## Abstract

We challenge the view that the relationship between money and prices is too loose in countries with low inflation rates and argue that cross-border portfolio shifts are the root cause of the volatility in real money balances. The novelty of this paper is that we model jointly in the euro area and the USA (1) the equilibrium in the money market that takes into account the cross-border portfolio shifts and (2) the equilibrium in the domestic asset markets, by finding a relation between domestic long-horizon expected stock and bond returns. We estimate a stable money demand in the long-run and find that the short-run correlation between annual inflation and model-based excess money growth is not statistically different from unity in both the euro area and the USA. We also find that the resulting long-run equity risk premium comoves counter-cyclically with quarterly real GDP growth in both economies.

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## Notes

The inability to identify a stable M2 demand function in the USA after the mid-90s is widely recognized (see Carlson et al. 2000; Duca 2000; Choi and Oh 2003; Duca and VanHoose 2004; Choi and Cook 2007). On the contrary, there are several studies showing a cointegrating relationship between US M1, GDP and interest rates (among the most recent Choi and Oh 2003; Ireland 2009; Calza and Zaghini 2010; Lucas and Nicolini 2012). We look at broad money, which include non-cash components that can usually be converted into cash very easily. We use M2 for the USA and employ M3 for the euro area, given its prominent role within the ECB as an indicator to assess risks to price stability.

Teles and Uhlig (2010) employ panel econometric techniques with random fixed effects to capture a permanent country-specific level-shift due to transaction technology developments. They investigate international cross-sections of countries, as carried out by McCandless and Weber (1995), and then concentrate on a pool of 14 countries, whose inflation rate was below 12 %. To visually show the results, Teles and Uhlig (2010) plot the cross-section of the (1970–2005) average inflation rate against the cross-section of the (1970–2005) average excess money growth. They find that the relationship between inflation and the growth rate of money in low-inflation OECD countries is tenuous at best in more recent times. Similar results are obtained by Grauwe and Polan (2005) when applying panel fixed effects models.

Several studies have estimated the money demand for broad money (M3) for the euro area. See for example Brand and Cassola (2004), Coenen and Vega (2001), Calza et al. (2001), Funke (2001), Golinelli and Pastorello (2002), Bruggeman et al. (2003), Gerlach and Svensson (2003), Artis and Beyer (2004), Greiber and Lemke (2005), Avouyi-Dovi et al. (2006), Carstensen (2006) and Dreger and Wolters (2009). All these models are not stable when using more recent data. An alternative approach is used by Greiber and Setzer (2007). They augment a standard money demand function with variables representing developments in the housing sector, such as property prices and property wealth. They find a positive stable relationship with either property prices or property wealth for the euro area over the period 1980 Q1–2006 Q4. The drawback of this model is that it considers gross wealth, rather than net wealth. We have re-estimated the Greiber and Setzer’s model using latest ECB housing wealth data, and it turns out that money is weakly exogenous and the system is no longer stable.

Some authors have suggested that the yield curve is no longer predicting economic growth in the more recent period (Haubrich and Dombrosky 1996; Stock and Watson 2003; Giacomini and Rossi 2006). For example, under a credible monetary regime with low persistence of inflation, a nominal shock will increase short interest rate, while only marginally affecting long-term interest rates. The yield curve is twisted, but this does not imply a negative impact on economic growth (Bordo and Haubrich 2004). Nevertheless, it is fact that since 1990, the US yield curve has twisted five times and was always followed by lower economic growth in the USA. This evidence, however, could be due to developments in short-term yields, which are reduced in recessions in an effort to stimulate economic activity. Ang et al. (2006) find that the short-term interest rate has more predictive power than any term spread.

If cross-border portfolio assets matter for the price level, an alternative approach would be to include in the model the quantity of these assets. However, this would imply a general equilibrium approach and high-quality data on portfolio assets, which is outside of the scope of this paper.

A long-term government bond must pay a higher risk premium, because both the inflation rate and the interest rate become more difficult to predict farther into the future. Such risk materializes only if the bondholder sells before maturity. Nevertheless, there is an opportunity cost, since the long-term bondholder forfeits the higher unexpected interest.

Campbell et al. (1999, p. 437) show that bond risk premia are a linear function of interest rates, whose sign can be either positive or negative, depending upon the covariance between consumption innovations and revisions in expected future consumption growth. If such covariance is positive (negative), then a positive consumption shock drives up expected future consumption growth and increases (decreases) interest rates; the resulting fall (increase) in bond prices makes bonds covary negatively (positively) with consumption and gives them negative (positive) risk premia.

The cointegration test between earnings yields and dividend yields in both the euro area and the US supports the hypothesis that the pay out ratio is stationary. The unit root tests indicate that dividend yield growth is I(0). The results are available from the authors upon request.

The FED model states that if the price-earnings ratio is above the bond yield, equity prices are expected to decline until the long-run equilibrium between the two variables is re-established. This regularity was used as an input by Alan Greenspan in a famous speech on market’s irrational exuberance in December 1996 (http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm).

In the less obvious case of the price–earnings ratio, the Phillips–Perron test statistics is \(-\)3.251 (

*p*value = 0.019) for the euro area and \(-\)2.457 (*p*value = 0.128) for the USA; the Elliott–Rothenberg–Stock test statistic is 7.985 for the euro area and 32.08 for the USA, while the Ng–Perron test statistic is \(-\)2.97 for the euro area and \(-\)0.89 for the USA. Given that the critical values of Elliott–Rothenberg–Stock test statistic range between 1.94 at 1 % and 4.22 at 10 % and the critical values of Ng–Perron test statistic range between \(-\)13.8 and \(-\)5.7, the null hypothesis that the price–earnings ratio has a unit root over the sample period into consideration cannot be rejected.If we estimated the Calza et al. (2001) model with the own rate of return of broad money for the euro area, \({\hbox {own}}_{t}^\mathrm{EA}\), the results would be the following: \(m_{t} ^\mathrm{EA}-p_{t}^\mathrm{EA}=\beta _{2,0}+\underset{(0.40)}{3.64}y_{t}^\mathrm{EA} +\underset{(5.39)}{27.85}\left( R_{t}^\mathrm{EA}-{\hbox {own}}_{t}^\mathrm{EA}\right) \) when using the long-term interest rate, \(m_{t}^\mathrm{EA}-p_{t}^\mathrm{EA}=\beta _{2,0} +\underset{(1.22)}{7.99}y_{t}^\mathrm{EA}+\underset{(11.63)}{57.93}\left( r_{t} ^\mathrm{EA}-{\hbox {own}}_{t}^\mathrm{EA}\right) \) when using the short-term interest rate, \(m_{t}^{EA}-p_{t}^{EA}=\beta _{2,0}-\underset{(1.06)}{0.65}y_{t}^{EA} +\underset{(11.92)}{34.23}\left( R_{t}^{EA}-own_{t}^{EA}\right) -\underset{(8.43)}{43.19}\left( r_{t}^{EA}-own_{t}^{EA}\right) \) when using both interest rates. The results are poorly with the incorrect sign for the opportunity cost of holding money. Similarly, we have constructed the time series used by Carstensen based on the German DAX30 before 1987 and Eurstoxx 50 after 1987. Specifically, we have constructed the 3-year moving average stock market returns and the 2-year moving average of realized volatility using the GARCH(1,1) based on daily stock returns as in Carstensen (2006). The Carstensen’s model estimated up to 2013Q2 suggests the presence of 2 cointegrating vectors and not 1 if it is estimated up to 2003Q2. Therefore, Carstensen’s model is no longer valid. Moreover, the parameters seem highly unstable.

We have also applied the elasticities estimated by Ireland for the US money demand on the model for the euro area, and the overall results do not change.

The results remain robust if we added a third lag.

M3 growth has been increasing at much higher rate than real GDP growth in the euro area. More specifically, the growth rate of real money was on average twice the growth rate of real GDP growth during the sample period and this justifies a higher elasticity value.

The analysis conducted before the dramatic sovereign debt crisis in the euro area in 2011 and 2012 can be found in De Santis (2012), which estimates the model up to 2010Q4. The results remain broadly invariant.

It is often argued that risk premia were low over this period. We would agree only as regards the bond premia. The savings glut hypothesis put forward by the FED Chairman Bernanke (“The global saving glut and the US current account deficit”, remarks at the Sandridge Lecture, 19 March 2005) postulates that the global economy experienced a positive savings shock causing a reduction in bond premia.

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## Acknowledgments

I would like to thank Gianni Amisano, Carlo Favero, Giovanni Lombardo, Harald Uhlig and Anders Warne for discussions, suggestions or comments. The views expressed in this paper are those of the author and do not necessarily reflect those of the European Central Bank or the Eurosystem.

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De Santis, R.A. Quantity theory is alive: the role of international portfolio shifts.
*Empir Econ* **49**, 1401–1430 (2015). https://doi.org/10.1007/s00181-014-0912-9

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DOI: https://doi.org/10.1007/s00181-014-0912-9