{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:H744BITHKBVM4XB4SPNYWIAKSJ","short_pith_number":"pith:H744BITH","schema_version":"1.0","canonical_sha256":"3ff9c0a267506ace5c3c93db8b200a924303f1358ed67b52a9ef0541c6e6c574","source":{"kind":"arxiv","id":"2104.03802","version":4},"attestation_state":"computed","paper":{"title":"Average Direct and Indirect Causal Effects under Interference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"stat.ME","authors_text":"Shuangning Li, Stefan Wager, Yuchen Hu","submitted_at":"2021-04-08T14:28:16Z","abstract_excerpt":"We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2104.03802","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-04-08T14:28:16Z","cross_cats_sorted":["econ.EM"],"title_canon_sha256":"34dbafdf0db94ba98ebe5e9c47fb535604aede792559e96308bdd9c0a290c0b7","abstract_canon_sha256":"5d00e654967a0a12f936f073f3492950e04d6c80795c263f22c0c216f0f7051f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:47:51.956838Z","signature_b64":"CxZnE9RWq9bi0G180hdILgxf+84Cv1wgynMTYP0LLb5M1bleuVBk/1Trp7EBNDDmJgfwvrgL1Y1KgD8iVzeiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ff9c0a267506ace5c3c93db8b200a924303f1358ed67b52a9ef0541c6e6c574","last_reissued_at":"2026-07-05T03:47:51.956196Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:47:51.956196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average Direct and Indirect Causal Effects under Interference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"stat.ME","authors_text":"Shuangning Li, Stefan Wager, Yuchen Hu","submitted_at":"2021-04-08T14:28:16Z","abstract_excerpt":"We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.03802","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.03802/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2104.03802","created_at":"2026-07-05T03:47:51.956254+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.03802v4","created_at":"2026-07-05T03:47:51.956254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.03802","created_at":"2026-07-05T03:47:51.956254+00:00"},{"alias_kind":"pith_short_12","alias_value":"H744BITHKBVM","created_at":"2026-07-05T03:47:51.956254+00:00"},{"alias_kind":"pith_short_16","alias_value":"H744BITHKBVM4XB4","created_at":"2026-07-05T03:47:51.956254+00:00"},{"alias_kind":"pith_short_8","alias_value":"H744BITH","created_at":"2026-07-05T03:47:51.956254+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.15119","citing_title":"Identification and Estimation of Staggered Difference-in-Differences with Network Spillovers","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ","json":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ.json","graph_json":"https://pith.science/api/pith-number/H744BITHKBVM4XB4SPNYWIAKSJ/graph.json","events_json":"https://pith.science/api/pith-number/H744BITHKBVM4XB4SPNYWIAKSJ/events.json","paper":"https://pith.science/paper/H744BITH"},"agent_actions":{"view_html":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ","download_json":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ.json","view_paper":"https://pith.science/paper/H744BITH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.03802&json=true","fetch_graph":"https://pith.science/api/pith-number/H744BITHKBVM4XB4SPNYWIAKSJ/graph.json","fetch_events":"https://pith.science/api/pith-number/H744BITHKBVM4XB4SPNYWIAKSJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ/action/storage_attestation","attest_author":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ/action/author_attestation","sign_citation":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ/action/citation_signature","submit_replication":"https://pith.science/pith/H744BITHKBVM4XB4SPNYWIAKSJ/action/replication_record"}},"created_at":"2026-07-05T03:47:51.956254+00:00","updated_at":"2026-07-05T03:47:51.956254+00:00"}