[For the two sample linear heteroscedastic regression model, moments of a popular two stage Aitken estimator are derived analytically. Even for small samples and/or near homoscedastic errors, the two stage procedure is surprisingly efficient relative to both unweighted least squares and the Gauss-Markov estimator. These exact results are compared with the author's previous calculations derived from Nagar approximations.]

[Conditions under which a single iteration approximation to the maximum likelihood estimator dominates ordinary least squares are approximated analytically for the class of linear models for which the eigenvectors of the error covariance matrix are known.]

usefulness of prior information. Viewed broadly, this theme has encompassed such diverse topics as the estimation of a system of simultaneous structural equations, the specification and estimation of distributed lags, and the formal integration of stochastic prior and sample information through Bayes' theorem. Without exception, the results have encouraged the incorporation of further prior information into our statistical procedures, in the sense that the judicious use of such information has produced unambiguously better estimators. That this need not be the case in a typical linear regression application is thus somewhat surprising and constitutes the topic of this paper. Here, we develop the relationship between the specification of the deterministic and the stochastic components of a linear model and show that whenever the covariance structure of the disturbance process is effectively misspecified,2 one can no longer justify the use of prior information about the deterministic part of the model. If the error covariance matrix differs substantively from that required by the Gauss-Markov theorem, the imposition of correct linear restrictions on the regression coefficients leads to less efficient estimators of some estimable functions of the parameters.3 Prior information can hurt! We begin by introducing notation and examining the efficiency of least squares estimators in linear models with varying amounts of prior information. An application of the theory of regular pencils then produces the main results (Section 3), practical implications are drawn in Section 4, and we conclude with an application (Section 5).

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

An important purpose in pooling time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables, e.g. latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions. Using instrumental variables and the time-invariant characteristics of the latent variable, we derive: 1. (1) a test for the presence of this effect and for the over-identifying restriction we use; 2. (2) necessary and sufficient conditions for identification of all the parameters in the model; and 3. (3) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups and Balestra-Nerlove estimates — particularly a significantly higher estimate of the returns to schooling.

From Fred Kahn's writings and experiences as a telecommunications regulator and commenter, we draw the following conclusions: prices must be informed by costs; costs are actual incremental costs; costs and prices are an outcome of a Schumpeterian competitive process, not the starting point; excluding incumbents from markets is fundamentally anticompetitive; and a regulatory transition to deregulation entails propensities to micromanage the process to generate preferred outcomes, visible competitors and expedient price reductions. And most important, where effective competition takes place among platforms characterized by sunk investment—land-line telephony, cable and wireless —traditional regulation is unnecessary and likely to be anticompetitive.

This paper is a revision of an earlier version presented at the European Econometric Meetings, 1982