Analysis of Distributed Lag Models with Applications to Consumption Function Estimation

SINCE KOYCK'S pioneering work, distributed lag models have come to play an important role in econometrics and much work has been done to develop methods for analyzing them-see e.g. Koyck 15, Klein 12, Solow 20, Fuller and Martin 5, Malinvaud 18, Hannan 9, Liviatan 17, Amemiya and Fuller 1, Zellner and Park 25, Thornber 21, Waud 23, Dhrymes 3, and Griliches 7. In the present paper we present maximum likelihood and Bayesian estimation procedures for estimating the parameters of a typical distributed lag model under four alternative sets of assumptions regarding disturbance terms' properties. Then these procedures and assumptions are employed in analyses of a sample of United States quarterly consumption data to illustrate their application and to show the sensitivity of inferences to the assumptions made about disturbance terms' properties. We also compute posterior probabilities associated with four alternative models. The plan of the paper is as follows. In Section 2, the model to be analyzed is described and alternative assumptions about disturbance terms are introduced. Section 3 contains a discussion of maximum likelihood techniques and application of them in the analysis of U.S. quarterly consumption data. Then in Sections 4 and