Chapter

Defining and identifying the effect of treatment on the treated

Sara Geneletti and A. Philip Dawid

in Causality in the Sciences

Published in print March 2011 | ISBN: 9780199574131
Published online September 2011 | e-ISBN: 9780191728921 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199574131.003.0034
Defining and identifying the effect of treatment on the treated

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The effect of treatment on the treated (ETT) is of interest to econometricians as a measure of the effectiveness of schemes (such as training programmes) that require voluntary participation from eligible members of the population; it is also of interest in epidemiologic and similar contexts in cases where treatment randomization is not possible. ETT has usually been expressed and analysed in terms of potential responses. Here the chapter describes a new approach to formulating and evaluating ETT, based on an alternative decision‐theoretic framework for causal inference. The chapter gives simple conditions under which ETT is well‐defined, and identifiable given data from both an observational study and a control group, and further conditions allowing identification of ETT from purely observational data, with the assistance of a suitable instrumental variable. The chapter further shows that the potential response formulation can be treated as a special case of our decision‐theoretic approach.

Keywords: effect of treatment on the treated; causal inference; conditional independence; confounding; self-selection; instrumental variables

Chapter.  9673 words.  Illustrated.

Subjects: Logic

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