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1. -I-I
ELSEVIER International Journal of Forecasting 13 (19t)7) 527-537
An estimation model for replicating the rankings of the world
competitiveness report
Muhittin Oral 'h'*, Habib Chabchoub ~
"Gr~duate School of Future ~hmak,ement Sahanci University. TuJa. [stan/nd. Turkey
"Sciences dc ['Administration. Unil'er~tt~: Laval. Stc I"oy. Ql,:l~e('. P.Q. G IK 7t'4. Cana~ht
~Facult~; des Sciem'~'x Economiqt,'s et de G~'stion d~' Slit~. Rm~te Aer,,drmm'. 302,~¢Sfit.r. Turli~ia
A I)st tact
The W~rld Competitiveness Report (WCR). a rep~rt annually pr~dttced by Itle lnslitutc l'~r Management Development.
which is based in Switzerland. is a study that rates and ranks the competitiveness ~1" a certain group of nalitmx (()ECD
countries iflus some newly emerging ectmtHnies) and is a widely qut)ted rep~rt in the intcrnati~mal media, especially by
g~)vermuenl and public leaders. Alth~ugh stmle ideas as to the nlelhothflt~gy used in the ratillg :rod ranking of cotmtrics are
given, the tlct,lil~,are hill lll-ovided ill the W(.'Rs. "l'heref(ire. the niellilldohlgy used ill the WCRs is ill I;.Ir~cpart tlnkntiwll Itl
the public.
An intclligeiit use of the WCR rctluircx :i I';llllcr siltintl untlcrstantlil)g ~ll'the nleihodllhlgy by its plltential users; pllliticiails.
clmlpany executives, and public p~llicy nuikcrs. The ~llljcclivc ~lf this l~:ipcr is tll unc/ivcr and uudcrst:uld Ihc nlcthtldol~lgy of
the W('R Ihrllugh exact relllic,tlillnxill"its r;.inkings :it :ill levels ill":iggrcgalilln. An extinl,itillll Infidel b:tsed lln nlaihelllatical
I~r~lgr.imlllillg is used to replicate lhc W(,R r:tnkings, ab 1~)~)7lil~,cvier gt.'icllcc ILV.
K~'vwor,ls' Parameter e~,timati~m;Multiple-criteria alutly~,is;RankiJlg;('~mll~.'titivene~,s
I. Introduction
It is important as well as necessary to study the
competitiveness of nations for at least two major
retlSOllS.
I.I. I"irm strategy formuhttimt
A nation, with it.'; natural resources, human capa-
bilities, political regimes, government organizations,
research and educational institutions, linancial sys-
tems, cultural and .social values, provides a competi-
tive environment in which the tirms are created,
organized, and managed. The competitive environ-
ment that a nation or country provides influences the
perft)rluance of its lirms at home ~.illdabroad. There-
fore, it is of prirne importance for company execu-
tives to know and understand the competitive en-
vironments in which they and their competitors tire
operating.
"Ct~rrcsponding auth~r. Graduate Scho~d of Fulure Manage-
ment. Sahanci University..Tuzla. Ir,tanbul. Turkey.. Tel.: (11)_1_
"~ ~
27 )557]; fax: ~.)()212 2814231.
1.2. Govermm'nt and pul~lic policy fi~rmulation
One of the major roles of a government is to
formulate government and public policies that will
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2. 528 M. Oral. H. Chahchoub / International Journal r~f Forecasting,, 13 r 10071 .¢27-537
be instrumental in increasing the real incomes of its
citizens by providing an advantageous competitive
environment for the firms operating in the country.
This implies that the governments also compete
against one another in creating and maintaining a
superior competitive environment. The competitive
environment of a countD' is shaped by policies in
different areas: taxation, finance, legislation and
regulation, justice and .security. economic interven-
tion. government expenditures, education, science
and technology, infra.structt, re. health, and many
others. This requires that policy makers need to
compar e and contrast the competitive environments
of other countries with that of their own in order to
come t,p with better and more effective policies.
The competitiveness of nation.s has been on the
research agenda for some time and the efforts in this
area c.specially intensified since the early 1980.s
(Ander.son and Dtnnnet. 1987: I)urand and Giorno.
1987: Keller. 1985). Most noticeable ones arc tho.sc
of Porter (1990) and the World Compctitivcnc.~s
Rcporl (WCR), annual report.s of the In.stitule for
Managemcnt l)cvclopmcnt (IMD). based in Switzer-
land. (The WCR.S were the joint ptublication.s of IMI)
and the World Fconomic I:t~runt until the latter
.started ptnt~liShing its own r:mking.s in 1996). Porter
(1990), cmph~y.s a methodology, which hc call.s 'The
National I)iamoml" to develop all agcnd:t of competi-
tive mea.sures for a nation to put.sue. The ha.sic idea
behind hi.s methodology i.s Io :malyzc the economy of
a country, .sector by .sector. in terms of: (i) factor
conditions. (ii) demand conditions, (iii) .supportil|g
and rehttcd industries, (iv) lirm .strategy, .structt,re.
aml rivalry. (v) government role, and (vii chance
factor. The result.s of the analy.si.s are then tran.s-
fi~rmed into a .set of recommcndation.s to form an
agenda for the country to adopt. The WCRs, on the
other haml. provide rankings of a .selected group of
cotmtric.s with re.spect to a .set of more th:m 350
political, .social. and economic indicator.,;. The rank-
ings are done at flmr aggregation levels: (i) compo-
.site indicator level, (ii) subfactor level, (iii) lactor
level, and (iv) overall Icvcl, which corrc.sponds to the
competitivcne.ss ranking of a cot,tory. Contrary to the
Porter studies, the WCRs do not sugge.st any par-
ticular prescription.,; or agenda.s for the countric.s to
pursue, but offer .some general idea.s a.s to the
competitive po.sition of nation.,;.
This paper concentrates on the methodology of the
WCR. Although the WCRs have impact on the
international community among politicians, company
executives, and researchers, the methodology used in
producing count D' ranking.s is not known in detail.
Based on the description given in the WCR. 1992.
Oral and Chabchoub (1996) attempted to reproduce
the WCR. 1992 rankings. Their general conclusion i.s
that the methodology as described in the WCR. 1992
is not sufficient to reproduce the WCR ranking,; at
any level of aggregation, and hence the WCR
methodology remain.s unknown to its readers.
The objective of this paper is to uncover the WCR
methodology. Given the findings of Oral and Chab-
choub (1996). we assume that the WCR fonnldas
used in the rating of countries at four levels arc not
known, except that they arc in additive form. Then
the que.stion becomes linding the parametcr.s of the
additivc formt, la.s that will reproduce the WCR
rankings at all levels of aggregation. An approach
based on mathcmatic:d programming will be t,.scd for
this purpose.
The organization of the paper is as follows:
Section 2 will provitlc a gcneral structtlrc of the
method used in the W('Rs. An c.stimation motlcl to
rcproth,ce the W('R rankings at the aggregation
lcvcl.s of composite indicator, subfaclor, factor, alld
the overall compctitivcuc.ss i.s given in Section 3.
Also tliscus.scd in Section 3 arc the results produced
by the estimation inotlcl and their implications.
Section 4 conclutle.s tile paper with some remarks
:rod stnggcstitm.s for further re.search.
2. The general structt, re of WCR r~lting and
ranking method
At the time of writing this paper, tile most recent
WCR is that of 1995 (WCR. 1995). However. it does
not contain much methodological inlbrmation, nei-
ther do tile 1993 and 1994 report.s (WCR, 1993.
19941. Tile too.st recent WCR which ha.s somewhat
detailed methodological content is the one that was
publi.shcd in 1992 (WCR. 1992). Therefore. we .shall
use the WCR (1992) its tile basis of the formt, lation
that will be developed in thi.s paper.
As can be observed from Fig. 1. the ratings and
ranking.s of countries arc done at fot,r levels of
aggregation: (i) composite indicator. (ii) .subfactor.
(iii) factor, and (iv)overall.

3. M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) 527-537 529
Aggregation Level 1: Grouping287 Indicatorsinto 82 CompositeIndicators
x7 = Es?+
,.,s/s ,.,s,:
Ratingand RankingCountriesAccordingto CompositeIndicators
Aggregation Level 2: Grouping82 CompositeIndicatorsinto 32 Subfactors
Y~ = ~":x;
leO~
Ratingand RankingCountriesAccordingto Subfactors
Aggregation Level 3: Grouping32 Subfactorsinto 8 Factors
k qQ
Ratingand RankingCountriesAccordingto Factors
Aggregation Level 4: Grouping8 Factorsinto OverallCompetitiveness
Ill)
OverallCompetitivenessRatingsof Cotmtries
Fig. 1. Generalstructureof the WCR methodology.
2. I.I. Tile composite indicator level
The WCR (1992) uses 287 indicators, which are
of two kinds. 'Hard data indicators', which constitute
approximately two thirds of the indicators, are the
statistics published by international organizations and
national institutes. 'Soft data indicators', on the other
hand. are the statistics obtained through the Execu-
tive Opinion Survey that is conducted annually by
IMD. The indicators are grouped into 82 composite
indicators. The aggregation is done according to the
following formula:
r Z" Z r
x/ = sJ + WeS/ ( I)
iEAjt iEA7
where x/ is the rating of the country in rank r with
respect to composite indicator j and w, is the weight
d
given to soft data indicator i, Aj is the set of
indicators consisting hard data that form composite
indicator j, and Aq the set of indicators consisting of
. • • q d
soft data that form composite m&catorj(Ai AAj =0
_ q a r,
and Aj-Aj UAi), and s~ is the standardized score
with respect to indicator i.
2.1.2. The subfactor level
The objective of this aggregation level is to group
the 82 composite indicators into a set of 32 subfac-
tors so that ratings and rankings of the countries can
be done at the subfactor level as well. Given the
description of this step in WCR (1992), the aggrega-
tion of the composite indicators into subfactors is
done by the following formula:

4. 530 M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) 527-537
r •
y, = Y~ x~ (2)
jEB I
where Bk is the set of composite indicators defining
subfactor k of factor l and xj"j is as defined by Eq.
(1). The meaning of Eq. (2) is simply that the rating
of the r th ranked country with respect to subfactor k
is the arithmetic sum of the scores obtained with
respect to the composite indicators forming the
subfactor in question.
2.1.3. The factor level
The objective of this aggregation is to convert the
ratings at the subfactor levels into the ratings at the
factor level so that rankings of the countries can be
done at the latter level. Through this aggregation, the
32 subfactors are grouped into 8 factors. The factor
rating of a country is a simple arithmetic sum of its
subfactor ratings: that is,
r r
z, -- Y, y~ <3)
k¢c~
where CI is the set of subfactors defining the factor l
and y: is as defined by Eq. (2).
2.1.4. The overall competitiveness level
The objective of this last aggregation level is to
obtain an overall competitiveness rating for each
country using the ratings obtained at the factor level.
The rating of the r th ranked country with respect to
competitiveness is given by
f" = ~ z~ (4)
lED
where z~ is as defined by Eq. (3). In other words, the
overall competitiveness of a country is determined
using an additive function of eight factors. The eight
factors used for this purpose are:
Infrastructure
Management
Scienceand Technology
People
markets and qualityof finan-
cial servicesin a country;
the extent to which the infra-
structure system of a country
is adequate to serve the basic
needs of business;
the extent to which firms are
run in an innovative, profit-
able, and responsiblemanner;
thescientificandtechnological
capacityof a country;
the availabilityand qualifica-
tions of humanresourcesin a
country.
The WCR (1992) studies the competitiveness of
two groups of countries. In the first group, the OECD
countries are included; namely, Australia, Austria,
Belgium, Canada, Denmark, France, Finland, Ger-
many, Great Britain, Greece, Ireland, Italy, Japan,
Netherlands, New Zealand, Norway, Portugal, Spain,
Sweden, Switzerland, Turkey, and United States. The
second group consists of newly industrialized coun-
tries: Brazil, Chile, Hong Kong, Hungary, India,
Indonesia, Malaysia, Mexico, Pakistan, Singapore,
South Korea, Taiwan, Thailand, and Venezuela. The
competitiveness rating and rankings are separately
done for these two groups of countries (this however
is no longer the case in the 1994 and 1995 WCRs
since they provide the ratings and rankings of all the
selected countries also in one single group) (WCR,
1994, 1995). In this paper, we shall concentrate only
on the OECD countries since our primary concern is
methodological rather than the countries themselves
per se.
In the following section, we shall provide an
estimation model to replicate the ratings and rank-
ings of the WCR at each aggregation level assuming
that the general structure of the methodology is as
described in Fig. I and that additive models are used
to estimate the ratings at each aggregation level.
Domestic Economic Strength
Internationalization
Government
Finance
an overall evaluation of the
domestic economy at the
macro level;
the extent to which a country
participates in the international
trade and investment [lows;
the extent to which govern-
ment policies and programs
are conducive to domestic and
international competitiveness;
the performance of capital
3. The estimation model for replicating the
WCR results
3. !. The estimation model
According to the 1992 publication (WCR, 1992),
the WCR methodology uses the formula in (1) to
rate the countries at the composite indicator level.

5. M Oral, H Chabchoub I International Journal of Forecasting 13 (1997)527-537 531
Therefore, the formula in Eq. (1) must also be valid
for the composite indicators which consist of only
'hard data' indicators. In other words, the formula in
(1) reduces to
:,?=E
lEA d
when A7 is an empty set, implying that the compo-
site indicator in question does not have any 'soft
data' indicator. Oral and Chabchoub (1996) showed
that the above formula did not reproduce the WCR
rankings for four 'hard data' based composite in-
dicators (namely, 'social security', 'patents', 'cost of
living', and 'national debt'). This means that the
coefficients of 'hard data' indicators are not always
equal to unity, contrary to what is described in WCR
(1992). Therefore, we have to assume that the
ratings at the composite indicator level are done
according to the following more general formula:
•;,= E .,is:,
+ E w s,, (5)
which means we no longer assume that w~= 1 for
i~A a. Here we do not know the values of wi's and
therefore we need to estimate them such that the
WCR rankings are reproduced at all levels. The
estimation of w/s will be obtained from a particular
mathematical programming model, which will be
henceforth called WEM (Weight Estimation Model).
The basic idea behind WEM is simple. In order to
increase the chances of replicating the WCR rankings
at all levels, we shall assume that one might assign
different weights to a given indicator for different
countries, rather than imposing the same weight for
all countries. This flexibility of assigning different
weights makes the model fit the data better. How-
ever, the same weight applies at all levels once a
weight is assigned to an indicator for a country.
Although different weights for an indicator are
allowed, WEM will seek to minimize the differences
between the countries regarding the importance of an
indicator.
3.1.I. WEM (Weight Estimation Model)
287
Minimiser ~ (X~ - XT ) (6)
E rk rt
W i S,
j-! Li-I
k=l ..... Kt
subject to
(r÷l) (r÷l) ~-~0
-- W~ S i
1~1 LI-I
r=l ..... 21
wT'sT'
k--I LI-I
-E w,-",.,.,,,-I
k=l L.j-I Li=I J
r,--- 1 ..... 21./= 1..... 8
j~l rk rk ~ w(r+l)ks r+l)* >0
Wi Si i --
- Li-I '- Li-I
G = 1..... 21,k= I ..... K I
I, I,
E w ,sT,-E '*'" rj=l,. 2l
W i IS i . • , ,
i'l i'l
j=l ..... J~
l ..... 21,
j-I i'1
(7)
(8)
(9)
(lO)
(ll)
• +
wi-xi <--0 i=l ..... 287. r=l ..... 22. (12)
¢
wi -X[" >--0 i= 1..... 287. r= 1..... 22. (13)
An interpretation of the above formulation is in
order. The objective function in (6) aims to eliminate
the differences between countries regarding the
weights of indicators. For instance, X~-xS=O
r ÷
implies that w~=X~ =xS. This means that the same
weight is to be assigned to indicator i for all
countries. If this is true for all the indicators then the
value of the objective function is equal to zero,
implying that the same set of weights apply for all
÷
countries. On the other hand, X~ -,It'S ¢-0 implies
that it is necessary to assign different weights to
indicator i for each country. The higher the value of
the objective function, the greater is the differences

6. 532 M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) .527-537
between the weights to be assigned from country to
country.
The constraints in (7) assure that, with the weights
to be estimated from WEM, the WCR overall
competitiveness ranking is obtainable. The first term
in (7) yields the rating of the country in Rank r
whereas the second term is the rating of the country
in Rank (r+ I). A nonnegative difference between
the two terms for r=l,2 ..... 21 implies that the
WCR overall competitiveness ranking is obtained.
The constraints in (8) are to assure that the WCR
ranking at factor level is also obtainable with the
weights to be estimated from WEM. Again, the first
term in (8) yields the rating of the country in Rank r~
with respect to Factor l whereas the second term is
the rating of the country in Rank (rI+ I). A nonnega-
tive difference between the two terms for rt=
1,2..... 21 and 1= 1,2..... 8 implies that the WCR
rankings at the factor level is obtainable. Similarly,
the constraints in (9) and (10) assure the replication
of the WCR rankings at the subfactor and composite
indicator levels, respectively. Thus we are in search
of those values of w, such that the WCR rankings are
reproducible at all four levels.
The constraints in (i i) play two distinct roles.
First, the constant on the right hand side indicates the
number of indicators delining subfactor k. This
avoids obtaining the trivial solution; that is, w~=0
for all r, i. Second, ( I 1) requires that each and every
sublactor is represented by at least one of its
indicators. This avoids the possibility of discarding a
subfactor in evaluating the countries. In other words,
each and every subfactor is accounted for in the
rating and ranking of countries. The constraints of
the type in (11) could have been chosen at the lowest
level of aggregation; that is at composite indicator
level. The reason for not doing so is that there are
several composite indicators consisting of only one
single indicator, implying there is no real aggrega-
tion of data across all composite indicators. At the
subfactor level, on the other hand, each subfactor
consists of at least two indicators, indicating a
consistent aggregation level across all subfactors.
The constraints in (12) and (13) are for the
purpose of maintaining the weights within certain
intervals. Through the minimization of the objective
function, these intervals are kept at a range as small
as possible. In other words, the constraints in (12)
are in search of a consensus on the weights to be
assigned to each criterion.
Although four different notations, for a given
indicator and a country, are used to make a distinc-
tion between four levels of aggregation, we have in
r r
reality w, = w~' = w,k= w/. For example, suppose
that the country with overall rank 7 (r=7) has the
rank 2 with respect to Factor l (r: = 2), 4 with respect
to subfactor k (rk=4), and 10 with respect to
. . . . r 7 •
composite mdlcator j (r,= 10), then w, =w~ m (7),
r 2 • • 14 • r 10
wi'= w, m (8), w/k= wi m (9), and w/= w i are
all the same. In other words, once the country and its
ranks at the four aggregation levels are known the
WEM model can be easily formulated for computa-
tional purposes by noting the above relationship.
There are two possibilities regarding the outcome
of running WEM. The first possibility is that there is
no solution to the optimization problem represented
by WEM. This implies that the rankings of the WCR
cannot be obtained whatever weights are used. The
other possibility is that there is at least one optimal
solution. If the optimal solution is unique then one
can conclude that the WCR rankings can be re-
produced by using a unique set of weights and no
other set of weights can reproduce the rankings. The
existence of multiple optimal solutions, on the other
hand, implies that the WCR rankings can be re-
produced and there are infinitely many sets of
weights that can do so.
According to the optimal solutions obtained from
WEM the set of indicators can be composed into
four disjoint subsets: the subset of unnecessary
indicators; the subset of completely agreed in-
dicators; the subset of strongly agreed indicators; and
the set of weakly agreed indicators. The first subset
r
corresponds to the set of indicators for which w~=0
for all r. This indicates that all the indicators in this
subset can be discarded since they have no impact on
the rating and ranking of the countries. The subset of
completely agreed indicators is the set of indicators
for which w~>0 and 2"7 -X," =0. For the indicators
in this subset, the identical weights are used across
the countries, because there is a complete agreement
as to the value of the weight to be used in the rating
and ranking of the countries. The subset of strongly
agreed indicators is the set of indicators for which
X7-g,--<e. where e is a sufficiently small positive
value, meaning that there is a 'strong' agreement on

7. M. Oral, H. Chabchoub I International Journal of Forecasting 13 (1997) 527-.537 533
the values to be assigned to the weights. The subset
of weakly agreed indicators, on the other hand,
consists of those indicators for which w~>0 and
X7-X~->,~. The implication of this is that although
it is agreed that the indicators in this subset are
important, there is no 'strong' agreement on the
weights to be assigned to the indicators since they
differ from one another, according to the country
being evaluated, by at least 6.
3.2. The computational results and their
implications
The WEM is run using the data of WCR (1992).
The first conclusion is that there are feasible solu-
tions, therefore at least one optimal solution, to the
problem in WEM. This implies that the WCR
rankings at all four levels can be reproduced by
using the weights obtained from WEM. The second
conclusion is that it is necessary to use, for some
indicators, different weights for different countries
since the optimal value of the objective function is
greater than 0, in fact equal to 46.01. In other words,
we cannot use the same set of weights for all
countries. In the case of some countries we need to
use different weights for a given indicator in order to
reproduce the WCR rankings. The third conclusion is
the arbitrariness of the rankings due to the existence
of multiple optimal solutions. There are infinitely
many sets of weights that provide the same WCR
rankings. This outcome is perhaps due to the high
number of criteria being used, the situation where it
is difficult to avoid multicollinearity between the 287
indicators employed in the ratings and rankings of
countries. In fact some of the 287 indicators are not
needed, and therefore can be discarded, as we shall
conclude below by examining the contents of the
four subsets we defined earlier.
3.2.1. The subset of unnecessary indicators
The optimal solutions obtained from WEM indi-
cate that there are 27 indicators for which w~= 0 for
all countries. In other words, these 27 indicators,
almost 10% of the total number of indicators, have
no importance at all, and hence are unnecessary, in
the ratings and rankings of countries. This reduces
the number of important indicators from 287 to 260,
For the list of the unnecessary indicators, the reader
is referred to Appendix A. A breakdown of the
unnecessary indicators is given in Table !. From
Table 1, one can easily observe that three out of 27
unnecessary indicators are related to 'Domestic
Economic Strength', six to 'Internationalization',
four to 'Government', two to 'Finance', eight to
'Infrastructure', none to 'Management', one to 'Sci-
ence and Technology', and three to "People'. This
breakdown suggests that the indicators in the cases
of 'Internationalization' and 'Infrastructure' are less
than useful in explaining the WCR ranking. On the
other hand, the indicators chosen for 'Management'
and 'Science and Technology' factors are more to
the point. Note that in Table 1 the number of
unnecessary indicators for 'Management' is zero,
implying that all the indicators chosen for this factor
are pertinent and used in ranking the competitiveness
of countries.
Table I
Number of indicators by factors
Factor Unnecessary Completely Strongly agreed Weakly agreed Total
indicators agreed indicators indicators indicators
Factor I 3 19 2 7 3 I
Factor 2 6 18 5 11 40
Factor 3 4 24 4 13 45
Factor 4 2 15 0 8 25
Factor 5 8 17 2 7 34
Factor 6 0 19 4 14 37
Factor 7 1 21 3 5 30
Factor 8 3 24 7 11 45
Total 27 157 27 76 287
Factor I: Domestic Economic Strength; Factor 2: Internationalization; Factor 3: Government Factor; Factor 4: Finance Factor; Factor 5:
Infrastructure; Factor 6: Management; Factor 7: Science and Technology; Factor 8: People.

8. 534 M. Oral. H. Chabchoub / International Journal of Forecasting 13 (1997) 527-537
3.Z2. The subset of completely agreed indicators
As given in Table 1, the number of indicators in
this subset is 157, which corresponds to 55% of the
total number of indicators. In other words, there is a
complete agreement as to the necessity of and the
weights to be assigned to the indicators in this
subset, because for these indicators we obtained
w/>0 and gi-g~=O, implying w~ =w~ for all
countries. Thus the same weight w~ is used in the
evaluation of all countries with respect to indicator i.
However, some of the indicators in this set are more
important than the others. The list of the ten most
important indicators (an indicator with wi>-2.0) is
given in Appendix B. When added to the number of
unnecessary indicators, we realize that the same set
of weights, in the case of 64% of the indicators (that
is 184 over 287), is used for all countries.
As can be observed from the breakdown of the
157 completely agreed indicators given in Table 1,
the factors 'Government' and 'People' are leading in
terms of number of indicators, albeit the other factors
are not lagging too much behind, and therefore as a
percentage they are very close to one another.
3.2.3. The subset of strongly agreed indicators
There are 27 indicators in this subset, as can be
seen in Table 1. The agreement as to the values of
weights to be assigned to the indicators in this subset
is considered to be 'strong' since X~ -X7 ~s where
c=0.1, a sufficiently small value within the context
of the problem. In other words, slightly different
weights are used in the evaluation of countries with
respect to indicator i. However, we observe that one
particular indicator (current account balance) is far
more important than the others, for it has an assigned
weight value of 3.06 while the rest have values
below 1.00. Given the numbers of indicators in the
previous two subsets and this subset, we can claim
that there is either a complete or a strong agreement
as to the necessity and the level of importance in the
case of 21 i indicators over 287, corresponding to a
percentage of 74%.
The breakdown of 27 strongly agreed indicators,
on the other hand, shows that two of them are related
to 'Domestic Economic Strength', five to 'Inter-
nationalization', four to 'Government', none to 'Fi-
nance', two to 'Infrastructure', four to 'Manage-
ment', three to 'Science and Technology', and seven
to 'People'.
3.2,4. The subset of weakly agreed indicators
The rest of the indicators are classified as im-
portant, but at different levels, varying from country
r .4- --
to country. Since w~>0 and X~-X~ >e, it is
necessary to use somewhat significantly different
weights (as can be observed from Appendix C) in the
evaluation of countries with respect to indicator i.
The number of such indicators is 76, corresponding
to about 26% of the indicators used in WCR (1992).
A breakdown of weakly agreed indicators is given in
Appendix C.
The breakdown of 76 weakly agreed indicators
shows that seven of them are related to 'Domestic
Economic Strength', eleven to 'Internationalization',
thirteen to 'Government', eight to 'Finance', seven to
'Infrastructure', fourteen to 'Management', five to
'Science and Technology', and eleven to 'People'.
This breakdown suggests that the indicators in the
cases of 'Internationalization', 'Government', 'Man-
agement' and 'People' are less than agreed upon as
to the weights to be assigned to each. On the other
hand, 'Science and Technology' has the smallest
number of indicators, five in all, for which one is
obliged to use somewhat different weights in order to
reproduce the WCR ranking. In this respect, 'Science
and Technology' is followed by 'Domestic Econ-
omic Strength', 'Infrastructure', and 'Finance', with
seven, seven and eight indicators, respectively.
3.2.5. The 23 most important indicators
Although 260 out of 287 indicators are used in
rating the competitiveness of countries, their levels
of importance vary considerably from one another.
The level of importance of an indicator is given by
-i-
the value of X~, which is the upper value for weight
w~. On the average, the value of w~ must be around
1.00, due to the constraints in WEM. An indicator is
considered important when X,+>2.00. It was found
÷
that there were 23 indicators with X, >2.00 and they
are given in Table 2. The first column of Table 2
includes the codes of the indicators. The first digit of
the code before the decimal point is for factor
identification, more specifically: I, Domestic Econ-
omic Strength; 2, Internationalization; 3, Govern-
ment; 4, Finance; 5, Infrastructure; 6, Management;
7, Science and Technology; 8, People. The two digits
following the decimal point are indicator identifica-
tion associated with the factor. Given this coding
system, one can easily observe that only one out of

9. M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) 527-537
Table 2
The list of the 23 most importantindicators(w~>0 and X; >2.00)
535
Code in the Indicator X; >2.00
WCR (1992)
!.01 Gross national product 2.883541
2.06 Current account balance 3.028652
2.07 Terms of trade index 3.143517
2.09 Trade to gross domestic product ratio 2.!34464
2.27 Export market diversification 3.055544
2.28 Diversificationindexfor commodityexports 2.804852
2.36 Tourism receipts 2.749741
3.09 Total external debt 4.070751
4.I0 Credit 2.366860
4.09 Corporate bond issues 2.102588
5.02 Crude petroleumproduction 2.647251
5.16 Arable area 2.528311
5.22 Railroads 2.953567
5.38 Telecommunicationsmarket size 3.600434
5.43 Distribution systems 4.541992
6.14 PriceIquality-ratio 2.910289
6.16 Total quality control 2.513214
6.18 Advertisingexpenditure 2.097907
7.25 Patents granted to residents 2.989712
8.12 Higher educationenrollment 2.148095
8.15 Efficiencyof national education 2.074759
8.16 School intake 3.238315
8.20 Computer literacy 2.067483
the 23 important indicators is related to 'Domestic
Economic Strength', six to 'Internationalization', one
to 'Government', two to 'Finance', five to 'Infra-
structure', one to 'Management', one to 'Science and
Technology' and three to 'People'. This breakdown
of the 23 most important indicators suggest that
every factor is important since each one of them is
represented by at least one indicator. However,
'Internationalization' and 'Infrastructure' are leading
in this respect.
4. Concluding remarks
This paper has shown that the WCR rankings, at
four different levels, can be reproduced by adhering
to the basic additive forms of rating used in the WCR
(1992). If one is interested only in the ranking of
countries, then the WEM can be used as a surrogate
for the WCR methodology. It has also been shown
that one does not need to use all of the indicators in
order to replicate the WCR ranking; in fact, 27 of
them are unnecessary. Moreover, it has been ob-
served that a unique set of weights cannot reproduce
the results of WCR, one needs to use different sets of
weights for different countries. These results in fact
seem to suggest the notion that the importance of a
criterion varies from one country to another.
The presence of multiple optimal solutions indi-
cates that there exist many sets of weights that
reproduce the WCR ranking. This implies that one
cannot be sure of the importance of a given criterion
in evaluating the competitiveness of countries. If one
is also interested in the importance of each criterion
in the case of a given country, there is no way of
knowing it due to the existence of multiple optimal
solutions. The meaning of all these is that although
the WCR ranking can be reproduced, its actual
methodology remains unknown. This precludes in-
telligent use of the WCR results by executives and
policy makers, which is against the very idea of
publishing it.
Methodologically speaking, this paper offers an
approach, based on mathematical programming, to
estimate the parameters of a given or assumed
analytical form. Most of the forecasting and econo-
metric models are based on some analytical forms
and then the parameters are estimated with respect to

10. 536 M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) 527-537
certain 'accuracy' criteria (Oral et al., 1992; Cosset
et al., 1993). All of these parameter estimation
techniques are in fact usually based on an "optimi-
zation' process and the choice of a particular accura-
cy criterion usually implies an 'inherit' optimization
technique that comes along with it. The WEM also
represents an optimization problem but it is flexible
in the sense that one can introduce one's own
criterion (objective function) and formulate con-
straints that are more meaningful in the context of
competitiveness ranking of countries at different
levels.
The other approach that could have been taken in
'predicting' the WCR methodology is to identify the
indicators that are necessary to reproduce the WCR
rankings at each level individually, rather than
identifying the indicators that are essential at all
levels simultaneously. This is beyond the scope of
this paper. However, the interested reader is referred
to Oral and Chabchoub (1996) for the results of such
an approach.
7.28
8.09
8.13
8.22
Change in patents granted to non-residents
Public expenditure on education
Pupil-teacher ratio (1st level)
In-company training
Appendix B. Completely agreed ten most
+
important indicators (w~>2.00 and X, =X~ =w~
for all countries)
Code in the Indicator w _>2.00
WCR (1992)
1.01 Gross national product 2.883541
2.07 Terms of trade index 3.143517
2.09 Trade to gross domestic product 2.134464
ratio
3.09 Total external debt 4.070751
5.02 Crude petroleum production 2.647251
5.16 Arable area 2.528311
5.22 Railroads 2.953567
5.38 Telecommunications market size 3.600434
5.43 Distribution systems 4.541992
8.20 Computer literacy 2.067483
Appendix A. Unnecessary indicators (w, =0 for
all countries)
Code in the Indicator
WCR (1992)
1.02
1.19
1.20
2.16
2.29
2.12
2.13
2.14
2.54
3.02
3.04
3.06
3.29
4.06
4.11
5.11
5.18
5.20
5.34
5.35
5.36
5.37
5.41
Gross domestic product
Private final consumption expenditures
Real growth in PFCE per capita
Growth in exports of gtxxls and services
hnport coverage
Exchange rate stability
Exchange rate index
Exchange rate policy
National culture
Central government total debt
Central government domestic debt
Central government foreign debt
Personal income tax
Variety of financial instruments
Local capital markets
Total indigenous energy
Reinvestment
Air transport
Electronic data processing market size
Office equipment production
Office equipment market size
Telecommunications production
Urbanization
Appendix C. Weakly agreed twelve most
important indicators (w~>0 and X+ -X7 >0.1
for all countries)
Code in the Indicator X; X,-
WCR (1992)
2.27 Export market divcrsifi- 3.055544 1.090236
cation
2.28 Diversification index for 2.804852 1.913433
commodity exports
2.36 Tourism receipts 2.749741 1.18656I
4.09 Corporate bond issues 2.102588 1.075570
4.10 Credit 2.366860 1.853351
6.14 Price/quality-ratio 2.910289 2.181372
6.16 Total quality control 2.513214 2.182851
6.18 Advertising expenditure 2.097907 1.384489
7.25 Patents granted to resi- 2.989712 2.322114
dents
8.12 tligher education enrol- 2.148095 1.364481
ment
8.15 Efficiency of national 2.074759 0.240652
education
8.16 School intake 3.238315 1.494887

11. M. Oral. H. Chabchoub I International Journal of Forecasting 13 (1997) 527-537 537
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Biographies: Professor Muhittin ORAL is currently at the
Graduate School of Future Management, Sabanci University,
lstanbul and Sciences de l'Administration. Universitd Laval,
Quebec. His research interests fall in the areas of competitiveness
analysis and strategy, group decision making and consensus
formation, research methodology and modeling, parameter estima-
tion using mathematical programming. Professor Oral has pub-
lished more than 60 articles in academic journals such as
Management Science. Operations Research, Journal of the Opera-
tional Research Society, European Journal of Operational Re-
search. Computers and Operations Research, Journal of Global
Optimization. International Journal of Forecasting. Technological
Forecasting and Social Change. lie Transactions, Journal of
Multinational Financial Management, International Journal of
Research in Marketing, Industrial Marketing Journal.
Dr. Habib CHABCHOUB received his Ph.D. in Operations and
Decision Systems from Universitd Laval, Quebec, Canada. His
research interests are competitiveness analysis at the national and
industry levels, policy formulation, multiple criteria analysis, and
mathematical programming. His previous article appeared in
European Journal of Operational Research.