linking process to outcome - inequality of educational ... · two types of educational inequality...

IEOpp and IEOutEmpricial applications

Conclusion

Linking process to outcomeInequality of educational opportunities and inequality of

educational outcomes

Maarten L. Buis

Department of Social Research MethodologyVrije Universiteit Amsterdamhttp://home.fsw.vu.nl/m.buis/

Maarten L. Buis Linking process to outcome


Conclusion

Two types of educational inequality

The difference between high and low status children in

I probabilities of passing transitions between levels ofeducation; Inequality of Educational Opportunity (IEOpp),or

I highest achieved level of education; Inequality ofEducational Outcome (IEOut).

I The aim of this presentation is to to relate IEOut to theIEOpps, because:

1. IEOpps (looking at the process) and IEOut (looking at theend result) are natural complements.

2. Allows for a natural way to study the effect of educationalexpansion, and the disadvantaged position of other socialgroups on IEOut.



Conclusion


The difference between high and low status children inI probabilities of passing transitions between levels of

education;

Inequality of Educational Opportunity (IEOpp),or







Conclusion



education; Inequality of Educational Opportunity (IEOpp),or







Conclusion




I highest achieved level of education;

Inequality ofEducational Outcome (IEOut).






Conclusion










Conclusion





I The aim of this presentation is to to relate IEOut to theIEOpps,

because:1. IEOpps (looking at the process) and IEOut (looking at the

end result) are natural complements.2. Allows for a natural way to study the effect of educational

expansion, and the disadvantaged position of other socialgroups on IEOut.



Conclusion










Conclusion







2. Allows for a natural way to study the effect of educationalexpansion

, and the disadvantaged position of other socialgroups on IEOut.



Conclusion










Conclusion

Outline

IEOpp and IEOut

Empricial applicationsThe NetherlandsUSA

Conclusion



Conclusion

Model of the process and the outcome

I Builds on the work by Mare (1981).

I The process is modeled as a sequential logit/Mare model.I The outcome is derived from this model.I This is a way of extracting more information from a

sequential logit/Mare model.



Conclusion


I Builds on the work by Mare (1981).I The process is modeled as a sequential logit/Mare model.

I The outcome is derived from this model.I This is a way of extracting more information from a




Conclusion


I Builds on the work by Mare (1981).I The process is modeled as a sequential logit/Mare model.I The outcome is derived from this model.

I This is a way of extracting more information from asequential logit/Mare model.



Conclusion


I Builds on the work by Mare (1981).I The process is modeled as a sequential logit/Mare model.I The outcome is derived from this model.I This is a way of extracting more information from a




Conclusion

Example

Figure: Hypothetical educational system

no education

primaryp1

secondaryp2

tertiaryp3 l3 = 16

exit1− p3l2 = 12

exit1− p2 l1 = 6

exit1− p1 l0 = 0



Conclusion

Modeling transition probabilities and the expectedlevel of education

pki =exp(αk + λkSESi)

1 + exp(αk + λkSESi)if yk−1 i = 1

E(ed) = (1−p1i)l0 +p1i(1−p2i)l1 +p1ip2i(1−p3i)l2 +p1ip2ip3i l3



Conclusion

IEOpps and IEOut

IEOut is the increase in expected highest achieved level ofeducation for a unit increase in SES, i.e. a first derivative:



Conclusion

IEOpps and IEOut

IEOut is the increase in expected highest achieved level ofeducation for a unit increase in SES, i.e. a first derivative:

∂E(ed)∂SES ={1× p1i(1− p1i)× [(1− p2)l1 + p2(1− p3)l2 + p2p3l3 − l0]}λ1+{p1i × p2i(1− p2i)× [(1− p3)l2 + p3l3 − l1]}λ2+{p1ip2i × p3i(1− p3i)× [l3 − l2]}λ3



Conclusion

IEOpps and IEOut




Conclusion

IEOpps and IEOut

proportion at risk

∂E(ed)∂SES ={1×p1i(1− p1i)× [(1− p2)l1 + p2(1− p3)l2 + p2p3l3 − l0]}λ1+{p1i×p2i(1− p2i)× [(1− p3)l2 + p3l3 − l1]}λ2+{p1ip2i×p3i(1− p3i)× [l3 − l2]}λ3



Conclusion

IEOpps and IEOut

variance of the variable indicating whether one passes or not

∂E(ed)∂SES ={1×p1i(1− p1i)×[(1− p2)l1 + p2(1− p3)l2 + p2p3l3 − l0]}λ1+{p1i×p2i(1− p2i)×[(1− p3)l2 + p3l3 − l1]}λ2+{p1ip2i×p3i(1− p3i)×[l3 − l2]}λ3



Conclusion

IEOpps and IEOut

expected increase in the level of education after passing

∂E(ed)∂SES ={1× p1i(1− p1i)×[(1− p2)l1 + p2(1− p3)l2 + p2p3l3 − l0]}λ1+{p1i × p2i(1− p2i)×[(1− p3)l2 + p3l3 − l1]}λ2+{p1ip2i × p3i(1− p3i)×[l3 − l2]}λ3



Conclusion

IEOpps and IEOut

expected level of education for those that pass

∂E(ed)∂SES ={1× p1i(1− p1i)× [(1− p2)l1 + p2(1− p3)l2 + p2p3l3−l0]}λ1+{p1i × p2i(1− p2i)× [(1− p3)l2 + p3l3−l1]}λ2+{p1ip2i × p3i(1− p3i)× [l3−l2]}λ3



Conclusion

IEOpps and IEOut

minus the expected level of education for those that fail




Conclusion

In words:

I IEOut = weighted sum of IEOpps

I weights = at risk × variance × gain



Conclusion

In words:

I IEOut = weighted sum of IEOppsI weights = at risk × variance × gain



Conclusion

The NetherlandsUSA

Outline

IEOpp and IEOut


Conclusion



Conclusion

The NetherlandsUSA

Simplified model of Dutch educational system

lo

2nd diplomap1

havo/vwop2

hbo/wop4 l5 = 1.35

exit1− p4l4 = 0.10

lbo/mavo1− p2

mbop3 l3 = −0.17

exit1− p3l2 = −0.71

exit1− p1

l1 = −2.10



Conclusion

The NetherlandsUSA

Data

I International Stratification and Mobility File (ISMF) on theNetherlands.

I 51 surveys held between 1958 and 2005 with informationon cohorts 1894-1978.

I 67,000 respondents aged between 27 and 65 withcomplete information.



Conclusion

The NetherlandsUSA

Variables

I Father’s occupational status is measured in ISEI scores,but recoded to range between 0 and 1.

I Level of education is scaled such as to maximize the directeffect of education on income , and

I it is standardized.I Time measured as a restricted cubic spline with one knot

in 1936.



Conclusion

The NetherlandsUSA

Variables



I it is standardized.

I Time measured as a restricted cubic spline with one knotin 1936.



Conclusion

The NetherlandsUSA

Variables



I it is standardized.I Time measured as a restricted cubic spline with one knot

in 1936.



Conclusion

The NetherlandsUSA

Change in IEOut over cohorts

1

1.5

2

2.5

3

effe

ct o

f fat

her’s

occ

up. s

tatu

s

1900 1920 1940 1960 1980

year of birth

menwomen



Conclusion

The NetherlandsUSA

Decomposition of IEOut

I IEOut is a weighted sum of IEOpps:

IEOut = w1 IEOpp1 + w2 IEOpp2 + w3 IEOpp3 + w4 IEOpp4

I The contribution of the first transition is: w1 IEOpp1

I This can be visualized as the area of a rectangle with widthw1 and height IEOpp1.

I IEOut is the sum of the areas of these rectangles



Conclusion

The NetherlandsUSA


I IEOut is a weighted sum of IEOpps:IEOut = w1 IEOpp1 + w2 IEOpp2 + w3 IEOpp3 + w4 IEOpp4






Conclusion

The NetherlandsUSA




I This can be visualized as the area of a rectangle

with widthw1 and height IEOpp1.




Conclusion

The NetherlandsUSA




I This can be visualized as the area of a rectangle with widthw1

and height IEOpp1.I IEOut is the sum of the areas of these rectangles



Conclusion

The NetherlandsUSA








Conclusion

The NetherlandsUSA

Decomposition of IEOut for men

−2

0

2

4

6

−2

0

2

4

6

−2

0

2

4

6

−2

0

2

4

6

0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4

1900 1915 1930 1945 1960 1975

havo/vwo vhbo/wo

lbo/mavo vmbo

lbo/mavo vhavo/vwo

lo vmore

log

odds

rat

io

weight

men



Conclusion

The NetherlandsUSA

Decomposition of IEOut for women

−2

0

2

4

6

−2

0

2

4

6

−2

0

2

4

6

−2

0

2

4

6

0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4 0 .2 .4

1900 1915 1930 1945 1960 1975

havo/vwo vhbo/wo

lbo/mavo vmbo

lbo/mavo vhavo/vwo

lo vmore

log

odds

rat

io

weight

women



Conclusion

The NetherlandsUSA

Decomposition of weights

I The weights are:at risk × variance × gain

I These three elements are all a function of the proportionsthat pass the transitions



Conclusion

The NetherlandsUSA

Decomposition of the weights for men

0

.5

1

prob

abili

ty

1900 1920 1940 1960 1980

year of birth

transition probability

0

.2

.4

.6

.8

1

prop

ortio

n

1900 1920 1940 1960 1980

year of birth

proportion at risk

0

.1

.2

varia

nce

1900 1920 1940 1960 1980

year of birth

variance

.5

1

1.5

2

2.5

leve

l

1900 1920 1940 1960 1980

year of birth

gain

0

.2

.4

wei

ght

1900 1920 1940 1960 1980

year of birth

weight

lo vmore

lbo/mavo vhavo/vwo

lbo/mavo vmbo

havo/vwo vhbo/wo



Conclusion

The NetherlandsUSA

Decomposition of the weights for women

0

.5

1

prob

abili

ty

1900 1920 1940 1960 1980

year of birth


0

.2

.4

.6

.8

1

prop

ortio

n

1900 1920 1940 1960 1980

year of birth

proportion at risk

0

.1

.2

varia

nce

1900 1920 1940 1960 1980

year of birth

variance

1

1.5

2

2.5

leve

l

1900 1920 1940 1960 1980

year of birth

gain

0

.2

.4

wei

ght

1900 1920 1940 1960 1980

year of birth

weight

lo vmore

lbo/mavo vhavo/vwo

lbo/mavo vmbo

havo/vwo vhbo/wo



Conclusion

The NetherlandsUSA

Data

I General Social Survey (GSS).I 20 surveys held between 1977 and 2004 with information

on cohorts 1913-1978.I 13,400 men aged between 27 and 65 with complete

information.



Conclusion

The NetherlandsUSA

Variables

I Father’s highest achieved level of education measured in(pseudo) years.

I Respondent’s highest achieved Level of education in(pseudo) years

I Time measured as a restricted cubic spline with one knotin 1946.



Conclusion

The NetherlandsUSA

Simplified model of the US educational system

less than high school

high school

bachelor 16

junior college 14

exit 12

exit 9



Conclusion

The NetherlandsUSA

Change in IEOut over cohorts

.15

.2

.25

.3

.35

.4

effe

ct o

f fat

her’s

edu

catio

n

1920 1940 1960 1980

year of birth

whiteblack



Conclusion

The NetherlandsUSA

Decomposition of IEOut for white men

0

.2

.4

0

.2

.4

0

.2

.4

0 .5 1 0 .5 1 0 .5 1 0 .5 1 0 .5 1 0 .5 1

1915 1925 1935 1945 1955 1965

bachelorv. high school orjunior college

junior collegev. high school orbachelor

high school or morev. less than high school

log

odds

rat

io

weight

white



Conclusion

The NetherlandsUSA

Decomposition of IEOut for black men

0

.2

.4

0

.2

.4

0

.2

.4

0 .5 1 0 .5 1 0 .5 1 0 .5 1 0 .5 1 0 .5 1

1915 1925 1935 1945 1955 1965

bachelorv. high school orjunior college

junior collegev. high school orbachelor

high school or morev. less than high school

log

odds

rat

io

weight

black



Conclusion

The NetherlandsUSA

Decomposition of the weights for white men

0

.5

1

prob

abili

ty

1920 1940 1960 1980

year of birth


.2

.4

.6

.8

1

prop

ortio

n

1920 1940 1960 1980

year of birth

proportion at risk

0

.1

.2

varia

nce

1920 1940 1960 1980

year of birth

variance

1

2

3

4

leve

l

1920 1940 1960 1980

year of birth

gain

0

.5

1

wei

ght

1920 1940 1960 1980

year of birth

weight

high school or more v.less than high school

junior college v.high school orbachelor

bachelor v.high school orjunior college



Conclusion

The NetherlandsUSA

Decomposition of the weights for black men

0

.5

1

prob

abili

ty

1920 1940 1960 1980

year of birth


.2

.4

.6

.8

1

prop

ortio

n

1920 1940 1960 1980

year of birth

proportion at risk

0

.1

.2

varia

nce

1920 1940 1960 1980

year of birth

variance

1

2

3

4

leve

l

1920 1940 1960 1980

year of birth

gain

0

.5

1

wei

ght

1920 1940 1960 1980

year of birth

weight

high school or more v.less than high school

junior college v.high school orbachelor

bachelor v.high school orjunior college



Conclusion

The NetherlandsUSA

The seqlogit package

I These graphs where made with the seqlogit package inStata.

I It can deal with any tree.I To install type within Stata ssc install seqlogit.



Conclusion

Outline

IEOpp and IEOut


Conclusion



Conclusion

Conclusion

I IEOut depends in an understandable way on the IEOppsand transition probabilities.

I IEOut is a weighted sum of IEOpps, and the weightsincrease if:

I the proportion at risk increases,I the proportion that passes is closer to .50,I the expected increase in level of education increases



Conclusion

Conclusion



I the proportion at risk increases,

I the proportion that passes is closer to .50,I the expected increase in level of education increases



Conclusion

Conclusion



I the proportion at risk increases,I the proportion that passes is closer to .50,

I the expected increase in level of education increases



Conclusion

Conclusion



I the proportion at risk increases,I the proportion that passes is closer to .50,I the expected increase in level of education increases



Conclusion

Conclusion

I This relationship can be used to:

I to relate IEOut to the IEOpps.I identify important and less important transitions,I to explain differences in IEOut with well documented

phenomena like educational expansion or racial differencesin educational attainment.



Conclusion

Conclusion

I This relationship can be used to:I to relate IEOut to the IEOpps.

I identify important and less important transitions,I to explain differences in IEOut with well documented




Conclusion

Conclusion

I This relationship can be used to:I to relate IEOut to the IEOpps.I identify important and less important transitions,

I to explain differences in IEOut with well documentedphenomena like educational expansion or racial differencesin educational attainment.



Conclusion

Conclusion

I This relationship can be used to:I to relate IEOut to the IEOpps.I identify important and less important transitions,I to explain differences in IEOut with well documented



linking process to outcome - inequality of educational ... · two types of educational inequality...

Documents