On the bias in flexible functional forms and an essentially unbiased form: The fourier flexible form

Abstract

The Fourier flexible form and its derived expenditure system are introduced. Subject to smoothness conditions on the consumer's true indirect utility function, the consumer's true expenditure system must be of the Fourier form over the region of interest in an empirical investigation. Arbitrarily accurate finite parameter approximations of the consumer's true expenditure system are obtained by dropping all high-order terms of the Fourier expenditure system past an appropriate truncation point. The resulting finite parametersystem is tractable in empirical studies. The reader who is primarily interested in applications need only read the second and fifth sections. The remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in Translog specifications.