This paper provides a formal econometric framework behind the newly developed difference-in-discontinuities design (DiDC). Despite its increasing use in applied research, there are currently limited studies of its properties. We formalize the theory behind the difference-in-discontinuity approach by stating the identification assumptions, proposing a nonparametric estimator, and deriving its asymptotic properties. We also provide comprehensive tests for one of the identification assumption of the DiDC and sensitivity analysis methods that allow researchers to evaluate the robustness of DiDC estimates under violations of the identifying assumptions. Monte Carlo simulation studies show that the estimators have desirable finite-sample properties. Finally, we revisit Grembi et al. (2016), which studies the effects of relaxing fiscal rules on public finance outcomes. Our results show that most of the qualitative takeaways of the original work are robust to time-varying confounding effects.

翻译：本文为新近发展的差分-断点设计（DiDC）提供了正式的计量经济学框架。尽管该方法在应用研究中日益普及，目前对其性质的研究仍较为有限。我们通过阐明识别假设、提出非参数估计量并推导其渐近性质，将差分-断点方法背后的理论形式化。同时，我们为DiDC的识别假设之一提供了系统性的检验方法，并提出了敏感性分析方法，使研究者能够在识别假设被违反时评估DiDC估计的稳健性。蒙特卡洛模拟研究表明该估计量具有理想的有限样本性质。最后，我们重新审视了Grembi等人（2016）关于放松财政规则对公共财政结果影响的研究。我们的结果表明，原始研究中的多数定性结论对时变混杂效应具有稳健性。