Antonio Morillas

A Fuzzy clustering approach to the key sectors of the Spanish economy

Abstract The search for key sectors in an economy has been and still is one of the more recurrent themes in input–output analysis. When using clustering techniques, sectors can only belong to a group, having a particular performance. But, actually, the same sector could be important from different perspectives at the same time, to a different degree. So, a fuzzy clustering approach is needed. In this work we propose a multidimensional approach to classify the productive sectors of the Spanish input–output table for 1995, based on three groups of variables: those related to their productive integration, others measuring their specific weight in the economy and finally some showing their economic dynamic. We also incorporate into the analysis the technological level, which being a categorical variable presents special methodological problems. All these questions are tackled applying a robust and fuzzy clustering analysis, which gives as a result a classification of sectors illustrating the role that each one plays in the Spanish economy.

Key Sectors, Industrial Clustering and Multivariate Outliers

Abstract In this paper a reflection is made on the problems that can arise in key sector analysis and industrial clustering, due to the usual presence of outliers when using multidimensional data related to the sectors in an input–output table. Multidimensional outliers are considered as being not only linked to the low number of clusters usually observed in this kind of study, but probably causing invalid results in most of the works involving multivariate statistical techniques, such as cluster and factor analysis. Actually, by comparing the key sectors of the Spanish economy obtained in Díaz et al. (2006) to the ones we get taking into account the problem the outliers pose, one can realize they greatly distort the results. On the other hand, it is shown that identification of outliers can be considered as a good and new procedure to help select the most important sectors in an economy.

I-O COEFFICIENTS IMPORTANCE: A FUZZY LOGIC APPROACH

In inter-industry studies, the technical coefficients have been analyzed with different methods in order to recognize those coefficients that can be considered to be important for an economy. Many critics have been posed to the procedures, the most remarkable one being their lack of connectivity with the values of the absolute flows behind the coefficients. In our approach, we define the importance of a technical coefficient as a fuzzy concept, and the grade of importance takes into account those absolute flows. This grade can be considered as a membership function, which is used to define a fuzzy graph associated to the I-O matrix. We apply this new procedure to the Spanish 2000 I-O matrix and compare our results to those reached by classical methods.

Some Experiences Applying Fuzzy Logic to Economics

Economy becomes a field of special interest for the application of fuzzy logic. Here we present some works carried out in this direction, highlighting their advantages and also some of the difficulties encountered. Fuzzy inference systems are very useful for Economic Modelling. The use of a rule system defines the underlying economic theory, and allows extracting inferences and predictions. We applied them to modelling and prediction of waged-earning employment in Spain, with Jang’s algorithm (ANFIS) for the period 1977-1998.

Robust Statistics and Fuzzy Industrial Clustering

The search for groups of important sectors in an economy has been and still is one of the more recurrent themes in input-output analysis. But a sector can probably be important for some questions at the same time, to a different degree. In this direction, a multidimensional fuzzy clustering analysis gives as a result a classification of sectors illustrating the different roles that each one plays in the economy. But multivariate outliers, witch have not been studied in the literature in previous applications of clustering techniques to input-output studies, have even worst effects in clustering than the univariate ones, due to their influence on the correlation matrices, and because their presence can mask the real clusters. We will show how fuzzy clustering and robust statistics should work together in this kind of studies, so the clustering can benefit from the use of robust statistics in data preparation, identification and computation of dissimilarities or deciding the best number of clusters and specially avoiding the dangerous effects coming from the presence of multivariate outliers.