Properties of Axioms for Multidimensional Poverty Measures
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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
23:11 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
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