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pith:TAXU5CIZ

pith:2026:TAXU5CIZI7CGHZY5FR6J43PI5S

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Never Too LATE: A Fully Stochastic Update to the Potential Outcome Framework

Hanti Lin

The instrumental variable estimand identifies the degree-of-compliance-weighted average treatment effect when potential outcomes are modeled as stochastic Bernoulli parameters.

arxiv:2605.12847 v1 · 2026-05-13 · stat.ME

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Claims

C1strongest claim

I propose a fully stochastic update to the Rubin causal model that drops the assumption of the unique-parallel-universe view: stochastic potential outcomes are introduced as Bernoulli parameters in their own (small) probability spaces, and are connected to observables via the factorization rule of a causal Bayes net. Within this framework, I define a Degree-of-compliance-weighted Average Treatment Effect (DATE) and prove that, under assumptions analogous to those used for the LATE but rewritten for the fully stochastic setting, the DATE equals the usual IV estimand.

C2weakest assumption

The factorization rule of a causal Bayes net connects the stochastic potential outcomes to observables, and the assumptions analogous to monotonicity, exclusion restriction, and instrument relevance hold when rewritten in terms of the stochastic Bernoulli parameters.

C3one line summary

A fully stochastic potential outcome model proves that the IV estimand identifies the degree-of-compliance-weighted average treatment effect (DATE) without assuming deterministic parallel universes.

References

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[1] Identification of Causal Effects Using Instrumental Variables 1996

[2] Causal Inference without Counterfactuals 2000

[3] Interpretation and Choice of Effect Measures in Epidemiologic Analysis 1987

[4] Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics 2020

[5] Identification and Estimation of Local Average Treatment Effects 1994

Receipt and verification

First computed	2026-05-18T03:09:11.883929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

982f4e891947c463e71d2c7c9e6de8ecbcc0b8b1df504638f3bcb1c979980af4

Aliases

arxiv: 2605.12847 · arxiv_version: 2605.12847v1 · doi: 10.48550/arxiv.2605.12847 · pith_short_12: TAXU5CIZI7CG · pith_short_16: TAXU5CIZI7CGHZY5 · pith_short_8: TAXU5CIZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TAXU5CIZI7CGHZY5FR6J43PI5S \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 982f4e891947c463e71d2c7c9e6de8ecbcc0b8b1df504638f3bcb1c979980af4

Canonical record JSON

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    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T00:45:56Z",
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