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

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 on 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

Global inequality, Gini coefficient, 1990-2010: alternative estimates (ppp 2005 ) 0.760 0.740 0.720 Household suvey data (HSD) 0.700 Gini coefficient 0.680 HSD normalized by HCE per capita in NA 0.660 HSD normalized by 0.640 GDP per capita in NA 0.620 0.600 1985 1990 1995 2000 2005 2010 2015 Year 8

Global inequality (Gini) and poverty a) with ppp 2005 and ppp 2011: 1990- 2010 (Household survey data) 0.760 60.0 0.740 50.0 Household suvey data (HSD) ppp 2005 figures 0.720 40.0 Povert Headcount (%) 0.700 Gini Coefficient Household suvey data (HSD) 0.680 30.0 ppp 2011 figures Poverty Headcount (HSD) 0.660 with PPP 2005 (green) and 20.0 PPP 2011 (purple) 0.640 10.0 0.620 0.600 0.0 1985 1990 1995 2000 2005 2010 2015 Year 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 9

Global GDP per capita and coverage rate of the HSD data: 1990-2010 11000 120.0 GDP per capita, global mean (ppp 2005) 10000 100.0 Ratio of HSD mean income/consumption per capita to HCE per capita 9000 80.0 Percent Dollars ppp 2005 8000 60.0 Ratio of HSD mean 7000 40.0 income/consumption per capita to GDP per capita 6000 20.0 5000 0.0 1985 1990 1995 2000 2005 2010 2015 Axis Title 10

Global inequality, 1990-2010: the influence of China Household Survey Data 0.760 China growing as the rest of the world 0.740 0.720 World without China 0.700 Gini coefficient World 0.680 0.660 0.640 0.620 0.600 1985 1990 1995 2000 2005 2010 2015 Year 11

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 y i the income of person i and d ij 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:   d y y ij i j 1   j d G  n d y i ij j j • This expression can then be expanded to find the equivalent of other usual expressions of the Gini coefficient. 13

Distance-sensitive Theil measures • In the same way , one may define the D-Theil and the D-MLD as: ~ 1 y y  1 y    d i i d i T Ln MLD Ln ~ ~ n y y n y i i i i i   ~  with: y d y / d i ij j ij j j • 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

Application to global inequality • An appealing set of distances in the case of global inequality is:  1 d if i and j are from the same country ij   d if not ij • δ = distance sensitivity coefficient – δ = 0 global inequality = mean inequality across countries – δ = 1 standard global inequality measures   – Intermediate cases: introversion   0 , 1     ,  – extraversion 1 15

D-Gini according to distance sensitivity coefficient: 1990-2010 0.75 0.7 0.65 0.6 Gini coefficient Gini90 0.55 Gini95 Gini2000 0.5 Gini05 Gini08 0.45 Gini10 0.4 0.35 0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Distance Sensitivity coefficient 16

The non-linearity issue ~ • Personalized mean extremely sensitive to δ in y i presence of a large population when δ is close to 0    .( ) y n y y ~  i i y    i 1 ( n 1 ) ~   y n ( y y )  i i        2 1 ( n 1 ) 17

The inversion of global inequality changes at low sensitivity to distance ( δ ) D-Gini difference with respect to 1990 according to distance senstivity coefficient : 1995-2010 4 3 2 Difference in D-Gini 1 DGini95-DGini90 DGini00-DGini90 0 DGini05-Dgini90 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 DGini08-DGini90 DGini10-DGini90 -1 -2 -3 -4 18 Distance sensitivity coefficient

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 d ij increases with y j , 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

1 Income mobility Stephen P. Jenkins London School of Economics Email: s.jenkins@lse.ac.uk Economic Journal 125 th Anniversary Session: (Almost) a century since Dalton (and Gini): where is inequality analysis going?

2 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

3 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) • Inter generational mobility: between generations • Intra generational mobility: within generations, over the life course Outline • Progress: retrospective (What have we learnt?) • Progress: prospective (What next?)

4 Progress Looking backwards

5 1. Concepts: “mobility” is intrinsically more complicated than “inequality” Mobility types Normative assessment 1. Relative (positional | rank | 1. Origin independence ↑ ~ EOpp ↑; poverty persistence ↓ exchange) ( good ) – Not everyone can be upwardly mobile 2. Absolute (individual level 2. Depends on social evaluation function, e.g. whether favour income growth) pro-poor growth ( good | bad ) – Income change may be + or – for a person 3. Good if longer-term 3. Reduction of inequality in inequality reduction desired longer-term (lifetime | (NB depends on benchmark) dynastic) income 4. Income risk 4. Bad for risk-averse individuals – Movement ~ unpredictability

6 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)

7 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

8 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 over a period than a cross-section sample suggests; turnover among the poor

9 Progress Looking forward A sample of suggestions

10 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

11 1. Concepts and measures • Move away from IGE (or IGC) for intergenerational studies, having first identified which mobility concept of 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”

12 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?

13 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 of 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)

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

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-A H ) × E (1-A Edu ) × I L (1-A INC ) ] 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) .

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 observed 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 observed distribution

Inequality Adjusted HDI (2011)

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 other indicators at all levels of achievements. - Data requirements cardinal (ratio scale) Stochastic dominance comparisons: 2 nd 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 other indicators at all levels of achievements. - Data requirements cardinal (ratio scale) Stochastic dominance comparisons: 2 nd order with many - variables requires cardinality. - Looks only at Kolm (Seth 2013: both) - How move to non-cardinal dimensions? - median

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

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

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 on 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 on breadth.

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)

Counting Methodology Achievement Matrix (equally valued dimensions) trix Dimensions   13 . 1 14 4 1 Persons   15 . 2 7 5 0    Y   12 . 5 10 1 0     20 11 3 1 z = ( 13 12 3 1 ) Cutoffs

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

Attainments (alternative) Construct attainment matrix (equal value case) 1 if person attains deprivation cutoff in a given domain 0 if not Domains é ù 1 1 1 1 ê ú Persons 1 0 1 0 a 0 = ê ú ê ú 0 0 0 0 ê ú ë 1 0 1 1 û Note Mirror of the deprivation matrix