Engel Functions, Panel Data, and Latent Variables

A system of consumer expenditure functions is estimated from Norwegian household budget data. Specific features of the approach are: (i) Panel data from individual households are used, which offer far richer opportunities for identification, estimation, and testing than cross section data. (ii) Measurement errors are carefully modelled. Total consumption expenditure is modelled as a latent variable; purchase expenditures on different goods and two income measures are used as indicators of this basic latent variable. The usual assumption of no measurement error in total expenditure is clearly rejected. (iii) The distribution of latent total expenditure across households, and its evolution over time, is estimated and important properties tested. (iv) The distribution of individual differences in preferences, represented by individual time invariant latent variables, are modelled, estimated, and tested. (v) We test the hypothesis that preferences are uncorrelated with total consumption expenditure, which is basic to virtually all cross section studies of consumer demand functions.