{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T19:43:49Z","timestamp":1784835829444,"version":"3.55.0"},"reference-count":42,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"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>Existing methods for estimating nonlinear dynamic models are either highly computationally costly or rely on local approximations which often fail adequately to capture the nonlinear features of interest. I develop a new method, the discretization filter, for approximating the likelihood of nonlinear, non\u2010Gaussian state space models. I establish that the associated maximum likelihood estimator is strongly consistent, asymptotically normal, and asymptotically efficient. Through simulations, I show that the discretization filter is orders of magnitude faster than alternative nonlinear techniques for the same level of approximation error in low\u2010dimensional settings and I provide practical guidelines for applied researchers. It is my hope that the method's simplicity will make the quantitative study of nonlinear models easier for and more accessible to applied researchers. I apply my approach to estimate a New Keynesian model with a zero lower bound on the nominal interest rate. After accounting for the zero lower bound, I find that the slope of the Phillips Curve is 0.076, which is less than 1\/3 of typical estimates from linearized models. This suggests a strong decoupling of inflation from the output gap and larger real effects of unanticipated changes in interest rates in post Great Recession.<\/jats:p>","DOI":"10.3982\/qe1353","type":"journal-article","created":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T13:37:04Z","timestamp":1610372224000},"page":"41-76","source":"Crossref","is-referenced-by-count":16,"title":["The discretization filter: A simple way to estimate nonlinear state space models"],"prefix":"10.3982","volume":"12","author":[{"given":"Leland E.","family":"Farmer","sequence":"first","affiliation":[{"name":"Department of Economics, University of Virginia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"key":"quan200121-bib-0001","volume-title":"Dynamic Economics: Quantitative Methods and Applications","author":"Adda","year":"2003"},{"key":"quan200121-bib-0002","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.jedc.2017.07.006","volume":"83","author":"Aruoba","year":"2017","journal-title":"Journal of Economic Dynamics and Control"},{"issue":"1","key":"quan200121-bib-0003","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1093\/restud\/rdx027","volume":"85","author":"Aruoba","year":"2018","journal-title":"The Review of Economic Studies"},{"issue":"2","key":"quan200121-bib-0004","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S0764-4442(97)84600-9","volume":"325","author":"Bakry","year":"1997","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences\u2014Series I\u2014Mathematics"},{"issue":"6","key":"quan200121-bib-0005","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1214\/aoms\/1177699147","volume":"37","author":"Baum","year":"1966","journal-title":"Annals of Mathematical Statistics"},{"issue":"3","key":"quan200121-bib-0006","doi-asserted-by":"crossref","first-page":"199","DOI":"10.2307\/3318520","volume":"2","author":"Bickel","year":"1996","journal-title":"Bernoulli"},{"issue":"4","key":"quan200121-bib-0007","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1214\/aos\/1024691255","volume":"26","author":"Bickel","year":"1998","journal-title":"Annals of Statistics"},{"key":"quan200121-bib-0008","first-page":"80","volume":"17","author":"Bucy","year":"1969","journal-title":"Journal of the Astronautical Sciences"},{"issue":"3","key":"quan200121-bib-0009","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0005-1098(71)90121-X","volume":"7","author":"Bucy","year":"1971","journal-title":"Automatica"},{"issue":"1","key":"quan200121-bib-0010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02331880309257","volume":"182","author":"Chen","year":"2003","journal-title":"Statistics"},{"issue":"1","key":"quan200121-bib-0011","first-page":"110","volume":"7","author":"Christiano","year":"2015","journal-title":"American Economic Journal: Macroeconomics"},{"issue":"3","key":"quan200121-bib-0012","first-page":"297","volume":"67","author":"Dixit","year":"1977","journal-title":"American Economic Review"},{"issue":"1","key":"quan200121-bib-0013","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1214\/10-AOS834","volume":"39","author":"Douc","year":"2011","journal-title":"Annals of Statistics"},{"issue":"5","key":"quan200121-bib-0014","doi-asserted-by":"crossref","first-page":"2254","DOI":"10.1214\/009053604000000021","volume":"32","author":"Douc","year":"2004","journal-title":"Annals of Statistics"},{"key":"quan200121-bib-0015","unstructured":"Farmer, L. 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