Proceedings of Statistics Canada Symposium 2002 Modelling Survey Data for Social and Economic Research ELIGIBLE NON-PARTICIPANT AND INELIGIBLE INDIVIDUALS AS A DOUBLE CONTROL GROUP IN REGRESSION DISCONTINUITY DESIGNS Erich Battistin 1 , Enrico Rettore 2 ABSTRACT The attractiveness of the Regression Discontinuity Design (RDD) either in its sharp or fuzzy formulation rests on close similarities with a formal experimental design. On the other hand, it is of limited applicability since rarely individuals are assigned to the treatment group on the basis of a pre-program measure observable to the analyst. Besides, it only allows to identify the mean impact of the program on a very specific sub-population of individuals. In this paper we show that the RDD straightforwardly generalizes to the instances in which the eligibility for the program is established with respect to an observable pre-program measure and eligible individuals can self-select into the treatment group according to an unknown process. This set-up also turns out very convenient to define a specification test on conventional non-experimental estimators of the program effect. Data requirements are made explicit. KEY WORDS: Program Evaluation; Second Control Group; Specification Tests. JEL Classification: C4, C8. 1. INTRODUCTION The central issue in the evaluation of public policies is to separate their causal effect from the confounding effect of other factors influencing the outcome of interest. Random assignment of units to the intervention produces treatment and control groups that are equivalent in all respects, except for their exposition status. Thus, in a completely randomized experiment any post-intervention difference between the two groups doesn't reflect pre-intervention differences by construction. As a result, differences between exposed and control units are entirely due to the intervention itself. However, in most instances randomization is unfeasible either for ethical reasons or simply because assignment to the treatment cannot be controlled by the analyst. Besides, even in those instances in which the analyst can randomize the assignment, units may not comply with the assigned status and either drop out of the intervention or seek an alternative program (see Heckman and Smith, 1995). A well-known and widely used example of randomized assignment is the JTPA program in the United States, which currently serves close to one million economically disadvantaged people every year (see Friedlander et al., 1997). Random assignment occurs prior to the actual enrolment in the program, but a consistent fraction of those randomized into the treatment group do not participate. For certain components of the JTPA, such a non-complying behaviour seems to be non-negligible (see, for example, Heckman et al., 1998b). In this situation, the ideal experiment is not fully realized since participation turns out (at least partly) voluntary: training is provided only for those individuals who meet certain criteria of need and comply with the result of randomization. It follows that participation depends on observable and unobservable characteristics of individuals that might be correlated with the outcome of interest. In this situation, differences between treated and control groups with respect to the outcome of interest might be the result of units’ self-selection into the intervention. The assessment of whether observed changes in the outcome of interest could be attributed to the intervention itself and not to other possible causes turns out to be even more complicated in a non-experimental setting. In this situation 1 Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, UK, erich_b@ifs.org.uk 2 Department of Statistics, University of Padova, Via Cesare Battisti 241, 35121 Padova, Italy, rettore@stat.unipd.it