Royal Economic Society Dalton, Data and the Distribution of Well - - PowerPoint PPT Presentation

Royal Economic Society

Research | Training | Policy | Practice

“Dalton, Data and the Distribution of Well-Being; Recent Developments in Inequalities in Rich OECD Countries ”

for the EJ 125th anniversary session: “A Century Since Dalton: Where is Inequality Research Going ?

Tim Smeeding University of Wisconsin-Madison and OECD

Lessons from Dalton 95 years later

• Measurement is my forte
• Dalton had little data but great ideas—this

presentation about the data and what it tells us

• Want to focus on “inequalities” and their effect
• n well-being and try to make 4 points:
• 1. Recent trends in rich countries
• 2. Multiple inequalities : income, wealth and cons.
• 3. From the cold to the hot– and data availability
• 4. Use of public admin. data in inequality research

– The gap between rich and poor has widened since 1980’s – Income inequality increased during both recession and boom periods up to the Great Recession (GR) – OECD countries recorded a historically high level of inequality before the GR; the GR squeezed market incomes but as the jobs & wages crisis persists post GR, and as fiscal consolidation has taken hold, inequality is on the rise again – The capture of a large share of income growth at the top of the distribution, especially since the GR, affects both consumption and wealth accumulation , individually and in the aggregate – The distribution of wealth is (much) more unequal than that of income

1.Recent developments in inequalities in OECD countries—the story

Large country differences in income inequality levels: Gini & ratio of average income -top to bottom quintile

Data refer to 2011 or latest year available. Source: OECD Income Distribution Database (http://www.oecd.org/social/soc/inequality-and-poverty.htm). Note: the Gini coefficient ranges from 0 (perfect equality) to 1 (perfect inequality). Gaps between poorest and richest are the ratio of average income of the bottom 10% to average income of the top 10%. Income refers to cash disposable income adjusted for household size.

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50

Income gap between top and bottom 10%

11 : 1 6 : 1 15 : 1 29 : 1 9 : 1 Income inequality in OECD countries (Gini coefficient)

Income inequality before and since the GR: Trends in selected countries 1985-2011/13

Long-term trends in inequality of disposable income (Gini coefficient)

Source: OECD Income Distribution Database, www.oecd.org/social/income-distribution-database.htm

0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 1985 1990 1995 2000 2005 2010 2012 Gini coefficient of income inequality

• The richest 10% receive 9.6 times more than the poorest 10% ( 1980s the

ratio stood at 7:1 )

A long-term rise in income inequality for most nations, 1985-2011/2013

Gini coefficients of income inequality, between mid-1980s and 2011/12

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 1985 2011 or latest Decreasing inequality Little change in inequality Increasing inequality

Source: OECD Income Distribution Database, www.oecd.org/social/income-distribution-database.htm

Real incomes at the top fell during the GR, but market/pre-tax income recovered quickly

Percentage changes in real pre-tax incomes across income groups, average of 9 OECD countries 2008 – 2010

Source: OECD 2014, Focus on Top Incomes and Taxation in OECD Countries: Was the Crisis a Game Changer? Based on World Top Income Database. Note: Incomes refer to pre-tax income, excluding capital gains.

Wealth is more unequally distributed than income when each are ranked alone

Share of income and wealth going to the top 10%, around 2012

Source: OECD wealth questionnaire and ECB-HFCS survey, OECD (2015, forthcoming).

10 20 30 40 50 60 70 80 NOR BEL ISL FIN LUX AUT NLD DEU CAN GRC ITA ESP FRA PRT GBR USA top 10% income share top 10% wealth share

• 2. Inequalities in the US: Income (Y), Net

Wealth (W) and Consumption (C )

• All series of US income (Y) inequality show rising

market and disposable income inequality

• But also US consumption (C) inequality is 80

percent as high as is Y inequality and had risen by 2/3 as much since 1985

• Net Wealth (W) inequality has also increased in

the USA 1989-2013

• Need to connect W to the other two to make

sense of flows -C, Y --and the stock—

• That is, Y,C,W together IN The SAME DATASET

FOR THE SAME INDIVIDUALS

Various Ginis for Income, Consumption and Wealth

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 Money Income After tax and Transfer Income (CBO) Consumption (PSID –

Attanasio/

Pistaferri) Consumption (CE - FJS) SCF Household \ Income (Wolff) SCF Household \ Wealth (Wolff)

10

Why all three ?

• Y flow measure, capacity to consume, preferred for

poverty, inequality work (also its components like earnings, income from capital, social transfers )

• C flow measure, actual consumption , expenditures

plus service flow from durables (preferred measure

• f well-being especially for theory-bound

economists, even if hard to measure )

• W stock measure, value at a point in time which

provides insurance, source for transfers in-vivos and at end of life ( bequests and inheritances)

US APC falls with income-- and wealth increases with income

Money Matters and not just INCOME :

The Demography & Economics of Inequality

• Question: Who lies where in the overall

distributions of C, Y and W in the USA ?

• IMPORTANT We rank everyone in each dataset

by overall Y,C,W ( just one ranking for each component, Y,C,W)

• For whole population, 20 percent of persons are

in each quintile

• Who lies where in each distribution ?
• How does W, as well as Y, affect C and real

well-being ?

For example, consider age alone

• Children (under age 18 ) with C, Y and W from

their parental living arrangements

• Childless adults (ages 18-64 )
• Elders ( age 65 plus )
• Here—see that demography matters !
• Next up for project , move to changes in real

values and trends , 1989-2010

• Assess W accumulation and affect on MACRO

variables like C , as well as inter-vivos transfers and inheritances

The Demography of Inequality by Age: Income, Consumption, and Wealth by Quintiles, 2010*

0% 5% 10% 15% 20% 25% 30% 35% 40%

Adults Elderly Children

Q1 Q2 Q3 Q4 Q5 0% 5% 10% 15% 20% 25% 30% 35% 40%

Adults Elderly Children

Q1 Q2 Q3 Q4 Q5 0% 5% 10% 15% 20% 25% 30% 35% 40%

Adults Elderly Children

Q1 Q2 Q3 Q4 Q5

Disposable Income Consumption Wealth

Sources: As calculated by Fisher, Johnson, Smeeding and Thompson (2015) for disposable income, consumption and wealth.

*Note: The data are for number of persons by age: children (less than 18); elders (65 and over), so person weighted. Overall inequality is not shown, but if so, it would be at 20 percent of the population overall in each

• quintile. Each quintile is ranked by its own measure (income,

consumption, or wealth) with an equivalence scale adjustment using the square root of household size. Adults are childless adults, ages 18-64. Parents living with their kids are counted with their children

• 3. Inequality in from the cold, but

feeling the heat

• Atkinson (1997 RES , Presidential Address )

got his wish—income distribution has come in from the cold !!

• But also inequality is now a hot political issue
• Data repositories like LIS and OECD are having

a harder time getting data on income inequality from their usual sources — e.g. Sweden for LIS and Japan for OECD

• Hopefully this pattern is just a blip

• 4. Better data systems to go forward or back

in inequality, IGM or other studies?

• USA NAS team plans to improve measures of

inequality and social mobility – build a social mobility architecture or “mini-registry” using US Census and public administrative data

• See January 2015 ANNALS volume for

background on the American Opportunity Study (AOS) to monitor IGM

• Dream-vision’ on next slides
• Idea is popular in many nations ( OECD, UK)

Steps along the way

• KEY— Personal Identity Keys – we ” PIK ”

the Census to get SSN from name, address,

• ccupation and so on in Censuses
• Then link across Censuses and ACS ( 5 year

summaries post 2000 )

• Use SSN to link to SSA and then IRS and
• ther administrative data as have others
• Put your study/survey in the middle to add

data on specific issues

Slide in/plug in survey possibilities

• WITH permission to link one can ‘look back’:

1. at parents/ grandparents as well as current generation :

• - with SIPP, or --NHANES/AdHealth/NES/GSS/Fragile

Families, etc. –as in Way #2

• 2. at children and grandchildren of a current generation :
• -with HRS, PSID, NLS ( e.g. find the ones you didn’t follow in

your survey and get at effects of complexity in LR),etc.

• 3. Or you can take an older sample of any outcomes, e.g.

kids, and ‘ look forward’ to see LR effects of ‘treatments ‘ :

• STAR/any job training program/any child care dataset, etc.
• 4. Link to any state or national survey/ admin. data where
• ne can skip ‘economic’ reporting and get better income and

earnings data from the federal registers in many cases

Thank you !

• smesding@lafollette.wisc.edu to keep up

with work on Y, C and W for same persons

Royal Economic Society

Global inequality, 1990-2010: alternative estimations

François Bourguignon

Paris School of Economics

RES, Manchester, March 2015

1

Motivation

• Debate about the global distribution of income:

– Is global inequality rising, declining, constant ? – Does the answer depend on the concept of inequality, the country sources, their normalization? – Is the recent history of a few specific countries essentially responsible for most of observed changes – e.g. China? – The decomposition between 'within' and 'between' country inequality

Anand-Segal (2008, 2014), Atkinson-Brandolini (2010), Bourguignon (2015), Lakner-Milanovic (2013), Milanovic (2002, 2012), Sala-i-Martin (2002, 2006), Sala-i-Martin - Pinkovskiy (2009),…

2

This paper

• Reports on results obtained for the 1990-2010

period with alternative estimation approaches based

• n OECD and World Bank data sets
• Experiments with a generalization of inequality

measures that takes into account varying 'distances' between individuals

3

Outline

1) Why study the global distribution of well-being? 2) Global inequality over 1990-2010: alternative estimates

– Main methodological concerns – Results

3) Distance sensitive measures of global inequality 4) Conclusion

4

1. Why study the global distribution of well-being?

• Global poverty – among world citizens- as a global normative

concern (MDGs, SDGs)

• Global poverty defined in relative, rather than absolute terms

calls for the measurement of global distribution and global inequality

• More generally, poor-rich catching-up global objective

concerns the world's poor and the world's rich

• Yet, the issue arises of how much comparisons with distant

countries matter in subjective evaluation of inequality

5

• 2. Global inequality over 1990-2010:

a) Main methodological concerns

• Comparing purchasing power across countries

– The ppp measurement issue: ICP 2011 vs. ICP 2005 vs. others

• Data sources and comparability

– Distribution statistics usually from household surveys: how comparable are they ? (And how comparable are secondary data from these surveys – e.g. quantile shares? )

• Should national means from HS be normalized by National

Accounts to improve comparability?

– Then, GDP or Household Consumption Expenditures?

• How to identify the sources of changes? (Between/within

decomposition ? )

6

b) Results: basic specifications

• Data sources:

– Oecd Income Distribution Database (for developed countries) – World Bank Povcal database for developing countries

• Sample: 108 countries for which at least three distribution data

data points are available over 1990-2010

• Income concept:

– Survey mean income/consumption (per capita) by deciles – Normalizing by Household Consumption Expenditures per capita – Normalizing by GDP per capita

• Calculations made with ppp 2005 and ppp 2011
• Simulations on China's/India's growth

7

8

0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.740 0.760 1985 1990 1995 2000 2005 2010 2015

Gini coefficient Year

Global inequality, Gini coefficient, 1990-2010: alternative estimates (ppp 2005)

Household suvey data (HSD) HSD normalized by HCE per capita in NA HSD normalized by GDP per capita in NA

9

0.0 10.0 20.0 30.0 40.0 50.0 60.0 0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.740 0.760 1985 1990 1995 2000 2005 2010 2015

Gini Coefficient Year

Global inequality (Gini) and poverty a) with ppp 2005 and ppp 2011: 1990- 2010 (Household survey data)

Povert Headcount (%)

a) PPP 2011 poverty line ajusted so as to generate with the ppp 20011 figures the same poverty headcount in 1990 as the 1.25 $ a

day poverty line with the ppp 2005 figures

Household suvey data (HSD) ppp 2005 figures Household suvey data (HSD) ppp 2011 figures Poverty Headcount (HSD) with PPP 2005 (green) and PPP 2011 (purple)

10

0.0 20.0 40.0 60.0 80.0 100.0 120.0 5000 6000 7000 8000 9000 10000 11000 1985 1990 1995 2000 2005 2010 2015

Dollars ppp 2005

Axis Title

Global GDP per capita and coverage rate of the HSD data: 1990-2010

Percent

GDP per capita, global mean (ppp 2005) Ratio of HSD mean income/consumption per capita to HCE per capita Ratio of HSD mean income/consumption per capita to GDP per capita

11

0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.740 0.760 1985 1990 1995 2000 2005 2010 2015

Gini coefficient Year

Global inequality, 1990-2010: the influence of China Household Survey Data

World World without China China growing as the rest of the world

3) 'Distance Sensitive' Inequality Measures

• Sensitivity to inequality logically depends on the distance

between an individual and those he/she compares with

• Neighbours matter more than people at the other side of the

globe

• This difference in 'comparability' worth considering in evaluating

'global' inequality

• A. Sen's critique of 'sub-decomposability'
• In a population of n persons, note yi the income of person i

and dij the 'comparability' or the distance between individuals i and j.

• Distance-sensitive income inequality measures: I(D, Y)

12

The D-Gini

• An intuitively appealing way of introducing distance within the

Gini measure is as follows:

• This expression can then be expanded to find the equivalent
• f other usual expressions of the Gini coefficient.

13

  

 

i j j ij j j i ij d

y d y y d n G 1

Distance-sensitive Theil measures

• In the same way , one may define the D-Theil and the D-MLD

as: with:

• These are standard expressions of inequality measures where

the mean income of the population has simply been 'personalized' through the distance matrix D

• This is easily generalized to other measures (Atkinson, …)

14





i i i i i d

y y Ln y y n T ~ ~ 1





i i i d

y y Ln n MLD ~ 1

 



j ij j j ij i

d y d y / ~

Application to global inequality

• An appealing set of distances in the case of global

inequality is:

• δ = distance sensitivity coefficient

– δ = 0 global inequality = mean inequality across countries – δ = 1 standard global inequality measures – Intermediate cases: introversion – extraversion

15

not if d country same the from are j and i if d

ij ij

  1  

1 ,  

 

  , 1 

16

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Gini coefficient Distance Sensitivity coefficient

D-Gini according to distance sensitivity coefficient: 1990-2010

Gini90 Gini95 Gini2000 Gini05 Gini08 Gini10

The non-linearity issue

• Personalized mean

extremely sensitive to δ in presence of a large population when δ is close to 0

17

 

2

) 1 ( 1 ) ( ~ ) 1 ( 1 ) .( ~            n y y n y n y y n y y

i i i i i

   

i

y ~

18

• 4
• 3
• 2
• 1

1 2 3 4 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Difference in D-Gini

Distance sensitivity coefficient

D-Gini difference with respect to 1990 according to distance senstivity coefficient : 1995-2010

DGini95-DGini90 DGini00-DGini90 DGini05-Dgini90 DGini08-DGini90 DGini10-DGini90

The inversion of global inequality changes at low sensitivity to distance (δ)

Conclusion

• On global inequality:

– Methodological differences lead to wide differences in the level of inequality – But to parallel declining paths over 1990-2010, with a clear acceleration in the 2000s – 2011/2005 differences in ppp lead to the same conclusion (but real problem for absolute poverty!!) – Evolution depends on the weight put on foreign countries in distance sensitive measures

19

Conclusion

• On 'distance sensitive inequality measures'

– Interesting generalization to be explored further

• How to parametrize the sensitivity to distance?

– Relationship with the between/within decomposition (δ = 0 is not the 'within', except for D-MLD) – Relation with 'generalized Gini' when dij increases with yj, but few properties in the general case – An interesting 'within country' potential application: distance between age groups

20

... To be continued

21

Royal Economic Society

Income mobility

Stephen P. Jenkins

London School of Economics Email: s.jenkins@lse.ac.uk

Economic Journal 125th Anniversary Session: (Almost) a century since Dalton (and Gini): where is inequality analysis going?

1

Dalton connections

• Reader in Economics, LSE
• 1945–7, Chancellor of Exchequer after Labour’s return to

government after 5 years of Coalition government

• Inequality high: at the other side of the Top Income share “U”
• Strongly progressive budgets, e.g. increased food subsidies, subsidised

council house rents, lifting of restrictions of house-building, financing of national assistance and family allowances, etc.

• Some Aspects of the Inequality of Incomes in Modern

Communities, 1925:

• Not only: Pigou-Dalton condition linking progressive transfers and

inequality reduction (Appendix from his Econ J article, 1920)

• But also: equality of opportunity discussion in “Justice and Inequality”

chapter (pp. 20–23)

• Education as an equaliser
• Inheritance of wealth

2

Income mobility

Longitudinal perspective to complement (repeated) cross- sectional perspective : income “dynamics”

• Same individuals followed over time, not different individuals

at each time point

• “Mobility” rather than inequality, poverty, or real income

levels, (joint distribution not marginal distributions)

• Intergenerational mobility: between generations
• Intragenerational mobility: within generations, over

the life course Outline

• Progress: retrospective (What have we learnt?)
• Progress: prospective (What next?)

3

Progress

Looking backwards

4

• 1. Concepts: “mobility” is intrinsically more

complicated than “inequality”

Mobility types

1. Relative (positional | rank | exchange)

– Not everyone can be upwardly mobile

2. Absolute (individual level income growth)

– Income change may be + or – for a person

3. Reduction of inequality in longer-term (lifetime | dynastic) income 4. Income risk

– Movement ~ unpredictability

Normative assessment

1. Origin independence ↑ ~ EOpp ↑; poverty persistence ↓ (good) 2. Depends on social evaluation function, e.g. whether favour pro-poor growth (good | bad) 3. Good if longer-term inequality reduction desired (NB depends on benchmark) 4. Bad for risk-averse individuals

5

• 1a. Concepts & measurement

Accompanied by:

• Proliferation of (scalar) measures
• Good: indices for each of mobility concepts
• Bad: link to normative discussion sometimes lost
• Over-reliance on IGE () as measure of intergenerational

(im)mobility – mixes up relative and absolute concerns (problem since motivation often in terms of EOpp concern and relative mobility)

• Implications in terms of social welfare much less developed
• Atkinson & Bourguignon (REStud 1982) and sibling articles

– Bivariate distribution analogue of Pigou-Dalton: the Correlation-Increasing Transfer (greater diagonality) and link to dominance conditions – Although relevant to evaluations of pure positional change mobility, the Atkinson–Bourguignon SWF is primarily sensitive to mobility as reversals (movement per se) rather than mobility as origin dependence

• Gottschalk and Spolaore (REStud 2002)
• Transition matrix context: e.g. Dardanoni (JET 1993)

6

• 2. Much more longitudinal data

Intragenerational:

• Household panel surveys
• PSID, SOEP, BHPS, HILDA, ECHP, … [EU-SILC]
• Linked administrative register data (tax, social security

contributions etc.)

• Nordic countries; USA; DE; …

Intergenerational:

• Follow-up (e.g. Rowntree study)
• Long-running household panel studies
• Long-running admin register data
• Long-running birth cohort studies (esp. UK)
• Innovations: use of names

7

• 3. Headline findings
• Intergenerational association (IGE) between (log)

earnings of fathers and sons often of order of association in heights

• Countries with the least father-son earnings mobility

tend to be those with the greatest cross-sectional inequality

• The Great Gatsby curve
• Substantial year-to-year intragenerational mobility,

but mostly short-distance moves, rather than long- distance

• Important policy implication: many more touched by poverty
• ver a period than a cross-section sample suggests; turnover

among the poor

8

Progress

Looking forward A sample of suggestions

9

• 1. Concepts and measures
• The role of longitudinal income averaging
• Intergenerational literature uses this to remove ‘transitory’

variation within each generation’s lifecourse

• Intragenerational literature uses lifetime average (permanent)

income to assess mobility as inequality reduction, and mobility as income risk



• Questions of measurement error: is it ‘classical’ (i.e.

transitory variation!)?

• More fundamentally, reference point relies on assumption of

individuals being able to smooth income (save/borrow), and ability to do so not varying with income level

10

• 1. Concepts and measures
• Move away from IGE (or IGC) for intergenerational

studies, having first identified which mobility concept

• f interest, and also use transition matrices move to

study asymmetries

• If EOpp and origin independence the concern, use rank-based

measures

• More studies of absolute mobility
• Cf. growing interest in trends in real income levels when

inequality growing

• More measures of income trajectories: move away

from a focus on 2 periods, to succinctly summarise and compare data for multiple periods

• The complexities of real-life trajectory “spaghetti”

11

• 2. Yet more longitudinal data
• Covering more time periods ~ mobility trends
• Remarkably few findings about income mobility trends

– UK is a prime example (by contrast with social class mobility)

• Longer panels ~ more complex patterns
• Intragenerational: data covering individuals’ full lives

restricted to a few countries currently

• Intergenerational: more generations than simply two

– Cf. Lindahl et al. (JHR 2015): 4 generations for a Swedish sample

• More fine-grained data: what’s happening from week to

week, month to month?

• Can and do people smooth? (cf. Hills et al. 2006)
• Administrative data providing terrific new possibilities
• Large samples, coverage of the rich, less measurement error
• But not perfect: e.g. particular definitions of earnings and

income; coverage defined by original purpose; covariates?

12

• 3. Different approaches
• Move focus on mobility in men’s (log) labour earnings
• Broaden the income concept to look at persistence in material

well-being: “income”!

• Study women as well!
• Dealing with the “zeros” (also relevant for men)
• Dealing with demography (homogamy; equivalence scales?)
• Going beyond summary measures to building models
• f income change within (and between) generations

that incorporate these elements too: hard!

• From reduced form poverty persistence equations to …
• … dynamics of lifetime labour earnings including non-

earning (cf. Bowlus & Robin, JEEA 2012) and microsimulation approaches (cf. pension or student loan modelling)

13

Further reading:

Handbook of Income Distribution, Volume 2A (eds. Atkinson and Bourguignon), 2015

14

Royal Economic Society

Multidimensional Inequality

Sabina Alkire, 1 April 2015, RES

with James Foster, OPHI & GW; Suman Seth, OPHI

Motivation

• Multidimensional nature of well-being
• Reduction income inequality: vital but incomplete
• What about inequality in other dimensions?

Or overlapping inequalities?

• And a focus on the poorest: ‘Leaving no one Behind’

2

Two Forms of Multidimensional Inequality

• Extension of the Pigou-Dalton concept

– Inequality within dimensions (Kolm 1976) – bistochastic matrix => coordinated smoothing – preserves the mean

• Positive association between dimensions

– (Atkinson and Bourguignon 1982) – switch in achievement relaxes positive association – preserves the marginal distributions

3

Motivation

• Multidimensional nature of well-being
• Concern for inequality in other dimensions;

and overlapping inequalities.

• Include a focus on the poorest: ‘Leaving no one

Behind’

4

Two Forms of Multidimensional Inequality

• Extension of the Pigou-Dalton concept

– Inequality within dimensions (Kolm 1976) – bistochastic matrix => coordinated smoothing – preserves the mean

• Positive association between dimensions

– (Atkinson and Bourguignon 1982) – switch in achievement relaxes positive association – preserves the marginal distributions – A large theoretical literature covers one or both

5

Methodological Challenges

Methodological Challenges

• Data

Methodological Challenges

• Data

– Ordinal or binary data are common

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability

– Demanding across distributions of ratio scale variables

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability
• Weights

– Demanding across distributions of ratio scale variables

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability
• Weights

– Demanding across distributions of ratio scale variables

• Policy-Relevance

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability
• Weights

– Demanding across distributions of ratio scale variables

• Policy-Relevance

– Subgroup Decomposability

Methodological Challenges

• Data

– Ordinal or binary data are common

• Access to electricity, insurance, pension, child mortality, attended birth
• Type of sanitation, water, immunizations completed, housing, occupation, disability
• Weights

– Demanding across distributions of ratio scale variables

• Policy-Relevance

– Subgroup Decomposability – Absolute/Relative; Attainment/Deprivation;

Inequality Adjusted HDI

• Released 2010; reported annually
• Extends Foster, Lopez-Calva, Szekely (2006) as per

UNDP (2010), Alkire and Foster (2010)

IHDI:

IHDI=[H(1-AH) × E(1-AEdu) × IL(1-AINC)]1/3

• Construct three dimensional welfare indices.
• Each dimensional-index is adjusted by the loss due to

inequality using 1-(Atkinson Inequality Measure) (geometric mean).

• The HDI is presently penalized for inequality between

dimensions (geometric mean).

Properties

Symmetry in dimensions, symmetry in people, replication invariance, normalization, linear homogeneity, monotonicity Subgroup consistency Rough Interpretation: The HDI level which, if assigned to all people, would produce the same social welfare than the

• bserved distribution

IHDI

Properties

Symmetry in dimensions, symmetry in people, replication invariance, normalization, linear homogeneity, monotonicity Subgroup consistency Rough Interpretation: The HDI level which, if assigned to all people, would produce the same social welfare than the

• bserved distribution

IHDI

Inequality Adjusted HDI (2011)

Criticisms

Restricted to cardinally meaningful data Life Expectancy, Years of schooling, Income Weights (inequality-adjusted welfare): govern tradeoffs across different levels of achievement of one indicator, and across

• ther indicators at all levels of achievements.
• Data requirements cardinal (ratio scale)
• Stochastic dominance comparisons: 2nd order with many

variables requires cardinality.

• Looks only at Kolm (Seth 2013: both)
• How move to non-cardinal dimensions? - median

IHDI

Criticisms

Restricted to cardinally meaningful data Life Expectancy, Years of schooling, Income Weights (inequality-adjusted welfare): govern tradeoffs across different levels of achievement of one indicator, and across

• ther indicators at all levels of achievements.
• Data requirements cardinal (ratio scale)
• Stochastic dominance comparisons: 2nd order with many

variables requires cardinality.

• Looks only at Kolm (Seth 2013: both)
• How move to non-cardinal dimensions? - median

IHDI

• Appropriate for ordinal data:
• finds the category that has the median person
• cut distribution at the median
• look at how far away are people from the median
• First order dominance up + first order dominated

down means more inequality.

Allison and Foster (2004)

Allison, R. A., and J. E. Foster. 2004. Measuring Health Inequality Using Qualitative Data. Journal of Health Economics. 23, 505-524.

• Appropriate for ordinal data:
• finds the category that has the median person
• cut distribution at the median
• look at how far away are people from the median
• First order dominance up + first order dominated

down means more inequality.

Allison and Foster (2004)

Allison, R. A., and J. E. Foster. 2004. Measuring Health Inequality Using Qualitative Data. Journal of Health Economics. 23, 505-524.

Criticisms

Does not (yet) consider more than 1 dimension at a time. How can we move forward with ordinal data?

• Cannot at this time, with Kolm type inequality; focus instead
• n breadth.

Allison Foster

Criticisms

Does not (yet) consider more than 1 dimension at a time. How can we move forward with ordinal data?

• Cannot at this time, with Kolm type inequality; focus instead
• n breadth.

Allison Foster

Counting Approach

Counting Approach

• A very particular solution, but allows us to move forward.

Counting Approach

• A very particular solution, but allows us to move forward.
• Addresses inequalities of AB type, very crudely.

Counting Approach

• A very particular solution, but allows us to move forward.
• Addresses inequalities of AB type, very crudely.

– But perhaps the most important inequalities are overlapping disadvantages (Dreze & Sen 2013)

Counting Approach

• A very particular solution, but allows us to move forward.
• Addresses inequalities of AB type, very crudely.

– But perhaps the most important inequalities are overlapping disadvantages (Dreze & Sen 2013)

• Based on a distribution of scores, convey meaningful

information on deprivations or attainments.

Counting Approach

• A very particular solution, but allows us to move forward.
• Addresses inequalities of AB type, very crudely.

– But perhaps the most important inequalities are overlapping disadvantages (Dreze & Sen 2013)

• Based on a distribution of scores, convey meaningful

information on deprivations or attainments.

• Use the score distribution for understanding inequality.

Counting Approach

• A very particular solution, but allows us to move forward.
• Addresses inequalities of AB type, very crudely.

– But perhaps the most important inequalities are overlapping disadvantages (Dreze & Sen 2013)

• Based on a distribution of scores, convey meaningful

information on deprivations or attainments.

• Use the score distribution for understanding inequality.
• Can be applied society-wide, or restricted to inequality

among the poor.

Counting Approach

Counting Approach

• Counting measures respect ordinal variables or when

variables are not cardinally meaningful

– Townsend (1979), Atkinson (2003) – Widely used in LAC, Europe

Counting Approach

• Counting measures respect ordinal variables or when

variables are not cardinally meaningful

– Townsend (1979), Atkinson (2003) – Widely used in LAC, Europe

• Many applications, but one of which is

– Adjusted Headcount Ratio (Alkire and Foster, 2011)

• Several national and international adaptations (MPI, Mexico, Chile…)
• Well-being measure: Bhutan’s Gross National Happiness Index
• Chronic extension: Alkire, Apablaza, Chakravarty and Yalonetzky (2014)

trix z = ( 13 12 3 1 ) Cutoffs Dimensions Persons              1 3 11 20 1 10 5 . 12 5 7 2 . 15 1 4 14 1 . 13 Y

Counting Methodology

Achievement Matrix (equally valued dimensions)

Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived Domains Persons              1 1 1 1 1 1 1 g z ( 13 12 3 1) Cutoffs

a0 = 1 1 1 1 1 1 1 1 1 é ë ê ê ê ê ù û ú ú ú ú

Attainments (alternative)

Construct attainment matrix (equal value case)

1 if person attains deprivation cutoff in a given domain 0 if not Domains Persons

Note

Mirror of the deprivation matrix

Deprivation Matrix

• Counting Deprivations (equal value case)

≥ 1 Domains c Persons ฀ g0  1 1 1 1 1 1 1               2 4 1 Deprivation count vector c = (0, 2, 4, 1) Apply unidimensional inequality measure to count vector

a0 = 1 1 1 1 1 1 1 1 1 é ë ê ê ê ê ù û ú ú ú ú

Attainments

Counting Attainments (equal value case)

1 if person attains cutoff in a given domain 0 if not Domains a Persons

Attainment vector a = (4, 2, 0, 3) Apply unidimensional inequality measure

4 2 3

Methodological Notes:

Dimensional Cutoffs:

• Dichotomise ordinal data, so that the resulting measure is robust to

monotonic transformations of underlying data and cutoffs: provides rigorous (if minimal) treatment of ordinal scales of measurement.

Values:

• ‘Weights’ are in this case relative values on the presence or absence of the

cutoff level in a dimension. Normatively, these values create cardinal comparability across dichotomised deprivations or attainments

Empirically:

• Deprivation or Attainment scores can be used for society-wide inequality

measures.

• As a first step, we illustrate inequality among the poor, because our data

may not distinguish adequately among upper end of distribution.

Deprivation Matrix Censored Deprivation Matrix, k=2

฀ g0  1 1 1 1 1 1 1             2 4 1            

฀ g0(k)  1 1 1 1 1 1             2 4            

Identification of Who is poor (AF)

Identification Who is poor?

If poverty cutoff is k = 2 Now censor the deprivation matrix

Censored deprivation vector: (0,2,4,0) – used for inequality among the poor

• Mean of matrix = MPI poverty measure .

• How to measure inequality?

– Depends on which properties we want the measure to satisfy – Empirically, can use any: Gini, Theil, Generalized Entropy, Atkinson, Variance, Coefficient of Variation, etc. – Absolute or Relative? Attainments or Deprivations? NB: We generate a measure of inequality among the poor, because it is not possible for a multidimensional poverty measure to reflect inequality among the poor and satisfy the policy-relevant property of dimensional breakdown. Otherwise MD poverty measures can also reflect inequality (Bourguignon and Chakravarty 2003, et al.)

Inequality Among the Poor

An example using global MPI: Variance

A inequality measure that satisfies some desirable proporties is:

An example using global MPI: Variance

A inequality measure that satisfies some desirable proporties is:

V 𝑦 = 𝛽

𝑢 [𝑦𝑗 − 𝜈 𝑦 ]2

𝑢 𝑗=1

An example using global MPI: Variance

A inequality measure that satisfies some desirable proporties is: V(x): positive multiple of variance of distribution x m(x): mean of distribution x t: Number of elements in x a > 0

Chakravarty 2001, Seth Alkire 2014

V 𝑦 = 𝛽

𝑢 [𝑦𝑗 − 𝜈 𝑦 ]2

𝑢 𝑗=1

Some Properties of Variance:

• Symmetry: Permutation of scores among the poor does not change inequality

Some Properties of Variance:

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Transfer Principle: Increase in inequality due to regressive transfer

between any two scores

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Transfer Principle: Increase in inequality due to regressive transfer

between any two scores – Identical to Association increasing deprivation rearrangement among the poor in counting approach framework

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Transfer Principle: Increase in inequality due to regressive transfer

between any two scores – Identical to Association increasing deprivation rearrangement among the poor in counting approach framework

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

• Normalization: Zero inequality when everyone has the same score

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Transfer Principle: Increase in inequality due to regressive transfer

between any two scores – Identical to Association increasing deprivation rearrangement among the poor in counting approach framework

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

• Normalization: Zero inequality when everyone has the same score

Some Properties of Variance:

• Additive Decomposability: Total inequality should be presented as

a sum of two components: a within-group component and a between group component

• Within-group Mean Independence: Total within-group component

does not change if there is no change in inequality within any subgroup

• Transfer Principle: Increase in inequality due to regressive transfer

between any two scores – Identical to Association increasing deprivation rearrangement among the poor in counting approach framework

• Symmetry: Permutation of scores among the poor does not change inequality
• Population Principle: Replicating the number of poor with same scores does not

change inequality

• Normalization: Zero inequality when everyone has the same score

Some Properties of Variance:

MPI Indicators and Weights

Indicator Weight Deprivation Cutoff Schooling 1/6 1 if no household member has completed five years of schooling; 0 otherwise Attendance 1/6 1 if any school-aged child in the household is not attending school up to class 8; 0 otherwise Nutrition 1/6 1 if any woman or child in the household with nutritional information is undernourished; 0 otherwise Mortality 1/6 1 if any child has passed away in the household; 0 otherwise Electricity 1/18 1 if the household has no electricity; 0 otherwise Sanitation 1/18 1 if the household’s sanitation facility is not improved or it is shared with other households; 0 otherwise Water 1/18 1 if the household does not have access to safe drinking water or safe water is more than a 30-minute walk (round trip); 0 otherwise Floor 1/18 1 if the household has a dirt, sand or dung floor; 0 otherwise Cooking fuel 1/18 1 if the household cooks with dung, wood or charcoal; 0 otherwise Assets 1/18 1 if the household does not own more than one of: radio, telephone, TV, bike, motorbike or refrigerator; and does not own a car or truck; 0 otherwise Source: Alkire and Santos (2014)

Haiti: Distribution of Deprivation Scores

5 10 15 20 25 0 - <0.1 0.1 - <0.2 0.2 - <1/3 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher Percentage of Population Deprivation Score 2006 2012 Multidimensionally Poor Non Poor

Haiti: Distribution of Deprivation Scores

5 10 15 20 25 0 - <0.1 0.1 - <0.2 0.2 - <1/3 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher Percentage of Population Deprivation Score 2006 2012 Multidimensionally Poor Non Poor

Haiti: Distribution of Deprivation Scores

5 10 15 20 25 30 35 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score 2006 2012

Haiti 2006-2012

Haiti 2006-2012

• Data: Demographic Health Surveys 2006 and 2012

Haiti 2006-2012

• Data: Demographic Health Surveys 2006 and 2012
• Results

MPI Incidence 2006 2012 Change 2006 2012 Change 0.335 0.248

• 0.087***

0.606 0.494

• 0.112***

Intensity Inequality among the Poor 2006 2012 Change 2006 2012 Change 0.553 0.503

• 0.050***

0.253 0.190

• 0.062***

Haiti 2006-2012

• Data: Demographic Health Surveys 2006 and 2012
• Results
• Reduction in MPI by reducing incidence, intensity as

well as inequality among the poor

MPI Incidence 2006 2012 Change 2006 2012 Change 0.335 0.248

• 0.087***

0.606 0.494

• 0.112***

Intensity Inequality among the Poor 2006 2012 Change 2006 2012 Change 0.553 0.503

• 0.050***

0.253 0.190

• 0.062***

Haiti 2006-2012

• Data: Demographic Health Surveys 2006 and 2012
• Results
• Reduction in MPI by reducing incidence, intensity as

well as inequality among the poor

MPI Incidence 2006 2012 Change 2006 2012 Change 0.335 0.248

• 0.087***

0.606 0.494

• 0.112***

Intensity Inequality among the Poor 2006 2012 Change 2006 2012 Change 0.553 0.503

• 0.050***

0.253 0.190

• 0.062***

Haiti: Sub-national Regions

MPI Inequality among the Poor

2006 2012

Change 2006 2012 Change

Aire Métropolitaine 0.195 0.162

• 0.033*

0.189 0.182

• 0.007*

Artibonite 0.418 0.316

• 0.102***

0.229 0.196

• 0.032**

Centre 0.545 0.391

• 0.154***

0.313 0.213

• 0.100***

Grand-Anse 0.455 0.378

• 0.078*

0.242 0.201

• 0.041***

Nippes 0.381 0.257

• 0.124***

0.207 0.139

• 0.067***

North 0.399 0.244

• 0.155***

0.319 0.198

• 0.121***

North-East 0.358 0.323

• 0.035

0.238 0.217

• 0.021*

North-West 0.395 0.311

• 0.084**

0.240 0.147

• 0.092***

South 0.336 0.249

• 0.087**

0.218 0.192

• 0.026**

South-East 0.398 0.307

• 0.091**

0.223 0.147

• 0.075***

India 1999-2006

India 1999-2006

• Data: Demographic Health Surveys 1998/99 and

2005/06

Seth & Alkire 2014

India 1999-2006

• Data: Demographic Health Surveys 1998/99 and

2005/06

Seth & Alkire 2014

• Results

MPI Incidence 1999 2006 Change 1999 2006 Change 0.300 0.251

• 0.050***

0.568 0.485

• 0.083***

Intensity Inequality among the Poor 1999 2006 Change 1999 2006 Change 0.529 0.517

• 0.012***

0.224 0.219

• 0.005*

India 1999-2006

• Data: Demographic Health Surveys 1998/99 and

2005/06

Seth & Alkire 2014

• Results
• Reduction in MPI by reducing incidence, intensity, but

not large reduction in inequality among the poor

MPI Incidence 1999 2006 Change 1999 2006 Change 0.300 0.251

• 0.050***

0.568 0.485

• 0.083***

Intensity Inequality among the Poor 1999 2006 Change 1999 2006 Change 0.529 0.517

• 0.012***

0.224 0.219

• 0.005*

India 1999-2006

• Data: Demographic Health Surveys 1998/99 and

2005/06

Seth & Alkire 2014

• Results
• Reduction in MPI by reducing incidence, intensity, but

not large reduction in inequality among the poor

MPI Incidence 1999 2006 Change 1999 2006 Change 0.300 0.251

• 0.050***

0.568 0.485

• 0.083***

Intensity Inequality among the Poor 1999 2006 Change 1999 2006 Change 0.529 0.517

• 0.012***

0.224 0.219

• 0.005*

India: Poorest of poor: little change

5 10 15 20 25 30 35 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score 1999 2006

India: Poorest of poor: little change

5 10 15 20 25 30 35 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score 1999 2006

Inequality within Subgroups & Disparity

Inequality within Subgroups & Disparity

• Measured Poverty (MPI) fell statistically significantly

for all Indian subgroups – States, Castes, Religions

Inequality within Subgroups & Disparity

• Measured Poverty (MPI) fell statistically significantly

for all Indian subgroups – States, Castes, Religions

• However, the reduction was not necessarily combined

with reduction in inequality among the poor (variance)

– Southern states reduced inequality among the poor – Poorest Subgroups such as Bihar, ST, and Muslims did not

Inequality within Subgroups & Disparity

• Measured Poverty (MPI) fell statistically significantly

for all Indian subgroups – States, Castes, Religions

• However, the reduction was not necessarily combined

with reduction in inequality among the poor (variance)

– Southern states reduced inequality among the poor – Poorest Subgroups such as Bihar, ST, and Muslims did not

• Important to analyse both measures

India: Sub-national Regions

10 20 30 40 50 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Karnataka 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Bihar 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Scheduled Tribes 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Muslims 1999 2006

India: Sub-national Regions

10 20 30 40 50 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Karnataka 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Bihar 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Scheduled Tribes 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Muslims 1999 2006

India: Sub-national Regions

10 20 30 40 50 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Karnataka 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Bihar 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Scheduled Tribes 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Muslims 1999 2006

India: Sub-national Regions

10 20 30 40 50 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Karnataka 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Bihar 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Scheduled Tribes 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Muslims 1999 2006

India: Sub-national Regions

10 20 30 40 50 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Karnataka 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Bihar 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Scheduled Tribes 1999 2006 5 10 15 20 25 30 1/3 - <0.4 0.4 - <0.5 0.5 - <0.6 0.6 - <0.7 0.7 - <0.8 0.8 - <0.9 0.9 & Higher

Percentage of Poor Population

Deprivation Score Muslims 1999 2006

35

Eight Inequality measures for 91 countries

(shown: inequality in MPI scores among the poor)

Concluding Remarks

• Two types of inequality are relevant
• Cardinal data requirements can often not be satisfied.
• IHDI-type measures also have very demanding weights.
• Measures like Allison Foster depict within-dimension

inequality using median, but not across dimensions

• Counting approaches generate a vector of scores that can

be used for measured inequality (censored or not)

• It is a first step, admittedly losing much richness of

information, but is practical with ordinal/binary data.

Thank you from the OPHI team

multidimensionalpoverty.org

Forthcoming June 2015

In the SDGs: Poverty is Multidimensional

Open Working Group Goal 1 Target 1.2: by 2030, reduce at least by half the proportion of men, women and children of all ages living in poverty in all its dimensions according to national definitions. Sixty-Ninth Session of the UN General Assembly Dec 2014. (A/RES/69/238)

• 5. Underlines the need to better

reflect the multidimensional nature

• f development and poverty...

UNSG Synthesis Report Dec 2014: 2.1 Shared Ambitions: ... Member States will need to fill key sustainable development gaps left by the Goals, such as the multidimensional aspects

• f poverty

5.1 Measuring the new dynamics ... Poverty measures should reflect the multi-dimensional nature of poverty.

In the SDGs: Poverty is Multidimensional

Open Working Group Goal 1 Target 1.2: by 2030, reduce at least by half the proportion of men, women and children of all ages living in poverty in all its dimensions according to national definitions. Sixty-Ninth Session of the UN General Assembly Dec 2014. (A/RES/69/238)

• 5. Underlines the need to better

reflect the multidimensional nature

• f development and poverty...

UNSG Synthesis Report Dec 2014: 2.1 Shared Ambitions: ... Member States will need to fill key sustainable development gaps left by the Goals, such as the multidimensional aspects

• f poverty

5.1 Measuring the new dynamics ... Poverty measures should reflect the multi-dimensional nature of poverty.

Adjusted Headcount Ratio

Adjusted Headcount Ratio = M0 = HA = m(g0(k)) = 3/8

Domains c(k) c(k)/d Persons H = multidimensional headcount ratio = 1/2 A = average deprivation share among poor = ¾ Note: Easily generalized to where deprivations have different values v1, v2, v3, v4 summing to d = 4 ฀ g0(k)  1 1 1 1 1 1               2 4 2 / 4 4 / 4

Adjusted Headcount Ratio

Properties

Invariance Properties: Symmetry, Replication Invariance, Deprivation Focus, Poverty Focus Dominance Properties: Weak Monotonicity, Dimensional Monotonicity, Weak Rearrangement, a form of Weak Transfer Composition Properties: Subgroup Consistency, Decomposability, Dimensional Breakdown

Note

No transfer property within dimensions

Requires cardinal variables!

No transfer property across dimensions

Here there is some scope

Royal Economic Society