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Would you be indifferent between holding cash in your wallet and holding a two-year maturity bond of a bank? If not, you should be interested in Divisia money calculations.

Standard simple-sum monetary aggregates, like M3 published by the ECB and other central banks, sum up monetary assets that are imperfect substitutes and provide different transaction and investment services. It is therefore difficult to interpret such aggregates.

More than three decades ago from the University of Kansas initiated a theoretically better way to measure the stock of money, which is called Divisia money. Divisia monetary aggregates are available for the United States (from the and the Federal Reserve Bank of St. Louis), for the United Kingdom (form the Bank of England) and many other countries, but not for the euro area. Using mostly US and UK data a growing academic literature found that Divisia aggregates are useful in assessing the impacts of monetary policy and they work better in econometric models than simple-sum measures of money.

No Divisa monetary aggregates are published for the euro area. In a working paper published today I calculated Divisia money indicators for the euro area. The dataset is downloadable from here. The good news is that I found that Divisia money aggregates work quite well in econometric models of the euro area and they lead to better results than simple-sum money indicators.

The theoretical derivation of a Divisia indicator is demanding, but the intuition is straightforward: it is calculated by weighting the changes in different money components (like cash, demand deposits, time deposits, etc.) with their usefulness in making transactions. In practice, the weight of an asset in Divisia aggregate is influenced by the difference between two yields: the yield on an asset which does not provide transaction service but only helps to transfer wealth from one period to the next, and the yield of the asset in question. For example, the yield on cash is zero so cash has a relatively high weight, while the yield on a two-year maturity bank bond is high, so it has a relatively lower weight in Divisia calculations.

The following chart compares the 12-month percent changes in euro area M3, as published by the ECB and as calculated by us using the Divisia formula. There are some notable differences. For example, there was an acceleration of money growth in late 2006 and 2007 according to the simple sum measure, but our Divisia measure suggests that there was no major increase in money growth that time. This indicates that while the standard monetary aggregate used by the ECB suggested that inflationary pressures were increasing, this was not the case with our Divisia measure. In 2009, the growth rate of simple sum M3 fell below zero, but our Divisia indicator suggested that money growth remained positive. And in recent months the growth rate suggested by Divisia money is somewhat higher than the growth rate of the simple sum M3, which is good news as Divisia money growth used to predict nominal GDP growth. However, even the most recent money growth rate (September 2014) is well below the growth rates observed in the first half of the 2000s so the outlook is not rosy yet.

Figure 1: 12-month percent change in M3 monetary aggregates

And finally let me share one of the results of my econometric calculations. The Figure below shows the estimated response of euro-area GDP to a shock in monetary aggregates. The response of output to a Divisia shock is positive and statistically significant about 5-7 quarters after the shock. This approximately 1.5 year horizon coincides perfectly with the horizon at which monetary policy it thought to have an effect on the economy. The output level response is temporary as the impulse-response function returns to zero, which is quite sensible because we would not expect a monetary shock to have a permanent impact on the level of output. While the shape of the responses to shocks to simple-sum monetary aggregates is similar, the impulse response function is never significant.

Figure 2: Response of euro-area GDP to a shock in monetary aggregate

The unmistakable conclusion is that Divisia money indicators should complement the analysis of monetary developments. I encourage the ECB to calculate and publish Divisia indices too.

In a working paper published today Zsolt Darvas calculated Divisia money indicators for the euro area.

Download the dataset.