OPHI

Properties of Axioms for Multidimensional Poverty Measures

Suman Seth

Introduction to the issues of identification and aggregation in a multidimensional setting. Axioms (properties) for multidimensional poverty measures that are natural extensions of the unidimensional framework. Development of an axiom specific to multidimensional measures.

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Video

Guide to the video

00:00 Introduction, focus axioms of multidimensional poverty measures

Part 1: Preliminary: Identification and Aggregation

02:31 Set up the multidimensional context of measurement, joint distribution and multiple dimensions

04:26 Introduction to the achievement matrix

07:16 Explanation of notations

09:07 The general achievement matrix

10:05 The two major steps: identification and aggregation

10:40 Identification in the counting approach (AF method)

16:42 Identification in the aggregated poverty line approach and critique

21:08 Aggregation What is the level of poverty?

Part 2: Axioms – Natural Extensions from the Unidimensional Case

23:02 Introduction

23:11 Invariance axioms: symmetry

24:00 Invariance axioms: replication invariance

24:24 Invariance axioms: scale invariance

29:00 Invariance axioms: focus, two types of focus axioms in the multidimensional setting: poverty focus and deprivation focus

27:38 Focus axioms relation to the two identification techniques

42:47 Continuity

43:57 Dominance axioms: monotonicity, two types of monotenocity axioms in the multidimensional setting: deprivation monotonicity and dimensional monotonicity.

48:36 Subgroup axioms – two types exist in the multidimensional setting – the first ones are population subgroup consistency and decomposability

50:48 The second type is dimensional subgroup consistency and decomposability.

53:45 Recap: transfer axiom in unidimensional space

55:26 The transfer axiom in multidimensional space

59:31 Uniform Majorization (UM)

60:29 Tranfers under UM in the multidimensional space

Part 3: An axiom solely in the multidimensional case

60:10 Introductions to why this axiom is necessary?  Tsui (2002), Bourguignon and Chakravarty (2003)

67:43 The mathematical representation of the weak rearrangement axiom

71:44 Question: How do you think poverty should change under an association decreasing rearrangement?

74:07 The axiom specific to the multidimensional case: weak rearrangement

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