FLEXIBILITY IN DYNAMIC DEMAND MODELLING AND ITS IMPLICATIONS FOR TESTING RESTRICTIONS

Abstract

SUMMARYThis paper has proposed and estimated a dynamic generalization of the Almost Ideal Demand System (AIDS) introduced by Deaton and Muellbauer. The dynamization consists of letting the AIDS parameters depend on lagged purchases in a non‐separable manner that allows a considerable degree of generality and flexibility in the nature of dynamic response. The flexible nature of AIDS, in conjunction with the flexible pattern of dynamization adopted, provided an unrestricted, dynamic framework which allows test of a host of nested hypotheses. Such hypotheses related to (a, the existence and nature of dynamic behaviour, (b) the validity of homogeneity and symmetry restrictions in the dynamic framework, (c) the structure of price responses within the AIDS set‐up, and (d) the presence of serial correlation in the residuals and its ability to detect the presence of dynamic misspecification. The data base consisted of a four‐item classification of U.K. nondurable consumer expenditure between 1900 and 1980.The principal result of this study is that on time series data of the sort used here a satisfactory approach to dynamic modelling must admit dynamic preference of a non‐additive type including commodity specific effects of lagged purchase of individual items. Such dynamic flexibility must be introduced within a framework which, itself, is of flexible functional form type. The present study establishes a dynamic version of AIDS which is a considerable improvement, on likelihood criterion, over the static version and can be recommended for future use. As n referee pointed out, however, the Pollak‐like dynamic AIDS extension proposed here places severe demands on the data by way of the large number of parameters that need to be estimated. Researchers who, unlike us, do not have long‐time series data, may need to enforce several a priori restrictions to achieve efficient estimation and power in hypothesis testing.The negative test results on homogeneity and symmetry, seen in most static demand studies, could not be reversed in the dynamic case. The hypothesis of a stable model between pre‐World War II and post‐World War II was tested and could not be rejected on the present data.The serial correlation parameter was found to be insignificant in all the estimated models. This throws doubt on the validity of the widespread use of this parameter to detect misspecification in estimated demand systems. The Deaton‐Muellbauer result that imposition of homogeneity leads to serially correlated residuals could not be reproduced in the present study. Also, the present results suggest that estimating AIDS in first difference form assuming serially uncorrelated errors in the transformed equation may lead to misspecification in view of our rejection of unit p in the original errors in the levels equation.Not long ago, Barten (1977) noted in an important survey paper, “the empirical complications introduced by endogenously changing preference have, until now, forced most researchers to confine their attention to the we of strongly separable (or additive) preferences. Undoubtedly, future research will try to apply dynamics to more general preference structures”. The present study represents, hopefully, a significant step in the desired direction of introducing flexible dynamics in flexible demand systems.