1. C15 Lectures, 2004 Lecture 2: Intergenerational Mobility Stephen Machin

2. 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

3. A Model of Intergenerational Mobility Solon (1999) HoLE Parental lifetime earnings in generation (t-1) is Y t-1 – allocated into consumption C and investment in children I Y t-1 = C t-1 + I t-1 Investment then yields a return r to children in their own generation, t: Y t = (1+r)I t-1 + E t where E is other determinants of earnings.

4. A Model of Intergenerational Mobility (Continued) Suppose parent maximises U = (1-  )logC t-1 +  logY t then will choose investment according to: I t-1 =  Y t-1 – [(1-  )/(1+r)]E t Substitution for I t-1 in the child earnings function gives Y t =  Y t-1 + u t If cov(Y t-1, E t ) = 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.

5. 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

6. Intergenerational Mobility and Inequality Atkinson (1981) JPKE Childhood consumption = c 1 Y t-1 Adulthood consumption = c 2 Y t Lifetime welfare W t = log(c 1 Y t-1 ) +  log(c 2 Y t ) Variance of lifetime welfare is Var(Wt) = Var(logY t-1 ) + 2  Cov(logY t-1,logY t ) +  2 Var(logY t )

7. Intergenerational Mobility and Inequality (Continued) If the intergenerational income transmission is logY t =  logY t-1 + u t and assume Var(logY t ) = Var(logY t-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.

8. Intergenerational Mobility and Inequality (Continued) Compared to  = 0  δ = 0.5δ = 1  = 0.2 16% 20%  = 0.4 24% 40%  = 0.6 48% 60%

9. Measurement of the Extent of Intergenerational Mobility 2 main approaches: 1). Regression Based Approach y i child = α + β y i parent + u i child where y is log(Y) and u an error term.  is intergenerational elasticity β = 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)

10. 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.

11. Measurement (Continued) - Quartile Transition Matrices A. Complete Mobility Parent’s Quartile Child’s QuartileTop2nd3rdBottom Top.25 2 nd.25 3 rd.25 Bottom.25 B. Complete Immobility Parent’s Quartile Child’s QuartileTop2nd3rdBottom Top1000 2 nd 0100 3 rd 0010 Bottom0001

12. 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

13. Measurement (Continued) – What is Y? y i child = α + β y i parent + u i child 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.

14. Measurement (Continued) – Transitory Versus Permanent y i child = α + β y i parent + u i child 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 y it, y is (s = parent’s generation; t = child’s generation) y it child = y i child + v it child ; y is parent = y i parent +v is parent

15. Measurement (Continued) – Transitory Versus Permanent In practice look at y it child = α + β y is parent + u it child 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(v is parent )]. So if there is no measurement error and Var(v is parent ) = 0 there is no bias. Further aggravated if look at specific samples. Sample homogeneity makes downward bias worse.

16. 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’.

17. 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.

18. 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) – Table 1. 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(v it parent )/T]

19. 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.

20. International Comparisons There are clear differences in intergenerational correlations across countries. CountryStudyElasticity FinlandJantti & Osterbacka(1996) Osterbacka (2001) 0.22 0.13 SwedenBjorklund and Jantti (1997) Bjorklund and Chadwick (2002) 0.28 0.25 GermanyWiegand (1997)0.34 USSolon (1992) Zimmerman (1992) 0.43 0.45 UKAtkinson et al (1983) Dearden, Machin and Reed (1997) 0.42 0.42-0.57

21. 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 (2003) look at changes over time in UK.

22. 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.

23. Earnings and Parental Income Across Generations Regression Coefficient Adjusted For Inequality Change Cross- Cohort Change Sample sizes NCDSBCS Sons.166 (.020).260 (.024).095 (.031)NCDS: 2246 BCS: 2053 Daughters.168 (.022).227 (.022).059 (.031)NCDS: 1908 BCS: 2017

24. 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 W t =  t H t + v t H t =  t W t-1 +  t Therefore W t =  t  t W t-1 + u t

25. 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

26. 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

27. Changes in HE Participation Marked differences by social class.

28. Degree Acquisition and Family Income Degree Acquisition by Age 23 Lowest 20 percentMiddle 60 percentHighest 20 percentEducational 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)

29. 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.