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= = 方法 = = 使用 RDD 进行估计的两种最常见的方法是非参数和参数(通常是多项式回归)。
= = 方法 = = 使用 RDD 进行估计的两种最常见的方法是非参数和参数(通常是多项式回归)。
编辑后：= = 方法 = = 使用RDD进行估计的两种最常见的方法是参数方法和非参数方法(通常是多项式回归)。
=== Non-parametric estimation ===
=== Non-parametric estimation ===
The most common non-parametric method used in the RDD context is a local linear regression. This is of the form:
The most common non-parametric method used in the RDD context is a local linear regression. This is of the form:
在RDD上下文中使用的最常见的非参数方法是局部线性回归。下面是这样的形式:
: <math>
: <math>
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
</math>
</math>
编辑后：
:
在RDD中最常见的非参数方法是局部线性回归。它的形式是:
<math>
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
</math>
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
Y = \alpha + \tau D + \beta_{1}(X-c) + \beta_{2}D(X-c) + \varepsilon ,
其中 c 是处理截止值，d 是一个二进制变量，如果 x ge c 是一个二进制变量，如果 h 是所用数据的带宽，我们有 c-h le x le c + h。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，而矩形核有更直接的解释。
其中 c 是处理截止值，d 是一个二进制变量，如果 x ge c 是一个二进制变量，如果 h 是所用数据的带宽，我们有 c-h le x le c + h。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，而矩形核有更直接的解释。
编辑后：
其中c是处理临界值，D是一个二值变量，
The major benefit of using non-parametric methods in an RDD is that they provide estimates based on data closer to the cut-off, which is intuitively appealing. This reduces some bias that can result from using data farther away from the cutoff to estimate the discontinuity at the cutoff.<ref name="Lee and Lemieux 2010" /> More formally, local linear regressions are preferred because they have better bias properties<ref name="Fan and Gijbels 1996"/> and have better convergence.<ref name="Porter 2003">{{cite journal |last=Porter |title=Estimation in the Regression Discontinuity Model |year=2003 |journal=Unpublished Manuscript |url=http://www.ssc.wisc.edu/~jrporter/reg_discont_2003.pdf }}</ref> However, the use of both types of estimation, if feasible, is a useful way to argue that the estimated results do not rely too heavily on the particular approach taken.
The major benefit of using non-parametric methods in an RDD is that they provide estimates based on data closer to the cut-off, which is intuitively appealing. This reduces some bias that can result from using data farther away from the cutoff to estimate the discontinuity at the cutoff.<ref name="Lee and Lemieux 2010" /> More formally, local linear regressions are preferred because they have better bias properties<ref name="Fan and Gijbels 1996"/> and have better convergence.<ref name="Porter 2003">{{cite journal |last=Porter |title=Estimation in the Regression Discontinuity Model |year=2003 |journal=Unpublished Manuscript |url=http://www.ssc.wisc.edu/~jrporter/reg_discont_2003.pdf }}</ref> However, the use of both types of estimation, if feasible, is a useful way to argue that the estimated results do not rely too heavily on the particular approach taken.