{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:X3M6OKZ5AEEGFNIOY44YTWTMBD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81b954057606b96deba59c3ac9c6df44a1423cf41cca16fe68956147ce5b79b7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-02T06:44:18Z","title_canon_sha256":"a04c68ec0682b485bac49b29a5bb52a3004ec8cdc821df70f462a48569daad17"},"schema_version":"1.0","source":{"id":"1109.0362","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0362","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0362v4","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0362","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"X3M6OKZ5AEEG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X3M6OKZ5AEEGFNIO","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X3M6OKZ5","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:2c17b20fb2f5ccb81ee544054789d3d8072b8c9daf5a61ac43e89591fdee574b","target":"graph","created_at":"2026-05-18T01:34:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper considers treatment effects under endogeneity with complex heterogeneity in the selection equation. We model the outcome of an endogenous treatment as a triangular system, where both the outcome and first-stage equations consist of a random coefficients model. The first-stage specifically allows for nonmonotone selection into treatment. We provide conditions under which marginal distributions of potential outcomes, average and quantile treatment effects, all conditional on first-stage random coefficients, are identified. Under the same conditions, we derive bounds on the (conditiona","authors_text":"Eric Gautier (TSE), Stefan Hoderlein","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-02T06:44:18Z","title":"A triangular treatment effect model with random coefficients in the selection equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0362","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d9cd71fe535fd3e2e8ff531ea57aa2c01b7cee1001e6fadb5234ca071013871f","target":"record","created_at":"2026-05-18T01:34:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81b954057606b96deba59c3ac9c6df44a1423cf41cca16fe68956147ce5b79b7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-02T06:44:18Z","title_canon_sha256":"a04c68ec0682b485bac49b29a5bb52a3004ec8cdc821df70f462a48569daad17"},"schema_version":"1.0","source":{"id":"1109.0362","kind":"arxiv","version":4}},"canonical_sha256":"bed9e72b3d010862b50ec73989da6c08cc14466607740133e731c114fd1d348a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bed9e72b3d010862b50ec73989da6c08cc14466607740133e731c114fd1d348a","first_computed_at":"2026-05-18T01:34:51.344252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:51.344252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N6lSaiXN+D9ZxQ7oz2g4LekuF+orIhf1r5UEJkaWLmMJ3npnF0I9Viz2XkOdIIwFnT8Jm3vdl9vRc/1macaUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:51.344696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0362","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9cd71fe535fd3e2e8ff531ea57aa2c01b7cee1001e6fadb5234ca071013871f","sha256:2c17b20fb2f5ccb81ee544054789d3d8072b8c9daf5a61ac43e89591fdee574b"],"state_sha256":"4e74d4d9548528bdb0e61fb61e1727819e7332440f94fe5ee29bacd8659c8f0b"}