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In a paper, Dasgupta, 2019 used Difference-in-Difference approach to see whether anticollusion laws implemented by different countries (staggered implementation) affect firms financial flexibility.

Dasgupta, 2019, p.2610 used an approach called "prediction model"

by only using pre-leniency observations and predict the probability that the firm will be convicted in the cartel case after the passage of a leniency law.

In particular, what they did is

First, we estimate the propensity of a firm to be convicted in a cartel case. We use a prediction model based on time-varying firm characteristics (asset size, leverage, and ROA), country characteristics (GDP and unemployment), and country fixed effects and three-digit SIC fixed effects.

I do not understand how they calculate the "probability that the firm will be convicted in the cartel case after the passage of a leniency law" like that by using STATA. The one command I can link to is "predict" but it seems not to work in this case.

Update:

From some suggestions, it seems that a good way is to use probit(or logit) model to predict the possibility as mentioned. But I do not understand how can we assign the value of dependent variable (0 and 1) in Dasgupta's study.

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    $\begingroup$ Have you looked at propensity treatment models? $\endgroup$ Dec 4, 2021 at 5:36
  • $\begingroup$ Hi @RegressFoward, is there any link for it then, I search with the keyword "propensity treatment models state" but it only shows the PSM (propensity matching score) $\endgroup$ Dec 4, 2021 at 5:37
  • $\begingroup$ After a while, I found this one (onlinelibrary.wiley.com/doi/full/10.1002/pds.3356), is it what you are talking about? $\endgroup$ Dec 4, 2021 at 5:47
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    $\begingroup$ It sounds like they are using a propensity treatment score method, there are a variety of approaches in that flavor. $\endgroup$ Dec 4, 2021 at 5:47
  • $\begingroup$ @RegressForward, if it is available, really hope that you can post an answer that can benefits all learners including me and get some internet points :D $\endgroup$ Dec 5, 2021 at 19:58

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I am not familiar with this specific text, however, I've been asked to elucidate and will do so as an answer, though I do not utilize these techniques often, so there are undoubtedly important elements I have missed.

There is a body of methods called propensity score methods. The primary issue these techniques address is that treatment is typically not exogenous (properly randomized)- many groups are likely to be treated because of their existing characteristics. Under these conditions if one naively estimates the effect of treatment, say through DID, one will estimate the effect of treatment on those that were already going to be treated anyway. The estimated DID coefficient will then be a biased estimate for the effects of treating the population as a whole.

The key thought of these techniques is to estimate the probability that a particular group will be treated, and then weight the estimation to back out the impact of treatment on the population as a whole. The manner in which this is done will vary, I recommend reading carefully the Dasgupta, 2019 paper for citations - they surely directly mention where their technique has come from in the methodology section. Searching other papers at random will provide other estimates.

As another note, you do not want to estimate the probability of treatment with probit/logit and use it as an instrument directly - it does not have the desired effect (see control function approaches (CFA), or 2 stage residual inclusion (2SRI)).

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  • $\begingroup$ Thank a lot @RegressFoward. I just updated the question after asking the author. Could you please have a look on that then. Thanks a heap $\endgroup$ Dec 6, 2021 at 2:28

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