In regression discontinuity (RD), the treatment is determined by a continuous score G crossing a cutoff c or not. However, often G is observed only as the ‘rounded-down integer S’ (e.g., birth year observed instead of birth time), and c is not an integer. In this case, the “cutoff sample” (i.e., the observations with S equal to the rounded-down integer of c) is discarded due to the ambiguity in G crossing c or not. We show that, first, if the usual RD estimators are used with the integer nature of S ignored, then a bias occurs, but it becomes zero if a slope symmetry condition holds or if c takes a certain “middle” value. Second, the distribution of the measurement error e = G-S can be specified and tested for, and if the distribution is accepted, then the cutoff sample can be used fruitfully. Third, two-step estimators and bootstrap inference are available in the literature, but a single-step ordinary least squares or instrumental variable estimator is enough. We also provide a simulation study and an empirical analysis for a dental support program based on age in South Korea.
Bibliographical noteFunding Information:
* Myoung-jae Lee’s research has been supported by a Korea University Grant (K2122221) and Sang Soo Park’s by another Korea University Grand (K1809281).. ** Corresponding Author, Professor, Department of Economics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea, Phone: +82-2-3290-2229, E-mail: firstname.lastname@example.org *** Co-Author, Senior Researcher, Korea International Trade Association, 511 Yeongdong-daero, Gangnam-gu, Seoul 06164, Korea, E-mail: email@example.com **** Third Author, Professor, Department of Economics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea, E-mail: firstname.lastname@example.org
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- Integer Running Variable
- Non-integer Cutoff
- Regression Discontinuity
ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)