12: The Trio Level-1.5 Algorithm for Bc-Gauheseq Regression

In applied regression analysis, the most important aspect in model specification is the choice of the functional forms of the dependent and independent variables. As Zarembka (1968) has noted, economic theory rarely indicates the appropriate forms under which the variables should appear, except for the signs of the regression coefficients which are expected to be positive or negative according to the assumptions made on the economic behavior of the dependent variable with respect to the changes of the explanatory variables. The three classical forms often encountered in econometric studies are the linear, semilog and log-linear forms due to their computational ease with a standard regression computer package. One way of letting the data determine the most appropriate functional form is the use of a class of power transformations considered by Box and Cox (1964). The main advantage of this approach is that statistical tests can be performed on the Box-Cox parameters to discriminate the estimated functional forms against the classical forms which all appear as special cases of the Box-Cox transformation. Early applications of this transformation can be found in various fields of economic analysis: monetary economics [Zarembka (1968), White (1972), Spitzer (1976, 1977)], income analysis [Heckman and Polachek (1974), Welland (1976)], production theory [Appelbaum (1979), Berndt and Khaled (1979)], and transportation [Kau and Sirmans (1976), Hollyer et al. (1979)].