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Implementing Stochastic Semi-Nonparametric Tests for Weak Separability to Define Money : An Empirical Study on US Data

This paper focuses on the weak separability of various monetary aggregates, narrow or broad as the DM4 one. Since weak separability is both a necessary and sufficient condition for aggregating over monetary assets, our paper has straightforward implications in terms of monetary measurement. It also returns key information about the definition of money. To test for weak separability, we implement the Barnett and de Peretti (2009) semi-nonparametric test for weak separability, partly based on the General Axiom of Reveal Preference. With regard to existing competing tests, their procedure is both: i) Necessary and sufficient, ii) Stochastic, i.e. dealing with measurement error in quantity data or small optimization error. Moreover, in this paper, we extend the test to also deal with incomplete adjustment, and introduce a new empirical econometric procedure to test for the separability condition, robust to measurement errors. Using monthly US data, spanning 1968:01 to 2012:12, our results support the weak separability of a broad monetary aggregate as DM4 or DM4-.