Philip Morris
Smokers' Burden on Society: Myth and Reality in Canada
Fields
- Author
- Raynauld, A.
- Vidal, J.
- Area
- CORPORATE AFFAIRS BRUSSELS/WAREHOUSE
- Type
- PSCI, PUBLICATION SCIENTIFIC
- BIBL, BIBLIOGRAPHY
- Litigation
- Stmn/Produced
- Request
- Stmn/R1-048
- Site
- E41
- Author (Organization)
- Analyse De Politiques
- Canadian Public Policy
- Univ of Montreal
- Canadian Public Policy
- Attachment
- 2501357035/2501357053
- 2501357036/2501357053
- Date Loaded
- 05 Jun 1998
- UCSF Legacy ID
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Document Images
Plusieurs auteurs soutiennentclue les fumeurs sont A ksourcedecoats eonsiderables pour la sociLt6:
frais d'hospitalisatioii-et de services medicaux et production pe=due_par le d6c&s prematur6 des.
fumeurs._Pour 1'ann6e 2986, au Canada, noas_estimons & s669 millions les coats supplementaires
relids & 1'usage du tabac. Farr contre, cornme la rd4iuction des_touts futurs de sant6 s'eleve it
$462
mdlions, Ies cofits externes. nets n'atteignent-que $207 millions. Ceaconts donnent lieu a un
transfert,
ntaia its sont surswmpensds par dautres #ransferts tels que lea taxes payees parr lea fitmeurs et
Ies
r6duetions des prestations des rdgimes de retraite:: En iAalit6,. il se produit ainsi un transfert
net
global des fumeurs en faveur des noa_fumeurs de 1'ordre do $4.3 milliards. Meme en considerant un
eventad trPs large d'hypothsw m6dicalPs, le sens de cette conciusion-ne change pas.
Several authors maintain that smokers impose a considerable burden on society through hospital-
ization and medical costs and lost output due to premature death. In this paper, supplementary costs
related to smoking are estimated at 669 million dollars for.the year 1986 in Canada. However, since
future health cost reductions reach 462 million, the net external costs generated do not exceed 207
million. These costs giv'e_ rise to transfers, but these in turn are more than compensated,by other
transfers such as taxes-paid by smokers and reduetions in pension benefits which lead to a net flow
overall of 4.3 billion dollars- in favour of non-smo3cers. The direction of this conclusion remains
unchanged even considering a wlde range of medical hypotheses.
I Introduct"ion = It is the purpose of this article to deter-
mine- if observations such as this one are
n here is a strong current ofopinion to the_.' - valid or not. The analysis -is based on two
L_effect that tobacco beingharmful ta the~ _ fundatriental. -eoncepts or Eriter,ia: exter-
heaiih,-emok~rsunpose`eiitraexpenditures= :_ nalities and_ inter-group transfera.. A
oa society and becor»e a-_ f`i_naiicial burden = smoker may bee responsible for hospitatixa
fio~r noxt-smokers. To _tluo~e only one repre- -_ tion costs viwhic.b become an external cost in
sentative esamp -1._- $aitlett- E.19$91,. Canada given - the public nature of the
~ svfites:
health_ care system. In. this` instance, the
smoker imposesacost on others. The ques-
The net result iofsmokirig in Canadal is that it _ tion then arises: who pays for what and who
coats eaeh Canadian _$18* annually in heslth.-benefits between smokers and- non- -
care related eustss so that 35% aP their iountry= smokers. This calls for an examination of
men can smoke. transfers between the two groups. In the
previous example, non-smokers finance a
Ca+sadio4Public policy=dnatyae de Politiques. lCVTII:3:300-,317 1992 Printed inCana+ielimprimtkau
Canads
~ ~~att!570s6

Table 1
Relative risks coefficients (44
Disease
Lowest value Highest value
Men Women Men Women
Malignant neoplasm of
oral cavity 2.76 1.22
esophagus 1.82 4.89
stomach 1.39 L31
pancreas L50 L42
larynx 6.52 3.25
trachea, bronchus and lung 3.76 2.03
cervix uteri L72
bladder 1.40 L66
kidney 1.20 n/a
Ischaemic heart disesses 1.58 1.30
Bronchitis and emphysema 12.07 n/a
13.00 3.25 -
6.43 4.89
1.80 2.30
3.10 2.50
13.59 6.52
14.20 5.00
3.00
2.89 2.80
2.66 2.66'
1.71 L78
24.70 24.70t
'zis table reads as follows: taking for example the highest value for men, the risk of death from
oral cavity can-
cer is 13 times higher for smokers than for non-smokers.
souHCS: US Department of Health and Human Services (USDHHS, 1982,1983,1984).
' The highest values are used as our basic assumptions, as stated above.
t A relative risk coefficient was not established for kidney cancer and pulmonary diseases in women;
therefore,
we adopted the coefficients given for men.
good proportion of supplementary health
costs, so that transfers go from non-
smokers to smokers. On the other hand,
smokers pay taxes on tobacco which bene-
fit non-smokers to a large extent. In this
case, the transfers go in the opposite direc-
tion. A complete balance sheet of revenues
and expenditures accruing to smokers and
non-smokers is necessary before one can
conclude whether or not smokers are a bur-
den on non-smokers.
-? Basic Assumptions
This study is based on three major assump-
tions:l/ smoking is harmful to the health of
smokers; 2/ smoking is not harmful to the
health of non-smokers; and, 3/ smokers
know that smoking is detrimental to their
health.
Smoking is Harmful to Smokers
Numerous medical studies show that con-
sumption of tobacco is harmful to the
health of smokers. Since our expertise does
not lie in the medical field, we simply use
the findings published by the Surgeon
General of the United States2 as working
hypotheses without endorsement 3 They
take the form of relative risk coefficients
(4.) associated with a broad range of dis-
eases.4 These coefficients give the relative
risk of dying if one is a smoker as opposed
to a non-smoker. Since several estimates
are often given for the same illnesses, we
have always chosen the highest values for
our calculations so as to avoid any sugges-
tion that we have selected hypotheses
favourable to our conclusions. It will be ob-
vious that with higher risk coefficients, re-
lated health cost estimates will also be
higher than otherwise. Table 1 gives the
highest and lowest estimates of risk coeffi-
cients as has been found in the Reports of
the Surgeon General.
The risk coefficients will be used to esti-
mate the proportion of costs imputable to
tobacco; those costs are broken down ac-
cording to the International Classification
of Diseases (ICD-9). As a result, a cor-
respondance had to be established between
the diseases given in Table 1 and those of
ICD-9.
For cancer of the oral cavity, we used the
Smokers' Burden on Society 301

broader category Malignant neoplasms of
the lip, oral cavity and pharynx. This is con-
sistent with our practice of always opting
for the least favourable choice. For cancers
of the oesophagus, stomach, pancreas,
larynx, trachea, bronchus and lung, cervix
uteri, and bladder, ICD-9 provided a corre-
sponding listing of diseases under the same
names. For bladder cancer, we chose Malig-
nant Genito-urinary Organ Tumors, Kid-
ney and Other Urinary Organs n.o.s., a sub-
category that includes kidney cancer but
extends beyond it. For ischaemic heart dis-
ease, a corresponding category of the same
name was chosen from ICD-9. Finally, for
bronchitis and emphysema, we selected the
very broad category Respiratory System
Diseases, Chronic Obstructive Pulmonary
Disease and Allied Conditions; as usual, we
made the choice to bear most unfavourably
upon our findings.
To the 11 diseases of Table 1 we as-
sociated 30 diseases, when considering the
three digit disaggregation of the ICD-9
classification.
The Health of Non-smokers
There is a widespread opinion to the effect
that smoking is harmful to the health of
non-smokers. It is based mainly on strong
statements made by the Surgeon General
of the United States, such as the following
one taken from his 1986 report (p.13):
Involuntary smoking is a cause of disease, in-
cluding lung cancer, in healthy non-smokers.
We found however that the evidence in sup-
port of this opinion is far from conclusive.
Concerning lung cancer among spouses,
the 1986 review of the US Surgeon General
is largely an examination of three prospec-
tive and ten retrospective studies.5 High-
lights of these findings, provided in his ta-
bles 7, 8 and 9, can be found in our Table 2.
In our judgment, Table 2 does not sup-
port the Surgeoii General's thesis, since
two thirds of the studies tabled - nine out
of 13 - do not provide relative risk coeffi-
cients statistically different from one. Of
302 Andre Raynauld and Jean-Pierre Vidal
the four studies which would support the
Surgeon General's thesis that smoking is
dangerous for non-smokers, the findings of
two are highly tenuous. With reference to
the study by Trichopoulos, the Surgeon
General (USDHHS, 1986) observes that
some biases may have arisen in the selec-
tion and interview process. As well 'the di-
agnosis of cancer was not confirmed for 35
per cent of the cases'. In the study by Cor-
rea et al. the sample was limited to 30 cases
overall. Finally, this comment found in the
Surgeon General's Report (USDHHS,
1986) and concerning the study of Gar-
finkel would make anyone suspicious of the
results obtained in this area of research:
Among the published studies on involuntary
smoking, this is the only one involving inde-
pendent verification of the diagnoses of all cases.
This verification showed that 13 percent of the
cases classified as lung cancer were not primary
cancers of the lung. This study showed that 40
percent of the women with lung cancer who had
been classified as non-smokers (or smoking not
stated) on hospital records had actually smoked,
compared with 9 percent of the controls. The in-
clusion of lung cancer patients who had actually
smoked, would have substantially increased the
odds ratio with inuoluntary smoking, because 81
percent of the potentially mis-classified cases
had husbands who smoked, compared with 68
percent of the 'true' non-smoking patients with
lung cancer.s
Other remarks by the Surgeon General
deserve attention. For example, on page 91
of the same report, we find this observation
concerning tobacco use by parents:
None of the studies with data on parental smok-
ing had sufficient numbers to examine the ef-
fects of parental smoking on non-smokers.
Similarly, we find this observation about
the use of tobacco in the workplace:
The workplace, an important source of tobacco
smoke exposure, was not considered in the early
studies on involuntary smoking. Later case-con-
2501357038

Table 2
Summary results on passive smoking relative risk coefficients for lung cancer
Prospective studies
Study Sample Cancers Significant results at 5%
Hirayama 1981, 1983, 1984 91,450
Garfinkel 1981 176,739
Gillis et al. 1984 2,744 200
153
14 ik = 1.9 for women whose
husbands smoked more than
20 cigarettes daily
None
None
Retrospective studies
Study Cancers Significant results at 5%
Trichopoulos 1981, 1983, 1984 77 41' = 2.5 for women whose
Correa et al. 1983
30 husbands smoked more than
20 cigarettes daily
V = 3.1 for thoee whose
Chan and Fung 1982
84 partners smoked more than
40 packs yearly
None
Koo et a1.1983, 1984 88 None
Iiabat and Wynder 1984 78 None
Wu et a1.1985 29 None
Garfinkel et al. 1985 134 >/i' = 2.1 for women whose
Lee et al. 1986
47 husbands smoked more than
20 cigarettes daily
None
Akiba et al. 1986 103 None
Pershagen (in print) 67 None
SoueCE: US Department of Health and Human Services (USDHHS, 1986).
trol studies provided some information on
tobacco exposure at work, but the data were
limited and inconclusive.
For all these reasons, we assume in this
study that smoking is not a cause of death
among non-smokers.7
Concerning the relationship of 'passive'
smoking to other cancers, the Surgeon
General writes:
There are, at present, insuff cient data to ade-
quately evaluate the role of involuntary smok-
ing in adult cancers other than primary carcin-
oma of the lung.
With regard to cardiovascular disease,
the Surgeon General writes:
More detailed characterizations of exposure to
ETS [Environmental Tobacco Smoke] and
specific types of cardiovascular disease as-
sociated with this exposure are needed before an
effect of involuntary smoking on the etiology of
cardiovascular disease can be established.
Smokers Know that Smoking is Detriment-
al to Their Health
Finally, we assume that smokers are aware
that smoking may be harmful to their
health. Such an assumption is especially
reasonable in Canada, where the tobacco
industry is required to display very promi-
nent warnings on all cigarette packages.
Indeed, such warnings must occupy an
area equal to 20 per cent of the principal
panels of the cigarette pack. They must be
'legible and prominently displayed in con-
trasting colours,' and the message is unam-
biguous:
Smoking reduces life expectancy.
Smoking is the major cause of lung cancer.
Smoking is a major cause of heart disease.
Smoking during pregnancy can harm the baby.
Smokers' Burden on Society 303

If the numerous anti-smoking cam-
paigns are added to these warnings, it
would be simply unrealistic to assume that
smokers are not aware that smoking may
be hazardous to their health.
Yet, one could argue that people still un-
derestimate the risks or do not pay enough
attention to these warnings. But this view
would not be consistent with the findings
of W.K Viscusi (1990):
This paper uses a national survey of 3,119 in-
dividuals to exaTMine the effect of lung cancer
risk perceptions on smoking activity. Both
smokers and nonsmokers greatly overestimate
the lung cancer risk of cigarette smoking, and
the extent of the overestimation is much greater
than the extent of underestimation.
One could still argue that in the 1940s
and 1950s when smoking was portrayed as
glamorous and good, people began smoking
but that now they find it very difficult to
quit.
This is correct as a statement of fact but
irrelevant in the context of this analysis.
The real point is whether there is or there
was a market failure giving rise to external
costs as opposed to private costs such as loss
of income due to premature death at-
tributed to tobacco.
Even in the 1940s nobody hid the truth
from smokers because nobody knew that
tobacco was so harmful to the health.
Indeed, the problem at hand is not a prob-
lem of information but rather of uncer-
tainty. Moreover, it is not because many see
smoking as addictive that an external cost
results automatically. Indeed, using a
rational addiction model, G.S. Becker and
F S. Murphy (1988) show that a consumer
may be perfectly aware that smoking is
harmful and addictive, and, in spite of that,
decide to smoke to maximize his/her utility
over time $
In other words, if decisions are taken in
full knowledge of the consequences as they
exist at the time the decision is made, this
becomes a purely private and rational deci-
sion involving no more than private utility
304 Andri Raynauld and Jean-Pierre Vidal
and costs.
III External Costs
To determine whether smokers are a bur-
den on society, one must first establish the
importance of external costs related to
smoking. In application of our first assump-
tion above, supplementary medical and
hospital costs are involved and they are
deemed to be external given the public na-
ture of the health care system in Canada.
We also include costs associated with fire
losses imputed to negligent smokers.
Various other costs are mentioned in the
literature but not included herein, such as:
1/ time lost on the job due to smoking; 2/ ab-
senteeism without loss of pay; 3/ additional
cleaning and ventilation costs in areas used
by smokers; 4/ the price non-smokers would
pay to be always smoke-free; and 5/ the
price relatives and friends would pay to re-
duce the risk of a smoker's death.
The first two categories of costs are held
to be negligible when they are compared
with all the other reasons or pretexts to
waste time on the job or stay away from
work. Moreover, in a majority of cases, the
alleged external cost is very much a private
cost; people are not paid when they do not
work or they lose either money or leisure
from taking 'sick days,' which are inter-
changeable with additional wages or days
off.
In any case, if smoking had been signifi-
cantly related to costs for the employer, or
to productivity, then smokers' wage rates
would certainly have reflected it. If they did
not, one cannot easily dismiss the idea that
smoking was an excuse that might easily be
substituted for another one, like having a
coffee or a soft drink. Furthermore, in a
study involving 33,032 individuals, C.E.
Bonilla (1989) found that smoking had no
bearing on absenteeism.
The same applies to cleaning and venti-
lation costs. If a systematic association had
been established involving smokers, mar-
ket forces would have led to lower salaries
and smokers would have internalized the
2501357040

Table 3-
Proportion of cigarette smokers among Canadians (percentages) 1986
35.40 33.60 18.60
31.40 25.30 11.30
Note: The proportion of smokers in the overall population is 22.12%. It is found by applying the
proportions of
Table 3 to the total population by age group and sex, found in Statistics Canada (1988), summing
them up and
taking the percentage. The 0 to 15 age group is assumed not to contain regular smokers.
sot:xcE: Health and Welfare Canada (1988).
costs. Time lost in the work place as well as
cleaning and ventilation costs are not real
external costs.
On the other hand, the price non-
smokers would pay to live in a smoke free
environment is a genuine externality. _
v-wever, smokers would undoubtedly be
r..iling to pay to smoke wherever they like
and not be blamed for it. This externality,
in the opposite direction, could very well
cancel out or even more than offset the ex-
ternal cost borne by non-smokers. This is
especially true now, since new laws and in-
ternal regulations forbid smoking in many
public and work places.
Finally, even if those close to smokers
were prepared to pay to reduce the risk of
death, this cost cannot be considered purely
external, since friends and relatives share
their concerns with the smoker, who is very
likely to take their views into account.
For those reasons, we have not included
these considerations in our evaluation.
On the other hand, if we follow the logic '
of the situation and demonstrate that
s kers risk premature death, we must ac-
cept the fact that smokers stop requiring
the health services they would have re-
quired had they not smoked and lived
longer. As we will see in section V
(Methodological Issues), several authors
support this logic.
Therefore, to arrive at a net value of ex-
ternalities, one has to calculate the reduc-
tion of health costs due to premature death
and balance it against the supplementary
costs attributable to smoking.
Additional Hospital Care Costs
The computation of supplementary hospi-
talization costs is based on the proportions
of cases attributable to smoking, for each
disease, each sex, and each age-group, pro-
portions that are called etiologic fractions
W and are defined as:
8(~i-i)
~- ,
8(¢-1) + 1
where 8 is the proportion of the population
by age and sex exposed to the risk factor and
V, is the relative risk coefficient 9 B is given
above in Table 3, and V, has already been
given in Table 1.
The computation of costs was then car-
ried out as follows:
(1) The number of hospital care days,
throughout Canada in 1986, was estab-
lished for each relevant disease or cate-
gory of disease, each sex, and each age-
group_10
(2) These numbers of days were then mul-
tiplied by the corresponding etiologic
fractions, by age, and by sex, to obtain
the number of hospital care days attribu-
table to smoking, that is, the number of
hospital care days that presumably
would have been saved had no one
smoked.
(3) The sum over diseases, sex, and age-
groups multiplied by $352.22, which is
taken to be the average cost of one hospi-
talization day, gave $546.5 million.ll
Although the calculations are very
simple, they are so numerous that it is im-
possible to give a detailed account of the
more than 7,000 pages of tables that could
Smokers' Burden on Society 305

Table 4
Additional hospital care costs: summary of intermediary results for men 1986
International classification
of diseases - 9th revision
(ICD - 9)
Malignant neoplasms
lip, oral cav. and phar. (140-149)
esophagus (150)
stomach (151)
pancreas (157)
larynx (161)
trachea, bronchus and lung (162)
bladder (188)
kidney and other urinary
organs n.o.s. (189)
Ischaemic heart diseases (410-414)
Chronic obstructive pulm. dis.
and allied cond. (490-496)
Overall
Total
number
of
hospital
days Proportion
attributable
to
smoking
(%) Hospital
days
attributable
to
smoking Imputed
hospital
cost
(million
dollars)
55,739 75 41,805 14.7
29,228 57 16,636 5.9
64,285 16 10,011 3.5
48,041 33 15,788 5.6
33,859 76 25,626 9.0
343,995 75 258,605 91.1
92,897 29 26,994 9.5
41,147 29 11,784 4.2
1,077,802 15 162,672 57.3
651,273 72 468,015 164.8
2,438,266 1,037,937 365.6
Notes:
Due to rounding, totals may differ slightly.
The proportion of days attributed to smoking is a weighted average of the etiologic fractions
defined above as the
proportion of cases attributable to smoking by age, sex, and disease. The etiologic fractions
themselves are some-
what higher than the average values. For instance, 89% of all days spent for men aged 25 to 44 and
suffering from
a chronic obstructive pulmonary disease were attributed to smoking. This might be surprising when
compared
with the average value of 72%, but it results from the fact that no cases were attributed to smoking
under the
age of 15.
Cancer of the cervix uteri has been deleted from this table but it has been taken into consideration
for women.
be accounted for in this whole study.
However, Table 4 has been constructed as
a heuristic device to show the kind of opera-
tions involved. Taking the first line as an
example, the total number of hospitaliza-
tion days spent for malignant neoplasms of
the lip, oral cavity, and pharynx was 55,739
in 1986 for men. Since the proportion at-
tributable to smoking was established at 75
per cent, the number of hospitalization
days attributed to smoking was 41,805. At
$352.22 per day, the corresponding cost
amounts to $14.7 million.
Additional Medical Services Costs
In this case, we had to extrapolate from
statistics relating to Saskatchewan to ar-
rive at an overall picture for Canada, be-
306 Andre Raynauld and Jean-Pierre Vidal
cause this is the only provincial authority
gathering the required data on the specific
illnesses.
With reference to Saskatchewan, during
1986-87, $4.7 million was spent for neo-
plasms; $4.7 million for diseases of the
circulatory system; and an additional $5
million for chronic obstructive pulmonary
diseases.l2
Since Saskatchewan's overall health
services cost $184.8 million in 1985, while
the cost for all Canada was $6.3 billion, we
arrived at a multiplication factor of 33.82,
which when applied to the previous num-
bers gave Canadian extrapolations of
$159.1 million for neoplasms; $160.2 million
for diseases of the circulatory system; and
$167.6 million for chronic obstructive pul-
2501357042

monary diseases.
Finally, assuming that the cost of medi-
cal services attributable to smoking was
proportional to the number of hospital days
due to the same cause, we obtained a cost
for medical services attributable to tobacco
of approximately $68 million: $22 million
for neoplasms; $5 million for diseases of the
circulatory system; and $41 million for dis-
eases of the respiratory system.
The Cost of Smokers' Negligence
In table 5 of the Federal Fire Commis-
sioner's annual report (Labour Canada,
1987), property losses from fires blamed on
smoking are listed at $52.2 million for 1986.
To these property losses we added $2
nillion for the nation's reduction in well-
being resulting from the loss of wooded
land. Our reasoning was as follows:
1/ We knew the fight against forest fires
costs $102.3 million in 1986, and that
fires blamed on 'recreation' account for
2 per cent of devastated areas (see
Petawawa National Forestry Institute,
1989).
2/ So, assuming that the government would
keep spending money to protect the en-
vironment until the value of the lost en-
vironment would be worth no more than
the money spent to protect it, we esti-
mated that the value of the wooded land
lost represented at most 2 per cent of
$102.3 million. Obviously, this is an over-
estimation because the category 'recrea-
tion' is much broader than the `neg-
ligence on behalf of a smoker' 13
The Reduction of Future Hospital Care
Costs
Consistent with the extreme assumptions
adopted for the hazards of smoking, we im-
puted 21,841 deaths to tobacco use by apply-
ing the etiologic fractions to the statistically
recorded deaths in Canada by cause, age,
and sex. Subsequently, a model repre-
senting the anticipated life and death of
each of these deceased individuals has been
constructed, assuming that all of them died
earlier than they would have had they not
smoked 14
The fundamental premise leading us to
infer a reduction in future cost is that al-
though smokers might have lived longer
had they never smoked, they would
nevertheless have been subject to the same
risks as any non-smoker. At one time or
another, they would have been ill, and,
eventually, most would have spent some
time in the hospital.
Consequently, in our 'life-and-death'
model, each prematurely deceased in-
dividual is classified according to the year
of his or her unavoidable demise (the mo-
ment when he or she would have died any-
way), the cause of that demise, and the age
that he or she would have reached at that
time. From this information, we computed
the following reduction in hospital care
costs:
L For each year, from 1986 to 2071, the
number of deaths by ICD-9 category and
by age was multiplied by the average
length of a hospital stay (in days) rele-
vant to each category and age. Summing
up over categories and ages, a number of
hospitalization days saved was then ob-
tained for each year from 1986 to 2071.
(There would be no survivors alive after
2071. Since no one died from smoking
before being 15 years old, nobody would
live beyond the age of 100 years: 2071-
1986 + 15).
2/ Again, for each year from 1986 to 2071,
the previously obtained numbers of
hospitalization days were multiplied by
the average cost of each day, established
at $352.22 for 1986-87, and assumed to
remain at that level in constant dollars.
3/ Finally, the present value was taken at
an annual compounded real discount
rate of 3 per cent.15
From the above calculations, we esti-
mated the reduction in hospital care cost at
$133.4 million.
It is worth indicating that this amount is
probably a significant underestimation,
since our calculations do not reflect hospi-
tal stays not directly related to the ultimate
death of the indiuiduals concerned.ls
Smokers' Burden on Society 307
I

The Reduction of Future Medical Services
Costs
From our 'life-and-death' model, we also
obtained the number of deceased smokers
who might have survived in each of the
years from 1986 to 2071. It was then
possible to estimate the value of medical
services saved because of these premature
deaths. Our methodology can be described
as follows:
1/ Had the dead smokers never smoked and
lived longer, we assumed that, at any
specific age, they would have required,
on average, the same kind of medical at-
tention as anyone else at that age; con-
sequently, their average medical costs
would have been the same as those of
other citizens.17
2/ We then applied the average cost of medi-
cal services, broken down into five-year
age spans, to the number of deceased
smokers who, presumably, would have
survived. As above, the present value
was taken at a 3 per cent discount rate.
The reduction in future medical services
was established at $123.5 million.
The Reduction in Residential Care
Facilities for the Aged
Finally, we considered the reduced expen-
diture on residential care facilities for the
aged.
1/ We assumed that the number of old age
beneficiaries of residential care, ex-
pressed as a percentage of the total popu-
lation by age group, would remain con-
stant after 1986,18 as well as the average
cost horne by society at $35.17 per day
(in 1986 dollars) is
2/ Subsequently, we applied the proportion
of old age beneficiaries to the number of
deceased smokers for each year from
1986 to 2071, taking into account age and
sex, to calculate how many of them
would have been beneficiaries had they
not succumbed in 1986.
3/ Finally, by straightforward multiplica-
tion of the above figures by $35.17, we ar-
rived at the annual amounts saved from
1986 to 2071.
308 Andre Raynauld and Jean-Pierre Vidal
Taking the present value, we arrived at
a reduced cost for residential care facilities
for the aged of $204.9 million.
The Net Cost of Externalities
Based on our extreme assumptions about
the risks run by smokers, we estimate the
net external cost of smoking in Canada for
1986 at $207 million.
This figure includes supplementary
costs presumably incurred because some
people smoke: $546.5 million in hospitali-
zation; $68.1 million in medical services;
$52.2 million in property losses from fire;
and $2 million for the destruction of part of
the nation's wooded land, for a total of
$668.8 million.
Reductions in future costs include:
$133.4 million in hospitalization; $123.5
million in medical services; and $204.9 mil-
lion in residential care facilities for the
aged. Substracting this $461.8 million re-
duction from the $668.8 million, we arrive
at a net external cost of $207 million.
IV Transfers
The next question is how much of this net
external cost of $207 million is paid by the
smokers themselves and how much is paid
by non-smokers. Put in these terms, it be-
comes obvious that the question is only a
small part of a much broader issue.
To determine whether smokers overall
constitute a financial burden on non-
smokers or on society as a whole, it is not
enough to determine if taxes paid by
smokers are sufficient to cover the expenses
they are responsible for. In addition we
have to estimate the relevant taxes smokers
would have paid had they lived longer and
also, we have to include the net savings re-
lated to pension benefits, which are reduced
by the early deaths of smokers.
The Transfers from Externalities
In the preceding section we established the
net external cost of smoking at approxi-
mately $207 million. Since we estimate that
69.15 per cent of taxpayers are non-
2501357044

smokers20 $143 million will be financed by
non-smokers. This amounts to a transfer of
$143 million from non-smokers to smokers.
However, there are people of working
age among the deceased smokers who
would have lived longer, had they not
smoked. Then, we must estimate the taxes
they would have paid. The following de-
scribes our methodology:
ll According to Health and Welfare Canada
(Table 6), in 1986, the costs of hospitali-
zation and medical services were $17.5
billion and about $7 billion respectively.
2/ According to Statistics Canada
(1989b:119), the cost of residential care
facilities for the aged was approximately
$3 billion, which means that applying
our 65 per cent rule, $2 billion was paid
for from public sources.
According to our calculations, there were
12 million Canadian workers in 1986.
4/ Thus, assuming that the costs were fully
recovered by the government from the
taxpayers, each taxpayer contributed
$2,252.70.
5/ Assuming that this contribution would
remain at that level in constant dollars,
we multiplied it by the number of
deceased taxpayers for each year after
1986.
Taking the present value as we did
before, we estimated the contribution of
deceased smokers, had they not smoked, at
$146 million. Of this amount, $100.9 million
(69.15%) represents a reduction of the fi-
nancial advantage to non-smokers. The net
transfer relative to external cost, from non-
--nokers to smokers, is therefore approxi-
-lately $244 million (143 + 100.9).
The Transfers through Tobacco Taxes
Smokers paid $4.1 billion in tobacco taxes,
over and above the taxes paid by non-
smokers in 1986. However, the transfer
going from smokers to non-smokers is not
equal to that amount because smokers
benefit as well as non-smokers from the
public services they finance. More pre-
cisely, since non-smokers represent 77.88
per cent of the population, they benefit
from smokers' taxes by approximately $3.2
billion.
To obtain this total of $4.1 billion, we
simply added the federal and provincial
consumption taxes on tobacco. Federal
taxes have been established at $1,948.3 mil-
lion: $277.3 million for the federal sales
tax;21 $1,107.5 million for the excise tax;
$552.6 million for the excise duty;22 and $11
million for the tariff duty.23 Provincial
sales taxes have been established at
$2,119.7 million. This estimate applies to
calendar year 1986, and comes from Statis-
tics Canada (1986) 24
The Transfers through Pension Plans
We assumed at the outset that smoking was
hazardous to health and that, as a con-
sequence, smokers had a shorter life expec-
tancy than non-smokers. Consistent with
that assumption, we find that if smokers die
earlier than non-smokers with similar pen-
sion benefits, there must be a transfer in
favour of non-smokers and to the detriment
of smokers. We estimate this transfer at
$1.4 billion.
In 1986, total contributions to A ension
plans amounted to $29.5 billion. Since
there were 11.8 million workers, the aver-
age contribution was about $2,504.13.
On average, for the same year, the Old
Age Security and Supplement regimes paid
out $4,604.71 to 107 per cent of the 65 and
over age group (because spouses' allow-
ances are also paid to those less than 65
years old, as are pensions to Canadians
abroad); Canada and Quebec Pension Plans
$2,865.73 to 96 per cent of those 65 and
over; and private pension plans $7,261.27
to 45 per cent of those 65 and over.
From these observations, we undertook
the following calculations:
1/ From the calculations we referred to pre-
viously, we know how many deceased
smokers would have worked, had they
not smoked, for each year after 1986. To
determine how much they would have
contributed to financing pension funds,
we multiplied that number by the aver-
age contribution of $2,504.13.
Smokers' Burden on Society 309

Table 5
Total net transfers from smokers to non-smokers 1986
In millions of dollars
Net external costs -244.0
Additional taxes paid 3,168.2
Pension plans 1,417.4
Total net transfers 4,341.5
Note: Due to rounding, total may differ.
2/ From the 'life-and-death' model, we also
know, for each year after 1986, how
many deceased smokers would have
been alive and over 65 years old had they
not smoked. To determine how much
they would have received from each type
of pension plan, it is sufficient to mul-
tiply their number, first, by the propor-
tion of those 65 and over receiving
money from that particular plan and,
second, by the average amount of bene-
fit paid out.
Taking the present value of the differ-
ences between additional contributions and
benefit payments for each relevant year
after 1986, we arrive at $2 billion. This is
the amount that would have been necessary
in 1986 to guarantee that the deceased
smokers would benefit from pension plans
exactly as non-smokers. Since smokers
would participate in gathering this sum,
only part of it is a transfer to non-smokers.
Using once again the proportion of
Canadian taxpayers who did not smoke in
1986 (69.15%), a transfer of $1.4 billion was
obtained.26
The Net Transfer
If we sum the transfers over the three cate-
gories above, we get Table 5.
From our assumptions and the above
analysis, it emerges that any notion that
smokers are a burden on society in general
or on the non-smoking population in partic-
ular is without foundation. Actually, for
1986 in Canada, non-smokers enjoyed a
standard of living $4.3 billion higher than
it would have been if there had been no
310 Andre Raynauld and Jean-Pierre Vidal
smokers at all, according to our assump-
tions and methodology.
V Methodological Issues
Our results differ very considerably from
the conclusions reached by several authors,
including those who examined the
Canadian situation.
These major differences come mainly
from the methodology used and involve a
number of considerations that may or may
not be held relevant to the analysis of the
financial burden of smokers on society.
There are three major issues: 1/ the re-
duction of future costs associated with the
assumed early deaths of smokers; 2/ the no-
tion of financial transfers between smokers
and non-smokers; and 3/ finally, the most
important one, the inclusion or exclusion of
personal income losses in the balance sheet.
The Reduction of Future Costs
Although E.R. Shillington (1977) and N.
Collishaw and G. Myers (1984) ignored the
reduction of future healths costs, we main-
tain that these savings must be deducted
from the supplementary costs associated
with smoking. It is a matter of very simple
logic to argue that if smokers die earlier
than non-smokers, between the time of
their early death and the time they would
have died had they not smoked they will not
use the services typically used by non-
smokers. In any case, in approaching the
problem in this way one may claim the sup-
port of several authors, such as A.B. Atkin-
son and J.L. Townsend (1977), W.F. Forbes
and M.E. Thompson (1983), G.T. Watts
(1983), R.E. Leu and T. Schaub (1983,
1984), and A. Markandya and D.W. Pearce
(1989)?7
In dollar terms, this item is not crucial,
but it is not negligible either. As already in-
dicated above, it reduces tobacco-related
health cost by $462 million.
Transfers
Financial transfers between smokers and
non-smokers are not considered in the ref-
2501357046

erence studies cited above. In our view,
such transfers, which determine who pays
and who benefits between smokers and
non-smokers respectively, are an essential
component in any assessment of the burden
that smokers may or may not impose on
society.
There are two steps in such an analysis.
First, one must incoporate taxes paid by
smokers, because on efficiency grounds
alone and consistent with the Pigovian ap-
proach, such taxes are a compensation for
the external costs generated. An optimal
tax in this context is one that just equals
this external cost at the margin. Up to this
point we follow A.B. Atkinson and 'r.W.
Meade (1974), as well as A. Markandya and
D.W. Pearce (1989). However, we make a
second, additional, step in this study. As the
calculations above indicate, total external
costs and taxes are adjusted by the relevant
proportions of smokers to derive transfers
in the strict sense of the word.
We take a broad view of transfers as it
should be. In addition to the taxes on
tobacco consumption, our transfers include
estimates of the net flow of pension con-
tributions and benefits between smokers
and non-smokers. The bottom line on over-
all transfers is given in Table 5.
Own Income Losses
Personal income losses are the main em-
phasis in most of the literature on the
'economic consequences' (cost) of smoking.
For example, personal income loss repre-
sents 86 per cent of the 'economic con-
sequences' in the study by Shillington
(1977); 77 per cent in Collishaw and Myers
(1984); and 55 per cent in USDHHS (1990).
It seems that all these were inspired more
or less directly by D.P. Rice (1966).
The concept of 'economic consequences'
was renamed 'economic cost' by Leu (1983),
and Leu and Schaub (1984), who ration-
alised it as the sum of the 'monetary private
costs' to smokers plus the 'monetary exter-
nal costs' of smoking. The 'economic cost'
of smoking would then be the sum of its pri-
vate and external components - that is, its
social cost - but without considering intan-
gible costs such as pain and suffering.
It is this concept of 'economic cost' that
has been applied to show what a burden
smokers are to society. The language used
in the Report to Congress, USDHHS (1990),
is unambiguous when the authors refer to
'the cost or value to society' (p.38) or when
they remark that 'smoking causes large
numbers of deaths and a very large dollar
cost to society' (p.40).
Ultimately, it is suggested that taxes on
tobacco should compensate for this huge
burden. As we remarked in the introduc-
tion, there are numerous published opin-
ions to this effect.
The fundamental issue to consider in
this case is whether own-income losses as-
sociated with the premature death of
smokers are a private cost or an external
cost. Our thesis is that such income losses
are a private cost and should not be in-
cluded in an analysis of the financial bur-
den of smokers on society.
The first argument in support of this
thesis has been included earlier as one of
our three basic assumptions in this study,
namely that smokers behave rationally and
are well-informed of any possible health
hazard from smoking.
It might still be argued, however, that
even though smokers have knowingly ac-
cepted the risk of sickness or early death,
they nevertheless impose a loss on society.
This evokes the image of smokers dying in
their forties and thereby depriving society
of another two decades of productive work.
Such reasoning may seem persuasive, but
it is almost invariably in error.
In fact, society tends to reward individu-
als strictly in accordance with the contribu-
tion it receives from each. It therefore
neither gains nor loses with the increase or
decrease of its overall numbers. When
another worker is introduced into the
economy, production rises, leading to the
growth of national product. But this does
not imply that society as a whole is any
more rich or prosperous.
This reasoning is not new or original.
Smokers' Burden on Society 311

Indeed, there is a strong consensus among
economists on this point. In the words of
E.J. Mishan (1971a):
the loss of potential future earnings, can be
rationalized only if the criterion adopted in any
economic reorganization turns on the value of
its contribution to GNP, or, more accurately, to
net national product. But although financial
journalists manage to convey the contrary im-
pression, maximizing GNP is not an acceptable
goal of economic policy.
Mishan's judgment highlights the
simple truth that the real victim of a death
is the dead person concerned, not society as
a whole.
The three methodological issues just
raised are largely responsible for the huge
differences between our empirical results
and those of our reference studies. The
myth and reality of the financial burden of
smokers do not rest on the minute details
of computations but on the relevant factors
to be considered in the analysis. The next
section will confirm this conclusion.
VI Sensitivity of Results to Relative
Risk Coefficients
Remembering that our results regarding
health costs are based on epidemiological
studies which differ widely in their find-
ings, a legitimate question arises about the
sensitivity of our conclusions to the relative
risk coefficients used. All calculations have
therefore been done again using 14 differ-
ent hypotheses covering a very wide range
of possible assumptions regarding relative
risk coefficients. They range from smoking
is not dangerous at all (,y = 0), to smoking
is ten times more dangerous than in the
worse scenario envisaged in the reports we
used (y= 10).
As expected, gross external costs in-
crease with the danger smoking poses to
health. When -y equals 0, tobacco use is
harmless to health, and the only external
cost is fire at $54 million. When Y equals 1,
relative risk coefficients being identical to
312 Andre Raynauld and Jean-Pierre Vidal
those assumed in section II, we get the same
result as in section III, of $668.8 million. Af-
terwards, costs tend to stabilize toward an
upper bound which cannot be exceeded: ob-
viously, when y- -, all the etiologic frac-
tions tend to 100 per cent, at which point no
further costs are left to be imputed.28
On the other hand, when smoking is
harmless, there is no reduction in future
costs; however, as it becomes increasingly
dangerous, it is accompanied by a reduction
in future costs. Two characteristics are
worth noting: first, the curve describing the
reduction in future costs increases at a
lower rate than the additional cost curve
does; and second, the rate of increase of the
reduction cost curve decreases more slowly
than the additional cost curve does.
These characteristics result in a very in-
teresting net external cost curve, shown on
Graph 1, which represents the difference
between gross external costs and reduction
of future costs.
It will be recalled that in our reference
scenario, where y equals 1, smokers im-
posed a net external cost of $207 million on
Canadians in 1986. As is apparent from
Graph 1, this net external cost appears to
be in the neighbourhood of a maximum:
whatever the relative risk coefficients one
chooses, the net external cost is never sig-
nificantly higher than $207 million. Reduc-
ing the risk brings a movement to the left
of ` y equals 1' and leads to a decline in net
external cost, but increasing the risk, al-
though it brings a movement to the right,
also leads to a decline in net external costs
because the reduction in future costs grows
at a faster rate than the increase of addi-
tional costs in present value (as of 1986).
Actually, if it were possible for relative
risk coefficients to be as high as when y
equals 10, we would have to conclude that
there would be a net external benefit of
$725,000 (which appears close to zero in
Graph 1).
The existence of this maximum of ap-
proximately $207 million, allows us to ob-
serve that, whatever the risk smoking poses
to health, the present level of taxation is un-
2501357048

1. NET COST 0r- EXTERNALITIES
justifiable on grounds of efficiency. In other
words, since the net external cost function
is not an increasing monotonic function of
the risk involved in tobacco use, there is no
level of danger at which the present level of
taxation would be justified.
As for the transfer between smokers and
non-smokers, whatever the danger tobacco
might pose to health, non-smokers always
enjoy a much higher standard of living be-
cause of smokers. Given our assumptions,
iokers are never a burden to non-
s.nokers: at worst, non-smokers receive ap-
proximately $3 billion from smokers, and at
best $7 billion. Without doubt, the net
global transfer flow is always to the advan-
tage of non-smokers and to the detriment
of smokers.
At the beginning of this paper, we noted
that many authors evaluated the 'economic
consequences' of smoking as one huge sum,
which has subsequently been interpreted
as a burden smokers would be imposing on
others. New taxes have been proposed and
justified on these grounds.
We have shown instead that net addi-
tional external costs borne by non-smokers
worked out to $244 million for Canada in
1986. However, smokers are responsible for
a much larger transfer flow in the other
direction. In the pension area alone, non-
smokers benefit from a transfer of $1.4 bil-
lion mainly because smokers tend to die
before non-smokers do if we use risk coeffi-
cients established by the medical profes-
sion. Finally, the massive tax burden borne
by smokers alone means that they account
for a further transfer of close to $3.2 billion
to the benefit of non-smokers. Overall, as
Table 5 indicates, smokers make a net over-
all contribution of $4.3 billion to the bene-
fit of non-smokers.
Whatever the degree of risk or danger at-
tributed to tobacco, the validity and direc-
tion of these conclusions remain un-
changed.
Smokers' Burden on Society 313
_,:h,.

Notes
1 See Forbes and Thompson (1978), Wilkinson et aL
(1978), Heins (1978), Kristein and Grove (1978),
Cady (1983), Warner (1983), Cady (1986) and Hof-
fenberg (1988). Studies on the 'economic con-
sequences' of smoking such as those of Shillington
(1977), Collishaw and Myers (1984) and the US
Department of Health and Human Services
(USDHHS,1990), have been interpreted as imply-
ing a financial burden on the part of smokers.
Strictly speaking, this implication is incorrect. See
also Rice (1966), Stoddart (1987), Choi and
Nethercott (1988), Freour et al. (1976), Luce and
Schweitzer (1978), Shultz (1985), Hinds (1986),
Gorsky, Schwartz and Dennis (1990), Gray et al.
(1988). A closely related literature claims to follow
'cost-bene6t' analysis. A typical example is found
in Forbes aqd Thompson (1982), and a criticism in
Woodfield (1984).
2 We used the Reports of the years 1982, 1983 and
1984. For a Canadian study, taking our relative
risk coefficients from an American source may ap-
pear to be a second best, especially if one believes,
as we do, that geographical variables may be im-
portant. However, some Canadian studies are in-
cluded in these reports.
3 Although we did not review the medical literature
systematically, we did come across some very dis-
turbing findings for the 'conventional wisdom'
about cigarette smoking and health. These lead us
to believe: first, that the results of epidemiological
studies might very well be strongly biased by the
omission of some crucial variables from the statis-
tical analyses, such as personality (especially risk
aversion) which is responsible for a larger set of
detrimental behaviours as well as beneficial ones,
like exercising; and second, that adequate care
had not always been taken in building the samples
used in epidemiological studies. See Seltzer (1989
and 1980). Sterling and Weinkam (1987), and Tol-
lison (1986).
4 We assume implicitly that the morbidity risk
coefficients are the same as the mortality risk
coefficients, because the statistics required to dis-
tinguish the two are inadequate. This assumption
is not favourable to our conclusions.
5 Prospective studies are based on a random sample
of individuals who are monitored over a number
of years to determine how many among them will
die of a lung cancer and were subject to smoke.
Retrospective studies by contrast examine, ex-
post, people who have died of a lung cancer and
seek to determine how many among them were
subjected to smoke. A retrospective study does not
give a relative risk coefficient (), strictly speak-
ing, but an approximation of it
6 Our emphasis in the text.
7 We do not deny that for those who are already vic-
tims of chronic obstructive lung disease, smoke
could be the cause of some discomfort. We do not
deny either that some people may complain of
minor eye irritations, and the like, if they stay long
enough in a room filled with thick smoke. How-
ever, what we do hypothesize is that it is far from
established that someone can contract a disease
requiring significant health care only because of
environmental tobacco smoke. Later, we will ex-
plain why we do not evaluate the sums non-
smokers would be willing to pay to avoid such
inconveniencies.
8 See also Chaloupka (1990), and Becker, Grossman
and Murphy (1990).
9 For further details on epidemiologic methods see
Miettinen (1972,1974), and Walter (1975; 1976).
10 Preliminary data for 1985-1986, from the Cana-
dian Health Information Center. These data will
be revised and published in the catalogue 82-206
(Statistics Canada, forthcoming b).
11 The average cost per day is taken from prelimi-
nary data from the Canadian Health Information
Center. Once revised, it will be published in table
117 of the catalogue 83-233 (Statistics Canada,
forthcoming a) for the year 1986-1987.
12 See Saskatchewan Cancer Foundation (1987:25),
and Saskatchewan Health, Medical Care In-
surance Branch (1989).
13 Marginal cost and benefit are increments. Usually
we assume these increments to be small. How-
ever, in the present circumstances, we have no
choice but to take the total cost as if it were an in-
crement over 0.
14 Appendixes are available from the authors upon
request. Appendix 1 gives the number of deaths
according to cause and sex. It also describes the
model which simulates what would have been the
life and death of smokers had they not smoked and
lived longer. Appendix 3 discusses the discrepancy
between our 21,841 estimate of the number of
deaths due to smoking and that of 35,131 from Col-
lishaw, Tostowaryk and Wigle (1988).
15 From 1946 to 1990, the ex post real rate of return
on 10-year Canadian bonds was never higher than
3%, except once in 1989. Indeed, it has been almost
nil or even negative for approximately two de-
cades, from the end of the 40s to the end of the 50s,
and from the mid-'70s to the mid-'80s. Thus, over
the long run, it is reasonable to believe that the
maximum real rate of return on risk-free assets is
not superior to 3%. Obviously, the discount rate
could be inferior, but then, our conclusions would
be even more favourable to smokers.
16 Additional medical services costs were found to be
$68 million compared to $546.5 million for addi-
tional hospital care costs which gives a ratio of one
to eight. We will find in the following section that
the reduction of future medical services costs is
$123.5 million. Applying the ratio.of one to eight
314 Andre Raynauld and Jean-Pierre Vidal 2501357050

would lead us to think that the reduction of future
hospital care costs could be as high as $988 mil-
lion.
17 We took as a reference the average costs as calcu-
lated by Regie de 1'Assurance Maladie du Quebec
(1987). We made two adjustments: one to recon-
cile the average payments on a fee-for-service
basis with overall medical services, and one to rec-
oncile the per capita medical service cost in Que-
bec with that in Canada.
18 During 1986, the total number of old age re-
cipients of residential care was established at
155,381. Assuming linear progression, this figure
is derived from an interpolation carried out for
June 1, between the March 1, 1986, figure of
154,502 (see Statistics Canada, 1989a) and the
158,019 figure of March 1, 1987, (see Statistics
Canada,1989b:119). The breakdown of this figure
by age-group was performed according to table 6
in (Statistics Canada, 1989a).
19 We first found that public sources account for 65%
of the residential care facilities income by sub-
stracting private financial sources (co-insurance,
$539 million; supplements for rooms, $26 million;
miscellaneous income, $46 million) from a total in-
come of $L73 billion (Table 9 of Statistics Canada,
1989a). We then took 65% of the average daily cost
of $54.40 (Statistics Canada, 1989b:119), to obtain
$35.17.
20 In an appendix, which is available from the
authors upon request, we explain how we obtained
the number of taxpayers among the smokers who
would have survived between 1986 and 2071 had
they not smoked.
21 This estimate is for calendar year 1986, and has
been supplied by the Department of Finance,
Government of Canada.
22 The estimates of the federal excise tax as well as
the federal excise duty apply to fiscal year 1986-
1987 and come from the Public Accounts (Canada,
1986).
3 The estimate of the tariff duty applies to the cal-
endar year and comes from Statistics Canada
(1986).
24 The figure published originally was $1,987.7 mil-
lion. This figure was increased to include revenues
from the general sales tax on tobacco in New-
foundland and Ontario.
25 The breakdown is as follows: $13,234,590 for Old
Age Security and Supplement; $7,394,088 for
Canada and Quebec Pension Plans; and,
$8,832,962 for private pension plans.
26 Although this approach based on averages is quite
rough, it still requires more than 250 tables, which
shows that a more precise estimation would have
required a study of its own. Detailed calculations
would certainly have to take into account the
changes in the number and age distribution of
beneficiaries, of spouse's allowances and of pen-
sions to survivors. As well, it would be necessary
to calculate the change in the amounts paid out
because a member of a couple dies. But, since the
average income between men and women differs,
it would also be necessary to take into account that
the amount offered by some programs depends on
general income and on other benefits already
being paid out.
27 Leu and Schaub (1983), have been criticized by
Forbes and Thompson (1985). A reply may be
found in Leu and Schaub (1985).
28 The form of the curve does not depend on the
transformation function, which is linear, but on
the etiologic fraction function (see section III).
More precisely, the higher the Euclidian norm
uik N, the higher will be the first derivative of the
cost function (which is positive) and the higher
will be the absolute value of the second derivative
(which is negative).
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