Clustered standard errors in 2-period Dif-in-Dif? in order to rectify invalid t-stats because of autocorrelation in Difference-in-Differences (DnD) models, Duflo et al (2004) propose (among other solutions) to collapse data so as to have a before-after DnD. My question: What if we already HAVE a before-after setting (e.g. pre-reform vs post-reform)? Would it be still ok to use clustered SE (provided the number of clusters would be high enough)? Or is it automatically wrong to use them EVEN IF we already have data that has 2 time periods only. 
Would appreciate any comments. Thanks. 
 A: Bertrand et al. propose collapsing so that you don't have to cluster your standard errors. Just use a common t-statistic comparing two groups with unequal variances for your test:
$$\begin{equation*} \frac{\bar{y}_1 - \bar{y}_0}{\sqrt{\frac{\hat \sigma^2_0}{N_0} + \frac{\hat \sigma^2_1}{N_1}}} \end{equation*}$$
See that this assumes no correlation between observations within the pre- and post-periods and no correlation between pre- and post-periods. The first is a common cross-section assumption and Bertrand et al. show that the latter is reasonable in the panel context.
The above works when you have a balanced panel with all individuals experiencing the intervention at the same time. If this is not the case, perform the following regression. For each individual, get a pre-period average of the outcome $y$, $\bar{y}_{i0}$ and similarly a post-period average $\bar{y}_{i1}$. Now, for each individual, there are two observations: before and after. Turn this into a panel with $2N$ rows, where $N$ is the number of individuals. Run a regression on these data, including individual fixed effects and a treatment indicator.
Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. “How Much Should We Trust Differences-In-Differences Estimates?” The Quarterly Journal of Economics 119 (1): 249–275.
