4a. Intergenerational Mobility

1
4a. Intergenerational Mobility
2
Empirical Evidence

• Best guesses.
• Sons whose fathers were unemployed when they
  were young are twice as likely to experience and
  unemployment spell when they reach adulthood
• and moreover the spells tend to be longer
• ONeill, D and O.Sweetman (1998)
  Intergenerational Mobility in Britain Evidence
  from Unemployment Patterns, Oxford Bulletin of
  Economics and Statistics, vol. 60, no. 4
  (November). pp. 431-449

3
Empirical Evidence (continued)

• Earnings Advantage
• Suppose we write relationship between sons and
  fathers earnings as
• In the literature ß is called the
  intergenerational earnings elasticity.

4

• Now lets compare offspring of rich parents (YPR)
  and poor parents (YPP).
• We can show that on average

5
Does the size of ß really matter?

• Lets assume that the earnings of the rich parent
  is 5 times that of poor parent

6
Empirical Evidence on size of ß

• Best Guesses
• United States .5
• United Kingdom .5
• Denmark .15
• Finland .18
• Norway .17

7
Broader International Comparisons
8
Empirical Evidence (Education)
9
Additional Readings

• Miles Corak (2006) Do poor Children become poor
  adults? Lessons from a Cross Country Comparison
  of Generation Earnings Mobility,
• IZA Discussion paper 1993http//ftp.iza.org/dp199
  3.pdf
• Hertz, T, T.Jayasundera, P. Piraino, S. Selcuk,
  N.Smith, A. Verashchagina (2007) The
  Inheritance of Educational Inequality
  International Comparisons and Fifty-Year Trends
  BE Journal of Economic Analysis and Policy
  http//www.bepress.com/cgi/viewcontent.cgi?article
  1775contextbejeap
• Solon, Gary (2004). A Model of Intergenerational
  Mobility Variation over Time and Place.In Miles
  Corak (editor). Generational Income Mobility in
  North America and Europe. Cambridge Cambridge
  University Press.

10
TheorySolon, Gary (2004). A Model of
Intergenerational Mobility Variation over Time
and Place.In Miles Corak (editor). Generational
Income Mobility in North America and Europe.
Cambridge Cambridge University Press.

• Permanent Income Model ß0 abstracting from
  genetic transfers of skills/preferences.
• Introduce Borrowing Constraints.
• Education of child is financed by reducing own
  consumption.

11
Model

• Family i contains one parent of generation t-1
  and one child of generation t.
• Family must allocate parents lifetime after tax
  earnings (1- )yi,t-1 between the parents own
  consumption Ci,t-1 and investment in childs
  human capital, Ii,t-1.
• Assume that parents cannot borrow against the
  childs prospective earnings and does not
  bequeath financial assets to the child.

12
Model (continued)

• The resulting budget constraint is

13
Preferences

• Assume that parents preferences can be
  represented by a Cobb-Douglas Utility function.
• a captures parents levels of altruism.

14
Technology

• The technology translating investment into human
  capital is given by
• ei,t denotes the initial endowment of the child

15
Technology (continued)

• The childs income is determined by a semi-log
  earnings function

16
Solution

• Combining constraints and preferences, we can
  rewrite the objective function as

17
Interior Solution

• Implications
• High income parents invest more in their children
• Partial crowding out of private investment by
  public investment
• Investment increasing in a
• Investment increasing in ?p.

18
Earnings Equation

• For x small, ln(1x)x

19
Nature of Government Transfers

• Assume
• Relative progressivity in public investment
  provided gt0.

20
Intergenerational Earnings Equation

• Looks like something we can estimate but
• error term not well behaved.
• Why not?

21
What gets estimated?

• Assuming stationarity the probability limit of
  the OLS estimator will equal
• With a bit of work we can show that in our case
  this amounts to

22
Determinants of intergenerational elasticity

• The commonly estimated intergenerational
  elasticity is greater as
• The heritability coefficient ? is greater
• Human capital investment is more productive
• Returns to human capital is greater
• Public investment in human capital is less
  progressive.

23
Steady state Cross-Sectional Inequality

• A first order autoregression with first order
  autoregressive error term can be written as a
  second order autoregression with white noise
  error term. This can be used to derive
  cross-section variance

24
More Developed Model

• Include financial transfers, uncertainty and the
  possibility that not all families are borrowing
  constrained.
• Mulligan, C (1997) Parental Priorities and
  Economic Inequality, Chapter 3, Appendix A.
• Han. S and C. Mulligan (2001) Human Capital,
  Heterogeneity and Estimated Degrees of
  Intergenerational Mobility Economic Journal,
  Vol. 111, pp. 207-243.