The economy of the Belgian regions tested with MULTIMOORA/Belgijos regionu ekonomika, ivertinta taikant MULTIMOORA metoda.
Brauers, Willem Karel M. ; Ginevicius, Romualdas
1. Introduction
The economy of the three Belgian Regions will be tested with
MULTIMOORA, an approach which combines three methods of multi-objective
optimization controlling each other: ratio systems, reference point
method and the full multiplicative form. At that moment these
Multi-Objective Optimization Methods have to fulfill as much as possible
essential conditions of robustness. What is here meant by robustness?
By 1953, which is quite recent for statistics (as well known,
statistics already existed in Roman times with the census of
population), robust became a statistical term as "strong, healthy,
sufficiently tough to withstand life's adversities" (Stigler
1973: 872). Nevertheless, already in 1969, statistician Huber (1969)
considered robustness as purely cardinal: as a compromise between a
normal distribution and its light deviations. At a later time Huber
(1981) wrote a more complete book on Robust Statistics. In 1994 on the
occasion of Huber's birthday his colleagues edited a book on Robust
Statistics (Rieder 1996). More recently the statisticians Casella and
Berger (2002) call a robust alternative the Median Absolute Deviation
for a sample [X.sub.1],....., [X.sub.n] (2002: 509).
The error term in a linear equation is the starting point for the
definition of robustness in econometrics (Darnell 1997: 355). In
addition robustness is not only linked to error terms or random
variables but also to residual terms, slack and dummy variables,
outliers etc. Darnell concludes: "given the somewhat arbitrary ad
hoc nature of the robust estimators..... these approaches have had
limited application in econometrics" (Darnell 1997: 356). Kennedy
(1998) recognizes the existence of robust estimators: "an estimator
whose properties while not quite best..." (Kennedy 1998: 298), he
continues "the topic of robustness has become quite popular
recently in econometrics, as researchers have become aware of the
extreme sensitivity of some of their estimation procedures". Other
well-known textbooks on econometrics do not even mention the name of
robustness, like Thomas (1985), Intriligator (1978), Madansky (1976),
Walters (1973), Wonnacott and Wonnacott (1970) and Johnston (1963). More
specificity is found by authors who consider robustness in forms of the
error distribution like Rhodes and Fomby (1988), Carter Hill et al.
(2008) and Verbeek (2008). A certain similarity can be found in Robust
Control Theory of engineering where Loss Functions determine
uncontrollable variations in product quality (Taguchi 1993).
Mills (1992) presents a Bayesian prediction test which is robust to
certain forms of non-normality in the error distribution. Moreover, from
the beginning Bayesian Analysis has to be characterized as cardinal,
nevertheless with a high grade of arbitrariness. This arbitrariness
could be softened by considerations on robustness (1). Anyway, cardinal
numbers form also the basis of robustness in the Poisson Distribution,
the t statistic and in Sampling (Sarndal et al. 1992).
However, we observe a move to a more vague and qualitative
definition of robustness, namely to the meaning of common language
(Webster's new Universal Unabridged Dictionary for robust: strong;
stronger, strongest), from a cardinal towards a qualitative scale: the
most robust one, more robust than..., as robust as...., robust, weak
robust, less robust than..., not robust etc., comparable to so many
other scales in multi-objective analysis, for instance mentioned by
Brauers (2004: 97-99).
A debate between Frisch (1933) and Tinbergen (1930) ensued as
whether or not Tinbergen had estimated structural form representations
robust to changes in policy regimes or reduced form representations not
robust to shifting policy regimes (Heckman 1992: 878). Kreps (1990)
maintains that more robustness is more important for bargaining theory
than for auction theory as more information is available in the latter
case than in the former. He esteems that robust predictions are crucial
although the meaning given to robustness may depend on the context (also
Vincke 1999: 186(2)). Edin and Ohlson (1991) examine that institutional
arrangements in the political process affect budget deficits.
Sensitivity Analysis indicates that the results are robust. Admati and
Pflei-derer (1994) speak of robustness in financial contracting. Another
qualitative approach of robustness is related to subjective probability
by Machina and Schmeidler (1992). Dasgupta and Maskin (2008) maintain
that the simple majority rule is the most robust voting rule. Finally,
the context will determine robustness in benchmarking, in scenario
writing and in simulation (Brauers and Zavadskas 2010).
Concluding on the remark that significance of robustness depends on
the context can be specified in different ways. First, robustness can be
considered cardinal or qualitative. Second, if robustness is indicated
as vague or arbitrary is it also not the case with inference statistics
Hoel (1971: 2) versus Hays (1974: 47) and Casella and Berger (2002:
VII), probability theory (Hays 1974: 47) and statistical specification
[Intriligator (1978: 2); Matyas and Sevestre (1992: chapter 9) versus
Thomas (1985: 71); Wonnacott and Wonnacott (1970: 312)]? Third,
robustness is characterized by completeness being present in the
statistical population, when defined as covering events and opinions
which are present, as well as in the statistical universe with events
and opinions not only present but also possible (Brauers and Zavadskas
2010). Consequently, this completeness of robustness justifies also the
making of a link with Multi-Objective Methods.
2. Conditions of Robustness in Multi-Objective Methods
For the researcher in multi-objective decision support systems the
choice between many methods is not very easy. Indeed numerous theories
were developed since the forerunners: Condorcet (1785: LVIII) [the
Condorcet Paradox, against binary comparisons], Gossen (1853) [law of
decreasing marginal utility], Minkowsky (1896: 1911) [Reference Point]
and Pareto (1906) [Pareto Optimum and Indifference Curves analysis] and
pioneers like Kendall [ordinal scales, since 1948], Roy et al. [ELECTRE
since 1966], Miller and Starr [Multiplicative Form for multiple
objectives, 1969], Hwang and Yoon [TOPSIS since 1981] and Saaty [AHP
since 1988].
We intend to assist the researcher with some guidelines for an
effective choice. In order to distinguish the different multi-objective
methods from each other we use the qualitative definition of robustness.
The most robust multi-objective method has to satisfy the following
conditions.
1) The method of multiple objectives in which all stakeholders are
involved is more robust than this one with only one decision maker or
different decision makers defending their own limited number of
objectives. All stakeholders mean everybody interested in a certain
issue. Consequently, the method of multiple objectives has to take into
consideration consumer sovereignty.
The method taking into consideration consumer sovereignty is more
robust than this one which does not respect consumer sovereignty.
Community indifference loci measure consumer sovereignty. Solutions have
to deliver points inside the zone of the highest possible community
indifference locus (Brauers 2008b).
2) The method of multiple objectives in which all non-correlated
objectives are considered is more robust than this one considering only
a limited number of objectives.
3) The method of multiple objectives in which all interrelations
between objectives and alternatives are taken into consideration at the
same time is more robust than this one with interrelations only examined
two by two.
4) The method of multiple objectives which is non-subjective is
more robust than this one which uses subjective estimations for the
choice and importance of the objectives and for normalization.
4.1) For the choice of the objectives
A complete set of representative and robust objectives is found
after Ameliorated Nominal Group Technique Sessions with all the
stakeholders concerned or with their representative experts.
4.2) For giving importance to an objective
With weights and scores importance of objectives is mixed with
normalization. On the contrary, Delphi can determine the importance of
objectives separately from normalization. In addition, as all
stakeholders concerned are involved, the Delphi method is nonsubjective.
4.3) For Normalization
The method of multiple objectives which does not need external
normalization is more robust than this one which needs a subjective
external normalization (Brauers 2007). Consequently, the method of
multiple objectives which uses non-subjective dimension-less measures
without normalization is more robust than this one which uses subjective
weights [weights were already introduced by Churchman et al. (1954,
1957)] or subjective nonadditive scores like in the traditional
reference point theory (Brauers 2004: 158-159).
5) The method of multiple objectives based on cardinal numbers is
more robust than this one based on ordinal numbers: "an ordinal
number is one that indicates order or position in a series, like first,
second, etc." (Kendall and Gibbons 1990: 1). Robustness of cardinal
numbers is based first on the saying of Arrow (1974: 256):
"Obviously, a cardinal utility implies an ordinal preference but
not vice versa" and second on the fact that the four essential
operations of arithmetic: adding, subtracting, multiplication and
division are only reserved for cardinal numbers.
6) The method of multiple objectives which uses the last recent
available data as a base is more robust than this one based on earlier
data.
7) Once the previous six conditions fulfilled the use of two
different methods of multiobjective optimization is more robust than the
use of a single method; the use of three methods is more robust than the
use of two, etc.
In order to define robustness successively the following points are
discussed:
-- the Ameliorated Nominal Group Technique,
-- the origin of Alternatives,
-- the Delphi Method,
-- the Multiplicative Form,
-- the Multi-Objective Optimization by Ratio Analysis Method
(MOORA) composed of two methods: ratio analysis and reference point
theory starting from the previous found ratios,
-- MULTIMOORA composed of the Multiplicative Form and of MOORA,
i.e. the combination of three methods. At that moment, we shall see if
all conditions of robustness are fulfilled and namely on the basis of
the economy of the Belgian regions.
3. The Ameliorated Nominal Group Technique as a source for
objectives
3.1. The original Nominal Group Technique of Van de Ven and Delbecq
(1971)
A group of especially knowledgeable individuals (experts),
representing all stakeholders, is formed, which comes together in a
closed meeting. A steering panel or a panel leader leads the group.
The nominal group technique consists of a sequence of steps, each
of which has been designed to achieve a specific purpose.
1) The steering group or the panel leader carefully phrases as a
question the problem to be researched. Much of the success of the
technique hinges around a well-phrased question. Otherwise the exercise
can easily yield a collection of truisms and obvious statements. A
successful question is quite specific and refers to real problems. The
question has to have a singular meaning and a quantitative form as much
as possible.
2) The steering group or the panel leader explains the technique to
the audience. This group of participants is asked to generate and write
down ideas about the problem under examination. These ideas too have to
have a singular meaning and a quantitative form as much as possible.
Participants do not discuss their ideas with each other at this stage.
This stage lasts between five and twenty minutes.
3) Each person in round-robin fashion produces one idea from his
own list and eventually gives further details. Other rounds are
organized until all ideas are recorded.
4) The steering group or the panel leader will discuss with the
participants the overlapping of the ideas and the final wording of the
ideas.
5) The nominal voting consists of the selection of priorities,
rating by each participant separately, while the outcome is the totality
of the individual votes. A usual procedure consists of the choice by
each participant of the n best ideas from his point of view, with the
best idea receiving n points and the lowest one a point. All the points
of the group are added up. Ranking is the democratic result for the
whole group.
3.2. The Ameliorated Nominal Group Technique of Brauers (1987)
6) Out of experience, one may say that there is still much wishful
thinking, even between experts. Therefore the group was also questioned
about the probability of occurrence of the event. In this way they
became more critical even about their own ideas. The probability of the
group is found as the median of the individual probabilities.
7) Finally, the group rating (R) is multiplied with the group
probability (P) in order to obtain the effectiveness rate of the event
(E):
RxP = E.
Once again, the effectiveness rates of the group are ordered by
ranking. Experience proves that the introduction of probabilities
decreases significantly the total number of points.
4. The origin of Alternatives
Project information for interested parties has to be as intensive
as possible. Otherwise imagination has to be intensive eventually with
the assistance of the Ameliorated Nominal Group Technique.
Some of the candidate alternatives are excluded if they do not
respond to conditions concerning lower bounds or upper limits. All
constraints concerning lower bounds or upper limits have to be hard
constraints, which form a sine qua non for the acceptance of the
candidate alternatives (Wierzbicki and Makowski 1992: 4).
Distinction has to be made between qualitative and quantitative
hard constraints. On the one hand, investments needed in a well-defined
region and not in other regions, complete financial guarantees to be
given for daughters of multinationals in case of failure, represent
examples of qualitative hard constraints.
On the other side, certain capacities in production not to be
exceeded unless new investments are made, the World Bank granting a loan
to a developing country unless an Internal Rate of Return of 12% is
guaranteed, geometrical constraints under the form of a limiting line,
surface or manifold, represent examples of quantitative hard
constraints.
5. The Delphi Technique to determine the importance of an objective
Delphi, so named after the Greek oracle, was first thought of as a
tool for better forecasting. In this sense, it seems that the first
experiments took place around 1948 (Quade and Boucher 1968: 334). Today
Delphi is no longer limited to forecasting alone. Dalkey and Helmer
(1963) at RAND Corporation first used Delphi in its present form around
1953.
The Delphi Method is a method for obtaining and processing
judgmental data. It consists of a sequenced program of interrogation (in
session or by mail) interspersed with feedback of persons interested in
the issue, while everything is conducted through a steering group.
The essential features of Delphi are the following:
1) the rather vague notion "persons interested in the
issue" is interpreted by Quade (1970: 9-10) as follows; "In
practice, the group would consist of experts or especially knowledgeable
individuals, possibly including responsible decision makers";
2) the steering group treats anonymously the sources of each input;
3) inputs should possess as much as possible a single meaning and a
quantitative form. The inputs with these characteristics are elicited
with feedback in a series of rounds;
4) opinions about the inputs are evaluated with statistical indexes
such as median and quartiles;
5) there is also a feedback of the statistical indexes with a
request for re-estimation after consideration of reasons for extreme
positions. The practice of Delphi reveals that after several rounds
convergence is shown between the various opinions (one of the main
advantages of the Delphi method);
6) there are two developments of Delphi: one is based on a meeting,
the other on the sending of questionnaires. The organization of a
meeting produces quicker results; the meeting, however, has to be
organized in such a way that communication between the panel members is
impossible. In order to speed up the meeting an on-line computer could
be installed. Everybody involved in the Delphi teamwork would have a
desk terminal linked to a computer and would be able to look at a
television screen giving the results calculated by the computer.
Convergence in opinion between all stakeholders allowing to give
more importance to objective results from a Delphi exercise, which could
provide the given objective with a Significance Coefficient.
For instance, giving a significance coefficient to pollution
abatement, the stakeholders are asked to give the following importance
to pollution abatement:
0, 1, 2 or 3.
Suppose that after several rounds convergence is reached on 3.
[Brauers (2008a: 170-173) brings a more detailed application].
The Attribution of Sub-Objectives represents another solution. The
Attribution Method is more refined than the Coefficient Method as the
attribution method succeeds in characterizing an objective better. For
instance, instead of giving a significance coefficient of three to
pollution abatement the objective "pollution abatement" is
divided into three sub-objectives: the Greenhouse Effect, Energy
Consumption and Other Pollution, each with their own characteristics.
6. The Full-Multiplicative Form
The following n-power form is called from now on a
full-multiplicative form in order to distinguish it from other rather
mixed forms, namely mixed with additive forms (for more details see:
Keeney and Raiffa 1993: 234):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
with: j = l,2,...,m; m= the number of alternatives; i = l, 2, ... ,
n; n being the number of objectives; [x.sub.ij] = response of
alternative j on objective i; [U.sub.j] = overall utility of alternative
j.
The overall utilities ([U.sub.j]), obtained by multiplication of
different units of measurement, become dimensionless.
Stressing the importance of an objective can be done by adding an
[alpha]-term or by allocating an exponent (a Significance Coefficient)
on condition that this is done with unanimity or at least with a strong
convergence in opinion of all the stakeholders concerned. Therefore, a
Delphi exercise may help.
How is it possible to combine a minimization problem with the
maximization of the other objectives? Therefore, the objectives to be
minimized are denominators in the formula:
[U'.sub.j] = [A.sub.j]/[B.sub.j], (2)
with: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
j = l, 2, ..., m; m= the number of alternatives; i = the number of
objectives to be maximized
with: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
n-i = the number of objectives to be minimized, with:
[U'.sub.j]: the utility of alternative j with objectives to be
maximized and objectives to be minimized.
7. The Full-Multiplicative Form and the Economy of the Belgian
Regions
On the one side the seven conditions for the most robust
multi-objective method present a theoretical construction, an ideal to
be aimed at. On the other side some Regional Statistics suitable for our
purpose are missing in Belgium.
A note on terminology is needed to clarify this issue. Gross
Domestic Product (GDP) in a certain year is the value added created on
the national territory, being a territorial concept. On the contrary,
Gross National Product (GNP) is the value added created by the civilians
and the permanent residents of a nation. Interpolated for a region, the
Gross Regional Domestic Product (GRDP) signifies the value added created
on a regional territory during a given year and the Gross Regional
Product (GRP) means the value added created by the permanent residents
of a region during that year.
In addition, transfer payments are a transfer of value added from
one group of the population to another group, from one region to another
or from one nation to another one. Consequently Transfer Payments are
not included in GRP or GNP but are considered in a Disposable Income.
Finally the National Public Debt has to be broken down in the Public
Debt of the regions (2).
For the first time the Center for Economic Studies of Leuven
University estimated the transfer payments between the Belgian regions
(Van Rompuy and Bilsen 1988). On the basis of this study KBC, Asset
Management continued the work for more recent years (Van Gompel and Van
Craeynest 2003). Table 1 summarizes the transfer payments from 1990
until 2005.
(a) W. Brauers, Het Bruto Regionaal Product van Vlaanderen.
Wallonie en Brussel, UA, Faculteit Toegepaste Economische Wetenschappen,
p.17 obtains for: Flanders 4.63bn. [euro], Wallonia--3.81bn. [euro] and
for Brussels 0.82bn. [euro], but including interest payments: 6.11bn.
[euro]--5.31bn [euro]--0.80bn [euro]. At that moment P. Kestens (ULB)
arrives at 6% of the Gross Regional Product of Flanders, certainly a
high figure (Divorce a la belge; l'economie dit non. Le separatisme
vu par des academiques, des patrons et des syndicalistes, Eco-Soir,
9/25/1992.).
(b) Since the end of 2000 the influence of the Lambermont Agreement
plays: more money is given to the French speaking Community to finance
their school system.
(c) Dury et al. 2008.
Facing the Maastricht norm (May 1997) for the Public Debt of 60% of
GDP, Belgium obtained an exception at 122.2%, on condition that this
figure would go down to 60% as soon as possible3. The successive Belgian
governments failed to fulfill this target. The lowest point was reached
in 2007 at 84%, at the moment of a for Belgium high economic growth.
Since then the figure increased again as the economic situation
deteriorated. After the estimations of the Belgian Department of Finance
(Documentatie-blad) the public debt will continue to rise (Table 2).
The high public debt of Belgium is mainly due to what is called a
"waffle- iron policy"; a Belgian waffle has to be turned
around such that both sides of the waffle are baked in an equal way. The
same occurred for the Belgian policy.
If Flanders received funds from the national treasury to support
its economic expansion, Wallonia wanted to receive an equal amount
without any economic need. The funds at the Flemish side were mostly
based on the economic calculus but not at the Walloon one. On the other
side, Wallonia asks transfer payments (gifts) from Flanders: "do
not kill the goose that lays the golden eggs".
It would not be difficult to estimate the non-effective investments
of the past and to allot them to the regions. This partition on
historical grounds could mean bankruptcy for Wallonia. Therefore from
the Flemish side the suggestion could come to divide the National Public
Debt otherwise.
--1/3 from the Gross Regional Product (GRP estimated)
Flanders 60.9%
Brussels 9.5%
Wallonia 29.6%
--1/3 from population
Flanders 58.0%
Brussels 9.3%
Wallonia 32.7%
--1/3 from territory
Flanders 44.29%
Brussels 0.53%
Wallonia 55.18%
TOTAL
--Flanders 54.40%
--Brussels 6.44%
--Wallonia 39.16%
This is extremely favourable for Brussels but very unfavourable for
Wallonia and ipso facto not acceptable. More equilibrated proportions
are obtained if the surface of each territory is left out.
- 1/2 from the Gross Regional Product (GRP):
Flanders 60.9%
Brussels 9.50%
Wallonia 29.6%
-1/2 from population:
Flanders 58.0%
Brussels 9.30%
Wallonia 32.7%
- TOTAL
Flanders 59.45%
Brussels 9.40%
Wallonia 31.15%
Going out from the Maastricht-norm of a National Public Debt of
122.2% of GDP the repartition over the regions would be as follows:
Flanders 116.4% of its GRP
Brussels 120.6% of its GRP
Wallonia 134.6% of its GRP
In table 3 different scenarios were taken into account as a basis
for the starting point of Maastricht, which we call from now on the year
zero like one speaks of ground zero meaning a new begin.
Suppose that the following objectives are advanced with the
scenarios as alternatives:
- maximization of:
Disposable Income per head for Wallonia
Brussels
Flanders
- minimization of:
Transfer payments from Flanders
Public Debt of Flanders as a % of its GRP
Public Debt of Wallonia as a % of its GRP
Public Debt of Brussels as a % of its GRP
The following scenarios are foreseen:
Scenario 0: the Scenario of the Status Quo
Scenario 0 shows the status quo with a strong Income Paradox
disfavouring Flanders, the highest transfer payments from Flanders and a
huge solidarity of Flanders to support a part of the national public
debt normally attributed to Wallonia and Brussels.
Scenario I: the Scenario of the Average Belgian
Compared to Scenario 0 the transfer payments are diminished in such
a way that the Income Paradox disappears and that the average Belgian
has the same income everywhere. Solidarity remains for the National
Public Debt.
Scenario II: the Scenario of an Unfavourable Growth Rate for
Flanders
Due to an unfavourable growth rate Flanders diminishes the transfer
payments but at the same time the Income Paradox disappears.
Nevertheless the solidarity in the national public debt remains.
Scenario III: the Scenario in which Flanders asks for the Partition
of the National Public Debt
Flanders not only contributes to transfer payments but also pays
interest charges on a part of the national public debt for which it is
not responsible. Therefore Flanders asks for the partition of the
national public debt.
Flanders is not demanding the reimbursement of the too high part of
the interest payments from the past on the national public debt. It
agrees on the repartition of the national public debt on the basis of
the GRP's and the population and not on historical grounds.
Scenario IV: the Scenario of an Unfavourable Growth Rate for
Flanders and at that moment asks also for the Partition of the National
Public Debt
Due to an unfavourable growth rate Flanders diminishes the transfer
payments and at the same time asks for the Partition of the National
Public Debt.
Scenario V: the Scenario of the Average Belgian but as compensation
Flanders asks for the Partition of the National Public Debt
The transfer payments are slightly diminished in such a way that
the Income Paradox disappears and that the average Belgian has the same
income everywhere, but as compensation Flanders asks for the Partition
of the National Public Debt.
Scenario VI: the Scenario where Flanders asks for the Partition of
the National Public Debt
Flanders asks for the Partition of the National Public Debt but the
transfer payments remain high and consequently the Income Paradox
reappears.
Scenario VII: the Scenario of Solidarity only for the Partition of
the National Public Debt
The transfer payments disappear but solidarity remains for the
National Public Debt.
Scenario VIII: the Scenario of no Solidarity at all
The transfer payments disappear and no solidarity remains for the
National Public Debt.
Scenario IX: the Scenario of an Optimal Economic Policy in Wallonia
The transfer payments are no more needed as Wallonia and also
Brussels come at the economic level of Flanders.
Scenario X: the Scenario where the Optimal Economic Policy in
Wallonia even agrees on the Partition of the National Public Debt
The transfer payments are no more needed as Wallonia and also
Brussels come at the economic level of Flanders and even more, they
agree on the Partition of the National Public Debt.
In table 4 the saying of Arrow (1974: 256) is of application:
"Obviously, a cardinal utility implies an ordinal preference but
not vice versa", whereas the ordinal preference does not only play
on the first but also on the last column. The Full Multiplicative Form
results in dimensionless numbers without cardinal meaning. Nevertheless
the split between the first four rankings, namely until Scenario VIII,
and the other ones is meaningful.
Due to the necessary numerous calculations we do not update the
Maastricht version. Anyway the illustration is certainly valuable. Does
the exercise satisfy the aforesaid robust conditions?
Concerning the first and second condition of robustness, if not all
stakeholders are involved, the authors tried to be as complete as
possible for the objectives of a welfare economy. It is true that a
well-being economy with objectives on security, health care, justice,
education, ecology and leisure is not covered. In addition, the method
taking into consideration consumer sovereignty is more robust than this
one which does not respect consumer sovereignty, which is certainly here
the case as the main part of the application is reserved for the
disposable income of the households.
Third condition: all interrelations between objectives and
alternatives are taken into consideration at the same time and not two
by two.
Fourth condition: the choice of objectives already discussed above
can be designated as robust inside certain limits. No special attention
was given to one or another objective; all objectives obtained the same
importance. Finally, non-subjectivity is satisfied by using
dimensionless measures, which make exogenous normalization unnecessary.
Fifth condition: the multiplicative form of the exercise is based
on cardinal numbers resulting in an ordinal kind of ranking.
The sixth condition is not fulfilled as only an illustration from a
distant past was given.
However, the full multiplicative form only uses a single method of
multi-objective optimization. On the contrary, the multi-objective
optimization by ratio analysis, MOORA, is more robust. Indeed, MOORA not
only satisfies the first six conditions, but in addition, satisfies the
seventh condition by using two different methods of multi-objective
optimization. MOORA is the most robust method as no other method up till
now exists satisfying the seven conditions better.
8. The MOORA Method
The method starts with a matrix of responses of all alternative
solutions on all objectives:
[x.sub.ij], (3)
with: [x.sub.ij] as the response of alternative j on objective i,
i = 1, 2,..., n as the objective, j = 1, 2, ..., m as the
alternatives.
The MOORA method consists of two parts: the ratio system and the
reference point approach.
We go for a ratio system in which each response of an alternative
on an objective is compared to a denominator, which is representative
for all alternatives concerning that objective (Brauers and Zavadskas
2006) prove that the most robust choice for this denominator is the
square root of the sum of squares of each alternative per objective).
[x.sub.ij.sup.*] = [x.sub.ij]/[square root of [m.summation over
(j=1)] [x.sup.2.sub.ij]] (4)
with: [x.sub.ij] = response of alternative j on objective i; j =
1,2,...,m; m = the number of alternatives, i = 1,2,...n; n = the number
of objectives, [x.sub.ij.sup.*] = a dimensionless number representing
the normalized response of alternative j on objective i.
For optimization, these responses are added in case of maximization
and subtracted in case of minimization:
[y.sub.j.sup.*] = [i=g.summation over (i=1)] [x.sub.ij.sub.*] -
[i=n.summation over (i= g + 1)] [x.sub.ij.sub.*], (5)
with: i = 1,2,...,g as the objectives to be maximized,
i = g+1, g+2,..., n as the objectives to be minimized,
[y.sub.j.sup.*] = the dimensionless response of alternative j with
respect to all objectives.
[y.sub.j.sup.*] can be positive or negative depending on the totals
of its maxima and minima.
An ordinal ranking of the [y.sub.j.sup.*] shows the final
preference.
Reference Point Theory will go out from the ratios [x.sub.ij.sup.*]
found in formula (4). In addition, one needs a Maximal Objective
Reference Point. The Maximal Objective Reference Point is called
realistic and non-subjective as the co-ordinates ([r.sub.i]), which are
selected for the reference point, are realized as an optimum in one of
the candidate alternatives. In this way arriving to:
([r.sub.i] - [x.sub.ij.sup.*]) (6)
with: i = 1,2, ..., n as the objectives,
j = 1,2, ..., m as the alternatives,
[r.sub.i] = the ith co-ordinate of the reference point,
[X.sub.ij.sup.*] = the normalized response of alternative j on
objective i as found in formula (4).
This matrix is subject to the Min-Max Metric of Tchebycheff (Karlin
and Studden 1966: 279280). Brauers (2008b: 98-103) proved that the
Min-Max metric is the most robust choice between all the possible
metrics of reference point theory.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
[absolute value of [r.sub.j] - [x.sub.ij.sup.*]] means the absolute
value, necessary if [X.sub.ij.sup.*] is larger than [r.sub.i] for
instance by minimization.
In order to give more importance to an objective versus the other
objectives its dimensionless number per alternative could be multiplied
with a Significance Coefficient. The Attribution of Sub-Objectives
represents another solution (Brauers 2002: 338).
9. The MOORA Method and the Economy of the Belgian Regions
Table 4 showed a ranking of the scenarios in its Full
Multiplicative Form for Year Zero. Annex A demonstrates the MOORA method
for the Belgian Regions in Year Zero. The conditions of robustness in
Multi-Objective Methods dictate the use of the last available data as a
base. However, a chain is only as strong as its weakest link. Also for
MOORA the data for transfer payments between the Belgian Regions are
only available until 2005 and in this way limiting the application until
2005. In addition, the Full Multiplicative Form was not repeated for
2005 due to the number of multiplications to be made. Table 5 applies
MOORA for the Belgian Regions in 2005.
Sources
The basis is formed by scenarios 0 (the status quo) and 9 and 10.
Scenario 0: Disposable Incomes: National Bank, Statistical Publications,
actual Regional Accounts, 137.
Transfer Payments, see Table 1.
Public Debt: Table 2.
Scenario 9: disposable income of Flanders identical for Wallonia
and Brussels: 16842.5 [euro]+ transfer payments provided per head 967
[euro] = 17809.5 [euro] (transfer payments Flanders per head: Dury et
al. (2008: 113).
Scenario 10: as sc.9 plus interest on revision part of public debt
not realized immediately a 4.2% (Documentatieblad, I, 2007: 54):
17809.5+ 30.7 [euro]= 17840.2 [euro]. Scenario 2: due to recession and
huge inflation Flanders to maintain its income per person reduces its
transfer payments to the half; for Wallonia a loss of 891.5 [euro] per
head (Dury et al. 2008: 113).
Scenario 3:
Maastricht 122.2% of GDP meant for Wallonia 134.6% of its GRP
Flanders 116.4% of its GRP
Brussels 120.6% of its GRP
On the 2005 91.5 % of GDP:
Wallonia 100.8% of its GRP
Flanders 87.2% of its GRP
Brussels 90.3 % of its GRP
Flanders: 16842.5 + interest 30.7 = 16873.2 [euro]
Wallonia: 14441.8 minus interest to be paid 56.32 [euro] = 14385.48
[euro]
Brussels:15096.1 - 7.61 [euro] = 15103.71 [euro]
Scenario 4: Scenario 2 + Scenario 3
Scenario 1: average Belgian, equalization by going down for
Flanders
Scenario 5: Scenario 1+ plus more or less Scenario 3
Scenario 6: as Scenario 0 but now with the redistribution of the
public debt
Scenario 7: no transfer payments but solidarity in the national debt:
profit for Flanders and Brussels loss for Wallonia
(Dury et al. 2008: 113):
Flanders 16842.5 + 967 = 17809.5 [euro]
Wallonia 14441.8 - 1783 = 12658.8 [euro]
Brussels 15096.1 + 211 = 15307.1 [euro]
Scenario 8: Scenario 7 + Scenario 3.
10. MULTIMOORA as a combination of the Full Multiplicative Form and
of MOORA
Following Table 6 shows a combination of the Full Multiplicative
Form and of MOORA under the name of MULTIMOORA. If the first 6
conditions of robustness are fulfilled as much as possible MULTIMOORA
becomes the most robust approach existing up till now.
One may say that all rankings are compatible until Scenario III.
Consequently the first seven rankings will be discussed.
10.1. Geographical Transfer Payments on discussion worldwide
The first four rankings are characterized by the absence of
transfer payments and the following three by the diminishing of transfer
payments. Transfer payments are quite common in daily life such as in
all kinds of insurances, but transfer payments which are considered here
are geographical, automatic and structural ones.
First of all geographical transfer payments can be automatic
through fiscal or para-fiscal channels such as social security. They are
also structural and not cyclical as they are maintained under all
circumstances and form an essential and enduring financial instrument
for a state or a region. This kind of transfer payments is very much
contested not only in Belgium but also by the richer regions in Germany
and Italy. In Belgium it caused even an Income Paradox at least until
1996: by the transfer payments the richer Flemish inhabitants came off
worst compared to the other Belgians (table 7).
One could argue that in Table 5 and in Appendix A transfer payments
are overestimated by giving them the same importance as private income
and public debt. This is not true as three objectives concern private
income and three public debts against only one objective for transfer
payments. More importance could even be given to private income and
public debt. Wallonia would not like to give more importance to public
debt due to the unfavourable position of Wallonia towards public debt.
Nevertheless by giving a significance coefficient of two to each of the
private income objectives transfer payments keep their crucial position
(see Appendix B). Indeed, the four scenarios with the negation of
transfer payments remain first ranked.
Instead of geographical, automatic and structural transfer payments
direct investments are to be preferred for reconversion of regions or
for developing of countries. Therefore the so-called Marshall Plan is a
good idea for Wallonia, but lesser means will be available as Wallonia
from now on has to finance its social security by itself. However the
possibility exists that Flemish firms will participate in the Marshall
Plan. For developing countries the old slogan "No Aid but
Trade" seems to be replaced by "No Aid but Investments",
a device seemingly followed by the Chinese in Africa. On the other side
the objective-oriented investments of the international organizations
are not always very successful. Pre-set filters such as a minimum of 12%
I.R.R is a disaster for the country in question4. Also Cost-Benefit
Analysis is not very effective for the following reasons:
1) Cost-Benefit Analysis usually concerns a single project but
theoretically one could compare the balance of costs and benefits for
different projects;
2) Cost-Benefit can be immoral, for instance if unemployment is
only measured by the obtained unemployment allowances notwithstanding
the moral attitude of the unemployed.
3) Translation into money terms is not always very successful if
the objectives are expressed in different units. It is true that private
income and transfer payments are already expressed in money terms but
the [euro] has not always the same meaning: the [euro] in private income
is not the same as the [euro] in transfer payments. After the
terminology (see paragraph 7 above) a [euro] can move from Private
Income to transfer payments but a [euro] can not move from transfer
payments to private income. Generally units of objectives are not
transferable into money units.
For all these shortcomings, investments in regions in reconversion
or in developing countries can better be analyzed by multiple objectives
keeping their own units.
10.2. Discussion of the Ranking of the Scenarios for an Optimal
Belgian Policy
10.2.1. Scenarios IX and X first ranked
In both Scenarios Wallonia and Brussels come at the economic level
of Flanders, even without transfer payments coming from Flanders,
whereas the economic growth rate of Flanders is maintained. In addition
in Scenario X Wallonia even agrees on the partition of the National
Public Debt unfavourable for Wallonia.
I) The outcome is a Win-Win operation for all parties concerned if
Flanders keeps a high growth rate. However, these scenarios have no
economic foundation, notwithstanding the so-called Marshall Plan of
economic development for Wallonia. We note for instance for Wallonia:
--level of work participation (age 15-64): 57.2% -> Lisbon
target: 70% [FOD Economy];
--level of work participation, women: 50.4% - Lisbon target: 60%
[FOD Economy];
--level of work participation (age 55-64): 33.6% - Lisbon target:
50% [FOD Economy];
--unemployment: 10.1% of the professional population [FOD Economy
2008,] but actually at 16%;
--45% of the working population works in government service or in
non-profit organizations (Forem 2009);
--1.21% of the Walloon territory is only occupied by firms (E. Domb
previously president of the Walloon Employers Association);
--"Walloons have no economic culture" (E. Domb, De Tijd
12/1/2010);
--Wallonia's main industry, the steel industry, is in decay.
Some positive developments have to be mentioned such as the growth of
Charleroi airport as the second airport of Belgium and the flourishing
science parks of Louvain-la-Neuve and Sart-Tilman.
Capital Brussels is also far away from the Flemish level:
--level of work participation (age 15-64): 55.6% [right arrow]
Lisbon target: 70% [FOD Economy];
--level of work participation, women: 48.4% [right arrow] Lisbon
target: 60% [FOD Economy];
--level of work participation (age 55-64): 39.7% [right arrow]
Lisbon target: 50% [FOD Economy];
--unemployment: 16% of the professional population [FOD Economy,
2008] but actually at 25%;
--the economy of Brussels is in decay:
1) Brussels as international financial center: all banks are in
foreign hands. The Brussels Stock Exchange is replaced by the
international Euronext.
2) Brussels was the decision center for the Belgian energy sector,
the mining industry, the metal and steel industry: all mines were closed
and the energy, metal and steel sectors came in foreign hands.
3) Some productions disappeared such as tobacco products. Other
sectors remain important but are mostly depending on the overall
activity in the whole of Belgium (measured in Gross Value Added for 2007
and compared with the national figures, Belgostat):
Electricity and gas distribution 31.52%,
Services: hotels and restaurants 22.68%,
Transport 13.1%,
Support of transport and travel agencies: 18.71%, Post
and telecommunications: 45.53%, Commerce and
exploitation of real estate: 14.6%, Computers: 29.76%,
Business services: 16.36%.
Flanders
--level of work participation (age 15-64): 66.5% [right arrow]
Lisbon target: 70% [FOD Economy];
--level of work participation, women: 60.8% [right arrow] Lisbon
target: 60% [FOD Economy];
--level of work participation (age 55-64): 34.3% [right arrow]
Lisbon target: 50% [FOD Economy];
--unemployment: 3.9% of the professional population [FOD Economy
2008] but actually at 7%; in fact overevaluated as in Belgium there is
no time limit on unemployment allowances;
--The economy of Flanders:
1) The chemical industry around Antwerp is the second in the world
after Houston (Texas).
2) The sea port of Antwerp is the second in Europe after Rotterdam.
3) The Gas terminal in Zeebrugge in one of the biggest in the
world.
4) Antwerp is the first trading center for diamonds in the world.
5) The Flemish textile industry is famous for carpets and other
refined products.
Scenario 8 (Table 5) gives the most realistic situation for
Wallonia with a disposable income per head of 12602.48 [euro], but
without the benefit of incoming transfer payments. With the ideal
situation of scenario 10 (17840.2 [euro]) Wallonia falls short of
41.56%, a situation never to be reached even with Chinese growth rates,
certainly when Flanders continues with an average growth rate of at
least 1.5%. In addition, in scenario 10 a public debt has to be covered
of 100.78% of its GRP (in the Maastricht norm even of 134.6%).
A similar situation occurs for Brussels. Scenario 7 gives the most
plausible situation for Brussels at 15307.1 [euro] against the ideal
situation of 17840.2 [euro] in scenario 10. The difference measures a
shortage of 16.55%. In addition after the 2005 figures a public debt has
to be covered of 90.3% of its GRP (in the Maastricht time it was even
120.6%).
II) Conclusion: Scenarios 9 and 10 are entirely unrealistic and
have not to be taken into consideration. One could argue that they have
not to be included as scenarios but rather withered away in a
preliminary filtering process, which would exclude impossible
situations. Nevertheless this way of thinking is false. By including
them in the aggregation process, the rights of the less favoured regions
are better taken into account.
10.2.2. Third Ranked but in fact First Ranked: Scenario VII, the
Scenario of Solidarity only for the Partition of the National Public
Debt
The transfer payments disappear but solidarity remains for the
National Public Debt. In order to have control on the transfer payments
the entire tax system has to move to the regions and also all
para-fiscal systems such as the social security allowances. The regions
could for example redistribute indirect taxation to the European Union
if the European Union would use the manipulation of indirect taxation as
an instrument of its economic policy.
Under these circumstances Belgium moves from a federal state to a
confederation of states, but not to secession as Flanders shows the
goodwill to maintain the status quo for the public debt. Indeed,
expressed in time zero (the Maastricht norm) the repartition of the
Public debt is as follows:
* Wallonia 122.2% of its GRP, much less than the mentioned 134.6%
of its GRP,
* Flanders 122.2% of its GRP,
* Brussels 122.2% of its GRP.
10.2.3. Fourth Ranked but in fact Second Ranked: Scenario VIII, no
Solidarity at all
This scenario means that the tax system is entirely regional and
also all para-fiscal systems such as the social security allowances. The
transfer payments disappear and no solidarity remains for the National
Public Debt. This scenario could mean a move either from a federal state
to a confederation of states or to complete secession.
10.2.4. Fifth Ranked but in fact Third Ranked: Scenario II, the
Scenario of an Unfavourable Growth Rate for Flanders
Due to an unfavourable growth rate e.g. of -3% and an inflation
rate of 1% the crucial border line of 3.3% is passed (Brauers 1999b:
8-9) and in order not to destabilize its own economy Flanders has to
diminish considerably its transfer payments. Nevertheless, the
solidarity in the national public debt is kept unchanged.
10.2.5. Sixth Ranked but in fact Fourth Ranked: Scenario IV, the
Scenario of an Unfavourable Growth Rate for Flanders with the decrease
of its transfer payments and in addition its demand for a new
repartition of the National Public Debt
The situation is comparable with the previous scenario but in
addition Flanders asks for a new repartition of the national public
debt.
10.2.6. Seventh Ranked but in fact Fifth Ranked: Scenario III, the
Scenario in which Flanders asks for a Repartition of the National Public
Debt
Flanders not only contribute for transfer payments but also pays
interest charges on a part of the national public debt for which it is
not responsible. Therefore Flanders asks for a repartition of the
national public debt. Automatically the transfer payments from Flanders
diminish. Disagreement about the ranking of the following scenarios
means that they are not taken into consideration.
10.2.7. Not Useful Ranked but historically in fact interesting:
Scenario I, the Scenario of the average Belgian and Scenario V the
average Belgian but with Flanders asking for a Repartition of the
National Public Debt
These scenarios where the most advanced region is punished as it is
obliged to diminish its income in favour of the less advancing regions
and in this way arriving at a national average has no chance at all in
Belgium. Nevertheless, it was the policy in Belgium for a while. In a
time of automatic and structural transfer payments "do not kill the
goose that lays the golden eggs".
11. An Optimum Economic Policy for Belgium
From the MULTIMOORA application for Belgium the following
conclusions can be drawn.
1) The scenario where the most advancing region has to decrease its
disposable incomes to the level of the less advancing regions has no
chance in the ranking of scenarios. Nevertheless it was the policy in
Belgium for a while, creating even an Income Paradox (see Table 7).
Flanders with the highest Gross Regional Product per head saw its
Disposable Income per head decrease even lower than the national
average.
2) In connection with the previous point geographical transfer
payments, which at the same time are automatic and structural, are
economically not acceptable between regions. They result in stationary
instead of progressive repercussions. Also elsewhere this statement,
even for countries, is generally recognized.
3) Accepting the previous points means that for controlling the
structural transfer payments each Belgian region needs its own taxation
system and that also all para-fiscal aspects, including Social Security,
are regionalized. In this way the comparative costs of each region come
fully into effect. The Monetary and Economic Union of Belgium, is past
history (Brauers et al. 1979: 47). Previously each Belgian region had a
favourite position towards the other regions. The monetary policy was
unified and the regions reacted in the same way to inflation, deflation
or devaluation, whereas the monetary policy was based on a common
agreement between all Belgians. The European Monetary Union brings the
monetary decisions much farther away from the Belgian regions. A mutual
favourite position for the Belgian regions in economic matters is also
no more possible inside the European Economic Union. Instead, a
confederation of Belgian states is born for economic matters.
4) The confederation of Belgian states for economic matters is
politically supported by the Belgian Constitution (1994) in its article
35 which says: "the Regions are entitled to all matters which are
not allotted to the federal government by law".
5) Flanders remains attached to the confederation if it shows
goodwill by not asking a redistribution of its share in the public
national debt.
6) If Flanders asks also the redistribution of its share in the
public national debt the following questions remain:
--which method is used to allocate each share per region in the
national public debt?
--once the national public debt is redistributed, does Flanders
prefer confederation or secession?
7) The most plausible scenarios namely scenario 7 and even more
scenario 8 show the real economic situation of Wallonia. They mean a
Win-Loss relation between Flanders and Wallonia. For Wallonia it
signifies a lesson of total reconversion of its economic policy and a
necessary mobilization of all its capabilities.
12. Conclusion
The remark that significance of robustness depends on the context
is specified in different ways. First, robustness can be considered
either in a statistics-econometrics meaning or as qualitative robust.
However, a move to a qualitative definition seems to join more and more
the meaning of common language, like strong, stronger, strongest,
translated as: the most robust one, more robust than..., as robust
as...., robust, weak robust, less robust than..., not robust etc.
Second, if robustness is indicated as vague or arbitrary perhaps it is
also the case with inference statistics, probability theory and
statistical specification.
Following conditions have to be satisfied for a robust method of
multi-objective optimization:
1) the method of multiple objectives in which all stakeholders are
involved is more robust than one in which only one decision maker or
different decision makers defending only a limited number of objectives
are involved. All stakeholders mean everybody interested in a certain
issue and finally ending up with the consumer. Consequently, the method
of multiple objectives which takes into consideration consumer
sovereignty is more robust than this one which does not respect consumer
sovereignty;
2) the method of multiple objectives in which all non-correlated
objectives are considered is more robust than this one in which only a
limited number of objectives is involved;
3) the method of multiple objectives in which all interrelations
between objectives and alternatives are taken into consideration at the
same time is more robust than this one in which the interrelations are
only examined two by two;
4) the method of multiple objectives which is non-subjective is
more robust than this one which uses subjective estimations for the
choice and the importance of the objectives and for normalization. For
instance, a method of multiple objectives which uses non-subjective
dimensionless measures is more robust than this one which for
normalization uses subjective weights or subjective non-additive scores
like in the traditional Reference Point Theory;
5) the method of multiple objectives based on cardinal numbers is
more robust than this one based on ordinal ones: an ordinal number is
one that indicates order or position in a series, like first, second,
etc.. The robustness of cardinal numbers is based on the saying of
Arrow: "Obviously, a cardinal utility implies an ordinal preference
but not vice versa" and also on the fact that adding, subtracting,
multiplication and division are only reserved for cardinal numbers;
6) the method of multiple objectives which uses the last recent
available data as a base in the response matrix is more robust than this
one based on earlier data;
7) once the previous six conditions fulfilled the use of two
different methods of multi-objective optimization is more robust than
the use of a single method; the use of three methods is more robust than
the use of two, etc.
As the need for external Normalization is not present, given the
dimensionless measures, and if the choice and importance of the
objectives is taken care of, eventually with the assistance of the
Ameliorated Nominal Group and Delphi Techniques, the Multiplicative Form
and the Multi-Objective Optimization by Ratio Analysis Method (MOORA)
satisfy the first six conditions. In addition, if we join together the
Multiplicative Form (one method) and MOORA two methods) we get the most
robust construction with the use of three different methods
(MULTIMOORA).
Does the test with MULTIMOORA on the economy of the Belgian Regions
satisfy the seven conditions of robustness? Concerning the first
condition, the stakeholders were substituted by the researchers of the
study. Consumer sovereignty was considered not only by the private
income per head in the three regions but even much more by the
disposable income after taking into account the transfer payments
between the regions.
The second condition is fulfilled as only non-correlated objectives
are considered. Third, all interrelations between objectives and
alternatives are taken into consideration at the same time.
Fourth, non-subjectivity is satisfied by using non-subjective
dimensionless measures, which makes further normalization unnecessary.
The choice of the objectives gives the impression of completeness. In
principle no objective receives more importance than the others by the
introduction of a significance coefficient or of different
sub-objectives. Nevertheless, one could argue that transfer payments are
overestimated by giving them the same importance as disposable income
and public debt. This is not true as three objectives concern disposable
income and three others the public debt against only one objective for
transfer payments. More importance could even be given to disposable
income and public debt. Wallonia would not like to give more importance
to public debt due to the unfavourable position of Wallonia towards
public debt. By giving a significance coefficient of two to each of the
disposable income objectives the transfer payments kept their original
crucial position (see therefore Appendix B).
Fifth, the multiplicative form and MOORA are based on cardinal
numbers. Sixth, this method uses the last recent available data.
However, as many different data are needed not always from the same time
period, like a chain having the value of the weakest link, 2005 had to
be chosen as a base.
One could think of aggregating the Multiplicative Form and MOORA
into one multiobjective system, called MULTIMOORA. In this way
MULTIMOORA becomes the fulfillment of the seven robustness conditions on
the basis of three different methods.
Maybe we are still far away of a closed system for Multi-Objective
Optimization. Nevertheless, we tried with the available means at our
disposition to come as nearby as possible to the seven conditions of
robustness for multi-optimization, perhaps the road to an ideal closed
system.
From the MULTIMOORA application for Belgium the following
conclusions could be drawn.
1) The scenario where the most advanced region has to diminish its
income in favour of the less advancing regions has no chance at all.
Nevertheless it was the policy in Belgium for a while creating even an
Income Paradox: Flanders as the most advanced region saw its income per
head falls even under the national average. In a time of automatic and
structural transfer payments "do not kill the goose that lays the
golden eggs".
2) Even a step further: geographical transfer payments, which are
automatic and structural, are not acceptable between regions of a
country. They result in immobility. The Belgian example illustrates this
point of view. It is better to promote direct investments.
3) Accepting the previous point means that each region will have
its own taxation system and that also all para-fiscal aspects, including
Social Security, are regionalized. In this way the comparative costs of
each region come fully into effect.
4) The best scenarios are those where the less advancing regions
try to reach the higher level of the most advancing country, even
without transfer payments in their favor. For Belgium these scenarios
are completely unrealistic. Wallonia falls short of 41.56%, a situation
never to be reached even with Chinese growth rates, certainly when
Flanders continues with an average growth rate of at least 1.5%. In
addition, Wallonia has to carry a national public debt of 100.78% of its
Gross Regional Product (in the Maastricht norm even of 134.6%).
A similar situation occurs for Brussels. The difference measures a
shortage of 16.55%. In addition Brussels has to cover a national public
debt of 90.3% of its Gross Regional Product (in the Maastricht time it
was even 120.6%).
5) The second best scenarios for Belgium are economically
confederative, without transfer payments, which are automatic and
structural.
6) The confederation of Belgian states is politically supported by
the Belgian Constitution (1994).
7) Flanders remains attached to the confederation if it shows
goodwill by not asking a redistribution of its share in the public
national debt.
8) If Flanders asks also for the redistribution of the public
national debt the following questions remain:
--which method is used to allocate each share per region in the
national public debt?
--if the national public debt is redistributed, does Flanders
prefer confederation or secession?
Appendix A
Table 8. MOORA applied on 7 objectives for the Belgian Regions (Year
Zero): Ratio System Part (8a until 8c) and Reference Point Approach
(8d-8e)
8a. Matrix of Responses of Alternatives on Objectives: ([x.sub.ij])
1 2 3 4
Wallonia Brussels Flanders Transfers
disposable disposable disposable from
Y/head Y/head Y/head Flanders/
(BEF) (BEF) (BEF) head in
BEF
MAX MAX MAX MIN
Scenario 0 692883 698809 676743 41771
Scenario 1 684076 684076 684076 34438
Scenario 2 657935 680457 699375 19139
Scenario 3 674574 699861 686881 31633
Scenario 4 657935 680457 699375 19139
Scenario 5 684076 684076 684076 34438
Scenario 6 692883 698809 676743 41771
Scenario 7 628380 664936 718514 0
Scenario 8 628380 664936 718514 0
Scenario 9 718514 718514 718514 0
Scenario 10 718514 718514 718514 0
5 6 7
Flanders Wallonia Brussels
Public Public Public
Debt in Debt % GRP Debt in
% GRP % GRP
MIN MIN. MIN
Scenario 0 122.2 122.2 122.2
Scenario 1 122.2 122.2 122.2
Scenario 2 122.2 122.2 122.2
Scenario 3 116.4 134.6 120.6
Scenario 4 116.4 134.6 120.6
Scenario 5 116.4 134.6 120.6
Scenario 6 116.4 134.6 120.6
Scenario 7 122.2 122.2 122.2
Scenario 8 116.4 134.6 120.6
Scenario 9 122.2 122.2 122.2
Scenario 10 116.4 134.6 120.6
8b. Sum of squares and their square roots
1 2 3 4
Wallonia Brussels Flanders Transfers
disposable disposable disposable from
Y/head Y/head Y/head Flanders/
(BEF) (BEF) (BEF) head in
BEF
MAX MAX MAX MIN
Scenario 0 4.80087E+11 4.88334E+11 4.57981E+1 1744816441
Scenario 1 4.6796E+11 4.6796E+11 4.6796E+11 1185975844
Scenario 2 4.32878E+11 4.63022E+11 4.89125E+11 366301321
Scenario 3 4.5505E+11 4.89805E+11 4.71806E+11 1000646689
Scenario 4 4.32878E+11 4.63022E+11 4.89125E+11 366301321
Scenario 5 4.6796E+11 4.6796E+11 4.6796E+11 1185975844
Scenario 6 4.80087E+11 4.88334E+11 4.57981E+11 1744816441
Scenario 7 3.94861E+11 4.4214E+11 5.16262E+11 0
Scenario 8 3.94861E+11 4.4214E+11 5.16262E+11 0
Scenario 9 5.16262E+11 5.16262E+11 5.16262E+11 0
Scenario 10 5.16262E+11 5.16262E+11 5.16262E+11 0
[SIGMA] 50391482461 52452413661 53669878859 7594833901
root 2244804.723 2290249.193 2316676.042 87148.3442
5 6 7
Flanders Wallonia Brussels
Public Public Public
Debt in Debt % GRP Debt in
% GRP % GRP
MIN MIN. MIN
Scenario 0 14932.84 14932.84 14932.84
Scenario 1 14932.84 14932.84 14932.84
Scenario 2 14932.84 14932.84 14932.84
Scenario 3 13548.96 18117.16 14544.36
Scenario 4 13548.96 18117.16 14544.36
Scenario 5 13548.96 18117.16 14544.36
Scenario 6 13548.96 18117.16 14544.36
Scenario 7 14932.84 14932.84 14932.84
Scenario 8 13548.96 18117.16 14544.36
Scenario 9 14932.84 14932.84 14932.84
Scenario 10 13548.96 18117.16 14544.36
[SIGMA] 155957.96 183367.16 161930.36
root 394.91513 428.21392 402.405716
8c. Objectives divided by their square roots and MOORA
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
(BEF) (BEF) (BEF)
MAX MAX MAX
Scenario 0 0.308660701 0.305123566 0.292118098
Scenario 1 0.30473742 0.298690641 0.295283409
Scenario 2 0.293092309 0.297110464 0.301887267
Scenario 3 0.300504535 0.305582904 0.296494196
Scenario 4 0.293092309 0.297110464 0.301887267
Scenario 5 0.30473742 0.298690641 0.295283409
Scenario 6 0.308660701 0.305123566 0.292118098
Scenario 7 0.279926353 0.290333472 0.310148673
Scenario 8 0.279926353 0.290333472 0.310148673
Scenario 9 0.320078621 0.313727433 0.310148673
Scenario 10 0.320078621 0.313727433 0.310148673
4 5 6
Transfers Flanders Wallonia
from Public Public
Flanders/ Debt in Debt % GRP
head in % GRP
BEF
MIN MIN MIN.
Scenario 0 0.47930916 0.309 0.285
Scenario 1 0.39516528 0.3094336 0.28537139
Scenario 2 0.21961404 0.3094336 0.28537139
Scenario 3 0.36297878 0.2947469 0.31432888
Scenario 4 0.21961404 0.2947469 0.31432888
Scenario 5 0.39516528 0.2947469 0.31432888
Scenario 6 0.47930916 0.2947469 0.31432888
Scenario 7 0 0.3094336 0.28537139
Scenario 8 0 0.2947469 0.31432888
Scenario 9 0 0.3094336 0.28537139
Scenario 10 0 0.2947469 0.31432888
7
Brussels
Public
Debt in
% GRP
MIN
sum rank
Scenario 0 0.3036736 -0.472 10
Scenario 1 0.3036736 -0.395 8
Scenario 2 0.3036736 -0.226 5
Scenario 3 0.2996975 -0.369 7
Scenario 4 0.2996975 -0.236 6
Scenario 5 0.2996975 -0.405 9
Scenario 6 0.2996975 -0.482 11
Scenario 7 0.3036736 -0.018 3
Scenario 8 0.2996975 -0.028 4
Scenario 9 0.3036736 0.045 1
Scenario 10 0.2996975 0.035 2
8d. Reference Point Theory with Ratios: co-ordinates of the
reference point equal to the maximal objective values
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
(BEF) (BEF) (BEF)
MAX MAX MAX
[r.sub.i] 0.320078621 0.313727433 0.310148673
4 5
Transfers Flanders
from Public
Flanders/ Debt in
head in % GRP
BEF
MIN MIN
[r.sub.i] 0 0.2947469
6 7
Wallonia Brussels
Public Public
Debt % GRP Debt in
% GRP
MIN. MIN
[r.sub.i] 0.2853714 0.2996975
8e. Reference Point Theory: Deviations from the reference point
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
(BEF) (BEF) (BEF)
MAX MAX MAX
Scenario 0 0.01141792 0.009 0.0180
Scenario 1 0.015341201 0.015036792 0.014865264
Scenario 2 0.026986312 0.016616969 0.008261405
Scenario 3 0.019574086 0.008144529 0.013654477
Scenario 4 0.026986312 0.016616969 0.008261405
Scenario 5 0.015341201 0.015 0.015
Scenario 6 0.01141792 0.008603867 0.018030575
Scenario 7 0.040152268 0.023393961 0
Scenario 8 0.040152268 0.023393961 0
Scenario 9 0 0 0
Scenario 10 0 0 0
4 5 6
Transfers Flanders Wallonia
from Public Public
Flanders/ Debt in Debt % GRP
head in % GRP
BEF
MIN MIN MIN.
Scenario 0 0.4793 0.014687 0.0000
Scenario 1 0.3952 0.014687 0.0000
Scenario 2 0.2196 0.014687 0.0000
Scenario 3 0.363 0.000 0.0290
Scenario 4 0.2196 0.0000 0.0290
Scenario 5 0.3952 0.0000 0.0290
Scenario 6 0.4793 0.0000 0.0290
Scenario 7 0 0.014687 0.0000
Scenario 8 0 0 0.028957
Scenario 9 0 0 0.000000
Scenario 10 0 0 0.028957
7
Brussels
Public
Debt in
% GRP
MIN
max. rank
min.
Scenario 0 0.0039761 0.47931 10
Scenario 1 0.0039761 0.39517 8
Scenario 2 0.0039761 0.21961 5
Scenario 3 0 0.36298 7
Scenario 4 0 0.21961 5
Scenario 5 0 0.39517 8
Scenario 6 0 0.47931 10
Scenario 7 0.0039761 0.04015 3
Scenario 8 0 0.04015 3
Scenario 9 0.0039761 0.01469 1
Scenario 10 0 0.02896 2
Appendix B
In Table 9 MOORA is applied on 7 objectives for the Belgian Regions
with a significant coefficient of 2 for Private Income in the three
Regions (year 2005).
The basis is Table 5c. Indeed Tables 9a and 9b are successively
equal to Tables 5a and 5b. At that moment formula (4) is applied:
All figures of columns 1, 2 and 3 of the private incomes of
Wallonia, Brussels and Flanders are multiplied by 2. For instance,
private income of Wallonia in scenario 0 becomes: 0.29032729*2 =
0.5806545.
[x.sup.*.sub.ij] = [x.sub.ij]/[absolute value of [m.summation over
(j=1)] [x.sup.2.sub.ij] (4)
In the ratio system part of MOORA the ranking remains entirely the
same if yes or no private incomes become more important compared to the
importance of the transfer payments and the national public debt. What
about the Reference Point?
The ranking of the Reference Point is different from the ranking of
the Ratio System Part when a Significance Coefficient of 2 is allotted
to the Private Income of each of the three regions.
Scenarios 9 and 10 are again first ranked which is unrealistic. The
other regions try to arrive at the high level of Flanders, which is
impossible given the fact that the transfer payments are abolished and
the economic structure of Wallonia and Brussels is too weak.
Scenario 4 is ranked 3rd. As mentioned above due to an unfavourable
growth and inflation rate in order not to destabilize its own economy
Flanders has to diminish the transfer payments significantly, namely to
2.92 billion [euro]. In addition Flanders asks for a new repartition of
the national public debt.
Scenario 2 is ranked 4th. The situation is comparable with the
previous scenario. Nevertheless the solidarity in the national public
debt is kept unchanged.
Scenario 7 is ranked 5th. The transfer payments disappear entirely
but solidarity remains for the National Public Debt.
Scenario 8 is ranked 6th. The transfer payments disappear and no
solidarity remains for the National Public Debt. This scenario could
mean a move either from a federal state to a confederation of states or
to complete secession.
Scenario 3 is ranked 7th. The national public debt is reapportioned
again and the transfer payments are halved.
If the significance coefficient of 2 on the private incomes gives a
certain difference in the reference point part compared to the ratio
system part of MOORA, the diminishment and even the complete abolition
of the transfer payments remains essential.
Table 9. Reference Point Part with a significance coefficient of 2
for the private incomes
9c. Objectives divided by their square roots [x.sup.*.sub.ij] and
MOORA
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
MAX MAX MAX
Scenario 0 0.29032729 0.28789971 0.29789633
Scenario 1 0.31952124 0.30311656 0.28112004
Scenario 2 0.27240523 0.28789971 0.29789635
Scenario 3 0.28919507 0.28804484 0.29843932
Scenario 4 0.28919507 0.28804484 0.29843932
Scenario 5 0.31952124 0.30311657 0.28112004
Scenario 6 0.29032729 0.28789971 0.29789633
Scenario 7 0.25448317 0.29192372 0.31499983
Scenario 8 0.25335096 0.29206885 0.31554283
Scenario 9 0.35802904 0.33964731 0.31499983
Scenario 10 0.35864621 0.34023279 0.31554283
4 5 6
Transfer Flanders Wallonia.
from Public Public
Flanders Debt Debt
MIN MIN MIN
Scenario 0 0.2995659 0.309 0.285
Scenario 1 0.5955419 0.3094282 0.2853794
Scenario 2 0.149783 0.3094282 0.2853794
Scenario 3 0.2995659 0.2947515 0.3143228
Scenario 4 0.149783 0.2947515 0.3143228
Scenario 5 0.5755359 0.2947515 0.3143228
Scenario 6 0.2995659 0.2947515 0.3143228
Scenario 7 0 0.3094282 0.2853794
Scenario 8 0 0.2947515 0.3143228
Scenario 9 0 0.3094282 0.2853794
Scenario 10 0 0.2947515 0.3143228
7
Brussels
Public
Debt
MIN
sum rank
Scenario 0 0.3036772 -0.322 7
Scenario 1 0.3036772 0.590 11
Scenario 2 0.3036772 0.190 6
Scenario 3 0.2996945 0.333 9
Scenario 4 0.2996945 0.183 5
Scenario 5 0.2996945 0.581 10
Scenario 6 0.2996945 0.332 8
Scenario 7 0.3036772 0.037 3
Scenario 8 0.2996945 0.048 4
Scenario 9 0.3036772 0.114 1
Scenario 10 0.2996945 0.106 2
9c (bis.) Objectives divided by their square roots [x.sup.*.sub.ij]
but with the private incomes multiplied by 2 and MOORA
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
MAX MAX MAX
Scenario 0 0.580654575 0.575799412 0.595792651
Scenario 1 0.639042489 0.606233124 0.562240071
Scenario 2 0.544810459 0.575799412 0.595792651
Scenario 3 0.578390144 0.576089675 0.596878644
Scenario 4 0.578390144 0.576089675 0.596878644
Scenario 5 0.639042489 0.606233124 0.562240071
Scenario 6 0.580654575 0.575799412 0.595792651
Scenario 7 0.508966343 0.58384743 0.629999656
Scenario 8 0.506701912 0.584137692 0.631085649
Scenario 9 0.716058085 0.679294628 0.629999656
Scenario 10 0.717292425 0.680465595 0.631085649
4 5 6
Transfer Flanders Wallonia.
from Public Public
Flanders Debt Debt
MIN MIN MIN
Scenario 0 0.2995659 0.309 0.285
Scenario 1 0.5955412 0.3094282 0.2853794
Scenario 2 0.149783 0.3094282 0.2853794
Scenario 3 0.2995659 0.2947515 0.3143228
Scenario 4 0.149783 0.2947515 0.3143228
Scenario 5 0.5755359 0.2947515 0.3143228
Scenario 6 0.2995659 0.2947515 0.3143228
Scenario 7 0 0.3094282 0.2853794
Scenario 8 0 0.2947515 0.3143228
Scenario 9 0 0.3094282 0.2853794
Scenario 10 0 0.2947515 0.3143228
7
Brussels
Public
Debt
MIN
sum rank
Scenario 0 0.3036772 0.554 7
Scenario 1 0.3036772 0.313 11
Scenario 2 0.3036772 0.668 6
Scenario 3 0.2996945 0.543 9
Scenario 4 0.2996945 0.693 5
Scenario 5 0.2996945 0.323 10
Scenario 6 0.2996945 0.544 8
Scenario 7 0.3036772 0.824 3
Scenario 8 0.2996945 0.813 4
Scenario 9 0.3036772 1.127 1
Scenario 10 0.2996945 1.120 2
9d. Reference Point Theory with Ratios: co-ordinates of the
reference point equal to the maximal objective values
rank
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
MAX MAX MAX
[r.sup.i] 0.71729243 0.68046560 0.63108565
4 5
Transfer Flanders
from Public
Flanders Debt
MIN MIN
[r.sup.i] 0.0000 0.2947515
6 7
Wallonia. Brussels
Public Public
Debt Debt
MIN MIN
[r.sup.i] 0.2853794 0.29969453
9e. Reference Point Theory: Deviations from the reference point
1 2 3
Wallonia Brussels Flanders
disposable disposable disposable
Y/head Y/head Y/head
MAX MAX MAX
Scenario 0 0.13663785 0.105 0.0353
Scenario 1 0.07824994 0.07423247 0.06884558
Scenario 2 0.17248197 0.10466618 0.035293
Scenario 3 0.13890228 0.10437592 0.03420701
Scenario 4 0.13890228 0.10437592 0.03420701
Scenario 5 0.07824994 0.074 0.069
Scenario 6 0.13663785 0.10466618 0.035293
Scenario 7 0.20832608 0.09661817 0.00108599
Scenario 8 0.21059051 0.09632790 0
Scenario 9 0.00123434 0.00117097 0.00108599
Scenario 10 0 0 0
4 5 6
Transfer Flanders Wallonia.
from Public Public
Flanders Debt Debt
MIN MIN MIN
Scenario 0 0.299566 0.014677 0.0000
Scenario 1 0.5955 0.014677 0.0000
Scenario 2 0.1498 0.014677 0.0000
Scenario 3 0.299566 0.000 0.0289
Scenario 4 0.149783 0.0000 0.0289
Scenario 5 0.5755 0.0000 0.0289
Scenario 6 0.299566 0.0000 0.0289
Scenario 7 0 0.014677 0.0000
Scenario 8 0 0 0.028943
Scenario 9 0 0.014677 0.000000
Scenario 10 0 0 0.028943
7
Brussels
Public
Debt
MIN
max. min.
Scenario 0 0.00398265 0.299566 7
Scenario 1 0.00398265 0.5955412 11
Scenario 2 0.00398265 0.172482 4
Scenario 3 0 0.299566 7
Scenario 4 0 0.149783 3
Scenario 5 0 0.575536 10
Scenario 6 0 0.299566 7
Scenario 7 0.00398265 0.20833 5
Scenario 8 0 0.21059 6
Scenario 9 0.00398265 0.014677 1
Scenario 10 0 0.02894 2
doi: 10.3846/jbem.2010.09
Received 20 March 2009, accepted 15 February 2010
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(1) A good overview of the problem of Robustness and Bayesian
Analysis is brought by Ruggeri (2008).
(2) Since 1999 the National Bank of Belgium provides statistics on
the Regional Private Incomes (also called primary incomes of the
households) but neither on the Gross Regional Domestic Products (which
involves the problem of the important commuter flows to Brussels) nor on
the Gross Regional Products. To close the gap to GRP one would need to
know: the cash flows of Belgian companies before taxes but after
distribution of dividends and the indirect taxation. This link is
missing as Regional Statistics are dictated by Europe, but Europe is not
interested in the national point of view as found in GNP and GRP. The
GRP's could be estimated after a method explained for 1996 (Brauers
1999a). However, here to simplify terminology we assume that the GRP
equals the Regional Private Income.
(3) The Maastricht criteria to join the EMU were roughly as
follows:
--Inflation: max 2%
--Deficit Public Budget: max 3% of the Gross Domestic Product (GDP)
--Public Debt smaller than 60% of GDP.
(4) Let us remember that the Internal Rate of Return (I.I.R) means
the interest rate against which the discounted cash flow equals the
investment over the foreseen lifetime of the project.
Willem Karel M. Brauers [1], Romualdas Ginevicius [2]
[1] Faculty of Applied Economics, University of Antwerp, Belgium
[2] Department of Enterprise Economics and Business Management, Vilnius
Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius,
Lithuania E-mails: 'willem.brauers@ua.ac.be (corresponding author);
[2] romualdas.ginevicius@vgtu.lt
Willem K. M. BRAUERS graduated as: Ph.D. in Economics (Un. of
Leuven), Master of Arts (in Economics) of Columbia Un. (New York),
Master in Management and Financial Sciences, in Political and Diplomatic
Sciences and Bachelor in Philosophy (Un. of Leuven). He is professor
ordinarius at the Faculty of Applied Economics and at the Institute for
Development Policy and Management of the University of Antwerp, Honorary
Professor at the University of Leuven, the Belgian War College, the
School of Military Administrators and the Antwerp Business School. He
was a research fellow in several American institutions like Rand
Corporation, the Institute for the Future, the Futures Group and
extraordinary advisor to the Center for Economic Studies of the
University of Leuven. He was consultant in the public sector, such as
the Belgian Department of National Defense, the Department of Industry
in Thailand, the project for the construction of a new port in Algeria
(the port of Arzew) and in the private sector such as the international
seaport of Antwerp and in electrical works. He was Chairman of the Board
of Directors of SORCA Ltd.Brussels, Management Consultants for
Developing Countries, linked to the worldwide group of ARCADIS and
Chairman of the Board of Directors of MARESCO Ltd. Antwerp, Marketing
Consultants. At the moment he is General Manager of CONSULTING, Systems
Engineering Consultants. Brauers is member of many international
scientific organizations. His specialization covers: Optimizing
Techniques with Different Objectives, Forecasting Techniques,
Input-Output Techniques and Public Sector Economics such as for National
Defense and for Regional Sub-optimization. His scientific publications
consist of twelve books and hundreds of articles and reports.
Romualdas GINEVICIUS. Professor, Dr, Head of the Department of
Enterprise Economics and Management, construction engineer and
economist. The author of more than 350 research papers and over 20
scientific books; editor-in-chief of the 'Journal of Business
Economics and Management' (located in ISI database 'Web of
Science') and the journal 'Business: Theory and
Practice'. Research interests: organization theory, complex
quantitative evaluation of social processes and phenomena.
Table 1. Total transfer payments in Public Finance (in billion [euro])
Flanders Wallonia Brussels
1990 3.76 -2.61 -1.15
1995 4.49 -3.33 -1.16
1996 (a) 4.57 -3.38 -1.19
1997 4.71 -3.73 -0.98
1998 4.62 -3.79 -0.83
1999 4.68 -3.88 -0.80.
2000 4.88 -4.11 -0.77
2001 (b) 5.27 -4.36 -0.91
2002 5.44 -4.44 -1.00
2005 (c) 5.84 -6.06 0.21
Table 2. Evolution of the Belgian Public Debt as a % of GDP
1993 peak 133.5
1997 Maastricht 122.2
2005 91.5
2006 88.2
2007 (lowest %) 84
2008 89.7
2009 97.5
2010 101.9
2011 103.9
2012 (new peak) 104.3
2013 103.4
2014 101.0
2015 97.4
Table 3. Matrix of Responses of Scenarios on Objectives for the
Belgian Regions at the Maastricht moment (a)
1 2 3 4
WALLONIA BRUSSELS FLANDERS TRANSFERS
Disposable Disposable Disposable from
Scenarios Y/head Y/head Y./head Flanders /
(in BEF) (in BEF) (in BEF) head
(in BEF)
MAX MAX MAX MIN
Scenario 0 692883 698809 676743 41771
Scenario 1 684076 684076 684076 34438
Scenario 2 657935 680457 699375 19139
Scenario 3 674574 699861 686881 31633
Scenario 4 657935 680457 699375 19139
Scenario 5 684076 684076 684076 34438
Scenario 6 692883 698809 676743 41771
Scenario 7 628380 664936 718514 0
Scenario 8 628380 664936 718514 0
Scenario 9 718514 718514 718514 0
Scenario 10 718514 718514 718514 0
5 6 7
FLANDERS WALLONIA BRUSSELS
Public Debt Public Debt Public Debt
Scenarios
% of GRP % of GRP % of GRP
MIN MIN MIN
Scenario 0 122.2 122.2 122.2
Scenario 1 122.2 122.2 122.2
Scenario 2 122.2 122.2 122.2
Scenario 3 116.4 134.6 120.6
Scenario 4 116.4 134.6 120.6
Scenario 5 116.4 134.6 120.6
Scenario 6 116.4 134.6 120.6
Scenario 7 122.2 122.2 122.2
Scenario 8 116.4 134.6 120.6
Scenario 9 122.2 122.2 122.2
Scenario 10 116.4 134.6 120.6
(a) calculations come from Brauers (1999b).
(1) BEF = 0.0247893
Table 4. Ranking of the Scenarios by the Full-Multiplicative Method
at the Year Zero
1 Scenario IX Optimal Economic Policy in 203,267
Wallonia and Brussels
2 Scenario X Optimal Economic Policy in 196,306
Wallonia and Brussels even
agreeing on the Partition of
the National Public Debt
3 Scenario VII Flanders asks for the 164,515
Partition of the National
Public Debt
4 Scenario VIII No Solidarity at all 158,881
5 Scenario II Unfavourable Growth Rate for 90
Flanders
6 Scenario IV Unfavourable Growth Rate for 87
Flanders and at that moment
asks also for the Partition of
the National Public Debt
7 Scenario III Partition of the National 54
Public Debt
8 Scenario I the Average Belgian 51
9 Scenario V Average Belgian but as 49
compensation Flanders asks for
the Partition of the National
Public Debt
10 Scenario O Status Quo 43
11 Scenario VI Flanders asks for the 42
Partition of the National
Public Debt
Table 5. MOORA applied on 7 objectives for the Belgian regions (year
2005): Ratio System Part (5a until 5c) and Reference Point Approach
(5d-5e)
5a. Matrix of Responses of Alternatives on Objectives: (xj)
1 2 3 4
Wallonia Brussels Flanders Transfer
Disposable Disposable Disposable from
Y/head Y/head Y/head Flanders
[euro] [euro] [euro] (bln [euro])
MAX MAX MAX MIN
Scenario 0 14441.8 15096.1 16842.5 5.84
Scenario 1 15894 15894 15894 11.61
Scenario 2 13550.3 15096.1 16842.5 2.92
Scenario 3 14385.48 15103.71 16873.2 5.84
Scenario 4 14385.48 15103.71 16873.2 2.92
Scenario 5 15894 15894 15894 11.22
Scenario 6 14441.8 15096.1 16842.5 5.84
Scenario 7 12658.8 15307.1 17809.5 0
Scenario 8 12602.48 15314.71 17840.2 0
Scenario 9 17809.5 17809.5 17809.5 0
Scenario 10 17840.2 17840.2 17840.2 0
5 6 7
Flanders Wallonia. Brussels
Public Public Public
Debt % Debt % Debt % GRP
of GRP of GRP
MIN MIN MIN
Scenario 0 91.5 91.5 91.5
Scenario 1 91.5 91.5 91.5
Scenario 2 91.5 91.5 91.5
Scenario 3 87.16 100.78 90.3
Scenario 4 87.16 100.78 90.3
Scenario 5 87.16 100.78 90.3
Scenario 6 87.16 100.78 90.3
Scenario 7 91.5 91.5 91.5
Scenario 8 87.16 100.78 90.3
Scenario 9 91.5 91.5 91.5
Scenario 10 87.16 100.78 90.3
5b. Sum of squares and their square roots
1 2 3 4
Wallonia Brussels Flanders Transfer
Disposable Disposable Disposable from
Y/head Y/head Y/head Flanders
[euro] [euro] [euro] (bln
[euro])
MAX MAX MAX MIN
Scenario 0 208565587 227892235 2836698 34.1056
Scenario 1 252619236 252619236 2526192 134.792
Scenario 2 183610630 227892235 2836698 8.5264
Scenario 3 206942035 228122056 2847049 34.1056
Scenario 4 206942035 228122056 2847049 8.5264
Scenario 5 252619236 252619236 2526192 125.888
Scenario 6 208565587 227892235 2836698 34.1056
Scenario 7 160245217 234307310 3171783 0
Scenario 8 158822502 234540342 3182727 0
Scenario 9 317178290 317178290 3171783 0
Scenario 10 318272736 318272736 3182727 0
[SIGMA] 2474383092 2749457968 3196559 380
root 49743.1713 52435.2741 56538.1261 19.494874
5 6 7
Flanders Wallonia. Brussels
Public Public Public
Debt % Debt % Debt
of GRP of GRP % GRP
MIN MIN MIN
Scenario 0 8372.25 8372.25 8372.25
Scenario 1 8372.25 8372.25 8372.25
Scenario 2 8372.25 8372.25 8372.25
Scenario 3 7596.8656 10156.608 8154.09
Scenario 4 7596.8656 10156.608 8154.09
Scenario 5 7596.8656 10156.608 8154.09
Scenario 6 7596.8656 10156.608 8154.09
Scenario 7 8372.25 8372.25 8372.25
Scenario 8 7596.8656 10156.608 8154.09
Scenario 9 8372.25 8372.25 8372.25
Scenario 10 7596.8656 10156.608 8154.09
[SIGMA] 87442.44 102800.90 90785.79
root 295.70669 320.6258 301.30680
5c. Objectives divided by their square roots and MOORA
1 2 3
Wallonia Brussels Flanders
Disposable Disposable Disposable
Y/head Y/head Y/head
[euro] [euro] [euro]
MAX MAX MAX
Scenario 0 0.2903273 0.2878997 0.29789633
Scenario 1 0.3195212 0.3031166 0.28112004
Scenario 2 0.2724052 0.2878997 0.29789635
Scenario 3 0.2891951 0.2880448 0.29843932
Scenario 4 0.2891951 0.2880448 0.29843932
Scenario 5 0.3195212 0.3031166 0.28112004
Scenario 6 0.2903273 0.2878997 0.29789633
Scenario 7 0.2544832 0.2919237 0.31499983
Scenario 8 0.253351 0.2920689 0.31554283
Scenario 9 0.3580290 0.3396473 0.31499983
Scenario 10 0.3586462 0.3402328 0.31554283
4 5 6
Transfer Flanders Wallonia.
from Public Public
Flanders Debt % Debt %
(bln of GRP of GRP
[euro])
MIN MIN MIN
Scenario 0 0.2995659 0.309 0.285
Scenario 1 0.5955419 0.3094282 0.2853794
Scenario 2 0.149783 0.3094282 0.2853794
Scenario 3 0.2995659 0.2947515 0.3143228
Scenario 4 0.149783 0.2947515 0.3143228
Scenario 5 0.5755359 0.2947515 0.3143228
Scenario 6 0.2995659 0.2947515 0.3143228
Scenario 7 0 0.3094282 0.2853794
Scenario 8 0 0.2947515 0.3143228
Scenario 9 0 0.3094282 0.2853794
Scenario 10 0 0.2947515 0.3143228
7
Brussels
Public
Debt
% GRP
MIN
sum rank
Scenario 0 0.30368 -0.322 7
Scenario 1 0.30368 -0.590 11
Scenario 2 0.30368 -0.190 6
Scenario 3 0.29969 -0.333 9
Scenario 4 0.29969 -0.183 5
Scenario 5 0.29969 -0.581 10
Scenario 6 0.29969 -0.332 8
Scenario 7 0.30368 -0.037 3
Scenario 8 0.29969 -0.048 4
Scenario 9 0.30368 0.114 1
Scenario 10 0.29969 0.106 2
5d. Reference Point Theory with Ratios: co-ordinates of the
reference point equal to the maximal objective values
1 2 3
Wallonia Brussels Flanders
Disposable Disposable Disposable
Y/head Y/head Y/head
[euro] [euro] [euro]
MAX MAX MAX
[r.sub.i] 0.35864621 0.3402328 0.31554283
4 5
Transfer Flanders
from Public
Flanders Debt %
(bln of GRP
[euro])
MIN MIN
[r.sub.i] 0.0000 0.2947515
6 7
Wallonia. Brussels
Public Public
Debt % Debt
of GRP % GRP
MIN MIN
[r.sub.i] 0.2853794 0.299695
5e. Reference Point Theory: Deviations from the reference point
1 2 3
Wallonia Brussels Flanders
Disposable Disposable Disposable
Y/head Y/head Y/head
[euro] [euro] [euro]
MAX MAX MAX
Scenario 0 0.0683189 0.052 0.0176
Scenario 1 0.039125 0.03711624 0.03442279
Scenario 2 0.086241 0.05233309 0.0176465
Scenario 3 0.0694511 0.05218796 0.01710350
Scenario 4 0.0694511 0.05218796 0.01710350
Scenario 5 0.039125 0.037 0.034
Scenario 6 0.0683189 0.05233309 0.0176465
Scenario 7 0.1041630 0.04830908 0.000543
Scenario 8 0.1052953 0.04816395 0
Scenario 9 0.0006172 0.00058548 0
Scenario 10 0 0 0
4 5 6
Transfer Flanders Wallonia.
from Public Public
Flanders Debt % Debt %
(bln of GRP of GRP
[euro])
MIN MIN MIN
Scenario 0 0.2996 0.014677 0.0000
Scenario 1 0.5955 0.014677 0.0000
Scenario 2 0.1498 0.014677 0.0000
Scenario 3 0.2996 0.000 0.0289
Scenario 4 0.14978 0.0000 0.0289
Scenario 5 0.5755 0.0000 0.0289
Scenario 6 0.2996 0.0000 0.0289
Scenario 7 0 0.014677 0.0000
Scenario 8 0 0 0.028943
Scenario 9 0 0 0.000000
Scenario 10 0 0 0.028943
7
Brussels
Public
Debt
% GRP
MIN
max. rank
min.
Scenario 0 0.00398 0.29957 7
Scenario 1 0.003982 0.59554 11
Scenario 2 0.00398 0.14978 5
Scenario 3 0 0.29957 7
Scenario 4 0 0.14978 5
Scenario 5 0 0.57553 10
Scenario 6 0 0.29956 7
Scenario 7 0.00398 0.10416 3
Scenario 8 0 0.1053 4
Scenario 9 0.00398 0.01468 1
Scenario 10 0 0.02894 2
Table 6. Ranking the Belgian Regions by MULTIMOORA
Full MOORA MOORA
Scenarios Multiplicative Ratio Reference
Form System Point
Year Zero Year Zero Year Zero
Scenario IX 1 1 1
Scenario X 2 2 2
Scenario VII 3 3 3
Scenario VIII 4 4 3
Scenario II 5 5 5
Scenario IV 6 6 5
Scenario III 7 7 7
Scenario I 8 8 8
Scenario V 9 9 8
Scenario O 10 10 10
Scenario VI 11 11 10
MULTIMOORA MOORA MOORA
Scenarios Ratio Reference
System Point
Year Zero 2005 2005
Scenario IX 1 1 1
Scenario X 2 2 2
Scenario VII 3 3 3
Scenario VIII 4 4 4
Scenario II 5 6 6
Scenario IV 6 5 5
Scenario III 7 9 7
Scenario I 8 11 11
Scenario V 9 10 10
Scenario O 10 7 7
Scenario VI 11 7 7
Table 7. Income Paradox in Belgium (1996)
in BEF * GRP per head Disposable
Income per
head
Flanders 869,976 676,743
Wallonia 752,452 692,883
Brussels 839,913 698,809
Belgium 828,693 684, 076
* 1 [euro] equaled 40.3399 BEF
Calculations in: W K. Brauers: het Bruto Regionale Product van
Vlaanderen, Wallonie en Brussel, Working Paper 99-2, RUCA, Faculty
of Applied Economics, University of Antwerp, 8-18.
