Copula-based methods and their application to multidimensional poverty analysis
- Autores: César García Gómez
- Directores de la Tesis: Ana Pérez Espartero (dir. tes.), Mercedes Prieto Alaiz (codir. tes.)
- Lectura: En la Universidad de Valladolid ( España ) en 2021
- Idioma: español
- Número de páginas: 210
- Tribunal Calificador de la Tesis: Luis Ayala Cañón (presid.), Manuel Úbeda Flores (secret.), Koen Decancq (voc.)
- Programa de doctorado: Programa de Doctorado en Economía por la Universidad de Burgos; la Universidad de Salamanca y la Universidad de Valladolid
- Materias:
- Enlaces
- Tesis en acceso abierto en: UVADOC
- Resumen
- español
En esta tesis, proponemos utilizar la metodología basada en cópulas para analizar la dependencia entre las dimensiones de la pobreza. Este enfoque, que ha sido recientemente introducido en el ámbito de la Economía del Bienestar, se centra en las posiciones de los individuos en las dimensiones, en lugar de en los valores específicos que esas dimensiones toman para tales individuos, y es particularmente útil cuando se mide la dependencia en contextos multivariantes, posiblemente no gaussianos y posiblemente no lineales, como los que solemos encontrar en los análisis multidimensionales de pobreza o bienestar. En particular, consideramos varios conceptos de dependencia multivariante basados en cópulas que son especialmente adecuados para el estudio de la pobreza multidimensional, a saber, los conceptos de concordancia multivariante, orthant dependence (dependencia en el ortante) y tail dependence (dependencia en las colas) multivariante.
- English
It is widely recognized that poverty is a multidimensional phenomenon involving not only income, but also other aspects such as education or health. In this multidimensional setting, analysing the dependence between dimensions becomes an important issue, since a high degree of dependence could exacerbate poverty. In fact, this interdimensional dependence is the key aspect of any multivariate analysis and, therefore, any sound multidimensional poverty assessment must appropriately account for the multivariate association between the dimensions.
However, the literature on multidimensional poverty has traditionally overlooked this crucial aspect, to the point that most of the multidimensional poverty indices proposed so far, and especially those most widely applied, are not sufficiently sensitive to the degree of multivariate association between the different dimensions of poverty.
In this thesis, we propose to use the copula methodology to deal with the dependence between the dimensions of poverty. This approach, which has recently gained attention in Welfare Economics, focuses on the positions of the individuals across dimensions, rather than on the specific values that those dimensions attain for such individuals, and is particularly useful when measuring dependence in multivariate, possibly non-Gaussian and possibly non-linear contexts, such as the ones we usually face in multidimensional poverty or welfare analyses. In particular, we consider several copula-based concepts of multivariate dependence which are especially suitable for the study of multidimensional poverty, namely the concepts of multivariate concordance, orthant dependence and multivariate tail dependence.
We first consider several multivariate extensions of Spearman’s rho, based on the concepts of orthant dependence and multivariate concordance. Among these extensions, the coefficient of average lower orthant dependence becomes especially relevant when analysing multidimensional poverty, as it captures the average probability of being simultaneously low-ranked in all dimensions of poverty. After that, we focus on the concept of multivariate tail dependence, with especial emphasis on multivariate lower tail dependence, which is particularly important in a multidimensional poverty analysis, since it captures the probability that an individual who is extremely low-ranked (extremely “poor”) in one dimension is also extremely poor in the other dimensions considered. Despite its theoretical appeal when it comes to analysing poverty from a multidimensional point of view, the concept of multivariate tail dependence has never been applied, to the best of our knowledge, in this field. Hence, this thesis provides a pioneering contribution. In particular, we propose, for the first time, the multivariate tail concentration function (TCF), a graphical tool that allows to analyse the degree of multivariate dependence between the dimensions of poverty in the tails of the joint distribution and allows, at the same time, to represent such dependence in a unit square, regardless of the poverty dimensions considered.
In the empirical application of this thesis, we apply these copula-based dependence concepts to quantify the degree of multivariate dependence between the three dimensions of the AROPE rate in the European Union (EU) countries and its evolution over the period 2008-2018. From the orthant dependence analysis, we can conclude that in the EU, low (high) values of income tend to occur simultaneously with low (high) values of the other two dimensions of poverty considered. Furthermore, in the vast majority of the EU countries, the average probability of being simultaneously low-ranked in all poverty dimensions tends to be higher than the average probability of being simultaneously high-ranked in all dimensions. We also find, for most countries, an increase in orthant dependence between poverty dimensions over the period 2008- 2014. That is, the probability to be simultaneously low (high) ranked in all poverty dimensions was higher in 2014 than in 2008. By contrary, over the post-crisis period of 2014-2018, we observe that in many EU countries the degree of multivariate orthant dependence between poverty dimensions remained rather stable, with evidence of a decrease in some countries.
Nevertheless, in the majority of the EU countries, multivariate orthant dependence between the dimensions of poverty was still higher in 2018 than in 2008.
From the multivariate tail dependence analysis, we can conclude that there is multivariate tail dependence both in the lower and in the upper joint tails of the distribution. Moreover, in the vast majority of the EU countries dependence in the lower tail tends to be higher than in the upper tail. We also find that, between 2008 and 2014, in most ot the EU countries there was an increase in multivariate lower tail dependence. By contrary, in the post-crisis period of 2014- 2018 we find that, in most of the countries, the degree of multivariate lower tail dependence between poverty dimensions remained rather stable. Moreover, if we consider the whole period analysed, only in three of the EU countries multivariate lower tail dependence between poverty dimensions seems to be clearly lower in 2018 than in 2008.
- español
