1. Family, Community and Long-Term Earnings Inequality
Paul Bingley, SFI Copenhagen
Lorenzo Cappellari, Università Cattolica Milano
Konstantinos Tatsiramos, University of Nottingham
Winter School on Inequality and Social Welfare Theory
Canazei, 10 January 2017

2. Motivation and Research Question
Two circumstances that can influence individuals’ earnings potential beyond their effort:
Family
Community (schools and youth neighborhoods)
What are the contributions of family, school and neighborhood in the income generation process?
Is family more important than community?
Do schools and/or neighborhoods matter?
What are the long-term effects of these factors? Do they vary over the life-cycle?
Bingley, Cappellari and Tatsiramos 2017

3. Bingley, Cappellari and Tatsiramos 2017
This paper
Using administrative data for 700,000 Danish men we model the joint earnings dynamics of siblings, neighbors and schoolmates between ages 24 and 51.
We use the model to decompose for the first time the sibling correlation of earnings into family, neighborhood and school effects.
We exploit two sources of variation:
Differences of communities within families: mobility and its timing
Partially overlapping peer groups within communities
Bingley, Cappellari and Tatsiramos 2017

4. Bingley, Cappellari and Tatsiramos 2017
Findings
Family is by far the most relevant factor that shapes the inequality of long-term earnings.
Overall, the impact of community is limited. But there is a significant effect in the initial phase of the working life (up to age 30), which fades away afterwards.
Not properly accounting for sorting of families into communities leads to upwardly biased community effects.
Bingley, Cappellari and Tatsiramos 2017

5. Bingley, Cappellari and Tatsiramos 2017
Outline of talk
Literature
Data
Model and identification
Results
Parameter estimates
Decompositions
Alternative identification strategies
Robustness
Bingley, Cappellari and Tatsiramos 2017

6. Bingley, Cappellari and Tatsiramos 2017
Literature
Bingley, Cappellari and Tatsiramos 2017

7. Sibling correlations
Omnibus measure of family and community effects (Corcoran et al., 1976; Solon et al., 1991; Altonji and Dunn, 1991).
Models of sibling effects in permanent incomes:
𝑦 𝑖𝑗 = 𝑎 𝑖𝑗 + 𝑓 𝑗 , 𝑎 𝑖𝑗 ~ 0, 𝑣𝑎𝑟 𝑎 ; 𝑓 𝑗 ~ 0, 𝑣𝑎𝑟 𝑓
𝑟 𝑆 = 𝑣𝑎𝑟 𝑓 𝑣𝑎𝑟 𝑎 +𝑣𝑎𝑟 𝑓
Share of inequality in permanent incomes accounted for by factors shared by siblings (loosely speaking inequality ‘between families’).
𝑟 𝑆 = in the US (Solon et al. 1991; Mazumder, 2008), 0.35 in SWE (Björklund et al., 2009), in DK (Björklund and Jannti, 2012), 0.43 in GER (Schnitzlein, 2014).
Bingley, Cappellari and Tatsiramos 2017

8. Decomposing sibling correlations
The idea of unpacking the sibling correlation goes back to Page and Solon (2003)
PSID: in 1968 households were sampled in clusters (blocks of houses)
𝑦 𝑖𝑗𝑛 = 𝑎 𝑖𝑗𝑛 + 𝑓 𝑗𝑛 + 𝑐 𝑛
Siblings: 𝑐𝑜𝑣 (𝑦 𝑖𝑗𝑛 ;𝑦 𝑖 ′ 𝑗𝑛 )=𝑣𝑎𝑟 𝑓 +𝑣𝑎𝑟 𝑐 +2𝑐𝑜𝑣 𝑓,𝑐
Neighbors: 𝑐𝑜𝑣( 𝑦 𝑖𝑗𝑛 ;𝑦 𝑖 ′ 𝑗 ′ 𝑛 )= 𝑣𝑎𝑟 𝑐 +2𝑐𝑜𝑣 𝑓,𝑐
Because of the PSID design they could not separate neighborhood (𝑣𝑎𝑟 𝑐 ) from sorting (𝑐𝑜𝑣 𝑓,𝑐 ).
2 moment restrictions and 3 parameters
They compare neighbors vs sibling correlations. 50%, upper bound
Bingley, Cappellari and Tatsiramos 2017

9. Decomposing sibling correlations
Oreopolous (2003) looks at randomized neighbors from a social housing experiment in Toronto
𝑐𝑜𝑣 𝑓,𝑐 =0 by design
Finds 𝑐𝑜𝑣 (𝑦 𝑖𝑗𝑛 ;𝑦 𝑖 ′ 𝑗 ′ 𝑛 )=0, i.e. neighborhoods don’t matter
Rauum et al. (2006) use the model of Page and Solon on Norwegian population data. They residualize on neighborhood fixed effects to limit sorting. Find sizeable neighborhood effects (30% of the overall sibling correlation).
Bingley, Cappellari and Tatsiramos 2017

10. Neighborhoods and schools
Focus on mean outcomes
Experimental evidence from the MTO project suggests little impact on economic outcomes (e.g. Ludwig et al., 2013).
Recent evidence instead finds effects that depend on the exposure to neighborhoods when young (Chetty et al. 2016; Chetty and Hendren, 2016)
Effect of class size:
Chetty et al. (2011): no effect on earnings at age 27 from the Tennessee STAR experiment.
Fredriksson et al. (2013): positive effect on adult earnings at ages 27 to 42 using class size rule in Sweden.
Leuven and Kokken (2015) find zero effect in Norway for earnings 20-48
Bingley, Cappellari and Tatsiramos 2017

11. Bingley, Cappellari and Tatsiramos 2017
Data
Bingley, Cappellari and Tatsiramos 2017

12. Bingley, Cappellari and Tatsiramos 2017
Brothers
Danish register: Brothers born
First two brothers sharing both biological parents
1-12 yrs age spacing
No twins; no adoptees
120k sibling pairs
380k singletons
Bingley, Cappellari and Tatsiramos 2017

13. Bingley, Cappellari and Tatsiramos 2017
Peers
We link brothers and singletons to their youth peers
Schoolmates: born in the same year and attending the same school on 31° October in the year they turn 15 (normally grade 9).
Exploit information from the National Pupil database which reports school identifier for 15 years old since 1973
1858 schools, with average 19.5 boys from the same birth cohort.
Neighbors: born in the same year and living in the same parish on 31° October in the year they turn 15.
Parish is the only place identifier recorded consistently throughout
2123 parishes, with average 14.6 boys from the same cohort
Bingley, Cappellari and Tatsiramos 2017

14. Bingley, Cappellari and Tatsiramos 2017
Peers
We use age 15 because we do not have information at earlier ages for schools
For selected cohorts we can retrieve information on parish back to age 10
Use it for robustness checks and to exploit differential timing of mobility for identification
Bingley, Cappellari and Tatsiramos 2017

15. Bingley, Cappellari and Tatsiramos 2017
Sources of variation
Brothers do not share the school or neighborhood when they attended different schools or lived in different neighborhoods at age 15
70% same school and neighborhood, 15% only same neighborhood, 6% only same school, 9% entirely different community
Among those with same school and neigborhood:
Moved between 10° and 15° birthday of brother 1 (15%)
Never moved or moved before brother 1 turned 10 (85%)
No full overlap between neighborhoods and public school catchment areas
Bingley, Cappellari and Tatsiramos 2017

16. Bingley, Cappellari and Tatsiramos 2017
Earnings
Gross annual income from labor 1984 – 2011 (2005 prices)
Life-cycle earnings age 24 – 51
Trim 0.25% at each tail
Require at least 3 consecutive observations
Otherwise fully unbalanced panel
Bingley, Cappellari and Tatsiramos 2017

17. Bingley, Cappellari and Tatsiramos 2017
Corr(B1,B2|Age B1=35)
Bingley, Cappellari and Tatsiramos 2017

18. Bingley, Cappellari and Tatsiramos 2017
Corr(B1,B2|Age B1=Age B2)
Bingley, Cappellari and Tatsiramos 2017

19. Bingley, Cappellari and Tatsiramos 2017
Corr(B1,B2|Age B1=Age B2)
Bingley, Cappellari and Tatsiramos 2017

20. Bingley, Cappellari and Tatsiramos 2017
Corr(Peers)
Bingley, Cappellari and Tatsiramos 2017

21. Bingley, Cappellari and Tatsiramos 2017
Corr(Unrelated)
Bingley, Cappellari and Tatsiramos 2017

22. Bingley, Cappellari and Tatsiramos 2017
Model
Bingley, Cappellari and Tatsiramos 2017

23. Joint earnings dynamics for groups of individuals
Individual earnings dynamics (Moffitt and Gottschalk, 1995; Meghir and Pistaferri, 2004)
Earnings dynamics of couples (Hyslop, 2001)
Bingley and Cappellari (2014) extend to earnings dynamics of triads (1 father; 2 sons)
This papers extends to joint earnings dynamics for groups of arbitrary size
Bingley, Cappellari and Tatsiramos 2017

24. Heterogeneous Income Profiles (HIP)
𝑦 𝑖𝑡 = 𝑎 𝑖 + 𝑏 𝑖 𝐴 𝑖𝑡 ; 𝑣𝑎𝑟 𝑎 , 𝑣𝑎𝑟 𝑏 , 𝑐𝑜𝑣 𝑎𝑏
If Cov(ab)<0 y
Var(y)
Age
Age
Bingley, Cappellari and Tatsiramos 2017

25. HIP on the shared components
Human capital models predict investments to induce a trade-off between starting earnings and life-cycle earnings growth (Mincer, 1958; Ben-Porath, 1967).
Earnings variance u-shaped in age.
Families determine human capital investments (Becker and Tomes, 1986).
Also communities might play a role.
Then both family and community correlation could be u-shaped in age.
Robustness to life-cycle bias (Haider and Solon, 2006)
Bingley, Cappellari and Tatsiramos 2017

26. Bingley, Cappellari and Tatsiramos 2017
Permanent Earnings
HIP + RIP:
𝑦 𝑖𝑓𝑠𝑛𝑎 = 𝛿 𝑐 𝜋 𝑡 𝜇 𝑓 + 𝜇 𝑠 + 𝜇 𝑛 + 𝛾 𝑓 + 𝛾 𝑠 + 𝛾 𝑛 𝑎+ 𝜔 𝑖𝑎 ;
𝜔 𝑖𝑎 = 𝜔 𝑖(𝑎−1) + 𝜉 𝑖𝑎 ; 𝑡=𝑐 𝑖 +24+𝑎
Shared components correlated both between and within dimension.
𝜇 𝑓 , 𝛾 𝑓 ~ 𝜎 𝜇Φ 2 , 𝜎 𝛾Φ 2 ,𝜎 𝜇𝛾Φ ; 𝜇 𝑠 ,𝛾 𝑠 ~ 𝜎 𝜇Σ 2 , 𝜎 𝛾Σ 2 , 𝜎 𝜇𝛾Σ
𝜇 𝑛 ,𝛾 𝑛 ~ 𝜎 𝜇N 2 , 𝜎 𝛾N 2 , 𝜎 𝜇𝛾N ; 𝜇 𝑓 , 𝜇 𝑠 , 𝜇 𝑛 ~ 𝜎 ΦΣ , 𝜎 ΦN , 𝜎 ΣN
The model allows for the sorting of families into communities
Bingley, Cappellari and Tatsiramos 2017

27. Bingley, Cappellari and Tatsiramos 2017
Moment restrictions
Brothers:
𝑐𝑜𝑣 𝑦 𝑖𝑓𝑠𝑛𝑎 ; 𝑦 𝑖 ′ 𝑓 𝑠 ′ 𝑛 ′ 𝑎 ′ =
[ 𝜎 𝜇Φ 2 + 𝜎 𝛾Φ 2 𝑎 𝑎 ′ + 𝜎 𝜇𝛾Φ 𝑎+ 𝑎 ′ +𝐼 𝑠= 𝑠 ′ 𝜎 𝜇Σ 2 + 𝜎 𝛾Σ 2 𝑎 𝑎 ′ + 𝜎 𝜇𝛾Σ 𝑎+ 𝑎 ′ +𝐼 𝑛= 𝑛 ′ 𝜎 𝜇Ν 2 + 𝜎 𝛾Ν 2 𝑎 𝑎 ′ + 𝜎 𝜇𝛾N 𝑎+ 𝑎 ′
+ 2 𝜎 ΦΣ +2 𝜎 ΦN +2 𝜎 ΣN ] 𝜋 𝑡 𝜋 𝑡 ′ 𝛿 𝑐 𝛿 𝑐 ′
The difference of sibling correlations between ‘staying’ and ‘moving’ families identifies community effects (moving between the 15° birthday of B1 and B2)
Bingley, Cappellari and Tatsiramos 2017

28. Bingley, Cappellari and Tatsiramos 2017
Moment restrictions
Peers:
𝑐𝑜𝑣 𝑦 𝑖𝑓𝑠𝑛𝑎 ; 𝑦 𝑖 ′ 𝑓 ′ 𝑠 ′ 𝑛 ′ 𝑎 ′ =
[𝐼 𝑠= 𝑠 ′ 𝜎 𝜇Σ 2 + 𝜎 𝛾Σ 2 𝑎 𝑎 ′ + 𝜎 𝜇𝛾Σ 𝑎+ 𝑎 ′ + 2 𝜎 𝜇ΦΣ +𝐼 𝑛= 𝑛 ′ 𝜎 𝜇Ν 2 + 𝜎 𝛾Ν 2 𝑎 𝑎 ′ + 𝜎 𝜇𝛾N 𝑎+ 𝑎 ′ +2 𝜎 𝜇ΦN +2 𝜎 𝜇ΣN ] 𝜋 𝑡 𝜋 𝑡 ′
The difference between sibling correlations and peers correlations identifies family effects
The difference between peers correlation and community effects identifies sorting effects
Bingley, Cappellari and Tatsiramos 2017

29. Identification of variance components
Three (sets of) moment conditions
‘Staying’ families
‘Moving’ families
Peers
for three (sets of) parameters
Family
Community
Sorting
Bingley, Cappellari and Tatsiramos 2017

30. Results

31. Idiosyncratic components (RIP - Random Walk)
Initial condition (age 24)
Brother 1 ( 𝜎 𝜔24,1 2 )
0.0822
(0.0133)
Brother2 ( 𝜎 𝜔24,2 2 )
0.0731
(0.0129)
Variance of innovations
Brother 1 ( 𝜎 𝜉1 2 )
0.0729
(0.0127)
Brother 2 ( 𝜎 𝜉2 2 )
0.0593
(0.0101)
Bingley, Cappellari and Tatsiramos 2017

32. Shared components (1) (HIP - Random Growth)
Variance of intercepts
Family ( 𝜎 𝜇Φ 2 )
0.1482
(0.0241)
School ( 𝜎 𝜇Σ 2 )
0.0173
(0.0082)
Neighborhood ( 𝜎 𝜇N 2 )
0.0203
(0.0095)
Variance of slopes
Family ( 𝜎 𝛾Φ 2 )
0.0026
(0.0004)
School ( 𝜎 𝛾Σ 2 )
0.0002
(0.0001)
Neighborhood ( 𝜎 𝛾N 2 )
0.0005
Bingley, Cappellari and Tatsiramos 2017

33. Shared components (2) HIP – Random Growth
Covariance between components
Family-School ( 𝜎 𝜇ΦΣ )
0.0074
(0.0033)
Family-Neighborhood ( 𝜎 𝜇ΦN )
0.0101
(0.0038)
School- Neighborhood ( 𝜎 𝜇ΣN )
0.0050
(0.0008)
Covariance intercepts-slopes
Family ( 𝜎 𝜇𝛾Φ )
(0.0019)
School ( 𝜎 𝜇𝛾Σ )
(0.0009)
Neighborhood ( 𝜎 𝜇𝛾N )
(0.0012)
Bingley, Cappellari and Tatsiramos 2017

34. Decomposition: Life cycle average
coeff.
s.e.
Brothers (F + C)
0.319
0.010
Family
0.298
0.012
Community (N + S)
0.021
0.009
Neighborhood
School
0.011
Bingley, Cappellari and Tatsiramos 2017

35. Bingley, Cappellari and Tatsiramos 2017
Decomposition: Age 24
coeff.
s.e.
Brothers
0.75
Family
0.48
Community
0.12
Sorting
0.15
Bingley, Cappellari and Tatsiramos 2017

36. Bingley, Cappellari and Tatsiramos 2017
Decomposition
Bingley, Cappellari and Tatsiramos 2017

37. Ignoring sorting effects
Only stayers
No family effects
coeff.
s.e.
Brothers
0.313
0.011
Family
0.268
School
0.029
0.001
0.044
Neighborhood
0.015
0.026
Community (N+S)
0.045
0.071
Bingley, Cappellari and Tatsiramos 2017

38. Larger community effects before age 30
Baseline 25 27 30
Coeff.
s.e.
Brothers
0.319
0.010
0.661
0.013
0.525
0.011
0.397
Family
0.298
0.012
0.483
0.019
0.399
0.015
0.323
Parish
0.095
0.020
0.063
0.033
School
0.084
0.017
0.041
0.009
Community
0.021
0.179
0.126
0.074
C/B
0.06
0.270
0.240
0.187
Bingley, Cappellari and Tatsiramos 2017

39. Comparison with the Literature
Page and Solon (2003): Siblings=0.31, Neighbors=0.16
Oreopoulos (2003):
All Toronto: Siblings=0.28, Neighbors=0.054
Public Housing: Siblings=0.26, Neighbors=0.00
Rauum et al (2006): Siblings =0.20, Neighbors=0.06
This paper:
Only community: Peers=0.071
Ignoring sorting: Siblings =0.31, Peers =0.045
Joint model: Siblings =0.31, Peers= 0.021
Bingley, Cappellari and Tatsiramos 2017

40. Identification: Brothers
«Moving» families: change of community in the time window between brothers’ 15° birthday
«Staying» families:
never changed community, or
did change community before older brother turned 15
An issue if these groups differ in relevant unobservables
We tackle the issue on a subset of younger cohorts (>1965) for whom we know parish since age 10, by either:
Use only movers and limit the comparison between movers and those moving parish between B1’s 10° and 15° birthday (early movers), thus exploiting variation in timing of move
Use only stayers 10-20, and compare sibling couples with high vs low degree of peers’ turnover (in-place mobility)
Bingley, Cappellari and Tatsiramos 2017

41. Bingley, Cappellari and Tatsiramos 2017
Timing of mobility
Brothers
Family
Neighborhood
School
Community (N+S)
C/B
Baseline
0.319
0.298
0.01
0.011
0.021
0.066
(0.01)
(0.012)
(0.009)
Cohorts > 1965
0.299
0.272
0.004
0.023
0.027
0.089
(0.008)
(0.011)
(0.010)
0.316
0.271
0.034
0.045
0.142
Only movers
(0.013)
Bingley, Cappellari and Tatsiramos 2017

42. Bingley, Cappellari and Tatsiramos 2017
Timing of mobility
Full sample
Only movers
Bingley, Cappellari and Tatsiramos 2017

43. Bingley, Cappellari and Tatsiramos 2017
In-place mobility
Brothers
Family
Community
C/B
Baseline
0.319
0.298
0.021
0.066
(0.01)
(0.012)
(0.009)
Inplace mobility
0.324
0.290
0.034
0.105
(0.020)
(0.018)
(0.008)
Bingley, Cappellari and Tatsiramos 2017

44. Bingley, Cappellari and Tatsiramos 2017
In-place mobility
Bingley, Cappellari and Tatsiramos 2017

45. Robustness: measurement error from point-in-time definition of peers
Bingley, Cappellari and Tatsiramos 2017

46. Robustness: Early neighborhood exposure
Brothers
Family
Neighborhood
School
Community
C/B
Baseline
0.299
0.272
0.004
0.023
0.027
0.089
(Cohorts > 1965)
(0.008)
(0.011)
(0.010)
Parental parish
0.329
0.307
0.018
0.022
0.066
when 15
(0.012)
(0.016)
(0.013)
0.356
0.325
0.011
0.020
0.031
0.088
when 14
(0.019)
(0.014)
0.030
0.086
when 13
0.349
0.312
0.019
0.037
0.106
when 12
(0.015)
(0.018)
0.289
0.261
0.017
0.028
0.097
when 11
(0.009)
0.294
0.267
0.009
0.094
when 10
Bingley, Cappellari and Tatsiramos 2017

47. Bingley, Cappellari and Tatsiramos 2017
Robustness
Brothers
Family
Neighborhood
School
Community
Baseline
0.319
0.298
0.01
0.011
0.021
(0.010)
(0.012)
(0.009)
Up to 2 children
0.344
0.318
0.017
0.009
0.026
(0.016)
(0.021)
(0.015)
Up to 3 children
0.296
0.286
0.020
-0.010
0.010
(0.013)
Excluding
0.329
0.308
singletons
(0.011)
Peers at 14 and 15
0.299
Main parish of
0.300
0.006
0.013
0.019
residence 14-18
Excluding private
0.311
0.291
0.005
0.015
schools
ZIP codes
0.322
0.313
-0.015
0.024
0.008
(0.014)
Bingley, Cappellari and Tatsiramos 2017

48. Bingley, Cappellari and Tatsiramos 2017
Summary
Demonstrate the value of analysing joint earnings dynamics of siblings and peers.
Sibling correlation u-shaped in age, consistent with human capital models.
Family is most of sibling correlation.
Community effects are relevant before age 30.
Ignoring family effects leads to substantial overestimation of community effects. Sorting.
Similar results when exploit variation in the timing of residential mobility or in-place mobility for identification
Bingley, Cappellari and Tatsiramos 2017

49. Appendix

50. Transitory shocks Coef. s.e. Initial condition (age 24)
Coef.
s.e.
Initial condition (age 24)
Brother 1 ( 𝜎 24,1 2 )
0.6385
0.0298
Brother 2 ( 𝜎 24,2 2 )
0.6062
0.0293
Variance of innovations at 25
Brother 1 ( 𝜎 𝜀1 2 )
0.4785
0.0246
Brother 2 ( 𝜎 𝜀2 2 )
0.4654
0.0247
Age splines in variance of innovations
Brother 1
26-28
0.0047
29-33
0.0035
34-38
0.0447
0.0060
39-43
0.0507
0.0045
44-51
0.0255
0.0041
Brother 2
0.0067
0.0057
0.0294
0.0084
0.0580
0.0314
0.0117
Bingley, Cappellari and Tatsiramos 2017

51. Within and between person covariance of transitory shocks
Autoregressive coefficient
Brother 1 ( 𝜌 1 )
0.4418
0.0034
Brother 2 ( 𝜌 2 )
0.4510
0.0045
Cross-person associations in transitory earnings
Sibling covariance of innovations ( 𝜎 𝑓 )
0.0009
0.0013
Peers covariance of transitory earnings (catch-all components)
Sharing both school and neighborhood ( 𝜆 𝑠𝑛 )
0.0008
Sharing only school ( 𝜆 𝑠 )
0.0019
Sharing only neighborhood ( 𝜆 𝑛 )
0.0010
Bingley, Cappellari and Tatsiramos 2017