Identification and estimation using a density discontinuity approach

This chapter reviews recent developments in the density discontinuity approach. It is well known that agents having perfect control of the forcing variable will invalidate the popular regression discontinuity designs (RDDs). To detect the manipulation of the forcing variable, McCrary (2008) developed a test based on the discontinuity in the density around the threshold. Recent papers have noted that the sorting patterns around the threshold are often either the researcher's object of interest or may relate to structural parameters such as tax elasticities through known functions. This, in turn, implies that the behavior of the distribution around the threshold is not only informative of the validity of a standard RDD; it can also be used to recover policy-relevant parameters and perform counterfactual exercises.