多时点双重差分法的潜在问题与解决措施

Potential Problems and Solutions of Staggered Difference-in-Difference Approach

多时点双重差分法具有准自然试验特征,可以相对干净地识别因果效应,广泛应用于与政策评估相关的研究中,但必须重视其可能存在的估计偏差问题。本文总结了多时点双重差分法存在的问题和相应的解决措施。通过梳理最新文献发现,多时点双重差分法回归系数识别的是组别—时间处理效应的加权平均,而非受处理个体的平均处理效应。在异质性处理效应下,多时点双重差分法估计系数有偏,严重时估计系数符号会与真实系数符号相反。目前文献上提出的解决措施可以归结为一个诊断方法和三类解决方法。其中,诊断方法为Goodman-Bacon的系数分解定理,三类解决方法分别是加总方法、两步回归法和堆叠型双重差分法。

As one of the mainstream causal inference methods,difference-in-difference approach has the characteristics of quasi-natural experiment and can relatively exogenously identify the causal effect,so it is favored by scholars at home and abroad.The interpretation of treatment effect estimated by difference-in-difference approach with a single treatment period is well known,but there are only a few studies discussing the interpretation and accuracy of treatment effect estimated by staggered difference-in-difference approach.Recently,some latest studies discuss these problems in detail.This paper,by means of sorting such literature,summarizes the interpretation of treatment effect,potential problems,and corresponding solutions of staggered difference-in-difference approach.The latest literature shows that the coefficient estimated by difference-in-difference approach with a single treatment period is unbiased regardless of the heterogeneity effect.Staggered difference-in-difference approach identifies the weighted average of different group-time treatment effects.The estimated coefficient is unbiased with homogeneity treatment effect but biased with heterogeneous treatment effect.Because some early-treated groups are taken as the control groups of the late-treatment groups,the estimated coefficients of this part are negative and finally result in the bias of the aggregated coefficient.In severe cases,the symbols of both estimated coefficient and real coefficient are opposite.According to the solutions given by the latest literature,the methods to solve the bias of estimated coefficient can be divided into'a diagnosis method'and'three kinds of solutions'.The diagnosis method is Goodman-Bacon decomposition theorem.It is used to diagnose the degree of bias by estimating the sizes and weights of different group-time treatment effect.The first is the aggregation method including two ways,all of which are to find comparable control groups for each treatment group and estimate each group-time treatment effect.Then the unbiased estimated coefficient can be obtained by averaging all the group-period effects weighted by the sample share.The second is two-step regression method involving two ways.The reason for uniformly terming the two ways as this name lies in that they are similar in the solutions and the unbiased coefficient can be gained by two steps.The third is the stacked difference-in-difference approach.It aims to find comparable control group for cohorts with the same treatment period and form a data set.This dataset includes the samples of treated group,never-treated group,and not-yet-treated group.Then it is to stack all the data sets and regress an augmented difference-in-difference specification.With the wide application of staggered difference-in-difference approach in empirical research of economics,it is necessary for empirical researchers to know how to deal with the problems of this method.