Investigating the Role of Real Divisia Money in Persistence-Robust Econometric Models

This paper investigates the causal relationships between real money and real activity. Whereas previous literature has mainly focused on simple-sum aggregates, we instead use Divisia ones, thus avoiding the so-called Barnett Critique. Standard Granger non-causality tests are implemented in two di¤erent frameworks: Fully Modi…ed VARs (Phillips, 1995) and surplus-lag VARX models (Bauer and Maynard, 2012). These two environments allow modeling mixtures of I(0)/I(1) variables with possible cointegration without pretesting for ntegration nor for the dimension of the cointegration space. Moreover the latter method is also robust to various other forms of persistence such as local-to-unity processes, long memory/fractional integration, or unmodeled breaks-in-mean in the causal variables. By implementing the tests on di¤erent sub-samples identi…ed by standard structural break tests, and using three di¤erent measures of money (DM4, DM4- and DM3), the tests suggest a unidirectional causality from activity to money. Moreover, from one period to another, the whole causal structure of the systems seem to change, as well as the stationarity of the series. At last, the two methodologies return similar results.