ORTHSC – Fry’s Orthogonalized Synthetic Control (carbon tax + Monte Carlo)

Estimator:

Orthogonalized Synthetic Control – mlsynth.ORTHSC

Source:

Fry, J. (2026). “Orthogonalized Synthetic Controls” (arXiv:2510.22828), with the author’s R reference (JosephPatrickFry/OrthogonalizedSyntheticControl).

Replication type:

Path A (the paper’s empirical result on Andersson’s data) and Path B (the paper’s size/power simulation), plus a live cross-check against the author’s R code.

Status:

Done – the empirical ATT, p-value, smoothing parameter, and CI reproduce the live R reference to the digit; the simulation reproduces the size-control / power pattern of Tables 1-2.

Durable check:

benchmarks/cases/orthsc_carbontax.py (orthsc_carbontax) and benchmarks/cases/orthsc_size_power.py (orthsc_size_power); plus mlsynth/tests/test_orthsc.py.

The empirical target

Fry’s working example applies the Orthogonalized SC to Andersson (2019)’s Swedish carbon-tax panel. The point estimate matches Andersson’s synthetic control – an average reduction of \(0.29\) metric tons of transport CO₂ per capita over 1990-2005 – but where Andersson’s placebo test (and, the paper shows, conformal and cross-fitting inference) fails to clear conventional significance, the orthogonalized t-test returns p = 0.00018.

The setup that makes this work is the donor split, and it took the Andersson paper to pin it down. Andersson’s donor pool is 14 OECD countries; he excluded Finland, Germany, Ireland, Italy, Netherlands, Norway, and the United Kingdom (carbon or large fuel-tax changes) and Austria, Luxembourg, Turkey (fuel tourism / outliers). Fry’s method uses the excluded carbon/fuel-tax countries as instruments – so the ORTHSC control pool is Andersson’s 14, and the instruments are his 7 excluded tax countries. With that split the public estimator reproduces the headline:

import pandas as pd
from mlsynth import ORTHSC

url = ("https://raw.githubusercontent.com/jgreathouse9/mlsynth/main/"
       "basedata/carbontax_fullsample_data.dta.txt")
df = pd.read_stata(url).rename(columns={"CO2_transport_capita": "Y"})
df["treat"] = ((df.country == "Sweden") & (df.year >= 1990)).astype(int)

res = ORTHSC({
    "df": df, "outcome": "Y", "treat": "treat", "unitid": "country",
    "time": "year",
    "controls": ["Australia", "Belgium", "Canada", "Denmark", "France",
                 "Greece", "Iceland", "Japan", "New Zealand", "Poland",
                 "Portugal", "Spain", "Switzerland", "United States"],
    "instruments": ["Finland", "Germany", "Ireland", "Italy", "Netherlands",
                    "Norway", "United Kingdom"],
    "display_graphs": False,
}).fit()
print(res.att, res.inference.p_value,
      res.method_details.parameters_used["smoothing_K"])
# -0.29013   0.000183   4

Live cross-check vs the author’s R

The author’s R reference (OrthoganilzedSCE over RegularizedEstimate.R / SeriesHAC.R) was run on the same panel. It installs with no CRAN access – limSolve / corpcor / comprehenr compile from the GitHub CRAN mirrors against the system R – and returns

Quantity	mlsynth (NumPy/cvxpy)	R reference
ATT \(\widehat{\tau}\)	\(-0.29013\)	\(-0.29013\)
p-value	\(0.000183\)	\(0.000183\)
smoothing \(K\)	\(4\)	\(4\)
95% CI	\([-0.4757,\,-0.1045]\)	\([-0.476,\,-0.105]\)

The control weights differ slightly between the two (limSolve’s ldei and cvxpy’s CLARABEL land on different, equally valid elements of the identified set), but the ATT and its p-value match to the digit. That is the paper’s central claim made operational: the Neyman-orthogonalized \(\widehat{\tau}\) is first-order insensitive to the nuisance weights, so a faithful port does not need to bit-match the reference’s weight solver.

The simulation (Tables 1-2)

Fry’s simulation study shows the orthogonalized t-test controls size where naive IV-SC, cross-fitting, and ArCo over-reject, while keeping high power. orthsc_size_power reproduces that behaviour on a linear-factor DGP (the treated unit a convex mix of controls plus idiosyncratic noise; instruments sharing the factors but independent of the treated unit’s shocks). At the \(5\%\) level over 200 replications:

\(T_0\)	\(T_2\)	size (effect = 0)	power (effect = \(-0.25\))
30	16	0.070	0.655
30	32	0.035	0.880
60	32	0.060	0.960

Size sits at or below the nominal level (up to Monte Carlo noise) and power rises with the post-period length – the qualitative content of the paper’s Tables 1 and 2. The runnable grid is in Orthogonalized Synthetic Control (Verification).

Lessons carried into the port

• The whole replication hinged on the donor split, not the numerics: the wrong pool gave ATTs of \(-0.17\) / \(-0.48\); Andersson’s 14-control / 7-instrument split gave \(-0.29013\) exactly.

• The reference’s SeriesHAC.R demeans only the last moment row (an off-by-one in the loop bound); because the sample moments are zero by construction it is harmless, and the port demeans all rows and still matches.

• The t-statistic carries a \(\sqrt{n}\) factor while the CI uses \(\sqrt{\widehat{V}}\) directly; both are reproduced as written so the p-value and the interval agree with the reference.