Abstract
This paper generalizes the model of Becker, Grossman, and Murphy (1994) to the multivariate case. The multivariate model generates Frisch demand functions where current consumption is related to prices of all goods, and lagged and future consumption of all goods. The theoretical restrictions are that current price effects (holding lagged and future consumption constant) are negative definite, and lagged and future consumption are proportional to one another, the proportionality factor being the consumer’s discount rate. The conditions for dynamic stability are derived, and the solution to the matrix difference equation is derived. General formulas for multivariate Frisch price elasticities with respect to different lengths of time are also derived. Finally, alternative econometric specifications are derived, showing how theoretical restrictions can be imposed to test the theory and to reduce the number of estimable parameters. It is also shown how the model can be modified to account for different discount rates by commodity when estimating the model using aggregate data.
Highlights
The workhorse of empirical analysis of dynamic demand is the rational addiction model of Becker, Grossman, and Murphy [1]
The theoretical restrictions are that current price effects are negative definite, and lagged and future consumption are proportional to one another, the proportionality factor being the consumer’s discount rate
Bask and Melkersson [2] and Pierani and Tiezzi [3] extend the rational addiction model to two goods, but do not analyze the restrictions imposed by theory or derive the dynamic properties of the model
Summary
The workhorse of empirical analysis of dynamic demand is the rational addiction model of Becker, Grossman, and Murphy [1]. This model has proved useful in estimating short-run and long-run demand elasticities, but it only allows for one commodity and one composite good. Bask and Melkersson [2] and Pierani and Tiezzi [3] extend the rational addiction model to two goods (and the composite good), but do not analyze the restrictions imposed by theory or derive the dynamic properties of the model. The purpose of this paper is to present the multivariate addiction model and analyze the restrictions imposed by theory as well as the dynamic properties of the solution to the matrix difference equation
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