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• Background and research problem• Main results• Model selection

– Continuous or discrete measures parental education and father’s occupational 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

Historical / biographical background

• Previous studies of trends in IEO in the Netherlands (NO CHANGE):– Dronkers et al. student cohorts (at age 12)

1965, 1973, 1981, 1989.– Peschar et al. on synthetic cohort one single

survey (NPAO 1982).

• De Graaf & Ganzeboom (1990, 1993) on synthetic cohorts in 10+ surveys: DECLINE.

15 november 2005 4

The historical trend

• Confirmed:– With linear regression– With loglinear models (uniform association,

scaled association (RC-2).– With ordered logits– With sequential logits (transition model)

[Shavit & Blossfeld 1993]: Dutch exceptionalism? Aggressive welfare state policies?

15 november 2005 5

Our explanation

• Use a lot of data, pooled surveys– Wider time window

– More statistical power

– Smoothing of survey peculiarities

– Concentrate on global distribution of education (not transitions)

• But note:– The estimated trend is far from trivial or small (-1% per

year)

15 november 2005 6

The problem

• Trend towards less IEO is well documented.

• Even the most recent accounts (Ganzeboom & Luijkx, 2004a, 2005b) find a linear trend.

• However, there is reason to believe that the trend cannot continue.

• When do we begin to observe a deceleration of the trend?

15 november 2005 7

Main results

• Model of IEO:– 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.– Significance was determined with parametric bootstrap

of Lowess-curves.

15 november 2005 8

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 9

Data

• International Stratification and Mobility File (ISMF) – on the Netherlands

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

• 80,000 respondents aged between 24 and 65, of which 40,000 have complete information on child's, father’s and mother’s education and father's occupation.

• Number of cases are unequally distributed over cohorts.

15 november 2005 10

0

500

1,000

1,500

2,000

2,500

nu

mb

er

of

ob

serv

atio

ns

1940 1960 1980age in which respondent is 12

number of observations per cohort

15 november 2005 11

Model 1: linear regression• Dependent variable is level 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 12

Two objections against linear education

• Regression coefficient is affected by both ‘real’ effects of parental characteristics on probabilities of making transitions and expansion of the educational distribution– 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 13

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

15 november 2005 14

Model 2:Stereotype Ordered Regression (SOR)

• SOR allows for unordered dependent variable

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

• The dependent variable is nominal, and SOR reveals latent ordering based on associations with independent variables.

15 november 2005 15

Model 3: Row Column Association 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 an extension of SOR as it also estimates an optimal scaling for FEGP

15 november 2005 16

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

matters• Modified Dominance model: Highest and lowest

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

15 november 2005 17

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 18

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 19

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 20

Linearity of trend, orthogonal polynomials

OLS SOR RC2trend t t t

FSES linear -10.85 -6.57 -20.15quadratic 6.94 4.39 4.41cubic 0.39 -0.39 -0.54

HI_ED linear -12.29 -4.63 0.50quadratic 0.94 1.07 5.27cubic -2.29 -2.08 2.61

LO_ED linear -6.97 -3.07 -0.87quadratic 2.10 1.59 1.96cubic 2.47 1.54 3.96

15 november 2005 21

Identifying periods with significant trend

• A negative slope means a negative trend.

• A positive slope means a positive trend.

• A zero slope means no trend, or not enough information.

15 november 2005 22

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 23

Data

• The ISMF dataset is converted into three new datasets, containing estimates of the association between father’s occupational status and child’s education for 60 annual cohorts.

• One dataset for each technique.• The precision of the estimates (the standard error)

is used to weigh the cohorts (weights are the inverse of error variances).

15 november 2005 24

Lowess curves: locally weighted scatterplot smooth• 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 25

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.• WLS 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 all techniques and connect the

dots.

15 november 2005 26

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 27

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 Generalized Cross Validation, and Akaike Information Criterion.

• Lower values mean a better trade-off.

15 november 2005 28

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 29

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 30

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, SOR, RC2

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

IEO could plausibly occur in a `new' dataset.

15 november 2005 31

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 32

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 33

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

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

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