Propensity score matching on panel data with treatment varying by periods I have a panel data of 200 individuals around 100 weeks. A latent ability issue for individual may cause the estimation for one IV biased. This IV is continuous variable.
Except for panel fixed-effect model, I also try to use propensity score matching (PSM) to handle this endogeneity issue. My first question is, is PSM an appropriate approach?
If doable, my plan is to discretize this IV into a binary treatment variable. In this case, the treatment variable for one individual may be different in different periods (e.g., 1 in period 1, 0 in period 2, ..., 1 in period 10....). But I'm not aware of any package can deal with this situation.
Any direction to proceed is appreciated. And any other identification strategy to solve this latent ability issue is also welcome deeply. 
Question also posted here.
 A: I don't really understand the context of this question, but two things come to mind.
You can use propensity scores with continuous treatments, so don't split up your treatment into categories. This is called the generalized propensity score and has been discussed in Hirano & Imbens (2004) and Fong, Hazlett, & Imai (2017), among others. Your goal with this method is to arrive at a sample for which treatment is independent of your covariates. There are a variety of ways of assessing independence, but looking at correlations between covariates and the treatment is one such way. Using the generalized propensity score requires several assumptions about distributions and functional form, but if those assumptions are valid, you can move forward.
Second, you can use marginal structural models and the other g-methods to handle multiple treatment statuses over time. There is a large literature on this method, but part 3 of Hernan & Robins online causal book goes into detail on it.
A: From your description it seems you have a need for dealing with unobserved heterogeneity (i.e. your 'latent ability issue'). Indeed, you can take this into account using a panel data model, such as a fixed effects model. 
Propensity score matching (PSM) has the aim of estimating treatment effects or potential outcomes in case of discrete treatments. You propose to create this treatment variable using discretisation of your endogenous independent continuous variable. This is acceptable if the cut-off point at which you divide your sample this way is a meaningful quantity. In that case, all subjects on both sides of the cut-off have a fixed deviation in their outcome variable, i.e. there is a treatment effect, with naturally defined treaments. 
Without knowing more about your study it is not possible to say whether there is an actual treatment here based on your continuous variable. If there is not, I would not recommend using this method, as you basically throw away information for the estimation of the treatment effect, which additionally is based on an arbitrary cut-off point. Also, estimating propensity scores is usually done when controlling for many variables, not just the one or few. With only a few you would be able to use matching directly on the variables, without any issues caused by high-dimensionality.
If your independent variable is endogeneous then the panel analysis may be enough to make up for this, provided the endogeneity is caused by omitted variable bias due to unobserved heterogeneity. In case there are other sources of unobserved heterogeneity then there are plenty of other options, such as instrumental variable analysis.
