Identification and Estimation Using a Density Discontinuity Approach

Abstract

This paper 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.

Homicides and the Age of Criminal Responsibility: A Density Discontinuity Approach

“…Instead, suppose one observes only the density of X (age) conditional on Y = 1 (crime engagement). Jales and Yu (2017) show that it is possible to identify the local average treatment effect of this policy in this setup. Under the standard RDD assumptions, 26 we have…”

“…The sharpness of the age rule for criminal prosecution in Brazil lends itself to a natural quasi-experiment, which we exploit to measure the degree to which a more strict punishment may influence the decision to engage in a crime. More specifically, we employ methods of density discontinuity designs (McCrary, 2008;Jales and Yu, 2017) to the frequency of (male) violent deaths by age using national death records in Brazil from 1996 to 2013 and looking for evidence of a discontinuous fall at the age of eighteen. 8 The key difference between our analysis and the traditional regression discontinuity design lies in that we are not working with a dependent variable that is a function of other covariates that determine treatment 7 The criminology literature has noted that participation in crimes increases the odds of violent victimization (Lauritsen et al, 1991;Nieuwbeerta and Piquero, 2008;Muftić and Hunt, 2013;Pyrooz et al, 2014, , among others).…”

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

“…This idea leads to falsification methods based on comparing the number or “density” of treated and control units near the cutoff. See Frandsen () for a related approach when the running variable takes discrete values (which is not the case in the Head Start application), and Jales and Yu () for a review of related approaches exploiting a discontinuity in density. 3. Placebo treatment effects .…”

Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework

“…Discontinuity design. The discontinuity design (DD) literature has expanded rapidly in recent years; interested readers are encouraged to refer to review papers by Imbens and Lemieux (2008), Kleven (2016) and Jales and Yu (2017). Recent auction applications include Coviello andMarinello (2014), andChoi, Neisheim andRazul (2016).…”