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This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multistep procedure in closed-form, which combines an eigenvalue\u2013eigenvector matrix decomposition and a linear instrumental variable estimation allowing for Hansen\u2013Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical illustration, we investigate the dynamic common factors and the spillover effects that explain the co-movements among the log daily realized volatilities of four European stock market indices.<\/jats:p>","DOI":"10.1017\/s0266466622000536","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T06:27:51Z","timestamp":1668061671000},"page":"705-751","source":"Crossref","is-referenced-by-count":1,"title":["INSTRUMENTAL VARIABLES INFERENCE IN A SMALL-DIMENSIONAL VAR MODEL WITH DYNAMIC LATENT FACTORS"],"prefix":"10.1017","volume":"40","author":[{"given":"Federico","family":"Carlini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Gagliardini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"S0266466622000536_r2","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhw088"},{"key":"S0266466622000536_r14","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhw060"},{"key":"S0266466622000536_r48","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(95)01753-4"},{"volume-title":"Contagion Phenomena with Applications in Finance","year":"2015","author":"Darolles","key":"S0266466622000536_r21"},{"key":"S0266466622000536_r66","doi-asserted-by":"crossref","first-page":"297","DOI":"10.3982\/ECTA15604","article-title":"Informational channels of financial contagion","volume":"88","author":"Trevino","year":"2020","journal-title":"Econometrica"},{"key":"S0266466622000536_r61","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(73)90019-5"},{"key":"S0266466622000536_r38","doi-asserted-by":"publisher","DOI":"10.2307\/1909577"},{"key":"S0266466622000536_r47","doi-asserted-by":"crossref","first-page":"1995","DOI":"10.3982\/ECTA8916","article-title":"Dynamic identification of dynamic stochastic general equilibrium models","volume":"79","author":"Komunjer","year":"2011","journal-title":"Econometrica"},{"key":"S0266466622000536_r63","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.03.001"},{"key":"S0266466622000536_r51","doi-asserted-by":"publisher","DOI":"10.1016\/S0261-5606(99)00016-9"},{"key":"S0266466622000536_r24","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.47.2.236.9835"},{"key":"S0266466622000536_r25","doi-asserted-by":"publisher","DOI":"10.1257\/aer.104.10.3115"},{"key":"S0266466622000536_r54","doi-asserted-by":"publisher","DOI":"10.2307\/2297912"},{"key":"S0266466622000536_r3","doi-asserted-by":"publisher","DOI":"10.1257\/aer.20120555"},{"key":"S0266466622000536_r59","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2853-8"},{"key":"S0266466622000536_r60","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1017\/S0266466600162012","article-title":"Tests of rank","volume":"16","author":"Robin","year":"2000","journal-title":"Econometric Theory"},{"key":"S0266466622000536_r23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.04.012"},{"key":"S0266466622000536_r58","first-page":"872","article-title":"Order estimation in ARMA-models by Lagrangian multiplier tests","volume":"11","author":"Poetscher","year":"1983","journal-title":"Annals of Statistics"},{"key":"S0266466622000536_r64","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1162\/1542476054729446","article-title":"Understanding changes in international business cycle dynamics","volume":"3","author":"Stock","year":"2005","journal-title":"Journal of the European Economic Association"},{"key":"S0266466622000536_r27","doi-asserted-by":"publisher","DOI":"10.1086\/659311"},{"key":"S0266466622000536_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2017.03.002"},{"key":"S0266466622000536_r19","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476999"},{"key":"S0266466622000536_r30","doi-asserted-by":"publisher","DOI":"10.1162\/003465300559037"},{"key":"S0266466622000536_r20","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.2455826"},{"key":"S0266466622000536_r9","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1214\/aoms\/1177729580","article-title":"Estimating linear restrictions on regression coefficients for multivariate normal distributions","volume":"22","author":"Anderson","year":"1951b","journal-title":"Annals of Mathematical Statistics"},{"key":"S0266466622000536_r29","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660809052X"},{"key":"S0266466622000536_r36","unstructured":"Hamilton, J. 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