被解釋變數是虛擬變數可以用DID嗎？

本人經濟學碩士在讀，最近在寫論文的時候遇到一個問題，我想看一下一項政策的效果，準備用DID以及PSM＋DID來解決，但是發現現有的關於DID的文獻被解釋變數都是連續變數（或許是我看的太少），而我的被解釋變數是0、1虛擬變數，可以直接reg嗎？或者logit?還忘眾大神不吝賜教！

直接reg或者logit都有問題。直接reg的問題跟linear probability model類似。直接在logit裡面加fixed effects也有問題，因為這個時候沒有辦法做de-meaning把fixed effects去掉，所以簡單的用unconditional maximum likelihood去估計logit model是不一致的。

有一支文獻研究這類情況，叫conditional logistic model或者fixed-effects logit model.

Stata "clogit"命令的幫助文件有一個簡介。http://www.stata.com/manuals13/rclogit.pdf

Greene教材第7版17章對conditional logit有詳細介紹。Greene, William H. 2012. Econometric analysis. Harlow: Pearson Addison Wesley. Chapter 17.

As @李一鳴 points out, using logit will lead to the complication of non-linear diff in diff.

Luckily, study has been done in "Identification and inference in nonlinear difference‐in‐differences models", Athey and Imbens.

The key idea is that, while the absolute amount(porbability) in nonlinear model is not fixed, the QUANTILE across time and location (I assume you need to take difference using time panel and use a "control" group) is fixed.

DID,PSM,PSM-DID,GSC都可以推廣到probit,logit,tobit等GLM中去的，見

Puhani.The treatment effect, the cross difference, and the interaction term in nonlinear DID models. IZA Discussion Paper 2008,No.3478.

Ai C,Norlon EC.Interaction terms in Logit and Probit Models. Economic Letters,2003,80:123-129.

Identification and Inference in Nonlinear Difference‐in‐Differences Models