C15 Lecture 2: Intergenerational Mobility

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C15 Lecture 2 Intergenerational Mobility

• Stephen Machin

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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

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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 (1r)It-1 Et
• where E is other determinants of earnings.

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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-?)/(1r)Et
• Substitution for It-1 in the child earnings
  function gives
• Yt ?Yt-1 ut
• If cov(Yt-1, Et) 0 then ß ( ?(1r)) 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.

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Implications

• Simple 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

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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) 2?Cov(logYt-1,logYt)
  ?2Var(logYt)

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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 ß (i.e. less mobility) to
  be associated with higher inequality.

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Intergenerational Mobility and Inequality
(Continued)

• Compared to ? 0 ?
• d 0.5 d 1
• ? 0.2 16 20
• ? 0.4 24 40
• ? 0.6 48 60

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Measurement of the Extent of Intergenerational
Mobility

• 2 main approaches
• 1). Regression Based Approach
• yichild a ß yiparent uichild
• where y is log(Y) and u an error term.
• ? is intergenerational elasticity
• ß 0 ? complete mobility as child earnings are
  independent of those of their parents.
• ß 1 ? complete immobility as child earnings
  are fully determined by the parental earnings.
• (could have ß lt 0 reversal)

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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.

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Measurement (Continued)- Quartile Transition
Matrices
A. Complete Mobility Parents Quartile Parents Quartile Parents Quartile Parents Quartile Parents Quartile
Childs Quartile Top 2nd 3rd Bottom
Childs Quartile Top .25 .25 .25 .25
Childs Quartile 2nd .25 .25 .25 .25
Childs Quartile 3rd .25 .25 .25 .25
Childs Quartile Bottom .25 .25 .25 .25
B. Complete Immobility Parents Quartile Parents Quartile Parents Quartile Parents Quartile Parents Quartile
Childs Quartile Top 2nd 3rd Bottom
Childs Quartile Top 1 0 0 0
Childs Quartile 2nd 0 1 0 0
Childs Quartile 3rd 0 0 1 0
Childs Quartile Bottom 0 0 0 1
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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

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Measurement (Continued) What is Y?

• yichild a ß yiparent 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.

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Measurement (Continued) Transitory Versus
Permanent

• yichild a ß yiparent 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 parents generation
  t childs generation)
• yitchild yichild vitchild yisparent
  yiparent visparent

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Measurement (Continued) Transitory Versus
Permanent

• In practice look at
• yitchild a ß yisparent uitchild
• In this formulation ß will be biased downwards
  if transitory components are present.
• It will be downward biased by a factor of Var(y)
  / Var(y) Var(visparent).
• 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.

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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.

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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.

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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
• ßV(y) / (V(y) V(visparent)/T

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Estimates (Continued)

• This is illustrated in Tables 2 and 3 of Solons
  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.

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Estimates (Continued) Solon (1992), Table 2
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Estimates (Continued) Solon (1992), Table 3
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Estimates (Continued) Zimmerman (1992), Table 2
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Estimates (Continued) Zimmerman (1992), Table
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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
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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.

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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.

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Earnings and Parental Income Across Generations
Regression Coefficient Adjusted For Inequality Change 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
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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 ?t?t Wt-1 ut

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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

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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

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Changes in HE Participation

• Marked differences by social class.

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Degree Acquisition and Family Income
Degree Acquisition by Age 23 Degree Acquisition by Age 23 Degree Acquisition by Age 23 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)
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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.