Why the ECB should look at M2

By: Georg Rich, Rich International Consulting

In my February 2007 contribution to the EMU Monitor I discussed a procedure for extracting information from the ECB’s second pillar, notably from the development of the monetary aggregates of the euro-zone, that could be used for cross-checking the policy conclusions drawn from its first pillar. The procedure was based on an econometric analysis of demand for the euro-zone monetary aggregate M3. I assumed that the ECB proceeds as follows: It estimates at regular intervals long-run money demand functions, relating the level of M3, deflated by the HICP consumer price index, to the level of real GDP and various interest rate variables, in particular, to the differential between the three-month euribor rate and the ten-year bond yield. I chose these explanatory variables because they had been shown to be important determinants of the demand for M3 in previous studies.

From the estimated money demand functions, I further assumed that the ECB at the end of each year derives a reference line describing the evolution of the nominal value of M3, likely to be consistent with its objective of keeping inflation slightly below 2 percent. The reference line thus determined was assumed to guide monetary policy for the subsequent five quarters. Moreover, I took account of the fact that the ECB is prepared to accommodate the increase in the demand for M3 arising from potential real growth in the euro-zone economy. Finally, in deriving the reference lines, the ECB was assumed to keep the refinance rate, that is, its policy instrument constant over the subsequent five quarters. Of course, the ECB was free to update its reference line within the year in the light of new information such as changes in its refinance rate. If during the subsequent five quarters the actual level of M3 exceeded/fell short of the reference line, the information extracted from the second pillar suggested that monetary policy was too expansionary/too tight and that the ECB should consider an adjustment in its refinance rate.

 

Figure 1: Growth in the euro-zone aggregates M2 and M3

 

 
Unfortunately, the results obtained for the aggregate M3 were not encouraging. In particular, the reference lines derived for the two most recent five-quarter periods (2006Q1 to 2007Q1 and 2007Q1 to 2008Q1) made little sense because of serious instabilities the demand for M3 emerging after 2005. Therefore, the question arises whether applying my procedure to an alternative monetary aggregate yields more convincing results than for M3. In the following, I perform my estimations and calculations for the euro-zone aggregate M2. Fig. 1 shows that there was a fairly close positive correlation between the growth in the aggregates M2 and M3. Nevertheless there were significant deviations at times even though the two aggregates generally moved in tandem. Therefore, it is possible that that demand for M2 may be more stable than demand for M3.

In line with the analysis presented in my February contribution, the ECB, say, at the end of 2006 is assumed to estimate a demand equation for real M2, covering the sample period 1998Q2 to 2006Q4. The staring date of the sample period is determined by the availability of data. Real M2 is defined as the nominal level of that aggregate divided by HICP consumer price index (all the variables are seasonally adjusted). The estimated real money demand equations are relatively simple: The ECB relates the log of real demand for M2 to the log of real GDP and the differential between the three-month euribor rate and the ten-year government bond yield. The estimates presented in the table are based on cointegration analysis. The Johansen cointegration test suggests that the three variables considered in the analysis are conintegrated. There exists at least one cointegrating equation, which I interpret as a long-run money demand function.

 

Estimated coefficients in equation for real M2 demand
(Dependent variable: log real M2)

Sample Period	Independent variables
	Log real GDP (income elasticity)	Interest differential	Constant
1998Q2 – 2003Q4	1.508 (21.8)	-0.048 (-9.5)	-6.291
1998Q2 – 2004Q4	1.522 (10.4)	-0.074 (-7.4)	-6.532
1999Q2 – 2004Q4	2.305 (11.9)	-0.046 (-6.1)	-17.731
1998Q2 – 2005Q4	1.884 (11.4)	-0.063 (-5.0)	-11.691
2000Q2 – 2005Q4	2.499 (14.2)	-0.047 (-8.0)	-20.522
1998Q2 – 2006Q4	1.947 (19.5)	-0.036 (-3.9)	-12.556
2001Q2 – 2006Q4	2.434 (19.0)	-0.047 (-9.0)	-19.577
Data source: ECB. Numbers in parentheses indicate t-values.

 

The estimates in the table raise a number of problems that need to be discussed. First, the results are sensitive to the choice of the interest rate variable in the money demand equation. If the interest differential is replaced by the euribor rate, the Johansen procedure does not point to any cointegration among the variables. Therefore, I rejected this specification. By contrast, if the interest rate differential is replaced by the bond yield, cointegration exists, but the coefficient for real GDP becomes unstable and tends to assume implausibly low values in the sample periods ending with 2003Q4 and 2004Q4. Fig. 2 shows why econometric studies are likely to underestimate the influence of real GDP on money demand in the early part of the period under consideration if the bond yield is employed as an interest rate variable. Fig. 2 relates the velocity of M2 (nominal GDP divided by nominal M2) to the euribor rate and the bond yield. Velocity clearly tended to decrease from 1997 to 2007. The downward trend in velocity could be explained by two factors: (1) The coefficient of the log in real money demand with regard to the log in real GDP – equivalent to the income elasticity of money demand – exceeds unity, that is, money demand rises proportionally more than GDP or (2) the downward trend in velocity reflects the decline in the bond yield over much of the sample period, that is, money demand rose relative to GDP because of falling bond yields. Although the decrease in interest rates no doubt tended to boost money demand, it is implausible to attribute the downward trend in velocity to movements in the bond yield alone. The bond yield stopped to decline in 2005 and rose again substantially thereafter. Yet, velocity continued to proceed on its downward course. If velocity had responded mainly to movements in the bond yield, it should have rebounded after 2005. For this reason, I suspect that equations including the bond yield provide misleading estimates of the income elasticity of money demand. A better bet is to use the interest rate differential. As the table clearly indicates, this specification yields estimates of the income elasticity exceeding unity, which in turn accounts mainly for the downward trend in velocity.

 

Figure 2: Velocity of M2 and interest rates

 

 

Second, the estimates provided in the table suggest that the income elasticity of M2 increased gradually over the period 1998-2006. It rose from about 1.5 in 1998Q2-2003Q4 to almost 2 in 1998Q2-2006Q4. The gradual increase in the income elasticity suggests that its estimates may be sensitive to the choice of sample period. To explore this problem, I assume that the ECB estimates its money demand equations also from sample periods of fixed length. At the end of each year, it estimates money demand functions from data based on the past 22 quarters. The estimated coefficients based on sample periods of fixed length are shown in the table too, which reveals a jump in the estimated income elasticity from about 1.5 to 2.3-2.4 from the first sample period to the subsequent periods with a fixed length of 22 quarters. To deal with the uncertainties arising from the size of the income elasticity, I assume that the ECB – at the end of each year – derives two versions of the money demand equation: one estimated from data based on a sample period with a fixed length of 22 quarters and the other one from data based on a sample period of varying length but always starting with 1998Q2.

In a next step, the ECB constructs a pair of reference lines for real M2 for the five-quarter period from 2007Q1 to 2008Q1. It derives a reference line from the real money demand equations based the sample periods of fixed and varying lengths each. To this end, the ECB inserts in the real money demand equations an expansion path for potential real GDP, which is assumed to be equal to the log-linear trend of the actual values.[1] Since the data for the actual level of real GDP are known only for the period up to 2007Q1, the values of its potential level for 2007Q2 onwards are extrapolated from the estimated trend. The ECB also takes account of the policy-induced portion of the interest rate differential. I assume that the ECB measures the policy-induced portion by the values of the interest differential (indiff) estimated from the following regression equation:

             indiff=2.743+0.485ref, R²=0.45, sample period: 1999Q1-2007Q2,

where ref denotes the ECB’s refinance rate.[2] The ECB also plugs into the real money demand equation the estimates of the policy-induced portion of the interest differential. The ECB derives the reference lines on the assumption that it will leave its refinance rate unchanged in the future. Thus the reference line indicates how real M2 should evolve were the ECB to leave its policy rate of interest unchanged.[3]

 

Figure 3: Actual Levels of M2 and Reference Lines

  

 

 

Lastly, the ECB determines analogous reference lines for nominal M2 by multiplying the quarterly reference values for real M2 with its objectives for the HICP index. These quarterly objectives are assumed to lie on an expansion path for the HICP index consistent with its aim of keeping inflation slightly below 2 percent per year. For simplicity, the expansion path for the HICP index is derived on the assumption that the ECB is willing to tolerate an increase in consumer prices of exactly 0.5 percent per quarter from 2007Q4 to 2008Q1.

The reference lines emerging from my procedure are displayed in Fig. 3. They are not only derived for the five-quarter period 2007Q1-2008Q1, but also for the three preceding five-quarter periods. The reference lines for the period 2004Q1 to 2007Q2 are based on the refinance rates actually set by the ECB. As already indicated, the reference line for 2007 is based on the assumption that the ECB will keep its refinance rate at the current level of 4 percent until the beginning of 2008.

The reference lines may be compared with the actual development of M2 for the period up to 2007Q2. Major deviations in the level of M2 from its reference lines imply that the signals extracted from money growth may be at variance with those obtained from the ECB’s first pillar, as the actual development of M2 may be inconsistent with the ECB’s inflation objective and its assumption about potential growth. As may be seen from Fig. 3, the actual development of M2 more or less conformed to the reference lines until the beginning of 2006. However, since then, the actual level has moved substantially above the reference values. The uncertainties about the size of the income elasticity do not appear to matter much as this conclusion holds regardless of the sample period chosen for estimating the money demand equations. Thus, my analysis suggests that the ECB’s current monetary stance is still too expansionary, a view probably shared by key officials at the Frankfurt institution.

On a final note, it is interesting to compare the reference lines derived for M2 with those presented for M3 in my February contribution (Fig. 4). Clearly, while the reference lines for M3 move around erratically, notably after 2005, those for M2 display a much more stable behaviour. Therefore, the aggregate M2 appears to provide more useful policy signals than the ECB’s preferred monetary variable M3.

 

Figure 4: Actual Levels of M3 and reference lines

 

 

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