Regression Discontinuity with Integer Score and Non-Integer Cutoff

Myoung-jae Lee, Hyae-Chong Shim and Sang Soo Park
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Hyae-Chong Shim: Korea International Trade Association

Korean Economic Review, 2023, vol. 39, 73-101

Abstract: 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.

Keywords: Regression Discontinuity; Integer Running Variable; Non-integer Cutoff (search for similar items in EconPapers)
JEL-codes: C21 C24 (search for similar items in EconPapers)
Date: 2023
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