{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T10:14:07Z","timestamp":1788603247939,"version":"build-2803163510"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2021,10]]},"abstract":"<jats:p>This paper establishes central limit theorems (CLTs) and proposes how to perform valid inference in factor models. We consider a setting where many counties\/regions\/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous microparameters estimated separately for each entity. The CLT applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. This paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.<\/jats:p>","DOI":"10.1017\/s0266466620000468","type":"journal-article","created":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T08:32:44Z","timestamp":1604910764000},"page":"1034-1074","source":"Crossref","is-referenced-by-count":3,"title":["LIMIT THEOREMS FOR FACTOR MODELS"],"prefix":"10.1017","volume":"37","author":[{"given":"Stanislav","family":"Anatolyev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anna","family":"Mikusheva","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,11,9]]},"reference":[{"key":"S0266466620000468_r13","doi-asserted-by":"publisher","DOI":"10.1142\/p591"},{"key":"S0266466620000468_r12","doi-asserted-by":"publisher","DOI":"10.1086\/260061"},{"key":"S0266466620000468_r27","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/5.1.1"},{"key":"S0266466620000468_r21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.01.034"},{"key":"S0266466620000468_r26","doi-asserted-by":"publisher","DOI":"10.3386\/w22425"},{"key":"S0266466620000468_r9","doi-asserted-by":"publisher","DOI":"10.1017\/S026646661600013X"},{"key":"S0266466620000468_r23","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.2943640"},{"key":"S0266466620000468_r28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.04.040"},{"key":"S0266466620000468_r11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00354037"},{"key":"S0266466620000468_r5","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990727"},{"key":"S0266466620000468_r6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2006.11.007"},{"key":"S0266466620000468_r18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.11.006"},{"key":"S0266466620000468_r7","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466614000127"},{"key":"S0266466620000468_r22","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00692.x"},{"key":"S0266466620000468_r3","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":"S0266466620000468_r25","unstructured":"Sarto, A.P. (2018) Recovering Macro Elasticities from Regional Data. Working paper, Massachusetts Institute of Technology."},{"key":"S0266466620000468_r1","unstructured":"Anatolyev, S. & Mikusheva, A. (2018) Factor Models with Many Assets: Strong Factors, Weak Factors, and the Two-Pass Procedure. Working paper, CERGE-EI and Massachusetts Institute of Technology. arXiv:1807.04094."},{"key":"S0266466620000468_r14","doi-asserted-by":"publisher","DOI":"10.3386\/w20884"},{"key":"S0266466620000468_r19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.02.004"},{"key":"S0266466620000468_r24","doi-asserted-by":"publisher","DOI":"10.1137\/1118064"},{"key":"S0266466620000468_r10","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466611000120"},{"key":"S0266466620000468_r8","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466613000169"},{"key":"S0266466620000468_r20","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13660"},{"key":"S0266466620000468_r2","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbu026"},{"key":"S0266466620000468_r16","doi-asserted-by":"publisher","DOI":"10.3982\/QE89"},{"key":"S0266466620000468_r17","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177696722"},{"key":"S0266466620000468_r15","unstructured":"Hahn, J. , Kuersteiner, G.M. , & Mazzocco, M. (2020) Central Limit Theory for Combined Cross-Section and Time Series. Working paper, University of California, Los Angeles and University of Maryland. arXiv:1610.01697."},{"key":"S0266466620000468_r4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00696.x"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466620000468","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T10:38:02Z","timestamp":1633603082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466620000468\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,9]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["S0266466620000468"],"URL":"https:\/\/doi.org\/10.1017\/s0266466620000468","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,9]]}}}