{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:6LH64D3X4GECHOFWS72LCE5XX2","short_pith_number":"pith:6LH64D3X","schema_version":"1.0","canonical_sha256":"f2cfee0f77e18823b8b697f4b113b7beac5a54e36229cdb54135cdbb27298274","source":{"kind":"arxiv","id":"2107.07942","version":6},"attestation_state":"computed","paper":{"title":"Flexible Covariate Adjustments in Regression Discontinuity Designs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"econ.EM","authors_text":"Christoph Rothe, Claudia Noack, Tomasz Olma","submitted_at":"2021-07-16T15:00:06Z","abstract_excerpt":"Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than existing methods and can accommodate many covariates. Our estimators are simple to implement and involve running a standard RD analysis after subtracting a function of the covariates from the original outcome variable. We characterize the function of the covariates that minimizes the asymptotic variance of these estimators. We also show that t"},"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":"2107.07942","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-07-16T15:00:06Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"8b970251da606679ea9eed952563c7991dba3e40040c011f58901e6b81f7995e","abstract_canon_sha256":"3943ed8067fabab0515a7adc493c2c91fe08f12a6a9b6553c1d18b4cdda9fbd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:36.947471Z","signature_b64":"zMYZ039euwgTYGNlWR9ejdmZwNACVE9RS+I00+TRJTh7XmbYi4HpmHhNxrwXyQ9LRHg9hpIO7Nh4b7kDr48OAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2cfee0f77e18823b8b697f4b113b7beac5a54e36229cdb54135cdbb27298274","last_reissued_at":"2026-07-01T01:17:36.946989Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:36.946989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flexible Covariate Adjustments in Regression Discontinuity Designs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"econ.EM","authors_text":"Christoph Rothe, Claudia Noack, Tomasz Olma","submitted_at":"2021-07-16T15:00:06Z","abstract_excerpt":"Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than existing methods and can accommodate many covariates. Our estimators are simple to implement and involve running a standard RD analysis after subtracting a function of the covariates from the original outcome variable. We characterize the function of the covariates that minimizes the asymptotic variance of these estimators. We also show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.07942","kind":"arxiv","version":6},"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/2107.07942/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":"2107.07942","created_at":"2026-07-01T01:17:36.947046+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.07942v6","created_at":"2026-07-01T01:17:36.947046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.07942","created_at":"2026-07-01T01:17:36.947046+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LH64D3X4GEC","created_at":"2026-07-01T01:17:36.947046+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LH64D3X4GECHOFW","created_at":"2026-07-01T01:17:36.947046+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LH64D3X","created_at":"2026-07-01T01:17:36.947046+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.00289","citing_title":"Extrapolation in Regression Discontinuity Design Using Comonotonicity","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2","json":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2.json","graph_json":"https://pith.science/api/pith-number/6LH64D3X4GECHOFWS72LCE5XX2/graph.json","events_json":"https://pith.science/api/pith-number/6LH64D3X4GECHOFWS72LCE5XX2/events.json","paper":"https://pith.science/paper/6LH64D3X"},"agent_actions":{"view_html":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2","download_json":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2.json","view_paper":"https://pith.science/paper/6LH64D3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.07942&json=true","fetch_graph":"https://pith.science/api/pith-number/6LH64D3X4GECHOFWS72LCE5XX2/graph.json","fetch_events":"https://pith.science/api/pith-number/6LH64D3X4GECHOFWS72LCE5XX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2/action/storage_attestation","attest_author":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2/action/author_attestation","sign_citation":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2/action/citation_signature","submit_replication":"https://pith.science/pith/6LH64D3X4GECHOFWS72LCE5XX2/action/replication_record"}},"created_at":"2026-07-01T01:17:36.947046+00:00","updated_at":"2026-07-01T01:17:36.947046+00:00"}