Author(s)

Quirino Paris¹, Francesco Caracciolo²

¹Department of Agricultural and Resource Economics, University of California, Davis, USA.
²Department of Agricultural Sciences, University of Naples, Federico II, Portici, Italy.

A test of the adding up condition in demand systems is crucial for determining whether a share format is admissible when the number of sample goods is smaller than the number of commodity choices available to consumers. This test requires the estimation of a demand system in a quantity format. It cannot be performed when a demand system is specified in share format. The share specification of any demand system is like a straight jacket: once worn, it forces the error covariance matrix to be singular and the adding up condition to hold whether or not the data generating process warrants it. The empirical verification of the adding up hypothesis uses a five-commodity sample selected from the Canadian Family Expenditure Survey with 4847 observations. Three specifications are considered: AIDS (Almost Ideal Demand System), QUAIDS (Quadratic AIDS) and EASI (Exact Affine Stone Index). The hypothesis is rejected in all three cases with a high level of confidence.

Adding up, Demand Systems, Quantity Format, Share Format

Paris, Q. and Caracciolo, F. (2017) Testing the Adding up Condition in Demand Systems. Open Journal of Statistics, 7, 290-304. doi: 10.4236/ojs.2017.72022.