Toshinobu Matsuda

Differential Demand Systems: A Further Look at Barten's Synthesis

Bartens synthetic model is attractive to applied researchers since it is useful for testing the adequacy of the competing functional forms of differential demand systems including the popular Rotterdam and almost ideal demand systems. This article shows that the synthetic model is not a mere artificial composite of the known differential demand systems as it has been considered, but rather viewed as a model in its own right. It is demonstrated that, at the individual consumer level, Bartens model has the same marginal budget shares as generated by specific forms of Engel curves formulated by the Box–Cox transformation.

Forms of Scale Curves and Differential Inverse Demand Systems

This article provides a new interpretation of the scale effects in differential inverse demand systems. A scale curve is defined as a curve that shows how the expenditure share of a good or service changes as the consumption level changes. It is shown that Brown, Lee, and Seales synthetic model has the same scale effects as do the Box-Cox scale curves. In this light, their model is not a mere composite but a model in its own right. An empirical illustration given for Japanese fresh food demand suggests that the underlying scale curves differ from both linear and loglinear forms.

Incorporating Generalized Marginal Budget Shares in a Mixed Demand System

This article extends a Rotterdam type of mixed demand system by replacing its constant marginal budget shares with the ones derived from originally defined and specified mixed Engel curves that take a generalized functional form using the Box-Cox transformation. An empirical illustration is given for Japanese demand for fresh and processed fruits and vegetables. The results show that the Rotterdam parameterization of marginal budget shares, which corresponds to those in linear mixed Engel curves, is preferred by the data, and that improper assumptions of the form of mixed Engel curves underlying a mixed demand system can bias its elasticities. Copyright 2004, Oxford University Press.

A trigonometric flexible consumer demand system

This paper proposes the first ever empirical specification of a trigonometric demand system. The new model is potentially useful because of some attractive features. It is flexible, amenable to exact aggregation over consumers, possessed of trigonometric Engel curves, which can oscillate, and able to have an unusually large regular region. With comparisons between the new model and two other popular models, an illustration is given for Japanese demand for non-durables and services. The new model shows relatively gentle Engel curves with an inflection point on each of them, which seem reasonable, given that aggregate expenditure is used in parameter estimation.

Linearizing the inverse quadratic almost ideal demand system

This article investigates the linear approximation to the inverse quadratic almost ideal demand system (IQUAIDS), a recently introduced flexible functional form with potential usefulness. Linearizing this nonlinear model is of practical importance because nonstationary data, which are likely to be used in inverse demand systems, can be handled more properly in linear models. The IQUAIDS is linearized by replacing the two aggregator functions with a number of alternative quantity indices and new composite variables. The results of an application to Japanese fresh food demand suggest that the IQUAIDS can be linearized with adequate accuracy in terms of elasticities.

A BOX-COX CONSUMER DEMAND SYSTEM NESTING THE ALMOST IDEAL MODEL ∗

This article proposes a consumer demand system that has a generalized functional form characterized by the Box-Cox transformation. The new model offers a wider range of responses to both price and expenditure changes than the existing price independent generalized linear models, including the almost ideal demand system. Even with these features, its functional form is relatively simple and easy to interpret and implement. An empirical illustration is given for Japanese demand for nondurable goods and services. The results show that the new model is preferable to the nested models in terms of relative explanatory power and producing reasonable elasticities. Copyright 2006 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.