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) HoLEParental 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) JPKEChildhood consumption = c1Yt-1

Adulthood consumption = c2Yt

Lifetime welfare Wt = log(c1Yt-1) + log(c2Yt)

Variance of lifetime welfare isVar(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 approachSplit 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 dataCross-section; Retrospective; Tracing; Longitudinal2) MeasurementWhat is Y?; Transitory vs permanent?3). InterpretationHow 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)yit

child = yichild + vit

child; yisparent = yi

parent +visparent

Measurement (Continued) – Transitory Versus Permanent

In practice look at yit

child = α + β yisparent + uit

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(vis

parent)].So if there is no measurement error and Var(vis

parent) = 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 ElasticityFinland Jantti & Osterbacka(1996)

Osterbacka (2001)0.220.13

Sweden Bjorklund and Jantti (1997)Bjorklund and Chadwick (2002)

0.280.25

Germany Wiegand (1997) 0.34US Solon (1992)

Zimmerman (1992)0.430.45

UK Atkinson et al (1983)Dearden, Machin and Reed (1997)

0.420.42-0.57

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: 2246BCS: 2053

Daughters .168 (.022) .227 (.022) .059 (.031) NCDS: 1908BCS: 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.