construction and evolution of a multidimensional well-being index for the spanish regions

Construction and Evolution of a MultidimensionalWell-Being Index for the Spanish Regions

Antonio Jurado • Jesus Perez-Mayo

Accepted: 20 September 2010 / Published online: 13 April 2011� Springer Science+Business Media B.V. 2011

Abstract The study presented here is an attempt to calculate a comparative multidimen-

sional index of economic well-being for the Spanish Autonomous Communities. Based on the

dimensions of adjusted consumption, real wealth, equity and economic security per inhabi-

tant, we obtain one relative index using a system of uniform weightings, a second resulting

from a factor analysis and a third provided by a DEA analysis. We elaborate the index for the

year 2000 and for 2006, thereby providing the relative results with greater robustness and

permitting some conclusions to be reached with regard to the evolution over time of the index.

Keywords Economic well-being � Factor analysis � Indicators � DEA

1 Introduction

The disparities in well-being evidenced by the Spanish Autonomous Communities1 (the 17

political-administrative regions of Spain, CC.AA. in their Spanish initials), while having

been for some time a cause for concern in economic and political debate, are currently

entering a phase in which their quantification is increasingly important.

On the one hand, European structural funds or the Spanish Interterritorial Compensation

Fund (FCI) use principally macromagnitudes2 as economic delimiters of shares, and could

A. JuradoDepartment of Economics, University of Extremadura, Caceres, Spain

J. Perez-Mayo (&)Department of Economics, University of Extremadura, Badajoz, Spaine-mail: [email protected]

1 Some authors, such as Ayala et al. (2011), Garcıa-Luque et al. (2009), Perez-Mayo (2008), or Poggi (2007)for example, included the territorial issue in the analysis of poverty, deprivation and social exclusion in Spain.2 The distribution of European structural funds is based, in the Objective 1 regions, solely on a percentageof average European income that indicates which regions will be recipients of such resources. However, theSpanish FCI (Interterritorial Compensation Fund) has to date employed a formula which, in addition to grossadded value, takes into consideration: the de jure population, the migratory balance, the number ofunemployed, geographical extent and population dispersion. Nevertheless, as we shall see below, our indexis much more ambitious with regard to the multidimensionality captured.

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Soc Indic Res (2012) 107:259–279DOI 10.1007/s11205-011-9835-4

be more ambitious in the quantification of this matter. On the other, increasing interest in

regional fiscal balances3 in the framework of a statutory restructuring should be accom-

panied by a parallel and more exhaustive broadening of the indicator to be employed when

taking decisions of an inter-regional nature.

In the national and international panorama of this type of study, in the majority of cases

the analysis has been based on a macromagnitude such as GDP, income or similar,

combined with some indicator of economic equity (inequality indices and/or poverty

indices). These are the so-called abbreviated welfare functions.

Many authors,4 such as Nordhaus and Tobin (1972), Sen (2001), Khan (1991), Stewart

(2005), or Stiglitz et al. (2009), have raised criticisms of the use of a single macromag-

nitude. Consequently, many studies have moved beyond purely economic indicators and

entered the field of social well-being. The measurement of social well-being includes

dimensions such as material well-being, education, health, and participation in the social

activity of the environment, or may even consider questions such as crime or the climate,5

which, although clearly influential, sharply increase the problem of arbitrariness in the

choice of variables and weightings.

Although inter-country comparisons are more common, regional-level studies have also

been undertaken, such as the above-mentioned work by Stewart (2002 and 2005), applied

to the European regions.

In the field of the most recent comparative regional studies in Spain, Marchante et al.

(2006) elaborate a well-being index for the Autonomous Communities, based on a

broadening of the Human Development Index (HDI) of the United Nations Development

Program (UNDP) and by using the following variables: life expectancy, infant mortality

rate, illiteracy, school enrolment and gross added value per capita (GAV p.c.). Ayala et al.

(2006) focus on the same territorial units, calculating abbreviated welfare functions as a

multiplicatory trade-off between an income component and an inequality component.

Studies such as that by Osberg and Sharpe (2000, 2003, 2005 and 2009) indicate how a

wider notion of economic well-being must include dimensions of wealth, inequality and

insecurity, components which neither the work by Marchante et al. (2006) nor the HDI

itself claim to encompass and which, in the case of wealth and insecurity, the study by

Ayala et al. (2006) preferred to leave untouched. In that same year, Murias et al. (2006)

estimated an economic well-being index based on the structure supplied by Osberg and

Sharpe. Their work uses only one of the three systems of weightings applied in the present

study, does not study evolution over time and selects the Spanish provinces as the terri-

torial units of study. Bearing in mind the high and increasing degree of decentralisation of

the Spanish administration, and that almost all policies that affect citizens’ well-being are

already the responsibility of the regional administrations (Autonomous Communities), we

consider it essential to take the regions as the territorial unit of reference.6

3 The study ‘‘The fiscal balances of the Autonomous Communities with the Central Public Administration,1991–2005’’, Uriel and Barberan (2007), was published on 28 November 2007. It is the first scientific reporton the subject, since Spanish governments had never previously made public results of this nature.4 In addition to the references in the text, brief reviews of some attempts to measure well-being, taking intoaccount different aspects than macromagnitudes, can be found in: Zolotas (1981), Daly and Cobb (1989),Cobb and Cobb (1994), Cobb et al. (1995), Anielski and Rowe (1999), Jackson (2004), or Wolff et al.(2005).5 A wider analysis of wellbeing can be found in, for example, Diener et al. (1995), Lelkes (2005), or Rojas(2007).6 A brief description of the Spanish administrative structure can be found in Annex 1.

260 A. Jurado, J. Perez-Mayo

123

Returning to the structure established by Osberg and Sharpe, they consider the HDI to

be a social well-being index (possibly the best known worldwide) with three components:

health, education and ‘‘economic resources’’. The authors focus their attention on this last

point. The index is based on GDP per capita and is intended to capture the capacity of

persons to ‘‘lead a long and healthy life, acquire knowledge and have access to the

resources necessary to achieve a decent standard of living’’ (UNDP 2004, p. 127). They

believe the measurement of the economic aspect of the HDI can clearly be improved and

propose the construction of an economic well-being index to replace the GDP employed.

The design used in their studies is, in our view, both the most efficient and simplest of

the economic well-being indices constructed to date. Thus, with the aim of making a

deeper contribution to this subject, in the ambit of the Spanish regions (where we believe

controversy will increase in the near future), we develop an initial approximation of a

regional economic well-being index, founded on the basic structure used by Osberg and

Sharpe in a comparison of a group of developed countries.

We must insist upon the point that our index is ‘‘economic’’ and, consequently, aspects

such as health and education are not included because would convert it into an index of

social well-being. That would be a much more ambitious project, which should wait, at

least, until the present research has matured.

The paper is structured in four sections. The first deals in detail with the methodological

aspect; it defines the dimensions which the index is intended to capture, the variables we

have been able to use to represent each dimension, and the different techniques employed

to treat the weightings. The second section quantifies the index for each of the Autonomous

Communities in the year 2000, using three different weighting systems. The third analyses

the evolution over time in the period 2000–2006, while the final section ends the study with

a brief description of conclusions and future intentions.

2 Methodology of the Study

The well-being index designed has been structured in four dimensions: adjusted con-

sumption, real wealth, equity and economic security. We consider that these capture the

most influential effects of the purely economic variables operating in what we have

attempted to include within the concept of economic well-being.

The consumption flow is perhaps the factor having the clearest influence on family well-

being and that of its members. We consider it important to find data that reflect the

consumption of both market goods and services and of public goods and services provided

by the distinct administrations.

Within the consumption flow, there are some factors for which it is totally or partially

impossible to obtain data in the regional sphere, such as: the consumption of leisure, the

shadow economy, disability-free life expectancy, some consumption costs such as that of

the journey to work, the consumption of products which seriously damage health or the

consumption of illegal products which lead to crime and produce collateral costs.

Adjusted private consumption was calculated using monetary and non-monetary

expenditure7 (separately, to detect possible differences in the weightings), extracted from

the Continuous Household Budget Survey (CHBS) for the year 2000 and from the

7 The expenditures registered in CHBS and HBS refer to both the monetary flow that the household andeach of its members spend on the payment of certain goods and services, and the non-monetary flowcontaining self-consumption, self-supply, wages in kind, free or subsidised food and rent imputed to the

Construction and Evolution of a Multidimensional Well-Being Index 261

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Household Budget Survey (HBS) for the year 2006. In the former case, we employed the

longitudinal file updated annually by the Spanish National Statistics Institute (INE) from

the quarterly surveys. Specifically, we employed in both cases the adjusted datum with a

parametric equivalence scale, with k equal to 0.5 and multiplied by life expectancy.

The life expectancy index has been used for several authors, i.e. Osberg and Sharpe

(2000), in measuring economic well-being. This expectancy has increased in the last years

in many countries and regions but not with the same strength. Despite the inter-regional

differences in life expectancy are not very notable we consider that long life is an

important factor of well-being in a society. The ‘‘extra years’’ of some regions in relation to

average life could have an economic value that should be included in the consumption

flows of individuals. Osberg and Sharpe (2000) said, ‘‘People care both about how much

they consume per year, and how many years they get to consume it’’.

The life expectancy index was obtained by the INE from the Analysis and demographic

studies (mortality data).

Adjusted public consumption was obtained from the data for total public consumption

supplied by the Regional Economic Balance Sheet (Autonomous Communities and

Provinces), years 2000–2005, and Cuadernos de Informacion Economica No. 203, April

2008, published by the Foundation of Confederate Savings Banks (FUNCAS).

Another variable taken into account in most of the studies is the working hours.

Especially, in a group of regions with similar leisure activities, the differences in hours

worked yearly per worker must influence on the well-being level. Moreover, the increasing

decentralization in Spain permits differences in labour legislation.

Any discussion of well-being must refer to intra- and inter-generational economic

equity. The traditional method of quantifying the first of these is to use inequality indices

or poverty indices. Ayala et al. (2006) offer a more exhaustive analysis of inequality in the

regional sphere. The indices of inequality and poverty intensity employed here were the

Gini index and the FGT 1, compiled by the authors from the HBS 2006 microdata and from

the longitudinal file 2000 obtained by the INE from the CHBS.

With regard to inter-generational equity, our intention is to provide a number of vari-

ables which attempt to measure the legacy which society will foreseeably leave to the

following generation, consisting of an accumulated capital which would serve as a pro-

ductive structure in the future society. However, this transfer should also include an

environmental equity, a solid foundation of research and a controlled public debt,8 which

would not excessively reduce the future capacities of the economy.

To quantify physical capital we use the nominal net capital stock obtained by the

Valencian Economic Research Institute (IVIE) in its study of the period 1964–2005.

Human capital is represented by the ratio of the working age population with higher

education to the total working age population. This data is obtained from the IVIE for the

year 2000, and for the year 2006 it has been calculated from the HBS 2006.

Footnote 7 continueddwelling in which the household resides (when it is the owner of the same, or the dwelling was granted freeof charge or at a very low price by other households or institutions).8 Regional public debt was initially included as an explanatory variable. However, when applying thefactorial analysis, an insignificant weighting, which recommended its elimination, was obtained. Further-more, from a theoretical point of view, regional debt would not be the same here as national debt because ofthree reasons. First, the Autonomous Communities’ debt is tightly controlled and regulated by the CentralTreasury. Second, it is principally assigned to investment and it is, therefore, debatable that it subtracts realwealth from the next generation. And, finally, figures for it may not be complete because the regionaladministrations usually spend in excess of their budgetary allocation (especially in recent years).


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Expenditure on R&D is captured by internal expenditure on R&D by Autonomous

Community, provided by the INE. Expenditure on environmental protection is taken from

the same source, specifically its survey of industrial companies’ expenditure on environ-

mental protection.

Lastly, economic insecurity is, from our point of view, one of the principal causes of the

absence of well-being in families in developed countries. The economic problems that may

accompany illness, divorce,9 old age and unemployment (especially in the absence of

benefit coverage) enormously reduce both present economic well-being and certainty

surrounding the standard of living in the near future.

Using once more the CHBS 2000 and the HBS 2006, we calculated the percentage of

expenditure on health in relation to monetary income10 and the poverty rate for over-65s.

The INE’s database used for obtaining the unemployment rate is the Economically Active

Population Survey (Annual results, Autonomous Communities). In addition, the unem-

ployment benefit coverage, calculated as the number of recipients in relation to the total

number of unemployed, comes from the State Public Employment Service.

To take into account the disparities in prices that may exist among the different regions,

the monetary expenditure, non-monetary expenditure, Gini index, FGT1 index and over-

65s poverty rate variables have been adjusted by applying purchasing power parities

(Alcaide and Alcaide 2008).

2.1 Calculation of the Index

To obtain the well-being index from the indicators (central column, Table 1 above), each

has been rescaled at the interval [0,1] in accordance with the methodology employed by the

UNO in the elaboration of the Human Development Index (HDI). The maximum and

minimum reference values are taken for the set of the Autonomous Communities and for

each indicator. Subsequently, using the expression (1), the value of each indicator in each

of the regions is determined. These values will range between 0 for the region having the

lowest value of the indicator and 1 for the Autonomous Community showing the greatest

value.

indicator of region i ¼ value of the variable in i�minimum reference value

maximum reference value�minimum reference valueð1Þ

Having transformed the indicators [0,1], it is possible to determine the values of each

dimension of economic well-being of the Autonomous Communities (adjusted consump-

tion, real wealth, equity and economic security). To obtain the values of the dimensions

9 We initially included the rate of divorce as a variable representative of the risk of single-parent poverty;however, when applying the weightings based on the factorial analysis the system assigned a positiverelation between well-being and divorce. Although the relation we intended to quantify was theoreticallynegative, the results show that in the Autonomous Communities where well-being was greatest the divorcerate was higher. The reason may be that upper-income families are more likely than lower-income familiesto be able to ‘‘permit themselves’’ to undergo divorce and the consequent loss of family income. In view ofthe results, we decided to eliminate this variable from our index.10 This variable is used as proxy for health status and its main economic effect on well-being. The healthexpenditure of the households in the HBS includes medicines, other pharmaceutical products, therapeuticmaterials, extra hospital medical and paramedical services and hospital services. Although the SpanishHealth System has a universal coverage, medicines prices or some therapeutic materials and services arepartially covered. Although there are some differences in certain expenditures (not very relevant) among theregional Health Systems, it is assumed in the analysis that the public health sectors are covering the samebenefits (in cash or in kind) because the evaluation of Regional Health Systems is not the aim of this paper.


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from the indicators, we applied uniform weighted averages,11 taking into account the

positive or negative sign corresponding to each indicator. Because the dimensions had

already been obtained, we did not proceed to the rescaling described above, and thus the

values are no longer between 0 and 1.

Subsequently, it was necessary to establish a system of weightings that would permit

their combination to construct the general index. One of the methodological options would

have been to initiate the calculation assuming that distribution is uniform (i.e. an impor-

tance of 25% for each dimension) and equitable for each indicator within each dimension.

However, as Osberg and Sharpe (2000) state, different weightings may be considered, such

as 40% for adjusted consumption, 10% for real wealth and 25% for each of the remaining

dimensions. Similarly, with regard to equity from a Rawlsian point of view, it is possible to

dedicate more attention to poverty than to inequality, with the resulting changes in the

weightings.

It must be borne in mind that a greater magnitude of ‘‘adjusted consumption’’ or of ‘‘real

wealth’’ represents greater well-being, while the opposite occurs with the other two

components. That is to say, the greater the value of ‘‘adjusted consumption’’ or of ‘‘real

wealth’’, and the lower the value of ‘‘equity’’ and ‘‘economic security’’, the greater will be

the well-being index obtained for the region.

Table 1 Structure of the well-being index

Structure of the economic well-being index for the CC.AA.

Dimensions Indicatorsa Variables

1.-Adjusted consumption 1.1.-Adjusted privateconsumption

1.1.1.-Equivalent adjusted monetaryexpenditureb

1.2.-Adjusted publicconsumption

1.1.2.-Equivalent adjusted non-monetaryexpenditureb

1.3.-(-) Hours worked yearlyper worker

1.1.3.-Life expectancy index

1.2.1.-Total public consumption per capita

1.3.1.-(-)Hours worked yearly per worker

2.-Real wealth—intergenerational equity

2.1.-Physical capital 2.1.1-Net capital stock p.c.

2.2.-Human capital 2.2.1-Rate of postgraduates/population

2.3.-R&D 2.3.1-Expenditure on R&D p.c.

2.4.- Environment 2.4.1-Company expenditure onenvironmental protection

3.-Equity 3.1.-(-) Gini index 3.1.1.-(-) Gini indexb

3.2.-(-) Poverty index 3.2.1.-(-) FGT 1 indexb

4.-Economic security 4.1.-(-) Risk of illness 4.1.1.-(-) % expenditure on health

4.2.-(-) Risk of over 65poverty

4.2.1.-(-) Poverty rate over 65sb

4.3.-(-) Risk ofunemployment

4.3.1.-(-) Unemployment rate

4.3.2.-Unemployment benefit coverage

a The minus sign in brackets before indicators means that a negative relation with the well-being index isassumedb Adjusted by the purchasing power parities provided by Alcaide and Alcaide (2008)

11 Our study also calculates the weightings using other methodologies (factorial analysis and efficiencyanalysis), to eliminate the arbitrariness which the exogenous application of the weightings may involve.


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That is, for example we have used four variables for constructing the dimension ‘‘Eco-

nomic Security’’. We put a positive sign in the variables ‘‘health expenditure’’, ‘‘poverty rate

over 65s’’ and ‘‘unemployment rate’’, and we put a negative sign in the variable ‘‘unem-

ployment benefit coverage’’. Then we added the four adjusted values (rescaled at the interval

[0,1]) with the mentioned signs. Finally, we put a negative sign to the whole dimension to

calculate the well-being index. Therefore, we are assuming that ‘‘health expenditure’’,

‘‘poverty rate over 65s’’ and ‘‘unemployment rate’’ has an obvious negative effect on the

well-being index while ‘‘unemployment benefit coverage’’ has the opposite effect.

In the case of the dimension ‘‘Equity’’, the procedure is the equivalent of that. We put

positive signs in the variables ‘‘Gini index’’ and ‘‘FGT1 index’’ but the whole dimension

has a negative sign.

2.2 Estimation of the Well-Being Index by Factor Analysis

An alternative methodology to that proposed above consists of the construction of an

indicator of the level of well-being of the distinct Autonomous Communities using mul-

tivariate statistical techniques. In the specialised literature, such models are known as latent

variable models, and are differentiated by the measurement scale of the observed variables

and that assumed for the non-observed variable, as Table 2 shows.

When constructing a metric well-being index based on variables of the same type, factor

analysis is the technique selected for the estimation. It is very similar to the standard

regression model, with the sole difference that some of its variables are unknown. Since it

is impossible to establish their value, this relationship is analysed indirectly.

Let p denote the observed variables and q the latent factors or variables. Thus, the

general model is expressed as:

xi ¼ ai0 þ ai1y1 þ ai2y2 þ � � � þ aiqyq þ ei; i ¼ 1; . . .; p ð2Þ

where y1, y2, …,yq are the factors, ei the residuals and ai0, ai1, …,aiq the factor loads. From

among the assumptions of the model, it should be emphasised that the factors are estimated

as standardised variables,12 i.e. with zero mean and unitary variance. Generally, when

applying this analysis the number of underlying factors is unknown. To decide the structure

of the factors it is necessary to examine the proportion of the variance they each explain.13

However, while Eq. 2 expresses the observed variables as linear combinations of the

factors, the objective of this study involves the inversion of this relationship, that is to say

the expression of the factors as linear combinations of the observed variables.

It can be demonstrated that Eq. 2 can be transformed into another model, given in

expression (3).14

yi ¼ ci1x1 þ ci2x2 þ � � � þ cipxp; i ¼ 1; . . .; q ð3Þ

This system of equations permits the estimation of well-being based on the information

contained in the set of variables selected. Before presenting the results, some comments

must be made regarding the application performed. Firstly, as the different dimensions of

12 Similarly, the indicators have been standardised to eliminate the possible effects of the distinct units ofmeasurement units.13 A common criterion in the literature consists of revising the eigenvalues of the correlation matrix andselecting those components whose eigenvalue is greater than one.14 Although the punctuations cij must be estimated, if the principal components model is chosen to extractthe factors (as in our case), the punctuations c are related with the coefficients a of Eq. 2.


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well-being have been established previously based on economic theory, it is not necessary

to explore further and decide how many factors exist. Additionally, in order to avoid

possible interference from some variables in other dimensions different to those to which

they are assigned, a dual process of estimation is undertaken:15 firstly, an index for each

dimension and, secondly, the joint well-being index from these indices.

Adjusted consumption = 0.3293*AdjPubCon + 0.3257*AdjMonExp

þ 0:4547 � AdjNonMonExp � 0.2719*HoursWork

Real Wealth = 0.3863*R&D Exp + 0.2757*Phys Cap + 0.3714*Human Cap

þ 0:2034 � Env Exp ð4ÞEquity = 0.5516*FGT1 + 0.5516*Gini

Security ¼� 0:0059 � Health + 0.1813*Pop over 65 + 0.5201*Unempl

� 0:5060 � Unemp Cov

Having estimated the partial indicators, the next step is to determine the model that permits

us to calculate the index of well-being for each of the regions, as shown by the following

expression.

Well-being = 0:3655 � Adjusted consumptionþ 0:4044 �Wealth � 0:2273

� Equity � 0:3129 � Security ð5Þ

Since a different method has been used, the coefficients of the model are not directly

comparable with the weightings proposed in the previous section.16 Nevertheless, the

analysis of their signs and values provides information concerning the relative importance

of each of the aspects considered. Thus, it is demonstrated that factors such as real wealth

or adjusted consumption are of great importance in the economic well-being of the Spanish

regions. This divergence between the relative importance of each indicator, depending on

whether use is made of the uniform weightings determined a priori or those estimated by

statistical analysis, may facilitate a sensitivity analysis of the uniform weightings. On this

point, the data appear to contradict the alternative proposal made by Osberg and Sharpe,

consisting of increasing the weight of adjusted consumption and reducing that of real

wealth.

These disparities with regard to the uniform distribution of weights are greater, and

more interesting, within each dimension. For example, R&D expenditure or the stock of

human capital are the most important indicators within the most significant dimension,

Table 2 Latent variable models

Observed variables

Latent variables Continuous Categorical

Continuous Factor analysis Latent feature models

Categorical Latent profile models Latent class models

Source Bartholomew et al. (2002)

15 It must be underlined that what is determined is not a structure of weightings, but instead the effect ofeach variable upon the factor.16 It can be shown that the coefficients of Eq. 5 do not sum to unity.


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‘‘real wealth’’. They are assumed to be, therefore, two key factors in the explanation of

regional differences in economic well-being.

2.3 Estimation by Efficiency Analysis

Efficiency analysis has principally been employed in the analysis of the production

function, to estimate how productive units maximise their output from a set of inputs or,

alternatively, how they minimise the inputs used for a set of outputs. There exist few

applications of this technique to the study of well-being or the standard of living, although

among the studies present in the literature mention should be made of Lovell et al. (1994),

Ramos and Silber (2005) or Ramos (2008). In contrast to these articles, in which para-

metric distance functions are employed to determine the weights of each indicator and to

determine the joint index of well-being, the present study uses the method of Data

Envelopment Analysis (DEA) to summarise the information contained in the indicators, to

calculate the weightings for each variable and, finally, to estimate the well-being index.

DEA was proposed by Charnes et al. (1978)17 to obtain an envelopment formed by all

the efficient units and leaving the remaining units under it. The measurement of efficiency

provided by DEA is relative, because each unit is compared with the rest. Consequently,

the data available determine the form and situation of the production boundary. To obtain

this envelopment, it is necessary to resolve a problem of mathematical optimisation for

each unit (in this case, Autonomous Community). The solution of this problem permits an

efficiency index to be assigned to them.

Confronting this problem as intuitively as possible, it is possible to formulate a frac-

tional programme, in which a maximisation or minimisation is performed (oriented to

output or oriented to input) of a total productivity ratio for each unit evaluated:18

Max h0ðu; vÞ ¼Ps

r¼1 uryr0Pmi¼1 vixi0

under

Psr¼1 uryrjPmi¼1 vixij

� 1; vi; ur � 0

j ¼ 1; . . .; n r ¼ 1; . . .; s i ¼ 1; . . .;m

ð6Þ

where h0 is the measure of efficiency of unit 0, yr0 is the quantity of output produced by the

unit, xi0 is the quantity of input i used by the unit, yrj; xij are the outputs and inputs of unit j

and vi; ur � 0 are the weightings determined by the solution to the problem.

This problem may be transformed into a problem of linear programming in order to

resolve it better. To achieve this, it is sufficient to maximise the numerator of the objective

function while keeping the denominator constant:

Max h0ðuÞ ¼Xs

r¼1

uryr0

underXm

i¼1

vixi0 ¼1;Xs

r¼1

uryrj �Xm

i¼1

vixij� 0; vi; ur � 0

j ¼ 1; . . .; n r ¼ 1; . . .; s i ¼ 1; . . .;m

ð7Þ

The linear programme selects the weights which maximise the virtual output of the unit

17 This model is named CCR, after the names of its authors.18 The problem oriented to output only presents itself when using this formulation in the empiricalapplication.


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ðuryr0Þ, given a unitary virtual input ðvixi0Þ. Furthermore, the virtual output can never

exceed the virtual input. Nevertheless, it is easier to calculate the efficiency indices if the

dual programme is used:

Max h0

underXn

j¼1

kjyrj� hyr0;Xn

j¼1

kjxij� xi0;Xn

j¼1

eij� xi0; kj� 0

j ¼ 1; . . .; n r ¼ 1; . . .; s i ¼ 1; . . .;m

ð8Þ

where eij is a vector comprised of ones.

3 Economic Well-Being Indices for the Year 2000

3.1 Results from the Application of Uniform Weightings

Observing the overall well-being index (Table 3), there are clearly two regions at the top

(Navarre and the Basque Country) and three at the bottom (Extremadura, Andalusia and

the Canary Islands). However, attending to the dispersion (mean ± standard deviation), it

is possible to create three groups of regions. In the group number 1 (well-being index over

mean ? s.d.) the Basque Country, Navarre, Madrid and Catalonia are, in the group number

2 (well-being index between mean - s.d. and mean ? s.d.) Castile-La Mancha, Balearic

Islands, Aragon, Asturias, La Rioja, Valencian Community, Castile and Leon, Murcia,

Galicia, Cantabria and Canary Islands are; and, finally, in the group number 3 (well-being

index under mean - s.d.) Andalusia and Extremadura are included.

Table 4 shows the values of the four components of the well-being index. It must be

remembered that a greater magnitude of ‘‘adjusted consumption’’ or of ‘‘real wealth’’

represents greater well-being, while the opposite occurs with the other two components. In

Table 3 Well-being index 2000PPP

Source Authors’ elaboration.Ranks appear in brackets

CC.AA Well-being

Andalusia (16) -0.2919

Aragon (7) 0.0044

Asturias (8) -0.0392

Balearic Islands (6) 0.0207

Basque Country (1) 0.2302

Canary Islands (15) -0.1878

Cantabria (14) -0.1701

Castile and Leon (11) -0.0875

Castile-La Mancha (5) 0.0306

Catalonia (4) 0.1219

Extremadura (17) -0.3055

Galicia (13) -0.1097

Madrid (3) 0.1504

Murcia (12) -0.0984

Navarre (2) 0.1744

Rioja (9) -0.0397

Valencian community (10) -0.0444


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other words, the greater the value of ‘‘adjusted consumption’’ or ‘‘real wealth’’, and the

lower that of ‘‘equity’’ and ‘‘economic security’’, the greater will be the index of well-being

obtained by that region. Following the same logic, negative values of ‘‘economic security’’

(because of high relative values in unemployment coverage) increase it.

Table 4 Components ofwell-being index 2000 PPP(uniform weightings)

Source Authors’ elaboration

CC.AA Adjustedconsumption

Realwealth

Equity Economicsecurity

Andalusia 0.1833 0.1409 0.9410 0.5512

Aragon 0.3994 0.334 0.6908 0.0783

Asturias 0.1284 0.2887 0.4703 0.1268

Balearic Islands 0.1625 0.2307 0.3922 -0.0408

Basque Country 0.5913 0.2443 0.1532 0.1926

Canary Islands 0.3836 0.3602 0.9291 0.3198

Cantabria 0.2391 0.3548 0.8572 0.3055

Castile and Leon 0.2940 0.4123 0.7080 0.2685

Castile-La Mancha 0.0445 0.2993 0.0000 0.1334

Catalonia 0.3684 0.1151 0.3271 0.1089

Extremadura 0.0452 0.2032 0.6922 0.5878

Galicia 0.0297 0.3522 0.3745 0.2408

Madrid 0.5998 0.2234 0.5508 0.1918

Murcia 0.1251 0.1607 0.4126 0.3750

Navarre 0.4228 0.3514 0.2032 0.0619

Rioja 0.2802 0.2866 0.4065 0.3725

Valencian community 0.0578 0.1433 0.4222 0.1764

Table 5 Well-being indexcomponents 2000 PPP(factor analysis weightings)


CC.AA Adjustedconsumption

Realwealth


Andalusia -0.4682 -0.8562 1.6905 1.9279

Aragon 0.7496 0.1545 0.7301 -0.6474

Asturias -0.6798 -0.2253 -0.1125 0.3020

Balearic Islands -0.4027 -0.4242 -0.4256 -1.9025

Basque Country 1.7455 1.6064 -1.3302 0.1546

Canary Islands 0.5566 -0.9665 1.6061 -0.4426

Cantabria -0.0508 -0.5436 1.3435 0.5681

Castile and Leon 0.0876 -0.0778 0.8087 0.5265

Castile-La Mancha -1.1614 -0.7176 -1.9469 -0.1579

Catalonia 0.5729 1.0601 -0.6253 -0.7860

Extremadura -1.4135 -1.4566 0.6841 2.1546

Galicia -1.0499 -0.8837 -0.4767 0.1060

Madrid 2.1674 2.5691 0.2655 0.0106

Murcia -0.8217 -0.3135 -0.4341 0.4470

Navarre 1.0399 0.9735 -1.1182 -1.5974

Rioja 0.1197 0.0105 -0.3746 -0.5135

Valencian community -0.9909 0.0910 -0.2845 -0.1499


123

In the case of the Basque Country, its extremely high adjusted consumption, equalled

only by Madrid, together with the best data regarding equity after Castile-La Mancha,

launches it to top position because of a regional per capita budget far above the values of

the remaining Communities. It must be underlined that Navarre and the Basque Country

have in force systems of Economic Contract and Economic Agreement, respectively,

which grant great financial and fiscal autonomy to the Foral Authorities. They manage the

greater part of taxes and contribute to general State revenue for the competencies not

assumed, via the payment of a quota or contribution established in the Contract/Agreement

with the State.

Third on the economic well-being index is Madrid. In this region, the highest values in

Spain for expenditure (monetary and non-monetary), expenditure on R&D, and human

capital are softened by lower than average values regarding environmental expenditure per

capita and, above all, regarding inequality, where it occupies the penultimate position.

Extremadura, Andalusia and the Canary Islands occupy the three lowest positions, using

practically whatever methodological option. The very high figures for inequity in Anda-

lusia and the Canaries and the low level of consumption and wealth in Extremadura are the

principal determinants of the lowest positions of these three Communities.

As explained in the introduction, the indicator most commonly employed to quantify

standards of living or well-being in distinct territorial units has been GDP per capita or an

equivalent macromagnitude. Figure 1 compares the distribution produced by our multi-

dimensional well-being index and the ranking that would result from using GDP per capita

(transformed to a 0–1 scale for an easier analysis). Sharp differences are apparent in some

Communities, which in our view confirm the need to construct an index such as that

proposed here. There are notable differences shown by Castile-La Mancha, for its

important improvements in equity in recent years, or by cases to the contrary such as La

Rioja, the Canary Islands, Cantabria or the Balearic Islands.

3.2 Results of the Factor Analysis

Despite the fact that when examining the extremes of the dimensions we find, in general,

the same regions, a common pattern among the Autonomous Communities is hard to find.

Fig. 1 Well-being index and GDP per capita 2000. Source Authors’ elaboration


123

Concretely, Madrid, the Basque Country and Navarre show the most favourable situations

in ‘‘Adjusted consumption’’; Madrid, the Basque Country and Catalonia in ‘‘Real Wealth’’;

Castile-La Mancha is notable in ‘‘Equity’’, followed by the Basque Country and Navarre;

and in ‘‘Economic security’’ the top positions are occupied by the Balearic Islands, Navarre

and Catalonia. The previous statement is confirmed: there is no clear and unequivocal

distribution of the indicators among the Autonomous Communities (Table 5).

At the other extreme of the partial indices, the Canary Islands, Extremadura and

Andalusia are noteworthy as the territories worst situated in the majority of the dimensions

considered.

Extremadura is dragged down due to its levels of consumption and wealth, Andalusia by

its poor figures for equity and security and the Canary Islands by a negative combination of

low figures for wealth and high levels of poverty and inequality (Table 5).

Note should be made of the broad consistency of the results obtained when calculating

the well-being indices with uniform weightings and through factor analysis: two much

differentiated groups can be observed at the extremes of the distributions. Factor analysis

results show relative improvements for Madrid (which moves to top position) and Navarre

and a decline for Castile-La Mancha (Table 6).

On this point, it is essential to remember the divergences, although slight, between the

uniform weightings and the factor analysis methods: the relative importance of adjusted

consumption and real wealth, and within the latter, of expenditure on R&D and of human

capital is greater than that considered in the system of uniform weightings. Thus, in

contrast to the descriptive analysis of the latter system, factor analysis, both in its direct

application and the weightings derived from it, permits the determination of the most

important factors in reducing regional disparities in well-being, with their corresponding

implications for economic policy. In other words, investment in research and development

and improved human capital appear to be key instruments for regional development.

Table 6 Well-being index2000 PPP (factor analysis)


CC.AA Well-being

Andalusia (16) -1.5048

Aragon (6) 0.3731

Asturias (11) -0.4085


Basque Country(2) 1.5415

Canary Islands (12) -0.4139

Cantabria (15) -0.7215

Castile and Leon (10) -0.3480

Castile-La Mancha (9) -0.2227

Catalonia (4) 1.0262

Extremadura (17) -1.9354

Galicia (14) -0.6659

Madrid (1) 1.7674

Murcia (13) -0.4684

Navarre (3) 1.5277

Rioja (7) 0.2938

Valencian community (8) -0.2138


123

3.3 Application of the Data Envelopment Analysis

With the objective of reflecting the negative effect of certain variables (i.e. when certain

variables increase, well-being decreases), maintaining at the same time positive values in

them all, we undertake a change of variable, calculating its inverse following the practice

usually applied in the literature.

Although the weightings obtained using this technique vary for each variable and

region, thereby permitting the CC.AA. to emphasise their strong points, the results are very

similar to those previously obtained (Table 8).

With regard to the factor analysis, a decline in the Canary Islands and improvements in

Asturias and Castile-La Mancha are notable. Once more, real wealth proves to be the key

to the improvement of regional well-being (Table 7).

4 Evolution in the Period 2000–2006

The present section aims to fulfil two objectives, by including the calculation of indices for

the year 2006. Firstly, to attempt to confirm the robustness of the results obtained for the

year 2000 and, secondly, to appreciate certain tendencies, despite the short time period

involved.

Although we have constructed similar indicators for earlier years (1980), the method-

ological problems posed by the absence of certain data, the changes of sources and, above

all, the existence of a regional political map extremely diverse with regard to competen-

cies, discouraged us from working with observations prior to the year 2000.

Table 7 Well-being indexcomponents 2000 PPP (DEAanalysis)


CC.AA. Adjustedconsumption

Realwealth


Andalusia 90.73 51.7 68.24 63.54

Aragon 94.7 77.12 74.51 99.71

Asturias 87.13 69.27 81.07 100

Balearic Islands 90.52 39.89 83.73 100

Basque Country 100 100 92.84 85.51

Canary Islands 96.01 39.98 68.61 73.82

Cantabria 92.49 60.71 70.29 76.55

Castile and Leon 95.94 70.04 74 81.57

Castile-La Mancha 84.89 58.36 100 90.06

Catalonia 94.6 93.57 85.84 89.88

Extremadura 82.86 29.96 74.63 64.46

Galicia 85.52 53.19 84.28 79.8

Madrid 100 93.98 78.3 84.59

Murcia 86.8 67.68 83.37 71.45

Navarre 96.15 96.46 90.67 100

Rioja 91.84 72.93 83.25 77.17

Valencian community 87.61 74.77 82.61 86.15


123

Tables 9 and 10 show the components and indices for the year 2006 according to the

three methodologies previously used. Without being exhaustive, two points with regard to

the time trend should be noted.

Table 8 Well-being index2000 PPP (DEA analysis)


CC.AA. Well-being

Andalusia (16) 80.93

Aragon (6) 95.21

Asturias (7) 94.21


Basque Country (1) 100

Canary Islands (13) 81.28

Cantabria (15) 85.81

Castile and Leon (8) 90.69

Castile-La Mancha (4) 96.71

Catalonia (5) 96.12

Extremadura (17) 69.66

Galicia (14) 84.63

Madrid (3) 97.46

Murcia (11) 86.05

Navarre (1) 100

Rioja (9) 89.16

Valencian community (10) 88.76

Table 9 Well-being index 2006 PPP

CC.AA. Uniform weightings Factor analysis DEA analysis

Andalusia -0.3487 (17) -1.7224 (17) 81.73 (15)

Aragon 0.0454 (6) 0.5347 (5) 93.39 (7)

Asturias 0.0607 (5) 0.4342 (7) 97.02 (3)

Balearic Islands 0.0742 (4) 0.4378 (6) 89.82 (10)

Basque Country 0.1965 (2) 1.4281 (3) 98.94 (2)

Canary Islands -0.2237 (14) -1.0495 (14) 69.66 (17)

Cantabria 0.0328 (8) 0.3433 (8) 96.25 (4)

Castile and Leon 0.0353 (7) 0.3260 (9) 93.90 (6)

Castile-La Mancha -0.1743 (13) -0.8217 (13) 84.49 (13)

Catalonia 0.0067 (9) 0.6078 (4) 92.74 (8)

Extremadura -0.2852 (15) -1.4069 (15) 80.24 (16)

Galicia -0.1144 (11) -0.2700 (10) 88.02 (11)

Madrid 0.1355 (3) 1.5263 (2) 94.20 (5)

Murcia -0.3050 (16) -1.4171 (16) 83.39 (14)

Navarre 0.2435 (1) 1.7627 (1) 100.00 (1)

Rioja -0.0847 (10) -0.3058 (11) 89.87 (9)

Valencian community -0.1412 (12) -0.4076 (12) 87.10 (12)

Source Authors’ elaboration. Ranks appear in brackets


123

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123

– Strongly heterogeneous evolutions in the period: Regions which improve in 2006 can

be found using any of the methodologies (Asturias, Cantabria, Castile and Leon,

Extremadura, Galicia and Navarre), others decline using any of them (Castile-La

Mancha, Catalonia, the Canary Islands, the Valencian Community, Madrid, Murcia and

the Basque Country), and the sign of the four remaining regions changes with the

method employed.

– In general, although the use of various techniques may generate a degree of initial

confusion, it also helps to provide robustness to certain conclusions. One example is

that the group of regions19 with greatest well-being, independently of the technique

employed, is comprised of the Basque Country, Navarre and Madrid. One-step below is

Catalonia, slightly above a large mean group (the Balearic Islands, Castile-La Mancha,

Asturias, Aragon, Castile and Leon, the Valencian Community). At the bottom of the

classification are the Canary Islands, Andalusia, Murcia and, lastly, Extremadura. In

this last case, it should be noted that Extremadura, following the adjustment for PPP,

leaves the final position. This fact is due to the lowest relative prices in Spain allow it to

exceed in well-being Andalusia and Murcia or Canary Islands in 2006 (depending on

methodology).

In general, greater parallelism can be observed among the results from uniform

weightings and the application of DEA than between either of them and the factor analysis.

5 Conclusions

The present study offers an attempt to construct a multidimensional index of economic

well-being for the Spanish Autonomous Communities. Given the high degree of decen-

tralisation of the nation and the need to have available instruments for the evaluation and

Table 11 Groups of regions according well-being index 2006 PPP

Well-beinglevel

Uniform weightings Factor analysis DEA analysis

Low Andalusia, Canary Islands,Extremadura, Murcia

Andalusia, Canary Islands,Extremadura, Murcia

Andalusia, Canary Islands,Extremadura

Medium Asturias, Aragon, BalearicIslands, Castile and Leon,Castile-La Mancha,Catalonia, ValencianCommunity

Asturias, Aragon, BalearicIslands, Castile and Leon,Castile-La Mancha,Catalonia, ValencianCommunity

Asturias, Aragon, BalearicIslands, Castile and Leon,Castile-La Mancha,Catalonia, Madrid, Murcia,Valencian Community

High Basque Country, Madrid andNavarre

Basque Country, Madrid andNavarre

Basque Country and Navarre


19 In Table 11, regions are classified according to their relative well-being levels according to the previouscriteria: low class is defined as well-being index under mean - s.d., high class as well-being index overmean ? s.d. and medium class contains the remaining cases (well-being index between mean – s.d. andmean ? s.d.).


123

tracking of national public policies, we believe it interesting to be able to evaluate and

compare the effects of such policies upon the well-being of citizens.

When it comes to measuring this well-being, we have attempted to overcome the

limitations of the most commonly used indicator, Gross Domestic Product per capita, by

adding factors such as the aggregate accumulation of productive stocks and the hetero-

geneity of individuals, both in the present (the distribution of potential consumption, that is

to say poverty and inequality) and the future (taking into consideration the insecurity of

future income).

In the construction of economic well-being indices for the comparison of territorial

units, there are two aspects in which arbitrariness is unavoidable: on one hand, in the

selection of the multidimensional indicators chosen to configure the index, and on the

other, in the way in which these indicators are weighted. In the first case, we have

attempted to reduce this arbitrariness by basing ourselves on a dimensional structure

created by Osberg and Sharpe and internationally recognised by many prestigious publi-

cations. In the second case, the use of three different, and we believe adequate, method-

ologies permits the results to be strengthened, although it limits the possibility of obtaining

a large number of quantifiable conclusions.

The empirical application of the methodologies proposed reveals great differences in the

national panorama. It can be observed that two groups appear at the extremes of the

distribution of the aggregate index, and this is repeated in the majority of the dimensions

considered.

Navarre, the Basque Country, Madrid and, at a certain distance, Catalonia, are notable

in the leading group, while Extremadura, Andalusia and the Canary Islands display the

worst results. When attempting to minimise arbitrariness in the weighting of variables by

using three different weighting systems, there appear changes of a certain importance for

some regions; however, the principal features of the regional ranking of well-being are

maintained, with few exceptions.

To conclude, we would like to make some comments regarding possible extensions of

this study. It would be useful to collect certain additional variables, such as hours of leisure

(or to adjust consumption by such hours), expenditure derived from travelling to work and

the level of durable goods, and better data for human and social capital, as well as adding

to the regional budget the expenditure of the regionalised Central Administration or some

information on the minimum incomes existing in each Autonomous Community. Presently,

the restricted availability of data is the principal obstacle to the majority of such advances.

We are aware that the construction of an index of this type will always be improvable

and permanently exposed to criticisms, which aim to contribute ideas. Nevertheless, we

consider that its arbitrary construction and considerable data restrictions in the regional

ambit must not discourage research aimed at filling, even partially, a lacuna of increasing

interest.

Acknonwledgments The authors would like to thank the Extremadura Government (Junta de Extrema-dura PRI08A137) and European Union Funds FEDER for the funding they have received. They are verygrateful for the useful referees’ comments.

Annex 1: A Brief Introduction to the Political Division in Spain

An autonomous community (A.C.) is the first-level political division of the Kingdom of

Spain, established in accordance with the Spanish Constitution. The Central Government

and 17 autonomous communities share political power in Spain. There are also two


123

autonomous cities, Ceuta and Melilla, situated in the African continent, though the lack of

significance of its samples and its particular social and economic situation make difficult to

include them in Spanish regional studies. We have decided, like most of the Spanish

regional researchers, not to include these two autonomous cities in this analysis.

Since 1978, a wide and fast decentralization process has been developed from the

Central Government to the Regional Authorities. Nowadays, almost all the policies have

been transferred to them, excepting some common areas as foreign policy, national

defense, pensions or the main fiscal taxes as VAT or Corporation Tax (the income tax is

divided into a national and regional shares). Moreover, Regional Governments and Par-

liaments are the main subjects in issues as education, health, culture, housing or social

exclusion.

Although, this decentralization has improved the efficiency of the regional spending in

the sense of a better knowledge of the people’s preferences, different problems related to

cohesion and solidarity between regions are becoming discussion topics.

The main characteristics of the Spanish autonomous communities are shown in

Table 12.

Table 12 Main characteristics of Spanish regions

GDP perhead2006 (%)

Unemploymentrate (%)2006

Activityrate2006

Population1-1-2007

%pop.(%)

Immigrants2007

% immigrant(%)

Andalucıa 77.5 12.68 55.32 8059.5 17.8 555.8 6.9

Aragon 107.2 5.54 56.59 1296.7 2.9 110.0 8.5

Asturias 90.5 9.31 49.85 1074.9 2.4 48.1 4.5

Balearic Islands 109.9 6.46 64.11 1030.7 2.3 180.4 17.5

Basque Country 128.5 6.97 58.07 2141.9 4.7 100.7 4.7

Canary Islands 89.2 11.68 61.02 2026.0 4.5 276.8 13.7

Cantabria 98.8 6.56 55.32 572.8 1.3 30.1 5.2

Castile and Leon 95.1 8.11 53.09 2528.4 5.6 121.8 4.8

Castile-LaMancha

77.7 8.81 55.03 1977.3 4.4 135.8 6.9

Catalonia 118.0 6.6 62.17 7210.5 16.0 923.2 12.8

Extremadura 67.9 13.43 51.58 1090.0 2.4 27.9 2.6

Galicia 82.9 8.48 53.61 2772.5 6.1 152.4 5.5

Madrid 130.7 6.37 63.57 6081.7 13.5 882.3 14.5

Murcia 83.6 7.85 58.98 1392.1 3.1 184.5 13.3

Navarre 125.5 5.3 60.67 605.9 1.3 51.1 8.4

Rioja 107.1 6.18 59.48 309.0 0.7 34.8 11.3

ValencianCommunity

91.7 8.37 59.62 4885.0 10.8 691.3 14.2

Ceuta(auton. city)

91.1 20.96 52.79 76.6 0.2 6.5 8.5

Melilla(auton. city)

90.4 13.38 52.5 69.4 0.2 13.2 19.1

Total Spain 100.0 8.51 58.32 45200.7 100.0 4526.5 10.0

Source INE (Spanish National Statistical Institute). Population and inmigrants are in thousands


123

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http://www.stiglitz-sen-fitoussi.fr/documents/rapport_anglais.pdf

http://www.stiglitz-sen-fitoussi.fr/documents/rapport_anglais.pdf

http://hdr.undp.org/en/media/hdr04_complete.pdf

construction and evolution of a multidimensional well-being index for the spanish regions

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