{"paper":{"title":"Granular Instrumental Variables in Large Panels: Identification and Inference Across Strong, Nearly Weak, and Weak GIV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"econ.EM","authors_text":"Gokul Gopalan Ramachandran","submitted_at":"2026-07-02T12:32:28Z","abstract_excerpt":"I develop the asymptotic theory of instrument strength for Granular Instrumental Variables (GIV) in large panels with both $N$ and $T$ growing. The strength of the GIV depends on the presence of dominant units. I formalise what dominance means and characterise three regimes of instrument strength. When a few units dominate the aggregate, the instrument is strong. The GIV estimator is consistent and asymptotically normal at the standard $\\sqrt{T}$ rate. When large units stand out but do not dominate, the instrument weakens. But I show that the parameter of interest remains recoverable. The GIV "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02095","kind":"arxiv","version":1},"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/2607.02095/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"}