WP-282: Catherine Hausman and David Rapson, "Regression Discontinuity in Time: Considerations for Empirical Applications" (August 2017) Full Paper
Recent empirical work in several economic fields, particularly environmental and energy economics, has adapted the regression discontinuity framework to applications where time is the running variable and treatment occurs at the moment of the discontinuity. In this guide for practitioners, we discuss several features of this "Regression Discontinuity in Time" framework that differ from the more standard cross-sectional RD. First, many applications (particularly in environmental economics) lack cross-sectional variation and are estimated using observations far from the cut-off. This is in stark contrast to a cross-sectional RD, which is conceptualized for an estimation bandwidth going to zero even as the sample size increases. Second, estimates may be biased if the time-series properties of the data are ignored, for instance in the presence of an autoregressive process. Finally, tests for sorting or bunching near the discontinuity are often irrelevant, making the methodology closer to an event study than a regression discontinuity design. Based on these features and motivated by hypothetical examples using air quality data, we offer suggestions for the empirical researcher wishing to use the RD in time design.