Counting and multidimensional poverty measurement
Research Highlights
► This paper proposes a new methodology for multidimensional poverty measurement, Mka = (ρk,Ma). ► Our identification step ρk uses dual cutoffs to identify a) dimensional deprivations and b) poverty. ► Our aggregate measure adjusts FGT measures to account for multidimensionality. ► Our first measure Mk0 = (ρk,M0) can be used with ordinal or categorical data. ► Our methodology Mka = (ρk,Ma) satisfies many desirable properties including decomposability.
Introduction
Multidimensional poverty has captured the attention of researchers and policymakers alike due, in part, to the compelling conceptual writings of Amartya Sen and the unprecedented availability of relevant data.2 A key direction for research has been the development of a coherent framework for measuring poverty in the multidimensional environment that is analogous to the set of techniques developed in unidimensional space. Recent efforts have identified several classes of multidimensional poverty measures, discussed their properties, and raised important issues for future work.3
This literature, however, has two significant challenges that discourage the empirical use of these conceptually attractive measures. First, the measurement methods are largely dependent on the assumption that variables are cardinal, when, in fact, many dimensions of interest are ordinal or categorical.4 Second, the method for identifying the poor remains understudied: most presentations either leave identification unspecified or select criteria that seem reasonable over two dimensions, but become less tenable when additional dimensions are used. These challenges are especially pertinent given that many countries are actively seeking multidimensional poverty measures to supplement or replace official income poverty measures.
The goal of this paper is to present a new methodology that addresses these substantive issues. In recent work, Atkinson (2003) discussed an intuitive ‘counting’ approach to multidimensional poverty measurement that has a long history of empirical implementation but thus far has largely been disconnected from the aforementioned literature.5 Our approach effectively melds these two approaches: We use a ‘counting’ based method to identify the poor, and propose ‘adjusted FGT’ measures that reflect the breadth, depth and severity of multidimensional poverty.6
In particular, we introduce an intuitive approach to identifying the poor that uses two forms of cutoffs. The first is the traditional dimension-specific deprivation cutoff, which identifies whether a person is deprived with respect to that dimension. The second delineates how widely deprived a person must be in order to be considered poor.7 Our benchmark procedure uses a counting methodology in which the second cutoff - which we call the poverty cutoff - is a minimum number of dimensions of deprivation; the procedure readily generalizes to situations in which dimensions have differential weights. This ‘dual cutoff’ identification system gives clear priority to those suffering multiple deprivations and works well in situations with many dimensions.
Our adjusted FGT measures are easy to interpret and directly generalize the traditional FGT measures. The ‘adjusted headcount’ measure applies to ordinal data and provides information on the breadth of multiple deprivations of the poor. It has a natural interpretation as a measure of ‘unfreedom’ and generates a partial ordering that lies between first and second order dominance.
The overall methodology satisfies a range of useful properties. A key property for policy is decomposability, which allows the index to be broken down by population subgroup (such as region or ethnicity) to show the characteristics of multidimensional poverty for each group. Furthermore, it can be unpacked to reveal the dimensional deprivations contributing most to poverty for any given group (this property is not available to the standard headcount ratio and is particularly useful for policy). It embodies Sen's (1993) view of poverty as capability deprivation and is motivated by Atkinson's (2003) discussion of counting methods for measuring deprivations.8
An important consideration in developing a new methodology for measuring poverty is that it can be employed using real data to obtain meaningful results. We provide illustrative examples using data from the US and Indonesia. Our results suggest that the methodology we propose is intuitive, satisfies useful properties, and can be applied to good effect with real world data.
We begin with some basic definitions and notation for multidimensional poverty in Section 2, and then Section 3 introduces our dual cutoff identification approach. The adjusted FGT family of poverty measures is presented in Section 4, while Section 5 introduces general weights. Section 6 provides a list of axioms satisfied by the combined methodology, Section 7 focuses on the special properties of the adjusted headcount ratio, and Section 8 discusses the choice of cutoffs. Empirical applications are presented in Section 9 while a final section offers some closing observations.
Section snippets
Notation
Let n represent the number of persons and let d ≥ 2 be the number of dimensions under consideration. Dimensions might relate to health, education, work, living standards, or empowerment for example. Let y = [yij] denote the n × d matrix of achievements, where the typical entry yij ≥ 0 is the achievement of individual i = 1,2,…,n in dimension j = 1,2,…,d. Each row vector yi lists individual i's achievements, while each column vector y*j gives the distribution of dimension j achievements across the set of
Identifying the poor
Who is poor and who is not? Bourguignon and Chakravarty (2003) contend that “a multidimensional approach to poverty defines poverty as a shortfall from a threshold on each dimension of an individual's well being”.12 Hence a reasonable starting place is to compare each individual's achievements against the respective deprivation cutoffs, and we follow that general strategy here. But deprivation cutoffs alone do not suffice to identify
Measuring poverty
Suppose, then, that a particular identification function ρk has been selected. Which multidimensional poverty measure M(y;z) should be used with it to form a methodology ? A natural place to begin is with the percentage of the population that is poor. The headcount ratio H = H(y;z) is defined by H = q/n, where q = q(y;z) = Σi = 1nρk(yi, z) is the number of persons in the set Zk, and hence the number of the poor identified using the dual cutoff approach. The resulting methodology (ρk,H) is entirely
General weights
By defining a poverty measurement methodology based on deprivation counts and simple averages, we have implicitly assigned an equal weight of wj = 1 to each dimension j. This is appropriate when the dimensions have been chosen to be of relatively equal importance. As Atkinson et al. observe, equal weighting has an intuitive appeal: “the interpretation of the set of indicators is greatly eased where the individual components have degrees of importance that, while not necessarily exactly equal, are
Properties
We now evaluate our new methodologies using axioms for multidimensional poverty measurement.22 The axiomatic framework for multidimensional measurement draws heavily upon its unidimensional counterpart. However, there is one key distinction: in the multidimensional context, the identification step is no
The case of the adjusted headcount ratio
The methodology ℳk0 = (ρk,M0) has several characteristics that merit special attention. First, it can accommodate the ordinal (and even categorical) data that commonly arise in multidimensional settings. This means that the methodology delivers identical conclusions when monotonic transformations are applied to both variables and cutoffs. In symbols, let fj denote a strictly increasing function on variable j = 1,…,d. Then where f(yi) is the vector whose jth entry is fj(yij), and f(z) is the vector
Choosing cutoffs
To implement our methodology, two general forms of cutoffs must be chosen: the deprivation cutoffs zj and the poverty cutoff k. We now briefly discuss the practical and conceptual considerations surrounding cutoff selection, and also provide some elementary dominance results for variable k.
The dual cutoffs in our approach are quite different from one another. Cutoffs like zj have long been used to identify deprivations in a dimension of interest. Consequently, in many variables there is a
Illustrative examples
We now illustrate the measurement methodology and its variations using data from the United States and Indonesia.
Concluding remarks
This paper proposes a methodology ℳkα for measuring multidimensional poverty whose ‘dual cutoff’ identification function ρk is a natural generalization of the traditional union and intersection identifications, and whose aggregation method Mα appropriately extends the FGT measures for the given ρk. We show that ℳkα satisfies a range of desirable properties including population decomposability; it also exhibits a useful breakdown by dimension once the identification step has been completed. The
Acknowledgements
We gratefully acknowledge research assistance by Afsan Bhadelia and Suman Seth, and support from the International Development Research Council IDRC and the Canadian International Development Agency CIDA. We thank the following for useful comments: Sudhir Anand, A.B. Atkinson, Francois Bourguignon, Jean-Yves Duclos, Karla Hoff, Ortrud Lessmann, Maria Ana Lugo, Martin Ravallion, Emma Samman, Amartya Sen, Jacques Silber, Shabana Singh, Martin van Hees, Yongsheng Xu, and Isleide Zissimos.
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