{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T13:52:30Z","timestamp":1791294750021,"version":"4.1.0"},"reference-count":53,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T00:00:00Z","timestamp":1774396800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72203032"],"award-info":[{"award-number":["72203032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["25FJLB051"],"award-info":[{"award-number":["25FJLB051"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Summary:<\/jats:title>\n                  <jats:p>We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the limiting distribution of the point estimator is not centred at zero, and test statistics do not follow their standard asymptotic distributions as in the absence of the fixed effects. To address the problem, we develop an analytical bias correction procedure to construct a bias-corrected likelihood. The resulting estimator follows an asymptotic normal distribution with mean zero. Moreover, likelihood-based test statistics\u2014including likelihood-ratio, Lagrange-multiplier, and Wald tests\u2014follow the limiting chi-squared distribution under the null hypothesis. Simulations demonstrate the effectiveness of the proposed correction method, and an empirical application to the labour force participation of single mothers underscores its practical importance.<\/jats:p>","DOI":"10.1093\/ectj\/utag007","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:43:49Z","timestamp":1774356229000},"source":"Crossref","is-referenced-by-count":0,"title":["Debiased inference for dynamic nonlinear panels with multidimensional heterogeneities"],"prefix":"10.1093","author":[{"given":"Xuan","family":"Leng","sequence":"first","affiliation":[{"name":"Xiamen University Department of Statistics and Data Science at School of Economics, , 422, Siming South Road, Xiamen 361005 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaming","family":"Mao","sequence":"additional","affiliation":[{"name":"Wang Yanan Institute for Studies in Economics, Xiamen University , 422, Siming South Road, Xiamen 361005 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yutao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Economics, Anhui University of Finance & Economics , 962, Caoshan Road, Bengbu 233030 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,3,25]]},"reference":[{"key":"2026100608512275900_bib1","first-page":"701","article-title":"Competition and innovation: An inverted-U relationship","volume":"120","author":"Aghion","year":"2005","journal-title":"Quarterly Journal of Economics"},{"issue":"3","key":"2026100608512275900_bib2","first-page":"450","article-title":"Children and their parents\u2019 labour supply: Evidence from exogenous variation in family size","volume":"88","author":"Angrist","year":"1998","journal-title":"American Economic Review"},{"key":"2026100608512275900_bib3","doi-asserted-by":"crossref","first-page":"277","DOI":"10.2307\/2297968","article-title":"Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations","volume":"58","author":"Arellano","year":"1991","journal-title":"Review of Economic Studies"},{"key":"2026100608512275900_bib4","doi-asserted-by":"crossref","first-page":"489","DOI":"10.3982\/ECTA6895","article-title":"Robust priors in nonlinear panel data models","volume":"77","author":"Arellano","year":"2009","journal-title":"Econometrica"},{"key":"2026100608512275900_bib5","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/1226508X.2016.1211811","article-title":"A likelihood-based approximate solution to the incidental parameter problem in dynamic nonlinear models with multiple effects","volume":"45","author":"Arellano","year":"2016","journal-title":"Global Economic Review"},{"key":"2026100608512275900_bib6","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.3982\/ECTA6135","article-title":"Panel data models with interactive fixed effects","volume":"77","author":"Bai","year":"2009","journal-title":"Econometrica"},{"key":"2026100608512275900_bib7","first-page":"1069","article-title":"Parametric bootstrap inference for stratified models with high-dimensional nuisance specifications","volume":"33","author":"Bellio","year":"2023","journal-title":"Statistica Sinica"},{"key":"2026100608512275900_bib8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1198\/jbes.2009.0012","article-title":"A penalty function approach to bias reduction in nonlinear panel models with fixed effects","volume":"27","author":"Bester","year":"2009","journal-title":"Journal of Business & Economic Statistics"},{"key":"2026100608512275900_bib9","doi-asserted-by":"crossref","first-page":"374","DOI":"10.2307\/1926774","article-title":"Child-care costs and family labor supply","volume":"70","author":"Blau","year":"1988","journal-title":"Review of Economics and Statistics"},{"key":"2026100608512275900_bib10","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1086\/513416","article-title":"Changes in the labor supply behavior of married women: 1980\u20132000","volume":"25","author":"Blau","year":"2007","journal-title":"Journal of Labor Economics"},{"key":"2026100608512275900_bib11","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.3982\/ECTA11576","article-title":"Female labor supply, human capital, and welfare reform","volume":"84","author":"Blundell","year":"2016","journal-title":"Econometrica"},{"key":"2026100608512275900_bib12","first-page":"47","volume-title":"Heterogeneity and Microeconometrics Modeling","author":"Browning","year":"2007"},{"key":"2026100608512275900_bib13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1368-423X.2009.00301.x","article-title":"Heterogeneity in dynamic discrete choice models","volume":"13","author":"Browning","year":"2010","journal-title":"Econometrics Journal"},{"key":"2026100608512275900_bib14","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1016\/j.jeconom.2013.11.005","article-title":"Dynamic binary outcome models with maximal heterogeneity","volume":"178","author":"Browning","year":"2014","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.2307\/2297110","article-title":"Analysis of covariance with qualitative data","volume":"47","author":"Chamberlain","year":"1980","journal-title":"Review of Economic Studies"},{"key":"2026100608512275900_bib16","doi-asserted-by":"crossref","first-page":"S1","DOI":"10.1111\/ectj.12093","article-title":"Multiple fixed effects in binary response panel data models","volume":"20","author":"Charbonneau","year":"2017","journal-title":"Econometrics Journal"},{"key":"2026100608512275900_bib17","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.jeconom.2020.04.004","article-title":"Nonlinear factor models for network and panel data","volume":"220","author":"Chen","year":"2021","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib18","doi-asserted-by":"crossref","first-page":"535","DOI":"10.3982\/ECTA8405","article-title":"Average and quantile effects in nonseparable panel models","volume":"81","author":"Chernozhukov","year":"2013","journal-title":"Econometrica"},{"key":"2026100608512275900_bib19","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1177\/1536867X1701700301","article-title":"Bias corrections for probit and logit models with two-way fixed effects","volume":"17","author":"Cruz-Gonzalez","year":"2017","journal-title":"Stata Journal"},{"key":"2026100608512275900_bib20","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1093\/restud\/rdv007","article-title":"Split-panel jackknife estimation of fixed-effect models","volume":"82","author":"Dhaene","year":"2015","journal-title":"Review of Economic Studies"},{"key":"2026100608512275900_bib21","article-title":"Dynamic heterogeneous distribution regression panel models, with an application to labor income processes","author":"Fern\u00e1ndez-Val","year":"2025"},{"key":"2026100608512275900_bib22","doi-asserted-by":"crossref","first-page":"453","DOI":"10.3982\/QE75","article-title":"Panel data models with nonadditive unobserved heterogeneity: Estimation and inference","volume":"4","author":"Fern\u00e1ndez-Val","year":"2013","journal-title":"Quantitative Economics"},{"key":"2026100608512275900_bib23","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jeconom.2015.12.014","article-title":"Individual and time effects in nonlinear panel models with large N,T","volume":"192","author":"Fern\u00e1ndez-Val","year":"2016","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib24","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1146\/annurev-economics-080217-053542","article-title":"Fixed effects estimation of large-t panel data models","volume":"10","author":"Fern\u00e1ndez-Val","year":"2018","journal-title":"Annual Review of Economics"},{"key":"2026100608512275900_bib25","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1017\/S0266466611000028","article-title":"Bias reduction for dynamic nonlinear panel models with fixed effects","volume":"27","author":"Hahn","year":"2011","journal-title":"Econometric Theory"},{"issue":"4","key":"2026100608512275900_bib26","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1111\/j.1468-0262.2004.00533.x","article-title":"Jackknife and analytical bias reduction for nonlinear panel models","volume":"72","author":"Hahn","year":"2004","journal-title":"Econometrica"},{"key":"2026100608512275900_bib27","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1086\/322086","article-title":"Micro data, heterogeneity, and the evaluation of public policy: Nobel Lecture","volume":"109","author":"Heckman","year":"2001","journal-title":"Journal of Political Economy"},{"key":"2026100608512275900_bib28","doi-asserted-by":"crossref","first-page":"411","DOI":"10.3982\/ECTA20712","article-title":"Bootstrap inference for fixed-effect models","volume":"92","author":"Higgins","year":"2024","journal-title":"Econometrica"},{"key":"2026100608512275900_bib29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139839327","volume-title":"Analysis of Panel Data","author":"Hsiao","year":"2014","edition":"(3rd ed.)"},{"key":"2026100608512275900_bib30","doi-asserted-by":"crossref","first-page":"227","DOI":"10.15609\/annaeconstat2009.134.0227","article-title":"Likelihood corrections for two-way models","volume":"134","author":"Jochmans","year":"2019","journal-title":"Annals of Economics and Statistics"},{"key":"2026100608512275900_bib31","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.3982\/QE1319","article-title":"Climate change and US agriculture: Accounting for multidimensional slope heterogeneity in panel data","volume":"11","author":"Keane","year":"2020","journal-title":"Quantitative Economics"},{"key":"2026100608512275900_bib32","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S1573-4463(86)01005-2","article-title":"Chapter 2: Female labor supply: A survey","volume-title":"Volume 1 of Handbook of Labor Economics","author":"Killingsworth","year":"1986"},{"key":"2026100608512275900_bib33","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1017\/S0266466615000341","article-title":"Bootstrap and k-step bootstrap bias corrections for the fixed effects estimator in nonlinear panel data models","volume":"32","author":"Kim","year":"2016","journal-title":"Econometric Theory"},{"key":"2026100608512275900_bib34","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1162\/003465398557384","article-title":"Child care costs as a barrier to employment for single and married mothers","volume":"80","author":"Kimmel","year":"1998","journal-title":"Review of Economics and Statistics"},{"key":"2026100608512275900_bib35","first-page":"181","article-title":"Children and gender inequality: Evidence from Denmark","volume":"11","author":"Kleven","year":"2019","journal-title":"American Economic Journal: Applied Economics"},{"key":"2026100608512275900_bib36","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1111\/1467-937X.t01-1-00025","article-title":"Orthogonal parameters and panel data","volume":"69","author":"Lancaster","year":"2002","journal-title":"Review of Economic Studies"},{"key":"2026100608512275900_bib37","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/1467-9868.00380","article-title":"Efficiency of projected score methods in rectangular array asymptotics","volume":"65","author":"Li","year":"2003","journal-title":"Journal of the Royal Statistical Society. Series B (Methodological)"},{"key":"2026100608512275900_bib38","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.jeconom.2022.07.002","article-title":"Uniform inference in linear panel data models with two-dimensional heterogeneity","volume":"235","author":"Lu","year":"2023","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib39","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1017\/S0266466615000328","article-title":"Dynamic linear panel regression models with interactive fixed effects","volume":"33","author":"Moon","year":"2017","journal-title":"Econometric Theory"},{"key":"2026100608512275900_bib40","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1111\/1468-0262.00194","article-title":"Measuring market power in the ready-to-eat cereal industry","volume":"69","author":"Nevo","year":"2001","journal-title":"Econometrica"},{"key":"2026100608512275900_bib41","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.jeconom.2020.04.009","article-title":"Heterogeneous structural breaks in panel data models","volume":"220","author":"Okui","year":"2021","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib42","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1093\/ectj\/utz019","article-title":"Kernel estimation for panel data with heterogeneous dynamics","volume":"23","author":"Okui","year":"2020","journal-title":"The Econometrics Journal"},{"key":"2026100608512275900_bib43","doi-asserted-by":"crossref","first-page":"3554","DOI":"10.1016\/j.jspi.2004.11.016","article-title":"Adjustments of the profile likelihood from a new perspective","volume":"136","author":"Pace","year":"2006","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2026100608512275900_bib44","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198736912.001.0001","volume-title":"Time Series and Panel Data Econometrics","author":"Pesaran","year":"2015"},{"key":"2026100608512275900_bib45","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0304-4076(94)01644-F","article-title":"Estimating long-run relationships from dynamic heterogeneous panels","volume":"68","author":"Pesaran","year":"1995","journal-title":"Journal of Econometrics"},{"key":"2026100608512275900_bib46","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1002\/jae.3950070206","article-title":"Some strange properties of panel data estimators","volume":"7","author":"Robertson","year":"1992","journal-title":"Journal of Applied Econometrics"},{"key":"2026100608512275900_bib47","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/978-3-662-02571-0_15","article-title":"Nonparametric estimation of time-varying parameters","volume-title":"Statistical Analysis and Forecasting of Economic Structural Change","author":"Robinson","year":"1989"},{"key":"2026100608512275900_bib48","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1162\/rest.88.4.641","article-title":"The log of gravity","volume":"88","author":"Silva","year":"2006","journal-title":"Review of Economics and Statistics"},{"key":"2026100608512275900_bib49","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1080\/07350015.1996.10524626","article-title":"Evidence on structural instability in macroeconomic time series relations","volume":"14","author":"Stock","year":"1996","journal-title":"Journal of Business & Economic Statistics"},{"key":"2026100608512275900_bib50","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1017\/S0266466613000017","article-title":"Testing homogeneity in panel data models with interactive fixed effects","volume":"29","author":"Su","year":"2013","journal-title":"Econometric Theory"},{"key":"2026100608512275900_bib51","article-title":"Panel Study of Income Dynamics (PSID). 1987\u20131997. Produced and distributed by the Institute for Social Research, University of Michigan, Ann Arbor, MI. https:\/\/psidonline.isr.umich.edu\/","author":"University of Michigan","year":"2025"},{"key":"2026100608512275900_bib52","first-page":"1","article-title":"Maximum likelihood estimation of misspecified models","author":"White","year":"1982","journal-title":"Econometrica"},{"key":"2026100608512275900_bib53","article-title":"Robustness against incidental parameters","author":"Woutersen","year":"2002"}],"container-title":["Econometrics Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/ectj\/advance-article-pdf\/doi\/10.1093\/ectj\/utag007\/67508439\/utag007.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/ectj\/advance-article-pdf\/doi\/10.1093\/ectj\/utag007\/67508439\/utag007.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T12:51:33Z","timestamp":1791291093000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/ectj\/advance-article\/doi\/10.1093\/ectj\/utag007\/8540257"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,25]]},"references-count":53,"URL":"https:\/\/doi.org\/10.1093\/ectj\/utag007","relation":{},"ISSN":["1368-4221","1368-423X"],"issn-type":[{"value":"1368-4221","type":"print"},{"value":"1368-423X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,25]]},"article-number":"utag007"}}