Optimal Experimental Design for Error Components Models

Social experiments are characterized by their high cost. A tempting alternative to the establishment of a contemporaneous statistical control group is preexempt observat ion of the treatment group. In this paper, the authors analyze the tr ade-off between these two types of "con-trol" as functions of their relative cost and information content in a multiperiod error compone nts framework, where the allocation of observations across the two gr oups is always done in an optimal manner. Solutions for the optimal p roportion of the sample to be devoted to the contemporaneous control group are presented and their behavior as a function of relevant para meters is studied.