Distribution of preferences and measurement errors in a disaggregated expenditure system

Abstract

Summary A complete system of consumer expenditure functions with 28 commodities is modeled and estimated by means of two-wave household panel data. The total consumption expenditure is treated as latent, with two income measures as observed indicators. The distribution of latent individual differences, interpreted as preference variation, is structured by a factor-analytic approach. Absence of measurement error in total expenditure is clearly rejected, as is also the standard assumption of uncorrelated measurement errors. The 2015 first- and second-order moments of the observed variables are modeled by means of 213 parameters in a reference model. Their maximum likelihood estimates have, with only a few exceptions, the expected sign and a reasonable magnitude. A notable finding is positive correlation between measurement errors of commodities belonging to major groups, e.g. foods, which may be explained by rational shopping behavior. The magnitude and ranking of the Engel elasticity estimates are not sensitive to whether the Engel functions are linear or quadratic.