This picture is greatly complicated when restrictions on the structural disturbance variances and covariances, (henceforth "covariance restrictions") are allowed.Koopmans Rubin, and Leipnik (1950) recognized the usefulness of such restrictions for identification and demonstrated their equivalence to bilinear restrictions on the coefficients.This work was pursued by Wegge (1965) j Rothenberg (1971), and especially Fisher (1963, 1965), surveyed in Fisher (19-66, Chapters 3 and 4).Structural estimation is also complicated by covariance restrictions: as pointed out by Rothenberg and Leenders (1964), system instrumental variables estimators (3SLS) are asymptotically inefficient when covariance i restrictions are present.Two features of these results are (i) the absence of useful necessary and sufficient conditions for identifiability in the presence of covariance restrictions, and (ii) the disappearance of the link between restrictions required for identification and instrumental variables required for estimation.The problem of incorporating covariance restric- tions Into the theory of identification and estimation is thus Incomplete.In this and a companion paper on estimation (Hausman-Taylor (1981)), we provide a simple, complete, and useful solution to the problem In terms of instrumental variables .In the present paper, we derive necessary and sufficient conditions for identifiability in linear simultaneous equations models subject to linear restrictions on the coefficients and covariances.The result, in practical

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica.

[In most statistical estimation problems, the distribution of errors is unknown, and the traditional assumption of normality is used for convenience. We investigate here the fragility of the inferences based on normality by hypothesizing a neighborhood of distributions around the normal distribution, and by identifying the set of alternative maximum likelihood estimates corresponding to the set of error distributions.]

[Forward and spot exchange rates are modelled as an unrestricted bivariate autoregression from weekly data on the New York foreign exchange market for June, 1973 to April, 1980. The null hypothesis that the forward exchange rate is an unbiased estimate of the corresponding future spot exchange rate is tested by means of a nonlinear Wald test and is rejected for all six currencies considered. The results cast doubt on a central assumption in many current models of exchange rate behavior.]