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Unidimensional Poverty Measurement: Axioms, Measures and Dominance

Suman Seth

Video 1: Unidimensional Poverty Measures and their axioms

  • Introduction to the two steps in poverty measurement: identification and aggregation.
  • Definition of the different types of axioms (properties) for poverty measures.

Video 2: Unidimensional Poverty Measures’ fulfillment of axioms and dominance

  • Properties of well-known unidimensional poverty measures and policy implications.
  • Unidimensional stochastic dominance (dominance conditions and their connection to poverty measures).

Key readings

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Video

Part I

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Guide to the video, video 1

00:00 Introduction

01:50 Introduction to the concepts of poverty measurement

09:33 Present three types of policy focus of a distribution of achievements; here focus is on the base of the distribution (poverty)

Part 1: Unidimensional Poverty Measures

11:58 Identification: who is poor?

16:37 Significance and definition of poverty line(s)

21:00 Aggregation: What is the level of poverty?

Part 2: Explanation of Axioms (or properties) of Poverty Measures

22:23 The list of axioms from Foster (2006), which properties do you want your measure to have?

24:16 Invariance axioms: symmetry axiom

27:21 Invariance axioms: replication axiom

29:22 Invariance axioms: focus axiom

30:27 Invariance axioms: scale invariance axiom

32:00 Invariance axioms: normalisation axiom

32:56 Dominance axioms: monotonicity axiom

35:48 Dominance axioms: transfer axiom

43:51 Continuity

45:56 Subgroup axioms: introduction

47:30 Subgroup axioms: subgroup consistency

51:16 Subgroup axioms: additive decomposability

53:04 Theorem of Foster and Shorrock for subgroup axioms

53:29 Advanced axiom: transfer sensitivity

Part II

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Guide to the video, video 2

00:00 Introduction and classifications of measures (basic and advanced)

Part 1: Basic Unidimensional Measures’ fulfillment of axioms and policy implications

02:27 The headcount ratio

07:11 The income gap ratio

09:59 The poverty gap ratio

21:18 The squared poverty gap

30:23 The Foster-Greer-Thorbecke class of measures, summary of measures

Part 2: Advanced Unidimensional Measures’ fulfillment of axioms

30:50 Sen-Shorrocks-Thon measures

34:07 Watts measure

37:22 Clark-Hemming-Ulph-Chakravarty Class of measures

Part 3: Unidimensional Dominance and Fulfillments of Axioms in Different Orderings

38:24 Which poverty line? (identification)

40:52 Which measure? (aggregation)

42:55 The dominance approach

44:15 Variable-line poverty orderings – order of stochastic dominance developed by Foster and Shorrocks (1988)

45:46 Poverty orderings based on the headcount ratio

49:44 First order stochastic dominance – including definition

52:31 What happens if the cumulative distribution function (CDF) of achievements cross? Second order stochastic dominance – including definition

57:37 What happens when the second order dominance curves cross? Third order stochastic dominance – including definition

59:10 In practice: limited range of poverty orderings

 

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Copyright holder: Oxford Poverty & Human Development Initiative
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Useful resources:

For supplementary reading on this topic view

Reading List

Key readings covered in these lectures

Video 1:

Foster, J.E. (2006). Poverty Indices. In Janvry, A. and Kanbur, R. (Eds). Poverty Inequality and Development: Essays in Honor to Erik Thorbecke. New York: Springer

Foster, J.E. and Sen, A. (1997). On Economic Inequality: After a Quarter Century. Annex to the Expanded Edition of A. Sen. On Economic Inequality. Oxford: Clarendon Press. Section A.6.

Video 2:

Foster, J.E. and Sen, A. (1997). On Economic Inequality: After a Quarter Century. Annex to the Expanded Edition of A. Sen. On Economic Inequality. Oxford: Clarendon Press. Section A.6.

Foster, J.E. and Shorrocks, A. (1988). Poverty Orderings and welfare Dominance. Social Choice and Welfare. 5: 179-198

Atkinson, A.B. (1987). On the Measurement of Poverty. Econometrica. 55:749-764