Identification and estimation of treatment effects with a regression-discontinuity design
Identification and estimation of treatment effects with a regression-discontinuity design
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DOI：
10.1111/1468-0262.00183
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发表时间：
2001-01-01
期刊：
影响因子：
6.1
通讯作者：
Van der Klaauw, W
中科院分区：
文献类型：
--
作者：
Hahn, JY;Todd, P;Van der Klaauw, W
回归不连续(RD)数据设计是一种准实验设计，其定义特征是接受治疗的概率作为一个或多个潜在变量的函数而不连续地变化。这种数据设计经常出现在经济和其他应用中，但很少被用作评估治疗效果的识别信息来源。在RD方法的第一次应用和讨论中，Thilethwaite和Campbell(1960)研究了学生奖学金对职业抱负的影响，他们利用这样一个事实：只有在测试分数超过门槛时才会颁发奖项。最近，Van der Klaauw(1997)估计了助学金对学生决定上某所大学的影响，考虑到了部分根据学生平均绩点和SAT分数的不连续函数来确定助学金金额的管理规则。Angrist和Lavy(1999)估计了班级规模对学生考试成绩的影响，他们利用了一项规则，该规则规定，当平均班级人数超过门槛时，应增加另一间教室。最后，Black(1999)使用了一种RD方法来评估父母是否愿意为更高质量的学校买单，方法是比较地理就学边界附近的房价。回归间断法在经济研究中具有潜在的广泛适用性，因为管理项目的地理边界或规则经常在治疗分配机制中造成可在该方法下利用的间断性。尽管在文献中已经对RD方法进行了一些讨论和应用，但重要的问题仍然是关于识别的来源和在最小参数限制下估计治疗效果的方法。在这里，我们表明，在以前的RD方法的应用中调用的识别条件往往过于强烈，并且在RD设计下，通过弱函数形式限制可以非参数地识别治疗效果。这一限制是不寻常的，因为它需要强加连续性假设，以便利用治疗分配机制中已知的不连续性。我们还提出了一种非参数估计治疗效果的方法，并将Wald估计器解释为RD估计器。
THE REGRESSION DISCONTINUITY (RD) data design is a quasi-experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables. This data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment. In the first application and discussion of the RD method, Thistlethwaite and Campbell (1960) study the effect of student scholarships on career aspirations, using the fact that awards are only made if a test score exceeds a threshold. More recently, Van der Klaauw (1997) estimates the effect of financial aid offers on students' decisions to attend a particular college, taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students' grade point average and SAT score. Angrist and Lavy (1999) estimate the effect of class size on student test scores, taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level. Finally, Black (1999) uses an RD approach to estimate parents' willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries. Regression discontinuity methods have potentially broad applicability in economic research, because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method. Although there have been several discussions and applications of RD methods in the literature, important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions. Here, we show that identifying conditions invoked in previous applications of RD methods are often overly strong and that treatment effects can be nonparametrically identified under an RD design by a weak functional form restriction. The restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism. We also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the Wald estimator as an RD estimator.