I follow Dasgupta, 2019 to set up the control and treatment variables for staggered implementation of laws among countries as events. The treatment and control groups are explained in one topic.

I am wondering if there is any reference paper or any explanation guiding how to perform the pre-trend analysis (equation) for this case. I did some searches and saw this topic. However, the answer from the expert not mention the econometrics way or the equation to test pre-trend analysis.

In Dasgupta,2019, last paragraph, section 4.2, I saw a paragraph denoting how he conduct the pre-trend test

To explore the dynamics of the issuance activities and leverage change, we create dummy variables corresponding to the following windows around the treatment year: from 1 to 4 years before the treatment; the treatment year and the 2 years after treatment; the next 3 years; and the years beyond. We find that firms first start growing and issuing equity over the first two sub-periods after the discussion about the leniency law passage started and there is no pre-trend once anticipation effect is taken into account.


1 Answer 1


So you typically need at least two pre-periods for both treatment and control in order to consider pre-treatment trends. Based on my review of the paper it seems that they do indeed have two (please correct me if that is incorrect!).

The intuition of testing pre-trends is simple. Let us use potential outcomes notation where $Y_0$ refers to the non-treated potential outcome and $Y_1$ refers to the treated potential outcome. The intuition is that during the pre-treatment periods any observed change is a change in $Y_0$.

Often people will just eyeball this by plotting the outcome over periods prior to treatment and periods post-treatment. Figure 1 seems to do this in the paper.

A more formal test could also be concocted. What you could do here is to drop all periods post-treatment and regress the outcome, $Y$, on group dummies, time dummies, and group-time dummies. If the coefficient on group-time dummies is not significant this can serve as a decent test of pre-trends. The idea here is almost identical to the DID in that we are controlling for within-group and within-time variation and so what we get is variation within both group and time before treatment. So if there already was some strong pre-treatment trend we should pick it up.

Though to be frank, I am not sure people bother to do a formal test like this in practice. Every DID paper I have seen usually just relies on the visual test. The reason for this is simply that in almost any practical case a significant pre-treatment trend should appear in a visual evaluation. I think if the visual inspection is concerning then using the formal examination may prove useful. Garthwaite et al. 2014 (Section IV.D) is a good example of using the visual test to check for pre-trends.

  • $\begingroup$ Thank you for your dedicated answer. I am wondering one part "What you could do here is to drop all periods post-treatment and regress the outcome, Y, on group dummies, time dummies, and group-time dummies". What is the group dummies., time dummies, and group-time dummies here then? Are they the whole sample of control and treatment concatenating together during the pre-treatment periods? $\endgroup$ May 31, 2021 at 5:06
  • 1
    $\begingroup$ These dummies are just indicators of control and treatment (groups), time periods prior to treatment, and their interaction. Yes you would concatenate the pre-treatment periods for this exercise. $\endgroup$
    – Ariel
    May 31, 2021 at 12:38
  • $\begingroup$ excuse me, I am surprising about "their interaction" here, what does this mean during the pre-treatment period then? Thank you. $\endgroup$ May 31, 2021 at 22:55
  • 2
    $\begingroup$ Sorry if this is unclear, I mean you should use two-way fixed effects and you should be checking for significance for the two-way dummies. $\endgroup$
    – Ariel
    May 31, 2021 at 23:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.