Download Intergenerational mobility and sample selection in short panels

Intergenerational mobility
Cheti Nicoletti
ISER, University of Essex
2009
Motivation
• Studies on intergenerational (im)mobility try to
examine the association between children’s and
parents’ socio-economic outcome (usually
income, earnings, occupational class or
prestige).
• It is believed that low intergenerational mobility
is indicative of unequal opportunities between
people born in advantaged and disadvantaged
families and that policy should improve
opportunities for those from disadvantaged
backgrounds.
Motivation
• Notice that two societies could have the
same level of inequality in earnings within
a generation but a completely different
level of intergenerational transmission of
earnings.
• A society where the relative position of a
person in the earnings distribution is
exactly inherited from the parents’ one is
considered unfair.
Previous studies
•
•
•
•
•
A first study of intergenerational transmission can be dated back to Galton
(1886) who regress children’s height on parents’ one.
More recently sociologists have studied intergenerational mobility and have
especially focused on the association between class positions of parents
and children (see Erikson and Goldthorpe 1992).
Economists have begun to be extensively interested in this topic after
Becker and Tomes (1979, 1986) developed a model of the transmission of
earnings, assets and consumptions from parents to children. Atkinson
(1981) and Atkinson, Maynard and Trinder (1983) are the first papers to
study intergenerational earnings mobility in the UK (men born in York in
1950 and traced to the late 1970s).
Review article: Solon, G. (1999) Intergenerational mobility in the labor
market, In O. Ashenfelter and D.Card (eds.) Handbook of Labor Economics,
Volume 3, Chapter 29, 1761-1800. Amsterdam: Elsevier.
Look for forthcoming chapter “Intergenerational income mobility and the
role of family background” in Handbook of Economic Inequality Markus
Jäntti and Anders Björklund
Intergenerational mobility equation
yi    xi  ui u i iid (0,  )
2
u
yi  log(earnings) for sons
xi  log(earnings) for fathers
OLS
( xi  x )( yi  y )


2
(
x

x
)
 i
Interngera tional elasticity
  cov( xi , yi ) / var( xi )
Intergener ational correlatio n

cov( xi , yi )
var( xi ) var( yi )
Data requirement
•
•
1.
2.
3.
We need to observe a long run permanent measure (income,
earnings, occupational prestige) for both fathers and their children
Possible data sources:
Panel data which follow individual across time (for example the
Panel Study of Income dynamic in US, the British Household
Panel Survey)
Cohort studies which follow people born in a specific cohort from
when born or other longitudinal studies (for example the British
Cohort Studies 1958 and 1970, National Longitudinal Survey in
the US)
Cross-sectional data with retrospective questions asked to
children about their fathers (for example Oxford Mobility Study,
which provides data on occupational class for children and their
fathers when they, the sons, were 14 years old.)
Measurement error on father’s
earnings
• We observe current earnings xit instead of a
permanent measure of earnings xi
xit=xi +εit
where εit iid (0,σε2 ) and independent of xi and yi
• This implies that we underestimate β ( for β>0)
cov( xit , yi )
cov( xi , yi )
cov( xi , yi )




var( xit )
var( xi )  var(  it )
var( xi )
~
• Notice that a similar error for yit would not bias β, but
it would bias the intergenerational correlation
Solution suggested by Solon
(1992) and Zimmerman (1992)
• If xit is observable for t=1,…T, we can consider
T
T
xit
xi   it
 it
xi    
 xi  
T t 1 T
T
t 1
t 1
Var ( it )
Var ( xi )  Var ( xi ) 
T
Cov( xi , yi )
Cov( xi , yi )
Cov( xi , yi )
Cov( xi , yi )
~




Var ( it )
Var ( xi )
Var ( xit ) Var ( xi )  Var ( it )
Var ( xi ) 
T
Cov( xi , yi )
Cov( xi , yi )
for T  


Var ( it )
Var ( xi )
Var ( xi ) 
T
T
Mazumder (2005) RES
Life cycle bias
• Earnings (even if averaged) can be a bad proxy
for permanent earnings if measured when
people are too old or too young (Life cycle bias).
• Solution: Control with a polynomial in age or age
dummies in the intergenerational equation
yi  
2
 xi   1ageson,i   2ageson,i
  3age father,i   4 age2father,i  ui
Life cycle bias
1.
2.
3.
Controlling for sons and fathers age in the
intergenerational mobility equation can help in
reducing the measurement error bias. But this
correction is not enough if the earnings growth is
heterogeneous across individuals.
Imposing and upper and a lower bound for sons and
fathers age can be a solution (ex. Blanden et al 2004
and 2007, 30-33; Gershuny 2002, 34-36; Ermsich and
Nicoletti 2007, 31-45).
Lee and Solon (2005) suggest to estimate an
intergenerational mobility equation using sons
observed at any age but allowing the elasticity to vary
across cohort and son’s age. (See for example
Ermsich and Nicoletti 2007)
Comparing Intergenerational
across cohorts in Britain
•
•
•
•
•
Comparing measure of intergenerational mobility across children (sons)
born in different cohorts is very difficult because of data comparability and
data availability issues.
It is for example difficult to observe earnings for both children and their
parents for very long cohort period
Blanden, Gregg, MacMillan (2007, The Economic Journal) compared
NCDS1958 and BC1970 (but the two datasets have a lot comparability
issues) and found a negative trend in mobility
Nicoletti, Ermisch (2007, The B.E. Journal of Economic Analysis & Policy)
compared children born from 1950 to 1972 using the BHPS (but they use a
two sample two stage procedure which usually provide an overestimation
of the intergenerational mobility) and found no trend for the period 1950-72
and a slight negative but not significant trend for the 1960-1972 period
Breene and Goldthorpe (2001, European Sociological Review) and
Goldthrope and Jackson (2007, British Journal of Sociology) studied class
mobility and found little change across the two generations when
considering measures of exchange mobility, in contrast to the negative trend
in mobility found in Blanden et al. (2004, 2007)) using the same two cohorts.
Advantages and disadvantages
of panel data
 Advantages
•
•
Repeated observations are available so that it is
easier to measure the long run economic status.
Panel surveys are usually based on representative
samples of the full population.
 Disadvantages
•
Coresidence selection: Son must be living together
with his father in at least one wave of the panel.
BHPS 1991-2003
1991
Cohort Child age
1997
2003
Child age
Child age
1988
3
9
15
1983
8
14
20
1978
13
19
25
1973
18
24
30
1968
23
29
35
1963
28
34
44
1958
33
39
45
How can the BHPS help us?
•
•
•
•
All BHPS respondents are asked to report occupational
characteristics of their parents when they were 14
THEREFORE
We know the occupational prestige, say HG, even for
sons and fathers living apart during the panel.
We can estimate the correlation of HG without any
coresidence selection.
We can consider the subsample of sons coresident with
the fathers at least once during the panel and assess the
relevance of the coresidence selection.
We can then compare different methods to correct for
the coresidence selection.
Taking account of
coresidence selection
Francesconi and Nicoletti (Journal of Applied
Econometrics, 2006) find that the intergenerational
mobility in occupational prestige is underestimated
when using the subsample of sons born between
1966 and 1985.
They try different estimation methods to correct for
sample selection and find that only the inverse
propensity score is able to attenuate the selection
problem
This sample selection evaluation is possible because all
BHPS respondents are asked to report occupational
characteristics of their parents when they were 14
Coresidence
• If we select only children coresident with their parents in at least
one wave of the panel, we can have a problem of sample selection.
The subsample is probably not a random sample.
• This can cause a bias in the estimation of β
yi    xi   i
yi  log(earnings) for sons
xi  log(earnings) for fathers
1 for children coresident
d 
i
otherwise
0
If yi  d i | Z i , xi then
we can use propensity score weightin g
Selection model
(coresidence model)
1 for children coresident
d  I (d i  0 ) d  
i
i
otherwise
0
d i  Z i   ui
*
*
'
Z=dummies for education, age, regions, ethnicity, religiosity
and two house price indexes
Propensity score
Pr( d  1 | Z )  Pr( d *i  0 | Z )  Pr(ui   Z 'i  )  F ( Z 'i  )
i
i
Pr( d  1 | Z ) 
i
i
i
exp( Z 'i  )
1  exp( Z i  )
'
if ui iid logistic
Pr( d  1 | Z )   ( Z 'i  ) if ui iid Normal
i
i
Selection problem
yi    xi   i
d i*  Z i'   ui
1 for children coresident
d 
i
otherwise
0
• Y=log son earnings X= log father earnings
• Z=dummies for education, age, regions, ethnicity, religiosity and
two house price indexes
• If ε depends of u Selection due to unobservables
• Ex. unobserved work abilities which are related to y and to the
probability to leave parental home earlier
• If ε depends of Z Selection due to observables
• Ex: Y|X depends on Z (education and age) then ε depends on Z
and we have selection due to observables
Selection due to observables:
Propensity score weighting estimation
yi    xi   i
d i  Z i   ui
*
'
1 for children coresident
d 
i
otherwise
0
• Y=log son earnings X= log father earnings
• Z=dummies for education, age, regions, ethnicity,
religiosity and two house price indexes
• If ε and u are independent but ε depends on some of
the Z (for education, age, etc.) Weighted least square
estimation of β with weights given by
  Pr(d  1 | Z )
i
i
1
 F (Z i  )
'
1
Coresidence selection model
Variable
Coeff
SE
Variable
Coeff
SE
No qualification
-0.684
0.391
Catholic
-0.186
0.214
Other qualification
0.209
0.18
Protestant
0.149
0.149
GSCE/O level
0.142
0.131
Other denominations
0.079
0.369
First degree
0.072
0.129
South East
-0.59
0.248
Age before leaving home
0.04
0.114
Rest of South East
-0.458
0.201
Age square
0.004
0.003
Anglia/Midlands
-1.285
0.254
North West
-1.324
0.274
house price index LAD
-4.074
0.431
Rest of North
-1.656
0.27
house price index region
1.503
0.269
Wales
-1.449
0.31
Scotland
-1.586
0.278
26.389
4.533
Black
-0.294
0.522
Indian
0.182
0.629
Constant
Pakistani/Bangladeshi
0.423
0.704
No. Obs
1090
Other Ethnicity
0.239
0.508
Pseudo R-square
0.333
Intergenerational mobility mediated
by education
•
•
•
•
•
y=α+xβ+ε
If ε and u are independent but ε depends on education
Then to take account that ε is not independent of
education (omitted variable) we can consider
y=αN+xβN+edu δ +ω Regression adjustment
βN is consistently estimated (because ω is independent of
u and of education)
β=Cov(x,y)/Var(x)=βN+Cov(x,edu)Var(x)-1δ
βN is the intergenerational association (elasticity) in
earnings net of the effect (or not mediated by) the
education.
(β-βN) is the intergenerational mobility in earnings
mediated by the education
Another solution for the
coresidence selection problem
using the BHPS
• PROBLEM: We can observe both sons’ and their
fathers’ earnings only if they have been living
together in at least 1 wave during the panel.
This is possible in 12% of the cases in our
sample (cohort period 1950-1972).
• SOLUTION: we use a TS2SLS estimator which
combines two separate samples from the BHPS
The two-sample two-stage least squares
(plim TS2SLS = plim TS2SIV)
The TS2SLS estimator combines two separate samples
from the BHPS:
• 1st dataset (Full sample) containing information on sons’
earnings, and fathers’ education and occupational
characteristics when sons were 14 years (collected
through retrospective questions to sons);
• 2nd dataset (Supplemental sample) containing
information on earnings and occupational characteristics
of potential fathers (Hope-Goldthorpe index; the
Cambridge scale; dummies to distinguish occupations in
professional, managerial and technical, skilled nonmanual, skilled manual and unskilled; 19 dummies for
socio–economic groups).
References 2SIV: Angrist and Krueger (1992), Arellano and
Meghir (1992), Ridder and Moffitt (2005), Inoue and
Solon (2005)
Two-sample two-stage
least squares estimator (TS2SLS)
Combining the two samples
1. Estimation of the log earnings equation
for fathers using the supplemental
sample (imputation regression)
x=Z+v
2. Estimation of the main equation using
the full sample and replacing (imputing) x
x  Zˆ
p
p
p lim x  Pz x
Previous studies on intergenerational
mobility using TS2SLS estimator
The choice of instruments in previous studies is quite often
dictated by the few variables available:
• Bjorklund and Jantti (1997) use education level and occupation in
Sweden,
• Fortin and Lefebvre (1998) use 16 occupational groups in Canada
• Grawe (2004) uses education levels for Ecuador, Nepal, Pakistan
and Peru.
Our potential IV are instead given by:
• Hope-Goldthorpe index; the Cambridge scale; dummies to
distinguish occupations in professional, managerial and technical,
skilled non-manual, skilled manual and unskilled; 19 dummies for
socio–economic groups, education level and age. (similarly to
Lefranc A, Trannoy A. 2005)
Intergenerational earnings mobility
(sons 31-45 and fathers 31-55)
First step: We estimate the imputation regression
We regress x on the following IV
•
•
•
•
•
the log Hope-Goldthorpe index,
4 dummies for managerial duties (self-employed, 1
manager, 2 foreman/supervisor, 3 not
foreman/supervisor)
3 education level dummies (no qualification or
some qualification, 1 further education
qualification, 2 first degree or higher)
age and age square
2 cohort groups (1930-1938, 1939-1946)
Variable
Log (Hope-Goldthorpe
score) cohort 1930-38
Log (Hope-Goldthorpe
score) cohort 1939-46
Education1, cohort
1930-38
Education1, cohort
1939-46
Education2, cohort
1930-38
Coeff
0.51
0.452
0.126
0.079
0.395
S.E.
Variable
Coeff
S.E.
0.123
Manager, cohort
1930-38
0.737
0.106
0.112
Manager, cohort
1930-46
0.313
0.078
0.073
Foreman/supervisor
cohort 1930-38
0.437
0.11
0.058
Foreman/supervisor
cohort 1939-46
0.078
0.081
0.145
No managerial duties
cohort 1930-38
0.459
0.089
0.108
0.071
Education2, cohort
1939-46
0.256
0.096
No managerial duties
cohort 1939-46
Cohort 1939-46
0.565
0.611
Age
0.259
0.097
-1.599
2.537
Age2
-0.003
0.001
Constant
Number of
observations
R2
896
0.259
Adjusted R-squared
0.246
Intergenerational earnings mobility
(sons 31-45 and fathers 31-55)
Second step:
y= +  x + u
y = son’s log earnings;
x = father’s log earnings;
,  and  are coefficients;
u is i.i.d (0, σ2)
We estimate  separately for rolling cohort groups
1950-55, 1951-56, 1952-57, …, 1967-1972
-0.200
0.000
0.200
0.400
0.600
0.800
Elasticities and correlations for
single year earnings
1950
1955
1960
1965
cohort
Elasticity
Lower CI
Correlation
Upper CI
-0.200
0.000 0.200 0.400 0.600 0.800
Elasticities and correlations for
average earnings
1950
1955
1960
1965
cohort
Elasticity
Lower CI
Correlation
Upper CI
Another sample selection problem:
Labour market selection
• The intergenerational occupational mobility can
be estimated only for people who are employed.
• This means the we can use only the subsample
of people who are employed and this can cause
a selection bias.
• This selection can be especially relevant when
estimating the association between earnings of
daughters and fathers because women have
usually more work interruptions.
Employment selection model
y=α+xβ+ε
d*=Z γ+u d=l(d*>0)
where
y is the daughter’s occupational prestige (log HopeGoldthorpe score)
x is her father’s occupational prestige
d=1 for daughters are employed at least in at least one
wave and 0 otherwise
Z=occupational prestige father, dummies for education,
age, regions, ethnicity, religiosity, marital status and
number of children aged between 0-2, 3-4.
Intergenerational mobility and
employment selection
yi    xi   i
d i  Z i   ui
*
'
where d i  I (d i*  0)
 If εi and ui are not independent then we have selection
due to unobservables (For example unobserved work
skills or cognitive skills which affect both the probability
of employment and earnings for daughters)
 If εi depends on Zi then we have selection due to
observables (for example education, age and work
experience which can affect both the probability of
employment and the daughters’ earnings)
Intergenerational mobility and
employment selection
yi    xi   i
d i  Z i   ui
*
'
• Since εi (yi) depends on some of the variables Zi
(for example education, age, etc.)
• We have first of all control for selection due to
observables
• This is possible using for example propensity
score weighting or regression adjustment.
Propensity score weighting
• First step: Estimation of the binary model for
the employment probability
d *i  Z 'i   ui P̂r( di  1 | Zi )  F ( Z 'i ˆ )
• Second step: Weighted least square estimation
(notice that the weights are estimated, so a proper estimation should
be adopted to estimate the standard errors)
WLS
( xi  x )( yi  y ) i


 ( xi  x )2  i
where  i  Pr( di  1 | Z i ) 1
Employment selection
Variable
Coeff
SE
Variable
Coeff
SE
No qualification
-1.274
0.234
No. children 0-2
-0.69
0.149
Other qualification
-0.473
0.22
No. children 3-4
-0.5
0.161
GSCE/O level
-0.312
0.173
No. children 5-11
-0.25
0.101
First degree
0.004
0.206
No. children 12-15
-0.39
0.143
No. children 16-18
-0.25
0.443
0.275
0.32
0.26
0.265
Anglia/Midlands
0.159
0.241
0.378
0.314
-0.2
0.248
Wales
0.558
0.395
Average age
0.562
0.155
South East
Average age square
-0.01
0.003
Rest of South East
Fathers’s status
0.044
0.203
North West
Married
0.673
0.172
Rest of North
Black
-5.953
2.15
Scotland
-0.13
0.28
Indian
-1.537
0.461
Constant
-5.95
2.15
Pakistani/Bangladeshi
-1.252
0.521
No. Obs
1090
Other Ethnicity
-0.419
0.513
Pseudo R-square
0.265
Selection due to unobservables
yi    xi   i
d i*  Z i'   ui
 If εi and ui are not independent then we have selection
due to unobservables (For example unobserved work
skills or cognitive skills which affect both the probability
of employment and earnings for daughters)
 Usually Heckman procedures are adopted, but these
procedure are not very adequate in the case of
intergenerational models because εi depends also on Z
(omitted variables problems)
 We need to control for selection on observables and
unobservables too by for example combining Heckman
and propensity score methods
Intergenerational mobility
Correlatio
n
Ignoring
selection
Average
10th
25th
50th
75th
90th
0.303
0.285
0.447
0.310
0.312
0.246
0.084
(0.000)
(0.028)
(0.050)
(0.048)
(0.057)
(0.037)
(0.032)
Correcting for employment selection
Weighting
Heckman
two-step
Weighting
Heckman
0.305
0.301
0.357
0.327
0.333
0.294
0.222
(0.000)
(0.032)
(0.058)
(0.047)
(0.050)
(0.039)
(0.041)
0.224
0.301
0.229
0.233
0.204
0.080
(0.029)
(0.062)
(0.043)
(0.046)
(0.033)
(0.028)
0.230
0.337
0.258
0.254
0.268
0.185
(0.030)
(0.064)
(0.065)
(0.054)
(0.046)
(0.056)
Some references for regressions
with sample selection
•
•
•
•
•
•
•
Buchinski, M. (2001) Quantile regression with sample selection: Estimation women
return to education in the U.S., Empirical Economics, 26, 86-113.
Ibrahim, J.G., Chen, M.-H., Lipsitz, S.R., Herring, A.H. (2005) Missing-data methods
for generalized linear models: A comparative review, Journal of the American
Statistical Association, 100, 469, 332-346.
Lipsitz, S.R., Fitzmaurice, G.M., Molenberghs, G., Zhao, L.P. (1997), Quantile
regression methods for longitudinal data with drop-outs, Applied Statistics, 46, 463476.
Robins, J. M., Rotnitzky, A. (1995), Semiparametric Effciency in Multivariate
Regression Models With Missing Data, Journal of the American Statistical
Association, 90, 122-129.
Vella F. (1998), Estimating models with sample selection bias: a survey',
The Journal of Human Resources, vol. 3, 127-169.
Wooldridge, J.M. (2007) Inverse probability weighted M-Estimation for
General missing data problems, Journal of Econometrics, 141, 2, 12811301.
Wooldridge, J.M. (2007) Inverse probability weighted M-Estimation for General
missing data problems, Journal of Econometrics, 141, 2, 1281-1301.