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REVIEW 2 major objections 5 minor 164 references

When an untestable bias bound dominates sampling noise, honest confidence intervals have zero local power, and the loss is intrinsic to honesty itself.

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2026-07-14 10:49 UTC pith:XG5OTYWQ

load-bearing objection Clean three-regime characterization of local power for honest intervals, with a minimax lower bound showing the parametric-rate dead zone is intrinsic to honesty itself. the 2 major comments →

arxiv 2607.10558 v1 pith:XG5OTYWQ submitted 2026-07-12 econ.EM

Local Asymptotic Power of Honest Confidence Intervals

Hugo Freeman This is my paper
classification econ.EM
keywords honest inferencebias-aware confidence intervalslocal asymptotic powerdead zonepartial identificationdifference-in-differencesinstrumental variablesregression discontinuity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Honest or bias-aware confidence intervals deliberately widen an estimate by a worst-case bound on untestable bias so that coverage holds uniformly over a class the data cannot rule out. This paper characterises the local power of the tests those intervals induce. Power is governed by how fast the bias bound shrinks relative to the sampling rate, producing three regimes: when the bound vanishes faster than the standard error, conservatism is asymptotically free; when the rates match, the power cost is bounded and explicit; and when the bound dominates—the typical parametric case—the honest test has zero local power and fails to reject local alternatives with probability approaching one. A minimax argument shows the loss is a property of honesty against untestable bias, not of any particular construction; no honest procedure recovers the power, and the standard bias-aware interval is rate-optimal. The practical recommendation is to report the half-width of the resulting power dead zone alongside every such interval.

Core claim

Local power of tests from honest confidence intervals is governed by the rate of the bias bound relative to the sampling rate. When the bound dominates (the usual parametric case), every honest interval has zero local asymptotic power: it covers local alternatives with probability approaching one. A minimax lower bound shows this loss is intrinsic to honesty itself—no honest procedure recovers it—and the standard bias-aware interval is rate-optimal among honest procedures. Partial identification is the limiting case of the same width-power duality.

What carries the argument

The power dead zone: the set of effects so close to the null that an honest test cannot separate them from the null, rejecting no more often than its nominal size. Its half-width equals twice the bias bound, because an adversary can shift the estimator centre by plus or minus the bound under both null and alternative, making the laws observationally equivalent whenever the true shift is smaller than that diameter.

Load-bearing premise

The maintained class of data-generating processes must be rich enough that a shift in the parameter of interest of size up to twice the bias bound can be nearly or exactly absorbed by changing an untestable nuisance, so the null and confounded alternative are hard or impossible to tell apart from the data.

What would settle it

Exhibit any honest procedure (uniform coverage over the same class) that, in an exactly confounded setting such as plausibly exogenous IV or honest DiD with fixed bound M, rejects local alternatives inside the window of half-width twice the bias bound with probability bounded away from the nominal size as sample size grows.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At parametric rates with fixed bias bounds (honest DiD under bounded parallel-trends violations, or IV under bounded exclusion failures), honest tests have no local power.
  • Reporting the dead-zone half-width 2 times the bias bound alongside bias-aware intervals discloses exactly which effect sizes the chosen bound forgoes the ability to detect.
  • Any confidence interval whose width fails to shrink fast enough has no local power in the interior of the set it traces out, and at best one-sided power at the boundary.
  • The standard bias-aware construction is rate-optimal; only relaxing strict honesty (tighter substantive bounds or undersized tests) can restore local power.
  • In matched-rate settings such as honest regression discontinuity, conservatism costs only a bounded, explicit inflation of the critical value rather than total power loss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Published applications that report bias-aware DiD or IV intervals may be featuring point estimates that sit inside the dead zone for the bounds they chose, so conventionally large t-statistics can become undetectable once honesty is imposed.
  • The recommended dead-zone disclosure effectively turns every bias-aware analysis into an explicit power-sensitivity report, not only a coverage guarantee.
  • Any adaptive or data-driven bound that remains of larger order than the sampling rate will inherit the same zero-power collapse under the paper’s width-power duality.
  • A direct check of the claim is to recompute the dead-zone half-width on existing replication packages and verify whether the reported point estimate lies outside it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper characterises the local asymptotic power of honest (bias-aware) confidence intervals that are now standard in DiD, IV, RD, and interactive fixed-effects settings. Power is organised by the rate of the user-supplied bias bound relative to the sampling rate, yielding three regimes: free when the bound vanishes faster than the SE; a bounded, explicit cost when the rates match; and zero local power when the bound dominates (the typical parametric case). Theorems 2–4 establish the regimes for the standard bias-aware construction; Theorem 5 and Corollary 2 show via a dual size-control / least-favourable-confounding argument that the loss is intrinsic to honesty itself and that the usual construction is rate-optimal. Exact confounding (Lemma 2) delivers a flat dead zone of half-width 2B̄ for IV and DiD with essentially no regularity; a Gaussian limit experiment recovers the sharp frontier at the matched rate. Partial identification is identified as the limiting case. Simulations across five designs and two empirical applications illustrate the regimes, and the paper recommends reporting the dead-zone half-width alongside bias-aware intervals.

Significance. Honest intervals are now routine in applied econometrics, yet their local-power cost has not been priced systematically. The three-regime taxonomy, the dead-zone concept, and the minimax lower bound are clean and useful contributions. The exact-confounding argument for plausibly exogenous IV and honest DiD is particularly sharp and assumption-light; the partial-identification duality supplies an independent route to the same conclusion. The disclosure recommendation (report 2B̄ in the units of the estimand) is immediately actionable and is illustrated on published RD and DiD applications. The derivations rest on standard tools (rescaled endpoints, continuous mapping, total variation / Neyman–Pearson bounds) under clearly stated assumptions, and the simulations and applications are designed to be reproducible. If the results hold as stated—which they appear to—the paper should become a standard reference for anyone constructing or interpreting bias-aware intervals.

major comments (2)
  1. [Abstract / §1 vs Theorem 5(i)] Abstract and §1 state that when the bound dominates, “the honest test has zero local power, failing to reject local alternatives with probability approaching one,” and that “No honest procedure recovers it.” Theorems 2–3 establish power → 0 for the standard bias-aware construction under Assumptions 1–2. Theorem 5(i), however, only bounds worst-case power by α (limsup Pr{A_n ∉ B_n} ≤ α under the least-favourable nuisance). The paper itself later notes (discussion of Proposition 2) that the minimax bound is α rather than zero and that this is sharp. The abstract’s stronger language should be aligned with the precise minimax statement so that the headline claim matches what is proved for every honest procedure.
  2. [Example 1 / §2.2–2.3, Assumption 3] Example 1 (weak factors) is used as a leading case throughout, and p. 17 asserts that Assumption 3 “applies straightforwardly” via Onatski’s detection boundary. Unlike IV and DiD (Lemma 2), no formal total-variation or modulus verification is given for the factor class; §2.3 only claims the qualitative content s(0)=0. This is not load-bearing for the parametric zero-power claim under the bias-aware construction (Theorems 2–4), nor for the exact-confounding settings, but if the factor example is to support the full minimax statement of Theorem 5, a more formal argument—or an explicit caveat that only the construction-level results are claimed for factors—would close the gap.
minor comments (5)
  1. [Definition 3 / Proposition 1] Definition 3 of the dead zone uses limsup inf_θ Pr{A_n ∉ B_n} ≤ α. It would help the reader if the text briefly cross-referenced that under exact confounding (Lemma 2, τ≡0) this coincides with the flat window |ξ|≤2b̄ of Proposition 1, while under approximate confounding (RD) the full-class frontier is the smooth Φ(s(ξ)−z_{1−α}) of Proposition 3.
  2. [Remark 1 / §4] Remark 1 (Pitman efficiency) is a useful restatement of the dead zone in sample-size currency. A one-sentence pointer back to it from the empirical applications (where the bound is fixed) would make the practical cost more concrete.
  3. [Figure 1 / Figure 3] Figure 3 caption and the surrounding text carefully distinguish the per-law sliding windows from the union (envelope) dead zone. The same distinction could be flagged once in the introduction near Figure 1 so that readers do not confuse half-width b̄ with 2b̄ before reaching §2.2.
  4. [§3.2 / Figure 6] In §3.2 the trend-adjusted (Δ^{SD}(0)) procedure is a helpful intermediate benchmark. Stating explicitly that it corresponds to asserting the untestable w=0 (one derivative up from the event-study’s δ=0) already appears in the text; a short parallel sentence in the figure caption would make the three-way comparison self-contained.
  5. [§2 notation] Minor notation: Θ_p is defined for exact asymptotic order, but n^δ B̄ → b̄ is sometimes written with a non-random limit and sometimes with p→. A uniform convention would reduce friction.

Circularity Check

0 steps flagged

No significant circularity: local-power regimes and the dead zone are derived consequences of honesty plus rate assumptions, not inputs renamed as results.

full rationale

The paper is self-contained asymptotic theory. Theorems 2–4 obtain zero or non-degenerate local power for the standard bias-aware interval directly from Assumptions 1–2 and the width–power duality of Lemma 1 (classical Pratt-type non-coverage of the rescaled limit interval). Theorem 5 and Corollary 2 extend the same rate transition to every honest procedure via dual size control (Definition 2 / honest coverage (2)) plus the confounding condition (Assumption 3); in the leading IV and DiD settings Lemma 2 verifies exact confounding with τ ≡ 0 from the class geometry alone. Proposition 1 recovers the sharp Gaussian frontier under a standard Le Cam limit experiment; Proposition 2 is the same width argument applied to a non-shrinking identified set. The dead zone (Definition 3) is defined as the set of perturbations whose exclusion cannot be guaranteed beyond size, then shown to contain |ξ| ≤ 2b̄—this is a proved property, not a self-definitional input. There are no fitted parameters re-labeled as predictions, no uniqueness theorems imported from the author’s prior work (sole author; no Freeman self-citations), and no ansatz smuggled via citation. Citations to Armstrong–Kolesár, Rambachan–Roth, Conley et al., Donoho, Low, etc. supply the settings and classical tools being analyzed, not load-bearing circular premises. Score 0 is the correct honest finding.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 1 invented entities

The paper works inside standard asymptotic statistics and the existing honest-inference framework. The only free parameters are the user-chosen bias bounds that define honesty; they are inputs, not fitted outputs. The load-bearing modeling assumptions are the rate of the bias bound, the existence of a least-favorable confounding pair, and asymptotic linearity / Lindeberg conditions for the Gaussian limit. No new physical entities are postulated; the 'dead zone' is a derived set, not an invented object with independent ontology.

free parameters (1)
  • user-specified bias bound B̄ (or M, γ̄, number of weak factors)
    Chosen by the analyst to index the class over which honesty is required; the entire power analysis is conditional on this choice and its rate δ relative to the sampling rate ε. Not estimated from data.
axioms (5)
  • domain assumption Asymptotic honesty (Definition 2 / uniform coverage (2)): limsup sup Pr{φ_n=1} ≤ α over the class P_n
    The paper's object of study; taken as the requirement that defines the class of procedures whose power is characterized.
  • domain assumption Assumption 3 (least-favorable confounding): TV distance between null and confounded alternative ≤ τ(Δ/2B̄)+o(1) for Δ ≤ 2B̄
    Information-theoretic dual of the worst-case bias; verified exactly for IV and DiD (Lemma 2), qualitatively for weak factors, approximately for RD via the modulus.
  • domain assumption Assumption 1: estimator admits bias decomposition β̂-β = B̂ + O_p(n^{-ε}) with se(β̂)=Θ_p(n^{-ε})
    Standard asymptotic linearity / rate condition for the estimators used in the four applied settings.
  • domain assumption Assumption 4 (Gaussian least-favourable limit experiment) for the sharp frontier
    Le Cam convergence of the localized experiment to a bounded normal mean; holds exactly under exact confounding and under asymptotic linearity + Lindeberg for the matched-rate case.
  • standard math Standard continuous-mapping / Portmanteau arguments for rescaled endpoints (Lemma 1)
    Classical weak-convergence tools used to convert interval width into local power.
invented entities (1)
  • power dead zone D no independent evidence
    purpose: The set of local perturbations of the truth whose exclusion probability cannot be guaranteed to exceed nominal size under the least-favorable nuisance; half-width 2B̄ under exact confounding.
    Named and formalized here (Definition 3) as the practical disclosure object; it is a derived set from the honesty requirement, not an independent physical or statistical object.

pith-pipeline@v1.1.0-grok45 · 32994 in / 3342 out tokens · 38286 ms · 2026-07-14T10:49:13.181793+00:00 · methodology

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read the original abstract

Confidence intervals that are conservative against an untestable bias, called bias-aware or honest, are now standard in DiD, IV, RD, and factor-model settings. This paper characterises the local power of the tests they induce. Power is governed by the rate of the bias bound relative to the sampling rate, giving three regimes: when the bound vanishes faster than the standard error, conservatism is asymptotically free; when the two are of the same order it costs a bounded, explicit amount; and when the bound dominates, the typical case at the parametric rate, the honest test has zero local power, failing to reject local alternatives with probability approaching one. A minimax argument shows this loss is intrinsic to honesty itself, not a property of any particular construction. No honest procedure recovers it, and the standard bias-aware interval is rate-optimal. Broadly, any confidence interval whose width fails to shrink fast enough has no local power in the interior of the set it traces out, and at best one-sided power at the boundary. Partial identification is the limiting case of this argument. Simulations and two empirical applications illustrate the three regimes. The practical recommendation is to report the half-width of the power "dead zone" alongside bias-aware intervals.

Figures

Figures reproduced from arXiv: 2607.10558 by Hugo Freeman.

Figure 1
Figure 1. Figure 1: The power dead zone. (a) The sharp honest power frontier πα(ξ) = Φ (|ξ|−2 ¯b)+/σ−z1−α  of Proposition 1: worst-case power (over the untestable bias) stays at the nominal level α across the dead zone |ξ| ≤ 2 ¯b (twice the bias bound) and rises only outside it; under any single bias the undetected window has half-width ¯b, and the dead zone is the union of these windows. (b) Observational equivalence. The e… view at source ↗
Figure 2
Figure 2. Figure 2: Weak vs. Strong factor model. Rejections for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The union dead zone realised by simulation: plausibly exogenous IV as in Section [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Weak factors n −1/2 local alternatives. Dashed blue line: Factor model; Solid red line: bias-aware intervals; Grey area: dead-zone. Left to Right: (N, T) ∈ {(50, 10),(200, 24),(1200, 70)} −0.4 −0.2 0.0 0.2 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Alternative Hyp. Rejection Rate −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.0 0.2 0.4 0.6 0.8 1.0 Alternative Hyp. Rejection Rate −0.03 −0.02 −0.01 0.00 0.01 0.02 0.03 0.0 0.2 0.4… view at source ↗
Figure 5
Figure 5. Figure 5: Strong factors n −1/2 local alternatives. Dashed blue line: Factor model; Solid red line: bias-aware intervals; Grey area: dead-zone. Left to Right: (N, T) ∈ {(50, 10),(200, 24),(1200, 70)} 3.2 Honest Difference-in-Differences The second design is the honest difference-in-differences setting of Rambachan and Roth (2023). An event study with three pre-treatment periods and one post-treatment period is summa… view at source ↗
Figure 6
Figure 6. Figure 6: Honest DiD rejections for n −1/2 local alternatives. Left to right: N ∈ {100, 500, 2500}. Blue dashed: event-study interval; green dot-dash: trend-adjusted ∆SD(0) interval; red solid: honest ∆SD(M) interval, M = 0.2. Shaded: the dead zone {power ≤ α}. Top to Bottom: strong pretrend; kinked violation; no pretrend. With strong pretrends the event-study window rests at the honest region’s right edge: the hone… view at source ↗
Figure 7
Figure 7. Figure 7: Honest RD rejection rates for n −2/5 local alternatives. Left to right: n ∈ {500, 2500, 12500}. Top to bottom: a = 1 curvature saturates, a = 0 linear. Blue dashed: conven￾tional local-linear interval; red solid: honest H¨older interval. Shaded: the realized dead zone {power ≤ α}, the alternatives the honest test cannot detect (where the red curve sits on/below α); green dotted lines: ±2 ¯b, the least-favo… view at source ↗
Figure 8
Figure 8. Figure 8: Rejection rates for n −1/2 local alternatives. Left to right: n ∈ {500, 2500, 12500}. Blue dashed: OLS interval (n −1/2 ); red solid: honest Lipschitz interval, C = 2 (n −1/3 ). Localised wedge (a > 0, honest needed): OLS rejects the truth; flat design (a = 0, honest not needed): OLS valid and sharper. Shaded: the dead zone {power ≤ α}; the honest interval shrinks only at n −1/3 , so in n −1/2 units the zo… view at source ↗
Figure 9
Figure 9. Figure 9: Plausibly-exogenous IV rejection rates for [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Incumbency advantage (Lee, 2008): conventional (blue) and honest bias-aware (red) confidence intervals, with the dead zone of the bias-aware procedure, half-width 2B¯ = 1.78 per￾centage points, shaded about the null β0 = 0 (the band has the same width about any null). The estimate (5.85 pp) lies far outside the dead zone: detectable despite the conservatism. period violation, the honest interval widens wi… view at source ↗
Figure 11
Figure 11. Figure 11: VAT pass-through to profits (Benzarti and Carloni, 2019): the honest interval for the 2009 profit effect as a function of the relative-magnitudes bound M¯ . Red bars exclude zero (significant); grey bars cover zero, so the honest interval now covers β0 = 0 and the estimate has entered the dead zone of the no-effect test. The lower limit crosses zero at the breakdown M¯ ≈ 1.75 (green dashed). The conventio… view at source ↗

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