Demeaned SC (Ferman & Pinto 2021) – via TSSC’s MSCa variant

Estimator:

Two-Step Synthetic Control – mlsynth.TSSC (the MSCa variant)

Source:

Ferman, B. and Pinto, C. (2021), “Synthetic controls with imperfect pretreatment fit,” Quantitative Economics 12:1197-1221.

Replication type:

golden cross-validation against the authors’ own R code, executed live via Rscript on every run.

Status:

verified – mlsynth’s MSCa reproduces the authors’ demeaned-SC quadratic program value-for-value on the identified Basque panel.

What the paper proposes

Ferman and Pinto (2021) study synthetic control when the pre-treatment fit is imperfect. They show that SC and related estimators are generally biased in that regime, and propose a demeaned synthetic control – donor weights on the simplex (non-negative, summing to one) together with a free intercept – as a bias-and-variance improvement over difference-in-differences, along with a specification test for it.

Why this uses TSSC (and why that is incidental)

mlsynth has no estimator called “demeaned SC,” and it does not need one: the demeaned SC is exactly the MSCa variant of Two-Step Synthetic Control – the Two-Step SC’s simplex-plus-intercept model. This case therefore validates the estimator, not TSSC’s variant-selection machinery; it reaches into the MSCa fit and ignores the Step-1 test. Adding a separate “demeaned SC” estimator or bolting an intercept onto VanillaSC would be redundant – MSCa already is it.

The reference is the authors’ own code

The reference is not transcribed numbers: it is the authors’ _aux.R :: synth_control_est_demean (a quadprog QP), reproduced verbatim in benchmarks/reference/ferman_demeaned_basque/reference.R and run live via Rscript on the same shipped panel every time the benchmark runs. The case BenchmarkSkipped``s when ``Rscript or quadprog is absent, so a missing R toolchain never turns the suite red.

Cross-validation – the identified case (1975)

The panel is the Basque Country / ETA terrorism study (Abadie & Gardeazabal 2003), basedata/basque_data.csv, with treatment in 1975. That year is chosen deliberately: it is the identified regime – twenty pre-treatment periods (1955-1974) against sixteen donors, so \(C < n\) and the demeaned-SC weights are unique. mlsynth’s MSCa QP and the authors’ quadprog QP then agree value-for-value:

Quantity	MSCa (mlsynth)	demeaned SC (R, live)
Cataluña weight	0.5605	0.5605
Rioja weight	0.2792	0.2792
Asturias weight	0.1064	0.1064
Madrid weight	0.0539	0.0539
free intercept	0.5922	0.5922
ATT (GDP per capita)	\(-0.797\)	\(-0.797\)

Donor-weight L1 distance \(\approx 10^{-4}\), the intercept agrees to \(\approx 10^{-5}\), and the ATT to \(\approx 4\times10^{-4}\) – the residual is just the two QP solvers’ tolerances.

A note on identification (why 1975, not 1970)

The paper is about imperfect pre-treatment fit, so it is worth being explicit about when the demeaned-SC estimate is even well-defined. With a 1970 cutoff the Basque panel is rank-deficient – sixteen donors against fifteen pre-treatment years, \(C > n\). The demeaned-SC weights are then not unique: many weight vectors fit the pre-period equally well, and mlsynth’s QP and the authors’ own constrOptim fallback legitimately land on different minimisers (a Rioja / Cataluña corner versus a Murcia-heavy corner), giving different ATTs. That is not a disagreement between implementations – it is non-identification of the estimand. Moving the cutoff to 1975 makes \(C < n\), the solution unique, and the two codes coincide. The benchmark pins the identified case; the non-identified contrast is documented here as the cautionary half of the story.

Verification

The check is committed as the ferman_demeaned_basque benchmark case (benchmarks/cases/ferman_demeaned_basque.py), which runs TSSC and the authors’ R demeaned SC live, side by side, and asserts the donor weights, the free intercept, and the ATT agree to solver tolerance. It appears on the Validation dashboard dashboard under TSSC. The fast offline unit test is mlsynth/tests/test_ferman_replication.py.