Analysis of Socio-Economic Conditions

Insights from a Fuzzy Multi-dimensional Approach

Gianni Betti, Achille Lemmi, Gianni Betti, Achille Lemmi

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000363548
• Edition: 1
• Topic: Economics
• Subtopic: Economic Conditions
• Index: Economics

Showcasing fuzzy set theory, this book highlights the enormous potential of fuzzy logic in helping to analyse the complexity of a wide range of socio-economic patterns and behaviour.

The contributions to this volume explore the most up-to-date fuzzy-set methods for the measurement of socio-economic phenomena in a multidimensional and/or dynamic perspective. Thus far, fuzzy-set theory has primarily been utilised in the social sciences in the field of poverty measurement. These chapters examine the latest work in this area, while also exploring further applications including social exclusion, the labour market, educational mismatch, sustainability, quality of life and violence against women. The authors demonstrate that real-world situations are often characterised by imprecision, uncertainty and vagueness, which cannot be properly described by the classical set theory which uses a simple true–false binary logic. By contrast, fuzzy-set theory has been shown to be a powerful tool for describing the multidimensionality and complexity of social phenomena.

This book will be of significant interest to economists, statisticians and sociologists utilising quantitative methods to explore socio-economic phenomena.

1 A Book in Honour of Professor Vijay Verma

Gianni Betti and Achille Lemmi

This is the fourth book edited by Gianni Betti and Achille Lemmi; it ­contains a balance between theoretical/methodological and empirical chapters prepared by a group of contributors who are a mix of luminaries in socio-economic fields (Jacques Silber, Vijay Verma, Francesca Bettio, Stephan Mussard, Monica Pratesi, María Noel Pi-Alperin, Tomasz Panek, among others) and a group of young and very promising researchers.

In the first of the three previous books they co-edited, Betti and Lemmi assembled advanced thinking about the multi-dimensional measurement of poverty, including the theoretical background, applications to cross-sections and longitudinal aspects of multi-dimensional fuzzy poverty analysis, with particular attention to the transitory, or temporary, conditions that often occur during transitions to a market economy (Lemmi and Betti, 2006a).

Next, Betti and Lemmi (2008a) collected an impressive set of contributions that emerged from the conference in Certosa di Pontignano in May 2005 in honour of two social scientists at the turn of the twentieth century: C. Gini and M. O. Lorenz. In particular, the main themes that Betti and Lemmi (2008b) presented in this second book were related to: innovation in the theory and methods on income inequality and concentration analysis, decomposition of inequality and empirical applications in applied economic analysis worldwide. These research themes are a consistent and relevant part of the recent economic, econometric and statistical methods and applications in the international academic literature.

Finally, in the third book, Betti and Lemmi (2013a) proposed an up-to-date and innovative survey of new methods for estimating poverty at the local level, as well as the most recent multi-dimensional methods used to examine the dynamics of poverty (Betti and Lemmi, 2013b). They argued that the most useful measures of poverty and inequality for policymakers and researchers are finely disaggregated into small geographic units. This volume was the first attempt to compile the most recent research results about local estimates of multi-dimensional deprivation (Betti and Lemmi, 2013c).

This collection is dedicated to the memory of Professor Vijay Verma, who passed away in September 2018, and also contains his new research in Chapter 7 on the jack-knife repeated replication technique for variance estimates of fuzzy poverty measures, with a foreword from his wife, Gillian Verma.

Verma greatly contributed to the development of the fuzzy, multi-dimensional and longitudinal approach to poverty measurement; his original ideas and suggestions have inspired many researchers over the past two decades. Directly or indirectly, his ideas are found in most of the chapters in this book.

The relationship between Vijay Verma and this volume’s editors evolved from purely academic links to a strong and long-lasting friendship, with common respect and trust. These common interests, in terms of research and a lust for life, drove Vijay to move from London to Siena in 2002; a few years later, Gillian joined Vijay, and they became fully ‘Sienese’.

In the early 1990s, Lemmi presented the then-brand-new fuzzy approach to poverty measurement at a Eurostat meeting on official poverty in Stockholm, which had previously been discussed at the Italian National Institute of Statistics (Istat), accompanied by the Istat researchers Giuliana Coccia and Mauro Masselli. After the presentation, Achille desperately looked for a place to smoke a cigarette, finding an open space where a nice-looking bearded gentleman was puffing on his cigarette. Achille joined him, and they started to discuss the presentation and the new and interesting idea of fuzzy versus Boolean states. ‘The bearded gentleman’ offered Achille congratulations on both the presentation and the new ideas in it. Afterwards, Achille returned to Mauro, who exclaimed enthusiastically in Roman dialect: ‘Anvedi! Avemo fatto un figurone! [Wow, we made a good impression!]. Do you know who he is? He is Vijay Verma, the father of ECHP [European Community Household Panel survey]’.

On that day, a fruitful collaboration began, under the direction of David Rose based at the Institute for Social and Economic Research (ISER) at the University of Essex, where several researchers from the University of Siena – Giulio Ghellini, Bruno Cheli, Nicoletta Pannuzi and Gianni Betti – later spent some months working with Vijay, under the supervision of Achille. This first collaboration ended with the first two seminal papers on the fuzzy-set approach to poverty measurement: Cheli et al. (1994) and Cheli and Lemmi (1995).

Gianni Betti first met Vijay Verma during the lectures that he delivered as part of the PhD course in applied statistics at the University of Florence during the academic year 1996–1997. Later, in November 1997, Gianni joined the ISER at the University of Essex, where Vijay was reproducing the British Household Panel Survey as the British ECHP. Vijay supervised Gianni in the calculation of special weights to be used in a pseudo-panel for estimating longitudinal equivalence scales (Betti, 1998), which became the basis for a collaboration to estimate the aggregated weights in the multi-dimensional and fuzzy approach. In the spring of 1998, Vijay and Gianni spent many mornings in Wivenhoe Park, one of the ‘squares’ at Essex University, defining the prevalence-correlation weights, first published in Betti and Verma (1998) and later presented at the sixth Islamic Countries Conference on Statistical Sciences in Lahore, Pakistan (Betti and Verma, 1999). Nearly a decade later, the paper was finally published, with some improvements, as Betti and Verma (2008).

The present collection gathers chapters of very high academic quality on multi-dimensional indices in the social sciences. Over the past three decades, several methodological studies in these fields have been developed, especially on poverty measurement, and multi-dimensional indices have recently become a key research topic in other fields, such as marital disruption, sustainability, violence against women, educational mismatch and quality of life. Most noteworthy is the use of fuzzy logic in these works. Fuzzy-set theory has been shown to be a powerful tool for describing the multi-dimensionality and complexity of social phenomena, replacing the classical crisp approach, which generally tends to overestimate or underestimate social dynamics.

Fuzzy-set theory, introduced by Zadeh in 1965, emerged in response to evidence that real situations are often characterised by imprecision, uncertainty and vagueness and cannot be described properly with the classical set theory, which represents reality with a simple true–false binary logic. Indeed, in the classical crisp approach, sets are characterised by sharp and clearly defined boundaries; thus, an item might fully belong or not belong at all to a set according to a bivalent condition. By contrast, in fuzzy-set theory, an item can belong to a set with partial degrees of membership between 0 and 1, not only with the extreme values.

For all these reasons, the objective of this collection is to explore the most up-to-date fuzzy-set methods for the measurement of socio-economic phenomena from a multi-dimensional and/or dynamic perspective. The chapters were selected based on three criteria: scientific quality, their ability to represent the leading paths in current scientific research, and the existence of a sort of scientific ‘file rouge’ among the contributions in order to present a homogeneous, useful and updated group of discussions.

We invited the most authoritative researchers worldwide to submit high-quality original research and surveys as chapters on the fuzzy measurement of socio-economic phenomena. The main themes are related in particular to descriptions of the evolution and recent research findings on multi-dimensional fuzzy poverty and social exclusion (Part 1, consisting of Chapters 2–7), the extension of the fuzzy multi-dimensional method to measuring the quality of life (QoL; Part 2, comprising Chapters 8–13), and the extension of the methods to specific social science fields, such as the labour market, educational mismatch, sustainability, industrial processes and violence against women (Part 3, made up of Chapters 14–20).

After this introduction, in Chapter 2, Bruno Cheli, Achille Lemmi, Nicoletta Pannuzi and Andrea Regoli describe the ‘Evolution of the Fuzzy-Set Approach to Multi-Dimensional Poverty Measurement’. The relevant key points in the chapter, which are preliminary to any discussion of the methods used for a multi-dimensional analysis of poverty, are the selection of the relevant dimensions and the indicators used to measure people’s achievements in these dimensions. They also mention the related issue of the choice of deprivation thresholds and the weights assigned to each dimension, but they do not discuss them in a full way as done in Betti et al. (2008). Rather, they simply state that the binary distinction between a ‘bad state’ and a ‘good state’ is too sharp because deprivation is likely to occur in degrees. Beginning with this consideration, they retrace and update the fuzzy-set approach (Zadeh, 1965) for measuring multi-dimensional poverty, which leads to the integrated fuzzy and relative method. This chapter is not only the basic reference point for the remaining chapters in the first section but also a starting point in the development of a fuzzy approach to the measurement of any phenomenon in the social sciences.

Chapter 3, by José Espinoza-Delgado and Jacques Silber on ‘Using Rippin’s Approach to Estimate Multi-Dimensional Poverty in Central America’, describes the mainstream approach to the measurement of multi-dimensional poverty in developing countries, which is insensitive to inequality among the poor and also overlooks intra-household inequality. Consequently, the authors of this chapter propose a departure from the mainstream approach and take an individual-based and inequality-sensitive view of multi-dimensional poverty when only dichotomised variables are available. They estimate multi-dimensional poverty among individuals between the ages of 18 and 59 living in Guatemala, El Salvador, Honduras, Nicaragua and Costa Rica. Overall, the most interesting finding is that people in Guatemala have the highest potential for multi-dimensional poverty, followed by those in Nicaragua; people in Costa Rica, by contrast, have by far the lowest probability of being poor. Honduras and El Salvador are in the middle, with Hondurans having a larger probability of multi-dimensional poverty than Salvadorans.

Chapter 4 analyses the measurement of poverty using the framework of the 2030 UN Agenda for Sustainable Development, in which one of the most important goals is to ‘eradicate poverty, in all its forms and dimensions’. This has been particularly necessary since 2008, when the global financial crisis started, and 2015, with the failure to achieve the millennium development goal of halving extreme poverty in the world. The chapter authors, Gianni Betti, Federico Crescenzi and Francesca Gagliardi, respond to the question ‘Can a neighbouring region influence poverty?’ using a fuzzy and longitudinal approach. They also discuss the adoption of a longitudinal measure proposed by Verma et al. (2017), which is based on the fuzzy-set approach to multi-dimensional poverty: the ‘fuzzy at-persistent-risk-of-poverty rate’. Then they estimate this measure at the regional level with small area estimation techniques by introducing a spatial correlation model. In this way, the approach takes into account whether a neighbouring region can influence poverty in all its forms and dimensions: the multi-dimensional dimension, the regional dimension and the longitudinal dimension.

In Chapter 5, Hossein Khoshbakht, Francesca Gagliardi and Ali Asadi use a multi-dimensional and fuzzy-set approach to measure poverty at the province level in Iran, offering the first attempt to use this approach for estimating poverty at the local level in that country. They go beyond conventional studies of poverty based simply on a dichotomy between those who are and are not poor defined in relation to a poverty line drawn only on the basis of income or total expenditure. They use the methodology in the Household Budget Survey in Iran, with a large set of indicators to examine the latent dimensions of non-monetary poverty for the period 2016–2017.

Another interesting application on an emerging country is reported in Chapter 6, ‘China’s Multi-dimensional Poverty and Trade’, by Elisabetta Croci Angelini and Yang Liu. They explain that, over the past 40 years of reform and opening-up, China’s economy has maintained rapid growth. Its achievements in poverty reduction have been remarkable: more than 700 million Chinese have been lifted out of poverty. Meanwhile, the volume of China’s import and export trade has risen several fold, and, in 2017, China became the world’s largest importer and exporter. By conducting an analysis at the provincial level, this chapter explores the links between poverty and trade and how poverty restricts participation in international trade. Assessments of poverty usually rely on a monetary variable, but in this chapter the authors adopt a multi-dimensional measurement of poverty calculated with a fuzzy-set methodology at the provincial level and compare it to the volume of trade, revealing an interesting relationship between multi-dimensional poverty and global trade.

Chapter 7, the final chapter in Part 1, presents the new and final research of Vijay Verma, in collaboration with Gianni Betti and Francesca Gagliardi. In this chapter, they further extend variance estimation to longitudinal multi-dimensional fuzzy poverty measures. The measures considered are based on fuzzy representations of individuals’ propensity for deprivation in monetary and different non-monetary dimensions and are derived from sample surveys with complex designs and fairly large samples. In particular, the chapter adopts a new longitudinal measure based on the fuzzy-set approach to multi-dimensional poverty proposed by Verma et al. (2017): the ‘fuzzy at-persistent-risk-of-poverty’ rate. The authors present a practical methodology for variance estimation – in particular, the jack-knife repeated replication method – for multi-dimensional measures of poverty and deprivation of households and individuals in a longitudinal context. They quantitatively illustrate the calculation procedures and difficulties in producing reliable and robus...