Why experimenters should not randomize, and what they should do instead
AbstractThis paper discusses experimental design for the case that (i) we are given a distribution of covariates from a pre-selected random sample, and (ii) we are interested in the average treatment effect (ATE) of some binary treatment. We show that in general there is a unique optimal non-random treatment assignment if there are continuous covariates. We argue that experimenters should choose this assignment. The optimal assignment minimizes the risk (e.g., expected squared error) of treatment effects estimators. We provide explicit expressions for the risk, and discuss algorithms which minimize it. The objective of controlled trials is to have treatment groups which are similar a priori (balanced), so we can ``compare apples with apples.'' The expressions for risk derived in this paper provide an operationalization of the notion of balance. The intuition for our non-randomization result is similar to the reasons for not using randomized estimators - adding noise can never decrease risk. The formal setup we consider is decision-theoretic and nonparametric. In simulations and an application to project STAR we find that optimal designs have mean squared errors of up to 20% less than randomized designs and up to 14% less than stratified designs..
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Bibliographic InfoPaper provided by Harvard University OpenScholar in its series Working Paper with number 36154.
Date of creation: Jan 2013
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-15 (All new papers)
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- Roland G. Fryer, Jr, 2013. "Information and Student Achievement: Evidence from a Cellular Phone Experiment," NBER Working Papers 19113, National Bureau of Economic Research, Inc.
- Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927, Cowles Foundation for Research in Economics, Yale University.
- Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
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