と題したエントリ(原題は「Regression Discontinuity and Event Studies in Time Series」)でFrancis Dieboldが、Catherine Hausman(ミシガン大)とDavid S. Rapson(UCデービス)の「Regression Discontinuity in Time: Considerations for Empirical Applications」というNBER論文ungated版)を紹介している*1

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.

この要旨で言及されているイベントスタディと推計帯域について、Dieboldは以下のように書いている(その際、論文のタイトルの一部である「Regression Discontinuity in Time」を[論文に倣って]RDiTと略している)。

It's interesting in part because it documents and contributes to the largely cross-section regression discontinuity design literature's awakening to time series. But the elephant in the room is the large time-series "event study" (ES) literature, mentioned but not emphasized by Hausman and Rapson. [In a one-sentence nutshell, here's how an ES works: model the pre-event period, use the fitted pre-event model to predict the post-event period, and ascribe any systematic forecast error to the causal impact of the event.] ES's trace to the classic Fama et al. (1969). Among many others, MacKinlay's 1997 overview is still fresh, and Gürkaynak and Wright (2013) provide additional perspective.
One question is what the RDiT approach adds to the ES approach, and related, what it adds to well-developed time-series toolkit of other methods for assessing structural change. At present, and notwithstanding the Hausman-Rapson paper, my view is "little or nothing". Indeed in most respects it would seem that a RDiT study *is* an ES, and conversely. So call it what you will, "ES" or "RDiT".
But there are important open issues in ES / RDiT, and Hausman-Rapson correctly emphasize one of them, namely issues and difficulties associated with "wide" pre- and post-event windows, which is often the relevant case in time series.
Things are generally "easy" in cross sections, where we can usually take narrow windows (e.g., in the classic scholarship exam example, we use only the test scores very close to the scholarship threshold). Things are also "easy" in time series *IF* we can take similarly narrow windows (e.g., high-frequency financial asset return data facilitate taking narrow pre- and post-event windows in financial applications). In such cases it's comparatively easy to credibly ascribe a post-event break to the causal impact of the event.
But in other time-series areas like macro and environmental, we might want (or need) to use wide pre- and post-event windows. Then the trick becomes modeling the pre- and post-event periods successfully enough so that we can credibly argue that no structural change is operative apart from that due to the event -- very challenging, but not hopeless.
Hats off to Hausman and Rapson for beginning to bridge the ES and regression discontinuity literatures, and for implicitly helping to push the ES literature forward.
この論文が興味深いのは、一つには、専らクロスセクションを対象としていた回帰不連続デザインの研究分野が時系列に目を向け始めたことを記録し、かつ、それに貢献したことにある。しかしそこで無視できないのが、時系列のイベントスタディ(ES)という一大研究分野である。ハウスマン=ラプソンはそれに言及しているが、強調はしていない。[一言でイベントスタディを要約すると、次のようになる:イベント前の期間をモデル化し、当てはめたイベント前モデルを使ってイベント後の期間を予測して、体系的な予測誤差をすべてイベントの影響に因るものだとする] イベントスタディは、古典的なファーマらの研究(1969)に遡る。そのほか、マッキンレーの1997年の概観も依然として新鮮であり、ギュルカイナク=ライト(2013)は追加的な見通しを提供する。


Finally, if the intervention may alter behavior in the neighborhood of the discontinuity, we would like to be able to test for this and, if necessary, control for it. In a cross-sectional RD, a density test such as the McCrary (2008) test is a key check for strategic behavior or selection. It is generally used to rule out these confounding factors, thus making it unnecessary to control for them. When time is the running variable, however, it is generally not possible to test for strategic behavior or selection around the threshold. While the researcher can check for discontinuities in other covariates at the threshold, and for discontinuities in the outcome variable at other thresholds, the researcher cannot check for discontinuities in the conditional density of the forcing variable. That the density of the forcing variable (time) is uniform renders such tests logically irrelevant.


*1:cf. 予告エントリ。なお、回帰不連続デザインについては、日本語のWikipediaが意外に(?)詳しい=回帰不連続デザイン - Wikipedia