# Event Study regression standard errors

When running an 'event study' diff in diff, i.e. :

$$y_{i,t} = \sum_{k\neq-1}\beta_k *1\{t=k\} + \lambda_t + \mu_i +error$$

where i is a group level(i.e. individual, county etc). and t is time, $$\lambda_t$$ are time fixed effects and $$\mu$$ are group fixed effects, and $$\beta$$ are the event study coefficients, i.e. the diff in diff between event year k relative to event year t=-1, one year before treatment.

When i typically run this specification, I run into errors with my confidence intervals being extremely large for each of the $$\beta$$'s.

Is there a well defined formula for the standard errors of each coefficient from the treatment effects in the event-study set up? are higher standard errors usually just problem of few observations used to identify each coefficient? I am just curious of the formula so i can think more systematically about what could be driving the high variability of my estimates

• It is customary to see intervals get wider as you move further from the omitted year. I assume you omitted the year immediately preceding the first treatment period. But how big are your intervals? Care to share your output? Commented Sep 15, 2020 at 20:07
• for sensitivity of the data analysis, I would rather not share the output for now. But the standard errors are pretty large for each coefficient, so I am wondering what factors go in to that-i.e. is the standard error for the coefficient in k = 4 a function of the Standard error of the mean of each mean of Y for k = 4 treat=1, k=4 treat=0, and k=-1, treat=1, and k=-1, treat = 0? Similar to a diff in diff/ I am just trying to understand what the driver of the high confidence intervals are and hopefully from that can find ways to address it Commented Sep 15, 2020 at 22:56
• How large are your standard errors? Also, what is your sample size ($n \times t$)? Many factors could be at play. It could be a sample size issue. It could be a collinearity problem. It might not be any problem at all. How many interactions do you have? Commented Sep 16, 2020 at 1:48