{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T20:45:34Z","timestamp":1648586734282},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,8,1]],"date-time":"2009-08-01T00:00:00Z","timestamp":1249084800000},"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":[[2009,8]]},"abstract":"<jats:p>Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV, and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulas for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new exact results are obtained by means of a uniform asymptotic expansion. An interesting consequence of the new theory is that the uniform asymptotic approximation provides the exact distribution of the OLS estimator in the model considered by Bergstrom (1962). This example appears to be the first instance in the statistical literature of a uniform approximation delivering an exact expression for a probability density.<\/jats:p>","DOI":"10.1017\/s0266466608090361","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:21:10Z","timestamp":1236158470000},"page":"958-984","source":"Crossref","is-referenced-by-count":4,"title":["EXACT DISTRIBUTION THEORY IN STRUCTURAL ESTIMATION WITH AN IDENTITY"],"prefix":"10.1017","volume":"25","author":[{"given":"Peter C.B.","family":"Phillips","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,8,1]]},"reference":[{"key":"S0266466608090361_ref13","unstructured":"Phillips P.C.B . (1982) Small Sample Distribution Theory in Econometric Models of Simultaneous Equations. Cowles Foundation Discussion Paper 617, Yale University."},{"key":"S0266466608090361_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/2526524"},{"key":"S0266466608090361_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1961.10480649"},{"key":"S0266466608090361_ref19","unstructured":"Phillips P.C.B. & Hajivassiliou V.A. (1987) Bimodalt ratios. Cowles Foundation Discussion Paper No. 842, Yale University."},{"key":"S0266466608090361_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/1914016"},{"key":"S0266466608090361_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012408"},{"key":"S0266466608090361_ref8","volume-title":"Special Functions and their Applications","author":"Lebedev","year":"1972"},{"key":"S0266466608090361_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/67.1.59"},{"key":"S0266466608090361_ref22","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00247"},{"key":"S0266466608090361_ref14","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/S1573-4412(83)01012-0","volume-title":"Handbook of Econometrics","author":"Phillips","year":"1983"},{"key":"S0266466608090361_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060439"},{"key":"S0266466608090361_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/1909891"},{"key":"S0266466608090361_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060427"},{"key":"S0266466608090361_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060415"},{"key":"S0266466608090361_ref9","doi-asserted-by":"publisher","DOI":"10.2307\/2951683"},{"key":"S0266466608090361_ref11","doi-asserted-by":"publisher","DOI":"10.2307\/2938359"},{"key":"S0266466608090361_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/1912937"},{"key":"S0266466608090361_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/2648878"},{"key":"S0266466608090361_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466608090361_ref5","volume-title":"Tables of Integrals, Series and Products","author":"Gradshteyn","year":"2000"},{"key":"S0266466608090361_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466698145012"},{"key":"S0266466608090361_ref20","volume-title":"Exercises in Econometrics, Volume II","author":"Phillips","year":"1978"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T19:27:00Z","timestamp":1554146820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090361\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["S0266466608090361"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090361","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}