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The Inverse Lewbel Demand System Open Access


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Eales, James
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demand systems
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Lewbel (1989) offered a demand model which nested both the indirect translog (ITL) of Christensen, Jorgensen, and Lau (1977) and almost ideal demand system (AIDS) of Deaton and Muellbauer (1980a, 1980b). It has the advantage, then of allowing the applied demand analyst to test the restrictions which imply the ITL and AIDS models directly. In terms of parametric analysis of demand, the increased generality of Lewbel's demand system should minimize the impact of maintained hypotheses on the outcome of the statistical analysis. All of these models have appealing theoretical properties, they correspond to a well defined preference structures, which is convenient for welfare analysis. These so-called PIGLOL preferences also have the property of consistent aggregation from the micro to the market level, while allowing nonlinear Engel curves. Second, the functional form of the preferences is \"flexible\" in that it can be thought of as a local second order approximation to an unknown preference structure. Third, homogeneity and symmetry restrictions depend only on estimated parameters and so are easily imposed and/or tested. There are commodities for which the assumption of predetermined prices at the market level may not be viable. Some of the earliest applied work in demand for agricultural products took current supplies as fixed and therefore specified ad hoc inverse demand curves for statistical evaluation. This alternative aggregation story is still employed, especially by those building market models, such as Freebairn and Rausser (1975) and Arzac and Wilkinson (1979). So, for example, if modeling demand for a perishabl commodity, the production of which is subject to long biological lags, the researcher might employ inverse demands. Production lags prevent market-level supply response, while perishability requires the commodity be consumed. Thus, price must adjust. Not all previous studies which have employed inverse demand structures have proceeded in an ad hoc manner. Heien, and Chambers and McConnell developed separable inverse demand systems and applied them to food commodities. Barten and Bettendorf developed an inverse Rotterdam system and applied it to the demand for fish. Christensen, et al. develop the direct translog demand system (as well as the indirect system). Both they and Jorgenson and Lau use the direct translog demand system to test demand restrictions. Huang used the theoretical development of Anderson and the distance function to generate a system of inverse demands, which were applied to composite food and nonfood commodities. Eales and Unnevehr also employed a particular distance function to develop an inverse AIDS model. In the sections that follow a model which nests both the direct translog (DTDS) and the inverse almost ideal demand system (IAIDS) is developed. This system will be referred to as the inverse Lewbel (ILDS). These three demand systems are then compared and contrasted and used to model Canadian demand for meat.
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