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I have a Panel Data Set from 2000 to 2013 and I want to use Propensity Score Matching to analyze it. The treatment variable varies between individuals over time, an individual can get treated any time in the observed period, but it also my not be treated at all. Therefore I cannot define pre-treatment periods since they are different for each individual. I also want to avoid that an individual that gets treated at a later point in time is matched to itself before it got the treatment.

Papers like Paper1 or Paper2 are very unprecise how they deal with those problems, or I do not quite understand the way they solve them.

I read many contributions about this topic (for example topic1, topic2 or topic3), but nothing of those helped me with my particular problem.

Therefore, to tackle this problem I thought of conducting a Propensity Score Matching Analysis periodwise, such that I look at 13 cross-sectional data sets, one for each year, and obtain 13 treatment effects.

Now, my first question is, if this is a proper way to conduct the analysis or if somebody knows another strategy?

Further, if this would be a proper way, I'd like to conduct a joint singificance test to test if the treatment effect is different form 0 over the whole observed period. I thought of a Wald test, but then I would have a problem with the treatment effects covariances since they are unknown. But is there any other way to do this?

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    $\begingroup$ One solution might be to do as you propose, but then append your matched data sets to each other with a cohort indicator and do a regression on treatment and cohort number (you could also include treatment by cohort interactions). That way you can get an estimate controlling for the cohort effects. No need to simultaneously test 13 differences at once when regression will give you a single estimate and test. $\endgroup$ – Noah Dec 11 '16 at 0:15
  • $\begingroup$ @Noah Thank you for the advice. But I think that I will stick to the approach by Sianesi (2004) $\endgroup$ – user24592 Dec 12 '16 at 20:48
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I am facing both problems above but apparently there is a solution to the issue of time variance of the treatment. Try using what is called proportional random assignment of treatment. If for instance 10% of your treated items occurred in 2010, then hypothetically assign that as treat year for 10% of the items in your control group. After this process you need to adjust your time series variable before further analysis. For more details read Petkova (2008)

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