{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T21:37:55Z","timestamp":1791927475031,"version":"4.3.4"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[1998,12,1]],"date-time":"1998-12-01T00:00:00Z","timestamp":912470400000},"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":[[1998,12]]},"abstract":"<jats:p>Diffuse priors lead to pathological posterior behavior \nwhen used in Bayesian analyses of simultaneous equation \nmodels (SEM's). This results from the local nonidentification \nof certain parameters in SEM's. When this a priori \nknown feature is not captured appropriately, it results \nin an a posteriori favoring of certain specific parameter \nvalues that is not the consequence of strong data information \nbut of local nonidentification. We show that a proper consistent \nBayesian analysis of a SEM explicitly has to consider the \nreduced form of the SEM as a standard linear model on which \nnonlinear (reduced rank) restrictions are imposed, which \nresult from a singular value decomposition. The priors\/posteriors \nof the parameters of the SEM are therefore proportional \nto the priors\/posteriors of the parameters of the linear \nmodel under the condition that the restrictions hold. This \nleads to a framework for constructing priors and posteriors \nfor the parameters of SEM's. The framework is used \nto construct priors and posteriors for one, two, and three \nstructural equation SEM's. These examples together \nwith a theorem, showing that the reduced forms of SEM's \naccord with sets of reduced rank restrictions on standard \nlinear models, show how Bayesian analyses of generally \nspecified SEM's can be conducted.<\/jats:p>","DOI":"10.1017\/s0266466698146017","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:45:46Z","timestamp":1027777546000},"page":"701-743","source":"Crossref","is-referenced-by-count":83,"title":["BAYESIAN SIMULTANEOUS EQUATIONS ANALYSIS USING REDUCED RANK \nSTRUCTURES"],"prefix":"10.1017","volume":"14","author":[{"given":"Frank","family":"Kleibergen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Herman K.","family":"van Dijk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[1998,12,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466698146017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T19:40:38Z","timestamp":1557517238000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466698146017\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1998,12]]}},"alternative-id":["S0266466698146017"],"URL":"https:\/\/doi.org\/10.1017\/s0266466698146017","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,12]]}}}