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

1. Nonlinear Trend in Inequality of Educational Opportunity in the Netherlands 1930-1989 Maarten L. Buis Harry B.G. Ganzeboom

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.

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.

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.

7. 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.

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.

10. 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.

11. 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

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

13. BICs

14. Scaling of father’s status

15. Scaling of education

16. Linearity of trend, orthogonal polynomials

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.

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.

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.

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.

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.

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.

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.

28. OLS SOR RC2