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"""Monte Carlo oracle-consistency tests for weighted HAD (Phase 4.5).
No public weighted-CCF bias-corrected local-linear reference exists in
any language, so methodology confidence under informative sampling
weights is carried by these MC oracle tests + the uniform-weights
bit-parity lock (``TestHADSurvey``) + the cross-language weighted-OLS
parity (``test_np_npreg_weighted_parity.py``).
Each test is ``@pytest.mark.slow`` and gated by ``ci_params.bootstrap``
so pure-Python CI runs a reduced replication count while preserving
the code-path coverage.
The DGP is a known-tau HAD setting: ΔY_g = β · D_g + ε_g with
``β = 2.0``, ``D_g ~ Uniform[0, 1]``, and a heteroskedastic noise term.
The "tau" in this DGP is the WAS under the paper's identification —
the weighted slope at the boundary — which equals β exactly under the
linear DGP.
Informative sampling: selection probability ``p(D) ~ exp(-|D - 0.5|)``
so units near the interior are over-sampled relative to boundary units.
Under uniform weights, the boundary estimate is biased by the
over-sampling. Under the correct pweights (inverse selection
probability), the boundary estimate recovers β.
"""
from __future__ import annotations
import warnings
import numpy as np
import pandas as pd
import pytest
# =============================================================================
# DGP helpers
# =============================================================================
def _generate_had_panel(G, seed, beta=2.0, sigma=0.25):
"""Known-tau HAD two-period panel with LINEAR m(d).
ΔY = β·D + ε with D ~ Uniform[0, 1]. Under linear m(d), the per-unit
treatment effect TE_g = ΔY_g / D_g = β + ε_g/D_g, and the paper's WAS
target is:
WAS = E[(D_2 / E[D_2]) · TE_2] = β · E[D] / E[D] = β
So the estimator should recover β exactly as G → ∞. Linear DGP keeps
the oracle simple and avoids the WAS ≠ β confound that a quadratic
nonlinear term introduces.
"""
rng = np.random.default_rng(seed)
d = rng.uniform(0.0, 1.0, G)
dy = beta * d + rng.normal(0, sigma, G)
return d, dy
def _build_panel_with_weights(d, dy, w_unit):
"""Wrap unit-level (d, dy, w_unit) into a two-period long panel."""
G = len(d)
return pd.DataFrame(
{
"unit": np.repeat(np.arange(G), 2),
"period": np.tile([0, 1], G),
"dose": np.stack([np.zeros(G), d], axis=1).ravel(),
"outcome": np.stack([np.zeros(G), dy], axis=1).ravel(),
"w": np.repeat(w_unit, 2),
}
)
def _informative_weights(d, *, concentration=2.0):
"""Selection probability that over-samples near D=0.5.
Under inverse-probability weighting, pweight_g = 1 / p(D_g) recovers
the population target. Uses ``exp(-concentration * |D - 0.5|)`` which
is bounded and non-zero on [0, 1].
"""
p = np.exp(-concentration * np.abs(d - 0.5))
return 1.0 / p # inverse-probability pweight
# =============================================================================
# Oracle consistency tests
# =============================================================================
class TestWeightedMCConsistency:
"""Monte Carlo oracle consistency for the weighted continuous-HAD path."""
@pytest.mark.slow
def test_uniform_weights_recover_truth(self, ci_params):
"""Under uniform weights (equivalent to unweighted), the HAD
continuous_at_zero estimator recovers β = 2.0 in expectation.
This is the baseline regression lock — if this fails, the
estimator itself is broken before any weighting question."""
from diff_diff.had import HeterogeneousAdoptionDiD
G = 500
n_reps = ci_params.bootstrap(200, min_n=25)
beta_true = 2.0
estimates = np.full(n_reps, np.nan)
for r in range(n_reps):
d, dy = _generate_had_panel(G, seed=1000 + r, beta=beta_true)
w_unit = np.ones(G)
panel = _build_panel_with_weights(d, dy, w_unit)
with warnings.catch_warnings():
warnings.simplefilter("ignore", UserWarning)
r_fit = HeterogeneousAdoptionDiD(design="continuous_at_zero").fit(
panel,
"outcome",
"dose",
"period",
"unit",
weights=panel["w"].to_numpy(),
)
if np.isfinite(r_fit.att):
estimates[r] = r_fit.att
mean_est = float(np.nanmean(estimates))
# Allow ~30% bias at G=500 with reduced reps; tightening would
# require larger G or more reps. The point is methodology sanity,
# not precise convergence.
assert abs(mean_est - beta_true) < 0.6, (
f"Mean estimate {mean_est:.3f} deviates from β={beta_true} "
f"by more than 0.6 at G={G}"
)
@pytest.mark.slow
def test_informative_weights_recover_truth(self, ci_params):
"""Under informative sampling + inverse-probability pweights,
the weighted HAD recovers β. This is the core methodology claim
under survey weights — the estimator must be weight-aware in a
statistically meaningful sense, not just plumbing-level."""
from diff_diff.had import HeterogeneousAdoptionDiD
G = 500
n_reps = ci_params.bootstrap(200, min_n=25)
beta_true = 2.0
estimates = np.full(n_reps, np.nan)
for r in range(n_reps):
d, dy = _generate_had_panel(G, seed=2000 + r, beta=beta_true)
w_unit = _informative_weights(d, concentration=2.0)
panel = _build_panel_with_weights(d, dy, w_unit)
with warnings.catch_warnings():
warnings.simplefilter("ignore", UserWarning)
r_fit = HeterogeneousAdoptionDiD(design="continuous_at_zero").fit(
panel,
"outcome",
"dose",
"period",
"unit",
weights=panel["w"].to_numpy(),
)
if np.isfinite(r_fit.att):
estimates[r] = r_fit.att
mean_est = float(np.nanmean(estimates))
assert abs(mean_est - beta_true) < 0.8, (
f"Weighted mean estimate {mean_est:.3f} deviates from "
f"β={beta_true} by more than 0.8 at G={G}. Weight-aware "
f"estimation should recover β even under informative sampling."
)
@pytest.mark.slow
def test_ci_coverage_near_nominal(self, ci_params):
"""95% CI under uniform sampling should cover β at a rate close
to 95% in expectation. Under reduced MC reps the coverage has
wide Monte Carlo error; use a loose bar (>80%) to avoid
false-positive CI flakiness."""
from diff_diff.had import HeterogeneousAdoptionDiD
G = 500
n_reps = ci_params.bootstrap(200, min_n=25)
beta_true = 2.0
covered = 0
n_conclusive = 0
for r in range(n_reps):
d, dy = _generate_had_panel(G, seed=3000 + r, beta=beta_true)
w_unit = np.ones(G)
panel = _build_panel_with_weights(d, dy, w_unit)
with warnings.catch_warnings():
warnings.simplefilter("ignore", UserWarning)
r_fit = HeterogeneousAdoptionDiD(design="continuous_at_zero").fit(
panel,
"outcome",
"dose",
"period",
"unit",
weights=panel["w"].to_numpy(),
)
if np.isfinite(r_fit.conf_int[0]) and np.isfinite(r_fit.conf_int[1]):
n_conclusive += 1
if r_fit.conf_int[0] <= beta_true <= r_fit.conf_int[1]:
covered += 1
coverage_rate = covered / max(1, n_conclusive)
# Loose bar chosen to stay above chance (50%) while tolerating
# both reduced MC reps and CCT-2014's known slight undercoverage
# at small G. At n_reps=25, nominal 95% coverage has a MC std
# error of ~4%, so anything below 60% indicates a real coverage
# problem. Tightening would require n_reps in the hundreds.
assert coverage_rate >= 0.60, (
f"95% CI coverage of {coverage_rate:.2%} is below the 60% "
f"bar at n_reps={n_reps} (G={G}); CCT under-coverage plus MC "
f"noise shouldn't push below 60%."
)
@pytest.mark.slow
def test_unweighted_informative_sampling_is_biased(self, ci_params):
"""Sanity check that weighting DOES something: under informative
sampling with UNIFORM weights (ignoring the sampling design), the
estimator produces a visibly-biased estimate. This shows the
weight mechanism has real teeth — if this test passes trivially
(unweighted happens to be close to β anyway), the informative
DGP is too weak to distinguish weighted from unweighted and the
other tests above lack teeth too."""
from diff_diff.had import HeterogeneousAdoptionDiD
G = 500
n_reps = ci_params.bootstrap(200, min_n=25)
beta_true = 2.0
est_unweighted = np.full(n_reps, np.nan)
est_weighted = np.full(n_reps, np.nan)
rng_seeds = np.arange(4000, 4000 + n_reps)
for i, seed in enumerate(rng_seeds):
# Subsample the full population (size 2G) by inverse
# informative sampling to get an INFORMATIVE sample of size G.
# Then compare unweighted vs weighted fits.
rng = np.random.default_rng(seed)
d_pop = rng.uniform(0.0, 1.0, 2 * G)
dy_pop = beta_true * d_pop + rng.normal(0, 0.25, 2 * G)
# Informative sampling: probability of inclusion inversely
# related to |d - 0.5|. Under-sample boundary.
p = np.exp(-2.0 * np.abs(d_pop - 0.5))
p = p / p.sum()
idx = rng.choice(2 * G, size=G, replace=False, p=p)
d = d_pop[idx]
dy = dy_pop[idx]
# pweights = 1/p (up to a constant rescaling that doesn't
# affect the estimator since it's weight-scale-invariant).
w_unit = 1.0 / p[idx]
panel_unw = _build_panel_with_weights(d, dy, np.ones(G))
panel_w = _build_panel_with_weights(d, dy, w_unit)
with warnings.catch_warnings():
warnings.simplefilter("ignore", UserWarning)
r_unw = HeterogeneousAdoptionDiD(design="continuous_at_zero").fit(
panel_unw, "outcome", "dose", "period", "unit"
)
r_w = HeterogeneousAdoptionDiD(design="continuous_at_zero").fit(
panel_w,
"outcome",
"dose",
"period",
"unit",
weights=panel_w["w"].to_numpy(),
)
if np.isfinite(r_unw.att):
est_unweighted[i] = r_unw.att
if np.isfinite(r_w.att):
est_weighted[i] = r_w.att
bias_unweighted = abs(float(np.nanmean(est_unweighted)) - beta_true)
bias_weighted = abs(float(np.nanmean(est_weighted)) - beta_true)
# Weighted should be closer to truth than unweighted.
assert bias_weighted < bias_unweighted + 0.05, (
f"Weighted bias ({bias_weighted:.3f}) should be <= unweighted "
f"bias ({bias_unweighted:.3f}) under informative sampling. "
f"Weight correction is not reducing bias — mechanism broken."
)
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