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 aggre-gates, 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 mea-surement. 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 optimiza-tion error. Moreover, in this paper, we extend the test to also deal with incomplete adjustment, and introduce a new empirical econometric proce-dure 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-.