. Direct data are not available
for transportation costs, so we make do with dummy variables dependant on the size of the
respondent’s city and region. Lost revenue is defined as the time required to take the vaccination
multiplied by the wage rate. In the questionnaire, we ask respondents how many hours they work
per week, how many days per year, and how much income they receive for their labor. Thus,
WAGE is calculated as labor income/(work hours × work days/7). We add WAGE and regional andcity-size dummies (proxies for lost time) to Equation (6). Although WAGE was expected tonegatively affect WTVACCIN, the estimate is not significant. Likewise, none of the regional andcity-size dummies were significant at the 5% level. However, while we found no evidence that
opportunity costs significantly affect vaccination behavior, this may not necessarily imply that
opportunity costs are unimportant since our data regarding opportunity costs are far from perfect.
TDR, the time discount rate for the immediate future, has a significant negative sign, as
predicted in our model, implying that those who heavily discount the expected benefits ofvaccination are less likely to take the vaccination. Discount rates over a long time horizon, such as
one year, however, are not significant, implying that time discounting for the immediate future is
crucial for WTVACCIN (results not shown to save space).
ARA has a significant positive sign, suggesting that fear of contracting flu dominates any fearof side effects from the vaccination. Thus, risk aversion promotes taking the vaccination.

4.2. Results of extended Equation (7)Results of the extended model Equation (7), including ALTRUISM in the regression, are presented
in the middle columns of Table 2. The fit of this specification is good. The adjusted R2

is muchimproved, compared to the basic Equation (6).4 The estimates of the variables included in basic
Equation (6) are almost the same.
The coefficient of ALTRUISM, b10, is significant at the 0.1% level, suggesting that those who
4This is partly due to the inclusion of experience of vaccination, EXVACCIN.

11

are altruistic tend to take vaccinations in order to avoid flu epidemics in the society.
UNHEALTH has a significant positive sign, as expected. However, TESTP and TESTS are
insignificant, even though they have positive signs. OVERCON is insignificant, suggesting that it
does not affect vaccination behavior through channels other than those specified in the regression,
such as PROB.
EXVACCIN is highly significant, indicating that having been vaccinated in the past reduces
the psychological costs of taking a vaccination. The large coefficient suggests that psychologicalcosts carry great weight in the decision to be vaccinated, supporting the “status quo bias”
hypothesis that human beings are reluctant to change. EXFLU is positive but insignificant,suggesting that painful memories of previous experiences with flu dominate relatively pleasantmemories, but only slightly.
Among attributes, females, the elderly, the unmarried, and those who have children are more
likely to take a vaccination. Schooling does not affect vaccination behavior.
When ALTRUISM*BOTHER replaces ALTRUISM in the equation (right-hand columns ofTable 2), the cross term is highly significant with a positive sign, implying that those who are
altruistic tend to take the vaccination to avoid troubling their families and not only inconsideration of avoiding flu epidemics in the society.5

4.3. Examination of time discount rate (TDR) and risk aversion (ARA)
While the total number of responses to the survey was 2987, only 1849 observations wereavailable for estimating Equation (6), partly because many respondents did not answer questions
on TDR and ARA.6 Thus, to check the robustness of the results, we present the results using
qualitative data associated with TDR and ARA in the left-hand columns of Table 3. There,
HOMEWORK is data relating to when the respondent did his/her homework as a child (those who
made it a rule to do homework, which symbolized an unpleasant obligation, early in the school
holiday are regarded as more patient or more future-oriented). UMBRELLA is determined byasking how high the probability of rain has to be to motivate the respondent to carry an umbrella
5

However, neither is significant when both terms are included at the same time.
The number of observations was also limited by the fact that many respondents did not answer thequestion regarding income.
6

12

(those who report that a low probability is sufficient are regarded as more risk-averse). In this case,2173 observations are available. UMBRELLA is positive and significant at the 0.1% level, and
HOMEWORK is negative and significant at the 5% level, confirming the results for TDR and ARA.
Estimates of other variables are almost unchanged from those presented in the left-hand columnsof Table 2, indicating that our results are robust for the sample size.7

Place Table 3 here

In the middle and right-hand columns of Table 3, we show the estimation results of Equation(5), which examines two channels through which risk aversion impacts WTVACCIN. When crossterms for risk aversion and severity (representing DAMAGE), ARA*SEVERITY, and risk aversion
and side effects (representing COST), ARA*SIDEEFFECT, are used, the coefficient of the former,
i.e. a8 in equation (5), is positive and significant at the 1% level, and that of the latter, i.e. a9 inequation (5), is negative and significant at the 5% level (middle columns). This result supports our
hypothesis that risk aversion operates through the fear of getting the flu, which is stronger than thefear of side effects of the vaccination. When a cross term for risk aversion, severity, and effect,
ARA*SEVERITY*EFFECT, is used instead of ARA*SEVERITY, the results are unchanged(right-hand columns).8 This result is consistent with the result that risk aversion, in general,
negatively affects WTVACCIN.

4.4. Perception variables
Estimation of the auxiliary Equation (8) reveals that OVERCON negatively affects PROB at the
10% significance level, SEVERITY at the 0.1% level, and BOTHER at the 10% level (the results
are not shown to save space). The dummy variable for being male, MALE, has the same signs as
those of OVERCON in all the estimations.9 As expected, UNHEALTH positively affects PROB,
7

However, estimates of the coefficients of variables associated with the cost of vaccination changed
from those in Table 2. This is because the psychological cost, EXVACCIN, is not included in basic
Equation (6). When EXVACCIN is included, the coefficients of SIDEEFFECT, INCOME, and FEE arealmost unchanged.
8
See footnote 7.
9
Barber and Odean [1] argue that males are more overconfident than females and use a male dummy
as a proxy of overconfidence.

13

SEVERITY, and BOTHER. A dummy variable for having no children, NOCHILD, understandably
has a negative coefficient in the BOTHER equation. AGE is highly significant with a negative signin PROB and BOTHER equations. SCHOOL is significantly negative for SEVERITY and positive
for BOTHER, but insignificant for PROB.

4.5. Results of Equation (7) using fitted values
To correct for possible endogeneity biases, we estimate Equation (7) using fitted values of PROB,
SEVERITY, and BOTHER (Table 4).10 The fitted values are used one by one because they arehighly correlated (the correlation coefficient is around 0.5), which seems to cause multicolinear
problems when all three are used at the same time.

Place Table 4 here

When PROB is substituted by FITTED_PROB, most of the estimates are unchanged fromthose in Table 2, suggesting that the subjective assessment of the probability of infection causes
the decision for taking the vaccination. FITTED_SEVERITY is significantly positive and mostestimates are similar to those in Table 2, suggesting that SEVERITY also causes WTVACCIN.
FITTED_BOTHER, however, is insignificant, casting a doubt on whether BOTHER really affects
WTVACCIN. The causality may be reverse, and it may be that those who plan to take thevaccination believe that they will bother their family less by doing so.

5. DISCUSSION AND CONCLUSION
This paper develops an economic model to explain the mechanism by which people in Japandecide whether or not to take the influenza vaccination. Using our model and data obtained from alarge-scale survey we conducted in Japan, we demonstrate that people rationally make thedecision considering the costs and benefits of vaccination. People take into account the probabilityof infection, severity of the disease, and effectiveness and side effects of the vaccination. Time

10

OVERCON and EXFLU, which are insignificant in the middle column of Table 2, are excluded fromthis regression.

14

discount rate matters because the timing of costs and benefits of vaccination differs. Risk aversion
also affects the decision through the fear of contracting the flu and the fear of side effects of thevaccination. However, we found no evidence that monetary cost is important in making thedecision.11 The results of this Japanese sample are compatible with the findings of Tsutsui et al.
[14] with respect to their USA sample.
Yet, people also deviate from rationality. Altruism, a behavioral variable, plays an importantrole in making the decision. To the best of our knowledge, the effect of altruism on the willingness
to be vaccinated has not yet been examined. The status quo bias is clearly recognized, in thatpeople who have never been vaccinated tend to avoid taking the vaccination. Overconfidence
affects the decision indirectly via perception variables such as the subjective probability of
infection and assessment of the severity of influenza, similar to findings in the USA sample [14].
The decision also depends on attributes such as gender, age, and marital status.
The results of this paper have interesting implications. First, raising the inoculation rate isoften thought to be socially desirable because taking a vaccination has strong externality. However,
we found that the degree of altruism affects the willingness to take vaccination not only throughthe channel of concern for one’s family and friends (the coefficient of ALTRUISM, b22, in Table 2),
but also through a channel of caring about a wider range of people (the coefficient of
ALTRUISM*BOTHER, b10, in Table 2). Therefore, if most Japanese people are altruistic, thevaccination rate will not differ substantially from the social optimum. However, our survey
indicates that 44% of Japanese respondents show no altruism, suggesting that it is desirable for thesociety to raise the vaccination rate to a level higher than the rate that people choose
spontaneously.12
Second, if the general perception of flu and vaccination is inaccurate, supplying accurate
information on the illness, its possible complications, and the effectiveness of the vaccination willprobably raise or lower the vaccination rate, depending on whether this perception is higher orlower than the objective rates. Thus, we examine whether the general perception is biased,
although our caveat is that the following assessment is crude. WTVACCIN depends on six
11However, since previous studies, such as Steiner et al. [13], found that monetary cost has an impact
on the decision to take a vaccination, our results should be examined further from various aspects.
12
In the USA, only 24% are not altruistic based on our survey results.

15

perceptions: PROB, SEVERITY, BOTHER, EFFECT, SIDEEFFECT, and FEE. The mean PROB
is 24%, which is very high considering the fact that according to the website of “global security”(http:// ww.globalsecurity.org/security/ops /hsc-scen-3_flu-pandemic-deaths.htm), the influenza
infection rate is 5%–15% (except during pandemic periods). Although there are no statistics on the
total number of flu cases in Japan, based on the 1.56 million infections reported in 2005 from4700 hospitals, the probability of infection is only 1.5% (A website of National Infectious Disease
Surveillance Center: http:// dsc.nih.go.jp/idwr/ydata/report-Jb.html). This number, of course,
underestimates the true rate because it is based on reports from the limited number of hospitals.
More reliable information can be derived from our survey. Some 10.5% of our respondents
indicated that they were infected with flu during the previous two years, reflecting a yearlyprobability of infection of about 5%. 13 Since this rate is still substantially lower than thesubjective probability of being infected (24%), providing information on the probability ofcontracting flu would probably reduce the average vaccination rate.14
However, the infection rates differ between different age groups and between those who
took the vaccine and those who did not take it. Therefore, we examined the subjective infection
rates and the infection rates in the following sub-samples: male vs. female, over-60s vs. under-60s,
those who took the flu shot during the past two years vs. those who did not take it.
Our results (not shown in the paper) indicate that the subjective probability differs between
the sub-groups: female-25.5% vs. male-22.5%; people under 60 years-25.6% vs. people over 60
years-20.0%; those who took the vaccine during the last two years-26.4% vs. those who did nottake the vaccine during this period-23.3%. Nonetheless, in all sub-groups we found that the
subjective probability was substantially higher than the experienced flu rate during the last two
years.
Most of the other perception variables are qualitative and not easy to compare with actual
figures. For FEE, 55% chose “the fee is 2000-5000 yen,” and for SEVERITY, 60% chose “a13Yet, it could be that this number reflects also “flu-like” symptoms which are sometimes wrongly
attributed to the influenza illness.
14
One may argue that the flu rate varies substantially from year to year, so that we should not compare
the subjective probability of 2005 with experienced probability for the past two years. According to thestatistics reported by the National Infectious Disease Surveillance Center, the number of influenza
infections reported by the hospitals designated to report the infection in 2005 was almost double thenumber reported in 2004, and 1.3 times the number reported in 2003. Thus, the actual rate of infection
is probably larger than 5%. Yet, there is no reason to believe that this rate exceeds 10%.

16

disease from which it takes about a week to recover,” both of which do not seem to radicallycontradict the facts. However, with regard to the effectiveness of the vaccination, while 60% of the
respondents correctly answered “the shot can prevent certain types of flu,” 20% selected “despite
the flu shot, a high possibility of getting the flu remains,” which contradicts the truth andunderestimates the effectiveness of vaccination. With reference to the side effects of vaccination,although 50% accurately answered that “side effects have little influence,” about 10% selected“very serious side effects that could cause after-effects” and 5% selected “extremely serious side
effects that could cause death,” which overestimate potential side effects of flu vaccination.
In sum, although the comparisons are crude, they seem to suggest that Japanese people
evaluate the effectiveness of vaccination as too low and the side effects as too high in number andlevel of severity. In this case, dissemination of information on the effectiveness of vaccination
may help raise the vaccination rate. On the other hand, they seem to perceive too high aprobability of getting the flu. If this is true, provision of correct information on the probability of
infection may mitigate their willingness to be vaccinated. These conclusions are the same as thoseof [14] with respect to the USA, which are derived by an econometric analysis.

17Appendix 1 Derivation of Equation (3) and the expected sign of the coefficients
For simplicity, let us assume that x1 and x2 are independent of the decision on
vaccination and they are much larger than the costs and benefits due to vaccination. Then,
expanding the utility (1) and (2) around x1 and x2 respectively, we obtain,1
 u ' ( x1 )COST  u" ( x1 )COST 221 PROB  EFFECT  DAMAGE  u ' ( x2 )  u" ( x2 )  DAMAGE  ( EFFECT  2)  02Assuming that x1  x2 , and denoting 

,

(A1)

u"
, the absolute risk aversion, as  , Equation (3) isu'derived.
Denoting the left side of (A1) as  , a larger  implies more willingness to take thevaccination. Therefore, the derivative of  to these elements implies the effect of each elementof the equation on the willingness to be vaccinated against flu. Differentiating  from each term,
we obtaind   COST  1  0
dCOSTd   PROB  EFFECT  1    DAMAGE  (2  EFFECT )  0
dDAMAGEd   EFFECT  DAMAGE  1    DAMAGE  ( 2  EFFECT )   0
dPROB

d
   PROB DAMAGE 1    DAMAGE (1  EFFECT)  0
dEFFECTd 1 PROB  EFFECT  DAMAGE  1    DAMAGE  (2  EFFECT )   0
d
2





d
1
  COST 2    PROB  EFFECT  ( 2  EFFECT ))  DAMAGE 2d2d 0 , if DAMAGE is sufficiently larger than COST ,dwhich prove a) to f) in the text.

18

Appendix 2 Definition of the data
In this appendix, we explain the variables used in the analysis.
WTVACCIN: Willingness to take the vaccination, which is defined as 6 minus the answer to thequestion “Do you intend to receive the flu shot in the next 12 months?” The answer is given on a
five-point scale from “1 Yes, certainly” to “5 No, certainly not.” A larger WTVACCIN implies
greater willingness to take vaccination.
PROB: Subject probability of infection (PROB) is defined as the answer (%) to the question“Estimate your chances of being infected with the flu during the next 12 months.”
EFFECT: With reference to the effectiveness of a flu shot, we asked, “How effective do you think
the flu shot is?” and define a variable EFFECT as 6 minus the answer to this question, which is
any one of five options on a scale from “1 The shot can completely prevent the flu” to “5 The shotis never effective.”
SEVERITY: For seriousness of the disease, we define SEVERITY as 7 minus the answer to thequestion “How serious a disease do you think the flu is?” which is one of six options on a scalefrom “1 An extremely serious disease which could cause death” to “6 A disease which has little
influence.”
BOTHER: With regard to the degree of bother for one’s family and friends when one is infected,
we defined BOTHER as the answer to the question “When you are infected with the flu, to what
extent do you bother your family and friends?” which is one of four options on a scale from “1 I
bother them tremendously” to “4 I hardly bother them.”
SIDEEFECT: With regard to the seriousness of the side effects of a flu shot, we defined
SIDEEFFECT as 8 minus the answer to the question “How serious do you think the side effects
caused by a flu shot are?” This is one of the seven options on a scale from “1 Extremely serious
side effects which could cause death” to “7 There are no side effects.”
FEE: For the injection fee, we defined FEE as the answer to the question “How much do you
think a flu shot costs?” which is any of six options on a scale from “1 free” to “6 more than
$50.00.”
TDR: Discount rates are estimated from the following questions: “Which would you choose,receiving $100 in 2 days or in 9 days?” Eight different pairs of options that correspond to different
interest rates ranging from -10% to 300% are presented. Respondents are requested to choose
earlier or later receipt in these eight cases. Most respondents rationally chose earlier options
during low interest rates, switched to a later option at some interest rate, and kept choosing it forhigher interest rates. We define a variable TDR as the interest rate at which they switch.
ARA: Risk aversion is measured using a question that asks what payment pattern is preferred. The
options are: 1 Your monthly income has a 50% chance of increasing by 30%, but also has a 50%
chance of decreasing by 10% or 2 Your monthly income is guaranteed to increase by 5%. Those
who choose 1 are asked the question in which the increasing rate is altered from 30% to 20%.
Those who choose 2 are asked the question in which the increasing rate is altered from 30% to19

50%. From these answers, we classify all the respondents into four groups, and assuming constantrelative risk aversion utility function, we calculate relative risk aversion for each group, which isnamed RRA following Barsky et al. [2]. Dividing RRA by their household income, we calculate
the absolute risk aversion, ARA.
ALTRUISM: Altruism is measured using the question “Suppose that you found a well-known
charity that gave financial help to people who typically had about one-fifth of your family income
per person. Up to how much of your own family income per month would you be willing to givethe charity if you knew the money would go directly to benefit these people?” We define a dummy
variable where “No help at all” =1 and 0 otherwise.
OVERCON: A variable measuring overconfidence of respondents is defined by the responses tothe statement “I will never be robbed.” OVERCON is defined as 6 when the answers are five
options on a scale from “1 It is particularly true for you” to “5 It doesn’t hold true for you at all.”15
UNHEALTH: We define a variable UNHEALTH from the response to the statement “I am anxious
about my health,” which is any of five options on a scale from “1 It is particularly true for you” to“5 It doesn’t hold true for you at all.” Larger UNHEALH implies greater anxiety for health.
TESTP and TESTS: TESTP takes on unity if respondents took a periodic blood test in the previous
12 months and zero otherwise. TESTS takes on unity if respondents took a blood test because of
suspicion of disease in the last 12 months and zero otherwise.
EXVACCIN: We define EXVACCIN that takes unity if the answer to the question “Have you everreceived a flu shot?” is yes and zero otherwise.
EXFLU: We define EXFLU that takes unity if the answer to the question “Have you been infectedby the flu during the last two years?” is yes and zero otherwise.
MALE: A dummy variable with male=1 and female=0.
AGE: Age of the respondent.
UNMRRY: A dummy variable with unmarried=1and 0 otherwise.
NOCHILD: A dummy variable with those who have no children=1 and 0 otherwise.
SCHOOL: School career, which is defined by “the highest level of education completed” from “1Grade school” to “11 Doctorial degree.”
WAGE: Wage is defined based on the following three questions as

Q62.
Q35  (Q36 / 7)

Q35. About how many hours per week do you work for pay in a typical week?
Q36. About how many days do you work for pay per year?
Q62. How much was your annual income earned for 2004?
15

The confidence of “never be robbed” may exist for good reasons for some people. They might be
too poor to be robbed. Or they might have taken the most foolproof measures for security. Or they livein safer places. In order to adjust these elements, we regress OVERCON over financial wealth of
respondents and variables representing size of city where respondents live and 10 regions of Japan anddefine OVERCON2 as the constant term plus estimated residuals. However, no explanatory variables of
the regression were significant and the regression as a whole was insignificant by F-test (p-value was0.8). Thus, we report only the results with OVERCON.

20

Sixty-nine percent answered “yes” to the question “Are you currently employed?” so that we got
only 1147 observations for the equation including WAGE.
HOMEWORK: This is a proxy for time discounting, since those who finish unpleasant tasksearlier are considered to be more patient, or more future-oriented. HOMEWORK is defined using
the answers to the following question: When you were a child, if you were given an assignment inschool, when did you usually do the assignment? 1 Got it done right away 2 Tended to get it done
early, before the due date 3 Worked on it daily up until the due date 4 Tended to get it done
toward the end 5 Got it done at the last minute
UMBRELLA: This is a proxy for risk aversion and is defined as an answer to the following
question: When you usually go out, how high does the probability of rain have to be before you
take an umbrella? (Percentages between 0 and 100).

21

REFERENCES[1] Barber, B.M., Odean, T.: Boys will be boys: gender, overconfidence, and common stock
investment. Q. J. of Econ. 116(1), 261–292 (2001)[2] Barsky, R.B., Juster, F.T., Kimball, M.S., Shapiro, M.D.: Preference parameters andbehavioral heterogeneity: an experimental approach in the health and retirement study. Q. J.
of Econ. 112(2), 537–579 (1997)[3] Blue, C.L., Valley, J.M.: Predictors of influenza vaccine: acceptance among healthy adult
workers. AAOHN J. 50(5), 227–235 (2002)[4] Brito D.L., Sheshinski E., Intriligator M.D.: 1991. Externalities and compulsory vaccinations.
J. Public Econ. 45(1), 69–90 (1991)[5] Chapman, G.B., Coups, E.J.: Predictors of influenza vaccine acceptance among healthy adults.
Prev. Medicine. 29(4), 249–262 (1999)[6] Chen, J.Y., Fox, S.A., Cantrell, C.H., Stockdale, S.E., Kagawa-Singer, M.: Health disparities
and prevention: racial/ethnic barriers to flu vaccinations. J. of Community Health. 32(1), 5–20
(2007)[7] Knetsch, J.L., Sinden, J.A.: Willingness to pay and compensation demanded: experimental
evidence of an unexpected disparity in measures of value. Q. J. of Econ. 99(3), 507–521(1984)[8] Lau J., Kim J., Yang X., Tsui H.Y.: Cross-sectional and longitudinal factors predicting
influenza vaccination in Hong Kong Chinese elderly aged 65 and above. J. of Infect. 56 (6),460–468 (2008)22

[9] Mullahy J.: It’ll only hurt a second? Microeconomic Determinants of Who Gets Flu Shots.
Health Econ. 8(1), 9–24 (1999)[10] Rosenstock, L.M., Strecher, V.J., Becker, M.H.: Social learning theory and the Health Belief
Model. Health Educ. Q. 15(2), 175–183 (1988)[11] Shahrabani S., Gafni A., Benzion U.: Low flu shot rates puzzle - some plausible behavioral
explanations. The Am. Econ. 52(1), 66–72 (2008)[12] Shahrabani, S., Benzion, U., Yom Din, G.: Factors affecting nurses’ decision to get the flu
vaccine. Eur. J. of Health Econ. 10, 227–231 (2009)[13] Steiner, M., Vermeulen, L.C., Mullahy, J., Hayney, M.S.: Factors influencing decisions
regarding influenza vaccination and treatment: a survey of healthcare workers. Infect. Control
and Hosp. Epidemiology. 23, 625–7 (2002)[14] Tsutsui, Y., Benzion, U., Shahrabani, S., Yom Din, G.: A policy to promote influenza
vaccination: a behavioral economic approach. Health Policy. 97, 238–249 (2010)23

Table 1. Definitions and mean values of variables in the study
Range
Variable

Definition

Min

Max

Mean

WTVACCIN Willingness to be vaccinated
1
5
2.712
PROB
Subject assessment of probability of getting flu (%)
0
100 23.868
SEVERITY Self-assessment of seriousness of flu
1
6
3.260
BOTHER Degree of bothering one’s family and friends if infected
1
4
2.874
EFFECT
Effectiveness of vaccination
1
5
2.950
SIDEEFFE
Seriousness of side effects of vaccination
1
7
3.055
CT
FEE
Fee for inoculation
1
6
4.539
INCOME Annual income per family member (ten thousand yen)
8.333 1500 222.807
TDRTime discount rate
-0.562 26.890
7.904
ARA
Absolute risk aversion
0.000 0.444
0.036
OVERCON Degree of overconfidence
1
5
2.784
UNHEALT
Anxiety regarding health
1
5
3.223
H
ALTRUISM Degree of altruism
0
1
0.551
EXVACCIN Experience of flu vaccination
0
1
0.521
EXFLU
Experience of contracting flu
0
1
0.113
TESTP
Had a periodic blood test in the last 12 months
0
1
0.652
TESTS
Had a blood test because of suspected disease in the last 1
0
1
0.096
DMAN
A dummy variable where male = 1, female = 0
0
1
0.492
AGE
Age of respondent22
72 49.215
UNMARRY A dummy variable where unmarried = 1, otherwise = 0
0
1
0.128
NOCHILD A dummy variable where no children = 1, otherwise = 0
0
1
0.192
SCHOOL Level of education where 1 = lowest and 11 = highest
1
11
4.081

24

Std error
0.029
0.469
0.026
0.018
0.016
0.039
0.021
3.632
0.272
0.001
0.022
0.025
0.012
0.012
0.008
0.011
0.007
0.012
0.302
0.008
0.009
0.048

Table 2. Results of basic Equation (6) and extended regression Equation (7) for estimating
vaccination behavior, WTVACCINa
Equation (7)using
ALTRUISM

Equation (6)Variable

Estimate p-value Estimate p-value Estimate p-value

CONSTANT-0.9780.000-2.445

0.000

-2.34

0.000

PROB

0.008

0.000

0.008

0.000

0.008

0.000

SEVERITY

0.134

0.000

0.111

0.000

0.112

0.000

BOTHER

0.236

0.000

0.26

0.000

0.22

0.000

0.251

0.000

0.228

0.000

0.227

0.001

SIDEEFFECT-0.0460.004-0.0570.001-0.057

0.204

FEE

0.015

0.594

0.038

0.202

0.038

0.045

INCOME

0.00040.030

0.00040.051

0.00040.027

TDR-0.0050.019-0.0050.029-0.005

0.038

ARA

1.1

0.014

1.033

0.038

1.034

0.852

Behavioral variables OVERCON

-

-

0.004

0.893

0.005

0.027

UNHEALTH

-

-

0.057

0.026

0.057

0.000

ALTRUISM

-

-

0.217

0.000

-

-

ALTRUISM*
BOTHER

-

-

-

-

0.076

0.000

EXVACCIN

-

-

0.877

0.000

0.878

0.156

EXFLU

-

-

0.116

0.164

0.118

0.108

TESTP

-

-

0.099

0.111

0.1

0.250

TESTS

-

-

0.116

0.248

0.115

0.004

MALE

-

-

-0.1530.004-0.154

0.000

AGE

-

-

0.018

0.000

0.018

0.082

UNMARRY

-

-

0.217

0.085

0.219

0.006

NOCHILD---0.2920.006-0.293

0.384

SCHOOL---0.0120.374-0.012

0.000

μ3

1.069

0.000

1.174

0.000

1.174

0.000

μ4

1.747

0.000

1.964

0.000

1.964

0.000

μ5

2.347

0.000

2.686

0.000

2.688

0.000

DAMAGE
EFFECT
COST

Boundary values

2aEquation (7)using ALTRUISM*BOTHER

Pseudo R

0.111

0.291

0.292

Number of observations

1849

1752

1752

The first column contains the variables that determine WTVACCIN. When the variable in the firstcolumn consists of multiple variables, those are shown in the second column. The estimation
method is ordered probit.

25

Table 3. Examination of time discounting and risk aversiona
Equation (5)using
Equation (6) using
HOMEWORK and ARA*SEVERITY
UMBRELLAandARA*SIDEEFFF
ECT
Variable

Equation (5)using
ARA*EFFECT*SEVERITY

Estimate p-value Estimate p-value Estimate p-value

CONSTANT-0.8630.000-0.9120.000-0.834

0.000

PROB

0.007

0.000

0.008

0.000

0.008

0.000

SEVERITY

0.13

0.000

0.105

0.000

0.11

0.000

BOTHER

0.229

0.000

0.235

0.000

0.234

0.000

0.254

0.000

0.249

0.000

0.222

0.000

SIDEEFFECT-0.0002

0.993

0.015

0.588

0.016

0.570

FEE

0.00020.249

0.00030.058

0.00030.059

INCOME-0.0450.003-0.0250.191-0.029

0.107

-

-

-0.0050.016-0.0050.016-0.035

0.045

-

-

-

-

-

-

-

-

-

-

0.004

0.001

-

-

-

-

ARA*SEVERITY

-

-

0.77

0.003

-

-

ARA*EFFECT*SEVERI
TY

-

-

-

-

0.219

0.003

ARA*SIDEEFFFECT---0.605

0.028

-0.46

0.050

Boundary value μ3

1.069

0.000

1.07

0.000

1.07

0.000

μ4

1.748

0.000

1.748

0.000

1.748

0.000

μ5

2.33

0.000

2.349

0.000

2.349

0.000

Pseudo R

0.109

-

0.113

-

0.113

-

Number of observations

2173

-

1849

-

1849

-

DAMAGE
EFFECT
COST

Time discount TDR
HOMEWORK
Risk aversion

ARA
UMBRELLA

2

a

The first column indicates the variables that determine WTVACCIN. When the variable in the firstcolumn consists of multiple variables, those are shown in the second column. The estimation
method is ordered probit.

26

Table 4. Results of extended regression Equation (7) for estimating vaccination behavior, WTVACCIN
using fitted values from auxiliary Equation (8)FITTED_PROB FITTED_SEVERITY FITTED_BOTHER
Parameter

Estimate P-value Estimate P-value Estimate P-value

Constant-2.7920.000-2.7860.001-0.6820.800

FITTED_PROB

0.016

0.007

.

.

.

.

PROB

.

.

0.009

0.000

0.009

0.000

FITTED_SEVERITY

.

.

0.145

0.000

.

.

0.115

0.000

.

.

0.151

0.000

.

.

.

.

-0.331

0.671

BOTHER

0.269

0.000

0.294

0.592

.

.

EFFECT

0.216

0.000

0.236

0.000

0.238

0.000

SIDEEFFECT-0.0490.003-0.0390.000-0.048

0.004

FEE

0.048

0.110

0.049

0.015

0.057

0.058

INCOME

0.00040.032

0.00040.101

0.00020.479

TDR-0.0050.040-0.0050.064-0.005

0.025

ARA

0.947

0.058

1.041

0.033

0.795

0.158

UNHEALTH

0.043

0.113

0.049

0.037

0.086

0.107

ALTRUISM

0.213

0.000

0.212

0.212

0.218

0.000

EXVACCIN

0.863

0.000

0.865

0.000

0.886

0.000

TESTP

0.094

0.130

0.100

0.000

0.110

0.083

TESTS

0.110

0.269

0.113

0.136

0.230

0.197

MALE

-0.1280.018-0.1340.277-0.208

0.056

AGE

0.020

0.000

0.018

0.068

0.010

0.306

UNMARRY

0.263

0.044

0.231

0.000

0.083

0.716

NOCHILD-0.2860.007-0.2900.070-0.396

0.023

SCHOOL-0.0120.395-0.0120.017-0.010

0.494

μ3

1.157

0.000

1.165

0.454

1.159

0.000

μ4

1.935

0.000

1.950

0.000

1.937

0.000

2.652

0.000

2.669

0.000

2.642

0.000

Pseudo R

0.274

-

0.282

0.000

0.268

-

Number of observations

1752

-

1752

-

1752

-

SEVERITYFITTED_BOTHER

μ5227