.. _replication-orthsc: ORTHSC -- Fry's Orthogonalized Synthetic Control (carbon tax + Monte Carlo) =========================================================================== :Estimator: :doc:`../orthsc` -- :class:`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 :math:`0.29` metric tons of transport CO\ :sub:`2` 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: .. code-block:: python 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 .. list-table:: :header-rows: 1 :widths: 30 24 24 * - Quantity - mlsynth (NumPy/cvxpy) - R reference * - ATT :math:`\widehat{\tau}` - :math:`-0.29013` - :math:`-0.29013` * - p-value - :math:`0.000183` - :math:`0.000183` * - smoothing :math:`K` - :math:`4` - :math:`4` * - 95% CI - :math:`[-0.4757,\,-0.1045]` - :math:`[-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 :math:`\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 :math:`5\%` level over 200 replications: .. list-table:: :header-rows: 1 :widths: 12 12 22 22 * - :math:`T_0` - :math:`T_2` - size (effect = 0) - power (effect = :math:`-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 :doc:`../orthsc` (Verification). Lessons carried into the port ----------------------------- * The whole replication hinged on the donor split, not the numerics: the wrong pool gave ATTs of :math:`-0.17` / :math:`-0.48`; Andersson's 14-control / 7-instrument split gave :math:`-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 :math:`\sqrt{n}` factor while the CI uses :math:`\sqrt{\widehat{V}}` directly; both are reproduced as written so the p-value and the interval agree with the reference.