Propensity score matching with difference in differences

[Yangjun Park]

Hello all,

I am planning to conduct a policy analysis study using the PSM-DID method, and I have panel data available.

My research is to verify the effect of a policy implemented from 2014 to 2016. Below are my questions:

1. I am going to set 2013 as the pre-treatment period and 2017 as the post-treatment period in my model. Is the time point at 2013 and 2017 too long? and potentially affecting the validity of the study?
2. Should I perform propensity score matching on the datasets for 2013 and 2017 separately, or should I firstly combine the data 2013 and 2017 and then perform propensity score matching?
3. Lastly, do the selected subjects in the dataset (case / control ) from 2013 and 2017 have to be same?

Thank you.

[Ambrogio Luciano]

Dear Yangjun Park,
did you find an answer? I have a doubt. If I perform Propensity Score Matching (PSM) before conducting Difference-in-Differences (DID), can I run the DID only on the subsample of treated and untreated units that have been "matched" by the PSM, excluding those excluded from the matching? In this case, I believe it's not necessary to include the propensity score (_psscore) in the DID regression, as the matching has already balanced the characteristics between the treated and untreated groups, making the propensity score redundant in the subsequent regression.

In other words:

PSM: I use matching to obtain a sample of treated and untreated units with similar characteristics (reducing selection bias). DID: I apply the DID methodology only on the "matched" sample, so there's no need to include the _psscore in the regression because the DID analysis is already comparing the treatment and control groups based on the characteristics balanced by the PSM.

Is it correct?

[Felix Bittmann]

This is not necessarily the best option. The typical 1:1 or 1:n matching appears outdated IMHO. I suggest an entropy weighting approach, which is similar to PSM. First, you generate EB weights based on your model and compute the region of common support. In this step you remove cases where no "good" match can be found. Then you estimate your DID model and use the EB weights as pweights. This balances all covariates of the EB model. The usage with kmatch is simple.

Regarding the original questions of post #1:

1. There is no clear answer to this as this can depend on many factors. The longer the time frame, the more other factors can influence the outcome and it might be harder to quantify the causal effect of the treatment.
2. I would balance on the covariates when the treatment is implemented, so in 2013.
3. In DID, you not necessarily need the same (identical) observations. If you have panel data, you do not need DID as you can use a panel regressions (for example, with FE, which is probably the most robust estimator). If you have only trend data, then DID is suitable.