Sahuc - Monetary Policy Euro area.pdf

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Money, Ination and Monetary Policy in the Euro Area

By S A -D J -G S

Both an empirical breakdown of the quantity theory of money and a shift in the volatility of nominal variables occurred in the euroarea over the period 19802007. A dynamic stochastic general equilibrium model with money is proposed and estimated over different subsamples to assess the drivers of these empirical facts.Our estimation results and counterfactual exercises provide evi-dence that a change in the degree of responsiveness of monetary authorities and the transition from a money growth to an inter-est rate rule explain much of the observed properties of nominal variables and their relationships.

Keywords: Quantity theory of money, monetary policy, DSGE model, Bayesian methods.JEL: E31, E51, E52.

The empirical breakdown of the quantity theory of money and the radical shiftin the volatility of most macroeconomic data are two prominent stylised facts char-acterizing the euro area over the period 19802007. Recent literature has focusedon such developments for several OECD countries. For instance, Sargent and Surico(2011) and Teles and Uhlig (2010) explain the large departures from a unitary moneygrowth/ination relation by the dependence of the coefficient estimate associatedwith the regression of the two variables to the policy rule parameters. In more recenttimes, the lowination countries should then see the relationship between inationand the growth rate of money becoming tenuous at best. Other studies, such asAndres et al. (2006) or Justiniano and Primiceri (2008), suggest that the decline inmacroeconomic volatility over the past thirty years is largely the result of smallershocks impinging on the economy (usually called the good luck hypothesis), withstructural changes having played at most a secondary role. There is therefore dis-agreement about the origin of changes both in the statistical properties of nominalvariables and in their relationships.

In this paper, we argue that a change in the degree of responsiveness of the mon-etary authorities and the transition from a money growth to an interest rate ruleexplain much of the stylised facts. To reach this conclusion, we rst show the signif-icant difference in the way monetary policy was conducted pre and postEuropeanMonetary Union (EMU). We then go on to demonstrate that this difference in policybehavior allows an understanding of the shift in macroeconomic behavior.

Avouyi-Dovi: Banque de France, 31 rue Croix des Petits Champs, 75049 Paris, France (e-mail:[email protected]); Sahuc: Banque de France, 31 rue Croix des Petits Champs, 75049 Paris,France (e-mail: [email protected]). We are grateful to Christophe Cahn, Patrick Fve,Benoit Mo jon, Christian Pster, Thomas Sargent and Richard Summer for comments. Special thanks toJulien Matheron, whose suggestions greatly improved the paper. The views expressed herein are those of theauthors and do not reect those of the Banque de France.

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The intuitions behind this result are as follows. The quantity theory implies that

any change in the monetary aggregate induces a variation in the same direction andsame magnitude of prices and of nominal interest rates. If price stability is theobjective of the monetary authorities, any price increase should result in a sharpcontraction in the money supply. As a consequence, both variances and covariancesbetween nominal variables decrease. But, implementing price stability or inationtargeting while the underlying theory establishes similar variations between pricesand the monetary aggregate necessarily induces a stronger fall of the covariances.This mechanical effect blurs the two quantity propositions. In addition, with aninterest elastic demand for real money balances, any shock that affects the path forexpected ination or the real interest rate causes money demand to shift. Whenthe central bank follows an interest rate rule rather than a money growth rule, themoney stock is endogenous and ination is xed by the policy rule. Money absorbsthe adjustment and the central bank can accommodate this jump in the money stockalmost instantaneously and with little cost. Consequently, the money stock respondsby shifting to clear the money market. It allows to explain why, in an economy withstochastic ination and an interest rate rule for monetary policy, the money growthrate is much more variable than the ination rate.

To demonstrate the role of these mechanisms, we consider a structural monetarymodel of the business cycle in which money is allowed to play a relevant role. Themodel combines a neoclassical growth core with several shocks and frictions. Itincludes features such as habit formation, money in the utility, investment adjust-ment costs, variable capital utilization, monopolistic competition in goods and labourmarkets, and nominal price and wage rigidities. We follow the Bayesian approach to

estimate several versions of the model. Unlike all previous papers that use an ad-hoc calvo-type employment adjustment equation to translate hours worked into theobserved employment series, we directly use a new series of quarterly hours workedfor the euro area. We consider two subsamples: 1980Q11998Q4 in imposing amoney growth rule and 1999Q12007Q4 in imposing an interest rate rule. Indeed,during the 1980s and 1990s, many European countries have employed either officialmoney growth targets (through a broadly dened monetary aggregate) or exchangerate policies in order to tie to the Deutschmark within the Exchange Rate Mecha-nism (Bernanke and Mishkin, 1992). In Germany for instance, the setting of targetsexplicitly takes into account the Bundesbanks long-term ination goal, estimatedpotential output growth and expected velocity trends, which are combined using the

quantitytheory equation to determine the desired money growth rate. From 1999,the European Central Bank (ECB) steered shortterm money market rates in orderto inuence the spending decisions of the private sector, monetary and nancial de-velopments and, ultimately, prices. This change in the monetary policy instrumentfollows the idea that money and hence credit does not have any crucial and construc-tive roles to play in monetary policy design (Woodford, 2008). 1 The money market is

1 The designation monetary policy instrument is a shortcut in macroeconomic modeling to represent infact intermediate targets which are variables that are neither under the direct day-to-day control of thecentral bank nor are the ultimate goals of policy, but that are used to guide p olicy. Values for instruments areusually set so that, given estimates of behavioral parameters such as the interest elasticity of money demand,intermediate targets for variables are reached in the longer term (quarter-to-quarter or year-to-year).

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then only useful for determining the supply of money which responds endogenously

to the demand of money. This consensus substituted the one put forward by MiltonFriedman that ination is always and everywhere a monetary phenomenon.The article is structured as follows. Section I presents the empirical evidence

that motivates the paper. Section II describes the structural model and Section IIIdescribes the estimation procedure and reports the estimation results. Section IVanalyses the drivers of the two stylised facts. A last section concludes.

I. Stylised Facts

A. The empirical breakdown of the quantity theory of money

The quantity theory of money can be expressed in terms of lowfrequency comove-ments between money growth and ination as well as between money growth andnominal interest rate. The lowfrequency approach, that does not require a host of encumbering theoretical or econometric assumptions, is achieved by using a lterthat extracts a longrun signal from time series data. Lucas (1980) has suggestedthe following lter (revisited by Whiteman, 1984, and Sargent and Surico, 2011):

xt ( ) = n

k= n

| k| xt+ k ,

where xt is the variable of interest, is a parameter comprised between 0 and 1, and = (1 )2/ (1 2 n +1 (1 )) is selected such that the sum of the weights isequal to 1. As approaches zero, no ltering occurs, while as approaches unity,the ltered series xt ( ) approaches the sample mean of the original series. FollowingLucas, we set = 0 .95.2 Given the size of our sample and the fact that long averagingdoes not appear in practice to deliver any greater improvement in t (McCallum andNelson, 2010), we set n = 4 .

Unit slopes of graphs of long twosided moving averages are used to characterisethe implications of the quantity theory of money. According to this theory, a plot of ination or nominal interest rates against money growth should produce data pointsthat lie along a 45degree line.

Figure 1 shows scatter plots of ltered M2 growth, ination and nominal shortterm interest rate (see Section III.A for details on the data used in our analysis).We split the sample in 1999 when the nal stage of the European Economic and

Monetary Union (EMU) was successfully launched. This date officially translatedregime change in monetary policy in the euro area. During the 1980s and 1990s,many European countries have either a monetary target (through a broadly denedmonetary aggregate) or exchange rate policies in order to tie to the deutschmarkthrough the Exchange Rate Mechanism. From 1999, the conversion rates of thecurrencies of the 11 members states initially participating in monetary union wereirrevocably xed and the ECB took over responsability for conducting the singlemonetary policy in the euro area. The ECB steers shortterm interest rates by

2 Sargent and Surico (2011) have tested other values of without affecting the variability of the elasticityof money relative to price.

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signalling its monetary policy stance and by managing the liquidity situation in the

money market.

. .

. + .

. + .

. + .

Figure 1. Scatter plots of ltered money growth, ination and interest rate

The graphs reveal that the quantity theory of money can be veried or not ac-cording to the reporting period. The scatters of points corresponding to the period19801998 show a concentration of points around the diagonal (45degree line), val-idating the quantity theory of money over that period. This result is conrmed bycalculating the slope of the regression associated with these points: 1.34 for the in-ation on money growth regression and 1.38 for the interest rate on money growthregression. This illustrates the fact that periods of sustained high ination are alwaysaccompanied by high growth rates of money, reinforcing the dictum that ination isalways and everywhere a monetary phenomenon. It was in this context that thearchitects of the ECB assigned a prominent role to money. In doing so, they wantedto acquire the credibility of the Bundesbank prior to the adoption of the euro.

But since 1999, the two scatters of points are at, resulting in slopes of the regres-sion lines close to zero. The quantity theory of money seems to have disappearedover the recent period. There is a marked deterioration in the ltered series oncethe postEMU period is considered. While the ination rate remained practicallyconstant at the 2% level, the rate of money growth took on an upward trend. This

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pattern created a divergent gap between the long term component of money growth

and ination after the introduction of the euro.

B. Changes in volatilities

In the period between the mid1990s and 2007, European economies enjoyed oneof the greatest economic growth periods, known as the Great Moderation due tothe low macroeconomic volatility in those years. The high growth rates of economicvariables with low volatility came simultaneously with ination under control andlow interest rates across the board of nancial assets, with practically inexistent riskpremia in many cases as a result of the underassessment of risk.

Table 1 summarises the evidence on volatility changes in ination, interest rateand money growth by showing their respective standard deviations for the preEMUand postEMU periods as well as the ratio between the two. We observe two strikingfeatures. First, the volatility of ination and the shortterm interest rate has declinedsharply, by a factor of 3. This resulted from the high credibility achieved by theECB in maintaining a low and stable ination rate, in line with its denition of pricestability. Second, the volatility of money growth increased from 0.52 to 0.60. 3

Table 1Standard deviation of quarterly ination, interest rate and money growth (19802007)

PreEMU PostEMU PostEMUPreEMU

Ination 0.718 0.189 0.263

Interest rate 0.769 0.236 0.307Money growth 0.515 0.601 1.167

There are two main reasons underlying this development. From a theoretical pointof view, when the interest rate becomes the monetary instrument, money becomesendogenous and clears the money market. This property makes it automatically morevolatile to meet money demand. From a cyclical point of view, the emergence of newnancial players and an array of innovative nancial instruments make the traditionalmoney supply gures harder to interpret. That increase in the volatility of moneygrowth is our second piece of evidence pointing to the presence of changes beyond

those that would result from a scaling down of volatility in all nominal variables.II. A mediumscale model for the euro area

The present section describes our microfounded model of the Euro area economy,which is close to Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters(2007). The model combines a neoclassical growth core with several shocks and fric-tions. It includes features such as habit formation, investment adjustment costs,variable capital utilization, monopolistic competition in goods and labour markets,

3 This increase in volatility is valid whatever the choice of the monetary aggregate (see Appendix A1).

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and nominal price and wage rigidities. The economy is populated by ve classes of

agents: producers of a nal good, intermediate goods producers, households, em-ployment agencies and the government. We adopt the specication investigated byJustiniano, Primiceri and Tambalotti (2010), except that (i) we allow for money inthe utility function and (ii) we introduce two types of monetary policy rules.

A. Household sector

E

Each household indexed by j [0, 1] is a monopolistic supplier of specialised laborN j,t . At every point in time t, a large number of competitive employment agenciescombine households labor into a homogenous labor input N t sold to intermediate

rms, according to

(1) N t = 10 N j,t 1 w,t d j w,t ,Prot maximization by the perfectly competitive employment agencies implies the

labor demand function

(2) N j,t =W j,tW t

w,t w,t 1

N t ,

where W j,t is the wage paid by the employment agencies to the household supplyinglabor variety j , while

(3) W t 10 W j,t 1 w,t 1 d j w,t 1is the wage paid by intermediate rms for the homogenous labor input sold to themby the agencies.

w,t measures the substitutability across labor varieties and its steadystate is thedesired steadystate wage markup over the marginal rate of substitution betweenconsumption and leisure. It is assumed to follow an ARMA(1,1) process in order to

capture the moving average, high frequency component of wages,

log(w,t ) = (1 w)log(w)+ w log (w,t 1)+ w,t w w,t 1, w,t i.i.d.N 0, 2w

H

The preferences of the j th household are given by

(4) Et

s=0 s b,t+ s log (C t+ s hC t+ s 1) +

m,t + s 1z,t + s1

M t+ sP t+ s

1

N 1+ j,t + s1 +

,

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where E t denotes the mathematical expectation operator conditional upon informa-

tion available at t.4

C t denotes consumption, M t /P t represents real balances, N j,t islabor of type j . The parameter is the subjective discount factor, h [0, 1] denotesthe degree of habit formation, is related to the interest rate elasticity of the moneydemand, and > 0 is the inverse of the Frisch elasticity. b,t and m,t are a dis-turbance of the discount factor and a velocity shock respectively, evolving accordingto

log(b,t ) = b log (b,t 1) + b,t , b,t i.i.d.N 0, 2b ,

and

log(m,t ) = m log (m,t 1) + m,t , m,t i.i.d.N 0, 2m .

As we explain below, households are subject to idiosyncratic shocks about whetherthey are able to reoptimise their wage. Hence, the above described problem makesthe choices of wealth accumulation contingent upon a particular history of wagerate decisions, thus leading to households heterogeneity. For the sake of tractability,we assume that the momentary utility function is separable across consumption,real balances and leisure. Combining this with the assumption of a complete set of contingent claims market, all the households will make the same choices regardingconsumption and money holding, and will only differ by their wage rate and supplyof labor. This is directly reected in our notations.

Household j s period budget constraint is given by

P t (C t + I t ) + T t + B t + M t Rt 1B t 1 + M t 1 + Q j,t + D t+ W j,t N j,t + Rkt ut K t 1 P t (u t ) K t 1 ,(5)

where I t is investment, T t denotes nominal lumpsum taxes (transfers if negative),B t is the one-period riskless bond, Rt is the nominal interest rate on bonds, Q j,t isthe net cash ow from households j portfolio of state contingent securities, Dt isthe equity payout received from the ownership of rms, and Rkt is the rental rate of capital. The capital utilization rate ut transforms physical capital K t into the serviceow of effective capital K t according to

(6) K t = ut K t 1,and the effective capital is rented to intermediate rms at the nominal rental rater kt . The costs of capital utilization per unit of capital is given by the convex function

(ut ). We assume that u = 1 , (1) = 0 , and we dene

u (1) / (1)1 + (1) / (1)

.

4 As tested by Ireland (2004) and Andrs et al. (2006), the assumption of non separable preferences in theutility function is rejected.

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the nal good and the prices of the intermediate goods

(11) P t 10 P i,t 1 p,t 1 dip,t 1

.

p,t measures the substitutability across differentiated intermediate goods and itssteady state is then the desired steadystate price markup over the marginal cost of intermediate rms. It is assumed to follow an ARMA(1,1) process in order to capturethe moving average, high frequency component of ination

log( p,t ) = 1 p log( p) + p log ( p,t 1) + p,t p p,t 1 , p,t i.i.d.N 0, 2 p .

I -

Intermediate good i is produced by a monopolist rm using the following produc-tion function

(12) Y i,t = K i,t [Z t N i,t ]1 Z t F,

where denotes the capital share, K i,t and N i,t denote the amounts of capital andeffective labor used by rm i, F is a xed cost of production that ensures that protsare zero in steady state, and Z t is an exogenous laboraugmenting productivity factorwhose growthrate, denoted by z,t Z t /Z t 1, evolves according to

log(z,t ) = z,t , z,t i.i.d.N 0, 2z .In addition, we assume that intermediate rms rent capital and labor in perfectly

competitive factor markets.Intermediate rms set prices according to a staggering mechanism. In each period,

a fraction p of rms cannot choose its price optimally, but adjusts it to keep upwith the increase in the general price level in the previous period according to theindexation rule

(13) P i,t = 1 p pt 1P i,t 1,

where the coefficient p [0, 1] indicates the degree of indexation to past prices. The

remaining fraction of rms chooses its price P i,t optimally, by maximizing the presentdiscounted value of future prots

(14) Et

s=0( p)s

t+ st

pt,t + s P i,t Y i,t + s W t+ s N i,t + s Rkt+ s K i,t + s ,

where

(15) pt,t + s = s =1 1 p pt+ v 1 s > 01 s = 0 ,9


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subject to the demand from nal goods rms given by equation (10) and the produc-

tion function (12). t+ s is the marginal utility of consumption for the representativehousehold that owns the rm.

C. Public sector

We assume that public spending G t is set according to

(16) Gt = 1 1g,t

Y t ,

In order allow extensive feedback from endogenous variables to money growth,monetary policy is set according to the following rule

(17) t = t 1

t

Y t zY t 1

y (1 )

r,t ,

where r,t is a monetary policy shock, evolving according to

log(r,t ) = r,t , r,t i.i.d.N 0, 2r .We consider two types of monetary policy rules depending on the instrument the

central bank uses. The rst is a money growth rule according to which the centralbank adjusts smoothly the growth rate of money, t = M t / ( z M t 1), in response

to movements in ination and output growth. The second is a Taylor rule accordingto which the shortterm nominal interest rate, t = R t /R , is adjusted smoothly inresponse to movements in ination and output growth.

D. Market clearing

Market clearing conditions on nal goods market are given by

Y t = C t + I t + Gt + (ut ) K t 1,(18) p,t Y t = ut K t 1

[Z t N t ]1 Z t F,(19)

where p,t = 1

0

P i,tP t

p,t p,t 1

di is a measure of the price dispersion.

III. Quantitative analysis

In this section, our formal econometric procedure is expounded. We then discussour results and check the ability of our models to reproduce the two stylised facts.

A. Data and econometric approach

The quarterly euro area data used in our empirical analysis are extracted fromthe AWM database compiled by Fagan et al. (2005), except the monetary aggregate

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and hours worked. Regarding nominal variables, ination is measured by the rst

difference of the logarithm of GDP deator (YED), the shortterm nominal interestrate is a three month rate (STN), and money growth is the rst difference of thelogarithm of M2.

Figure 2. Quarterly data for the euro area (1980Q12007Q4)

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Regarding real variables, output growth is the rst difference of the logarithm

of real GDP (YER), consumption growth is the rst difference of the logarithm of real consumption expenditures (PCR), investment growth is the rst difference of the logarithm of real gross investment (ITR), wage growth is the rst difference of the logarithm of nominal wage (WRN) divided by GDP deator, and growth of total hours worked are the rst difference of the logarithm of total hours worked.Real variables are divided by the working age population, extracted from the OECDEconomic Outlook. Ohanian and Raffo (2012) have build a new dataset of quarterlyhours worked for 14 OECD countries. We have then made an average of their seriesof hours worked for France, Germany and Italy to obtain a series of total hours forthe euro area. Interestingly, the series thus obtained is very close to that provided bythe ECB on the common sample, i.e. 1995Q12007Q4. The series for M2 is availablefrom the ECB statistical warehouse since 1980Q1, which is therefore the startingdate for our analysis. The data are reported in Figure 2.

We are interested in two versions of the loglinearised model: 5

A model with a money growth rule (MG), estimated from 1980Q1 to 1998Q4;

A model with an interest rate rule (IR), estimated from 1999Q1 to 2007Q4.The choice of the nal date prevents our estimates from being distorted by thenonlinearities induces by the different size of the shocks and the zero lowerbound on nominal interest rates.

We follow the Bayesian approach to estimate the models (see An and Schorfheide,2007, for an overview). Letting denote the vector of structural parameters to be

estimated and S

T {S

t }T t=1 the data sample, we use the Kalman lter to calcu-late the likelihood L( , S T ), and then combine the likelihood function with a prior

distribution of the parameters to be estimated, ( ), to obtain the posterior distrib-ution, L( , S T )( ). Given the specication of the model, the posterior distributioncannot be recovered analytically but may be computed numerically, using a Monte-Carlo Markov Chain (MCMC) sampling approach. More specically, we rely on theMetropolisHastings algorithm to obtain a random draw size of 1,000,000 from theposterior distribution of the parameters.

We use growth rates for the non-stationary variables in our data set (output, con-sumption, investment, money and the real wage) and express gross ination, grossinterest rates and the rst difference of the logarithm of hours worked in percent-age deviations from their sample mean. We write the measurement equation of theKalman lter to match the eight observable series with their model counterparts.Thus, the statespace form of the model is characterised by the state equation

X t = A ( )X t 1 + B ( ) t , t i.i.d.N (0, ) ,where X t is a vector of endogenous variables, and t is a vector of innovations to theeight structural shocks; and the measurement equation

S t = C ( ) + D X t + t , t i.i.d.N (0, ) ,

5 See Appendix A2 for further details on the procedure used to induce stationarity.

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where S t is a vector of observable variables, that is,

S t = 100[ log Y t , log C t , log I t , log( W t /P t ) , log N t , log( M t /P t ) , t , R t ];

and t is a vector of measurement errors.The model contains nineteen structural parameters, excluding the parameters rela-

tive to the exogenous shocks. We calibrate six of them : the discount factor is set to0.99, the capital depreciation rate to 0.025, the capital share in the CobbDouglasproduction function is set to 0.30 (McAdam and Willman, 2008), the steadystateprice and wage markups p and w are set to 1.20 and 1.35 respectively (Everaert andSchule, 2008), and the steadystate share of government spending in output is set to0.20 (the average value over the sample period). The remaining thirteen parametersare estimated. The prior distribution is summarised in Table 2. Our choices are inline with the literature, especially with Smets and Wouters (2007), Sahuc and Smets(2008) and Justiniano et al. (2010). As regards the interest rate elasticity of themoney demand , we assign it a Gamma density prior with mean 10 and standarddeviation 5.

B. Estimation results

The estimation results for the two models are summarised in the righthand sidepanels of Table 2, where the posterior mean and the 90% condence interval arereported. Several results are worth commenting on. First, as regards the interestrate elasticity of the money demand, , we nd a value of 22 for the model with amoney growth rule and of 17 for the model with an interest rate rule. Such values,combined with the respective steadystate values of ination and of economic growth,imply an interest semi-elasticity of money demand at 1.59 for the rst sub-sampleand at 2.92 for the second one 6.

As regards the behavior of households, we rst nd that the habit persistenceparameter h differs between periods, indicating that the reference for current con-sumption was about 42% (resp. 68%) of past consumption from 1980 to 1998 (resp.from 1999 to 2007). Second, the inverse of the elasticity of labor disutility, , issimilar across the samples and is approximately equal to 2.2. The wage indexationparameter is w 0.40 in the two model versions, slightly higher than the price in-dexation parameter p 0.35. This reects a now standard result that the euro area

data do not require too high a degree of price indexation. The probability that rmsare not allowed to re-optimise their price is p = 0.89 (resp. p = 0 .71) in the rstsub-sample (resp. in the second sub-sample). It implies an average duration of pricecontracts of about 36 months on the period 19801998 and 14 months on the period19992007. The probability of no wage change is w 0.70, implying an averageduration of wage contracts of about 13 months. All these numbers are consistentwith the results reported in the survey done by Druant et al. (2012).

6 These values are close to the point estimates found in recent papers, see for instance Reynard (2004) andDorich (2009).

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The policy parameters , y (0.66, 1.06) and = 0 .49 indicate that, during

the period 19801998, money growth was moving smoothly with a little weight onination and a larger weight on output growth. As expected, the gure is differentfor the period 19992007. Indeed, the policy parameters , y (1.74, 0.20) and = 0 .81 indicate that the ECB acts very gradually with a large weight on ination,consistent with its mandate.

The estimates of the serial correlation of shocks display a difference between the twosamples. For instance, the serial correlation of wage markup and preference shocks isstronger in the rst subsample while the serial correlation of velocity and investmentshocks is higher in the second subsample. Finally, notice that the standard error of the velocity shock is slightly higher in the recent period.

C. Model evaluation

In this subsection, we analyze the performance of the models at replicating the twostylised facts. To do so, we generate 1000 samples of size consistent with the empiricalcounterpart (after a burn-in period of 1000 observations) from the two model versionsusing the posterior estimates. For each simulation, we compute the lowfrequencyrelationships between ltered money growth, ination and the nominal interest rate.The results of this exercise are displayed in Figure 3.

. . . . .

. . . . .

Panel a. Model with a money growth rule (1980Q11998Q4)

. . . . .

. . . . .

Panel b. Model with an interest rate rule (1999Q12007Q4)

Figure 3. Simulated coefficients of the regressions on ltered data

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First, we observe that the model with a money growth rule (period 19801998)

replicates quite well the two quantity theory propositions: the mean of the coefficientof the regression of ination on money growth is 0.91 and the mean of the coefficientof the regression of the nominal interest rate on money growth is 0.70 (panel a).Second, the model with an interest rate rule (period 19992007) also reproduces theempirical fact of absence of quantity theory. Indeed, the mean of the coefficient of the regression of ination on money growth is 0.04 and the mean of the coefficientof the regression of the nominal interest rate on money growth is 0.03 (panel b).This exercise conrms that our structural model is able to reproduce the rst stylisedfact.

Let us focus now on the second stylised fact, the shift in macroeconomic volatility.To do so, we use the simulated data and compute their standard deviations. Table3 reports the simulated standard deviation for the two models. Given that Bayesianestimation operates by trying to match the entire autocovariance function of thedata, there is a tension between matching standard deviations and other secondmoments of the data. Therefore, the researcher should not expect perfect accountingof the observed volatilities. Despite this, the models are able to replicate to a largeextent the empirical evidence at hand. Indeed, the theoretical framework successfullydelivers the differences in size of the slowdown in the volatility of ination and nominalinterest rate, as observed in the data.

Table 3Model Fit: Standard Deviations

1980Q11998Q4 1999Q12007Q4

Data Model (MG) Data Model (IR)

Mean 90% CI Mean 90% CI

Ination 0.718 0.736 [0.551,0.954] 0.189 0.248 [0.186,0.314]

Interest rate 0.769 0.784 [0.627,0.979] 0.236 0.227 [0.174,0.310]

Money growth 0.515 0.674 [0.555,0.830] 0.601 0.805 [0.727,0.912]

Note: For each 1000th parameter draw from the posterior distribution, 1000 samples with the same

length as the data are generated (after discarding 1000 initial observations). This table reports themean and the 90 percent condence interval (within square brackets).

However, the modelimplied standard deviations for money growth is larger thanthat in the data. The reason is that the model imposes a common trend betweenoutput and money. This constraint is quite strong since the two series show differ-ent trends. To compensate, the volatility of money growth should increase. Thisdifference in trends is identical in both models. Thus, it does not alter the relativedifference between the two variances of money growth. We can conclude that themodel proposed in this paper is a good candidate for analyzing the two stylised facts.

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IV. Assessing the drivers of both stylised facts

In this section, we analyze the model drivers of both the breakdown of the twoquantity propositions and the change in the macroeconomic volatility. Our aim is tounderstand whether changes in monetary policy, shocks or private sector coefficientsacross subsamples are responsible for the two empirical facts. To do so, we startfrom the model (MG) hereafter referred to as benchmark and perform two setsof counterfactual exercises. The rst set is summarised below:

Counterfactual (1) : we analyze the role played by monetary policy (shifts inthe coefficients and the instrument).

Counterfactual (2) : we study the relevance of the good luck hypothesis, i.e. therole of the size and source of the shocks hitting the economy.

Counterfactual (3) : we assess the relevance of a change in the structure of theeconomy ( i.e. a modication of preferences and technology).

For illustration purposes, let us consider Counterfactual (1) . We proceed by per-forming 1000 simulations for each 1000th draw in the posterior simulator using thefollowing procedure. We simulate the model economy for 80 periods (after a burn-inof 1000 observations) using the parameter estimates vector characterizing the 19801998 period but with the estimated interest rate rule obtained on the 19992007sample period. We then compute (i) the low frequency relationships between ltered

money growth, ination and the nominal interest rate, and (ii) the standard devia-tion of the endogenous variables. The other counterfactual exercises are performedin the same way.

.

.

.

.

.

.

. . . . . .

( )

( ) ( )

( )( )

( )( )

( )

Figure 4. Coefficients of the regressions on ltered data: Counterfactuals.

Note: The two crosses correspond to the models (MG) and (IR); Thebullets correspond to the counterfactuals 16.

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Figure 4 reports the lowfrequency relationships between ltered money growth,

ination and the nominal interest rate. First, there is no signicant difference be-tween Counterfactual (3) and the benchmark, indicating that the potential changesin preferences and technology by the private sector did not inuence the two quantitypropositions. Second, although the good luck hypothesis Counterfactual (2) doesnot modify the relationship between money growth and nominal interest rate, thatbetween money growth and ination deteriorates. Indeed the slope of the regressionof money growth on ination changes from 0.909 to 0.562. Finally, Counterfactual (1) clearly shows that monetary policy is the key factor explaining the breakdownof the quantity theory of money. The slope of the regression of money growth onination (resp. money growth on nominal interest rate) changes from 0.909 (resp.0.702) to 0.286 (resp. 0.172).

Table 4 reports the standard deviations generated in each counterfactual simu-lation. The simulations lead to conclusions in line with previous remarks. In-deed, imposing the economic structure from the model (IR) into the model (MG)Counterfactual (3) increases strongly the standard deviations of the nominal vari-ables, which is inconsistent with the empirical regularities. By contrast, Counterfac-tual (1) and Counterfactual (2) allow a dramatic reduction of the standard deviationsof ination and nominal interest rate. However, only Counterfactual (1) , i.e. the ex-ercise in which the interest rate rule from model (IR) is imposed in the model (MG),leads to an increase in the standard deviation of money growth.

Table 4Counterfactuals: Standard Deviations

Specication Variable

Ination Interest rate Money growth

Mean 90% CI Mean 90% CI Mean 90% CI

(MG) 0.736 [0.551,0.954] 0.784 [0.627,0.979] 0.674 [0.555,0.830]

(1) 0.337 [0.257,0.420] 0.452 [0.385,0.528] 0.990 [0.895,1.099]

(2) 0.600 [0.392,0.961] 0.572 [0.434,0.763] 0.583 [0.450,0.848]

(3) 1.121 [0.763,1.659] 0.991 [0.649,1.493] 0.852 [0.579,1.287]

(4) 0.736 [0.586,0.915] 0.820 [0.672,1.014] 1.130 [0.981,1.310]

(5) 0.255 [0.196,0.322] 0.641 [0.518,0.788] 0.494 [0.461,0.528]

(6) 1.011 [0.692,1.397] 1.004 [0.718,1.372] 0.786 [0.550,1.098]

Note: For each 1000th parameter draw from the posterior distribution, 1000 samples with the same

length as the data are generated (after discarding 1000 initial observations). This table reports the

mean and the 90 percent condence interval (within square brackets).18


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The signicant effect of monetary policy to reproduce the two stylised facts led to

scrutinise its characteristics in order to evaluate their respective contributions. Todo that, we carry out the following set of counterfactual exercises:

Counterfactual (4) : We analyze the role played by the type of policy instru-ment (money growth, M t , versus interest rate, Rt ). To realise this exercise,we target the standard deviation of ination calculated in the model (MG) anddeduce the coefficients of an interest rate rule consistent with this value. Wethen simulate as explained above.

Counterfactual (5) : We study the relevance of the degree of reactivity , i.e.the greater or lesser interest rate response to ination and to the growth rateof output , y . To do that, we target the standard deviation of ination

calculated in the model (IR) and deduce the coefficients of a money growth ruleconsistent with this value. We then simulate as explained above.

Counterfactual (6) : We assess the relevance of the degree of gradualism , i.e.a change in the value of the parameter .

Figure 4 shows that the regressions obtained in Counterfactuals (4) and (6) do notdiffer signicantly from the one obtained with the benchmark model. While the policyinstrument and the degree of gradualism seem to play a minor role, a monetary policyshift towards a more aggressive antiinationary stance, as implemented from 1999 inthe euro area, leads to a breakdown of the quantity theory of money ( Counterfactual (5)) . Turning to the analysis of standard deviations, we note that the stronger

reactivity by the monetary authority allows to explain the sharp drop in the volatilityof all the nominal variables. However, only a shift from a money growth rule toan interest rate rule provides a marked increase in the volatility of money growth(Counterfactual (5)) .

The underlying mechanisms are the following. On the one hand, the breakdownof the quantity theory of money when reacting sufficiently aggressively to incipientinationary pressures is linked to the change in the variancecovariance matrix of the macroeconomic variables. The quantity theory implies that any change in themonetary aggregate induces a variation in the same direction and same magnitudeof price and of nominal interest rate. If price stability is the goal of central bank,any increase in prices should result in a sharp contraction in the money supply. Asa consequence, both variances and covariances between nominal variables decrease.But, implementing price stability or ination targeting while the underlying theoryestablishes similar variations between prices and the monetary aggregate necessar-ily induces a stronger fall of the covariances. This mechanical effect blurs the twoquantity propositions.

On the other hand, the interest rate as an instrument of monetary policy allowsunderstanding of the increase in the volatility of money growth. With an interestelastic demand for real money balances, any shock that affects the path for expectedination or the real interest rate causes money demand to shift. When the centralbank follows an interest rate rule, the money stock is endogenous and ination isxed by the policy rule. Money absorbs the adjustment and the central bank can

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accommodate this jump in the money stock almost instantaneously and with little

cost. It is the money stock, rather than the price level, that responds by shiftingdownward to clear the money market. Hence, in an economy with stochastic inationand an interest rate rule for monetary policy, the money growth rate is much morevolatile than the ination rate (Gavin et al. , 2005). This explanation comes on topof the possible composition effect of the monetary aggregates. Indeed, M2 comprisestwo distinct categories (associated with portfolio motives and transaction purposes,respectively) that are expected to move in opposite directions following a movementin the short-term interest rate. If the remunerated category of M2 exercises a strongerinuence than the most liquid category, an increase in the interest rate will result ineven higher M2 growth. We observe, however, that M1 volatility is greater than M2volatility over the postEMU period (see Appendix A.1).

V. Conclusion and nal remarks

We have estimated a structural monetary model of the euro area business cycle toexamine the sources of both the empirical breakdown of the quantity theory of moneyand the shift in the volatility of nominal variables over the period 19802007. Ourresults suggest that a more antiinationary monetary policy and the transition froma money growth to an interest rate rule explain these macroeconomic developments.More generally, we shed light on the strong link between the quantity theory of moneyand the conduct of monetary policy. Periods of improvements (resp. impairments)in the conduct of monetary policy or in the functionning of the money market arecharacterised by an empirical breakdown (resp. return) of the quantity theory of

money.A very recent illustration is the return of the quantity of money concomitantly withthe implementation of nonstandard measures (see Appendix A3). But, contrary tohistorical changes in the degree of responsiveness or instrument of the central bank,unit slopes in scatter plots emerge because the usual interest rate channel is broken.Since 2008, the relationship between the expected path of policy rates and marketrates broke down because the liquidity premia widened and became volatile. TheLehman Brothers bankruptcy caused a freeze in the interbank market, forcing theECB to inject its funding capacity into it. The predominance of this liquidity channelmainly affected banks and central bank balance sheets. After lowering its interestrates drastically to a level close to zero, the ECB has eased monetary conditionsby increasing sharply the size of its balance sheet. However, given the atony of the economy and the heightened uncertainty, banks prefer hoarding cash insteadof spending it. Liquidity has then circulated among nancial institutions but wasnot transmitted to the real economy. Consequently, the huge increase in liquiditydid not trigger ination pressures. In addition, such a liquidity can be sterilizedby symmetrical operations of withdrawal. The ination rate remained practicallyconstant at the 2% level over the past four years. Moreover, the presence of excessliquidity in the overnight market and the resulting recourse to the deposit facilityimplied a fall in the euro interbank overnight money market rate. The evolution of theinterest rate has then become independent of ination. The traditional relationshipsbetween ination, money growth and interest rate seem no longer valid.

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With a larger sample available, the model and our approach would be used and

probably extended to examine more carefully the crisis period. For now, the recentbehavior of the monetary aggregates suggests that the quantity theory of money isuseful for detecting nancial stress, supporting McCallum and Nelson (2010).

REFERENCES

An S. and Schorfheide F. 2007. Bayesian Analysis of DSGE Models, Econo-metric Reviews , 26, 113172.Andres A., Hansen G. and Ohanian L. 2007. Why Have Business Cycle Fluc-tuations Become Less Volatile?, Economic Theory , 32, 4358.

Andrs J., Lopez-Salido J. and Valls J. 2006. Money in an Estimated Busi-ness Cycle Model of the Euro Area, The Economic Journal , 116, 457477.

Bernanke B. and Mishkin F. 1992. Central Bank Behavior and the Strategy of Monetary Policy: Observations from Six Industrialized Countries. in O. Blanchardand S. Fischer (eds), NBER Macroeconomics Annual , 183238, Cambridge: MITPress.

Christiano L., Eichenbaum M., and Evans C. 2005. Nominal Rigidities andthe Dynamic Effects of a Shock to Monetary Policy, Journal of Political Economy ,113, 145.

Dorich J. 2009, Resurrecting the Role of Real Money Balance Effects, Working Paper #2009-24 , Bank of Canada.

Druant M., Fabiani S., Kezdi G., Lamo A., Martins F. and Sabbatini R.2012. Firms Price and Wage Adjustment in Europe: Survey Evidence on NominalStickiness, Labour Economics , 19, 772782.

Everaert L. and Schule W. 2008. Why It Pays to Synchronize Structural Re-forms in the Euro Area Across Markets and Countries, IMF Staff Papers , 55,356366.

Fagan G., Henry J., and Mestre R. 2005. An Area-Wide Model (AWM) forthe Euro-Area, Economic Modelling , 22, 3959.

Gavin W., Keen B. and Pakko M. 2005. The Monetary Instrument Matters,Federal Reserve Bank of St. Louis Review , 87, 633658.

Ireland P. 2004. Moneys Role in the Monetary Business Cycle, Journal of Money, Credit and Banking , 36, 969983.

Justiniano A. and Primiceri G. 2008. The Time Varying Volatility of Macro-economic Fluctuations, American Economic Review , 98(3), 604641.

Justiniano A., Primiceri G., and Tambaloti A. 2010. Investment Shocks andBusiness Cycles, Journal of Monetary Economics , 57, 132145.

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Appendix not Intended for Publication

A1. Robustness: Results for M1, M2 and M3 aggregates

Table A11Coefficients of the regressions on ltered data (19802007)

on m R on m

PreEMU PostEMU PreEMU PostEMU

M1 0.63 0.08 0.57 0.25

M2 1.34 0.03 1.38 0.12

M3 1.16 0.10 1.08 0.01

Table A12Standard deviation of the growth of various monetary aggregates (19802007)

PreEMU PostEMU PostEMUPreEMU

M1 0.69 1.31 1.89

M2 0.52 0.60 1.17

M3 0.53 0.61 1.15

A2. Models details

A. Nonlinear equilibrium conditions

This section reports the rstorder conditions for the agents optimizing problemsand the other relationships that dene the equilibrium of the baseline model.

Effective capital:

K t = ut K t 1Capital accumulation:

K t = (1 ) K t 1 + i,t 1 S I tI t 1

I t

Marginal utility of consumption:

t = b,t

C t hC t 1

h b,t+1C t+1 hC t

Consumption Euler equation:

t = R t E t t+1P t

P t+123


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Money demand equation:

t = b,t m,t 1z,t

M t+ sP t+ s

+ E t t+1P t

P t+1

Investment equation:

1 = Qt i,t 1 S I tI t 1

I tI t 1

S I tI t 1

+ Ett+1t

Q t+1 i,t +1I t+1I t

2

S I t+1I t

Tobins Q:

Q t = E tt+1t

Rkt+1P t+1

u t+1 (u t+1 ) + (1 ) Qt+1

Capital utilisation:Rkt = P t

(ut )

Production function:

Y i,t = K i,t [Z tN i,t ]1 Z t F

Labor demand:W t = (1 ) Z t

K tZ t N t

MC t

Capital renting:

Rkt = K tZ t N t

1MC t

Price setting:

E t

s=0( p)s

t+ st

Y t,t + s P t pt,t + s p,t+ s MC t+ s = 0

Aggregate price index:

P t = (1 p) (P t )1/ (p,t 1) + p 1 p

pt 1P t 1

1/ (p,t 1) (p,t 1)

Wage setting:

Et

s=0( w)s t+ s N t,t + s

W tP t+ s

wt,t + s b,t+ s w,t + sN t,t + s

t+ s= 0

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Aggregate wage index:

W t = (1 w) (W t )1/ (w,t 1) + w z

1 p wt 1W t 11/ (w,t 1) (w,t 1)

Government spending:

Gt = 1 1g,t

Y t

Monetary policy rule:

t = t 1

t

Y tY t 1 z

y (1 )

r,t

Resource constraint:

Y t = C t + I t + Gt + (u t ) K t 1 p,t Y t = u t K t 1

[Z tN t ]1 Z t F

B. Stationary equilibrium

To nd the steadystate, we express the model in stationary form. Thus, for thenonstationary variables, let lowercase denote their value relative to the technologyprocess Z t :

yt Y t /Z t kt K t /Z t kt K t /Z t it I t /Z t ct C t /Z tgt Gt /Z t t t Z t wt W t / (Z t P t ) wt W t / (Z t P t ) mt M t / (Z t P t )

where we note that the marginal utility of consumption t will shrink as the economygrows, and we express the wage in real terms. Also, denote the real rental rate of capital and real marginal cost by

r kt Rkt /P t and mc t MC t /P t ,

and the optimal relative price as

pt P t /P t .Then we can rewrite the model in terms of stationary variables as follows.

Effective capital:

kt = ut kt 1

z,t

25


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Capital accumulation:

kt = (1 )kt 1z,t

+ i,t 1 S I tI t 1

z,t xt


t = b,t

ct hct 1z,t

Eth b,t+1

z,t +1 ct+1 h ct

z,t +1


t = R t E t t+1

z,t +1 t+1


t = b,t m,t m t + E t

t+1z,t +1 t+1


1 = q t i,t 1 S it

it 1z,t

it

i t 1z,t S

it

i t 1z,t

+ Et t+1 t z,t +1

q t+1 i,t +1i t+1i t

z,t +12

S it+1it

z,t +1

Tobins Q:

q t = E t t+1 tz,t +1

r kt+1 ut+1 (ut+1 ) + (1 ) Q t+1

Capital utilisation:r kt =

(ut )


yi,t = ki,t N 1 i,t F

Labor demand:wt = (1 )

ktN t

mc t

Capital renting:

r kt = ktN t

1

mc t

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Price setting:

Et

s=0( p)s

t+ s t

yt,t + s ptP t

P t+ s pt,t + s p,t+ s mc t+ s = 0

Aggregate price index:

1 = (1 p) ( pt )1/ (p,t 1) + p 1 p

pt 1

1 t

1/ (p,t 1) (p,t 1)

Wage setting:

E t

s=0(w)s t+ s N t,t + s wt

P tP t+ s

Z tZ t+ s

wt,t + s b,t+ s w,t + sN t,t + s t+ s

= 0

Aggregate wage index:

wt = (1 w) (wt )1/ (w,t 1) + w z 1 p

wt 1

wt 1 t z,t

1/ (w,t 1) (w,t 1)


gt = 1 1

g,tyt


t = t 1

t

z,t yt z yt 1

y (1 )

r,t


yt = ct + x t + gt + (ut ) kt 1/ z,t p,t yt = ut kt 1 N 1 t F

C. Steady state

We use the stationary version of the model to nd the steady state, and we letvariables without a time subscript denote steadystate values. First, the expressionfor Tobins Q implies that the rental rate of capital is

r k = z

(1 )

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and the price-setting equation gives marginal cost as

mc = 1 p

.

The capital/labor ratio can then be retrieved using the capital renting equation:

kN

= mcr k

1/ (1 ),

and the wage is given by the labor demand equation as

w = (1 ) mc kN

.

The production function gives the output/labor ratio as

yN

=kN

F N

,

and the xed cost F is set to obtain zero prots at the steady state, implying

F N

=kN

w r k kN

.

The output/labor ratio is then given by

yN

= w + r k kN

= rk

kN

.

Finally, to determine the investment/output ratio, use the expressions for effectivecapital and physical capital accumulation to get

ik

= 1 1

z z ,

implying thati

y =

i

k

k

N

N

y = 1

1

z

z

rk .

Given the government spending/output ratio g/y , the consumption/output ratiois then given by the resource constraint as

cy

= 1 iy

gy

.

In addition, we have:

R = z

.

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D. Loglinearised version

We loglinearise the stationary model around the steady state. Let t denote thelog deviation of the variable t from its steadystate leve l :

t log t

.

The log-linearised model is then given by the following system of equations for theendogenous variables.

Effective capital:

kt + z,t = u t + kt 1

Capital accumulation:

kt = 1

z kt 1 z,t + 1 1

z(t + i,t )


t = h z

( z h ) ( z h)ct 1

2z + h2 ( z h ) ( z h)

ct + h z

( z h ) ( z h)E t ct+1

h z

( z h ) ( z h)z,t +

h z( z h ) ( z h)

E t z,t +1

+ z

z h b,t

h z h

E t b,t+1


t = E t t+1 + R t Et t+1 Et z,t +1


m t = 1 (b,t + m,t ) 1

t 1(R 1) R t


t = 11 +

(t 1 z,t ) + 1 +

Et (t+1 + z,t +1 ) + 1

k 2z (1 + ) (q t + i,t )

Tobins Q:

q t = (1 )

zEt q t+1 + 1

(1 ) z

Et r kt+1 (r t E t t+1 )

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Capital utilisation:

ut = 1 uu rkt


yt = Y + F

Y kt + (1 ) n t

Labor demand:wt = mc t + kt n tCapital renting: r kt = mc t (1 ) kt + (1 ) n t

Phillips curve:

t = p

1 + p t 1 +

1 + p

Et t+1 + (1 p) (1 p)

p 1 + p (mc t + p,t )

Wage curve:

wt = 11 +

wt 1 + 1 +

Et wt+1 (1 w) (1 w)

w (1 + ) 1 + ww 1(mrs t + w,t )

+ w1 +

t 1 1 + w

1 + t +

1 +

Et t+1 11 +

z,t + 1 +

E t z,t +1

Marginal rate of substitution:

mrs t = wt n t t + b,t


gt = yt + 1 g/y

g/y g,t


t = t 1 (1 ) t + y (yt yt 1 + z,t ) + r,t


yt = cy

ct + iy

t + gy

gt + r k k

y ut

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A3. Scatter plots for the period 20082011

We extend our sample to include the years 2008 to 2011 and apply the lowfrequency approach. Figure A31 displays the resulting scatters of points for thecurrent crisis period. While the slopes were at or even negative until 2007, we ndthat they revert positive over the past four years. In addition, one can even see aconcentration of points around the diagonal. Such ndings reveal a return of thequantity theory of money.

Figure A31. Scatter plots of ltered money growth, ination and interest rate

31

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