IT IS WELL KNOWN that least-squares estimates of the coefficients of a regression equation are inconsistent if any of the regressors are measured with error. The nature of these inconsistencies has been examined by Aigner [1], Blomqvist [2], Chow [3], Levi [5], McCallum [6], and Wickens [10] for the case in which a single regressor is subject to measurement error. The purpose of this study is to examine the nature of these inconsistencies when more than one variable is measured with error. We begin by reviewing the case of one variable measured with error, developing a unified treatment of issues which previously have been discussed separately. Concentrating on the case in which two regressors are measured with error, we then examine how the predictions of the one erroneously measured regressor model must be qualified when more than one regressor is subject to measurement error.

Positive public-utility models should capture incentives of regulators. Regulatory objectives are specified by appeal to standard human concerns and politics and processes peculiar to public-utility regulation. Constraints that serve the regulator are thereby derived, and connections between regulatory objectives and rules illuminated. Theoretical rationales emerge for "rate-of-return" regulation under certainty, and a largely neglected type of rate-of-return regulation under uncertainty. Motives of human regulators may explain other regulatory forms as well.

Positive models of public-utility regulation should capture personal incentives of regulators. A regulatory objective function is specified by appea l to standard human concerns coupled with politics and processes pecu liar to public-utility regulation. Constraints a rational regulator w ould impose on the firm are thereby derived, and connections between regulatory objectives and regulatory rules illuminated. Results inclu de theoretical rationales for "rate-of-return" regulation in a worl d of certainty, and a largely neglected type of "rate-of-return" re gulation under (symmetric) uncertainty. Other forms of regulation sho uld also be explicable in terms of personal motives of human regulato rs. Copyright 1988 by American Economic Association.