{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T19:44:31Z","timestamp":1780343071208,"version":"3.54.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,8,18]],"date-time":"2009-08-18T00:00:00Z","timestamp":1250553600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:p>In this paper we derive an alternative asymptotic approximation to the sampling distribution of the limited information maximum likelihood estimator and a bias-corrected version of the two-stage least squares estimator. The approximation is obtained by allowing the number of instruments and the concentration parameter to grow at the same rate as the sample size. More specifically, we allow for potentially nonnormal error distributions and obtain the conventional asymptotic distribution and the results of Bekker (1994, <jats:italic>Econometrica<\/jats:italic> 62, 657\u2013681) and Bekker and Van der Ploeg (2005, <jats:italic>Statistica Neerlandica<\/jats:italic> 59, 139\u2013267) as special cases. The results show that when the error distribution is not normal, in general both the properties of the instruments and the third and fourth moments of the errors affect the asymptotic variance. We compare our findings with those in the recent literature on many and weak instruments.<\/jats:p>","DOI":"10.1017\/s0266466609100117","type":"journal-article","created":{"date-parts":[[2009,8,18]],"date-time":"2009-08-18T08:32:59Z","timestamp":1250584379000},"page":"633-645","source":"Crossref","is-referenced-by-count":20,"title":["MANY INSTRUMENTS ASYMPTOTIC APPROXIMATIONS UNDER NONNORMAL ERROR DISTRIBUTIONS"],"prefix":"10.1017","volume":"26","author":[{"given":"Martijn van","family":"Hasselt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,8,18]]},"reference":[{"key":"S0266466609100117_ref16","unstructured":"Van der Ploeg J. (1997) Instrumental Variable Estimation and Group-Asymptotics. Ph.D. dissertation, Rijksuniversiteit Groningen, The Netherlands."},{"key":"S0266466609100117_ref9","doi-asserted-by":"publisher","DOI":"10.1093\/0198774036.001.0001"},{"key":"S0266466609100117_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139164863.006"},{"key":"S0266466609100117_ref5","unstructured":"Chao J.C. & Swanson N.R. (2004) Asymptotic Distribution of JIVE in a Heteroscedastic IV Regression with Many Weak Instruments. Working paper, Rutgers University."},{"key":"S0266466609100117_ref4","volume-title":"Probability and Measure","author":"Billingsley","year":"1995"},{"key":"S0266466609100117_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2951662"},{"key":"S0266466609100117_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/1912160"},{"key":"S0266466609100117_ref10","doi-asserted-by":"crossref","unstructured":"Hansen C. , Hausman J.A. , & Newey W.K. (2006) Estimation with Many Instrumental Variables. Working paper, MIT.","DOI":"10.1920\/wp.cem.2006.1906"},{"key":"S0266466609100117_ref6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00632.x"},{"key":"S0266466609100117_ref1","unstructured":"Anderson T. & Kunitomo N. (2006) On Asymptotic Properties of the LIML Estimator with Possibly Many Instruments. Working paper, University of Tokyo."},{"key":"S0266466609100117_ref13","doi-asserted-by":"publisher","DOI":"10.2307\/1909352"},{"key":"S0266466609100117_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100046685"},{"key":"S0266466609100117_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511614491.007"},{"key":"S0266466609100117_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.09.002"},{"key":"S0266466609100117_ref11","doi-asserted-by":"crossref","unstructured":"Hausman J.A. , Newey W.K. , Woutersen T. , Chao J.C. , & Swanson N.R. (2007) Instrumental Variable Estimation with Heteroscedasticity and Many Instruments. Working paper, MIT.","DOI":"10.1920\/wp.cem.2007.2207"},{"key":"S0266466609100117_ref3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9574.2005.00296.x"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466609100117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T20:18:59Z","timestamp":1556482739000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466609100117\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,18]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["S0266466609100117"],"URL":"https:\/\/doi.org\/10.1017\/s0266466609100117","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,18]]}}}