Testing exact aggregation in income and household characteristics: the effects of aggregation across goods

Exact aggregation in income and household characteristics are tested using Canadian cross-sectional microdata. Over 100 data sets of homogeneous households are used, making it possible to conduct a large number of independent hypothesis tests. Tests are also conducted to determine whether the homogeneous household groups can be grouped into more heterogeneous data sets. Six different kinds of demand systems are estimated to ensure the robustness of the results to separability/aggregation structure.

Exact aggregation in income, family size, region of residence and housing tenure status are strongly rejected, but exact aggregation in age of head of household is not. Restrictions which would allow pooling of households of different sizes, regions and tenure status are also strongly rejected. The test results exhibit a little sensitivity to the expenditure aggregates used, but not to the extent that the results would be different.

The results imply that aggregate demand functions which use time series data should include many statistics from the joint distribution of income and household characteristics. In addition, when using data at the micro-level, the amount of heterogeneity in households' behaviour is much greater than usually assumed. This calls for the use of much more homogeneous household groups in the estimation of demand models than are typically employed.