A Flexible Multistage Demand System Based on Indirect Separability.

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A Flexible Multistage Demand System Based on Indirect Separability.

GianCarlo Moschini [*]

The notion of indirect separability is exploited to derive a new multistage demand system. The model allows a consistent parameterization of demand relations at various budgeting stages and it fulfills the requirement of flexibility while satisfying separability globally. Two propositions are derived to characterize flexible and separable functional forms, which lead to the specification of a flexible and separable translog (FAST) demand system. The model is particularly attractive for modeling large complete demand systems and is illustrated with an application to Canadian food demand.

1. Introduction

To be useful for most policy analysis applications, demand systems need to be specified in terms of disaggregated commodities based on relevant conditioning variables, that is, usually one needs to specify a large complete demand system. If at the same time one wants to use parametric specifications that are not too constraining, such as standard flexible functional forms (FFF), then the data requirement may be prohibitive. A workable solution of this problem entails imposing restrictions on the problem solved by consumers, typically by assuming a separable structure for consumer preferences (Blackorby, Primont, and Russell 1978) [1] In particular, certain separability conditions allow the consumer's expenditure allocation problem to satisfy two-stage (multistage) budgeting rules. As shown by Gorman (1959), a simplified two-stage budgeting is possible under two alternative conditions: homothetic weak separability of the direct utility function, or strong separability (block additivity) of the direct utility function with group sub-utility functions the dual of which have the so-called generalized Gorman polar form (GGPF). Such perfect price aggregation conditions underlie a number of multistage complete demand systems. Models relying on strong separability cum GGPF include Brown and Heien (1972), Blackorby, Boyce, and Russell (1978), Anderson (1979), and Yen and Roe (1989). Homothetic weak separability was used by Jorgenson, Slesnick, and Stoker (1997). [2]

Because the conditions for perfect price aggregation are often deemed too restrictive in empirical applications, attempts have been made to model demand based on the hypothesis of direct weak separability only. Although direct weak separability (DWS) per se is neither necessary nor sufficient for standard two-stage budgeting, it does provide the necessary and sufficient conditions for the existence of conditional (second-stage) demand functions defined only on group prices and group expenditure allocations (Pollak 1971). Because such conditional demand functions typically depend on a small set of variables (data on which is easily found for most applications), some empirical studies have pursued the estimation of second-stage demand functions in isolation (say, demand for food items as function of food prices and expenditure allocated to food). Examples include Barr and Cuthbertson (1994), Gao, Wailes, and Cramer (1997), Kinnucan et al. (1997), and Spencer (1997). But such a widespread approach is highly que stionable because the conditional demand parameters thus estimated are rarely of interest for policy analysis (Hanemann and Morey 1992). In certain instances, a conditional analysis can provide useful information (Browning and Meghir 1991). But in general, the economic question ...

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