# Money Neutrality, Monetary Aggregates and Machine Learning
## 1 Introduction
Reference [12] investigate the relationship between money growth uncertainty and the level of economic activity in the United States. They use a bivariate VARMA, GARCH-in-mean, asymmetric BEKK model, and they show that increased Divisia money growth volatility is associated with a lower average growth rate of real economic activity. Also, according to their findings, there are no effects of simple-sum money growth volatility on real economic activity, except with the Sum M1 and perhaps Sum M2M aggregates. Moreover, Reference [13] tested the balanced growth hypothesis and classical money demand theory in the context of a multivariate stochastic process consisting of the logarithms of real per capita consumption, investment, money balances, output, and the opportunity cost of holding money. They have made comparisons among traditional simple sum monetary aggregates and the Divisia monetary aggregates. According to their results, Divisia monetary aggregates can and should play an important role in monetary growth theory and money demand theory. Numerous studies show that the Divisia have significant forecasting ability in predicting various macroeconomic variables, compared to the corresponding simple sum. Reference [14] compare the forecasting ability of the simple sum and Divisia monetary aggregates with respect to U.S. GDP using the Support Vector Regression (SVR) methodology. The dataset spans from 1967Q1 to 2011Q4. According to the empirical findings, the Divisia outperforms the simple sum in predicting the U.S. GDP. Reference [15]show that the Divisia monetary aggregates can be useful in gauging the stance of monetary policy and estimating the effects of that monetary policy on output and inflation. Reference [16] nowcast the Chinese monthly GDP growth rate using a dynamic factor model, incorporating as indicators the Divisia M1 and M2, simple sum along with additional information from a large panel of other relevant time series data. The empirical findings show that the Divisia are better indicators than the simple sum monetary aggregates and provide better nowcasting results. Reference [17] shows that forecasts of USA real GDP from a four-variable vector autoregression are most accurate when a Divisia aggregate is included rather than a simple sum aggregate. The innovations of this empirical work are: (a) We compare the forecasting ability of the simple sum and the Divisia monetary aggregates on the economic activity using the Eurocoin index (The Eurocoin is computed by the Bank of Italy and the CEPR. ): An index coincident with the euro area business cycle that includes information on the underlying growth rate of the euro area GDP and it is published monthly in contrast to the GDP that is available only quarterly; (b) we depart from the traditional econometrics area and employ the support vector machines (SVM) methodology for classification from the machine learning toolbox; and (c) we focus our tests to the Eurozone area. We use machine learning in the effort to address the suspected non-linearities in the data generating mechanism of the models. The cases of studies that employ machine learning are very sparse, and the vast literature uses traditional econometrics over the last three decades on this subject. The paper is interesting for both the computer science and economics communities: For computer scientists, the paper concludes that the Eurocoin index can be better forecasted with simple sum and Divisia monetary aggregates M1, M2, and M3; for economists, it shows evidence that money neutrality is not true. The paper is organized as follows: In Section 2, we briefly discuss the methodology and the data, then in Section 3, we present our empirical results. Section 4 concludes the paper.