{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:48:48Z","timestamp":1787507328912,"version":"build-2736575974"},"reference-count":38,"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>\n                    Indirect Inference (I\u2010I) estimation of structural parameters\n                    <jats:italic>\u03b8<\/jats:italic>\n                    requires matching observed and simulated statistics, which are most often generated using an auxiliary model that depends on instrumental parameters\n                    <jats:italic>\u03b2<\/jats:italic>\n                    . The estimators of the instrumental parameters will encapsulate the statistical information used for inference about the structural parameters. As such, artificially constraining these parameters may restrict the ability of the auxiliary model to accurately replicate features in the structural data, which may lead to a range of issues, such as a loss of identification. However, in certain situations the parameters\n                    <jats:italic>\u03b2<\/jats:italic>\n                    naturally come with a set of\n                    <jats:italic>q<\/jats:italic>\n                    restrictions. Examples include settings where\n                    <jats:italic>\u03b2<\/jats:italic>\n                    must be estimated subject to\n                    <jats:italic>q<\/jats:italic>\n                    possibly strict inequality constraints\n                    <jats:italic>g<\/jats:italic>\n                    (\n                    <jats:italic>\u03b2<\/jats:italic>\n                    )&gt;0, such as, when I\u2010I is based on GARCH auxiliary models. In these settings, we propose a novel I\u2010I approach that uses appropriately modified unconstrained auxiliary statistics, which are simple to compute and always exists. We state the relevant asymptotic theory for this I\u2010I approach without constraints and show that it can be reinterpreted as a standard implementation of I\u2010I through a properly modified binding function. Several examples that have featured in the literature illustrate our approach.\n                  <\/jats:p>","DOI":"10.3982\/qe986","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:51:29Z","timestamp":1580111489000},"page":"113-159","source":"Crossref","is-referenced-by-count":4,"title":["Indirect inference with(out) constraints"],"prefix":"10.3982","volume":"11","author":[{"given":"David T.","family":"Frazier","sequence":"first","affiliation":[{"name":"Department of Econometrics and Business Statistics, Monash University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Renault","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Warwick"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"issue":"3","key":"quan200068-bib-0001","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/j.jfineco.2015.03.002","volume":"117","author":"Ait-Sahalia","year":"2015","journal-title":"Journal of Financial Economics"},{"key":"quan200068-bib-0002","volume-title":"High-Frequency Financial Econometrics","author":"Ait-Sahalia","year":"2014"},{"issue":"3","key":"quan200068-bib-0003","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1111\/1540-6261.00460","volume":"57","author":"Andersen","year":"2002","journal-title":"Journal of Finance"},{"key":"quan200068-bib-0004","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/B978-0-444-50897-3.50005-5","volume-title":"Handbook of Financial Econometrics: Tools and Techniques","author":"Andersen","year":"2010"},{"issue":"6","key":"quan200068-bib-0005","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1111\/1468-0262.00082","volume":"67","author":"Andrews","year":"1999","journal-title":"Econometrica"},{"issue":"5","key":"quan200068-bib-0006","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.3982\/ECTA9456","volume":"80","author":"Andrews","year":"2012","journal-title":"Econometrica"},{"issue":"4","key":"quan200068-bib-0007","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1111\/0034-6527.00310","volume":"71","author":"Calzolari","year":"2004","journal-title":"The Review of Economic Studies"},{"issue":"1","key":"quan200068-bib-0008","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.jeconom.2018.03.014","volume":"205","author":"Calzolari","year":"2018","journal-title":"Journal of Econometrics"},{"key":"quan200068-bib-0009","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.jempfin.2015.01.002","volume":"31","author":"Creel","year":"2015","journal-title":"Journal of Empirical Finance"},{"key":"quan200068-bib-0010","volume-title":"Modeling Stock Market Volatility: Bridging the Gap to Continuous Time","author":"Engle","year":"1996"},{"issue":"2","key":"quan200068-bib-0011","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1198\/073500101316970403","volume":"19","author":"Eraker","year":"2001","journal-title":"Journal of Business & Economic Statistics"},{"issue":"441","key":"quan200068-bib-0012","first-page":"359","volume":"93","author":"Fernandez","year":"1998","journal-title":"Journal of the American Statistical Association"},{"issue":"9","key":"quan200068-bib-0013","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1016\/j.spa.2007.01.001","volume":"117","author":"Francq","year":"2007","journal-title":"Stochastic Processes and their Applications"},{"key":"quan200068-bib-0014","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1198\/jasa.2009.0117","volume":"104","author":"Francq","year":"2009","journal-title":"Journal of the American Statistical Association"},{"key":"quan200068-bib-0015","doi-asserted-by":"crossref","unstructured":"Frazier, D. 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