{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:17:26Z","timestamp":1785403046450,"version":"3.56.0"},"reference-count":65,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:00:00Z","timestamp":1769558400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"funder":[{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["Tier 1 RG51\/24"],"award-info":[{"award-number":["Tier 1 RG51\/24"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["Tier 2 MOE-000767-00"],"award-info":[{"award-number":["Tier 2 MOE-000767-00"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["Discovery Grant DP200101498"],"award-info":[{"award-number":["Discovery Grant DP200101498"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["Discovery Grant DP210103094"],"award-info":[{"award-number":["Discovery Grant DP210103094"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"abstract":"<jats:p>\n                    Pretesting for exogeneity has become routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares or IV-based method is appropriate. Guggenberger (2010a,\n                    <jats:italic>Econometric Theory<\/jats:italic>\n                    , 26, 369\u2013382) shows that the second-stage test \u2013 based on the outcome of a Durbin-Wu-Hausman-type pretest in the first stage \u2013 exhibits extreme size distortion, with asymptotic size equal to 1 when the standard critical values are used. In this paper, we first show that both conditional and unconditional on the data, standard wild bootstrap procedures are invalid for two-stage testing. Second, we propose an identification-robust two-stage test statistic that switches between OLS-based and weak-IV-robust statistics. Third, we develop a size-adjusted wild bootstrap approach for our two-stage test that integrates specific wild bootstrap critical values with an appropriate size-adjustment method. We establish uniform validity of this procedure under conditional heteroskedasticity or clustering in the sense that the resulting tests achieve correct asymptotic size, regardless of whether the identification is strong or weak. Our procedure is especially valuable for empirical researchers facing potential weak identification. In such settings, its power advantage is notable: whereas weak-IV-robust methods maintain correct size but often suffer from relatively low power, our approach achieves better performance.\n                  <\/jats:p>","DOI":"10.1017\/s0266466625100327","type":"journal-article","created":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T08:13:27Z","timestamp":1769588007000},"page":"1-33","source":"Crossref","is-referenced-by-count":0,"title":["IDENTIFICATION-ROBUST TWO-STAGE BOOTSTRAP TESTS WITH PRETESTING FOR EXOGENEITY"],"prefix":"10.1017","author":[{"given":"Firmin","family":"Doko Tchatoka","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/028g18b61","id-type":"ROR","asserted-by":"publisher"}],"name":"Adelaide University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjie","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e7b5302","id-type":"ROR","asserted-by":"publisher"}],"name":"Nanyang Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,28]]},"reference":[{"key":"S0266466625100327_r17","doi-asserted-by":"publisher","DOI":"10.1017\/S026646662000016X"},{"key":"S0266466625100327_r34","doi-asserted-by":"publisher","DOI":"10.3982\/QE989"},{"key":"S0266466625100327_r41","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-economics-092123-111021"},{"key":"S0266466625100327_r2","doi-asserted-by":"crossref","first-page":"721","DOI":"10.3982\/ECTA7015","article-title":"Hybrid and size-corrected subsampling methods","volume":"77","author":"Andrews","year":"2009a","journal-title":"Econometrica"},{"key":"S0266466625100327_r54","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2019.1592754"},{"key":"S0266466625100327_r1","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.3982\/ECTA9456","article-title":"Estimation and inference with weak, semi-strong, and strong identification","volume":"80","author":"Andrews","year":"2012","journal-title":"Econometrica"},{"key":"S0266466625100327_r64","doi-asserted-by":"crossref","unstructured":"Wang, W. , & Zhang, Y. (2025). Gradient wild bootstrap for instrumental variable quantile regressions with weak and few clusters. Preprint. arXiv:2408.10686.","DOI":"10.2139\/ssrn.4938803"},{"key":"S0266466625100327_r30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.11.003"},{"key":"S0266466625100327_r55","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdab097"},{"key":"S0266466625100327_r22","doi-asserted-by":"publisher","DOI":"10.1111\/ectj.12042"},{"key":"S0266466625100327_r38","doi-asserted-by":"publisher","DOI":"10.1198\/073500108000000024"},{"key":"S0266466625100327_r32","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1251"},{"key":"S0266466625100327_r15","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA16557"},{"key":"S0266466625100327_r3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.02.001"},{"key":"S0266466625100327_r25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2020.04.022"},{"key":"S0266466625100327_r18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.003"},{"key":"S0266466625100327_r60","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2018.07.003"},{"key":"S0266466625100327_r58","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466625100327_r10","first-page":"450","article-title":"Children and their parents\u2019 labor supply: Evidence from exogenous variation in family size","volume":"88","author":"Angrist","year":"1998","journal-title":"The American Economic Review"},{"key":"S0266466625100327_r56","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.10.008"},{"key":"S0266466625100327_r52","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466622000433"},{"key":"S0266466625100327_r29","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609100026"},{"key":"S0266466625100327_r21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.04.035"},{"key":"S0266466625100327_r35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050048"},{"key":"S0266466625100327_r19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00247.x"},{"key":"S0266466625100327_r36","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2017.1307579"},{"key":"S0266466625100327_r16","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00139"},{"key":"S0266466625100327_r45","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2023.105602"},{"key":"S0266466625100327_r43","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050036"},{"key":"S0266466625100327_r50","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2022.04.001"},{"key":"S0266466625100327_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.02.001"},{"key":"S0266466625100327_r8","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-economics-080218-025643"},{"key":"S0266466625100327_r11","doi-asserted-by":"publisher","DOI":"10.2307\/2937954"},{"key":"S0266466625100327_r13","doi-asserted-by":"publisher","DOI":"10.1162\/rest.90.3.414"},{"key":"S0266466625100327_r57","doi-asserted-by":"publisher","DOI":"10.1177\/1536867X19830877"},{"key":"S0266466625100327_r48","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecosta.2021.11.009"},{"key":"S0266466625100327_r61","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2015.12.016"},{"key":"S0266466625100327_r51","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2508"},{"key":"S0266466625100327_r65","unstructured":"Yap, L. (2024). Inference with many weak instruments and heterogeneity. Preprint. arXiv:2408.11193."},{"key":"S0266466625100327_r44","unstructured":"Ligtenberg, J. W. (2023). Inference in IV models with clustered dependence, many instruments and weak identification. Preprint, arXiv:2306.08559."},{"key":"S0266466625100327_r20","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.07221"},{"key":"S0266466625100327_r63","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2024.105727"},{"key":"S0266466625100327_r66","doi-asserted-by":"publisher","DOI":"10.1016\/j.euroecorev.2022.104112"},{"key":"S0266466625100327_r47","doi-asserted-by":"publisher","DOI":"10.2307\/1914241"},{"key":"S0266466625100327_r6","doi-asserted-by":"publisher","DOI":"10.3386\/t0299"},{"key":"S0266466625100327_r24","doi-asserted-by":"publisher","DOI":"10.1111\/ectj.12021"},{"key":"S0266466625100327_r26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2024.105821"},{"key":"S0266466625100327_r5","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609100051"},{"key":"S0266466625100327_r40","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2017.06.004"},{"key":"S0266466625100327_r31","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466611000375"},{"key":"S0266466625100327_r59","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2020.109157"},{"key":"S0266466625100327_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2022.12.012"},{"key":"S0266466625100327_r28","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00204-5"},{"key":"S0266466625100327_r53","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2017.05.001"},{"key":"S0266466625100327_r62","first-page":"1886","article-title":"Bootstrap-based selection for instrumental variables model","volume":"35","author":"Wang","year":"2015","journal-title":"Economics Bulletin"},{"key":"S0266466625100327_r33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.09.009"},{"key":"S0266466625100327_r49","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2019.1677473"},{"key":"S0266466625100327_r12","doi-asserted-by":"publisher","DOI":"10.1162\/003355399556061"},{"key":"S0266466625100327_r14","doi-asserted-by":"publisher","DOI":"10.3368\/jhr.50.2.317"},{"key":"S0266466625100327_r39","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009403"},{"key":"S0266466625100327_r4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.01.002"},{"key":"S0266466625100327_r7","doi-asserted-by":"publisher","DOI":"10.1093\/qje\/qjx023"},{"key":"S0266466625100327_r27","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2710"},{"key":"S0266466625100327_r42","doi-asserted-by":"publisher","DOI":"10.1257\/aer.20211063"},{"key":"S0266466625100327_r46","unstructured":"Lim, D. , Wang, W. , & Zhang, Y. (2024b). A dimension-agnostic bootstrap Anderson-Rubin test for instrumental variable regressions. Preprint. arXiv:2412.01603."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466625100327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T08:13:30Z","timestamp":1769588010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466625100327\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,28]]},"references-count":65,"alternative-id":["S0266466625100327"],"URL":"https:\/\/doi.org\/10.1017\/s0266466625100327","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,28]]}}}