Vijay Verma

Fuzzy measures of the incidence of relative poverty and deprivation: a multi-dimensional perspective

In this paper we present a methodology for the study of multi-dimensional aspects of poverty and deprivation. The conventional poor/non-poor dichotomy is replaced by defining poverty as a matter of degree, determined by the place of the individual in the income distribution. The fuzzy poverty measure proposed is in fact also expressible in terms of the generalised Gini measure. The same methodology facilitates the inclusion of other dimensions of deprivation into the analysis: by appropriately weighting indicators of deprivation to reflect their dispersion and correlation, we can construct measures of non-monetary deprivation in its various dimensions. These indicators illuminate the extent to which purely monetary indicators are insufficient in themselves in capturing the prevalence of deprivation. An important contribution of the paper is to identify rules for the aggregation of fuzzy sets appropriate for the study of poverty and deprivation. In particular, we define a ‘composite’ fuzzy set operator which takes into account whether the sets being aggregated are of a ‘similar’ or a ‘dissimilar’ type. These rules allow us to meaningfully combine income and the diverse non-income deprivation indices at the micro-level and construct what we have termed ‘intensive’ and ‘extensive’ indicators of deprivation. We note that mathematically the same approach can be carried over to the study of persistence of poverty and deprivation over time.

Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.

The Fuzzy Set Approach to Multidimensional Poverty: the Case of Italy in the 1990s

Most of the methods designed for the analysis of poverty share two main limitations: (i) they are unidimensional, i.e. refer to only one proxy of poverty such as low income or consumption expenditure; (ii) they need to dichotomize the population into the poor and the non-poor by means of the so-called poverty line.

A comparative analysis of school-to-work transitions in the European Union1

The present paper describes some aspects of ‘school-to-work’ transition by analyzing the employment situation of individuals as a function of the time elapsed since the completion of education or training. Our perspective is interdisciplinary, comparative and dynamic, with special focus on the patterns in southern European countries. In the literature, most of the studies have had the basic approach of constructing indicators based on retrospective information on the time of first leaving continuous education, and current information on status and characteristics of the persons economic activity – expressing the status of activity as a function of the time elapsed since leaving continuous education. In this approach, essentially cross-sectional (though in part retrospective) information is interpreted as if it pertains to real cohorts. Much of this comparative analysis of school-to-work transitions in EU countries has been based on the EU Labour Force Survey, the 2000 round of which incorporated a special module to collect information on the subject. Our basic approach is to use the longitudinal data from the European Community Household Panel to identify, at the time of each wave, the persons most recently completed education and training, and study this in relation to the persons current employment situation and other characteristics as a function of the time elapsed since that completion. Hence, in form at least, our approach is similar to that of earlier studies based on the LFS, though there are considerable differences in substantive content and statistical methodology resulting from the use of different types of data. We also demonstrate how data from a panel survey may be cumulated over time to obtain a more adequate sample size.

Comparability in multi-country survey programmes

Abstract The rise of multi-country programmes for the generation of comparable data is one of the most salient developments in the area of practical survey work. Starting from the central concept of “comparability”, this paper identifies a dozen criteria determining the degree of comparability achieved in multi-country survey programmes, and describes and characterises some twenty major such programmes in terms of those criteria. Multi-country survey programmes differ greatly in the relative importance given to international aspects concerning centralisation of operations and standardisation of procedures, on the one hand, and national aspects concerning their sensitivity to specific circumstances and statistical priorities of individual countries, on the other. The paper also identifies some special technical issues arising specifically from international nature of the programmes.

Cumulation of poverty measures to meet new policy needs

Reliable indicators of poverty and social exclusion are an essential monitoring tool. Policy research and application increasingly require statistics disaggregated to lower levels and smaller subpopulations. This paper addresses some statistical aspects relating to improving the sampling precision of such indicators for subnational regions, in particular through the cumulation of data.