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Frank Cowell: UB Public Economics Inequality and Poverty June 2005 Public Economics: University of Barcelona Frank Cowell

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Presentation on theme: "Frank Cowell: UB Public Economics Inequality and Poverty June 2005 Public Economics: University of Barcelona Frank Cowell"— Presentation transcript:

1 Frank Cowell: UB Public Economics Inequality and Poverty June 2005 Public Economics: University of Barcelona Frank Cowell http://darp.lse.ac.uk/ub

2 Frank Cowell: UB Public Economics Issues to be addressed Builds on lecture 2 Builds on lecture 2  “Distributional Equity, Social Welfare” Extension of ranking criteria Extension of ranking criteria  Parade diagrams  Generalised Lorenz curve Extend SWF analysis to inequality Extend SWF analysis to inequality Examine structure of inequality Examine structure of inequality Link with the analysis of poverty Link with the analysis of poverty

3 Frank Cowell: UB Public Economics Major Themes Contrast three main approaches to the subject Contrast three main approaches to the subject  intuitive  via SWF  via analysis of structure Structure of the population Structure of the population  Composition of inequality and poverty  Implications for measures The use of axiomatisation The use of axiomatisation  Capture what is “reasonable”?  Find a common set of axioms for related problems

4 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Relationship with welfare rankings

5 Frank Cowell: UB Public Economics Inequality rankings Begin by using welfare analysis of previous lecture Begin by using welfare analysis of previous lecture Seek inequality ranking Seek inequality ranking We take as a basis the second-order distributional ranking We take as a basis the second-order distributional ranking  …but introduce a small modification The 2nd-order dominance concept was originally expressed in a more restrictive form. The 2nd-order dominance concept was originally expressed in a more restrictive form.

6 Frank Cowell: UB Public Economics Yet another important relationship The share of the proportion q of distribution F is given by The share of the proportion q of distribution F is given by L(F;q) := C(F;q) /  (F) Yields Lorenz dominance, or the “shares” ranking Yields Lorenz dominance, or the “shares” ranking For given , G Lorenz-dominates F  W(G) > W(F) for all W  W 2 The Atkinson (1970) result: The Atkinson (1970) result: G Lorenz-dominates F  means:   for every q, L(G;q)  L(F;q),   for some q, L(G;q) > L(F;q)

7 Frank Cowell: UB Public Economics The Lorenz diagram 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 proportion of income proportion of population L(G;.) L(F;.) L(.; q) q Lorenz curve for F practical example, UK

8 Frank Cowell: UB Public Economics original income + cash benefits gross income - direct taxes disposable income - indirect taxes post-tax income + non-cash benefits final income Official concepts of income: UK What distributional ranking would we expect to apply to these 5 concepts?

9 Frank Cowell: UB Public Economics Impact of Taxes and Benefits. UK 2000/1. Lorenz Curve

10 Frank Cowell: UB Public Economics Assessment of example We might have guessed the outcome… We might have guessed the outcome… In most countries: In most countries:  Income tax progressive  So are public expenditures  But indirect tax is regressive So Lorenz-dominance is not surprising. So Lorenz-dominance is not surprising. But what happens if we look at the situation over time? But what happens if we look at the situation over time?

11 Frank Cowell: UB Public Economics “Final income” – Lorenz

12 Frank Cowell: UB Public Economics “Original income” – Lorenz 0.00.10.20.30.40.5 0.6 0.7 0.8 0.9 1.0   Lorenz curves intersect   Is 1993 more equal?   Or 2000-1?

13 Frank Cowell: UB Public Economics Inequality ranking: Summary Second-order (GL)-dominance is equivalent to ranking by cumulations. Second-order (GL)-dominance is equivalent to ranking by cumulations.  From the welfare lecture Lorenz dominance equivalent to ranking by shares. Lorenz dominance equivalent to ranking by shares.  Special case of GL-dominance normalised by means. Where Lorenz-curves intersect unambiguous inequality orderings are not possible. Where Lorenz-curves intersect unambiguous inequality orderings are not possible. This makes inequality measures especially interesting. This makes inequality measures especially interesting.

14 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Three ways of approaching an index Intuition Social welfare Distance

15 Frank Cowell: UB Public Economics An intuitive approach Lorenz comparisons (second-order dominance) may be indecisive Lorenz comparisons (second-order dominance) may be indecisive But we may want to “force a solution” But we may want to “force a solution” The problem is essentially one of aggregation of information The problem is essentially one of aggregation of information  Why worry about aggregation? It may make sense to use a very simple approach It may make sense to use a very simple approach Go for something that you can “see” Go for something that you can “see”  Go back to the Lorenz diagram

16 Frank Cowell: UB Public Economics 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 0.5 proportion of income proportion of population Gini Coefficient The best-known inequality measure?

17 Frank Cowell: UB Public Economics Equivalent ways of writing the Gini: Equivalent ways of writing the Gini: 1. Normalised area above Lorenz curve The Gini coefficient 2. Normalised difference between income pairs.

18 Frank Cowell: UB Public Economics Intuitive approach: difficulties Essentially arbitrary Essentially arbitrary  Does not mean that Gini is a bad index  But what is the basis for it? What is the relationship with social welfare? What is the relationship with social welfare? The Gini index also has some “structural” problems The Gini index also has some “structural” problems  We will see this in the next section What is the relationship with social welfare? What is the relationship with social welfare?  Examine the welfare-inequality relationship directly

19 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Three ways of approaching an index Intuition Social welfare Distance

20 Frank Cowell: UB Public Economics SWF and inequality Issues to be addressed: Issues to be addressed:  the derivation of an index  the nature of inequality aversion  the structure of the SWF Begin with the SWF W Begin with the SWF W Examine contours in Irene-Janet space Examine contours in Irene-Janet space

21 Frank Cowell: UB Public Economics Equally-Distributed Equivalent Income O xixi xjxj   The Irene &Janet diagram   A given distribution   Distributions with same mean   Contours of the SWF E (F)(F) (F)(F) F   Construct an equal distribution E such that W(E) = W(F)   EDE income   Social waste from inequality   Curvature of contour indicates society’s willingness to tolerate “efficiency loss” in pursuit of greater equality

22 Frank Cowell: UB Public Economics Atkinson assumed an additive social welfare function that satisfied the other basic axioms. Atkinson assumed an additive social welfare function that satisfied the other basic axioms.  (F) I(F) = 1 – ——  (F) Mean income Ede income Welfare-based inequality x  1 -  – 1 u(x) = ————,   1 –  Introduced an extra assumption: Iso-elastic welfare. Introduced an extra assumption: Iso-elastic welfare. From the concept of social waste Atkinson (1970) suggested an inequality measure: From the concept of social waste Atkinson (1970) suggested an inequality measure: W(F) =  u(x) dF(x)

23 Frank Cowell: UB Public Economics The Atkinson Index Given scale-invariance, additive separability of welfare Given scale-invariance, additive separability of welfare Inequality takes the form: Inequality takes the form: Given the Harsanyi argument… Given the Harsanyi argument…  index of inequality aversion  based on risk aversion. More generally see it as a stament of social values More generally see it as a stament of social values Examine the effect of different values of  Examine the effect of different values of   relationship between u(x) and x  relationship between u′(x) and x

24 Frank Cowell: UB Public Economics Social utility and relative income 12345 -3 -2 0 1 2 3 4      U x / 

25 Frank Cowell: UB Public Economics Relationship between welfare weight and income 012345 0 1 2 3 4  =1/2  =0  =1       U' x / 

26 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Three ways of approaching an index Intuition Social welfare Distance

27 Frank Cowell: UB Public Economics A further look at inequality The Atkinson SWF route provides a coherent approach to inequality. The Atkinson SWF route provides a coherent approach to inequality. But do we need to approach via social welfare But do we need to approach via social welfare  An indirect approach  Maybe introduces unnecessary assumptions, Alternative route: “distance” and inequality Alternative route: “distance” and inequality Consider a generalisation of the Irene-Janet diagram Consider a generalisation of the Irene-Janet diagram

28 Frank Cowell: UB Public Economics The 3-Person income distribution 0 Irene's income Janet's income Karen's income i x k x x j ray of equality Income Distributions With Given Total

29 Frank Cowell: UB Public Economics Inequality contours 0 i x k x x j   Set of distributions for given total   Set of distributions for a higher (given) total   Perfect equality   Inequality contours for original level   Inequality contours for higher level

30 Frank Cowell: UB Public Economics A distance interpretation Can see inequality as a deviation from the norm Can see inequality as a deviation from the norm The norm in this case is perfect equality The norm in this case is perfect equality Two key questions… Two key questions… …what distance concept to use? …what distance concept to use? How are inequality contours on one level “hooked up” to those on another? How are inequality contours on one level “hooked up” to those on another?

31 Frank Cowell: UB Public Economics Another class of indices Consider the Generalised Entropy class of inequality measures: Consider the Generalised Entropy class of inequality measures: The parameter  is an indicator sensitivity of each member of the class. The parameter  is an indicator sensitivity of each member of the class.   large and positive gives a “top -sensitive” measure   negative gives a “bottom-sensitive” measure Related to the Atkinson class Related to the Atkinson class

32 Frank Cowell: UB Public Economics Inequality and a distance concept The Generalised Entropy class can also be written: The Generalised Entropy class can also be written: Which can be written in terms of income shares s Which can be written in terms of income shares s Using the distance criterion s 1−  / [1−  ] … Using the distance criterion s 1−  / [1−  ] … Can be interpreted as weighted distance of each income shares from an equal share Can be interpreted as weighted distance of each income shares from an equal share

33 Frank Cowell: UB Public Economics The Generalised Entropy Class GE class is rich GE class is rich Includes two indices from Henri Theil: Includes two indices from Henri Theil:   = 1:  [ x /  (F)] log (x /  (F)) dF(x)   = 0: –  log (x /  (F)) dF(x) For  < 1 it is ordinally equivalent to Atkinson class For  < 1 it is ordinally equivalent to Atkinson class   = 1 – . For  = 2 it is ordinally equivalent to (normalised) variance. For  = 2 it is ordinally equivalent to (normalised) variance.

34 Frank Cowell: UB Public Economics Inequality contours Each family of contours related to a different concept of distance Each family of contours related to a different concept of distance Some are very obvious… Some are very obvious… …others a bit more subtle …others a bit more subtle Start with an obvious one Start with an obvious one  the Euclidian case

35 Frank Cowell: UB Public Economics GE contours:  2

36 Frank Cowell: UB Public Economics GE contours:  2  25   −  − 

37 Frank Cowell: UB Public Economics GE contours: a limiting case  −∞ Total priority to the poorest Total priority to the poorest

38 Frank Cowell: UB Public Economics GE contours: another limiting case Total priority to the richest Total priority to the richest  +∞

39 Frank Cowell: UB Public Economics By contrast: Gini contours Not additively separable Not additively separable

40 Frank Cowell: UB Public Economics Distance: a generalisation The responsibility approach gives a reference income distribution The responsibility approach gives a reference income distribution  Exact version depends on balance of compensation rules  And on income function. Redefine inequality measurement Redefine inequality measurement  not based on perfect equality as a norm  use the norm income distribution from the responsibility approach Devooght (2004) bases this on Cowell (1985) Devooght (2004) bases this on Cowell (1985)  Cowell approach based on Theil’s conditional entropy  Instead of looking at distance going from perfect equality to actual distribution...  Start from the reference distribution

41 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Structural issues

42 Frank Cowell: UB Public Economics Why decomposition? Resolve questions in decomposition and population heterogeneity: Resolve questions in decomposition and population heterogeneity:  Incomplete information  International comparisons  Inequality accounting Gives us a handle on axiomatising inequality measures Gives us a handle on axiomatising inequality measures  Decomposability imposes structure.  Like separability in demand analysis first, some terminology

43 Frank Cowell: UB Public Economics A partition population share subgroup inequality income share j j s j I j (ii) (i) (iii) (iv) The population The population Attribute 1 Attribute 1 One subgroup One subgroup Attribute 2 Attribute 2 (1) (2) (3) (4) (5) (6)

44 Frank Cowell: UB Public Economics What type of decomposition? Distinguish three types of decomposition by subgroup Distinguish three types of decomposition by subgroup In increasing order of generality these are: In increasing order of generality these are:  Inequality accounting  Additive decomposability  General consistency Which type is a matter of judgment Which type is a matter of judgment  More on this below  Each type induces a class of inequality measures  The “stronger” the decomposition requirement…  …the “narrower” the class of inequality measures

45 Frank Cowell: UB Public Economics adding-up property weight function 1:Inequality accounting This is the most restrictive form of decomposition: accounting equation

46 Frank Cowell: UB Public Economics 2:Additive Decomposability As type 1, but no adding-up constraint:

47 Frank Cowell: UB Public Economics population shares 3:General Consistency The weakest version: income shares increasing in each subgroup’s inequality

48 Frank Cowell: UB Public Economics A class of decomposable indices Given scale-invariance and additive decomposability, Given scale-invariance and additive decomposability, Inequality takes the Generalised Entropy form: Inequality takes the Generalised Entropy form: Just as we had earlier in the lecture. Just as we had earlier in the lecture. Now we have a formal argument for this family. Now we have a formal argument for this family. The weight  j on inequality in group j is  j =  j  s j 1−  The weight  j on inequality in group j is  j =  j  s j 1− 

49 Frank Cowell: UB Public Economics What type of decomposition? Assume scale independence… Assume scale independence… Inequality accounting: Inequality accounting:  Theil indices only (   Here  j =  j or  j = s j Additive decomposability: Additive decomposability:  Generalised Entropy Indices General consistency: General consistency:  moments,  Atkinson,... But is there something missing here? But is there something missing here?  We pursue this later

50 Frank Cowell: UB Public Economics What type of partition? General General  The approach considered so far  Any characteristic used as basis of partition  Age, gender, region, income  Induces specific class of inequality measures ... but excludes one very important measure Non-overlapping in incomes Non-overlapping in incomes  A weaker version  Partition just on the basis of income  Allows one to include the "missing" inequality measure Distinction between them is crucial for one special inequality measure Distinction between them is crucial for one special inequality measure

51 Frank Cowell: UB Public Economics Different (equivalent) ways of writing the Gini: Different (equivalent) ways of writing the Gini: Normalised area under the Lorenz curve Normalised area under the Lorenz curve The Gini coefficient Normalised pairwise differences Normalised pairwise differences A ranking-weighted average A ranking-weighted average But ranking depends on reference distribution But ranking depends on reference distribution 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 proportion of income proportion of population Gini Coefficient

52 Frank Cowell: UB Public Economics Partitioning by income... x*x* N1N1 N2N2 0 x ** N1N1 x' x   Case 2: effect on Gini differs in subgroup and population x'x   Case 1: effect on Gini is same in subgroup and population   Non-overlapping income groups   Overlapping income groups   Consider a transfer:Case 1   Consider a transfer:Case 2 x

53 Frank Cowell: UB Public Economics Non-overlapping decomposition Can be particularly valuable in empirical applications Can be particularly valuable in empirical applications Useful for rich/middle/poor breakdowns Useful for rich/middle/poor breakdowns Especially where data problems in tails Especially where data problems in tails  Misrecorded data  Incomplete data  Volatile data components Example: Piketty-Saez on US (QJE 2003) Example: Piketty-Saez on US (QJE 2003)Piketty-Saez on US (QJE 2003)Piketty-Saez on US (QJE 2003)  Look at behaviour of Capital gains in top income share  Should this affect conclusions about trend in inequality?

54 Frank Cowell: UB Public Economics Top income shares in US

55 Frank Cowell: UB Public Economics Choosing an inequality measure Do you want an index that accords with intuition? Do you want an index that accords with intuition?  If so, what’s the basis for the intuition? Is decomposability essential? Is decomposability essential?  If so, what type of decomposability? Do you need a welfare interpretation? Do you need a welfare interpretation?  If so, what welfare principles to apply?

56 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty …Identification and measurement

57 Frank Cowell: UB Public Economics Poverty analysis – overview Basic ideas Basic ideas  Income – similar to inequality problem?  Consumption, expenditure or income?  Time period  Risk  Income receiver – as before  Relation to decomposition Development of specific measures Development of specific measures  Relation to inequality  What axiomatisation? Use of ranking techniques Use of ranking techniques  Relation to welfare rankings

58 Frank Cowell: UB Public Economics Poverty measurement How to break down the basic issues. How to break down the basic issues. Sen (1979): Two main types of issues Sen (1979): Two main types of issues  Identification problem  Aggregation problem Jenkins and Lambert (1997): “3Is” Jenkins and Lambert (1997): “3Is” Jenkins and Lambert (1997) Jenkins and Lambert (1997)  Identification  Intensity  Inequality Present approach: Present approach:  Fundamental partition  Individual identification  Aggregation of information population non-poor poor

59 Frank Cowell: UB Public Economics Poverty and partition Depends on definition of poverty line Depends on definition of poverty line Exogeneity of partition? Exogeneity of partition? Asymmetric treatment of information Asymmetric treatment of information

60 Frank Cowell: UB Public Economics Counting the poor Use the concept of individual poverty evaluation Use the concept of individual poverty evaluation Simplest version is (0,1) Simplest version is (0,1)  (non-poor, poor)  headcount Perhaps make it depend on income Perhaps make it depend on income  poverty deficit Or on the whole distribution? Or on the whole distribution? Convenient to work with poverty gaps Convenient to work with poverty gaps

61 Frank Cowell: UB Public Economics The poverty line and poverty gaps x x* 0 poverty evaluation income xixi xjxj gigi gjgj

62 Frank Cowell: UB Public Economics Poverty evaluation g 0 poverty evaluation poverty gap x = 0 Non-Poor Poor gigi A gjgj B   the “head-count”   the “poverty deficit”   sensitivity to inequality amongst the poor   Income equalisation amongst the poor

63 Frank Cowell: UB Public Economics Brazil 1985: How Much Poverty? Rural Belo Horizonte poverty line Rural Belo Horizonte poverty line Brasilia poverty line Brasilia poverty line compromise poverty line compromise poverty line   A highly skewed distribution   A “conservative” x*   A “generous” x*   An “intermediate” x*   The censored income distribution $0$20$40$60$80$100$120$140$160$180$200$220$240$260$280$300

64 Frank Cowell: UB Public Economics The distribution of poverty gaps $0$20$40$60 gaps

65 Frank Cowell: UB Public Economics ASP Additively Separable Poverty measures Additively Separable Poverty measures ASP approach simplifies poverty evaluation ASP approach simplifies poverty evaluation Depends on own income and the poverty line. Depends on own income and the poverty line.  p(x, x*) Assumes decomposability amongst the poor Assumes decomposability amongst the poor Overall poverty is an additively separable function Overall poverty is an additively separable function  P =  p(x, x*) dF(x) Analogy with decomposable inequality measures Analogy with decomposable inequality measures

66 Frank Cowell: UB Public Economics A class of poverty indices ASP leads to several classes of measures ASP leads to several classes of measures Make poverty evaluation depends on poverty gap. Make poverty evaluation depends on poverty gap. Normalise by poverty line Normalise by poverty line Foster-Greer-Thorbecke class Foster-Greer-Thorbecke class Foster-Greer-Thorbecke

67 Frank Cowell: UB Public Economics Poverty evaluation functions p(x,x*) x*-x

68 Frank Cowell: UB Public Economics Empirical robustness Does it matter which poverty criterion you use? Does it matter which poverty criterion you use? Look at two key measures from the ASP class Look at two key measures from the ASP class  Head-count ratio  Poverty deficit (or average poverty gap) Use two standard poverty lines Use two standard poverty lines  $1.08 per day at 1993 PPP  $2.15 per day at 1993 PPP How do different regions of the world compare? How do different regions of the world compare? What’s been happening over time? What’s been happening over time? Use World-Bank analysis Use World-Bank analysis  Chen-Ravallion “How have the world’s poorest fared since the early 1980s?” World Bank Policy Research Working Paper Series 3341 World Bank Policy Research Working Paper Series 3341World Bank Policy Research Working Paper Series 3341

69 Frank Cowell: UB Public Economics Poverty rates by region 1981

70 Frank Cowell: UB Public Economics Poverty rates by region 2001

71 Frank Cowell: UB Public Economics Poverty: East Asia

72 Frank Cowell: UB Public Economics Poverty: South Asia

73 Frank Cowell: UB Public Economics Poverty: Latin America, Caribbean

74 Frank Cowell: UB Public Economics Poverty: Middle East and N.Africa

75 Frank Cowell: UB Public Economics Poverty: Sub-Saharan Africa

76 Frank Cowell: UB Public Economics Poverty: Eastern Europe and Central Asia

77 Frank Cowell: UB Public Economics Empirical robustness (2) Does it matter which poverty criterion you use? Does it matter which poverty criterion you use? An example from Spain An example from Spain Data are from ECHP Data are from ECHP OECD equivalence scale OECD equivalence scale Poverty line is 60% of 1993 median income Poverty line is 60% of 1993 median income Does it matter which FGT index you use? Does it matter which FGT index you use?

78 Frank Cowell: UB Public Economics Poverty in Spaion 1993—2000

79 Frank Cowell: UB Public Economics Overview... Inequality rankings Inequality measurement Inequality and decomposition Poverty measures Poverty rankings Inequality and Poverty Another look at ranking issues

80 Frank Cowell: UB Public Economics An extension of poverty analysis Finally consider some generalisations Finally consider some generalisations What if we do not know the poverty line? What if we do not know the poverty line? Can we find a counterpart to second order dominance in welfare analysis? Can we find a counterpart to second order dominance in welfare analysis? What if we try to construct poverty indices from first principles? What if we try to construct poverty indices from first principles?

81 Frank Cowell: UB Public Economics Poverty rankings (1) Atkinson (1987) connects poverty and welfare. Atkinson (1987) connects poverty and welfare. Atkinson (1987) Atkinson (1987) Based results on the portfolio literature concerning “below-target returns” Based results on the portfolio literature concerning “below-target returns” Theorem Theorem  Given a bounded range of poverty lines (x * min, x * max )  and poverty measures of the ASP form  a necessary and sufficient condition for poverty to be lower in distribution F than in distribution G is that the poverty deficit be no greater in F than in G for all x * ≤ x * max. Equivalent to requiring that the second-order dominance condition hold for all x *. Equivalent to requiring that the second-order dominance condition hold for all x *.

82 Frank Cowell: UB Public Economics Poverty rankings (2) Foster and Shorrocks (1988a, 1988b) have a similar approach to orderings by P, Foster and Shorrocks (1988a, 1988b) have a similar approach to orderings by P,1988a But concentrate on the FGT index’s particular functional form: But concentrate on the FGT index’s particular functional form: Theorem: Poverty rankings are equivalent to Theorem: Poverty rankings are equivalent to  first-order welfare dominance for a = 0  second-degree welfare dominance for a = 1  (third-order welfare dominance for a = 2.)

83 Frank Cowell: UB Public Economics Poverty concepts Given poverty line z Given poverty line z  a reference point Poverty gap Poverty gap  fundamental income difference Foster et al (1984) poverty index again Foster et al (1984) poverty index again Cumulative poverty gap Cumulative poverty gap

84 Frank Cowell: UB Public Economics TIP / Poverty profile i/n p(x,z)/n G(x,z) 0 Cumulative gaps versus population proportions Cumulative gaps versus population proportions Proportion of poor Proportion of poor TIP curve TIP curve Cumulative gaps versus population proportions Cumulative gaps versus population proportions Proportion of poor Proportion of poor TIP curve TIP curve   TIP curves have same interpretation as GLC   TIP dominance implies unambiguously greater poverty

85 Frank Cowell: UB Public Economics Poverty: Axiomatic approach Characterise an ordinal poverty index P(x,z) Characterise an ordinal poverty index P(x,z)  See Ebert and Moyes (JPET 2002) See Ebert and Moyes (JPET 2002) See Ebert and Moyes (JPET 2002) Use some of the standard axioms we introduced for analysing social welfare Use some of the standard axioms we introduced for analysing social welfare Apply them to n+1 incomes – those of the n individuals and the poverty line Apply them to n+1 incomes – those of the n individuals and the poverty line Show that Show that  given just these axioms…  …you are bound to get a certain type of poverty measure.

86 Frank Cowell: UB Public Economics Poverty: The key axioms Standard ones from lecture 2 Standard ones from lecture 2  anonymity  independence  monotonicity  income increments reduce poverty Strengthen two other axioms Strengthen two other axioms  scale invariance  translation invariance Also need continuity Also need continuity Plus a focus axiom Plus a focus axiom

87 Frank Cowell: UB Public Economics A closer look at the axioms Let D denote the set of ordered income vectors Let D denote the set of ordered income vectors The focus axiom is The focus axiom is Scale invariance now becomes Scale invariance now becomes Independence means: Independence means: Define the number of the poor as Define the number of the poor as

88 Frank Cowell: UB Public Economics Ebert-Moyes (2002) Gives two types of FGT measures Gives two types of FGT measures  “relative” version  “absolute” version Additivity follows from the independence axiom Additivity follows from the independence axiom

89 Frank Cowell: UB Public Economics Brief conclusion Framework of distributional analysis covers a number of related problems: Framework of distributional analysis covers a number of related problems:  Social Welfare  Inequality  Poverty Commonality of approach can yield important insights Commonality of approach can yield important insights Ranking principles provide basis for broad judgments Ranking principles provide basis for broad judgments  May be indecisive  specific indices could be used Poverty trends will often be robust to choice of poverty index Poverty trends will often be robust to choice of poverty index Poverty indexes can be constructed from scratch using standard axioms Poverty indexes can be constructed from scratch using standard axioms


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