The key assumption in regression discontinuity analysis is that the distribution of potential outcomes varies smoothly with the running variable around the cutoff. In many empirical contexts, however, this assumption is not credible; and the running variable is said to be manipulated in this case. In this paper, we show that while causal effects are not point identified under manipulation, one can derive sharp bounds under a general model that covers a wide range of empirical patterns. The extent of manipulation, which determines the width of the bounds, is inferred from the data in our setup. Our approach therefore does not require making a binary decision regarding whether manipulation occurs or not, and can be used to deliver manipulation‐robust inference in settings where manipulation is conceivable, but not obvious from the data. We use our methods to study the disincentive effect of unemployment insurance on (formal) reemployment in Brazil, and show that our bounds remain informative, despite the fact that manipulation has a sizable effect on our estimates of causal parameters.

中文翻译：

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具有受控运行变量的回归间断设计中治疗效果的界限

回归不连续性分析中的关键假设是，潜在结果的分布随着截止点附近的运行变量而平稳变化。但是，在许多经验背景下，这种假设都不可信。据说运行变量是可操纵的在这种情况下。在本文中，我们表明，虽然在处理过程中无法确定因果关系，但在涵盖广泛经验模式的通用模型下，可以得出清晰的界限。从确定设置的宽度的操纵程度可以从我们设置中的数据推断出。因此，我们的方法不需要就是否发生操纵做出二元决策，并且可以用于在可以想到操纵但从数据中看不到操纵的情况下进行鲁棒的推断。我们使用我们的方法研究了失业保险对巴西的（正式）再就业的抑制作用，并表明，尽管操纵对我们的因果参数估计有相当大的影响，但我们的研究范围仍然是有益的。