Metonymy and cross-section demand

Cross-section consumer expenditure data are frequently used to draw conclusions about consumer demand behavior. Such conclusions, however, are justified only under certain assumptions, which are often left unstated in the empirical demand literature. An assumption of this type, the metonymy hypothesis, was stated rigorously and exploited by Härdle et al. when analyzing the monotonicity of aggregate demand functions. The purpose of the present paper is to examine the metonymy hypothesis in more detail. We prove that the distribution of demand vectors derived from a not necessarily metonymic population is identical with the distribution derived from some metonymic population. This implies, in particular, that the metonymy hypothesis cannot be rejected or confirmed on the basis of data from a single cross-section.