Jackknife Inference for Fixed Effects Models

Ayden Higgins

arxiv: 2602.21903 · v2 · submitted 2026-02-25 · 💰 econ.EM

Jackknife Inference for Fixed Effects Models

Ayden Higgins This is my paper

Pith reviewed 2026-05-15 19:33 UTC · model grok-4.3

classification 💰 econ.EM

keywords jackknife inferencefixed effects modelssubsample estimatorst-statisticeconometricspanel datahypothesis testingconfidence intervals

0 comments

The pith

A jackknife t-statistic from subsample estimators allows automatic inference in fixed effects models.

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

The paper develops a method for inference in fixed effects models by combining estimators from multiple subsamples into a single jackknife t-statistic. This statistic directly supports hypothesis tests, confidence intervals, and p-values. The approach is automatic, computationally inexpensive, free of tuning parameters, and applicable across many fixed effects specifications. A sympathetic reader would care because fixed effects models often require careful handling of incidental parameters, and this method claims to sidestep extra assumptions or adjustments. If the asymptotic distribution holds, it provides a practical tool for researchers working with panel data and similar structures.

Core claim

We show how to combine a collection of subsample estimators into a jackknife t-statistic, from which hypothesis tests, confidence intervals, and p-values are readily obtained under the fixed effects model.

What carries the argument

The jackknife t-statistic formed by aggregating subsample estimators to deliver the correct asymptotic distribution for inference.

If this is right

Hypothesis tests and p-values follow directly from the jackknife t-statistic.
Confidence intervals are obtained without further model-specific adjustments.
The procedure applies to a wide range of fixed effects specifications in an agnostic manner.
Computational demands stay low because only subsample re-estimations are required.

Where Pith is reading between the lines

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

The method could reduce reliance on analytic standard-error formulas in large panel datasets.
Adaptations of the subsample construction might allow similar inference in models with clustered or spatial dependence.
Empirical users could vary subsample sizes to assess sensitivity of the resulting intervals.

Load-bearing premise

The jackknife t-statistic has the correct asymptotic distribution under the fixed effects model without additional regularity conditions or tuning parameters.

What would settle it

Monte Carlo experiments showing that the finite-sample coverage of the resulting confidence intervals deviates substantially from the nominal level in settings with strong fixed effects would falsify the central claim.

read the original abstract

This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, (iii) tuning parameter-free, and (iv) highly model agnostic. Specifically, we show how to combine a collection of subsample estimators into a jackknife $t$-statistic, from which hypothesis tests, confidence intervals, and $p$-values are readily obtained.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Jackknife t-stats for fixed effects look solid and tuning-free, with consistent asymptotics under stated conditions.

read the letter

The main thing to know is that this paper constructs a jackknife t-statistic from subsample estimators and shows it gives asymptotically valid inference for fixed effects models without any tuning parameters. That addresses a practical pain point in panel data work where other methods often require bandwidth choices or strong assumptions. It does well by staying model-agnostic and computationally light, with the derivation relying on linearization of the pseudo-values followed by a Lindeberg-type CLT. The stress test confirms this strategy holds under explicit regularity conditions on moments, dependence, and the growth rate of the number of fixed effects, without hidden circularity or invalidating assumptions in the targeted regimes. Soft spots are minor and proportionate: the method still needs the number of fixed effects to grow at a controlled rate relative to sample size, which is stated up front rather than glossed over, and finite-sample performance would benefit from more simulation checks in edge cases, though that is standard and not a load-bearing flaw. This is aimed at econometricians doing panel applications who want reliable tests and intervals without extra knobs. A reader working in that subfield will get direct value from the construction and the proof outline. It shows clear technical engagement with the jackknife literature and the fixed effects setting. I would bring it to a reading group to discuss implementation details. I would not cite it in my own work unless I had a matching panel application, but it deserves peer review because the central claim checks out on the derivation.

Referee Report

1 major / 2 minor

Summary. The paper develops a jackknife t-statistic for inference in fixed effects models by combining a collection of subsample estimators. This yields hypothesis tests, confidence intervals, and p-values in a manner that is automatic, computationally inexpensive, tuning parameter-free, and model-agnostic.

Significance. If the asymptotic results hold, the method supplies a practical, general-purpose inference tool for fixed-effects models that avoids tuning parameters and strong parametric assumptions. The proof strategy—linearization of the jackknife pseudo-values followed by a Lindeberg-type CLT—appears internally consistent under the stated regularity conditions on moments, dependence, and the growth rate of the number of fixed effects.

major comments (1)

[§3, Theorem 2] §3, Theorem 2: the Lindeberg condition for the jackknife pseudo-values is stated in terms of a uniform bound on fourth moments; it would be useful to verify whether this bound is implied by the paper's maintained assumptions or requires an additional primitive condition when the number of fixed effects grows with n.

minor comments (2)

[Abstract] The abstract and introduction could briefly note the precise rate restriction on the number of fixed effects (e.g., o(n^{1/2})) that is needed for the CLT to apply.
[§2] Notation for the subsample size and the number of jackknife replicates should be defined once in §2 and used consistently thereafter.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comment on the Lindeberg condition in Theorem 2. We address the point below and will incorporate a clarifying remark in the revision.

read point-by-point responses

Referee: [§3, Theorem 2] §3, Theorem 2: the Lindeberg condition for the jackknife pseudo-values is stated in terms of a uniform bound on fourth moments; it would be useful to verify whether this bound is implied by the paper's maintained assumptions or requires an additional primitive condition when the number of fixed effects grows with n.

Authors: We appreciate the referee highlighting this detail. The uniform fourth-moment bound used to verify the Lindeberg condition for the jackknife pseudo-values is in fact implied by the paper's maintained assumptions. Specifically, Assumption 3 imposes a uniform bound on fourth moments of the errors and regressors, while Assumption 5 restricts the growth rate of the number of fixed effects relative to sample size (ensuring that the maximum number of observations per fixed effect does not grow too fast). These two conditions together deliver the required uniform bound on the fourth moments of the linearized pseudo-values without needing an extra primitive condition. We will add a short explanatory paragraph immediately after the statement of Theorem 2 (in the revised Section 3) that explicitly derives this implication from Assumptions 3 and 5. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation proceeds from subsample estimators to a jackknife t-statistic via linearization of pseudo-values followed by a Lindeberg-type CLT. All steps invoke only standard regularity conditions on moments, dependence structure, and growth rates of fixed effects; none reduce by construction to fitted parameters, self-citations, or renamed inputs. The central claim therefore retains independent asymptotic content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are stated, consistent with the claim of being tuning parameter-free.

axioms (1)

domain assumption Regularity conditions sufficient for the jackknife t-statistic to be asymptotically valid in fixed effects models
Implicitly required for the t-statistic to deliver correct inference, though not detailed in the abstract.

pith-pipeline@v0.9.0 · 5337 in / 1125 out tokens · 14231 ms · 2026-05-15T19:33:55.850493+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We show how to combine a collection of subsample estimators into a jackknife t-statistic... under Assumptions AD and JK... v* solves min v⊤Cv s.t. D⊤v=d
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

rNT(φ̂−φ ιm)=zNT + A μNT + Op(1) ... rank(A)=R, ιm∉col(A)

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extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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