Distribution of Preferences and Measurement Errors in a Disaggregated Expenditure System

Abstract

A complete system of consumer expenditure functions with 28 commodity groups is modelled and estimated by means of Norwegian household panel data. Measurement errors are carefully modelled. Total consumption expenditure is modelled as a latent variable, purchase expenditures on different goods and two income measures are considered as indicators of this basic variable. The distribution of individual differences in preferences, represented by individual, time invariant latent variables in the expenditure functions, is structured by means of a two level utility tree which permits a parsimonious parameterization. The usual assumption of no measurement error in total expenditure is clearly rejected. The standard assumption in factor analysis of uncorrelated measurement errors is also clearly rejected. In particular, we find positive correlation between measurement errors (purchase residuals) of food groups which may be explained by rational shopping behavior of the households. The purchase residuals for automobiles show negative serial correlation and positive correlation with the volatile components of latent total expenditure, which is reasonable for such a durable good. The first and second order moments of the observed variables, which are the input in the analysis, consist of 2015 elements which are modelled by means of 213 structural parameters in our reference model. The maximum likelihood estimates of the latter have, with only a few exceptions, the expected sign and a reasonable size.