{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T17:47:01Z","timestamp":1785779221277,"version":"3.56.0"},"reference-count":42,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. This allows for data\u2010driven selection of valid and relevant instruments and provides additional robustness against invalid instruments. Our approach extends previous work through a scale\u2010invariant prior structure and accommodates non\u2010Gaussian outcomes and treatments, offering greater flexibility than existing methods. The computational strategy uses conditional Bayes factors to update models separately for the outcome and treatments. We prove that this model selection procedure is consistent. In simulation experiments, gIVBMA outperforms current state\u2010of\u2010the\u2010art methods. We demonstrate its usefulness in two empirical applications: the effects of malaria and institutions on income per capita and the returns to schooling. A software implementation of gIVBMA is available in Julia.<\/jats:p>","DOI":"10.1002\/jae.70070","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T15:17:59Z","timestamp":1779463079000},"page":"669-683","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Model Averaging in Causal Instrumental Variable Models"],"prefix":"10.1002","volume":"41","author":[{"given":"Gregor","family":"Steiner","sequence":"first","affiliation":[{"name":"Department of Statistics University of Warwick  Coventry UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark","family":"Steel","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Warwick  Coventry UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1255(199901\/02)14:1<57::AID-JAE501>3.0.CO;2-G"},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2937954"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400829828"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA9626"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00144"},{"key":"e_1_2_13_7_1","first-page":"201","volume-title":"Aspects of Labour Market Behaviour: Essays in Honour of John Vanderkamp","author":"Card D.","year":"1995"},{"key":"e_1_2_13_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.05.012"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1093\/wber\/lhl001"},{"key":"e_1_2_13_10_1","first-page":"73","volume-title":"Handling Sparsity via the Horseshoe. 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