Methods Based on Selection on Unobservables

  • Giovanni Cerulli
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 49)


This chapter covers econometric methods for estimating average treatment effects (ATEs) of social and economic programs under the assumption of “selection on unobservables”. When nonobservable factors significantly drive the nonrandom assignment to treatment, recovering consistent estimations of average treatment effects relying only on observables is no longer possible. As a consequence, econometric methods only based on assuming “selection on observables” become inappropriate. This chapter illustrates methods suitable for dealing with unobservable selection, thus critically discussing various Instrumental-variables (IV) approaches, by introducing the Heckman Selection-model, and by illustrating the Difference-in differences (DID) estimator both in a repeated cross section and in a longitudinal data structure. The chapter concludes by focusing on a number of applications of previous methods using built-in and user-written Stata commands on real and simulative datasets.


Average Treatment Effects (ATE) Repeated Cross Sections Select Models (SM) Longitudinal Data Structure Heckit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abadie, A. (2005). Semiparametric difference-in-differences estimators. Review of Economic Studies, 72, 1–19. doi: 10.1111/0034-6527.00321.CrossRefGoogle Scholar
  2. Abadie, A., Angrist, J., & Imbens, G. (2002). Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica, 70, 91–117. doi: 10.1111/1468-0262.00270.CrossRefGoogle Scholar
  3. Angrist, J. D. (1991). Instrumental variables estimation of average treatment effects in econometrics and epidemiology (Working Paper No. 115). National Bureau of Economic Research.Google Scholar
  4. Angrist, J. D., & Imbens, G. W. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association, 90, 431–442. doi: 10.1080/01621459.1995.10476535.CrossRefGoogle Scholar
  5. Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association, 91, 444–455. doi: 10.1080/01621459.1996.10476902.CrossRefGoogle Scholar
  6. Angrist, J. D., & Krueger, A. B. (1991). Does compulsory school attendance affect schooling and earnings? Quarterly Journal of Economics, 106, 979–1014.CrossRefGoogle Scholar
  7. Angrist, J. D., & Krueger, A. B. (2001). Instrumental variables and the search for identification: From supply and demand to natural experiments. Journal of Economic Perspectives, 15, 69–85.CrossRefGoogle Scholar
  8. Angrist, J. D., & Pischke, J.-S. (2008). Mostly harmless econometrics: An empiricist’s companion. Princeton, NJ: Princeton University Press.Google Scholar
  9. Autor, D. H. (2003). Outsourcing at will: The contribution of unjust dismissal doctrine to the growth of employment outsourcing. Journal of Labor Economics, 21, 1–42.CrossRefGoogle Scholar
  10. Bertrand, M., Duflo, E., & Mullainathan, S. (2004). How much should we trust differences-in-differences estimates? Quarterly Journal of Economics, 119, 249–275. doi: 10.1162/003355304772839588.CrossRefGoogle Scholar
  11. Blundell, R., & Costa Dias, M. (2000). Evaluation methods for non-experimental data. Fiscal Studies, 21, 427–468. doi: 10.1111/j.1475-5890.2000.tb00031.x.CrossRefGoogle Scholar
  12. Bound, J., Jaeger, D. A., & Baker, R. M. (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association, 90, 443–450. doi: 10.1080/01621459.1995.10476536.Google Scholar
  13. Burnett, N. J. (1997). Gender economics courses in liberal arts colleges. Journal of Economic Education, 28, 369–376. doi: 10.1080/00220489709597940.CrossRefGoogle Scholar
  14. Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and applications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  15. Card, D. (1992). Using regional variation in wages to measure the effects of the federal minimum wage. Industrial & Labor Relations Review, 46, 22–37.CrossRefGoogle Scholar
  16. Card, D., & Krueger, A. B. (1994). Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. American Economic Review, 84, 772–793.Google Scholar
  17. Card, D., & Krueger, A. B. (2000). Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania: Reply. American Economic Review, 90, 1397–1420.CrossRefGoogle Scholar
  18. Cerulli, G. (2012). An assessment of the econometric methods for program evaluation and a proposal to extend the difference-in-differences estimator to dynamic treatment. In S. A. Mendez & A. M. Vega (Eds.), Econometrics: New research. New York: Nova. Chapter 1.Google Scholar
  19. Cerulli, G. (2014). ivtreatreg: A command for fitting binary treatment models with heterogeneous response to treatment and unobservable selection. Stata Journal, 14, 453–480.Google Scholar
  20. Donald, S. G., & Lang, K. (2007). Inference with difference-in-differences and other panel data. Review of Economics and Statistics, 89, 221–233. doi: 10.1162/rest.89.2.221.CrossRefGoogle Scholar
  21. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424–438.CrossRefGoogle Scholar
  22. Hahn, J., & Hausman, J. (2005). Estimation with valid and invalid instruments. Annales d’Economie et de Statistique, 79–80, 25–57.Google Scholar
  23. Heckman, J. J. (1978). Dummy endogenous variables in a simultaneous equation system. Econometrica, 46, 931–959.CrossRefGoogle Scholar
  24. Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrica: Journal of the Econometric Society, 47, 153–161.CrossRefGoogle Scholar
  25. Heckman, J. (1997). Instrumental variables: A study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources, 32, 441. doi: 10.2307/146178.CrossRefGoogle Scholar
  26. Heckman, J., Ichimura, H., Smith, J., & Todd, P. (1998). Characterizing selection bias using experimental data (Working paper N. w6699). Cambridge: National Bureau of Economic Research.Google Scholar
  27. Heckman, J., & Vytlacil, E. (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. Journal of Human Resources, 33, 974. doi: 10.2307/146405.CrossRefGoogle Scholar
  28. Heckman, J. J., & Vytlacil, E. J. (2001). Instrumental variables, selection models, and tight bounds on the average treatment effect. In P. D. M. Lechner & D. F. Pfeiffer (Eds.), Econometric evaluation of labour market policies (ZEW economic studies, pp. 1–15). Heidelberg: Physica.CrossRefGoogle Scholar
  29. Imbens, G. W., & Angrist, J. D. (1994). Identification and estimation of local average treatment effects. Econometrica, 62, 467–475. doi: 10.2307/2951620.CrossRefGoogle Scholar
  30. Lach, S. (2002). Do R&D subsidies stimulate or displace private R&D? Evidence from Israel. Journal of Industrial Economics, 50, 369–390.CrossRefGoogle Scholar
  31. Lee, M. (2005). Micro-econometrics for policy, program and treatment effects (OUP catalogue). Oxford: Oxford University Press.CrossRefGoogle Scholar
  32. Meyer, B. D., Viscusi, W. K., & Durbin, D. L. (1995). Workers’ compensation and injury duration: Evidence from a natural experiment. American Economic Review, 85, 322–340.Google Scholar
  33. Murray, M. P. (2006). Avoiding invalid instruments and coping with weak instruments. Journal of Economic Perspectives, 20, 111–132. doi: 10.1257/jep.20.4.111.CrossRefGoogle Scholar
  34. Nelson, C. R., & Startz, R. (1990a). Some further results on the exact small sample properties of the instrumental variable estimator. Econometrica, 58, 967–976.CrossRefGoogle Scholar
  35. Nelson, C. R., & Startz, R. (1990b). The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one. Journal of Business, 63, S125–S140.CrossRefGoogle Scholar
  36. Nicoletti, C., & Peracchi, F. (2001). Two-step estimation of binary response models with sample selection. Fac. Econ. Tor Vergata Univ. Rome.Google Scholar
  37. Phillips, P. C. B. (1983). Exact small sample theory in the simultaneous equations model. In Z. Griliches & M. D. Intriligator (Eds.), Handbook of econometrics (1st ed., Vol. 1, Chap. 8, pp. 449–516). Amsterdam: Elsevier.Google Scholar
  38. Rivers, D., & Vuong, Q. H. (1988). Limited information estimators and exogeneity tests for simultaneous probit models. Journal of Econometrics, 39, 347–366.CrossRefGoogle Scholar
  39. Sargan, J. D. (1958). The estimation of economic relationships using instrumental variables. Econometrica, 26, 393–415. doi: 10.2307/1907619.CrossRefGoogle Scholar
  40. Smith, J. A., & Todd, P. E. (2005). Does matching overcome LaLonde’s critique of nonexperimental estimators? Journal of Econometrics, 125, 305–353. doi: 10.1016/j.jeconom.2004.04.011.CrossRefGoogle Scholar
  41. Stock, J. H., & Yogo, M. (2002). Testing for weak instruments in linear IV regression (NBER Technical Working Paper No. 0284). National Bureau of Economic Research, Inc.Google Scholar
  42. Villa, J. M. (2014). DIFF: Stata module to perform differences in differences estimation, Statistical software components. Boston College Department of Economics.Google Scholar
  43. Wooldridge, J. M. (2001). Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press.Google Scholar
  44. Wooldridge, J. (2008). Introductory econometrics: A modern approach. Florence, KY: Cengage Learning.Google Scholar
  45. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Giovanni Cerulli
    • 1
  1. 1.Research Institute on Sustainable Economic GrowthCNR-IRCrES National Research Council of ItalyRomaItaly

Personalised recommendations