Wout Ultee University of Haifa November 25, 2012

1. From questions about absolute mobility rates to questions about relative mobility chances- is that progress ?! WoutUltee University of Haifa November 25, 2012

2. 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

3. 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

4. THIS IS THE GINI, WITH A VALUE OF ZERO IF ALL HOUSEHOLDS HAVE EQUAL INCOME AND ONE IF ONE HOUSEHOLD HAS ALL THE INCOME

5. 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

6. 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?

7. 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

8. 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?

10. 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

11. 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

12. 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)

13. 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

14. THIS LED SOCIOLOGISTS TO DEVELOP TECHNIQUES FOR THE ANALYSIS OF SO-CALLED 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. ARE SOCIOLOGISTS REALLY INTERESTED IN MOBILITY/STABILITY OR ARE THEY INTERESTED IN (UN)EQUAL CHANCES?

23. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 500 0 500 PARENT LOW 100 400 500 MARGINALS 600 400 1000

24. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 500 0 500 PARENT LOW 100 400 500 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

25. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 300 200 500 PARENT LOW 300 200 500 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

26. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 400 100 500 PARENT LOW 200 300 500 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

27. 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)

28. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 400 100 500 PARENT LOW 200 300 500 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

29. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH 400 100 500 PARENT LOW 200 300 500 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

30. 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)

31. (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

32. NOW MORE GENERALLY

33. CHILD HIGH CHILD LOW MARGINALS PARENT HIGH A B A + B PARENT LOW C D 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

34. 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

35. 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?