主流多维贫困指标中固有的不正当激励的快速解决方案（英）

Produced by the Research Support TeamAbstractThe Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about developmentissues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry thenames of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely thoseof the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank andits affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.Policy Research Working Paper11113Most multidimensional poverty measures used in practice,including the global Multidimensional Poverty Index, arebased on the adjusted headcount ratio. This paper showsthat this poverty index provides perverse incentives. Poli-cies that minimize this index prioritize targeting the leastintensely poor individuals, rather than the most intenselypoor individuals. This paper proposes a quick-fix solutionthat tweaks the adjusted headcount ratio without affectingthe identification of the poor. The resulting index satisfiesThis paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by theWorld Bank to provide open access to its research and make a contribution to development policy discussions around theworld. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author maybe contacted at bdecerf@worldbank.org. the same properties as the adjusted headcount ratio, exceptfor Dimensional Breakdown. The paper argues that thisis not a sufficient reason to discard this index, by pro-viding two examples illustrating key limitations of thedecomposition across dimensions permitted by Dimen-sional Breakdown. This decomposition does not providethe necessary information to find optimal policies. Moreimportantly, this decomposition may mislead policy makerson the underlying sources of progress. AQuick-FixforPerverseIncentivesInherentinMainstreamMultidimensionalPovertyMeasures.∗BenoitDecerfJEL:I32,D63.Keywords:MultidimensionalPoverty,GlobalMPI,AdjustedHead-countRatio,DimensionalBreakdown.∗Acknowledgments :I thank Kimberly Blair Bolch, Jakob Dirksen, Bilal Malaeband Ricardo Nogales for their helpful comments and suggestions.All errors remainmine. The findings, interpretations, and conclusions expressed in this paper are entirelythose of the author and should not be attributed in any manner to the World Bank,to its affiliated organizations, or to members of its Board of Executive Directors or thecountries they represent. 1IntroductionPrioritarianism suggests that social protection policy efforts should targetin priority worse off individuals. Therefore, prioritarian poverty measuresshould not provide incentives to target the least intensely poor individualsbefore targeting the most intensely poor individuals. This is one of the twomain criticisms raised bySen(1976) against the headcount ratio.In this paper, we show that the adjusted headcount ratio (Alkire andFoster,2011) provides such perverse incentives and we propose a quick-fix solution. Such solution could prove useful as multidimensional povertymeasures are increasingly used in academic studies and policy analysis,and most of these practical applications rely on the adjusted headcountratio.2This is for instance the case of the global Multidimensional PovertyIndex (MPI), monitored by UNDP-OPHI, and of the World Bank’s Multi-dimensional Poverty Measure.3 These perverse incentives may thus affectpolicies. For instance,Santos et al.(2023) recently proposed an algorithmsearching for the policy that minimizes the adjusted headcount ratio un-der a budget constraint. The perverse incentives inherent to the adjustedheadcount ratio thus push their algorithm to target the deprivations of theleast intensely poor individuals.The problem arises under the adjusted headcount ratio because an indi-vidual’s poverty contribution “jumps” when the individual escapes poverty.Our quick-fix solution consists in decreasing the poverty contributions ofpoor individuals by an amount equal to this “jump”. The solution we pro-pose thus preserves the Alkire-Foster poverty identification method buttweaks the adjusted headcount ratio index. Also, we show that this solu-tion gets rid of this perverse incentive and does not affect the comparisonsmade by the adjusted headcount ratio when no individual escapes poverty.Our solution yields an index that satisfies the same properties as the ad-justed headcount ratio except for Dimensional breakdown. We argue thatthe violation of Dimensional breakdown needs not be a sufficient reason todiscard our solution. Dimensional breakdown implies that, after the iden-tification of poor individuals has taken place, the index can be de