Multidimensional Poverty: Measurement, Estimation, and Inference

Abstract

Multidimensional poverty measures give rise to a host of statistical hypotheses that are of interest to applied economists and policy-makers alike. In the specific context of the generalized Alkire–Foster (Alkire and Foster, 2008) class of measures, we show that many of these hypotheses can be treated in a unified manner and also tested simultaneously using a minimum p-value approach. When applied to study the relative state of poverty among Hindus and Muslims in India, these tests reveal novel insights into the plight of the poor which are not otherwise captured by traditional univariate approaches.

Keywords:

• FGT measures
• Multidimensional poverty measurement
• Multiple testing

JEL Classification:

• C1
• C12
• I3
• I32
• O1

ACKNOWLEDGMENTS

We wish to thank James Foster, Sabina Alkire, and participants at the Oxford Poverty & Human Development Initiative workshop on Robustness Methods for Multidimensional Welfare Analysis for their comments. We also wish to thank Chrysanthi Hatzimasoura for alerting us to an error in our original R code.

Notes

In contrast, statistical tests relating to the univariate approach to poverty analysis are well established; see, for example, Anderson (1996), Davidson and Duclos (2000), Barrett and Donald (2003), and Linton et al. (2005).

For concreteness, we have chosen to frame our discussion in the context of the AK measure. However, our methodology may also be extended, for example, to test hypotheses that arise from the multidimensional orderings of Maasoumi and Lugo (2008) and Duclos et al. (2006). See also Kakwani and Silber (2008) for an overview of these and other approaches.

In some situations, it may be of interest to allow the value of α to be dimension-dependent. Although we have not formulated P _α(·) to explicitly account for this possibility, we note that such an extension can easily be accommodated.

The subscript on the poverty line vector highlights the fact that we allow for the prespecified (exogenous) poverty lines to differ across any two populations.

For a given probability measure P, the notation Pf denotes the expectation with repect to P, i.e., .

See, for example, Westfall and Young (1993) on the use of MinP tests. Also, see Romano and Wolf (2005) and Hso et al. (2010) for a discussion of related procedures.

The assumption of mutual independence is made here for illustrative purposes. In practice, we can generally expect some degree of dependence among the hypotheses under test; however, it is only in the case of perfect dependence that we can be guaranteed of appropriate error rate control if we adopt the strategy of independently testing several hypotheses on the basis of individual (unadjusted) p-values.

‖·‖ denotes the standard Euclidean norm.

Bhattacharya (2007), for example, discusses in detail the effect of ignoring the sampling design of the NSS on inequality measurement.

As pointed out by one of the referees, this is likely to bias the results since households typically have different sizes and household size is likely correlated with both poverty and religion.

We thank an anonymous referee for suggesting that we investigate the correlation among dimensions.

*Pucca refers to brick and mortar structures.

Boldface values are statistically significant at the 5% nominal level.

Boldface values are statistically significant at the 5% nominal level.

For the sake of brevity we consider only the P ₀ measure and multidimensional headcount H.

Regional and religious disaggregation of poverty in India is explored in greater depth in Mitra (2011).

Boldface values are statistically significant at the 5% nominal level.

The views expressed here are those of the author and should not be attributed to the World Bank or any affiliated organization.