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Bureau of Labor Statistics > Office of Survey Methods and Research > Publications > Browse Research Papers

A Complete Characterization of the Implications of Slutsky Symmetry for the Linear, Log‐Linear, and Semi‐Log Incomplete Demand System Models

Roger H. von Haefen

Abstract

This paper extends previous research by LaFrance [1985, 1986, 1987] by deriving the necessary parameter restrictions for two additional classes of incomplete demand system models to have symmetric Slutzky substitution matrices in a local neighborhood of price and income values. In contrast to LaFrance's previous research, this paper considers models that treat expenditures and expenditure shares as the dependent variables in the specified incomplete demand systems. Along with the eight models considered by LaFrance, the sixteen alternative specifications considered here represent a complete characterization of the implications of Slutzky symmetry for the linear, log-linear, and semi-log incomplete demand system models.