A Dynamic Version of The Linear Expenditure Model

Abstract

qi yj + (xjpjyj). Pi Stone, who applied this model in several papers (1954, 1964, 1965), suggested the parameters could either be given a time trend or allowed to depend on the past history of the branch of demand to which they relate. We want to explore the second suggestion and to see what happens when the y's are explained by past choices. In doing so, our approach will be close to the one followed by R. A. Pollak in (1970). Pollak redefines the y's as linear functions of consumption in the previous period, while we redefine these as linear functions of current values of state variables representing stocks of durable goods or habits. This has the advantage of bringing durable goods into the picture and in particular permits the introduction of a depreciation rate. Our approach is different from Pollak's in another respect: short-run behavior will be shown to be a partial adjustment to long-run equilibrium, thus permitting estimation of a reaction coefficient for each commodity. To a large extent, we follow the line of thought suggested by Houthakker and Taylor in the second edition of Consumer Demand in the U.S. (1970, chap. 5) in dynamizing the quadratic utl1it3 function. Improvements include the ex, ici t formulation of the partial adjustment procl. ;s implied in the maximization behavior anu specific consideration of the covariance structure of the error term.

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