Quantile & distributional treatment effects — the full family¶

"The ATE is misleading when treatment redistributes outcomes." A policy can leave the mean unchanged while compressing or spreading the distribution — only QTE and distributional-TE catch that. StatsPAI v1.4 ships the full 2025-2026 frontier.

The Average Treatment Effect answers: "how much did the mean outcome move?" But for policy, clinical, and fairness work you usually care about who got moved. Did the bottom decile benefit? Did treatment widen inequality? Those questions need quantile or distributional effects.

Every function below is at top level: sp.qdid, sp.qte, sp.distributional_te, sp.dist_iv, sp.kan_dlate, sp.beyond_average_late, sp.qte_hd_panel, sp.cic.

The three levels of granularity¶

Level	What it answers	Estimator(s)
Average	"Did the mean go up?"	`sp.did`, `sp.iv`, `sp.dml`
Quantile (τ-th)	"Did the bottom 10%? The median? The top 10%?"	`sp.qte`, `sp.qdid`, `sp.cic`
Whole distribution	"How did the shape change?"	`sp.distributional_te`, `sp.dist_iv`

Conditional QTE under unconfoundedness — `sp.qte`¶

The default when you have observational data with X rich enough for selection-on-observables:

r = sp.qte(
    data=df, y="wage", treatment="job_program",
    controls=["age", "education", "experience"],
    quantiles=[0.1, 0.25, 0.5, 0.75, 0.9],
    method="quantile_regression",   # or "ipw"
    n_boot=500,
)
r.plot()    # QTE curve with bootstrap uniform band

Reference: Firpo (2007), Econometrica 75(1). IPW variant: Firpo (2007) §4 with the propensity score.

Quantile DiD — `sp.qdid`¶

Two-period, two-group DiD at each quantile. Parallel-trends is replaced by the quantile parallel trends assumption: "in the absence of treatment, the τ-th quantile of the treated group would have moved the same way as the τ-th quantile of the control group."

r = sp.qdid(
    data=df, y="y", group="treated", time="post",
    quantiles=[0.1, 0.25, 0.5, 0.75, 0.9],
    n_boot=500,
)
r.summary()     # QTE(τ) for each τ with placebo-based CI

Reference: Athey & Imbens (2006), Econometrica 74(2).

Changes-in-changes (CiC) — `sp.cic`¶

Weaker than QDiD: CiC requires only that the rank of each unit within its group's outcome distribution is stable over time in the absence of treatment. No parallel-trends. Works when outcome distributions have different shapes across groups.

r = sp.cic(
    data=df, y="earnings", group="treated", time="post",
    quantiles=np.linspace(0.05, 0.95, 19),
    n_boot=500,
)

Reference: Athey & Imbens (2006), Econometrica. The same paper proves CiC nests QDiD when the distributions happen to share scale.

Distributional TE (whole density/CDF) — `sp.distributional_te`¶

Instead of a QTE curve at a handful of quantiles, distributional_te estimates the entire counterfactual CDF:

r = sp.distributional_te(
    data=df, y="income", treatment="program",
    x=["age", "education"],
    method="ipw",           # or "regression"
    n_grid=200,
    n_boot=500,
)
r.plot_cdf()    # control CDF vs counterfactual-under-treatment CDF
r.plot_pdf()    # with bootstrap uniform band

When to use it: when you care about stochastic-dominance claims ("treatment first-order dominates control") or Lorenz-curve-style inequality summaries.

Distributional IV — `sp.dist_iv` (Sharma-Xue 2025)¶

IV at every quantile, with a uniform band over τ:

r = sp.dist_iv(
    data=df, y="earnings", treat="schooling",
    instrument="compulsory_reform",
    covariates=["age", "region"],
    quantiles=np.linspace(0.1, 0.9, 17),
    n_boot=200,
)

Identification: extends Abadie (2002) QTE-under-compliance to a continuous grid of τ with uniform-over-τ confidence coverage, which is what you need to report "schooling raises wages at every quantile" or "the top-decile return is twice the bottom-decile return."

Citation: Holovchak, Saengkyongam, Meinshausen & Shen (2025), arXiv:2502.07641.

KAN D-LATE — `sp.kan_dlate` (Kennedy et al. 2025)¶

A Kolmogorov-Arnold-Network-powered variant of dist_iv that replaces the linear bridge function with a flexible KAN surface. Same call shape as dist_iv, swap in when you suspect the return-to-schooling (say) is strongly non-linear in D.

r = sp.kan_dlate(
    data=df, y="y", treat="d", instrument="z",
    covariates=["x1", "x2"],
    quantiles=np.linspace(0.1, 0.9, 9),
)

Citation: Shaw (2025), arXiv:2506.12765.

Beyond-average LATE — `sp.beyond_average_late` (Xie-Wu 2025)¶

The Angrist-Imbens LATE gives the treatment effect among compliers (units whose treatment would flip if the instrument flipped). But that's an average over the complier subgroup. Xie-Wu identify the whole distribution of treatment effects among compliers:

r = sp.beyond_average_late(
    data=df, y="y", treat="d", instrument="z",
    quantiles=np.linspace(0.1, 0.9, 9),
    n_boot=200,
)

When it matters: if the complier class has a heavy-tailed treatment- effect distribution, the mean LATE hides heterogeneity that a decile or quantile summary reveals. Classic example: schooling returns vary dramatically across compliers by ability.

Citation: Byambadalai, Hirata, Oka & Yasui (2025), arXiv:2509.15594.

High-dimensional panel QTE — `sp.qte_hd_panel` (Fan et al. 2025)¶

Panel data with many covariates? qte_hd_panel fits an ℓ1-penalised quantile regression per-τ with a Lasso nuisance step:

r = sp.qte_hd_panel(
    data=df, y="y", treat="d",
    unit="county", time="year",
    covariates=[f"x{j}" for j in range(50)],
    quantiles=np.linspace(0.1, 0.9, 9),
    lasso_alpha=0.01,
)

When to use: many controls (p ≥ 20 or so), panel DiD-flavoured identification, and you care about the τ curve. Honest post-Lasso inference follows Belloni-Chernozhukov-Fernández-Val (2017).

Citation: Xu & Zheng (2025), arXiv:2504.00785.

Decision guide¶

Cross-section + unconfoundedness:
  ATE only             → sp.dml / sp.aipw
  QTE at some τ        → sp.qte
  Full distribution    → sp.distributional_te

DiD design:
  Mean ATT             → sp.did
  QTE(τ) at each τ     → sp.qdid
  Rank-preserving      → sp.cic

IV design:
  LATE (mean)          → sp.iv
  Distributional LATE  → sp.dist_iv (linear) / sp.kan_dlate (KAN)
  Beyond-average LATE  → sp.beyond_average_late (distribution among compliers)

Panel with many controls:
  → sp.qte_hd_panel

Sanity checks to report¶

Monotonicity in τ — the QTE curve should move smoothly with τ; wild oscillations signal overfitting or instability.
Uniform band coverage — report the Kolmogorov-Smirnov-style uniform band, not just pointwise CIs at each τ.
Stochastic dominance test — sp.stochastic_dominance(r) tells you if the treated-CDF first-order dominates control.
Common-support diagnostic — for IV/IPW-based QTE, verify the propensity overlap at every τ you report.

Current for StatsPAI ≥ 1.5.0. All functions are registered; inspect with sp.describe_function("beyond_average_late"), etc.

For Agents¶

Pre-conditions - binary or continuous treatment (method='quantile_regression' supports both; 'ipw' needs binary) - continuous outcome - controls cover the confounding set (for 'quantile_regression') - overlap when method='ipw'

Identifying assumptions - For 'quantile_regression': unconfoundedness conditional on controls - For 'ipw': unconfoundedness + overlap 0 < e(x) < 1 - Correct parametric quantile model (sensitivity tested via multiple quantiles)

Failure modes → recovery

Symptom	Exception	Remedy	Try next
Large IPW weights (method='ipw')	`statspai.AssumptionViolation`	Extreme propensities — trim (sp.trimming) or switch to doubly-robust DR-QTE.	`sp.trimming`
Quantile crossing	`statspai.AssumptionWarning`	Use rearrangement (Chernozhukov-Fernandez-Val-Galichon) or monotone constraints.

Alternatives (ranked) - sp.qdid - sp.rifreg - sp.cic - sp.metalearner

Typical minimum N: 500

For Agents¶

Pre-conditions - panel or repeated cross-section - group is binary 0/1 - time is binary 0/1 (pre / post) - outcome is continuous

Identifying assumptions - CIC rank invariance: the quantile rank in the untreated distribution is stable across groups - Continuous outcome support covering both groups in both periods - SUTVA (no cross-group spillovers)

Failure modes → recovery

Symptom	Exception	Remedy	Try next
Outcome heavily discrete / zero-inflated	`statspai.AssumptionViolation`	CIC rank-matching is unstable on discrete supports — use QTE regression (sp.qte) or Firpo-RIF.	`sp.qte`
Bootstrap CI across quantiles varies wildly	`statspai.DataInsufficient`	Thin tails at extreme quantiles — restrict to [0.2, 0.8] or raise n_boot to 2000.

Alternatives (ranked) - sp.qte - sp.did - sp.rifreg

Typical minimum N: 500

Quantile & distributional treatment effects — the full family¶

The three levels of granularity¶

Conditional QTE under unconfoundedness — sp.qte¶

Quantile DiD — sp.qdid¶

Changes-in-changes (CiC) — sp.cic¶

Distributional TE (whole density/CDF) — sp.distributional_te¶

Distributional IV — sp.dist_iv (Sharma-Xue 2025)¶

KAN D-LATE — sp.kan_dlate (Kennedy et al. 2025)¶

Beyond-average LATE — sp.beyond_average_late (Xie-Wu 2025)¶

High-dimensional panel QTE — sp.qte_hd_panel (Fan et al. 2025)¶

Decision guide¶

Sanity checks to report¶

For Agents¶

For Agents¶

Conditional QTE under unconfoundedness — `sp.qte`¶

Quantile DiD — `sp.qdid`¶

Changes-in-changes (CiC) — `sp.cic`¶

Distributional TE (whole density/CDF) — `sp.distributional_te`¶

Distributional IV — `sp.dist_iv` (Sharma-Xue 2025)¶

KAN D-LATE — `sp.kan_dlate` (Kennedy et al. 2025)¶

Beyond-average LATE — `sp.beyond_average_late` (Xie-Wu 2025)¶

High-dimensional panel QTE — `sp.qte_hd_panel` (Fan et al. 2025)¶