Spectral Utility Functions and the Design of a Stationary System - Bowden, Roger J. (Econometrica, 1977)
abstract: the conventional approach to the design of stochastic systems operates, either directly or indirectly, by minimising the variance of the model. this procedure can be regarded as a natural extension of the stability analysis of a deterministic system, according to which the degree of stability is inversely related to the absolute value of its largest characteristic root. very often, however, the policymaker is not indifferent to the frequency composition of economic fluctuations. he may, for example, have a marked dislike for short-term fluctuations. we formalize this notion by setting up a spectral utility function as a criterion for steady-state optimisation, and show that the results from such an optimisation may conflict with those yielded by the conventional approach. large characteristic roots may not necessarily be bad! the scheme of the paper is as follows. because the ideas involved may be unfamiliar we shall spend some time on a rather intuitive motivation for what follows. this is done in section i. in section ii the notion of a spectral utility function is introduced and its evaluation discussed. we then return to the example of section i to give it a more precise treatment. section iii contains extensions, principally to the multivariate case.;