Zuhair A. Hassan

Maximum likelihood estimation of linear expenditure systems with serially correlated errors: An application

Abstract The present paper uses Canadian data for the period 1947–1972 and three commodity groups to examine the empirical importance of restrictions imposed by autocorrelated disturbances on the static linear expenditure system, LES. For comparison a simple habit persistence model is also estimated. Results of applications of likelihood ratio tests indicate that autocorrelation is present in the data, that a simple habit persistence hypothesis on the structure is implied and that the restrictions imposed by the form of the utility function and maximization problem are inconsistent with the data whether or not adjusted for the autocorrelation in errors. Despite these differences, the estimated price and income elasticities remain fairly constant across the various specifications of the LES that were considered.

Alternative Estimates of Static and Dynamic Demand Systems for Canada

Selected static and dynamic demand systems are applied to Canadian data for the period 1947–1972. Four commodity groups—durables, semi-durables, services and nondurables—are used for the major portion of the analysis. For the static systems, results for nine commodity groups are provided as a comparison. Income and price elasticity estimates, following from the static systems are, with the exception of the double log, proved reasonably similar. The estimates from the two dynamic systems, the dynamic linear expenditure and state adjustment models, appeared more plausible particularly for services and durable goods, where persistence in consumption patterns is generally observed. As related to other estimates from United States and Canadian data, these results seem to be more stable and more in agreement with a priori reasoning.

Testing for Habit Formation, Autocorrelation and Theoretical Restrictions in Linear Expenditure Systems

The purpose of this paper is to present full information maximum likelihood estimates of linear expenditure systems (LES) and to test for habit formation, autocorrelation and regularity conditions using the likelihood ratio procedure. Estimators for the model and associated tests are based on annual Canadian data for the years 1957-1972. The results obtained provide a basis for helping to clarify concerns with the appropriateness of the LES and an evaluation of alternative characterizations for persistence in consumption patterns. The linear expenditure system has been used in many empirical demand studies. Stone [18], Parks [13], Yoshihara [22], Pollak and Wales [15], Phlips [14], Powell [16] and Deaton [6] and others have presented estimates of the static and simple habit formation variants of the linear expenditure system. Lluch and Williams [11], MacKinnon [12], and Green, Hassan, and Johnson [8] have provided estimates of the LES assuming autoregressive errors. More recently, Howe, Pollak, and Wales [10] estimated the LES considering simultaneously effects of autocorrelation and habits. In this paper we extend our earlier work on autocorrelation and habit formation by developing results which permit a broader basis for evaluating the implications of persistence in consumption behavior for the LES. The plan of the study is as follows. Section II contains a brief review of the LES includ

FURTHER EVIDENCE ON THE STRUCTURE OF CONSUMER DEMAND IN THE U. S.: AN APPLICATION OF THE SEPARABILITY HYPOTHESIS*

The applied economic literature abounds with reports on the estimation of parameters of consumer demand functions. Early attempts were hindered by an inadequate understanding of the theory and inappropriate statistical methods. In following the developments both from the point of view of the evolution of methods and the applied results the patterns are rather clear. Until rather recently demand parameters were estimated by single equation least squares methods. However, as the theory and econometric methods developed, it became clear that these early results were only under special circumstances correct. That is, it became clear that specific demand equations should be estimated within the complete systems explaining market prices and quantities. This observation spawned a number of empirical studies incorporating simultaneous equations methods in estimating systems of demand functions. Results obtained by this more general approach were again however of rather limited generality. The limitations in this case were due to the ad hockery involved in specifying the systems. More specifically, since demand equations contain all