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.
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?