twowayfeweights

stata

twowayfeweights命令

1.如何解释回归对异质性处理效果的稳健性的总结措施？

 当双向固定效应回归只有一个处理变量时，该命令报告了处理系数β对不同组别和不同时间的处理异质性的稳健性的两个总结措施。 第一个是在de Chaisemartin & D'Haultfoeuille (2020a)的推论1的第（i）点中定义的。它相当于跨治疗组和跨时间段的治疗效果的标准差的最小值，在此情况下，β和对治疗者的平均治疗效果（ATT）可能是相反的符号。当这个数字很大时，这意味着只有在各组和各时期的治疗效果存在大量异质性的情况下，β和ATT才可能是相反的符号。当这个数字较低时，这意味着即使没有大量的跨组和跨时间段的治疗效果异质性，β和ATT也可以是相反的符号。第二个总结性措施是在de Chaisemartin & D'Haultfoeuille (2020a)的推论1的第（ii）点中定义的。 它相当于跨治疗组和时间段的治疗效果的标准差的最小值，在此情况下，β可能与所有治疗组和时间段的治疗效果的符号不同。

2.如何判断第一个总结性措施是高还是低？

 假设第一个总结性措施等于x，如何判断x是治疗效果异质性的低量还是高量？这不是一个容易回答的问题，但这里有一种可能性。 让我们假设，你认为先验合理的假设是，每个组和时间段的治疗效果的绝对值不能大于某个实数B>0。如果你试图评估β对异质性效果的稳健性，那么β大概会落在你对治疗效果的先验合理值的范围内，因此，认为B至少和|β|一样大似乎是公平的。 现在让我们再假设一下，治疗组和时间段的治疗效果是从均匀分布中提取的。 那么，为了使该分布的平均值为0，而其标准差为x，治疗效果应该在[-sqrt(3)x,sqrt(3)x]区间内均匀分布。如果|beta|>=sqrt(3)x，那么平均数为0、标准差为x的均匀分布的治疗效果与你先验的治疗效果的合理值是一致的，所以x可能不是一个令人难以置信的高额治疗效果异质性，并且ATT可能等于0。 另一方面，如果|beta|<sqrt(3)x，x可能是也可能不是令人难以置信的高额治疗效果异质性，这取决于B<sqrt(3)x或B>=sqrt(3)x。

3.我如何判断第二个总结性措施是高还是低？

 同样，让我们假设你认为先验合理的假设是，每个组和时间段的治疗效果的绝对值不能大于某个实数B>，同样，认为B至少和|beta|一样大似乎是公平的。为了固定思路，让我们假设β>0。让我们也假设接受治疗的群体和时间段的治疗效果是从一个均匀分布中抽取的。那么，我们可以认为这些效应都是负的，标准差等于x，例如，如果它们是从[-2sqrt(3)x,0]区间均匀抽取的。如果|beta|>=2sqrt(3)x，那么分布在[-2sqrt(3)x,0]区间上的治疗效果似乎与你先验的治疗效果的合理值范围相符，所以x可能不是治疗效果异质性的一个令人难以置信的高量。
另一方面，如果|beta|<2sqrt(3)x，x可能是也可能不是令人难以置信的高额治疗效果异质性，这取决于B<2sqrt(3)x或B>=2sqrt(3)x。
如果治疗组和时间段的治疗效果都是负的，就不可能遵循正态分布，所以我们在此不讨论这种可能性。

How can one interpret the summary measures of the regression's robustness to heterogeneous treatment effects?

 When the two-way fixed effects regression has only one treatment variable, the     command reports two summary measures of the robustness of the treatment coefficient     beta to treatment heterogeneity across groups and over time.  The first one is     defined in point (i) of Corollary 1 in de Chaisemartin & D'Haultfoeuille (2020a). It     corresponds to the minimal value of the standard deviation of the treatment effect     across the treated groups and time periods under which beta and the average treatment     effect on the treated (ATT) could be of opposite signs. When that number is large,     this means that beta and the ATT can only be of opposite signs if there is a lot of     treatment effect heterogeneity across groups and time periods. When that number is     low, this means that beta and the ATT can be of opposite signs even if there is not a     lot of treatment effect heterogeneity across groups and time periods. The second     summary measure is defined in point (ii) of Corollary 1 in de Chaisemartin &     D'Haultfoeuille (2020a).  It corresponds to the minimal value of the standard     deviation of the treatment effect across the treated groups and time periods under     which beta could be of a different sign than the treatment effect in all the treated     group and time periods.


 How can I tell if the first summary measure is high or low?
 Assume that the first summary measure is equal to x. How can you tell if x is a low     or a high amount of treatment effect heterogeneity? This is not an easy question to     answer, but here is one possibility.  Let us assume that you find it a priori     reasonable to assume that the treatment effect of every group and time period cannot     be larger in absolute value than some real number B>0.  If you are trying to assess     beta's robustness to heterogeneous effects, beta presumably falls within your range     of a priori plausible values for the treatment effect, so it seems fair to argue that     B is at least as large as |beta|.  Now let us also assume that the treatment effects     of the treated groups and time periods are drawn from a uniform distribution.  Then,     to have that the mean of that distribution is 0 while its standard deviation is x,     the treatment effects should be uniformly distributed on the [-sqrt(3)x,sqrt(3)x]     interval. If |beta|>=sqrt(3)x, then uniformly distributed treatment effects with mean     0 and standard deviation x are compatible with your a priori plausible values for the     treatment effect, so x may not be an implausibly high amount of treatment effect     heterogeneity, and the ATT may be equal to 0.  If on the other hand |beta|<sqrt(3)x,     x may or may not be an implausibly high amount of treatment effect heterogeneity,     depending on whether B<sqrt(3)x or B>=sqrt(3)x.


 How can I tell if the second summary measure is high or low?
 Assume that the second summary measure is equal to x. Again, let us assume that you     find it a priori reasonable to assume that the treatment effect of every group and     time period cannot be larger in absolute value than some real number B> Again, it     seems fair to argue that B is at least as large as |beta|. To fix ideas, let us     assume that beta>0.  Let us also assume that the treatment effects of the treated     groups and time periods are drawn from a uniform distribution. Then, one could have     that those effects are all negative, with a standard deviation equal to x, for     instance if they are uniformly drawn from the [-2sqrt(3)x,0] interval. If     |beta|>=2sqrt(3)x, then treatment effects distributed on the [-2sqrt(3)x,0] interval     seem compatible with your a priori plausible range of values for the treatment     effect, so x may not be an implausibly high amount of treatment effect heterogeneity.
If on the other hand |beta|<2sqrt(3)x, x may or may not be an implausibly high amount     of treatment effect heterogeneity, depending on whether B<2sqrt(3)x or B>=2sqrt(3)x.
If the treatment effects of the treated groups and time periods are all negative,     they cannot follow a normal distribution, so we do not discuss that possibility here.