Everything you wanted to know about the returns to education – but were afraid to ask

1. Everything you wanted to know about the returns to education – but were afraid to ask Ian Walker Lancaster University Management School and Paul Bingley SFI Copenhagen

2. Lancaster • Top 100/10/5 • Economics research strengths in Education / Labour, Macro / forecasting, IO / applied micro • If you are a good MSc student • We have PhD scholarships available • 3 ESRC CASE awards – alcohol, u/e, absenteeism • Open studentships (2 ESRC, 2 School) • Contact ian.walker@lancaster.ac.uk • If you are finishing your PhD • We have two lectureships available • One macro, one any area • See you at RES job market event? Or email me

3. Background • Thousands of studies of wage determination • Strong focus on the effect of “S” on “w” • Harmon et al Labour Economics 2003 meta • This talk: • Not a survey • But an attempt to illustrate many of the issues in one dataset • Isolates what we (think we) know • from we could know, • And from what we know will be hard to know

4. Important issues • One big issue has been endogeneity of S • coeff on S picks up not just the effect of S on w • But also the effect of other factors not included that are correlated with S (like “ability”, A) • OLS biased upwards • A smaller issue has been measurement error • If S contaminated by ME then OLS coeff “attenuated” (biased towards 0) • Estimating returns to S (and unobserved skills) over time has been a very big issue • Many specification issues

5. Becker’s HC Earnings Function • Workhorse model of wage determination • wi= Xi β + αSi + uiwhere X includes a quadratic in experience (or age) • But ui = γAi + ei and if cov(Ai,Si) >0 • then plimαOLS = α+ γ(σAS2/ σS2) > αifγ>0 • Note that if S = S + v (measurement error) • then plimαOLS =α.(1 - σ2v / σ2S ) <αifσ2v > 0 • We (think we) have learned quite a lot about all of this from IV studies • But possibly not the ATE of S on w

6. Minority issues • A unit of S is the same for everyone • may be quality differences (correlated with S) • αmay also depend on S • Nonlinearity, qualifications, “sheepskin” • “Separability” assumption • Effect of S on w is independent of age • αis assumed independent of everything • but it may depend on other things, αi=α(Vi)+vi • Observed and unobserved heterogeneity • V might include institutions and “grades” • Some of v may be “luck”, some may be “productivity” • We know very little about any of this

7. Motivation: increasing inequality • α changing over time? • The rich are getting richer • US (73+), UK (77+), and even in Denmark (89+)

8. Motivation: understanding why? • In our simple model • wi = Xi β + αSi + ui • where ui = γAi + ei and cov(Ai,Si)>0 • then plim αOLS = α+ γ(σAS2/ σS2) • Rising var(w), given S, X, β , andunobserved A, could be due to: • α higher returns to education • γhigher returns to unobservable skills • σe2 more measurement error in wages • σAS greater selectivity in schooling

9. Alternatives to OLS estimation • Eliminate “ability bias” by controlling for A • But A and S highly correlated • And our measures of A are often affected by S • Matching methods assume problem away • No selection on unobservables • Unbiased estimate of αiffσAS= 0 is true • But γnot identified if σAS= 0 is true • IV • But IV estimation does not estimate ATE • IVs may affect people observed from different years and cohorts differently • so interpretation of LATE varies across time

10. Existing literature • Juhn et al (JPE 1993) - rising var(w) in US • When var(w) rose, where, and for who • Beaudry (JoLE 05), Lemieux (AER 06) • Cawley et al in Arrow et al (eds) 2000 • A * S * t interaction - hard to identify • But all US CPS studies problematic • Because S imputed from data on “some college”, “college”, HS graduation • Induces changes in ME in S • And changes in w data • Workers have more complex remuneration in more recent data

11. The twins solution • Estimate returns to bothS and A • over time (and across cohorts) • Huge panel – identical MZ’s, fraternal DZ’s • MZ’s may allow us to identify causal effect of S • Small, but rising fast since early 90’s • DZ’s then may allow us to infer returns to ability • Large, but falling slowly since early 90’s • Measurement error problem in S • Important problem for us • but qualifications are accurately measured • Address endogenous ΔS with credible (?) IV • Suggests that “ability bias” in MZ diffs is small

12. Twins methodology • Δwi = ΔXi β + αΔSi + γΔAi + Δei • where Δ is the within-twin pair difference • If the twins are MZs, then we eliminate (?) the unobservables, i.e. ΔAi = 0 • and usually most ΔX’s=0 • so regress Δw on ΔS for unbiased estimate of α • But, within-twin differencing exacerbates ME in S • ME in ΔSi may be large • Use IV based on alternative measures of S

13. Existing MZ twins literature

14. Double trouble: Bound & Solon, Neumark(EconEducRev 1999) • Measurement error in S • S=S*+v where S* is true S • Differencing S data exaggerates ME bias • Our S is “normed” from qualifications data • so ME in ΔSis probably very large • plim(αWT) =α(1 - r/(1-ρ)) • wherer = σ2v/σ2S , butρ= cov(S1,S2) ≈ 1 • Need to use IV to deal with ME • Princeton work uses cross-reported ΔSas IV • We have lots of x-reports

15. More double trouble: • Why do identical twins differ in S? • ΔS may not be random • individual-specific component of A may remain • Need to instrument ΔS for this reason (even if ME=0) • Education reforms may not work as IVs • Twins have same values of the Z’s? • Family background probably won’t either • Twins have same • Bonjour et al (AER 2004) • But we (think we) do have an IV idea • and DZ estimate of α provides tighter upper bound on the true α than OLS does.

16. Our contribution 2: Dealing withmeasurement error • S comes from admin registers • Low measurement error in qualifications • So get unattenuated estimates of college premium • But to get S we need to “norm” the quals data • High var(S) associated with any highest qual • So we probably have very large ME in S • Alternative measures of S • Princeton work uses x-reported S • We have twin’s spouse’s S as well as conventional x-reports from survey data

17. Our contribution 3: Dealing with endogenous ΔSi • Sdifferencesmay not be random • Individual component of A not differenced out • Need an instrument to purgeΔSiofremaining A diffs • something that affects twin 1’s S but not twin 2’s • School sizeaffects if twins can be separated • Important in DK - teacher gets fixed in grade 1 • Twins in 1-class school smaller Δ(ΔS) than in 2+ class • Expect bigger effect from instruments for DZs • Since more ΔAiremains than for MZs

18. Danish data • Merge several administrative databases via CPR • Use 1970 Census to link children to mums • dob identifies multiple births • 1970+ match via birth records • About 1000 Danish multiple pregnancies each year • More Danish triplets than Princeton has twins • Twins odds about 1 in 80 • Triplet odds about 1 in 8000

19. Twins sample selection • Over ½ m twin-year working age obs • Around 24k pairs over up to 25 years • Drop the triplets, quads…. • Select MZs, same-sex DZs, age 25-55 • Select if earnings observed (at least twice) between 1980-2005 • Select working full-time and full-year • to reduce the problem that we have only annual earnings not hourly wage rate • 4185 MZ pairs, 6343 DZ pairs

20. Variables • Income data comes from tax returns • we don’t have good hours of work data • Schooling data • Not available for “special” schools • Few IVF cases yet, and no immigrants • Zygosity questionnaire • 4 “peas in a pod?” type questions • 96% match to DNA in small subsample • Christensen et al (Twins Research 2003) • Christensen et al (BMJ 2006) • similar test scores at 16 as singletons • Even though they average 900 grams lighter

21. Summary statistics

22. Distribution of ΔS

23. Basic resultstwins and singletons compared • Pool data across waves, adjust std errs • Singleton (we have these too) estimates • αmS=0.031 (0.0005) αfS=0.037 (0.0005) • Treating twins as singletons we get • αmMZ=0.030 (0.0005) αfMZ=0.037 (0.0006) • Almost same for DZs • Twins are just like singletons • IV (using twin spouse S as IV) • αmMZ=0.065 (0.0011) αfMZ=0.054 (0.0014) • Conclusion • Implied very low reliability – 0.5 for m, 0.7 for f

24. Basic FE results – twin differences • Expect huge attenuation bias in OLS on twin differences (ie FE estimation) • MZsαm= 0.005 (0.001) αf= 0.009 (0.001) • DZsαm= 0.018 (0.001) αf= 0.025 (0.001) • So FEIV estimates much higher, especially for DZs • MZsαm= 0.045 (0.010) αf= 0.044 (0.008) • DZsαm= 0.095 (0.006) αf= 0.054 (0.006) • Conclusion • Large returns (by DK standards) of 4½ % on average over 80’s and 90’s

25. Returns over time • Rolling 10 year window over 1980-2002 • MZs yield αt(return to observed skills) • DZs yield αt+ γt (σAS2/σS2)c • whereγ = return to unobserved skill • (σAS2/σS2)c is fixed for all members of cohort c • So difference between MZ and DZ estimates is proportional to return to unobserved skills • We have a long panel • So its also possible to distinguish cohort effects

26. Returns over time (no cohort effects)

27. Extension 1:Time, cohort and lifecycle effects • Time dimension of data identifies time variation in γt • If the panel were balanced then we could treat (σAS /σS2) as a constant • Estimate γtfrom the balanced part of the data • Different birth cohorts identifies σASc. • Estimates suggest that recent cohorts have lower σASc • γtgets correspondingly higher in recent years • But still not significantly rising

28. Extension 2:Endogenous ΔS • Problem that ΔS might be correlated with ΔA • A is not (entirely) a family effect • So αbiased upwards because of ΔA bias • Need an IV for ΔS (even if no ME)? • Usual suspects won’t work • Need var that affects twin 1’s S but not twin 2’s • Different classes • We don’t know if twins were separated • But twins could be separated if 2+ classes • 46% of schools have single class entry

29. Extension 2: Endogenous ΔS • Twins in 1-class schools have smaller ΔS • MZs Δ1,2+ΔS = -0.30 male, -0.22 female • DZsΔ1,2+ΔS = -0.19 male , -0.14 female • 1-class twins have same Δw | ΔS as 2-class • Classes affects w only through S • IV estimation eliminates remaining A bias • MZsαm = 0.040 (0.009) αf = 0.041 (0.009) • DZsαm = 0.043 (0.015) αf = 0.043 (0.021) • Conclusion: • very small ΔA-bias in MZ FE, larger in DZ FE

30. Extension 3:Nonlinear effects • Nonlinear schooling effects • interaction between twin average S and ΔS • α(S) significantlydecreasing in S • No change in convexity over time • Returns to college vs high school • No ME in college degree reporting • 1990’s returns to “Bachelor” about 30% • 1990’s returns to “Masters” about 15% • Rising college premium over time • With strong cohort effects • No rise in returns to unobserved skills

31. Extension 4:Self and cross reported S • Available from the new twins omnibus survey • Match to register data via CPR • All DK twins included in survey • Response rate 80%+ of pairs • Little attenuation when using conventional x-reports as IVs for self-reported S • OLS MZsαm = 0.038 (0.011) αf = 0.039 (0.013) • IV MZsαm = 0.041 (0.017) αf = 0.042 (0.019) • Other useful information • Childhood illnesses, birth weight, best friend’s background and behaviour ......

32. Conclusion • There is a lot that we know (or can know) from the data we have • But there is a lot we still don’t know • Only better data will enable us to know more • Diminishing returns to econometric ingenuity have set in • With much better data there is not much that cannot be known • Slides available from Liam • PS Remember - apply to Lancaster