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The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 \u2212 \u03b5<jats:sub><jats:italic>P<\/jats:italic><\/jats:sub>, where \u03b5<jats:sub><jats:italic>P<\/jats:italic><\/jats:sub> is the pretest nominal size, for a parameter space that allows for local non\u2010exogeneity of the instruments but rules out weak instruments. Copyright \u00a9 2011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.1251","type":"journal-article","created":{"date-parts":[[2011,6,3]],"date-time":"2011-06-03T13:52:11Z","timestamp":1307109131000},"page":"1138-1160","source":"Crossref","is-referenced-by-count":24,"title":["On the size distortion of tests after an overidentifying restrictions pretest"],"prefix":"10.1002","volume":"27","author":[{"given":"Patrik","family":"Guggenberger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gitanjali","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,6,2]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1257\/aer.91.5.1369"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730090"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/2951781"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA7015"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609100051"},{"key":"e_1_2_9_7_1","unstructured":"AndrewsD ChengX GuggenbergerP.2009.Generic results for establishing the asymptotic size of confidence intervals and tests. 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