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Intertemporal allocation of consumption, savings and leisure : an application using Japanese data Darrough, M. N.

Abstract

The purpose of this study is to investigate theoretical frameworks used in formulating models of consumption for individuals and for the whole economy, which are based on the behavioral postulate of utility maximization. Furthermore, the proposed models are subjected to an empirical application using Japanese data. These data are constructed by the author from various sources. Relevant to this task are the concepts of a consistent two-stage maximization procedure, functional separability and aggregation. Four methods of aggregation over goods are extensively discussed. Furthermore, aggregation of individual demand functions is carried out over all people who possess identical utility functions but different incomes. Then the aggregate share equations become functions of all prices, the mean expenditure (wealth) and the distribution of expenditure (wealth) in the economy. Two flexible functional forms, i.e., the translog function and the Generalized Leontief function are used to approximate non-homothetic inverse indirect utility functions. Three models of consumption are specified and estimated. The first two models are atemporal models dealing with food, consumer durables, miscellaneous goods and leisure for the whole economy, based on aggregation by homothetic separability. The third model is the intertemporal model for the representative consumer, using Leontief aggregation to aggregate goods in the future. This aggregation method allows one to take into account demographic shifts in the economy. The computational algorithm is basically an iterative version of generalized nonlinear least squares. An arbitrarily chosen equation is deleted and the remaining N-l equations are estimated to obtain the maximum likelihood estimates. Null hypotheses to be tested are: symmetry and homotheticity conditional on symmetry. The likelihood ratio test procedure is employed to determine the validity of these hypotheses. In the three good model, homotheticity is decisively rejected, while it is not rejected in the leisure model. Homotheticity is again decisively rejected in the intertemporal model. In addition, since both monotonicity and curvature are violated, we impose monotonicity in order to obtain economically meaningful estimates. One of the more significant findings in this study relates income and leisure in the Japanese case. Leisure is income inelastic in the leisure model. Moreover, present leisure in the intertemporal model turns out to be an inferior good.

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