Admissible clustering of aggregator components: a necessary and sufficient stochastic semi-nonparametric test for weak separability

In aggregation theory, the admissibility condition for clustering together components to be aggregated is blockwise weak separability, which also is the condition needed to separate out sectors of the economy. Although weak separability is thereby of central importance in aggregation and index number theory and in econometrics, prior attempts to produce statistical tests of weak separability have performed poorly in Monte Carlo studies. This paper deals with semi-nonparametric tests for weak separability. It introduces both a necessary and sufficient test, and a fully stochastic procedure allowing to take into account measurement error. Simulations show that the test performs well, even for large measurement errors.