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</math>
</math>
其中<math>c</math>是处理临界值，<math>D</math>是一个二值变量，如果<math>X \ge c</math>是一个二进制变量，如果<math>h</math>是所用数据的带宽，我们有<math> c - h \le X \le c + h </math>。不同的斜坡和拦截符合截止线两侧的数据。通常使用矩形核心(不加权)或三角形核心。研究倾向于三角形核<ref name="Fan and Gijbels 1996">{{cite book |last1=Fan |last2=Gijbels|author2-link= Irène Gijbels |title=Local Polynomial Modelling and Its Applications |year=1996 |location=London |publisher=Chapman and Hall |isbn=978-0-412-98321-4 }}</ref>，而矩形核有更直接的解释。<ref name="Lee and Lemieux 2010"/>
其中<math>c</math>是处理临界值，<math>D</math>是一个二值变量，如果<math>X \ge c</math>是一个二进制变量，如果<math>h</math>是所用数据的带宽，我们有<math> c - h \le X \le c + h </math>。不同的斜坡和拦截符合截止线两侧的数据。通常使用矩形核心(不加权)或三角形核心。研究倾向于三角形核<ref name="Fan and Gijbels 1996">{{cite book |last1=Fan |last2=Gijbels|title=Local Polynomial Modelling and Its Applications |year=1996 |location=London |publisher=Chapman and Hall |isbn=978-0-412-98321-4 }}</ref>，而矩形核有更直接的解释。<ref name="Lee and Lemieux 2010"/>
*一个政治家以微弱优势获胜的选举。<ref name="Lee 2008">{{cite journal |last=Lee |title=Randomized Experiments from Non-random Selection in U.S. House Elections |year=2008 |journal=[[Journal of Econometrics]] |volume=142 |issue=2 |pages=675–697 |doi=10.1016/j.jeconom.2007.05.004 |citeseerx=10.1.1.409.5179 }}</ref><ref name="de la Cuesta Imai 2016">{{cite journal |last1=de la Cuesta, B |last2=Imai, K |title=Misunderstandings About the Regression Discontinuity Design in the Study of Close Elections |year=2016 |journal=[[Annual Review of Political Science]] |volume=19 |issue=1 |pages=375–396 |doi=10.1146/annurev-polisci-032015-010115 |doi-access=free }}</ref>
*一个政治家以微弱优势获胜的选举。<ref name="Lee 2008">{{cite journal |last=Lee |title=Randomized Experiments from Non-random Selection in U.S. House Elections |year=2008 |journal=[[Journal of Econometrics]] |volume=142 |issue=2 |pages=675–697 |doi=10.1016/j.jeconom.2007.05.004 |citeseerx=10.1.1.409.5179 }}</ref><ref name="de la Cuesta Imai 2016">{{cite journal |last1=de la Cuesta, B |last2=Imai, K |title=Misunderstandings About the Regression Discontinuity Design in the Study of Close Elections |year=2016 |journal=[[Annual Review of Political Science]] |volume=19 |issue=1 |pages=375–396 |doi=10.1146/annurev-polisci-032015-010115 |doi-access=free }}</ref>
*在教育研究领域中分数线将学生分类到干预项目中。<ref name="Moss">{{cite journal |last1=Moss |first1=B. G. |last2=Yeaton |first2=W. H. |last3=Lloyd |first3=J.E. | year= 2014 |title =Evaluating the Effectiveness of Developmental Mathematics by Embedding a Randomized Experiment Within a Regression Discontinuity Design.| journal= [[Educational Evaluation and Policy Analysis]] |volume=36 |issue=2 |pages= 170–185|doi=10.3102/0162373713504988|s2cid=123440758 }}</ref>
*在教育研究领域中分数线将学生分类到干预项目中。<ref name="Moss">{{cite journal |last1=Moss |first1=B. G. |last2=Yeaton |first2=W. H. |last3=Lloyd |first3=J.E. | year= 2014 |title =Evaluating the Effectiveness of Developmental Mathematics by Embedding a Randomized Experiment Within a Regression Discontinuity Design.| journal= [[Educational Evaluation and Policy Analysis]] |volume=36 |issue=2 |pages= 170–185|doi=10.3102/0162373713504988}}</ref>
同时学生不能操纵他们的分数，从而改变自己的干预状态。举两个例子，学生说服老师使其通过分数线，或学生被允许重新参加考试。前一种情况下，那些没有通过分数线但是说服了老师的学生不同于那些没有通过分数线也没有说服老师的学生。这产生了选择偏差，因为现在干预组和控制组的学生存在差别，即潜在的协变量在两组学生中是不连续的，不满足以上假设。后一种情况下，一些学生可能决定重新参加考试，一旦通过就停止重考，这也导致了选择偏差，因为只有一部分学生会决定重新参加考试，即那些第一次就未通过分数线的学生。<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>
同时学生不能操纵他们的分数，从而改变自己的干预状态。举两个例子，学生说服老师使其通过分数线，或学生被允许重新参加考试。前一种情况下，那些没有通过分数线但是说服了老师的学生不同于那些没有通过分数线也没有说服老师的学生。这产生了选择偏差，因为现在干预组和控制组的学生存在差别，即潜在的协变量在两组学生中是不连续的，不满足以上假设。后一种情况下，一些学生可能决定重新参加考试，一旦通过就停止重考，这也导致了选择偏差，因为只有一部分学生会决定重新参加考试，即那些第一次就未通过分数线的学生。<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 |url=http://arks.princeton.edu/ark:/88435/dsp015138jd866 }}</ref>
== 优势 ==
== 优势 ==
* 当正确实施和分析研究时，RDD 产生了对局部处理效果的无偏估计。<ref name="Rubin">{{cite journal |last=Rubin |title=Assignment to Treatment on the Basis of a Covariate |journal=Journal of Educational and Behavioral Statistics |year=1977 |volume=2 |issue=1 |pages=1–26 |doi=10.3102/10769986002001001 |s2cid=123013161 }}</ref>在测量处理效果方面，RDD 几乎可以和随机实验一样好。
* 当正确实施和分析研究时，RDD 产生了对局部处理效果的无偏估计。<ref name="Rubin">{{cite journal |last=Rubin |title=Assignment to Treatment on the Basis of a Covariate |journal=Journal of Educational and Behavioral Statistics |year=1977 |volume=2 |issue=1 |pages=1–26 |doi=10.3102/10769986002001001 }}</ref>在测量处理效果方面，RDD 几乎可以和随机实验一样好。
* 作为一项准实验，RDD不需要事先随机化，并规避随机分配的道德问题。
* 作为一项准实验，RDD不需要事先随机化，并规避随机分配的道德问题。
*符合假设的RDD研究可以产生类似于随机研究估计的处理效果估计。<ref>{{cite journal|doi=10.3102/0162373713504988|title=Evaluating the Effectiveness of Developmental Mathematics by Embedding a Randomized Experiment Within a Regression Discontinuity Design|journal=Educational Evaluation and Policy Analysis|volume=36|issue=2|pages=170–185|year=2014|last1=Moss|first1=B. G.|last2=Yeaton|first2=W. H.|last3=Lloyd|first3=J. E.|s2cid=123440758}}</ref>
*符合假设的RDD研究可以产生类似于随机研究估计的处理效果估计。<ref>{{cite journal|doi=10.3102/0162373713504988|title=Evaluating the Effectiveness of Developmental Mathematics by Embedding a Randomized Experiment Within a Regression Discontinuity Design|journal=Educational Evaluation and Policy Analysis|volume=36|issue=2|pages=170–185|year=2014|last1=Moss|first1=B. G.|last2=Yeaton|first2=W. H.|last3=Lloyd|first3=J. E.}}</ref>
== 进一步阅读 ==
== 进一步阅读 ==
* {{cite book |last1=Angrist |first1=J. D. |author-link=Joshua Angrist |last2=Pischke |first2=J.-S. |title=Mostly Harmless Econometrics: An Empiricist's Companion |year=2008 |chapter=Getting a Little Jumpy: Regression Discontinuity Designs |publisher=Princeton University Press |pages=251–268 |isbn=978-0-691-12035-5 }}
* {{cite book |last1=Angrist |first1=J. D. |last2=Pischke |first2=J.-S. |title=Mostly Harmless Econometrics: An Empiricist's Companion |year=2008 |chapter=Getting a Little Jumpy: Regression Discontinuity Designs |publisher=Princeton University Press |pages=251–268 |isbn=978-0-691-12035-5 }}
* {{Cite journal | last1 = Cook | first1 = Thomas D. | year = 2008 | title = 'Waiting for Life to Arrive': A history of the regression-discontinuity design in Psychology, Statistics and Economics | journal = [[Journal of Econometrics]] | volume = 142 | issue = 2 | pages = 636–654 | doi = 10.1016/j.jeconom.2007.05.002}}
* {{Cite journal | last1 = Cook | first1 = Thomas D. | year = 2008 | title = 'Waiting for Life to Arrive': A history of the regression-discontinuity design in Psychology, Statistics and Economics | journal = [[Journal of Econometrics]] | volume = 142 | issue = 2 | pages = 636–654 | doi = 10.1016/j.jeconom.2007.05.002}}
* {{cite journal |last1=Imbens |first1=Guido W. |first2=Jeffrey M. |last2=Wooldridge |year=2009 |title=Recent Developments in the Econometrics of Program Evaluation |journal=[[Journal of Economic Literature]] |volume=47 |issue=1 |pages=5–86 |doi=10.1257/jel.47.1.5 |url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:3043416 }}
* {{cite journal |last1=Imbens |first1=Guido W. |first2=Jeffrey M. |last2=Wooldridge |year=2009 |title=Recent Developments in the Econometrics of Program Evaluation |journal=[[Journal of Economic Literature]] |volume=47 |issue=1 |pages=5–86 |doi=10.1257/jel.47.1.5 |url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:3043416 }}
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本中文词条由Wits审校，[[用户:薄荷|薄荷]]编辑，如有问题，欢迎在讨论页面留言。