Nonlinear Trend in Inequality of Educational Opportunity in the Netherlands 1930-1989

15 november 2005 1

Nonlinear Trend in Inequality of Educational Opportunity in the

Netherlands 1930-1989

Maarten L. Buis

Harry B.G. Ganzeboom

15 november 2005 2

Outline

• Main results• Model selection

– Continuous or discrete education and father’s status

– Importance mother’s education relative to father’s education

– Difference in effect between sons and daughters

• Non-linearity in trend in effects: identify periods of negative, positive, and no trend.

15 november 2005 3

Main results

• Model selection– distinction between highest and lowest educated parent

is more important than distinction between father and mother, or same-sex-parent.

– Effects of parental education and father’s occupational status is the same for sons and daughters

• Non-linearity in trend– Effect of father’s status decreases non-linearly over

time, slowing down significantly around 1970– parental education decreases most likely linearly.

15 november 2005 4

1930 1950 1970 1990

12

34

56

7

OLSsignificant trend

year in w hich respondent is 12

IEO

1930 1950 1970 1990

12

34

56

7

OLSsignificant change in trend


IEO

1930 1950 1970 1990

24

68

10SOR

significant trend


IEO

1930 1950 1970 1990

24

68

10

SORsignificant change in trend

year in w hich respondent is 12IE

O

1930 1950 1970 1990

12

34

5

RC2significant trend

nyear in w hich respondent is 12

IEO

1930 1950 1970 1990

12

34

5RC2

significant change in trend


IEO

15 november 2005 5

Data

• International Stratification and Mobility File (ISMF)

• 49 surveys held between 1958 and 2003 with information on cohorts 1930-1989.

• 80,000 observations, of which 66,000 have complete information on child's, father’s and mother’s education and father's status.

• Number of cases are unequally distributed over cohorts.

15 november 2005 6

0

500

1000

1500

2000

2500

Fre

qu

en

cy

1920 1940 1960 1980 2000year in which respondent is 12

Number of obeservations per cohort

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Model 1: linear regression• Dependent variable is years of education

and treated as continuous.• Parental education is either entered as

father’s and/or mother’s education, highest and/or lowest educated parent, or education of same sex parent

• Father’s occupational status is measured in ISEI scores

• Trend in effects are measured as third order orthogonal polynomials or lowess curves.

15 november 2005 8

Two objections against linear education

• Regression coefficient is effected by both ‘real’ effects of parental characteristics on probabilities of making transitions and educational expansion– True, if education is studied as a process – False, if education is studied as an outcome

• education is discrete– this does not have to be a problem if there is no

concentration in the lowest or highest category.

15 november 2005 9

0

.2

.4

.6

.8

1pr

opor

tion

1940 1960 1980year in which respondent is 12

higher tertiarylower tertiaryhigher secondarylower secondary

primary or less

highest achievedlevel of education

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Model 2:Stereotype Ordered Regression (SOR)

• SOR allows for ordered dependent variable

• SOR will estimate (sequentially) an optimal scaling of education and the effect of independent variables on this scaled education.

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Model 3: Row Collumn Model II (RC2)

• Objection against use of ISEI: – Effect of father’s occupation is better

represented by small number of discrete classes, rather than on continuous scale.

• Classes used are EGP classification.

• RC2 is extension of SOR that also estimates an optimal scaling for EGP

15 november 2005 12

Father’s and mother’s education

• Conventional model: Only father matters• Individual model: Both mother and father matter• Joint model: Effect of father and mother are equal• Dominance model: Highest educated parent

matter• Modified Dominance model: Highest and lowest

educated parent matter• Sex Role model: Same sex parent matters

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BICsname no. model OLS SOR RC2Baseline model 0a FIS*BYR 3̂*FEM + BYR_D*FEM

0b FIS*BYR 3̂ + BYR_D*FEM

conventional model 1a (0a) + FED*BYR 3̂*FEM -10375 -20352 -341121b (0a) + FED*BYR 3̂ -10414 -20391 -341571c (0b) + FED*BYR 3̂ -10433 -20418 -34194

individual model 2a (0a) + FED*BYR 3̂*FEM + MED*BYR 3̂*FEM -11003 -21043 -345662b (0a) + FED*BYR 3̂ + MED*BYR^3 -11075 -21124 -346592c (0b) + FED*BYR 3̂ + MED*BYR^3 -11093 -21148 -34698

joined model 3a (0a) + (FED=MED)*BYR^3*FEM -11065 -21120 -345803b (0a) + (FED=MED)*BYR^3 -11104 -21159 -346243c (0b) + (FED=MED)*BYR^3 -11121 -21183 -34662

dominance model 4a (0a) + HI_ED*BYR 3̂*FEM -10923 -20923 -345524b (0a) + HI_ED*BYR 3̂ -10961 -20963 -345964c (0b) + HI_ED*BYR 3̂ -10980 -20989 -34634

modified dominance model 5a (0a) + HI_ED*BYR 3̂*FEM + LO_ED*BYR 3̂*FEM -11071 -21094 -347055b (0a) + HI_ED*BYR 3̂ + LO_ED*BYR^3 -11149 -21180 -34797

5c (0b) + HI_ED*BYR 3̂ + LO_ED*BYR^3 -11166 -21204 -34835

sex-role model 6a (0a) + SS_ED*BYR^3*FEM -10231 -20217 -337366b (0a) + SS_ED*BYR^3*FEM -10261 -20252 -337426c (0b) + SS_ED*BYR^3 -10275 -20283 -33790

15 november 2005 14

Scaling of father’s status

EGP mean(ISEI) RC2I Service class, higher grade 66.5 1.000II Service class, lower grade 56.4 0.838IIIa Routine non-manual employees 48.6 0.651

IIIb Personal service workers 41.7 0.370

IVa Small proprietors with employees 45.4 0.467

IVb Small proprietors without employees 44.7 0.184

V Manual foremen and technicians 41.3 0.216VI Skilled manual workers 34.8 -0.148VIIa Semi- and unskilled manual workers 29.7 -0.354VIIb Agricultural workers 17.5 -0.553IVc Farmers and smallholders 29.1 0.000

15 november 2005 15

Scaling of education

education mean(educyr) SOR RC2

primary or less 6.0 0.000 0.000

lower secondary 9.3 0.348 0.299

higher secondary 11.0 0.646 0.601

lower tertiary 14.9 0.813 0.793

higher tertiary 17.1 1.000 1.000

15 november 2005 16

Linearity of trend, orthogonal polynomials

OLS SOR RC2

trend t p t p t p

FSES linear -10,850 0,000 -6,573 0,000 -20,148 0,000

quadratic 6,940 0,000 4,387 0,000 4,410 0,000

cubic 0,390 0,694 -0,386 0,699 -0,536 0,591

HI_ED linear -12,290 0,000 -4,628 0,000 0,504 0,614

quadratic 0,940 0,349 1,065 0,112 5,267 0,000

cubic -2,290 0,022 -2,080 0,037 2,614 0,009

LO_ED linear -6,970 0,000 -3,068 0,000 -0,866 0,386

quadratic 2,100 0,036 1,587 0,112 1,955 0,050

cubic 2,470 0,014 1,540 0,123 3,962 0,000

15 november 2005 17

Identifying periods with significant trend

• A negative slope means a negative trend.

• A positive slope mean a positive trend.

• A zero slope means no trend.

15 november 2005 18

Identifying periods with significant change in trend

• An accelerating trend means that a negative trend becomes more negative, so a negative change in slope.

• A decelerating trend means that a negative trend becomes less negative, so a positive change in slope.

• A constant trend means no change in slope.

15 november 2005 19

Data

• The ISMF dataset is converted into a new dataset, containing estimated IEO for 60 annual cohorts.

• The precision of the estimates (the standard error) is used to weigh the cohorts.

15 november 2005 20

Lowess

• We have a dataset consisting of estimates of IEO for each annual cohort which used only information from that cohort

• If we think that IEO develops like a smooth curve over time, than nearby estimates also contain relevant information.

• The lowess curve creates an improved estimate of the IEO for each cohort using information from nearby cohorts.

• It results in a smooth line by connecting the lowess estimates.

• Estimates of the trend and change in trend at each cohort can also be obtained from this curve.

15 november 2005 21

Lowess curve in 1949

• Point on lowess curve in 1949• Select closest 60% of the points.• Give larger weights to nearby points.• Adjust weights for precision of estimated IEO.• Normal regression of IEO on time, time squared and time

cubed on weighted points.• Predicted value in 1949, is smoothed value of 1949.• First derivative in 1949 is trend in 1949.• Second derivative in 1949 is change in trend in 1949.• Repeat for all cohorts and connect the dots.

15 november 2005 22

1930 1940 1950 1960 1970 1980 1990

12

34

56

7

(a) Observations Within the Windowspan = 0.6

year in which respondent is 12

IEO

1949

1930 1940 1950 1960 1970 1980 1990

0.0

0.5

1.0

1.5

2.0

(b) Tricube Weights


Tric

ube

Ker

nel W

eigh

t

1949

1930 1940 1950 1960 1970 1980 1990

0.0

0.5

1.0

1.5

2.0

(c) Tricube (+), Precision (x),and Joint (o) Weights


wei

ghts

1949

1930 1940 1950 1960 1970 1980 1990

12

34

56

7

(d) Weighted Third Degree Polynomial(size of circle proportional to weight)


IEO

1949

IEO^

1949

15 november 2005 23

Selecting spans

• Percentage closest points (span) determines the smoothness of the lowess curve.

• Trade-off between smoothness and goodness of fit.

• Can be judged visually by comparing lowess curves with different spans.

• Numerical representations of this trade-off are Generalize Cross Validation, and Akaike Information Criterion.

• Lower values mean a better trade-off.

15 november 2005 24

1930 1950 1970 1990

12

34

56

7

OLS, span=.5


ieo

1930 1950 1970 1990

12

34

56

7

OLS, span=.6


ieo

1930 1950 1970 1990

12

34

56

7

OLS, span=.7


ieo

1930 1950 1970 1990

24

68

10SOR, span=.5


ieo

1930 1950 1970 1990

24

68

10

SOR, span=.6


ieo

1930 1950 1970 1990

24

68

10

SOR, span=.7


ieo

1930 1950 1970 1990

12

34

5

RC2, span=.5


ieo

1930 1950 1970 1990

12

34

5

RC2, span=.6


ieo

1930 1950 1970 1990

12

34

5

RC2, span=.7


ieo

15 november 2005 25

0.2 0.4 0.6 0.8 1.0

0.38

0.39

0.40

0.41

0.42

(a) Generalized CrossValidation

span

gcv

0.2 0.4 0.6 0.8 1.0

3035

4045

(b) Akaike InformationCriterion

span

aic

0.2 0.4 0.6 0.8 1.0

0.62

0.64

0.66

0.68

0.70


span

gcv

0.2 0.4 0.6 0.8 1.0

4550

55


span

aic

0.2 0.4 0.6 0.8 1.0

0.08

80.

090

0.09

20.

094

0.09

60.

098

0.10

0


span

gcv

0.2 0.4 0.6 0.8 1.0

1520

2530

35


span

aic

15 november 2005 26

Bootstrap confidence intervals

• Confidence interval gives the range of results that could plausibly occur just through sampling error.

• Make many `datasets' that could have occurred just by sampling error.

• Fit lowess curves through each `dataset'.• The area containing 90% of the curves is the 90%

confidence interval.• The estimates of IEO are regression coefficient with

standard errors.• The standard error gives information about what values of

IEO could plausibly occur in `new' dataset.

15 november 2005 27

1930 1940 1950 1960 1970 1980 1990

23

45

6

(a) Lowess Smooths in theFirst 25 Bootstrap Samples


IEO

1930 1940 1950 1960 1970 1980 1990

-40

-20

020

40

(b) Trend in IEO in theFirst 25 Bootstrap Samples


tren

d, c

hang

e in

IE

O p

er 1

00 y

ears

1930 1940 1950 1960 1970 1980 1990

-800

-600

-400

-200

020

040

0

(c) Change in Trend in IEO in theFirst 25 Bootstrap Samples


chan

ge in

tre

nd p

er 1

00 y

ears

15 november 2005 28

1930 1950 1970 1990

12

34

56

7

(a) Lowess Smooth and90% Confidence Envelope

year in w hich respondent is 12IE

O1930 1950 1970 1990

-30

-10

010

30

(c) Trend in IEO and90% Confidence Envelope


tren

d, c

hang

e in

IEO

per

100

yea

rs

1930 1950 1970 1990

-600

-200

020

0

(d) Change in Trend in IEO and90% Confidence Envelope


chan

ge in

tren

d pe

r 10

0 ye

ars

1930 1950 1970 1990

24

68

10



IEO

1930 1950 1970 1990

-60

-40

-20

020

40


year in w hich respondent is 12tr

end,

cha

nge

in IE

O p

er 1

00 y

ears

1930 1950 1970 1990

-600

-200

200

600



chan

ge in

tren

d pe

r 10

0 ye

ars

1930 1950 1970 1990

12

34

5



IEO

1930 1950 1970 1990

-15

-50

510

15



tren

d, c

hang

e in

IEO

per

100

yea

rs

1930 1950 1970 1990

-300

-200

-100

010

0


year in w hich respondent is 12ch

ange

in tr

end

per

100

year

s

OLS

SOR

RC2

15 november 2005 29

1930 1950 1970 1990

12

34

56

7

OLSsignificant trend


IEO

1930 1950 1970 1990

12

34

56

7

OLSsignificant change in trend


IEO

1930 1950 1970 1990

24

68

10

SORsignificant trend


IEO

1930 1950 1970 1990

24

68

10

SORsignificant change in trend


IEO

1930 1950 1970 1990

12

34

5

RC2significant trend

nyear in w hich respondent is 12

IEO

1930 1950 1970 1990

12

34

5RC2

significant change in trend


IEO

Nonlinear Trend in Inequality of Educational Opportunity in the Netherlands 1930-1989

Documents

fem byr

discrete education

years of education

scaled education

effects of parental

optimal scaling of education

equaldominance model

egp fathers