Synthetic Controls model for a Poisson regression

[Isabella Trombini]

Dear Statlisters,

I have a question regarding the Synthetic Control (SC) method. I believe I cannot directly use a Poisson model with the standard SC approach, as it seems like trying to fit a square peg (a likelihood-based model) into a round hole (a least-squares-based weighting algorithm). While I could log-transform the data, more than half of my observations are zero, which complicates things.

Is there a Stata package that addresses this issue? Alternatively, can I use a Poisson model with CEM weights?

A related question: suppose I’m not using a count model, but the majority of my observations are either zero or a large number — can Poisson still be appropriate in such a case?

Thank you in advance for your insights.

[Felix Bittmann]

I am not sure how exactly you create the CEM weights, but in general, poisson does allow pweights.

If you have excess zeroes, a zero inflated model might be suitable, see: https://www.stata.com/manuals/rzip.pdf

[Joao Santos Silva]

Dear Isabella Trombini,

With several co-authors, I have been working on that issue. If you contact me by email, I can send you a preliminary version of the paper (not yet ready for general circulation).

About your question, indeed, Poisson regression may still be appropriate in that case; note that whether the positive observations are large or small will depend on the scale of the data. Depending on what you are studying, you may want to consider a two-part model, such an hurdle model, but I would not use zero inflated models, certainly not with data that are not counts.

Best wishes,

Joao

[Jeff Wooldridge]

It’s hard to give advice without knowing more about the scenario. Do you have common timing? How large are N and T? How many control and treated units? Synthetic control was developed for certain scenarios, and it often does well. Sometimes it works well with a short number of time periods or many treated units. But the inference is based on linearity and large T0 (periods before) and T1 (periods after). If you have large N and not very large T you can use nonlinear diff-in-diffs using flexible Poisson regression. For any nonnegative outcome.