衡量全球贫困和不平等的底层编码（英）

11349 Bottom-Coding for the Measurementof Global Poverty and Inequality Nishant YonzanMinh C. NguyenChristoph LaknerAart KraayDean JolliffeHaoyu WuGabriel Lara Ibarra Development Data GroupProsperity Vertical &Fiscal Policy and Growth Global DepartmentApril 2026 A verified reproducibility package for this paper isavailable athttp://reproducibility.worldbank.org,clickherefor direct access. Policy Research Working Paper11349 Abstract Distribution sensitive welfare and poverty measures aredesigned to respond to low values of individual income orconsumption. However, very small positive values can havean extreme influence on many distribution sensitive mea-sures, and some measures are not defined for nonpositivevalues.Although income or consumption is often trun-cated or bottom-coded at some strictly positive thresholdto avoid these difficulties, it is unclear where the thresh-old should be drawn and data providers follow different practices. This paper systematically explores various optionsfor bottom-coding consumption and income distributionswhen calculating summary welfare and poverty measuresfor cross-country and over-time comparisons. Using morethan 800 consumption surveys from across the world andemploying various methodologies, the paper suggests that$0.25 per person per day in 2017 purchasing power parityis a suitable bottom-coding threshold in this setting. This paper is a product of the Development Data Group, Development Economics, the Office of the Chief Economist,Prosperity Vertical, and the Fiscal Policy and Growth Global Department. It is part of a larger effort by the World Bankto provide open access to its research and make a contribution to development policy discussions around the world. PolicyResearch Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted atnyonzan@worldbank.org. A verified reproducibility package for this paper is available athttp://reproducibility.worldbank.org, clickherefor direct access. The 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. Bottom-Coding for the Measurement ofGlobal Povertyand Inequality Nishant YonzanⓡMinh C. NguyenⓡChristoph LaknerⓡAart Kraay ⓡDean JolliffeⓡHaoyu WuⓡGabriel Lara Ibarra1 Keywords:Bottom code, consumption floor, measurement errors, distribution-sensitive index,parametric tail JEL Classifications:C1, D60, I32 1.Introduction Many distribution sensitivepoverty and welfaremeasures, as well as inequality measures, aredesigned to respond strongly to low values of individualconsumption or income. However, it iswell known that this desiredsensitivityalsoimplies thatverysmall valuesof consumptionorincomecan be highlyinfluential when makingcomparisons based on distribution sensitive indices(Cowell and Victoria-Feser, 1996; Cowell and Flachaire, 2007). Consider for example a standardAtkinson welfare index𝐴𝐴𝜀𝜀(𝑐𝑐) =�1𝑁𝑁∑𝑐𝑐𝑖𝑖1−𝜀𝜀𝑁𝑁𝑖𝑖=1�11−𝜀𝜀, where𝑐𝑐= (𝑐𝑐1, …𝑐𝑐𝑁𝑁)∈ 𝑅𝑅>0𝑁𝑁represents thedistribution of consumptionacross𝑁𝑁individuals in a society. When the coefficient of inequalityaversion𝜀𝜀is greater than one, the Atkinson index approaches zero when theconsumptionof justone personapproaches zero, irrespective of the consumptionof everyone else in society. These concerns aboutpotentially excessive sensitivityof welfare comparisonsto lowmeasuredvalues of individualconsumption are not hypothetical.Consider the case ofBenin in 2015.Average consumption per person per day is$3, but 3percent of observations report extremelylow, below $0.25,daily per capita consumption.2Using all observations, theAtkinson index with𝜀𝜀= 2for Benin is equal to $1.09.Dropping just 3percent of observations with very lowconsumption results in asharp increase in the Atkinson index to $1.40.Recalling the equallydistributed equivalent income interpretation of the Atkinson index, this increase in welfare isequivalent to a$1.40/$1.09 × 100 = 29percent increase in consumptionfor everyone in Benin.Althoughmany users may in general want to base poverty and welfare comparisons ondistribution-sensitive measures, they maybe uncomfortable withtheextreme sensitivityof thesemeasurestoa small count of presumably implausibly low values of consumption. Concerns about sensitivity are compounded by the presumptionthat near-zero values ofobserved consumptionlikelyreflecterror in