This paper attempts to determine conditions under which distributed lag analysis is appropriate. Results indicate that lag functions are stable and linear under fairly general (but constant) objective criteria and decision constraints as long as the underlying economic environment is characterized by a stationary Gauss-Markov process, and observed environmental variables are Gaussian perturbations of that process. The results appear particularly useful for specifying the lag distribution inherent in subjective parameters in specific decision problem contexts. 1. INTRODUC'TION IN AN EARLIER PAPER, Taylor [11] dealt with the problem of determining lag distributions on the basis of optimization assumptions in a dynamic model of uncertainty. Taylor's conclusions, however, are somewhat disturbing in that they indicate only a narrow class of decision problems with uncertainty can be studied in a distributed lag framework. Taylor addresses only an exemplary model of inventory control and by assuming that (i) the firm's cost function can be expressed as a sum of strictly quadratic and linear terms, (ii) all production constraints are linear equalities, and (iii) observed demands are perturbations of unobserved components which follow a Gauss-Markov process, he is able to show that a distributed lag exists in the decision rule. By making yet additional assumptions, he is also able to demonstrate stability of the lag distribution. The purpose of this paper is to generalize the class of decision-makers' objective criteria and the constraint set description under which distributed lag analysis can find some theoretical justification. Although Taylor relies heavily on Kalman filtering theory to derive his results, the equivalent Bayesian approach is used explicitly in this paper for purposes of completeness and continuity.2 Results show that the lag function is stable and linear under more general conditions than Taylor's, although the lag function may enter the resulting econometric model nonlinearly. If econometric investigators are willing to consider nonlinear functions of lag distributions (or approximation of nonlinear functions by linear functions), the results should provide a basis for distributed lag analysis in a much broader class of problems than do Taylor's previous results. Furthermore, it is found that econometric equations which include the distributed lag linearly may exist outside of the set of cases considered by Taylor. The following section begins by specifying the general decision theoretic framework in which we shall operate throughout the paper. The existence of lag functions is made evident. In Section 3, Taylor's environmental system is