{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T10:39:28Z","timestamp":1790678368407,"version":"4.1.0"},"reference-count":78,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2014,4,16]],"date-time":"2014-04-16T00:00:00Z","timestamp":1397606400000},"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":[[2014,10]]},"abstract":"<jats:p>This paper deals with asymptotically efficient estimation in exchangeable nonlinear dynamic panel models with common unobservable factors. These models are relevant for applications to large portfolios of credits, corporate bonds, or life insurance contracts. For instance, the Asymptotic Risk Factor (ARF) model is recommended in the current regulation in Finance (Basel II and Basel III) and Insurance (Solvency II) for risk prediction and computation of the required capital. The specification accounts for both micro- and macrodynamics, induced by the lagged individual observations and the common stochastic factors, respectively. For large cross-sectional and time dimensions<jats:italic>n<\/jats:italic>and<jats:italic>T<\/jats:italic>, we derive the efficiency bound and introduce computationally simple efficient estimators for both the micro- and macroparameters. The results are based on an asymptotic expansion of the log-likelihood function in powers of 1\/<jats:italic>n<\/jats:italic>, and are linked to granularity theory. The results are illustrated with the stochastic migration model for credit risk analysis.<\/jats:p>","DOI":"10.1017\/s0266466614000024","type":"journal-article","created":{"date-parts":[[2014,4,16]],"date-time":"2014-04-16T08:23:44Z","timestamp":1397636624000},"page":"961-1020","source":"Crossref","is-referenced-by-count":17,"title":["EFFICIENCY IN LARGE DYNAMIC PANEL MODELS WITH COMMON FACTORS"],"prefix":"10.1017","volume":"30","author":[{"given":"Patrick","family":"Gagliardini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Gourieroux","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,4,16]]},"reference":[{"key":"S0266466614000024_ref57","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995566"},{"key":"S0266466614000024_ref51","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1955-0076206-8"},{"key":"S0266466614000024_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.10.024"},{"key":"S0266466614000024_ref41","doi-asserted-by":"publisher","DOI":"10.21314\/JCR.2009.101"},{"key":"S0266466614000024_ref50","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466614000024_ref73","doi-asserted-by":"publisher","DOI":"10.1198\/016214502388618960"},{"key":"S0266466614000024_ref72","first-page":"187","volume-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"Stein","year":"1956"},{"key":"S0266466614000024_ref71","doi-asserted-by":"publisher","DOI":"10.1086\/209665"},{"key":"S0266466614000024_ref67","first-page":"1","article-title":"Marginal densities of instrumental variable estimators in the general single equation case","volume":"2","author":"Phillips","year":"1983","journal-title":"Advances in Econometrics"},{"key":"S0266466614000024_ref8","unstructured":"Basel Committee on Banking Supervision (2003) The New Basel Capital Accord. Consultative Document of the Bank for International Settlements, April 2003, Part 3: The Second Pillar."},{"key":"S0266466614000024_ref75","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1986.10478240"},{"key":"S0266466614000024_ref24","volume-title":"Working paper","author":"Dhaene","year":"2006"},{"key":"S0266466614000024_ref7","unstructured":"Basel Committee on Banking Supervision (2001) The New Basel Capital Accord. Consultative Document of the Bank for International Settlements, April 2001, Part 2: Pillar 1, Section \u201cCalculation of IRB Granularity Adjustment to Capital\u201d."},{"key":"S0266466614000024_ref60","first-page":"621","article-title":"M\u00e9moire sur la probabilit\u00e9 des causes par les \u00e9v\u00e9nements","volume":"6","author":"Laplace","year":"1774","journal-title":"M\u00e9moires de math\u00e9matique et de physique pr\u00e9sent\u00e9s \u00e0 l\u2019Academie Royale des Sciences par divers savants, dans ses assembl\u00e9es"},{"key":"S0266466614000024_ref74","first-page":"20","article-title":"Discussion of Cox and Reid (1987)","volume":"49","author":"Sweeting","year":"1987","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"S0266466614000024_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/0198774036.001.0001"},{"key":"S0266466614000024_ref52","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/86.3.573"},{"key":"S0266466614000024_ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2008.05.010"},{"key":"S0266466614000024_ref30","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00541.x"},{"key":"S0266466614000024_ref77","unstructured":"Vasicek O . (1991) Limiting Loan Loss Probability Distribution. KMV Technical report."},{"key":"S0266466614000024_ref21","unstructured":"de Finetti B . (1931) Funzione Caratteristica di un Fenomeno Aleatorio. In Atti della Reale Accademia dei Lincei 6, Memorie, Classe di Scienze Fisiche, Matematiche e Naturali, 4, 251\u2013299."},{"key":"S0266466614000024_ref68","doi-asserted-by":"publisher","DOI":"10.2307\/1911699"},{"key":"S0266466614000024_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1718-3"},{"key":"S0266466614000024_ref65","doi-asserted-by":"publisher","DOI":"10.2307\/1914288"},{"key":"S0266466614000024_ref66","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(78)90016-7"},{"key":"S0266466614000024_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/S1042-9573(03)00040-8"},{"key":"S0266466614000024_ref78","unstructured":"Woutersen T . (2002) Robustness Against Incidental Parameters. Working paper."},{"key":"S0266466614000024_ref49","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00533.x"},{"key":"S0266466614000024_ref43","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1980.tb00297.x"},{"key":"S0266466614000024_ref70","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(00)00090-7"},{"key":"S0266466614000024_ref63","doi-asserted-by":"publisher","DOI":"10.1016\/j.jempfin.2006.05.002"},{"key":"S0266466614000024_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbankfin.2011.12.013"},{"key":"S0266466614000024_ref55","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0027-2"},{"key":"S0266466614000024_ref1","volume-title":"Advanced Econometrics","author":"Amemiya","year":"1985"},{"key":"S0266466614000024_ref54","first-page":"3 ,249","article-title":"Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data","author":"Huber","year":"2009","journal-title":"Annals of Applied Statistics"},{"key":"S0266466614000024_ref4","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":"S0266466614000024_ref28","volume-title":"Working paper","author":"Duffie","year":"1998"},{"key":"S0266466614000024_ref69","first-page":"87","article-title":"Affine stochastic mortality","volume":"38","author":"Schrager","year":"2006","journal-title":"Insurance: Mathematics and Economics"},{"key":"S0266466614000024_ref34","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbi013"},{"key":"S0266466614000024_ref59","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(99)00044-5"},{"key":"S0266466614000024_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jempfin.2006.12.003"},{"key":"S0266466614000024_ref19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1987.tb01422.x","article-title":"Parameter orthogonality and approximate conditional inference","volume":"49","author":"Cox","year":"1987","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"S0266466614000024_ref32","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00053"},{"key":"S0266466614000024_ref25","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198772101.001.0001","volume-title":"Optimization in Economic Theory","author":"Dixit","year":"1990"},{"key":"S0266466614000024_ref23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion)","volume":"39","author":"Dempster","year":"1977","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"S0266466614000024_ref15","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-28982-8","volume-title":"Inference in Hidden Markov Models","author":"Capp\u00e9","year":"2005"},{"key":"S0266466614000024_ref27","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2009.01495.x"},{"key":"S0266466614000024_ref3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00629.x"},{"key":"S0266466614000024_ref53","doi-asserted-by":"publisher","DOI":"10.2307\/1914016"},{"key":"S0266466614000024_ref31","doi-asserted-by":"publisher","DOI":"10.1162\/003465300559037"},{"key":"S0266466614000024_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(87)90015-7"},{"key":"S0266466614000024_ref17","first-page":"8,537","article-title":"Bankruptcy prediction with industry effects","author":"Chava","year":"2004","journal-title":"Review of Finance"},{"key":"S0266466614000024_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS634"},{"key":"S0266466614000024_ref48","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060245"},{"key":"S0266466614000024_ref6","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00273"},{"key":"S0266466614000024_ref56","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697731"},{"key":"S0266466614000024_ref13","unstructured":"Brady B. & Bos R. (2004) Record Default in 2001: The Result of Poor Credit Quality and a Weak Economy. Technical report, Standard & Poor\u2019s."},{"key":"S0266466614000024_ref35","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbr010"},{"key":"S0266466614000024_ref46","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466611000028"},{"key":"S0266466614000024_ref10","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.0012"},{"key":"S0266466614000024_ref14","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2008.01416.x"},{"key":"S0266466614000024_ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.07.001"},{"key":"S0266466614000024_ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2004.01.006"},{"key":"S0266466614000024_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbankfin.2004.08.006"},{"key":"S0266466614000024_ref36","first-page":"325","article-title":"Second-order efficiency of maximum likelihood estimators","volume":"36","author":"Ghosh","year":"1974","journal-title":"Sankya Series A"},{"key":"S0266466614000024_ref5","unstructured":"Arellano M. & Hahn J. (2006) A Likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects. Working paper."},{"key":"S0266466614000024_ref44","article-title":"Creditmetrics","author":"Gupton","year":"1997","journal-title":"Technical report, The Risk Metrics Group"},{"key":"S0266466614000024_ref45","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00344"},{"key":"S0266466614000024_ref62","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4266(02)00277-7"},{"key":"S0266466614000024_ref61","first-page":"659","article-title":"Modeling and forecasting US mortality","volume":"87","author":"Lee","year":"1972","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466614000024_ref76","unstructured":"Vasicek O . (1987) Probability of Loss on Loan Portfolio. KMV Technical report."},{"key":"S0266466614000024_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-003-0107-2"},{"key":"S0266466614000024_ref38","unstructured":"Gordy M. & Heitfield E. (2002) Estimating Default Correlation from Short Panels of Credit Rating Performance Data. Working paper, Federal Reserve Board."},{"key":"S0266466614000024_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00531650"},{"key":"S0266466614000024_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013396"},{"key":"S0266466614000024_ref18","doi-asserted-by":"crossref","first-page":"713","DOI":"10.3982\/ECTA7432","article-title":"Efficient semiparametric estimation of the Fama\u2013French model and extensions","volume":"80","author":"Connor","year":"2012","journal-title":"Econometrica"},{"key":"S0266466614000024_ref26","doi-asserted-by":"crossref","first-page":"2254","DOI":"10.1214\/009053604000000021","article-title":"Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime","volume":"32","author":"Douc","year":"2004","journal-title":"Annals of Statistics"},{"key":"S0266466614000024_ref64","first-page":"449","article-title":"On the pricing of corporate debt: The risk structure of interest rates","volume":"29","author":"Merton","year":"1974","journal-title":"Journal of Finance"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466614000024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,25]],"date-time":"2024-05-25T22:59:26Z","timestamp":1716677966000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466614000024\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,16]]},"references-count":78,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["S0266466614000024"],"URL":"https:\/\/doi.org\/10.1017\/s0266466614000024","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,16]]}}}