# Money Neutrality, Monetary Aggregates and Machine Learning
## 4 Conclusion  
In this study, using the money supply, we attempt to forecast, out-of-sample, the economic activity within the euro area. In this macroeconomic setting, we innovate by employing in the empirical section a machine learning methodology, the support vector machines (SVM) for binary classification. Moreover, instead of using the low frequency (quarterly) GDP time series to measure economic activity, we use the Eurocoin index that is available in monthly frequency from January 2001 to June 2018. The Eurocoin is an index that measures the growth rate of the euro area GDP, and it is produced by the Bank of Italy and the CEPR. Furthermore, we use two alternative sets of monetary aggregates as a proxy for money supply: The commonly used by most statistical agencies and central banks all over the world simple sum monetary aggregates and the theoretically correct, as they are constructed according to the index numbers theory, Divisia monetary aggregates proposed by the Barnett Critique [5,6]. Both aggregates are used in three levels of aggregation, from the narrow M1 to the broader M2 and M3 aggregates. The forecasting methodology employed comes from the area of machine learning and is the support vector machines supervised algorithm for classification. Two alternative kernels are used in the taring process: The linear and radial basis function (RBF). First, we train the best possible Autoregressive Models (AR) to forecast the Eurocoin. Next, we train structural models by adding one-by-one each of the six alternative monetary aggregates (simple sum M1, simple sum M2, simple sum M3, Divisia M1, Divisia M2 and Divisia M3). This empirical setup allows us to derive significant inference in several directions. First, we can compare the forecasting accuracy of the simple sum and the Divisia monetary aggregates in terms of the Eurocoin index (euro area GDP growth rate). Second, in the case that some of the aggregates can adequately forecast economic activity better than the best AR models, this can be interpreted as evidence against money neutrality; money, in that case, would matter for the economy. The money supply at \(t\) forecasts economic activity at \(t+1\). If the structural models (with the use of the monetary aggregates) cannot forecast the Eurocoin index better than the AR models, then we can conclude that money is neutral as it cannot adequately forecast economic activity: The money supply at \(t\) cannot forecast the economic activity at \(t+1\). The empirical results show that the structural models that use the monetary aggregates (using the linear kernel) outperform the autoregressive ones in terms of forecasting accuracy. In that case, the money supply (expressed by the simple sum and Divisia monetary aggregates) affects the economic activity, thus, since money can forecast economic activity as measured by the Eurocoin index, we provide empirical evidence against money neutrality: Money seems to matter. Moreover, the Divisia monetary aggregates outperform the relevant, simple sum ones both in-sample and out-of-sample. In one case only (the M1 out-of-sample) the two aggregates have the same accuracy. The best overall out-of-sample forecasting accuracy is achieved with the Divisia M2 monetary aggregate reaching 82.05%. Thus, we conclude that the Divisia monetary aggregates, overall, outperform the simple sum ones in terms of forecasting the Eurocoin index. The policy implications of these results are obvious for the European Central Bank (ECB) when designing and implementing monetary policy in the euro area. The money supply was abandoned as a target for the monetary policy three decades ago as it did not seem to adhere closely to economic activity. As a result, the monetary aggregates were replaced by the interest rate as a tool for the implementation of monetary policy by most large central banks around the world.