How to code treatment intensity and months of exposure to treatment for pre-treatment rounds?

[Titir Bhattacharya]

Hi,

I am working on a difference in difference analysis based on a panel data of 5 rounds. The treatment, say A, was introduced between rounds 2 and 3. Thus rounds 1,2 are pre treatment rounds, and rounds 3,4,5 are post treatment rounds. The difference in difference estimator would be obtained from an interaction between dummy for post treatment rounds,treatment intensity, months of exposure to treatment.

Now given this framework, months of exposure is negative for pre-treatment rounds. I am confused whether to code these negative values as 0 or missing.

Also, should I code treatment intensity in pre-treatment rounds as zero or missing? I have currently coded them as missing.

Any help in this regard would be greatly appreciated.

Thanks,

[Clyde Schechter]

You cannot code them as missing if you intend to include treatment intensity in your regression. Remember that any observation that has a missing value for any variable in the regression is omitted from estimation. So if all your pre-treatment observations are missing treatment intensity, you will have no pre-treatment observations in the regression and your model will implode. You should code treatment intensity as zero when there is no treatment.

Whether to code the months of exposure as zero or negative in the pre-treatment observations is a substantive question, so without an understanding of what the treatment is, your question cannot be answered. In the majority of situations, zero would be the correct modeling choice. But there are odd circumstances where coding it as negative numbers could make real-world sense.

All of that said, the structure you are describing here does not quite fit the classic DID mold. Apparently your treatment is not a simple "treated vs untreated" distinction: there are degrees of intensity of treatment you quantify, and you believe that duration of treatment also affects the outcome. The classical DID is an interaction between pre-post era and a treatment vs no treatment group indicator. But there is nothing in your data that is quiet analogous to a treatment vs no treatment group. In fact, your treatment intensity and duration variables are themselves, basically, interactions between pre-post time and treatment status. So I think in this case your pre-post dummy and its interaction are redundant and including them will just complicate interpreting the results. It seems to me that you probably should not include them in the model. Perhaps there is a case for including a variable that distinguishes the ever treated from the never treated cases, so you adjust for baseline differences between them. But the information carried by the pre-post dummy and its interaction with intensity and duration of treatment appears to be redundant and these variables are likely to just confuse things.

[Titir Bhattacharya]

Thank you Clyde for your explanation. Yes, I do not have a untreated group in my analysis. I'll follow your advice and drop the pre-post dummy and its interaction.