Pith Number

pith:26RXUZKT

pith:2026:26RXUZKTAP4LTTRDA5EQ2NECES

not attested not anchored not stored refs pending

Stacked Triple Differences

Meng Hsuan Hsieh

A linear regression on stacked four-cell triple-difference data identifies a cell-size-weighted average of treatment effects.

arxiv:2604.22982 v2 · 2026-04-24 · econ.EM

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\usepackage{pith}
\pithnumber{26RXUZKTAP4LTTRDA5EQ2NECES}

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

I prove that, at each post-treatment event-time, a linear regression with fully saturated fixed-effects applied to the stacked dataset identifies a strictly positive, cell-size-weighted average of stack-level conditional average treatment effects, with stack weights proportional to stack-level cell sizes.

C2weakest assumption

The assumption that clean comparison cohorts satisfy pairwise parallel trends with treated cohorts within each stack, and that treatment-ineligible units provide valid counterfactuals without anticipation effects or spillovers.

C3one line summary

Stacked DDD appends self-contained stacks of treated and clean comparison cohorts to identify a cell-size-weighted average of stack-level conditional average treatment effects via saturated fixed-effects regression.

Receipt and verification

First computed	2026-05-20T00:04:32.622677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7a37a655303f8b9ce2307490d348224a0349c9735f9cba9fefbc0a678d2ffac

Aliases

arxiv: 2604.22982 · arxiv_version: 2604.22982v2 · doi: 10.48550/arxiv.2604.22982 · pith_short_12: 26RXUZKTAP4L · pith_short_16: 26RXUZKTAP4LTTRD · pith_short_8: 26RXUZKT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/26RXUZKTAP4LTTRDA5EQ2NECES \
  | 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: d7a37a655303f8b9ce2307490d348224a0349c9735f9cba9fefbc0a678d2ffac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8e63d817684d32803a75e43ad2d3f1b0bb30c7c0c76eec2531adc24bdd05170",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.EM",
    "submitted_at": "2026-04-24T19:51:17Z",
    "title_canon_sha256": "f3db225d0745829b33f9e17bfda2d43c337cf9c3d80441192d46eec901430206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22982",
    "kind": "arxiv",
    "version": 2
  }
}