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Summary Economic Analysis of Inequality: Core lectures (powerpoint lesnotities)

Name: Economic Analysis of Inequality: Core lectures (powerpoint lesnotities)
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Course: Economic Analysis of Inequality (with Capita Selecta) Studiegidsnummer: 2300PSWEAI Studierichting: Sociologie, SEW, keuzevak andere richtingen (master) Prof: Koen Decancq Het examen is een openboek examen, dus deze samenvatting mag je meenemen naar uw examen. Het bevat alle powerpointdia's...

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Economic Analysis of Inequality
(Koen Decanq)

CORE LECTURES: Powerpointpresentaties + lesnotities

, 1

Inhoud
Lecture 1: From principles to policy (27/9) ............................................................................................... 4
1.0. Practicalities...................................................................................................................................... 4
The Exam ............................................................................................................................................. 4
1.1. Setting the scene............................................................................................................................... 4
1.1.1 Hot topic ..................................................................................................................................... 4
1.1.2 Roadmap ..................................................................................................................................... 4
1.2. Normative reasons (because of our value judgments about inequality) ............................................. 8
Lecture 2: Charting Income Distributions (2/10) ..................................................................................... 10
2.1. Introduction .................................................................................................................................... 10
2.1.1 Concepts ................................................................................................................................... 10
2.2. 4 types of functions ......................................................................................................................... 11
2.2.1 Probability Density Function ...................................................................................................... 12
2.2.2 Cumulative Distribution Function (CDF) ..................................................................................... 16
2.2.3 Quantile Function ...................................................................................................................... 18
2.2.4 Lorenz Curve ............................................................................................................................. 19
Lecture 3: Partial Social Evaluations ....................................................................................................... 22
3.1. Social Welfare Functions ................................................................................................................. 22
3.1.1 Continuity (CONT) ..................................................................................................................... 22
3.1.2 Separability (SEP) ...................................................................................................................... 23
3.1.3 Population Replication (POP) ..................................................................................................... 24
3.1.4 Anonymity (ANOM) ................................................................................................................... 24
3.1.5 Monotonicity (MON) ................................................................................................................. 25
3.1.6 A class of Social Welfare Functions ............................................................................................ 25
3.2. Stochastic Dominance ..................................................................................................................... 26
3.2.1 First order stochastic dominance ............................................................................................... 26
3.2.2 Second order stochastic dominance .......................................................................................... 28
3.2.3 Third order stochastic dominance ............................................................................................. 32
3.2.4 And beyond… ............................................................................................................................ 34
Lecture 4: Complete Social Evaluations .................................................................................................. 35
4.0. Recall .............................................................................................................................................. 35
4.1. Iso-elastic social welfare functions .................................................................................................. 35
4.2. Equally Distributed Equivalent......................................................................................................... 41

, 2

4.2.1 So far we obtained .................................................................................................................... 41
4.2.2 Equally Distributed Equivalent ................................................................................................... 41
4.3 Reading for this lecture .................................................................................................................... 43
Lecture 5: Partial inequality comparisons (18/10) .................................................................................. 44
5.1 The generalized Lorenz curve ........................................................................................................... 44
5.1.1 Generalized Lorenz Curve .......................................................................................................... 44
5.1.2 Generalized Lorenz dominance.................................................................................................. 45
5.2 The Lorenz curve .............................................................................................................................. 47
5.2.1 Lorenz dominance (equal means) .............................................................................................. 47
5.2.2 Lorenz dominance and invariance ............................................................................................. 50
Lecture 6: Complete inequality comparisons (23/10) ............................................................................. 56
6.0 Introduction ..................................................................................................................................... 56
6.1 The Atkinson Family ......................................................................................................................... 56
Remember ......................................................................................................................................... 56
Founding Family................................................................................................................................. 57
6.2 The Gini family ................................................................................................................................. 60
6.3 The Generalized Entropy family (NOT ON EXAM).............................................................................. 70
Subgroup decomposability ................................................................................................................. 71
In sum.................................................................................................................................................... 72
Lecture 7: Measuring Poverty (25/10) .................................................................................................... 73
7.0 Introduction ..................................................................................................................................... 73
7.0.1 Measuring poverty .................................................................................................................... 73
7.1 Poverty line ...................................................................................................................................... 73
7.1.1 Absolute poverty line ................................................................................................................ 73
7.1.2. Relative poverty line ................................................................................................................. 73
7.1.3. Weakly relative poverty line ..................................................................................................... 74
7.2 Poverty measures (complete poverty comparisons) ......................................................................... 75
7.2.1 Focus ......................................................................................................................................... 75
7.2.2 Monotonicity............................................................................................................................. 78
7.2.3 Transfer..................................................................................................................................... 79
7.3 Poverty dominance (partial poverty comparisons) ........................................................................... 82
7.3.1 Fixed measure, all poverty lines ................................................................................................. 82
7.3.2 All measures, fixed poverty line (NOT EXAMEN) ........................................................................ 83

, 3

Lecture 8: Quantifying Redistribution (13/11) ........................................................................................ 84
8.0 Literature ......................................................................................................................................... 84
8.1 Income taxation ............................................................................................................................... 84
8.2 Impact of (income) taxation on inequality ........................................................................................ 90
Lecture 9: Optimal redistribution (15/11) ............................................................................................... 98
9.1 How much should we redistribute? .................................................................................................. 98
9.1.1 When Pigou-Dalton transfers are possible ................................................................................. 98
9.1.2 When Pigou-Dalton transfers are NOT possible ......................................................................... 99
9.2 The social planner wants to choose the level of redistribution so that a social welfare function 𝑊(. ) is
maximized given the constraints she faces. .......................................................................................... 102
X.Some conclusions/Interesting points................................................................................................. 103
X.0 Structure ........................................................................................................................................ 103
X.1. Lecture 1-3 .................................................................................................................................... 103
X.1.1 First order stochastic dominance ............................................................................................. 103
X.1.2 Second order stochastic dominance ........................................................................................ 104
X.1.3 Two person Graph ................................................................................................................... 105
X.2 Lecture 4-5 ..................................................................................................................................... 106
X.2.1 Lorenz dominance and invariance ........................................................................................... 106
X.2.2 Gini family ............................................................................................................................... 106
X.3 Lecture 6-7 ..................................................................................................................................... 107
X.3.1 Poverty deficit ......................................................................................................................... 107
X.4 Lecture 8 ........................................................................................................................................ 107
X.4.1 Impact of taxation on inequality .............................................................................................. 107

, 4

Lecture 1: From principles to policy (27/9)
Core: different people may have different perspectives to look at welfare, wellbeing…

1.0. Practicalities
The Exam
 Study material
o Articles on Blackboard (read it in a clever way)
o Slides on Blackboard
o Personal notes taken at lectures (most important)
 Graphs you have to make it by yourself
o No reproduction, but understanding of material!
 Open-book, written exam about material covered in core lectures
 Take-home exam about material covered in additional lectures
o When you come to the exam of the written exam you give it back

1.1. Setting the scene
1.1.1 Hot topic
 Not only more interest in the street, media, policymakers, but also in the academic world
o Ex. Pickety, Stiglitz
 This is an economic course

1.1.2 Roadmap
1. What is inequality?

3 Concepts:

 (Social) welfare: Evaluation of (income) distribution according to its size and inequality (see lecture
3-4): what is the better (most desirable) distribution, the core
o Grootte van de pizza + verdeling ervan
 Inequality: Evaluation of (income) distribution according to its inequality (see lecture 5-6)
o Verdeling van de pizza (geen nadruk op de grootte)
 Poverty: Evaluation of lower part of (income) distribution (see lecture 7)

 Different concepts! (think of China nowadays, inequality raises and poverty decreases)
 Creating conceptual clarity is one of the main aims of the course

, 5

Survey exercise

 More ethically intuitions/normative
 How we can measure inequality knowing that there are different intuitions
 We try to describe the normative side of economy

8

7
currency of "Hypothesia"

6

5

4 Programme X
Programme Y
3

2

1

0
Ann Bob Charlotte Danny

 The pizza is bigger in Y, but more equal in X

6

5
currency of "Hypothesia"

4

3 Programme X
Programme Y
2

1

0
Ann Bob Charlotte Danny

 X is equal
 Y is not equal
 If you take from Ann (X) to Danny (X) -> you reach the Y distribution (= transfer that is called Pigou-
Dalton: take from the poor give to the rich: inequality goes up)
 Y is more unequal than X

, 6

6
currency of "Hypothesia"
5

4

3 programme X
Programme Y
2

1

0
Ann Bob Charlotte Danny

 Now we compare pizza’s from another size
 Reaching Y is doubling all people’s income from X
o Intuition 1: inequality is the same
o Intuition 2: inequality is increased
o Some think relative, some think absolute

2. Why should we care about inequality?

2.1 Instrumental reasons (because of the consequences of inequality on other outcomes)

 Recent epidemiological insights (Wilkinson & Pickett, 2009)
o X-axe is always income inequality
o Y-axe is a bad thing (health problem, crime…)
o Positive relation, not at all a causal relation (maximum a correlation)
o http://www.youtube.com/watch?v=cZ7LzE3u7Bw (! Part of the study material)

, 7

 Economists are predominantly interested in the effect of inequality on economic output (GDP) or
its growth (not interested in crime, health…)
 Founding father: Simon Kuznets
o Kuznets curve: horizontal: low to high GDP/output – gini first raises then decreases
o Unfortunately life is more complicated
 Recent revival: Piketty (Capital), Milanovic (Global Inequality)
 Establishing the (causal) effect of inequality on economic growth is a VERY DIFFICULT question

 Because inequality is not an exogenous variable (given)
 (it is not assigned randomly to countries)
 Causal empirical statements are hard to make (see your econometrics course)
 Also theoretically it is a hard question
 Monopoly effect: the rich may gain a lot by protecting their acquired positions (rent seeking)
o The rich try to protect their rent, organize the society that the poor not becoming rich
o USA: education system: the rich don’t want the poor becoming rich
o USA: no progressive taxation system
 Incentive effect: Inequality creates incentives for investment and entrepreneurs (a little bit of
inequality is good).
o Wealth generated by the rich trickles down to lower parts of distribution
 Which of both effects, the incentive or the monopoly effect, is the biggest

, 8

1.2. Normative reasons (because of our value judgments about inequality)
Inequality is unfair

 When is a social situation fair? What is fair?
o We think inequality isn’t fair
o The central question in the work of John Rawls
 Impartiality as crucial requirement for fairness: Rawls proposes to think about the society
behind a veil of ignorance
o Thought experience: jump out of a plane and fall in the shoes of a rich/poor person
healthy/sick person – the situation in the plane: sitting there, how we are going to organize
the society (fair society behind the veil of ignorance)
 How would/should individuals behave behind such a veil of ignorance?
 Answer of Rawls: use the difference principle = you look at the guy who is the worst off (ex. Plane-
shoe), he has to be best off

 The difference principle: evaluate a social situation by looking at the worst-off individual

An example: in which society you wil land (plane-shoe exemple)

 The worst thing that can happen in A (ind 1), in situation B (ind 3)

 For Rawls it doesn’t matter only the person who is worst off

, 9

Harsanyi

 How would/should individuals behave behind such a veil of ignorance?
 Answer of Rawls: use the difference principle
 Answer of Harsanyi: use expected utility (as if it were a lottery)

Open philosophical (ethical) debate about what a fair income distribution is.

 Yet, most people will agree about the ingredients of the problem:

o The size of economic output (the size of the cake) – mister average

o The inequality distribution of economic output (the distribution of the cake) – mister
Rawls

o How to trade off to the both??

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