IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

On longitudinal analysis of poverty conceptualised as a fuzzy state

Listed author(s):
  • Gianni Betti


    (Università di Siena)

  • Bruno Cheli


    (Università di Pisa)

  • Vijay Verma


    (Università di Siena)

When poverty is viewed as a matter of degree, i.e. as a fuzzy measure, two additional aspects are introduced into the analysis compared with the conventional poor/non-poor dichotomous approach: (i) the choice of membership functions i.e. quantitative specification of individuals' or households' degrees of poverty and deprivation; and (ii) the choice of rules for the manipulation of the resulting fuzzy sets, rules defining their complements, intersections, union and averaging. Specifically, for longitudinal analysis of poverty using the fuzzy set approach, we need joint membership functions covering more than one time period, which have to be constructed on the basis of the series of cross-sectional membership functions over those time periods. In this paper we propose a general rule for the construction of fuzzy set intersections, that is, rules for the construction of longitudinal poverty measures from a sequence of cross-sectional measures. On the basis of the results obtained, various fuzzy poverty measures over time can be constructed as consistent generalisations of the corresponding conventional (dichotomous) measures. Examples are rates of any-time, persistent and continuous poverty, distribution of persons and poverty spells according to duration, rates of exit and re-entry into the state of poverty, etc. The proposed rule has been developed in a logical, step-by-step, manner, satisfying the required marginal constraints. This is important since there are reasons to believe that, hitherto, the rules of fuzzy set operations in the context of multi-dimensional and longitudinal poverty analysis have not been well or widely understood. In an annex to this paper, we also present some numerical illustrations using survey data from the Italian European Community Household Panel, 1994-2001, with breakdown by Macro-region in Italy. The main objective, however, is to provide quantitative comparison between the conventional and fuzzy approaches. Noteworthy from a methodological point is the difference in the performance of the approaches concerning persistence of poverty. Movements in and out of poverty may be somewhat over-estimated (and hence the persistent or continuous poverty rates under-estimated) with the conventional approach, perhaps because it gives too much weight even to small movements across the poverty line.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 32.

in new window

Length: 26 pages
Date of creation: 2006
Handle: RePEc:inq:inqwps:ecineq2006-32
Contact details of provider: Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Gianni Betti & Bruno Cheli & Riccardo Cambini, 2004. "A statistical model for the dynamics between two fuzzy states: theory and an application to poverty analysis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 391-411.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:inq:inqwps:ecineq2006-32. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maria Ana Lugo)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.