可能是出去讲多了，Jeff老爷子呢，想尝试写一篇
survey-type的文章，
他本来想题目叫
"50 Ways to Do Diff-in-Diffs"。
但是，今天他又把题目改为了
"Eight is Enough"：
他提出了八种等价的方法：
环境：
T = 2，两期平衡面板。D是处理组，f2_t是第二期虚拟变量，W_t = D*f2_t 是处理变量。Y_1和Y_2是第一期和第二期的结果变量。ΔY = Y_2 - Y_1。X是时间不变的控制变量。X_dm = X - Xbar_1 （处理组的均值）。
1. OLS ΔY on 1, D, X, D*X_dm (cross sec)
2. Pooled OLS of Y_t on 1, W_t, W_t*X_dm, D, X, D*X, f2_t, f2_t*X; ATT is coef on W_t (t = 1,2)
3. Random effects estimation with same variables in (2).
4. FE estimation of (2), where D, X, D*X drop out.
Imputation versions of each:
5. OLS ΔY on 1 X using D = 0. Get residuals TE^_FD. Average TE^_FD over treated units.
6. POLS of Y_t on 1, D, X, D*X, f2_t, f2_t*X using W_t = 0 (control obs). TE_t^_POLS resids. ATT is average of TE_t^_POLS over W_t = 1 (treated observations)
7. RE estimation in (6), TE_t^_RE are resids (same as POLS). ATT is average of TE_t^_RE over W_t = 1.
8. POLS of Y_t on 1, C, f2_t, f2_t*X using W_t = 0 (control obs) where C are unit fixed effects. Resids are TE_t^_FE. Average TE_t^_FE over W_t = 1.
Wooldridge, Jeffrey M. "Two-way fixed effects, the two-way mundlak regression, and difference-in-differences estimators." Available at SSRN 3906345 (2021).
Wooldridge, Jeffrey M. "Simple approaches to nonlinear difference-in-differences with panel data." The Econometrics Journal 26.3 (2023): C31-C66.
Lee, Soo Jeong, and Jeffrey M. Wooldridge. "A Simple Transformation Approach to Difference-in-Differences Estimation for Panel Data." Available at SSRN 4516518 (2023).
Papke, Leslie E., and Jeffrey M. Wooldridge. "A simple, robust test for choosing the level of fixed effects in linear panel data models." Empirical Economics 64.6 (2023): 2683-2701.
