SCMO — Synthetic Control with Multiple Outcomes (Tian et al. 2026; Sun et al. 2025)

Estimator:

Synthetic Control with Multiple Outcomes (SCMO) — mlsynth.SCMO

Source:

Tian, W., Lee, S., & Panchenko, V. (2026), “Synthetic controls with multiple outcomes,” Econometrics Journal (the concatenated variant); and Sun, L., Ben-Michael, E., & Feller, A. (2025), “Using Multiple Outcomes to Improve the Synthetic Control Method,” Review of Economics and Statistics (the averaged variant).

Replication type:

Path A — Tian et al.’s German-reunification balance table reproduced cell by cell — and Path B — the concatenated simulation (Tian Table 1, also the Sun et al. Simulation1.R output) and the averaged regime contrast (Sun et al. Appendix D).

Status:

Verified — empirical balance and both simulations reproduced.

Validation strategy

The two SCMO papers share the German-reunification illustration and tell the same story from two angles: matching the synthetic control on several related outcomes — rather than a single long outcome trajectory — sharpens the identification of the latent factors and reduces post-treatment bias. The concatenated scheme (Tian-Lee-Panchenko, following the same stacking as Sun et al.) stacks the standardized pre-period outcomes; the averaged scheme (Sun-Ben-Michael-Feller) matches their per-period average, which cancels idiosyncratic noise when the outcomes share a common factor.

Path A — German reunification balance (Tian et al. Table 2)

On basedata/germany_augmented.csv (West Germany + 16 OECD donors), SCMO matches West Germany to the donors on nine economic indicators in the single year 1989. The fitted synthetic West Germany reproduces Tian et al.’s printed 1989 balance table cell by cell — for the concatenated (multiple-outcomes) synthetic, reconstructed from res.donor_weights:

Outcome (1989)	West Germany	Synthetic (multiple)	mlsynth
GDP per capita	18994.0	19029.8	19029.8
CPI	2.8	3.1	3.06
Trade openness	57.7	59.1	59.06
Total tax revenue	36.2	34.1	34.07
Real GDP growth	3.9	4.1	4.12

The single-outcome synthetic reproduces the “Synthetic (single outcome)” column (1989 GDP per capita \(19075.9\)). The concatenated SC — fit on one year’s nine indicators, never shown the GDP path — tracks West Germany’s pre-1990 GDP to a root-mean-squared error of \(110\) (vs. \(74\) for the conventional SC fit directly to 30 years of GDP). The post-1990 effect is reported only graphically in the paper (Tian et al. Figure 1), so no ATT number is asserted against the paper; mlsynth’s deterministic ATTs (concatenated \(-1463\), averaged \(-1720\)) ride along as regression guards. Durable case: scmo_germany.

Path B — concatenated simulation (Tian et al. Table 1)

Tian et al.’s Section-3 factor model — identical to the Sun et al. replication package’s Simulation1.R — draws \(N = 30\) units whose outcomes share the unit predictors. As the number of related outcomes \(K\) grows, the post-treatment bias falls while the pre-treatment fit rises toward the true noise floor (rather than overfitting to near-zero). mlsynth reproduces all nine cells of Table 1 across \(T_0 \in \{1, 5, 10\}\) and \(K \in \{1, 5, 10\}\) (e.g. at \(T_0 = 5\) the bias is \(1.21 / 1.04 / 1.00\), pre-fit \(0.46 / 0.95 / 1.02\)), at \(M = 250\) draws (the paper uses 5,000). The DGP lives in mlsynth.utils.scmo_helpers.simulation.simulate_tian(). Durable case: scmo_concatenated_mc.

Path B — averaged regime contrast (Sun et al. Appendix D)

Sun et al. report their Monte Carlo as box plots (Figures D.1, D.2), so the benchmark matches the published geometry rather than numeric cells. Under a common factor shared across outcomes (rho = 1), the multi-outcome schemes beat the separate single-outcome SC and averaging reduces bias; under purely idiosyncratic factors (rho = 0), the outcomes share no signal and averaging hurts (the separate SC is best). mlsynth reproduces this common-vs-idiosyncratic adaptivity (common \(T_0 = 10, K = 10\): averaged bias \(0.91\) < separate \(1.03\); idiosyncratic: averaged \(1.23\) > separate \(1.00\)). The DGP lives in mlsynth.utils.scmo_helpers.simulation.simulate_sun(). Durable case: scmo_averaged_mc.