Download From questions about absolute mobility rates to questions about

From questions about absolute
mobility rates to questions about
relative mobility chances
- is that progress ?!
Wout Ultee
University of Haifa
November 25, 2012
A COMMON MEASURE FOR INCOME
INEQUALITY IS THE GINI-COEFFICIENT
THERE ARE SEVERAL FORMULA’S FOR
COMPUTING GINI’S
AN EASY WAY TO UNDERSTAND THE
GINI IS AS FOLLOWS
TAKE A SOCIETY CONSISTING OF N HOUSEHOLDS
MAKE ALL POSSIBLE PAIRS OF HOUSEHOLDS
AND COMPUTE FOR EACH PAIR THE DIFFERENCE
BETWEEN THE INCOMES OF THE TWO HOUSEHOLDS
TURN NEGATIVE INCOME DIFFERENCES INTO POSITIVE
VALUES BY TAKING ABSOLUTES
THEN SUM ALL THE DIFFERENCES
DIVIDE THIS SUM BY TWO, BY THE AVERAGE HOUSEHOLD
INCOME AND BY THE SQUARE OF THE NUMBER OF
HOUSEHOLDS
THIS IS THE GINI, WITH A VALUE OF
ZERO IF ALL HOUSEHOLDS HAVE
EQUAL INCOME AND ONE IF ONE
HOUSEHOLD HAS ALL THE INCOME
GINI’S NOT ONLY CAN BE COMPUTED, AS USUAL,
FOR COUNTRIES
THEY ALSO CAN BE CALCULATED FOR SMALLER
UNITS OF COUNTRIES, IN THE USA STATES
GINI’S ALSO MAY BE COMPUTED FOR LARGER
UNITS THAN COUNTRIES, FOR INSTANCE THE
WHOLE EUROPEAN UNION
GLENN FIREBAUGH
THE NEW GEOGRAPHY OF GLOBAL INCOME
INEQUALITY
2003
COMPUTED GINI’S FOR THE WHOLE WORLD
FIREBAUGH’S RESULTS WERE, AT FIRST SIGHT,
RATHER SURPRISING AND ON AT LEAST ONE
CONFERENCE HE WAS HEAVILY ATTACKED AND
NOT BELIEVED AT ALL
WHEREAS IN MOST COUNTRIES OF THE
WORLD INCOME INEQUAILTY IS RISING
FOR THE WORLD AS A WHOLE INCOME
INEQUALITY IS DECLINING
HOW IS THIS POSSIBLE, OR IS FIREBAUGH
DEAD WRONG?
FIREBAUGH’S RESULTS NOT ONLY HOLD FOR GINI’S
BUT ALSO FOR OTHER MEASURES OF INCOME INEQUALITY
THE IMPORTANT CLUE IS THAT THE GINI AND OTHER MEASURES
OF INCOME INEQUALITY IS INDEPENDENT OF THE MEAN INCOME
OF A COUNTRY
YET MEAN INCOME DIFFERS BETWEEN THE WORLD’S COUNTRIES
INCOME INEQUALITY FOR THE WHOLE WORLD IS SOMETHING
LIKE THE SUM OF THE INEQUALITY IN EVERY COUNTRY
PLUS THE DIFFERENCES IN AVERAGE INCOME BETWEEN THE
COUNTRIES OF THE WORLD
PLUS A WEIGHT FOR A COUNTRY’S NUMBER OF INHABITANTS
NOW AVERAGE INCOME HAS NOT BEEEN RISING IN ALL
COUNTRIES OF THE WORLD EQUALLY
THE PAST THREE DECADES AVERAGE INCOME HAS BEEN
RISING MOST IN CHINA AND INDIA
CHINA AND INDIA DO NOT ONLY BELONG TO THE POOREST
COUNTRIES OF THE WORLD
CHINA AND INDIA ALSO BELONG TO THE COUNTRIES OF THE
WORLD WITH THE HIGHEST NUMBER OF INHABITANTS
THE ADDITIONS TO THE FIREBAUGH EQUATION DID THE TRICK
CRITICS LATER CALCULATED WHAT WORLD INCOME
INEQUALITY WOULD LOOK LIKE WITHOUT CHINA AND INDIA:
DOES THIS MAKE MUCH SENSE?
INCOME INEQUALITY USUALLY IS CALCULATED
FOR ANNUAL HOUSEHOLD INCOME
THE GINI WOULD BE LARGER IF IT WERE
CALCULATED FOR MONTHLY HOUSEHOLD
INCOME
AND EVEN LARGER IF IT WERE CALCULATED FOR
WEEKLY
HOUSEHOLD INCOME
GINI’S ARE CALCULATED FOR ANNUAL INCOME,
BECAUSE IN THE RICH COUNTRIES OF THE
WORLD STATES LEVY TAXES ON A YEARLY BASIS
FOR THE NETHERLANDS IN THE 1980S
THE GINI FOR YEARLY HOUSEHOLD
INCOME IS HIGHER THAN THE GINI FOR
THREE-YEARLY HOUSEHOLD INCOME
BUT THE GINI FOR THREE-YEARLY
HOUSLHOLD INCOME DID NOT DIFFER
MUCH FROM THE GINI FOR FIVE-YEARLY
HOUSEHOLD INCOME
ALL THESE PHENOMENA HINT AT INCOME MOBILITY
HOW MUCH INCOME MOBILITY IS THERE?
THE FOR SOCIOLOGISTS INTERESTING QUESTION IS
ABOUT INTERGENERATIONAL INCOME MOBILITY:
THE STRENGTH OF THE ASSOCIATION BETWEEN
PARENTAL INCOME AND CHILD’S INCOME (WITH THE
AGE OF PARENTS AND CHILDREN BEING MORE OR
LESS THE SAME)
THE EASY WAY TO ANSWER THIS QUESTION IS BY
COMPUTING CORRELATIONS BETWEEN PARENTAL
AND CHILD’S INCOME
HOWEVER, MOST 40-YEAR OLD CHILDREN DO
NOT KNOW THE INCOME OF THEIR PARENTS
WHEN THESE PARENTS WERE 40 YEARS OLD
WHAT CHILDREN KNOW IS THEIR OWN
OCCUPATION AND THE OCCUPATION OF THEIR
PARENT
SOCIOLOGISTS HAVE SCHEMES FOR ASSIGNING
THESE OCCUPATIONS TO A LIMITED NUMBER OF
CLASSES, RANKED FROM HIGH TO LOW
THIS LED SOCIOLOGISTS TO DEVELOP
TECHNIQUES FOR THE ANALYSIS OF SOCALLED SQUARE TABLES
TABLES WITH AS MAY ROWS AS COLUMNS
EACH ROW AND COLUMN STANDING FOR
ONE SOCIAL CLASS
WITH THE CLASS SCHEMA BEING THE
SAME FOR PARENTS AS FOR THEIR
CHILDREN
AND SOCIOLOGISTS MADE MANY A
MISTAKE WHEN ANALYZING SQUARE
TABLES
THE OECD MADE THESE MISTAKES TOO,
OR CAME CLOSE TO MAKING THEM
IT MADE TABLES FOR
INTERGENERATIONAL INCOME MOBILITY
WITH FIVE CATEGORIES FOR PARENTAL
INCOME AND FIVE FOR THE INCOME OF
THEIR CHILDREN
THE CATEGORIES WERE THE RICHEST
QUINTILE, THE ONE BUT RICHEST
QUINTILE, THE MIDDLE QUINTILE, THE
ONE BUT POOREST QUINTILE AND THE
POOREST QUINTILE
THE DATA SHOWED THAT THERE WAS
MORE INTERNERATIONAL STABILITY IN
THE UNITED STATES THAN IN
DENMARK
WITH MORE STABILITY IN THE
POOREST (FIRST) QUINTILE OF THE USA
THAN IN THE RICHEST (FIFTH) QUINTILE
OF THE USA
THESE FIGURES ONLY PERTAIN TO THE MAIN
DIAGONAL OF A SQUARE TABEL
SOCIOLOGISTS WOULD LIKE TO SEE THE FIGURES FOR
THE OTHER CELLS TO AND COMMENT ON THEM
SOCIOLOGISTS WOULD LIKE TO SAY MORE ABOUT
UPWARD AND DOWNWARD MOBILITY
SOME SOCIOLOGISTS HAVE SAID ABOUT A FIVE BY
FIVE TABLE
THAT X% OF THE WHOLE POPULATION MOVED ONE
STEP UP, Y% ONE STEP DOWN, TWO, THREE, FOUR, Z%
FIVE STEPS UP AND A% FIVE STEPS DOWN
HOWEVER, THESE FIGURES MAY BE
MISLEADING, SINCE ONLY PERSONS AT THE
BOTTOM CAN MOVE FIVE STEPS UP, AND ONLY
PERSONS AT THE TOP FIVE STEPS DOWN
A SOCIOLOGIST ALWAYS SHOULD COMPUTE THE
PERCENT OF PERSONS WITH THE LOWEST
ORIGIN WINDING UP IN THE
HIGHEST DESTINATION
A SOCIOLOGIST SHOULD ALSO RECOGNIZE THAT
IT IS ‘EASIER’ FOR SOMEONE FROM THE ONE
BUT HIGHEST ORIGIN TO REACH THE HIGHEST
DESTINATION THAN FOR A PERSON OF THE
LOWEST ORIGIN
SINCE INCOME INEQUALITY IS LESS IN
DENMARK THAN IN THE USA
IT SHOULD BE CLEAR THAT THE DISTANCE
BETWEEN THE POOREST AND THE RICHEST
QUINTILE IS LARGER IN THE USA
THAN IN DENMARK
THE FIRST (SECOND, ETC) QUINTILE IN
DENMARK IS NOT IDENTICAL TO THE FIRST
QUINTILE (SECOND) IN THE USA AS FAR AS
INCOME SHARE GOES
IN FRANCE DOWNWARD MOBILITY (AS A
PERCENTAGE OF THE WHOLE POPULATION) IS
INCREASING ,
NOT BECAUSE, FOR PEOPLE STARTING OUT IN THE
UPPER CLASS, THE PROBABILITY OF SLIDING
ׂDOWN FROM THE UPPER CLASS IS RISING
BUT BECAUSE THE PERCENT OF THE POPULATION
IN THE UPPER CLASS IS RISING
SO, THE QUESTION OF HOW MUCH
INTERGERNATIONAL MOBILITY THERE IS IN
A COUNTRY AT A CERTAIN POINT IN TIME
IS TOO IMPRECISE
BECAUSE IT DOES NOT TALK ABOUT
MOBILITY FROM WHAT TO WHAT
ARE SOCIOLOGISTS REALLY
INTERESTED IN
MOBILITY/STABILITY OR ARE
THEY INTERESTED IN
(UN)EQUAL CHANCES?
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
500
100
0
400
500
500
MARGINALS
600
400
1000
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
500
100
0
400
500
500
MARGINALS
600
400
1000
THERE IS UPWARD MOBILITY IN THIS SOCIETY
BUT ALL THE MOBILITY THERE IS, IS THERE BECAUSE
MORE PLACES BECAME AVAILABLE AT THE TOP
THE MOBILITY IS NOT THERE BECAUSE CHANCES IN THIS
SOCIETY BECAME MORE EQUAL
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
300
300
200
200
500
500
MARGINALS
600
400
1000
THERE IS UPWARD MOBILITY AND DOWNWARD
MOBILITY IN THIS SOCIETY
AND THE CHILDREN FROM LOW ORIGINS HAVE THE
SAME CHANCES TO A HIGH DESTINATION AS THE
CHILDREN FROM HIGH ORIGINS
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
400
200
100
300
500
500
MARGINALS
600
400
1000
THERE IS UPWARD MOBILITY AND DOWNWARD
MOBILITY IN THIS SOCIETY
AND THE CHILDREN FROM LOW ORIGINS HAVE WORSE
CHANCES FOR A HIGH DESTINATION THAN THE
CHILDREN FROM HIGH ORIGINS
GOLDTHORPE SAID IN 1980 IN SOCIAL MOBILITY
AND CLASS STRUCTURE IN MODERN BRITAIN THAT
SOCIETIES WITNESS A COMPETITION FOR THE HIGH
PLACES, WITH THE LOOSERS WINDING UP IN THE
LOW PLACES
AND THAT THE PERSONS FROM HIGH ORIGINS ARE
ADVANTAGED AND FROM LOW ORIGINS
DISADVANTAGED
GOLDTHORPE FOUND A WAY TO QUANTIFY THIS
(DIS)ADVANTAGE
IN THIS HE FOLLOWED THE ENGLISH TRADITION OF
BETTING, WHERE PEOPLE SPEAK ABOUT ‘’THE
CHANCES ARE FIFY FIFTY’’ AND ABOUT “ODDS”
(THE ODDS WERE AGAINST HIM)
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
400
200
100
300
500
500
MARGINALS
600
400
1000
IN THIS TABLE THE PERCENT OF PERSONS FROM A HIGH
ORIGIN IN A HIGH DESTINATION IS (400/500)*100
THE PERCENT OF PERSONS OF HIGH ORIGIN IN A LOW
DESTINATION IS (100/500)*100
THE CHANCES OR ODDS FOR A PERSON OF HIGH ORIGIN
TO ATTAIN A HIGH DESTINATION RATHER THAN A LOW
DESTINATION ARE (400/500)/(100/500)=400/100=4.00
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
400
200
100
300
500
500
MARGINALS
600
400
1000
IN THIS TABLE THE PERCENT OF PERSONS FROM A LOW
ORIGIN IN A HIGH DESTINATION IS (200/500)*100
THE PERCENT OF PERSONS OF LOW ORIGIN IN A LOW
DESTINATION IS (300/500)*100
THE CHANCES OR ODDS FOR A PERSON OF LOW ORIGIN
TO ATTAIN A HIGH DESTINATION RATHER THAN A LOW
DESTINATION ARE (200/500)/(300/500)=200/300=0.67
WE NOW ARE ABLE TO COMPUTE AN
ODDS RATIO FOR THE OUTCOME OF THE
COMPETITION BETWEEN PERSONS OF
HIGH ORIGIN AND LOW ORIGIN FOR
HIGH RATHER THAN LOW
DESTIONATIONS
WE JUST DEVIDE THE TWO ODDS,
IN THIS CASE (400/100)/(200/300)
(400/100)/(200/300) =
400*300/100*200=
6
IN A SOCIETY WITH EQUAL CHANCES, THE ODDS RATIO IS 1
THE MORE AN ODDS RATIO SYRPASSES ONE, THE MORE
UNEWUAL IS THE OUTCOME OF THE COMPETITION
THE ODDS RATIO DOES NOT HAVE AN UPPER BOUND
IF THE ODDS RATIO IS LESS THAN ONE
PERSONS FROM LOW ORIGINS ARE ADVANTAGED, AND
PERSONS FROM HIGH ORIGINS ARE DISADVANTAGED
THIS HAPPENED IN THE SOCIET UNION UNDER
CHROETSJOV
NOW MORE GENERALLY
CHILD HIGH CHILD LOW MARGINALS
PARENT HIGH
PARENT LOW
A
C
B
D
A+B
C+D
MARGINALS
A+C
B+D
A+B+C+D
THE ODDS RATIO FOR THIS TABLE IS
A*D/B*C
THAT IS WHY THE ODDS RATIO IS ALSO CALLED THE
CROSS PRODUCT
IN THE FORMULA FOR THE ODDS RATIO
NO TERMS STAND FOR MARGINAL
FREQUENCIES
THAT IS WHY THE ODDS RATIO MEASURES THE
OUTCOME OF A COMPETITION, INDEPENDENT
OF THE STRUCTURE OF THE COMPETITION
THAT IS, INDEPENDENT OF THE NUMBER OF
PLACES AVAILABLE NOW AND THE NUMBER OF
PLACES IN EARLIER COMPETITIONS
WHAT TO DO, NOT WITH A SQUARE 2*2
TABLE,
BUT WITH A SQUARE 3*3 TABLE AND A
SQUARE 4*4 TABLE?
IS THE IDEA OF DISTANCE PROPERLY
QUANTIED THIS TIME?