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The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a \u201cdouble robustness\u201d property analogous to that of popular partially linear regression estimators. By contrast, the conventional VAR confidence interval with short\u2010to\u2010moderate lag length can severely undercover for misspecification that is small, difficult to detect statistically, and cannot be ruled out based on economic theory. The VAR confidence interval has robust coverage if, and only if, the lag length is so large that the interval is as wide as the LP interval.<\/jats:p>","DOI":"10.3982\/ecta23345","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T13:05:52Z","timestamp":1784207152000},"page":"1313-1343","source":"Crossref","is-referenced-by-count":4,"title":["Double Robustness of Local Projections and Some Unpleasant VARithmetic"],"prefix":"10.3982","volume":"94","author":[{"given":"Jos\u00e9 Luis","family":"Montiel Olea","sequence":"first","affiliation":[{"name":"Department of Economics, Cornell University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikkel","family":"Plagborg-M\u00f8ller","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Qian","sequence":"additional","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian K.","family":"Wolf","sequence":"additional","affiliation":[{"name":"Department of Economics, MIT"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2026]]},"reference":[{"issue":"1","key":"ecta70056-bib-0001","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.jeconom.2007.01.013","volume":"141","author":"Ai","year":"2007","journal-title":"Journal of Econometrics"},{"issue":"1","key":"ecta70056-bib-0002","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/j.1751-5823.2011.00131.x","volume":"79","author":"Alessi","year":"2011","journal-title":"International Statistical Review"},{"issue":"1","key":"ecta70056-bib-0003","doi-asserted-by":"crossref","first-page":"77","DOI":"10.3982\/QE1609","volume":"12","author":"Armstrong","year":"2021","journal-title":"Quantitative Economics"},{"issue":"6","key":"ecta70056-bib-0004","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.3982\/ECTA18597","volume":"90","author":"Armstrong","year":"2022","journal-title":"Econometrica"},{"issue":"4","key":"ecta70056-bib-0005","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"issue":"2","key":"ecta70056-bib-0006","doi-asserted-by":"crossref","first-page":"521","DOI":"10.3150\/11-BEJ410","volume":"19","author":"Belloni","year":"2013","journal-title":"Bernoulli"},{"issue":"3","key":"ecta70056-bib-0007","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0304-4076(93)90029-5","volume":"59","author":"Braun","year":"1993","journal-title":"Journal of Econometrics"},{"key":"ecta70056-bib-0008","series-title":"Springer Series in Statistics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-0320-4","volume-title":"Time Series: Theory and Methods","author":"Brockwell","year":"1991","edition":"second edition"},{"issue":"8","key":"ecta70056-bib-0009","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1016\/j.jmoneco.2008.09.010","volume":"55","author":"Chari","year":"2008","journal-title":"Journal of Monetary Economics"},{"issue":"1","key":"ecta70056-bib-0010","doi-asserted-by":"crossref","first-page":"C1","DOI":"10.1111\/ectj.12097","volume":"21","author":"Chernozhukov","year":"2018","journal-title":"The Econometrics Journal"},{"issue":"4","key":"ecta70056-bib-0011","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.3982\/ECTA16294","volume":"90","author":"Chernozhukov","year":"2022","journal-title":"Econometrica"},{"issue":"2","key":"ecta70056-bib-0012","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1214\/07-AOS500","volume":"36","author":"Genovese","year":"2008","journal-title":"The Annals of Statistics"},{"key":"ecta70056-bib-0013","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez-Casas\u00fas, Oriol and Frank Schorfheide (2025), \u201cMisspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs.\u201d Technical Report 33474, National Bureau of Economic Research.","DOI":"10.3386\/w33474"},{"issue":"2","key":"ecta70056-bib-0014","doi-asserted-by":"crossref","first-page":"246","DOI":"10.2307\/2345178","volume":"139","author":"Granger","year":"1976","journal-title":"Journal of the Royal Statistical Society. 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