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= = 所需假设 = = 断点回归设计要求除了干预变量和结果变量之外，所有潜在的相关协变量均应是连续的，

= = 所需假设 = = 断点回归设计要求除了干预变量和结果变量之外，所有潜在的协变量在断点处均应是连续的，一个充分但不是必要的条件是，干预分配在临界值处“和随机分配一样好”。如果这种说法成立，那就保证了接受干预的样本与那些没有接受干预的样本是可比的，因为干预与否在断点处实际上是随机的。

Treatment assignment at the threshold can be "as good as random" if there is randomness in the assignment variable and the agents considered (individuals, firms, etc.) cannot perfectly manipulate their treatment status. For example, suppose the treatment is passing an exam, where a grade of 50% is required. In this case, this example is a valid regression discontinuity design so long as grades are somewhat random, due either to the randomness of grading or randomness of student performance.

Treatment assignment at the threshold can be "as good as random" if there is randomness in the assignment variable and the agents considered (individuals, firms, etc.) cannot perfectly manipulate their treatment status. For example, suppose the treatment is passing an exam, where a grade of 50% is required. In this case, this example is a valid regression discontinuity design so long as grades are somewhat random, due either to the randomness of grading or randomness of student performance.

如果在分配变量和被考虑的代理人(个人、公司等)中存在随机性，在阈值处理分配可以“和随机性一样好”并不能完全控制他们的治疗状况。例如，假设治疗通过了一个考试，其中50% 的等级是必需的。在这种情况下，这个例子是一个有效的回归不连续设计，只要成绩是随机的，无论是由于随机的评分或随机的学生表现。

如果在分配变量和被考虑的代理人(个人、公司等)中存在随机性，在阈值处理分配可以“和随机性一样好”并不能完全控制他们的治疗状况。例如，假设治疗通过了一个考试，其中50% 的等级是必需的。在这种情况下，这个例子是一个有效的回归不连续设计，只要成绩是随机的，无论是由于随机的评分或随机的学生表现。

Students must not also be able to perfectly manipulate their grade so as to determine their treatment status perfectly. Two examples include students being able to convince teachers to "mercy pass" them, or students being allowed to retake the exam until they pass. In the former case, those students who barely fail but are able to secure a "mercy pass" may differ from those who just barely fail but cannot secure a "mercy pass". This leads to [[selection bias]], as the treatment and control groups now differ. In the latter case, some students may decide to retake the exam, stopping once they pass. This also leads to [[selection bias]] since only some students will decide to retake the exam.<ref name="Lee and Lemieux 2010">{{cite journal |last1=Lee |last2=Lemieux |title=Regression Discontinuity Designs in Economics |year=2010 |journal=[[Journal of Economic Literature]] |volume=48 |issue=2 |pages=281–355 |doi=10.1257/jel.48.2.281 |s2cid=14166110 |url=http://arks.princeton.edu/ark:/88435/dsp015138jd866 }}</ref>

Students must not also be able to perfectly manipulate their grade so as to determine their treatment status perfectly. Two examples include students being able to convince teachers to "mercy pass" them, or students being allowed to retake the exam until they pass. In the former case, those students who barely fail but are able to secure a "mercy pass" may differ from those who just barely fail but cannot secure a "mercy pass". This leads to [[selection bias]], as the treatment and control groups now differ. In the latter case, some students may decide to retake the exam, stopping once they pass. This also leads to [[selection bias]] since only some students will decide to retake the exam.<ref name="Lee and Lemieux 2010">{{cite journal |last1=Lee |last2=Lemieux |title=Regression Discontinuity Designs in Economics |year=2010 |journal=[[Journal of Economic Literature]] |volume=48 |issue=2 |pages=281–355 |doi=10.1257/jel.48.2.281 |s2cid=14166110 |url=http://arks.princeton.edu/ark:/88435/dsp015138jd866 }}</ref>