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The Box-Cox transformation is used to compare alternative functional forms of market value equations. Based on evidence from a panel of 480 publicly-traded U.S manufacturing companies and two additional data sets used previously in the literature, the semilog form of a Tobin's q equation is found to be strongly preferred to the commonly estimated linear form. We provide illustrations in which inferences can be affected by the choice of functional form.

Abstract--We obtain expressions for the restricted least squares estimator and its covariance matrix in the classical regression model when the matrix of regressors is not necessarily of full rank. The standard expressions for the restricted least squares estimator are not usable in the short rank case because they rely on the unrestricted estimator. But, in the presence of restrictions, the restricted least squares estimator may be computable even if the unrestricted estimator is not. Our derivation produces some additional, useful algebraic results for least squares computation. [ABSTRACT FROM AUTHOR]

The Box-Cox difference transformation permits the selection of either the first difference or percentage change form of a time series regression model. Monte Carlo evidence on the small sample properties of the transformation parameter Lambda indicates that the difference transformation works quite well even in samples of size 30. Likelihood ratio testing is compared to an asymptotically equivalent alternative Lagrange Multiplier test. It is shown that values of R2 can often be higher for the incorrect transformation. [ABSTRACT FROM AUTHOR]

Abstract--A maximum likelihood method for estimating and testing for the proper functional form in first difference regression models is developed. The parametric transformation of the regression variables we propose includes simple first differences and percentage changes as special cases. The method has a simple relationship to the familiar Box-Cox test, and the coefficient estimation and LR testing are easily implemented with standard regression packages. We apply the new method to three published studies: the St. Louis equation, a money demand model, and a model relating poverty to economic growth. [ABSTRACT FROM AUTHOR]

Econometrics textbooks customarily discuss the general linear model, and then in several subsequent chapters the standard econometric problems of autocorrelation, heteroscedasticity, functional form, and simultaneous equations estimation are each discussed in turn. The G.E.P. Box-G.R. Cox test has been increasingly used as a test for functional form and is now standard in many econometrics texts, but there is not often any attempt made to combine the test with standard econometric problems such as autocorrelation or heteroscedasticity or to indicate that a unified approach is possible. In this article the authors attempt to make several contributions to the literature in this area. Given that most textbook approaches to econometrics begin with ordinary least squares, and then discuss standard econometric problems such as autocorrelation and heteroscedasticity, there seems to be no reason why the Box-Cox test should not be used in conjunction with analogous variations of the standard model when there is evidence of autocorrelation or heteroscedasticity.