Synthetic control and Poisson pseudo-maximum-likelihood (PPML) estimator

[sunnystorm22]

Could you the synthetic control combined with the Poisson pseudo-maximum-likelihood (PPML) estimator? And do you know of any example of papers that uses this approach?

For context: I wish to run a DiD on time series trade data. I have only one unit in my treatment group, which represents export from state A to state B over 100 months. My control group consists of exports from state A to a minimum of 10 other countries in the same time period.

This poses at least two challenges:

1. The presence of a substantial number of zeroes in the dataset.
2. Possible breach of the homoskedasticity assumption due to the difference in the number of treated vs untreated units.
   My question is: Would it be sufficient to run a DiD with a PPML to deal with these issues?
   Or, would it be better to run a synthetic control with a PPML estimator?

[mikenguyen13]

Hi @sunnystorm22,

It's possible to use synthetic control with PPML, but I would advise caution. The challenge lies in not fully understanding the trade-off between the extensive and intensive margins—it becomes a mix of the two. Additionally, synthetic control requires a different assumption, specifically that you assume parallel trends in ratios rather than levels.

For more details, you can refer to Chen and Roth (2023) or check out a recap in my book here.

If it were me, I would use the log effects with a calibrated extensive margin value approach.

Regarding the second issue of heteroskedasticity, if you proceed with synthetic control, you can rely on bootstrapped standard errors. In that case, I wouldn’t be too concerned about heteroskedasticity.

Best,
Mike