## 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).

### Video Part I

Guide to 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

53:04 Theorem of Foster and Shorrock for subgroup axioms

### Part II

Guide to video 2

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

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

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

## Further resources

Watch a presentation by Suman Seth on Unidimensional Poverty Measurement from OPHI’s 2014 Summer School in Oxford.