BEGRIP UITLEG PAGINA
1st order stochastic 1) All social welfare functions that are based on an increasing set of 17
dominance functions that agree on something
2) The first part is equivalent to this test: look at the CDF (F) and see if
the one CDF is above the other one
PROOF page 17
This is not useful if the CDF’s cross second order, impose 6th property
2 cases Lorenz Curve Equal means and different means 30
2 questions 1) Identification of the: Who is poor? What defines them? (sociologists) 47
2) Aggregation of poverty: how much poverty is there in the society?
(economists)
2th order stochastic Partial social evaluation 18
dominance We shrink the set of social judgements over which we require unanimity and
add another property to our list of properties for a desirable welfare function
= a Pigou-Dalton (or a progressive) transfer
3 aspects of poverty Incidence, intensity and inequality 48
3th order stochastic Let’s be even less ambitious and add another property. The diminishing 20
dominance transfer principle.
- A positive 3th derivative
- We give more weight to what happens at the bottom
- Look at the area under the area
- Also beyond: we can gradually impose stronger principles involving
more complicated composite transfers (but interpretation and
empirical test are challenging)
5 basic properties for W Continuity (CONT), separability (SEP), population replication (POP), anonymity 14
(ANON) and monotonicity (MON)
ability Part of why vertical equity principle 58
Equal utility loss for all (concave utility function) GRAPH
Absolute frequencies How many people have an income of x. (number of individuals) 7
- Histogram page 8
Absolute LC Use when absolute invariance, it uses and alternative method to “cancel out” 34
the effect of the size, compared to standard (relative) LC
You subtract the mean so you get 2 distributions with the same
average of 0
Absolute position Absolute amount of growth 2
- Differences between poor and rich
Absolute poverty line The poverty line is an absolute number and does not depend on distribution 47
The poverty line captures the minimum needed for physical subsistence, the
money you need to not die Z
Administrative data Tax- authorities 7
In principle all individuals, but actually non-representative. Important socio-
demographic information is missing (education) and information depends on
tax legislation
Anonymity (ANON) The names do not matter in the ranking of two income distribution. 16
- This property reflects the veil of ignorance
- We evaluate only based on distribution
- Who gets what = completely irrelevant
Anti-poverty policy All people should have sufficient needs to means, to have a sufficient life 71
Sufficientarianism Decent standard of living
AROPE 60% if median income 49
Median is much more stable then mean, but tends to be lower
1
, Atkinson Example page 27 27
Atkinson theorem (CASE Allows us to compare the social welfare functions who have the 5 basic 31
1 where equal means in properties + TRANS with the Lorenz Curve
LC) Whenever there is Lorenz dominance, all functions which satisfy the
properties CONT, POP, ANON, SEP, and TRANS agree = inequality
indices
Foundation from welfare economics
Plot cumulative proportion of the population (ordered from rich to poor)
against the cumulative proportion of total income (graphs page 32)
When LC closer to 45° line and not cross this LC dominates the other LC
Atkinson-Kolm-Sen A percentage. The % of income you would be able to pay to Robin Hood 38
inequality measure Part of Atkinson family
Average income Multiply each of the proportions with the income level itself 10
- Is interesting but only on partial view of the distribution
Average tax rate How much tax liabilities do you pay on your income. Page 59 = for Belgium 57 + 59
Benefit principle Part of vertical equity principle 58
Due to Mattheus effect make the rich more than proportional use of public
goods, hence they should pay more
Between countries Empirical results 44
Gini coefficient goes down but only for the not bottom sensitivity people
Bottom sensitivity High inequality aversion
Canonical poverty Satisfy the Transfer principle in context of poverty measuring 52
measures
CASE 1: equal means Look at distributions with the same size (mean), so that social welfare equals 31
inequality
The generalized LC/average = Lorenz Curve
Atkinson theorem
CASE 2: different means Look at distributions with different means and use an invariance principle 33
The Lorenz curve is the generalized Lorenz curve of the distribution of income
relative to the mean rather than incomes themselves
Causal effect Establishing (causal) effect of inequality on economic growth is very difficult 4
- Because inequality is not an exogenous variable, it is determined from
within the system
Class of social welfare All the properties are satisfied 16
function
Complete social Make social evaluations based on one specific sociale welfare function 22
evaluation You will be able to compare f.e. 2 countries (was not with partial social
evaluation)
Concentration curve Rank people according to the X distribution (from poor to rich) and adding up 60
their proportion in the Y distribution (health care).
The only difference between LC and this cure = adding up the proportion in the
Y distribution instead of the X distribution
Continuity (CON) Small changes in the income distributions do not change the ranking of two 14
income distributions
- W(.) is a continuous function
Country-specific median Relative philosophy and political reasons (see page) 50
Cumulative distribution Derived form PDF. What % of the people have less then that income level, who 10 + 11
function (CDF) are poorer then x
Start with 0 and add up the portions up to x (EX. Page 11)
2
1st order stochastic 1) All social welfare functions that are based on an increasing set of 17
dominance functions that agree on something
2) The first part is equivalent to this test: look at the CDF (F) and see if
the one CDF is above the other one
PROOF page 17
This is not useful if the CDF’s cross second order, impose 6th property
2 cases Lorenz Curve Equal means and different means 30
2 questions 1) Identification of the: Who is poor? What defines them? (sociologists) 47
2) Aggregation of poverty: how much poverty is there in the society?
(economists)
2th order stochastic Partial social evaluation 18
dominance We shrink the set of social judgements over which we require unanimity and
add another property to our list of properties for a desirable welfare function
= a Pigou-Dalton (or a progressive) transfer
3 aspects of poverty Incidence, intensity and inequality 48
3th order stochastic Let’s be even less ambitious and add another property. The diminishing 20
dominance transfer principle.
- A positive 3th derivative
- We give more weight to what happens at the bottom
- Look at the area under the area
- Also beyond: we can gradually impose stronger principles involving
more complicated composite transfers (but interpretation and
empirical test are challenging)
5 basic properties for W Continuity (CONT), separability (SEP), population replication (POP), anonymity 14
(ANON) and monotonicity (MON)
ability Part of why vertical equity principle 58
Equal utility loss for all (concave utility function) GRAPH
Absolute frequencies How many people have an income of x. (number of individuals) 7
- Histogram page 8
Absolute LC Use when absolute invariance, it uses and alternative method to “cancel out” 34
the effect of the size, compared to standard (relative) LC
You subtract the mean so you get 2 distributions with the same
average of 0
Absolute position Absolute amount of growth 2
- Differences between poor and rich
Absolute poverty line The poverty line is an absolute number and does not depend on distribution 47
The poverty line captures the minimum needed for physical subsistence, the
money you need to not die Z
Administrative data Tax- authorities 7
In principle all individuals, but actually non-representative. Important socio-
demographic information is missing (education) and information depends on
tax legislation
Anonymity (ANON) The names do not matter in the ranking of two income distribution. 16
- This property reflects the veil of ignorance
- We evaluate only based on distribution
- Who gets what = completely irrelevant
Anti-poverty policy All people should have sufficient needs to means, to have a sufficient life 71
Sufficientarianism Decent standard of living
AROPE 60% if median income 49
Median is much more stable then mean, but tends to be lower
1
, Atkinson Example page 27 27
Atkinson theorem (CASE Allows us to compare the social welfare functions who have the 5 basic 31
1 where equal means in properties + TRANS with the Lorenz Curve
LC) Whenever there is Lorenz dominance, all functions which satisfy the
properties CONT, POP, ANON, SEP, and TRANS agree = inequality
indices
Foundation from welfare economics
Plot cumulative proportion of the population (ordered from rich to poor)
against the cumulative proportion of total income (graphs page 32)
When LC closer to 45° line and not cross this LC dominates the other LC
Atkinson-Kolm-Sen A percentage. The % of income you would be able to pay to Robin Hood 38
inequality measure Part of Atkinson family
Average income Multiply each of the proportions with the income level itself 10
- Is interesting but only on partial view of the distribution
Average tax rate How much tax liabilities do you pay on your income. Page 59 = for Belgium 57 + 59
Benefit principle Part of vertical equity principle 58
Due to Mattheus effect make the rich more than proportional use of public
goods, hence they should pay more
Between countries Empirical results 44
Gini coefficient goes down but only for the not bottom sensitivity people
Bottom sensitivity High inequality aversion
Canonical poverty Satisfy the Transfer principle in context of poverty measuring 52
measures
CASE 1: equal means Look at distributions with the same size (mean), so that social welfare equals 31
inequality
The generalized LC/average = Lorenz Curve
Atkinson theorem
CASE 2: different means Look at distributions with different means and use an invariance principle 33
The Lorenz curve is the generalized Lorenz curve of the distribution of income
relative to the mean rather than incomes themselves
Causal effect Establishing (causal) effect of inequality on economic growth is very difficult 4
- Because inequality is not an exogenous variable, it is determined from
within the system
Class of social welfare All the properties are satisfied 16
function
Complete social Make social evaluations based on one specific sociale welfare function 22
evaluation You will be able to compare f.e. 2 countries (was not with partial social
evaluation)
Concentration curve Rank people according to the X distribution (from poor to rich) and adding up 60
their proportion in the Y distribution (health care).
The only difference between LC and this cure = adding up the proportion in the
Y distribution instead of the X distribution
Continuity (CON) Small changes in the income distributions do not change the ranking of two 14
income distributions
- W(.) is a continuous function
Country-specific median Relative philosophy and political reasons (see page) 50
Cumulative distribution Derived form PDF. What % of the people have less then that income level, who 10 + 11
function (CDF) are poorer then x
Start with 0 and add up the portions up to x (EX. Page 11)
2
