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I am running a difference in difference (DiD) model on the effects of job-training on earnings. My data consists of a staggered adoption design whereby units receive treatment at different times, but once a unit is trained, it is regarded as a treated unit for all the following time periods. My data has $N=4000$ and $T=6$.

My data appears to suffer from the famous Ashenfelter’s dip problem. In that the mean earnings of participants in training programs decline during the period just prior to participation. I am aware that this biases my DiD estimates. To partially deal with them I run an event study model, including dummy variables of leads and lags of training. However, this is not a real solution. I was wondering whether there are other approaches I can use to identify the causal effect of the training (matching?). What is the standard technique scholars use? Any suggestion would be immensely appreciated.

=== UPDATE ===

To better explain the source of the bias: trainees can decide to get into the program whenever they want. They do not have incentives to slack off their efforts in anticipation of the training, but they have strong incentives to select into the program if, for whatever reason, their earnings decline. If I correctly understand the challenge, in this case, is that the participants would be likely to mean revert also without the training either by increasing their job efforts, job search or alternatives.

The challenge is hence to distinguish the effects of the training from the mean reversion of the participants

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    $\begingroup$ Is this because treatment targets people who are having a rough time? Or it because trainees know that they will go into the program in the near future, and slack off in their job search or work effort? Your institutional details can matter for the remedy. $\endgroup$
    – dimitriy
    Commented Mar 22, 2021 at 20:37
  • $\begingroup$ Thanks for the question @DimitriyV.Masterov. Trainees can decide to get into the program whenever they want. They do not have incentives to slack off their efforts in anticipation of the training, but they have strong incentives to select into the program if, for whatever reason, their earnings decline. If I correctly understand the challenge, in this case, is that the participants would be likely to mean revert also without the training either by increasing their job efforts, job search or alternatives. Any idea of how I could address this? $\endgroup$
    – Alex
    Commented Mar 23, 2021 at 9:18
  • $\begingroup$ Did my answer clear things up? $\endgroup$
    – dimitriy
    Commented Mar 26, 2021 at 5:02

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I would try to model the pre-treatment trends in various ways to see how sensitive the results are to those assumptions. Alternatively, you can explore a propensity-score-weighted DID. There are some examples here (in my answer and also the second link in the original question; both involve a simpler setup than you have with the variable treatment timing).

The first option is attractive if you have enough pre-treatment data to implement it well. The second is more involved and may not play nice with the variable treatment timing, but there have been some recent work in this area that looks promising and also includes code.

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  • $\begingroup$ Dear @DimitriyV.Masterov, thanks a lot for your kind reply! I have a couple of follow up questions. First, in practice, I am not sure what modelling pre-treatment trends in various ways ways would entail. Do you know of any paper, workflow or package that could guide me through this analysis? In any case I fear that having T=6 and a staggered adoption design my pre-treatment period would be insufficient. 2) I read Sant'Anna's paper, but my understanding is that it only allows estimating the ATT if the selection depends on covariates. Is this robust to selection on the lag dependent variable? $\endgroup$
    – Alex
    Commented Mar 26, 2021 at 9:56
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    $\begingroup$ You would put in a person-specific time trend, your model would have $\beta_i \cdot t$ term in it. I think you should be able to do matching using the lagged y, but to be honest, I haven't yet fully understood this literature. $\endgroup$
    – dimitriy
    Commented Mar 26, 2021 at 22:52

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