고려대학교

초록/요약

The treatment effect analysis model where the participation into a program is determined by observable characteristic lies on either side of a threshold is called as Regression Discontinuity(RD) design. In particular, when the probability of participation on either side of a threshold is less or larger than 1 or 0 due to unobservable self-selection such as non-compliance, this case is called "fuzzy RD" design. It is well known from the literature on the estimation methods which can be applied to fuzzy RD design, such as LLR (Hahn et al. (2001)) and TSSL(Robinson (1988) and Porter (1999)). Although LLR and TSSL aim to estimate the same d, one of them is fail to estimate the treatment effect under conflicting condition with each other. When the participation into a program is close to sharp RD design, LLR outperforms TSSL because denominator of TSSL goes to 0: On the other hand, when there is no difference in the probability of participation on either side of a threshold, TSSL is recommendable due to poor performance of LLR whose denominator goes to 0. In this paper, we consider two methods, how to choose one of them, and how to use both estimators at the same time when we do not decide whether the case is close to sharp RD or fuzzy RD. First, we introduce 'pre-estimation' which use the test for sharpness of E(di|xi) at xi = t, as a criterion for selection of one of them. Another method is a weighted average between LLR and TSSL by MDE. The variance of LLR increases as the pattern of E(di|xi) at xi = t is close to fuzzy RD and the variance of TSSL increases as the pattern of E(di|xi) at xi = t is close to sharp RD. However MDE shows smaller variance than LLR and TSSL for all sample size in the case between sharp RD and fuzzy RD, and there is no difference of MAE between TSSL and MDE even in fuzzy RD. Because MDE corrects the variance of LLR and TSSL, not the bias, if there exists endogeneity problem between the equations of yi and di, TSSL has a bias, then MDE also follows the bias of TSSL regardless of the sample size. LLR is robust to the endogeneity problem in the case closed to sharp RD. However, when g(xi) change continuously and sharply at xi = t, g(xi) is similar to the pattern of E(di|xi), TSSL based on a non-parametric method and MDE surpass LLR based on a linear model. Considered that the case exactly fitted to sharp RD or fuzzy RD is rare, if there is no endogeneity problem, MDE estimates the treatment effect more efficiently than using one of LLR and TSSL.