c15 lecture 2: intergenerational mobility stephen machin
TRANSCRIPT
C15 Lecture 2: Intergenerational Mobility
Stephen Machin
Issues
• Defining intergenerational mobility
• Measuring intergenerational mobility in economic and social status
• Estimates of the extent of intergenerational mobility
• International comparison and changes over time
A Model of Intergenerational Mobility
• Solon (1999) HoLE
Parental lifetime earnings in generation (t-1) is Yt-1 – allocated into consumption C and investment in children I
Yt-1 = Ct-1 + It-1
Investment then yields a return r to children in their own generation, t:
Yt = (1+r)It-1 + Et
where E is other determinants of earnings.
A Model of Intergenerational Mobility (Continued)
Suppose parent maximises U = (1-)logCt-1 + logYt then will choose investment according to:
It-1 = Yt-1 – [(1-)/(1+r)]Et
Substitution for It-1 in the child earnings function gives
Yt = Yt-1 + ut
If cov(Yt-1, Et) = 0 then β (= (1+r)) is the correlation between child and parent earnings. A larger implies reduced mobility in that child and parent earnings are more strongly correlated across generations.
ImplicationsSimple model reveals:• Several mechanisms may underpin
intergenerational mobility• Very much an empirical question how big is
the intergenerational correlation• Unpacking the transmission mechanisms may
be a complex process• Despite its simplicity careful specification of
empirical models is required• Data requirements to estimate mobility are
stringent
Intergenerational Mobility and Inequality
• Atkinson (1981) JPKE
Childhood consumption = c1Yt-1
Adulthood consumption = c2Yt
Lifetime welfare Wt = log(c1Yt-1) + log(c2Yt)
Variance of lifetime welfare is
Var(Wt) = Var(logYt-1) + 2Cov(logYt-1,logYt) + 2Var(logYt)
Intergenerational Mobility and Inequality (Continued)
If the intergenerational income transmission is logYt = logYt-1 + ut and assume Var(logYt) = Var(logYt-1) = Var(logY) then
Var(W) = Var(logY)[1 + 2 + 2]
which implies a higher β (i.e. less mobility) to be associated with higher inequality.
Intergenerational Mobility and Inequality (Continued)
Compared to = 0 δ = 0.5 δ = 1
= 0.2 16% 20%
= 0.4 24% 40%
= 0.6 48% 60%
Measurement of the Extent of Intergenerational Mobility
2 main approaches:
1). Regression Based Approachyi
child = α + β yiparent + ui
child
where y is log(Y) and u an error term. is intergenerational elasticityβ = 0 complete mobility as child earnings are independent of those of their parents.β = 1 complete immobility as child earnings are fully determined by the parental earnings.(could have β < 0: reversal)
Measurement (Continued)
2). Transition matrix approach
Split child and parent Y distributions into equal sized quantiles and look at transitions across generations.
e.g. quartiles split into 4, deciles into 10 etc.
Measurement (Continued)- Quartile Transition Matrices
A. Complete Mobility
Parent’s Quartile
Child’s Quartile Top 2nd 3rd Bottom
Top .25 .25 .25 .25
2nd .25 .25 .25 .25
3rd .25 .25 .25 .25
Bottom .25 .25 .25 .25
B. Complete Immobility
Parent’s Quartile
Child’s Quartile Top 2nd 3rd Bottom
Top 1 0 0 0
2nd 0 1 0 0
3rd 0 0 1 0
Bottom 0 0 0 1
Measurement (Continued) – Issues
1). Types of data
Cross-section; Retrospective; Tracing; Longitudinal
2) Measurement
What is Y?; Transitory vs permanent?
3). Interpretation
How big?; Equality of opportunity
Measurement (Continued) – What is Y?
yichild = α + β yi
parent + uichild
For economists Y typically earnings or income (and sometimes education).
But wide range of other studies in other disciplines: e.g. original Galton 1886 study of height (at UCL); or big literature in sociology on social class origins and destinations.
Measurement (Continued) – Transitory Versus Permanent
yichild = α + β yi
parent + uichild
Issue is y should reflect lifetime earnings, but will be measured with error in most cases due to transitory fluctuations in measured earnings.
Recorded y is yit, yis (s = parent’s generation; t = child’s generation)
yitchild = yi
child + vitchild; yis
parent = yiparent +vis
parent
Measurement (Continued) – Transitory Versus Permanent
In practice look at
yitchild = α + β yis
parent + uitchild
In this formulation β will be biased downwards if transitory components are present.It will be downward biased by a factor of Var(y) / [Var(y) + Var(vis
parent)].
So if there is no measurement error and Var(visparent) =
0 there is no bias.Further aggravated if look at specific samples. Sample homogeneity makes downward bias worse.
Estimates of the extent of intergenerational mobility
• Early literature (US): intergenerational correlation of log earnings about 0.2. Becker and Tomes (1986) Journal of Labor Economics ‘Aside from families victimised by discrimination, regression to the mean in earnings in the United States and other rich countries appears to be rapid’.
Estimates (Continued)
• Much of this work based on specific samples and often on cross-section (and sometimes retrospective) data. So scope for downward bias.
• Confirmed by Solon (1992) and Zimmerman (1992) American Economic Review papers.
Estimates (Continued)• Solon (1992) uses longitudinal data from
the US Panel Survey of Income Dynamics to set up sample of 348 father-son pairs (fathers earnings in late 1960s, sons in early 1980s).
• One ‘solution’ to possible downward bias is offered by these data – time average (T periods) multiple earnings measures: Bias reduced:
β[V(y) / {(V(y) + V(visparent)/T}]
Estimates (Continued)
• This is illustrated in Tables 2 and 3 of Solon’s paper.
• Zimmerman (1992) uses a different data source, but with very similar findings – 876 father-son pairs from US National Longitudinal Study. Table 2 summarises results – around 0.4 for time averaged specifications. Table 15 transition matrix.
Estimates (Continued) – Solon (1992), Table 2
Estimates (Continued) – Solon (1992), Table 3
Estimates (Continued) – Zimmerman (1992), Table 2
Estimates (Continued) – Zimmerman (1992), Table 15
International Comparisons• There are clear differences in intergenerational
correlations across countries.
Country Study Elasticity
Finland Jantti & Osterbacka(1996)
Osterbacka (2001)
0.22
0.13
Sweden Bjorklund and Jantti (1997)
Bjorklund and Chadwick (2002)
0.28
0.25
Germany Wiegand (1997) 0.34
US Solon (1992)
Zimmerman (1992)
0.43
0.45
UK Atkinson et al (1983)
Dearden, Machin and Reed (1997)
0.42
0.42-0.57
Changes Over Time
• Most work looks at point in time comparison (not so surprising given data requirements).
• Given links between inequality and the intergenerational elastcicity, movements over time may also be of interest.
• Blanden, Goodman, Gregg and Machin (2004) look at changes over time in UK.
Changes Over Time (Continued)
• Based upon data from the 1958 and 1970 British birth cohorts, the extent of intergenerational mobility in economic status has reduced substantially over time.
Earnings and Parental Income Across Generations
Regression Coefficient Adjusted For Inequality Change
Cross-Cohort Change
Sample sizes
NCDS BCS
Sons .166 (.020) .260 (.024) .095 (.031) NCDS: 2246
BCS: 2053
Daughters .168 (.022) .227 (.022) .059 (.031) NCDS: 1908
BCS: 2017
Mechanisms
• A very simple and stylized theoretical model shows a stronger link between parent and child incomes when there is higher inequality and greater links between parental income and education
• Wt = tHt + vt
• Ht = tWt-1
+ t
• Therefore Wt = tt Wt-1+ ut
Rising Wage and Educational Inequality Lead to Falling
Mobility• Two factors thus combine to form the
intergenerational mobility parameter:
- higher t (more wage inequality) implies lower
mobility
- higher t (closer links between education and
parental earnings/income) implies lower mobility as increased educational inequality reinforces cross-generation persistence
Education as a Transmission Mechanism
• Seems to operate via increased educational inequality. Strong increase in sensitivity of education to family income.
• Increased educational inequality has acted to reinforce and raise immobility in economic status across generations
Changes in HE Participation
Marked differences by social class.
48%
27%
18%
4%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
1960 1970 1980 1990 2000
Top 3 Social Classes Bottom 3 Social Classes
Degree Acquisition and Family Income
Degree Acquisition by Age 23
Lowest 20 percent Middle 60 percent Highest 20 percent Educational Inequality
NCDS 1981 .06 .08 .20 .14 (.01)
BCS 1993 .07 .15 .37 .30 (.02)
BHPS 1999 .09 .23 .46 .37 (.05)
Change 1981-1993 .01 .07 .17 .15 (.02)
Change 1993-1999 .02 .08 .09 .07 (.06)
Change 1981-1999 .03 .15 .26 .23 (.06)
Implications• Cross-generation mobility in economic status
falls across cohorts for children going through the education system in the 1970s and 1980s.
• Part of this is due to an increased sensitivity of education to parental income (this continues to rise into the 1990s as well).
• To the extent that increased educational inequality drives reduced cross-generation mobility, policies to do with widening participation in HE are important.