{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BVSDYNGSUV4JA6XIPYAGRCPWMT","short_pith_number":"pith:BVSDYNGS","canonical_record":{"source":{"id":"2105.03737","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-05-08T16:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"40a13d82cf50ed6a50be91dbdff08f79081fc4c01eff119669048b6de9f9f8a7","abstract_canon_sha256":"3fea09e8774f0ac15eab2c2eb537b4271e0a5fcdc66a8eb76b7d80d585852dcc"},"schema_version":"1.0"},"canonical_sha256":"0d643c34d2a578907ae87e006889f664ea7d5e2c0e5e01fbef59e6e5f8d16546","source":{"kind":"arxiv","id":"2105.03737","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.03737","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2105.03737v3","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.03737","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"BVSDYNGSUV4J","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"BVSDYNGSUV4JA6XI","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"BVSDYNGS","created_at":"2026-07-05T06:19:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BVSDYNGSUV4JA6XIPYAGRCPWMT","target":"record","payload":{"canonical_record":{"source":{"id":"2105.03737","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-05-08T16:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"40a13d82cf50ed6a50be91dbdff08f79081fc4c01eff119669048b6de9f9f8a7","abstract_canon_sha256":"3fea09e8774f0ac15eab2c2eb537b4271e0a5fcdc66a8eb76b7d80d585852dcc"},"schema_version":"1.0"},"canonical_sha256":"0d643c34d2a578907ae87e006889f664ea7d5e2c0e5e01fbef59e6e5f8d16546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:19:14.490211Z","signature_b64":"Pe/N6ktyu7hhaOss1HAVtP9lVXE4RDbMC+VERTi/23L5z6pvOMiw/9PexS66lm0MMSDvyKGnbL2y4FW/Bm8UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d643c34d2a578907ae87e006889f664ea7d5e2c0e5e01fbef59e6e5f8d16546","last_reissued_at":"2026-07-05T06:19:14.489868Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:19:14.489868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.03737","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9kOCCQ991JozbsNqJlgzoODgWFcoClF5sX4t2DHJVU6LItXCRtXSnJLr0g56DpQ5f+dOEMmTBccMgjT+L/dDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:40:01.454676Z"},"content_sha256":"af11fd138f47f265d7f1d45329f9d2344279fe81c1cefb8450be24f284e4988d","schema_version":"1.0","event_id":"sha256:af11fd138f47f265d7f1d45329f9d2344279fe81c1cefb8450be24f284e4988d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BVSDYNGSUV4JA6XIPYAGRCPWMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Difference-in-Differences Estimation with Spatial Spillovers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"econ.EM","authors_text":"Kyle Butts","submitted_at":"2021-05-08T16:43:02Z","abstract_excerpt":"Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In this paper, I introduce a potential outcomes framework to model spillover effects and decompose the estimate's bias in two parts: (1) the control group no longer identifies the counterfactual trend because their outcomes are affected by treatment and (2) changes in treated units' outcomes reflect the effect of their own treatment status and the effect from the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.03737","kind":"arxiv","version":3},"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/2105.03737/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjAp5UsnzIMXCXAVDwMSuHIRxymfvi6//NGCIm8Nion7KSnsWGHDK/WgvrB4On05eKI9zGBJuutKRz4/atm4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:40:01.455509Z"},"content_sha256":"c5d78eafd79ff695148782bdac7eb84e2f63a6f7727dec6471dbc702dc5ff014","schema_version":"1.0","event_id":"sha256:c5d78eafd79ff695148782bdac7eb84e2f63a6f7727dec6471dbc702dc5ff014"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/bundle.json","state_url":"https://pith.science/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T07:40:01Z","links":{"resolver":"https://pith.science/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT","bundle":"https://pith.science/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/bundle.json","state":"https://pith.science/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVSDYNGSUV4JA6XIPYAGRCPWMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BVSDYNGSUV4JA6XIPYAGRCPWMT","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":"3fea09e8774f0ac15eab2c2eb537b4271e0a5fcdc66a8eb76b7d80d585852dcc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-05-08T16:43:02Z","title_canon_sha256":"40a13d82cf50ed6a50be91dbdff08f79081fc4c01eff119669048b6de9f9f8a7"},"schema_version":"1.0","source":{"id":"2105.03737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.03737","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2105.03737v3","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.03737","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"BVSDYNGSUV4J","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"BVSDYNGSUV4JA6XI","created_at":"2026-07-05T06:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"BVSDYNGS","created_at":"2026-07-05T06:19:14Z"}],"graph_snapshots":[{"event_id":"sha256:c5d78eafd79ff695148782bdac7eb84e2f63a6f7727dec6471dbc702dc5ff014","target":"graph","created_at":"2026-07-05T06:19:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.03737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In this paper, I introduce a potential outcomes framework to model spillover effects and decompose the estimate's bias in two parts: (1) the control group no longer identifies the counterfactual trend because their outcomes are affected by treatment and (2) changes in treated units' outcomes reflect the effect of their own treatment status and the effect from the","authors_text":"Kyle Butts","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-05-08T16:43:02Z","title":"Difference-in-Differences Estimation with Spatial Spillovers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.03737","kind":"arxiv","version":3},"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:af11fd138f47f265d7f1d45329f9d2344279fe81c1cefb8450be24f284e4988d","target":"record","created_at":"2026-07-05T06:19:14Z","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":"3fea09e8774f0ac15eab2c2eb537b4271e0a5fcdc66a8eb76b7d80d585852dcc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.EM","submitted_at":"2021-05-08T16:43:02Z","title_canon_sha256":"40a13d82cf50ed6a50be91dbdff08f79081fc4c01eff119669048b6de9f9f8a7"},"schema_version":"1.0","source":{"id":"2105.03737","kind":"arxiv","version":3}},"canonical_sha256":"0d643c34d2a578907ae87e006889f664ea7d5e2c0e5e01fbef59e6e5f8d16546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d643c34d2a578907ae87e006889f664ea7d5e2c0e5e01fbef59e6e5f8d16546","first_computed_at":"2026-07-05T06:19:14.489868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:19:14.489868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pe/N6ktyu7hhaOss1HAVtP9lVXE4RDbMC+VERTi/23L5z6pvOMiw/9PexS66lm0MMSDvyKGnbL2y4FW/Bm8UCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:19:14.490211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.03737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af11fd138f47f265d7f1d45329f9d2344279fe81c1cefb8450be24f284e4988d","sha256:c5d78eafd79ff695148782bdac7eb84e2f63a6f7727dec6471dbc702dc5ff014"],"state_sha256":"4db42246b1d192ab72cb2cae93d14c259a166af246315ad54a2e06b4b2495800"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAYMmjsUYXHIft0yHbMPv5/nQ2yJhoj89OQtl6tVnf0bnWUrVpvIxgs0wOsP74XhjHl9kgUyMvryvyh/yXcKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T07:40:01.462251Z","bundle_sha256":"c29258c627e3a4fab7c2717e59806eb7c4876c4803771d0016b1c3072f31f8bd"}}