Multi-valued Treatment Effects
The term multi-valued treatment effects refers to a collection of population parameters capturing the impact of a treatment variable on an outcome variable when the treatment takes multiple values. For example, in labour training programmes participants receive different hours of training or in anti-poverty programmes households receive different levels of transfers. Multi-valued treatments may be finite or infinite as well as ordinal or cardinal, and naturally extend the idea of binary treatment effects, leading to a large collection of treatment effects of interest in applications. The analysis of multi-valued treatment effects has several distinct features when compared to the analysis of binary treatment effects, including: (i) a comparison or control group is not always clearly defined, (ii) new parameters of interest arise that capture distinct phenomena such as nonlinearities or tipping points, (iii) correct statistical inference requires the joint estimation of all treatment effects (as opposed to the estimation of each treatment effect separately) in general, and (iv) efficiency gains in statistical inference may be obtained by exploiting known restrictions among the multi-valued treatment effects.
KeywordsCausal inference Generalised propensity score Identification Matching estimators Program evaluation Semiparametric estimation Semiparametric efficiency Treatment effects Unconfoundedness
JEL ClassificationsC14 C21 C31
- Florens, J.P., J.J. Heckman, C. Meghir, and E.J. Vytlacil. 2010. Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects. Econometrica 76: 1191–1206.Google Scholar
- Heckman, J.J., and E.J. Vytlacil. 2007. Econometric evaluation of social programs, Part I: Causal models, structural models and econometric policy evaluation. In Handbook of econometrics, vol. 6B, ed. J.J. Heckman and E.E. Leamer, 4779–4874. Amsterdam: North-Holland.Google Scholar
- Hirano, K., and G. Imbens. 2004. The propensity score with continuous treatments. In Applied bayesian modeling and causal inference from incomplete data perspectives, ed. A. Gelman and X.L. Meng. New York: Wiley.Google Scholar
- Nekipelov, D. 2008. Endogenous multi-valued treatment effect model under monotonicity. Working paper, UC-Berkeley.Google Scholar