The Importance of Functional Form in the Estimation of Welfare: Discussion

Kling's results appear to indicate that the choice of functional forms for simple demand rela-tionships relative to the underlying "true" functional form and the error characteristics will result in widely differing estimates of wel-fare in the form of consumer surplus. An ex-amination of her results indicates that, if each underlying form and error distribution is equally probable, the semilog form performs slightly better than the linear form relative to minimizing total probable mean error. This conclusion is consistent with conventional wisdom with regard to goodness of fit. If, on the other hand, the linear or semilog forms are more likely to be appropriate, then choosing the linear form is somewhat better than the semilog form as an error-minimizing strategy. This result is somewhat counter to the current literature. The real question is the issue of the correct underlying form of the demand function, and this problem cannot be solved without some reference to demand theory and/or the sample characteristics. While the functional forms which Kling uses may be derived from under-lying utility functions for the simple regres-sions (two variables) in her study, they gen-erally are not consistent with more complex cases. Thus, since functional form appears to be a significant factor in welfare estimate vari-ation, and the welfare measure is dependent upon a utility maximization paradigm, it seems imperative to choose functional forms derived from utility theory. Further, for nonmarket recreation data, de-mand studies frequently (if not overwhelm-ingly) have truncated data sets, in that the data are limited to positive observations on the de-pendent variable. The use of any of the thre