Dear Statalists,

there are at least two user-written software packages with respect to the synthetic control approach.

The original parametric version (‚synth‘) of Abadie, A., Diamond, A., and J. Hainmueller. [2010] and the non-parametric version (‚npsynth‘) of G. Cerulli [2017].

I am trying to figure out (and searching for help) what makes the first approach parametric and the second non-parametric?

On the one hand, the former parametric version applies a quadratic programming routine (i.e. interior point method of Vanderbei, R.J. 1999) that matches the total average pre-intervention covariates (diagonal positive semidefinite V-matrices) of the unaffected pool units towards the best fit (i.e. RMSPE) of the observed (treated) units. Regarding Abadie, there is (so far I understand) no limitation regarding the distribution of the applied data.

On the other hand, the non-parametric version applies a kernel-matching process (fixed bandwidth) to resemble the pre-intervention trajectory oft he observed unit (on an annual level!) with the covariates of the untreated (pool) units. Likewise, the combination with the lowest RMSPE serves as the best fit. Here is further information incl. a methodological comparison: uk17_Cerulli.pdf (stata.com)

Hope there is an expert in this forum that could help me with my question (or could give me a hint for further investigation).

Thank you and wish you all a nice weekend!