Empirical Economics

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

Bounding average treatment effects using linear programming

  • Lukáš LafférsEmail author


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.


Partial identification Bounds Average treatment effect Sensitivity analysis Linear programming 

JEL Classification

C4 C6 I2 



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.


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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

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