Advertisement

Empirical Economics

, Volume 57, Issue 3, pp 727–767 | Cite as

Bounding average treatment effects using linear programming

  • Lukáš LafférsEmail author
Article

Abstract

This paper presents a method of calculating sharp bounds on the average treatment effect using linear programming under identifying assumptions commonly used in the literature. This new method provides a sensitivity analysis of the identifying assumptions and missing data in two applications. The first application looks at the effect of parents’ schooling on children’s schooling, and the second application studies the effect of mandatory arrest policy on domestic violence recidivism. This paper shows that even a mild departure from identifying assumptions may substantially widen the bounds on average treatment effects. Allowing for a small fraction of the data to be missing also has a large impact on the results.

Keywords

Partial identification Bounds Average treatment effect Sensitivity analysis Linear programming 

JEL Classification

C4 C6 I2 

Notes

Acknowledgements

This research was supported by VEGA Grant 1/0843/17. This paper is a revised chapter from my 2014 dissertation at the Norwegian School of Economics. I would like to thank Monique de Haan for generously providing me with the data used in this paper, as well as Christian Brinch, Andrew Chesher, Christian Dahl, Gernot Doppelhofer, Charles Manski, Peter Molnar, Adam Rosen, Erik Sorensen, Ivan Sutoris and Alexey Tetenov for valuable feedback. Special thanks goes to the referees and the editor for carefully reading through the manuscript and for suggesting the second application.

References

  1. Antonovics KL, Goldberger AS (2005) Does increasing women’s schooling raise the schooling of the next generation? Comment. Am Econ Rev 95:1738–1744CrossRefGoogle Scholar
  2. Balke A, Pearl J (1994) Counterfactual probabilities: computational methods, bounds, and applications. In: de Mantaras LR, Poole D (eds) Uncertainty in artificial intelligence, vol 1. Morgan Kaufmann, pp 46–54Google Scholar
  3. Balke A, Pearl J (1997) Bounds on treatment effects from studies with imperfect compliance. J Am Stat Assoc 439:1172–1176Google Scholar
  4. Behrman JR, Rosenzweig MR (2002) Does increasing women’s schooling raise the schooling of the next generation? Am Econ Rev 92:323–334CrossRefGoogle Scholar
  5. Behrman JR, Rosenzweig MR (2005) Does increasing women’s schooling raise the schooling of the next generation? Reply. Am Econ Rev 95:1745–1751CrossRefGoogle Scholar
  6. Berk RA, Sherman LW (1988) Police responses to family violence incidents: an analysis of an experimental design with incomplete randomization. J Am Stat Assoc 83:70–76Google Scholar
  7. Carter M (2001) Foundations of mathematical economics. MIT Press, CambridgeGoogle Scholar
  8. Chiburis RC (2010) Bounds on treatment effects using many types of monotonicity. Working paper, Department of Economics, University of Texas at AustinGoogle Scholar
  9. de Haan M (2011) The effect of parents’ schooling on child’s schooling: a nonparametric bounds analysis. J Labor Econ 29:859–892CrossRefGoogle Scholar
  10. Demuynck T (2015) Bounding average treatment effects: a linear programming approach. Econ Lett 137:75–77CrossRefGoogle Scholar
  11. Freyberger J, Horowitz JL (2015) Identification and shape restrictions in nonparametric instrumental variables estimation. J Econ 189:41–53CrossRefGoogle Scholar
  12. Galichon A, Henry M (2009) A test of non-identifying restrictions and confidence regions for partially identified parameters. J Econ 152:186–196CrossRefGoogle Scholar
  13. Hauser RM (2005) Survey response in the long run: the Wisconsin longitudinal study. Field Methods 17:3–29CrossRefGoogle Scholar
  14. Henry M, Onatski A (2012) Set coverage and robust policy. Econ Lett 115:256–257CrossRefGoogle Scholar
  15. Hirano K, Porter JR (2012) Impossibility results for nondifferentiable functionals. Econometrica 80:1769–1790CrossRefGoogle Scholar
  16. Holmlund H, Lindahl M, Plug E (2011) The causal effect of parents’ schooling on children’s schooling: a comparison of estimation methods. J Econ Literature 49:615–51CrossRefGoogle Scholar
  17. Honore BE, Tamer E (2006) Bounds on parameters in panel dynamic discrete choice models. Econometrica 74:611–629CrossRefGoogle Scholar
  18. Imbens GW, Manski CF (2004) Confidence intervals for partially identified parameters. Econometrica 72:1845–1857CrossRefGoogle Scholar
  19. Kim JH (2014) Identifying the distribution of treatment effects under support restrictions. Available at SSRNGoogle Scholar
  20. Lafférs L (2013) Inference in partially identified models with discrete variables. Working paperGoogle Scholar
  21. Lafférs L (2013) A note on bounding average treatment effects. Econ Lett 120:424–428CrossRefGoogle Scholar
  22. Lafférs L (2017) Identification in models with discrete variables. Comput Econ, forthcomingGoogle Scholar
  23. Manski CF (1990) Nonparametric bounds on treatment effects. Am Econ Rev 80:319–23Google Scholar
  24. Manski CF (1995) Identification problems in the social sciences. Harvard University Press, CambridgeGoogle Scholar
  25. Manski CF (1997) Monotone treatment response. Econometrica 65:1311–1334CrossRefGoogle Scholar
  26. Manski CF (2003) Partial identification of probability distributions. Springer, New YorkGoogle Scholar
  27. Manski CF (2007) Partial identification of counterfactual choice probabilities. Int Econ Rev 48:1393–1410CrossRefGoogle Scholar
  28. Manski CF (2008) Partial identification in econometrics. In: Durlauf SN, Blume LE (eds) The new Palgrave dictionary of economics. Palgrave Macmillan, BasingstokeGoogle Scholar
  29. Manski CF, Pepper JV (2000) Monotone instrumental variables, with an application to the returns to schooling. Econometrica 68:997–1012CrossRefGoogle Scholar
  30. Martin D (1975) On the continuity of the maximum in parametric linear programming. J Optim Theory Appl 17:205–210CrossRefGoogle Scholar
  31. Munkres JR (2000) Topology, 2nd edn. Prentice Hall, Englewood CliffsGoogle Scholar
  32. Romano JP, Shaikh AM (2008) Inference for identifiable parameters in partially identified econometric models. J Stat Plan Inference 138:2786–2807CrossRefGoogle Scholar
  33. Romano JP, Shaikh AM (2010) Inference for the identified set in partially identified econometric models. Econometrica 78:169–211CrossRefGoogle Scholar
  34. Rubin DB (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66:688–701CrossRefGoogle Scholar
  35. Sherman LW, Schmidt JD, Rogan DP (1992) Policing domestic violence: experiments and dilemmas. Free Press, New YorkGoogle Scholar
  36. Siddique Z (2013) Partially identified treatment effects under imperfect compliance: the case of domestic violence. J Am Stat Assoc 108:504–513CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Natural SciencesMatej Bel UniversityBanská BystricaSlovakia

Personalised recommendations