Abstract
an initial Lorenz curve (which satisfies some regularity conditions), is presented. The method is applied to the exponential family since they use the exponential Lorenz curves as their generating curves. Several properties of these families are analyzed, including the population function, inequality measures, and Lorenz orderings. Finally, an application is presented for data from various countries. The family is shown to perform well in fitting the data across countries. The results are very robust across data sources.
Highlights
The purpose of this paper is to introducea parametricfamilyof Lorenz curves thatare obtained by a general method.In a recentpaper,Sarabia, Castillo, and Slottje (1999) (SCS) introduceda methodthatallowed forthe buildingof hierarchiesof Lorenz curves when some regularityconditionsare satisfied.They introducedtheParetofamily,whichwas foundto be a flexibleformand which fitsactual income distributiondata well
The exponentiaml odelsappearto be verygood approximationtos actualincomedistribution data.The resultsarerobustto differendtatasetsfordifferenctountriefsromvariouspartsof theworld.Perhapsthemostattractivfeeatureof theproffereedstimationmethodis thatit is robustT. he onlycostofthismethodis someloss offlexibility
Summary
The purpose of this paper is to introducea parametricfamilyof Lorenz curves thatare obtained by a general method.In a recentpaper,Sarabia, Castillo, and Slottje (1999) (SCS) introduceda methodthatallowed forthe buildingof hierarchiesof Lorenz curves when some regularityconditionsare satisfied.They introducedtheParetofamily,whichwas foundto be a flexibleformand which fitsactual income distributiondata well. The strategyused hereis to applya Lorenz curve hierarchythatcontains(as special cases) Lorenz curves derived fromthis general method.In section 2 we introducethe notationand some necessarybackgroundinformationT. He generalmethodis presentedin section, which startsfroman initialLorenz curve Lo(p) (which is called the generatingcurve) and builds a familywithan increasingnumberof parameters.These in turncan be interpretedin termsof elasticitiesof Lo(p). The authors are gratefulto the Direcci6n General de Investigaci6nCientifficya Tecnica (DGICYT) (project PB96-1261) forpartial supportof thiswork.Commentsby two anonymousrefereeshave greatlyimprovedthe paper.The usual caveat holds. An exampleof an applicationof ournew methodologiys presentedin section.
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