{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T18:51:50Z","timestamp":1792608710016,"version":"4.5.0"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T00:00:00Z","timestamp":1524614400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p>This article studies two-step sieve M estimation of general semi\/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-<jats:italic>n<\/jats:italic>estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.<\/jats:p>","DOI":"10.1017\/s0266466618000014","type":"journal-article","created":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T10:06:08Z","timestamp":1524650768000},"page":"1281-1324","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":19,"title":["NONPARAMETRIC TWO-STEP SIEVE M ESTIMATION AND INFERENCE"],"prefix":"10.1017","volume":"34","author":[{"given":"Jinyong","family":"Hahn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhipeng","family":"Liao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geert","family":"Ridder","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,4,25]]},"reference":[{"key":"S0266466618000014_ref10","unstructured":"Chernozhukov, V. , Escanciano, J. , Ichimura, H. , & Newey, W. (2016) Locally Robust Semiparametric Estimation. Working paper, MIT."},{"key":"S0266466618000014_ref14","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.3982\/ECTA5317","article-title":"Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects","volume":"76","author":"Florens","year":"2008","journal-title":"Econometrica"},{"key":"S0266466618000014_ref32","doi-asserted-by":"crossref","first-page":"420","DOI":"10.3368\/jhr.50.2.420","article-title":"Control function methods in applied econometrics","volume":"50","author":"Wooldridge","year":"2015","journal-title":"Journal of Human Resources"},{"key":"S0266466618000014_ref6","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jeconom.2014.04.009","article-title":"Sieve M inference of irregular parameters","volume":"182","author":"Chen","year":"2014","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref26","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.2307\/2951752","article-title":"The asymptotic variance of semiparametric estimators","volume":"62","author":"Newey","year":"1994","journal-title":"Econometrica"},{"key":"S0266466618000014_ref17","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA7108","article-title":"Identification and estimation of triangular simultaneous equations models without additivity","volume":"77","author":"Imbens","year":"2009","journal-title":"Econometrica"},{"key":"S0266466618000014_ref22","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1214\/12-AOS995","article-title":"Nonparametric regression with nonparametrically generated covariates","volume":"40","author":"Mammen","year":"2012","journal-title":"Annals of Statistics"},{"key":"S0266466618000014_ref1","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1162\/REST_a_00251","article-title":"A practical asymptotic variance estimator for two-step semiparametric estimators","volume":"94","author":"Ackerberg","year":"2012","journal-title":"Review of Economics and Statistics"},{"key":"S0266466618000014_ref12","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1111\/1467-937X.00236","article-title":"Nonparametric estimation of sample selection models","volume":"70","author":"Das","year":"2003","journal-title":"Review of Economic Studies"},{"key":"S0266466618000014_ref23","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1017\/S0266466615000134","article-title":"Semiparametric estimation with generated covariates","volume":"32","author":"Mammen","year":"2016","journal-title":"Econometric Theory"},{"key":"S0266466618000014_ref5","doi-asserted-by":"crossref","first-page":"5549","DOI":"10.1016\/S1573-4412(07)06076-X","volume-title":"Handbook of Econometrics","volume":"6B","author":"Chen","year":"2007"},{"key":"S0266466618000014_ref16","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.jeconom.2010.05.005","article-title":"Characterization of the asymptotic distribution of semiparametric M estimators","volume":"159","author":"Ichimura","year":"2010","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref2","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1111\/j.1468-0262.2005.00609.x","article-title":"Cross section and panel data estimators for nonseparable models with endogenous regressors","volume":"73","author":"Altonji","year":"2005","journal-title":"Econometrica"},{"key":"S0266466618000014_ref8","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1111\/1468-0262.00461","article-title":"Estimation of semiparametric models when the criterion function is not smooth","volume":"71","author":"Chen","year":"2003","journal-title":"Econometrica"},{"key":"S0266466618000014_ref4","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.jeconom.2007.01.016","article-title":"Censored regression quantiles with endogenous regressors","volume":"141","author":"Blundell","year":"2007","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref24","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1080\/07350015.1985.10509471","article-title":"Estimation and inference in two-step econometric models","volume":"3","author":"Murphy","year":"1985","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466618000014_ref25","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0165-1765(84)90083-1","article-title":"A method of moments interpretation of sequential estimators","volume":"14","author":"Newey","year":"1984","journal-title":"Economics Letters"},{"key":"S0266466618000014_ref11","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1111\/1468-0262.00454","article-title":"Identification in nonseparable models","volume":"71","author":"Chesher","year":"2003","journal-title":"Econometrica"},{"key":"S0266466618000014_ref3","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1111\/j.1467-937X.2004.00299.x","article-title":"Endogeneity in semiparametric binary response models","volume":"71","author":"Blundell","year":"2004","journal-title":"Review of Economic Studies"},{"key":"S0266466618000014_ref27","doi-asserted-by":"crossref","first-page":"S217","DOI":"10.1111\/j.1368-423X.2008.00263.x","article-title":"Two-step series estimation of sample selection models","volume":"12","author":"Newey","year":"2009","journal-title":"Econometrics Journal"},{"key":"S0266466618000014_ref21","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1017\/S0266466602183034","article-title":"Semiparametric estimation of partially linear models for dependent data with generated regressors","volume":"18","author":"Li","year":"2002","journal-title":"Econometric Theory"},{"key":"S0266466618000014_ref9","doi-asserted-by":"crossref","first-page":"289","DOI":"10.2307\/2998559","article-title":"Sieve extremum estimates for weakly dependent data","volume":"66","author":"Chen","year":"1998","journal-title":"Econometrica"},{"key":"S0266466618000014_ref7","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.jeconom.2013.10.002","article-title":"Sieve inference on possibly misspecified semi-nonparametric time series models","volume":"178","author":"Chen","year":"2014","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref28","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1111\/1468-0262.00037","article-title":"Nonparametric estimation of triangular simultaneous equations models","volume":"67","author":"Newey","year":"1999","journal-title":"Econometrica"},{"key":"S0266466618000014_ref15","doi-asserted-by":"crossref","first-page":"315","DOI":"10.3982\/ECTA9609","article-title":"The asymptotic variance of semi-parametric estimators with generated regressors","volume":"81","author":"Hahn","year":"2013","journal-title":"Econometrica"},{"key":"S0266466618000014_ref13","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.jeconom.2013.06.004","article-title":"Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing","volume":"178","author":"Escanciano","year":"2014","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref20","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1111\/1468-0262.00304","article-title":"Nonparametric censored and truncated regression","volume":"70","author":"Lewbel","year":"2002","journal-title":"Econometrica"},{"key":"S0266466618000014_ref31","volume-title":"Econometric Analysis of Cross Section and Panel Data","author":"Wooldridge","year":"2002"},{"key":"S0266466618000014_ref29","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.2307\/2171831","article-title":"The dynamics of productivity in the telecommunications equipment industry","volume":"64","author":"Olley","year":"1996","journal-title":"Econometrica"},{"key":"S0266466618000014_ref18","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1016\/j.jeconom.2007.01.014","article-title":"Endogeneity in quantile regression models: A control function approach","volume":"141","author":"Lee","year":"2007","journal-title":"Journal of Econometrics"},{"key":"S0266466618000014_ref19","unstructured":"Lee, Y . (2015) Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models. Working paper, UC-Irvine."},{"key":"S0266466618000014_ref30","doi-asserted-by":"crossref","first-page":"2555","DOI":"10.1214\/aos\/1030741085","article-title":"On methods of sieves and penalization","volume":"25","author":"Shen","year":"1997","journal-title":"Annals of Statistics"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466618000014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T08:41:57Z","timestamp":1720255317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466618000014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,25]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["S0266466618000014"],"URL":"https:\/\/doi.org\/10.1017\/s0266466618000014","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,25]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2018\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}