Skip to main content

College education and wages in the U.K.: estimating conditional average structural functions in nonadditive models with binary endogenous variables

Abstract

Recent studies debate how the unobserved dependence between the monetary return to college education and selection into college can be characterised. This paper examines this question using British data. We develop a semiparametric local instrumental variables estimator for identified features of a flexible correlated random coefficient model. These identified features are directly related to the marginal and average treatment effect in policy evaluation. Our results indicate that returns to college systematically differ between actual college graduates and actual college non-graduates. They are on average higher for college graduates and positively related to selection into college for 96% of the individuals. The dependence between selection into college and returns to college education is strongest for individuals with low math test scores at the age of 7, individuals with less educated mothers, and for working-class individuals.

References

  1. Battistin E, Rettore E (2008) Ineligible and eligible non-participants as a double comparison group in regression-discontinuity designs. J Econom 142(2): 715–730

    Article  Google Scholar 

  2. Berger MC, Black D, Smith J (2001) Evaluating profiling as a means of allocating government services. In: Lechner M., Pfeiffer F (eds) Econometric evaluation of labour market policies. Physica, Heidelberg, Germany, pp 59–84

    Chapter  Google Scholar 

  3. Björklund A, Moffitt R (1987) The estimation of wage gains and welfare gains in self-selection models. Rev Econ Stat 69(1): 42–49

    Article  Google Scholar 

  4. Blundell R, Dearden L, Sianesi B (2005) Evaluating the impact of education on earnings in the UK: models, methods and results from the NCDS. J R Stat Soc Ser A 168(3): 473–512

    Article  Google Scholar 

  5. Blundell R, Powell JL (2003) Endogeneity in nonparametric and semiparametric regression models. In: Hansen L (eds) Advances in economics and econometrics. North Holland, Amsterdam

    Google Scholar 

  6. Bound J, Jaeger DA, Baker RM (1995) Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. J Am Stat Assoc 90(430): 443–450

    Google Scholar 

  7. Card D (2001) Estimating the return to schooling: progress on some persistent econometric problems. Econometrica 69(5): 1127–1160

    Article  Google Scholar 

  8. Carneiro P, Lee S (2009) Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality. J Econom 149(2): 191–208

    Article  Google Scholar 

  9. Carneiro P, Meghir C, Parey M (2007) Maternal education, home environments and the development of children and adolescents. CEPR Discussion Paper No. 6505, CEPR, London, U.K.

  10. Cleveland WS, Grosse E, Shyu WM (1991) Local regression models. In: Chambers JM, Hastie TJ (eds) Statistical models in S. Wadsworth/Brooks-Cole, Pacific Grove, CA, pp 309–376

    Google Scholar 

  11. Currie J, Moretti E (2003) Mothers education and the intergenerational transmission of human capital: evidence from college openings. Q J Econ 118(4): 1495–1532

    Article  Google Scholar 

  12. Fan J (1992) Design-adaptive nonparametric regression. J Am Stat Assoc 87(420): 998–1004

    Article  Google Scholar 

  13. Fan J, Zhang W (1999) Statistical estimation in varying coefficient models. Ann Stat 27(5): 1491–1518

    Article  Google Scholar 

  14. Frölich M (2007) Nonparametric IV estimation of local average treatment effects with covariates. J Econom 139(1): 35–75

    Article  Google Scholar 

  15. Goldberger AS (1989) Economic and mechanical models of intergenerational transmission. Am Econ Rev 79(3): 504–513

    Google Scholar 

  16. Griliches Z (1977) Estimating the returns to schooling: some econometric problems. Econometrica 45(1): 1–22

    Article  Google Scholar 

  17. Hastie T, Tibshirani R (1993) Varying-coefficient models. J R Stat Soc Ser B (Methodological) 55(4): 757–796

    Google Scholar 

  18. Haveman R, Wolfe B (1995) The determinants of children’s attainments: a review of methods and findings. J Econ Lit 33(4): 1829–1878

    Google Scholar 

  19. Heckman JJ, Urzua S, Vytlacil E (2006) Understanding instrumental variables in models with essential heterogeneity. Rev Econ Stat 88(3): 389–432

    Article  Google Scholar 

  20. Heckman JJ, Vytlacil EJ (1998) Instrumental Variables methods for the correlated random coefficient model: estimating the average rate of return to schooling when the return is correlated with schooling. J Hum Resour 33(4): 974–987

    Article  Google Scholar 

  21. Heckman JJ, Vytlacil EJ (1999) Local instrumental variables and latent variables models for identifying and bounding treatment effects. Proc Natl Acad Sci 96: 4730–4734

    Article  Google Scholar 

  22. Heckman JJ, Vytlacil EJ (2000) The relationship between treatment parameters within a latent variable framework. Econ Lett 66(1): 33–39

    Article  Google Scholar 

  23. Heckman JJ, Vytlacil EJ (2001) Local instrumental variables. In: Hsiao C, Morimune K, Powell J (eds) Nonlinear statistical modeling. Proceedings of the thirteenth international symposium in economic theory and econometrics: essays in Honor of Takeshi Amemiya. Cambridge University Press, Cambridge, pp 1–46

    Chapter  Google Scholar 

  24. Heckman JJ, Vytlacil EJ (2005) Structural equations, treatment effects, and econometric policy evaluation. Econometrica 73(3): 669–738

    Article  Google Scholar 

  25. Hirano K, Imbens GW, Ridder G (2003) Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71(4): 1161–1189

    Article  Google Scholar 

  26. Imbens GW, Angrist JD (1994) Identification and estimation of local average treatment effects. Econometrica 62(2): 467–475

    Article  Google Scholar 

  27. Klein TJ (2010) Heterogeneous treatment effects: instrumental variables without monotonicity?. J Econom 155(2): 99–116

    Article  Google Scholar 

  28. Mincer J (1974) Schooling, experience, and earnings. Columbia University Press, New York

    Google Scholar 

  29. Newey WK (1997) Convergence rates and asymptotic normality for series estimates. J Econom 79: 147–168

    Article  Google Scholar 

  30. Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1): 41–55

    Article  Google Scholar 

  31. Solmon LC, Taubman PJ (1973) Does college matter? Some evidence of the impacts of higher education. Academic Press, New York

    Google Scholar 

  32. Staiger D, Stock JH (1997) Instrumental variables regression with weak instruments. Econometrica 65(3): 557–586

    Article  Google Scholar 

  33. Vytlacil E (2002) Independence, monotonicity, and latent index models: an equivalence result. Econometrica 70(1): 331–341

    Article  Google Scholar 

  34. Willis RJ, Rosen S (1979) Education and self-selection. J Polit Econ 87(5, Part 2: Education and income distribution):S7–S36

  35. Wooldridge JM (2007) Instrumental variables estimation of the average treatment effect in correlated random coefficient models. In: Millimet D, Smith J, Vytlacil E (eds) Advances in econometrics: modeling and evaluating treatment effects in econometrics, vol 21. Elsevier, Amsterdam

    Google Scholar 

  36. Xia Y, Li WK (1999) On the estimation and testing of functional-coefficient linear models. Stat Sinica 9: 735–757

    Google Scholar 

Download references

Acknowledgments

This paper is based on the second chapter of my Ph.D. thesis, which I defended in July 2006 at the University of Mannheim. I am especially grateful to Erich Battistin, Richard Blundell, Pedro Carneiro, Andrew Chesher, Johannes Gernandt, Stefan Hoderlein, Enno Mammen, Melanie Schienle, and Edward Vytlacil for stimulating discussions and helpful comments on earlier versions of this paper. Moreover, I would like to thank Richard Blundell, Lorraine Dearden, as well as Leslie McGranahan for sharing their data. I would like to thank UCL for its hospitality during the academic year 2003/4, the European Commission for financial support through the Marie Curie program, and the Deutsche Forschungsgemeinschaft for financial support through SFB/TR 15. Furthermore, I would like to thank the audiences of various conference and seminar presentations for valuable comments. Finally, I would like to thank the three referees and the editor for their detailed comments and suggestions.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Tobias J. Klein.

Electronic Supplementary Material

The Below is the Electronic Supplementary Material.

ESM 1 (PDF 26 kb)

Rights and permissions

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Cite this article

Klein, T.J. College education and wages in the U.K.: estimating conditional average structural functions in nonadditive models with binary endogenous variables. Empir Econ 44, 135–161 (2013). https://doi.org/10.1007/s00181-010-0355-x

Download citation

Keywords

  • Returns to college education
  • Correlated random coefficient model
  • Local instrumental variables estimation

JEL Classification

  • C14
  • C31
  • J31