{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:33:13Z","timestamp":1759638793971},"reference-count":83,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then \n            <jats:italic>nonparametric weak instruments<\/jats:italic> are defined as a sequence of reduced\u2010form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized as \n            <jats:italic>concurvity<\/jats:italic>, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments and shows that it achieves desirable asymptotic properties. A data\u2010driven procedure is proposed for the choice of the penalization parameter. The findings of this paper provide useful implications for empirical work. To illustrate them, Monte Carlo results are presented and an empirical example is given in which the effect of class size on test scores is estimated nonparametrically.\n          <\/jats:p>","DOI":"10.3982\/qe975","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T12:51:29Z","timestamp":1580129489000},"page":"161-202","source":"Crossref","is-referenced-by-count":6,"title":["Nonparametric estimation of triangular simultaneous equations models under weak identification"],"prefix":"10.3982","volume":"11","author":[{"given":"Sukjin","family":"Han","sequence":"first","affiliation":[{"name":"Department of Economics, University of Texas at Austin"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"key":"quan200052-bib-0001","doi-asserted-by":"crossref","first-page":"955","DOI":"10.2307\/1912684","volume":"45","author":"Amemiya","year":"1977","journal-title":"Econometrica"},{"key":"quan200052-bib-0002","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.3982\/ECTA9456","volume":"80","author":"Andrews","year":"2012","journal-title":"Econometrica"},{"key":"quan200052-bib-0003","author":"Andrews","journal-title":"Quantitative Economics"},{"key":"quan200052-bib-0004","volume-title":"Advances in Econometrics: Proceedings of the Ninth World Congress of the Econometric Society","author":"Andrews","year":"2007"},{"key":"quan200052-bib-0005","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1017\/S0266466600005478","volume":"6","author":"Andrews","year":"1990","journal-title":"Econometric Theory"},{"key":"quan200052-bib-0006","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.3982\/ECTA12868","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"key":"quan200052-bib-0007","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.3982\/ECTA12030","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"key":"quan200052-bib-0008","doi-asserted-by":"crossref","first-page":"979","DOI":"10.2307\/2937954","volume":"106","author":"Angrist","year":"1991","journal-title":"The Quarterly Journal of Economics"},{"key":"quan200052-bib-0009","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1162\/003355399556061","volume":"114","author":"Angrist","year":"1999","journal-title":"The Quarterly Journal of Economics"},{"key":"quan200052-bib-0010","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/09-SS054","volume":"4","author":"Arlot","year":"2010","journal-title":"Statistics Surveys"},{"key":"quan200052-bib-0011","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.jeconom.2015.02.014","volume":"186","author":"Belloni","year":"2015","journal-title":"Journal of Econometrics"},{"key":"quan200052-bib-0012","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.3982\/ECTA6069","volume":"76","author":"Blundell","year":"2008","journal-title":"Econometrica"},{"key":"quan200052-bib-0013","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1111\/j.1468-0262.2007.00808.x","volume":"75","author":"Blundell","year":"2007","journal-title":"Econometrica"},{"key":"quan200052-bib-0014","doi-asserted-by":"crossref","first-page":"62","DOI":"10.2307\/146315","volume":"33","author":"Blundell","year":"1998","journal-title":"Journal of Human Resources"},{"key":"quan200052-bib-0015","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1002\/(SICI)1099-1255(1998090)13:5<435::AID-JAE506>3.0.CO;2-K","volume":"13","author":"Blundell","year":"1998","journal-title":"Journal of Applied Econometrics"},{"key":"quan200052-bib-0016","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1111\/j.1467-937X.2004.00299.x","volume":"71","author":"Blundell","year":"2004","journal-title":"The Review of Economic Studies"},{"key":"quan200052-bib-0017","first-page":"443","volume":"90","author":"Bound","year":"1995","journal-title":"Journal of the American Statistical Association"},{"key":"quan200052-bib-0018","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1017\/S0266466614000966","volume":"32","author":"Breunig","year":"2016","journal-title":"Econometric Theory"},{"key":"quan200052-bib-0019","unstructured":"Breza, E. 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