{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T15:51:20Z","timestamp":1762271480276},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":8113,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econ Theory"],"published-print":{"date-parts":[[1988,8]]},"abstract":"<jats:p>We derive asymptotic expansions of the distributions of test statistics for over-identifying restrictions in a system of simultaneous equations under the null and the non-null hypotheses. We investigate the effects of the normality assumption for disturbances on the test statistics based on their asymptotic expansions. We also study the power functions of test statistics based on their asymptotic expansions. After modifying their critical regions to the same significance level, the power function of Basmann's statistic is larger than that of the likelihood ratio test when the variance of disturbances is sufficiently small. However, the difference in powers of the two test statistics disappears as the sample size grows larger.<\/jats:p>","DOI":"10.1017\/s0266466600012056","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:11:46Z","timestamp":1287393106000},"page":"248-274","source":"Crossref","is-referenced-by-count":2,"title":["Approximate Distributions and Power of Test Statistics for Overidentifying Restrictions in a System of Simultaneous Equations"],"prefix":"10.1017","volume":"4","author":[{"given":"Naoto","family":"Kunitomo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600012056_ref020","doi-asserted-by":"publisher","DOI":"10.2307\/1912516"},{"key":"S0266466600012056_ref019","volume-title":"Aspects of multivariate statistical analysis","author":"Muirhead","year":"1982"},{"key":"S0266466600012056_ref001","first-page":"565","article-title":"An asymptotic expansion of the distributions of the limited information maximum likelihood estimate in a simultaneous equation system","volume":"9","author":"Anderson","year":"1974","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600012056_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(80)90031-7"},{"key":"S0266466600012056_ref011","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1970.10481072"},{"key":"S0266466600012056_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/1909575"},{"key":"S0266466600012056_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90035-5"},{"key":"S0266466600012056_ref017","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.2307\/1913858","article-title":"The exact finite sample distribution function of the limited information maximum likelihood identifiability test statistics","volume":"40","author":"Donald","year":"1972","journal-title":"Econometrica"},{"key":"S0266466600012056_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/2526123"},{"key":"S0266466600012056_ref021","first-page":"97","volume-title":"Advances in Econometrics","volume":"II","author":"Rhodes","year":"1983"},{"key":"S0266466600012056_ref004","unstructured":"Anderson, T.W. & Fang, K.T. . Distributions of quadratic forms and Cochran's theorem for elliptically contoured distributions and their applications. Technical Report No. 54, Department of Statistics, Stanford University, 1982."},{"key":"S0266466600012056_ref006","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729752"},{"key":"S0266466600012056_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/1912691"},{"key":"S0266466600012056_ref007","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001135X"},{"key":"S0266466600012056_ref005","unstructured":"Anderson, T.W. & Fang, K.T. . On the theory of multivariate elliptically contoured distributions and their applications. Technical Report No. 54, Department of Statistics, Stanford University, 1982."},{"key":"S0266466600012056_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1911225"},{"key":"S0266466600012056_ref008","first-page":"229","article-title":"The numerical values of some key parameters in econometric models","volume":"16","author":"Anderson","year":"1980","journal-title":"Journal of Econometrics"},{"key":"S0266466600012056_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1960.10483365"},{"key":"S0266466600012056_ref003","volume-title":"An introduction to multivariate analysis","author":"Anderson","year":"1984"},{"key":"S0266466600012056_ref016","unstructured":"Magdalinos, A.M. The local power of the tests of overidentifying restrictions. Unpublished Manuscript, 1986."},{"key":"S0266466600012056_ref014","first-page":"156","article-title":"Asymptotic expansions of the distribution of estimates of coefficients in simultaneous equation system when the disturbances are small","volume":"32","author":"Kunitomo","year":"1981","journal-title":"The Economic Studies Quarterly"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600012056","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T05:03:06Z","timestamp":1636434186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600012056\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,8]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1988,8]]}},"alternative-id":["S0266466600012056"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600012056","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,8]]}}}