Topic 2:Inequality

-relative vs absolute; four principles;

Lorenz curves,gini coefficient,…etc

Inequality

• Definitions and measurements

• Theoretical & empirical debate:inequality & growth

• Jenkins & Micklewright (2007) NewDirections in the Analysis of Inequalityand Poverty, ISER working paper 2007-11.

2.1. Definition

• Who has benefited from economicgrowth?

• By how much? Who has been madeworse off?

• Inequality also affects other economicgoals

Cont’d

• “Economic inequality is the fundamentaldisparity that permits one individualcertain material choices while denyinganother individual those very samechoices” RAY, p. 170

2.1. cont’d

• Ethically why should some be treateddifferently? (gender/race discrimination)

• Hard to resolve the ethical dilemma onphilosophical grounds.

• Some are simply born to poverty orprosperity and some „had it coming tothem‟ via preferences/decisions (childborn in Congo vs a lazy student with 2.2instead a first-exogenous/endogenous )

Cont’d

• A practical goal is “tolerable levels ofinequality”

• Tolerance is determined by socialvalues/attitudes and by expectations ofeconomic policy‟s results

• Changes in relative inequality are moreacceptable if there are absolute gains forall

2.1. cont‟d

• Sen (1992) “Equality of what?” (Y, health…?)

• heterogeneity of human beings

• The multiplicity of variables in terms of whichinequality can be judged

• The first consideration implies preferences fordifferent measures amongst different people

Cont‟d

• Distinguish between achievement andfreedom to achieve – the latter is largelyignored

• X is richer than y but lives under adictator (so inequality is a slipperyconcept and is linked with broaderissues such as freedom and security)

2.1. cont‟d

• Equality should be measured in terms of

functionings and capabilities, not income

• Often => wealth/income/economic

inequality

• The distribution of income -source of

many of problems and is related to the

process of growth/development

WHICH CONCEPT IS

APPROPRIATE?

• Inequality in current income flows?

• Inequality in the distribution of wealth

(e.g. land and other assets)?

• The distribution of lifetime income?

2.2. Measurement

• The size distribution of income shows

the frequency with which the various

amounts are distributed in the sample

• But ignores the source of the income

[RAY, ch. 6, fig. 6.2, p. 176 & fig. 6.3, p.

177-Historgram example]

Cont’d

• We can measure the location (mean,

median etc.) and dispersion (range,

standard deviation) of the distribution

• Quintiles(y) by % of income earned(x).

E.g. the poorest quintile earns 9% of the

total income.

2.2. cont’d

• But what is of interest, changes in

A.The distribution of absolute income (the

whole range of actual values)?

OR

B. Relative income inequality in the

distribution of income (the dispersion

of income in the distribution)?

2.2. cont’d

• Measures of income inequality are not

objective due to normative assumptions about

who matters

• It is typically assumed in these analyses that

Social welfare = f (income, inequality)

+ve -ve

• But increases in inequality do not necessarily

mean that overall welfare has declined(China)

Data and empirical issues

• Reliability of income and consumption data for inequality measurement

• Source: household surveys

• There are errors in income (reporting & measurement error)

Cont’d

• Some products/services are not recorded

• Consumption data are often used, butthey understate inequality/incomedifferentials

• Many transactions are not undertakenin cash

2.2. cont’d

• Common ownership rights - not

captured

• Estimation of income and consumption

has a high variance (why?

Covariate/idiosyncratic shocks- former

understates and latter overstates

inequality)

Cont’d

• Sample survey limitations - recall error,

short period of reference (e.g. last week),

remote villagers and other marginal

groups not captured

• Price indices are unavailable e.g. for

rural-urban price differentials

INEQUALITY MEASUREMENT

CRITERIA (RAY, ch. 6)

• 1. Anonymity principle

- who has what/how much is irrelevant for measurement

- meaning we can always arrange our income distribution as y1, y2 … yn

• 2. Population principle

- population size is irrelevant. Only population shares matters.

- cloning the entire population should not alter inequality

2.2. cont’d

3. Relative income principle

– Absolute values irrelevant.

- Like principle 2 above, the incomeshares not the absolute levels ofincome should matter (i.e. what % ofthe total income earned went to thepoorest/richest quintile?).

Cont’d

4. The Dalton principle (the Pigou-DaltonPrinciple)

If we can move from one distribution toanother by transferring resources fromthe relatively poor to the relatively rich(i.e. regressive transfer) we will end upwith a more unequal distribution thanbefore

FORMAL APPROACH

• For all i = 1, 2, …, n with incomes yi the

income distribution is (y1, y2,…, yn)

• An inequality index I = I (y1, y2,…, yn)

can be defined over all (y1, y2,…, yn).

• The value of I (e.g. a Gini coefficient)

represents the inequality of the

distribution.

• Lorenz curve is its graphical

counterpart.

• The larger the value of I the greater the

inequality of the distribution of income

Anonymity principle

I is completely insensitive to the ordering

of y1 y2 … yn

Knowing „who gets how much‟ does not

affect I.

Population principle

• For every identical income distribution

I(y1, y2,…, yn) = I(y1, y2,…, yn; y1,

y2,…, yn)

Cloning the population has no effect on I.

Relative income principle

• For every positive number > 0,

I(y1, y2,…, yn) = I( y1, y2,…, yn)

Example: Doubling the income of everyone is

irrelevant to the magnitude of I.

Pigou- Dalton principle

• For every income distribution and

every transfer > 0,

I(y1,…,yi,…,yj,…,yn) < I(y1,…,yi-

,…,yj+ ,..,yn) ; whenever yi yj

Regressive transfers increase I (e.g. IFS‟s

criticism of UK gov‟ts plans - 2010).

LORENZ CURVES

• A Lorenz curve plots the cumulative

percentage of total income(y) received

against the cumulative percentage of the

population(x) who receive it, in

ascending order of income

[RAY, ch. 6, figure 6.4, p. 179]

2.2. cont’d

• A 45-degree line represents the line of

absolute equality (y=x)

• Increasing inequality is indicated when the

Lorenz curve falls further below this line

THE LORENZ CRITERION:

A. If one Lorenz curve lies wholly above

another, the first represents a more

equal income distribution than the

second

[RAY, ch. 6, figure 6.5, p. 180]

2.2. Cont’d

B. If two Lorenz curves coincide, the two

distributions are equally unequal

C. If two Lorenz curves intersect we

cannot make any clear judgement

about relative inequality

[RAY, ch. 6, figure 6.7, p. 183]

Lorenz-consistency

• An inequality measure is Lorenz-consistent iff it is simultaneouslyconsistent with the anonymity,population, relative income and Daltonprinciples.

2.2. Cont’d

• Formally an inequality measure isLorenz-consistent if, for every pair ofincome distributions, (y1, y2,…, yn) and(z1, z2,…, zn):

I(y1, y2,…, yn) I(z1, z2,…, zn)

whenever the Lorenz curve of (y1, y2,…,yn) lies everywhere to the right of (z1,z2,…, zn)

[RAY, ch. 6, figure 6.6, p. 182]

2.2. Cont’d

• Lorenz curves and measures based

on them are mean independent

Thus, they are relative inequality and

not absolute inequality measures

Formula MEASURES [RAY, ch. 6, pp. 186-9; Sen (1997)]

• Notation:

m - distinct incomes

j - classes of income

n - number of people

y - income

2.2. cont’d

• Range

• Meanm

j jj ynn 1

1

)(1

minmax yyR

m

j jnn1

1. Range

It is

A. A crude measure

B. Useful when complete data is not

available on income distribution.

C. Ignores everyone in between

D. Does not satisfy the Dalton principle.

2. The Kuznets ratio (KR)

The share of income of the richest x%

divided by the share of income of the

poorest y%. The ratios are basically

components of the Lorenz curve. Good

when data is missing.

KR = share of income of richest x%

share of income of poorest y%

Not the whole distribution used

3. The mean absolute

deviation

– uses the idea that inequality is

proportional to the distance from mean

income (first measure to take the

whole distribution; insensitive to

Dalton principle-why?)

j

m

ji

j ynn

M1

4.The coefficient of variation

– gives more weight to larger deviations

from the mean and is less sensitive

than M. So insensitivity to Dalton

addressed

m

j

j

jy

n

nC

1

2)(1

5. The Gini coefficient

– is the sum of differences between all

possible pairs of incomes divided by

population squared and mean income

(why multiplying by 2? Since yi-yk =d=

yk-yi i.e. deviations counted and

summed twice)

kjk

m

k

j

m

j

yynnn

G11

22

1

Measures summary

• Most measures are additively

decomposable

• Contribution to overall inequality!

• Therefore, we can calculate between-

groups or within-groups Gini

coefficients.

Example

• We sub-divide the population of UK into

groups of Whites, Blacks and Asians and

computer the respective between-group

G‟s.

• In some instances it is interesting to

look the within-group inequalities (e.g.

among whites).

Gini coefficient

• G measures the area between the

Lorenz curve and the line of absolute

equality as a percentage of the total area

under this line (0 = perfect equality, 100

= perfect inequality)

[TOD, ch. 5, figure 5.3, p. 214]

• The Gini coefficient is Lorenz-consistent

and is widely used in empirical work

Other measures

• Decile or fractile comparisons are frequently

cited, they are just parts of the Lorenz curve

• Both the coefficient of variation and the Gini

coefficient are useful, but give conflicting

indications when Lorenz curves cross -

incomplete measures of true inequality

• Sen‟s, Enthropy and Atkinson‟s indices

2.3. Income inequality: causes

(policy level)

• The functional distribution of income dividesincome according to its source (e.g. land,labour, capital, transfers)

[RAY, ch. 6, figure 6.1, p. 172]

• An extended functional distribution approachcaptures conflicts between industrial sectors,modes of production and geographical location

• This understanding of the sources of incomeinequality may influence how we judge theoutcome

2.3. cont’d

Bigsten‟s (1987) categorization of causes:

• Institutional Determinants

– type of economic system

• Determinants of the Functional Distribution

- factor proportions

- technology (both affect returns to labour)

2.3. cont’d

• Determinants of Both Function & Size

- sectoral structure

(labour-intensive or not)

- regional structure (rural-urban)

- factor markets (market imperfections)

- commodity markets (relative price

changes)

2.3. cont’d

• Determinants of Size Distribution

- asset ownership (e.g. land, capital)

- possession of human capital

- social stratification (e.g. discrimination)

2.3. What can be done?

• HISTORY

- 1950s/1960s – growth will eliminate inequality

- 1970s/1980s – redistribution with growth

- Chenery (1974) advocated targeting certain groups e.g. landless, unemployed, working poor

- basic needs strategy

2.3. cont’d

• International Labour Office (1976)argued for direct effort at alleviatingbasic wants (food, shelter, clothing;healthcare, education, water)

• More recently debate focuses on linksbetween inequality and economic growth(Jenkins & Micklewright, 2007)

Any lesson from FIFA rules

Milanovic, Globalization and Goals: DoesSoccer Show the Way?

“Soccer is the most globalized sport withan almost fully free circulation of labor(players). This has led to a concentrationof quality among the top, that is therichest, clubs. …

• ….But on the other hand, the existence

of the FIFA requirement that players

cannot change national teams has

produced the opposite effects: greater

equality in the quality of national teams.

• …If soccer is a paradigm for world

economy, it shows that certain

inequality features that are fostered by

globalization need to be moderated

through the existence of some

overarching (global) rules whose

objective is to redistribute the gains

from globalization. FIFA's rules do

precisely that”.

Regulation of prices

[Sundrum(1990),chs.15-16; TOD,ch.5]

- promoting competitive market conditions

- removing factor price distortions

(e.g. reducing subsidies to capital)

- price ceilings for essential commodities

- minimum wages (government determined)

- controlling inflation

2.3. cont’d

• Regulation of production

- improve the relative position of

agriculture

- encouraging labour-intensive techniques

• Re-distributive policies

- promoting equality of opportunity

(e.g. in education and health care)

2.3. cont’d

- redistribution of assets (e.g. land reform;

Not like Mugabe)

- redistribution of incomes (through

progressive taxation and transfer

payments)

- subsidising public consumption goods

available to the poor (e.g. health care)

2.4 Inequality & growth:

Empirical level

• Growth will usually only result in

redistribution to the poor as a result of

government social expenditure policies

(e.g. via pro-poor interventions)

• Redistributive policies may also promote

economic growth e.g. reducing crime and

political instability, increasing nutrition

and labour productivity levels

2.4. cont’d

• Also they may reduce market failures in

land, labour and, especially, credit

markets

• Developing countries could grow faster,

and more equitably, by shifting

investment towards rural, labour-

intensive activities especially farming

2.4 cont’d

• Does growth increase or decrease income inequality?

- Inequality is not well correlated with

income ( e.g. Bolivia & Cameroon: GNP

per capita , 1,010 for both but gini 0.60

& 0.45 respectively)

[TOD, ch. 5, table 5.3, p. 229]

2.4. cont’d

• KUZNETS‟ INVERTED U-HYPOTHESIS

• Kuznets (1955, 1963) found a statisticalassociation between income levels andinequality across countries - an invertedU-shaped pattern[TOD, ch. 5, figure5.10, p. 227]

• He concluded that growth would lead torising inequality in the early stages ofdevelopment.

2.4. cont’d

• Why?

- structural change (agriculture

industry)

- little scope for redistribution of benefits

• However, further growth would reduce

inequality if there is an/a;

- increase in agricultural productivity /

wages

- transfer payments from rich to poor

2.4. cont’d

• EVIDENCE ON THE KUZNETS

CURVE/HYPOTHESIS

• Cross-sectional analysis provides some

support [RAY, ch. 7, figure 7.1, p. 203]

• However the evidence is not convincing

[TOD, ch. 5, figure 5.11, p. 230]

• Time-series studies indicate that inequality

falls over the course of development (e.g.

Deininger & Squire, 1996)

2.4. cont’d

• Causality could run in both directions;

growth inequality

or

inequality growth

. Simultaneous equations set up.

2.4. cont’d

• Does initial inequality affect subsequent growth?

Greater initial inequality hinders growth if:

a. poor lack access to credit for investment

b. low incomes low demand for local products

c. the rich don‟t save to finance investment

d. the poor are socially and politically excluded

2.4. cont’d

• Lower initial inequality hinders growthif:

- the incentives to save are reduced by re-

distributive policies (if capital flight is

encouraged )

- re-distributive policies require higher

levels of taxation which are bad for

promoting economic growth

2.4. cont’d

• Inequality and Growth: evidence

• Traditionally negative relationship

between initial inequality and

subsequent growth (e.g. Deininger &

Squire 1996; for an opposing view see

Forbes 2000)

• However, the evidence is mixed

[TOD, ch. 5, figure 5.14, p. 233]

• However, the evidence is mixed

[TOD, ch. 5, figure 5.14, p. 233]

• -ve growth and higher G: 20 countries

• -ve growth and lower G: 3 countries

• +ve growth and lower G: 10 countries

• +ve grwoth and higher G: 26 countries

• (WDI, 2007)

2.4. cont’d

• Initial inequality in land-crucial

• Do inequalities perpetuate themselvesthrough consumption patterns, lack of accessto capital markets or human capitalinvestments?

• If yes, then there is a rationale for governmentintervention and policy formation in thesemarkets