Event Study with One Treatment and One Control Group

[Trevor Andrew]

I have one treatment and one control group. I would like to estimate and event study manually (for my understanding) and also using some command that makes it easy to graph the even study.

I estimate regular difference-in-difference with the following code which works as expected:

reg outcome i.treatment##i.post

For event study estimates I use the following code:

reg outcome i.treatment##i.time

Only point estimates are provided. Standard errors, t-statistics etc are omitted. Can someone help me understand what is happening? And maybe provide alternative stata commands that can check for pre-trends and graph the event study coefficients. And just to double check, the treatment#time coefficients are the ones I should be looking at for pre-trends analysis?


Here is the data:

clear
input byte(outcome treatment time post)
10 0  1 0
15 0  2 0
 9 0  3 0
 4 0  4 0
10 0  5 0
31 0  6 0
20 0  7 0
17 0  8 0
 5 0  9 0
11 0 10 1
27 0 11 1
16 0 12 1
32 0 13 1
23 0 14 1
19 0 15 1
 1 0 16 1
 7 0 17 1
 6 0 18 1
12 0 19 1
13 0 20 1
15 1  1 0
17 1  2 0
 6 1  3 0
 3 1  4 0
20 1  5 0
34 1  6 0
27 1  7 0
15 1  8 0
14 1  9 0
13 1 10 1
19 1 11 1
 6 1 12 1
 7 1 13 1
19 1 14 1
20 1 15 1
21 1 16 1
27 1 17 1
26 1 18 1
24 1 19 1
23 1 20 1
end

[Clyde Schechter]

Only point estimates are provided. Standard errors, t-statistics etc are omitted. Can someone help me understand what is happening?

In your data, you have exactly one observation for each combination of treatment and time. Consequently, you have as many right hand side variables in the regression as there are observations. This leaves no degrees of freedom for estimation of inferential statistics--that is why you don't get any.

In my field, we don't do anything that we call "event studies." My knowledge of that term is derived from what I have seen here on Statalist. And in all the ones that I have seen, time is not modeled as individual years (or other units of time) but rather is modeled in periods. Usually the periods correspond to before the event, some period including the event itself and perhaps some number of units of time immediately before or after the event, and perhaps another period that follows the aforementioned period and continuing either until the next event-surrounding period or to the end of observed time. That is, something similar to post, but slightly more fine-grained. I have seen variants where the time of the event is a period by itself and there are multiple periods preceding or following the event that also contain only one time unit, but there are always some periods that are multiple time units.

I imagine that specifically modeling time in your study requires a knowledge of the outcome and how you believe it works in the real world so that you can decide about taking into account anticipatory effects, sustained or decaying impact on the outcome, etc. So I can't suggest anything more specific than what is in the preceding paragraph.

[Jeff Wooldridge]

In economics there's a lot of interest in dynamic effects, and that can come in the form of the "leads and lags" (event study) estimation show above or "lags only" which would interact the treatment with the time dummies in the post treatment periods only. But, as Clyde says, one simply cannot allow such flexibility with one control and one treated unit.

I should also say that when you do the traditional DiD, your standard errors are suspect because they ignore any serial correlation across time (and heteroskedasticity, but that's typically not the main issue).

[Trevor Andrew]

So you are saying that I cannot include all leads and lags when I have one treated and one control unit or no leads and lags at all? When I include 3 leads and three lags interacted with the treatment indicator, stata does provide point estimates, standard errors, etc.