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Central bank misperceptions and the role of money in interest rate rules

by Guenter Beck and Volker Wieland

October 2008 No 147

NBB WORKING PAPER No. 147 - OCTOBER 2008

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ISSN: 1375-680X (print)ISSN: 1784-2476 (online)

NBB WORKING PAPER - No. 147 - OCTOBER 2008

Central bank misperceptionsand the role of money in interest rate rules*Guenter Beck, Johann Wolfgang Goethe University Frankfurt

Volker Wieland, Johann Wolfgang Goethe University Frankfurt and CEPR

Abstract

Research with Keynesian-style models has emphasized the importance of the output gap forpolicies aimed at controlling inflation while declaring monetary aggregates largely irrelevant. Critics,however, have argued that these models need to be modified to account for observed moneygrowth and inflation trends, and that monetary trends may serve as a useful cross-check formonetary policy. We identify an important source of monetary trends in form of persistent centralbank misperceptions regarding potential output. Simulations with historical output gap estimatesindicate that such misperceptions may induce persistent errors in monetary policy and sustainedtrends in money growth and inflation. If interest rate prescriptions derived from Keynesian-stylemodels are augmented with a cross-check against money-based estimates of trend inflation,inflation control is improved substantially.

JEL Classification: E32, E41, E43, E52 and E58

Keywords: monetary policy under uncertainty, money, output gap uncertainty, quantity theory andTaylor rules

Guenter BeckProfessor of Monetary TheoryJohann Wolfgang Goethe UniversityPostbox 2960325 Frankfurt am MainGERMANYEmail: gbeck@wiwi.uni-frankfurt.deFor further Discussion Papers by this author see:www.cepr.org/pubs/new-dps/dplist.asp?authorid=155005

Volker WielandChair for Monetary Theory and PolicyJohann Wolfgang Goethe UniversityPostbox 94D-60325 Frankfurt am MainGERMANYEmail: wieland@wiwi.uni-frankfurt.deFor further Discussion Papers by this author see:www.cepr.org/pubs/new-dps/dplist.asp?authorid=152242

* We thank Athanasios Orphanides for providing his data on historical U.S. output gap revisions and ChristinaGerberding for the Bundesbank’s real-time data set with output gap revisions. Furthermore, Wieland thanks theEuropean Central Bank that he visited as Wim Duisenberg Research Fellow and the Stanford Center forInternational Development for the hospitality extended while part of this research was accomplished. An earlierversion of this paper was presented at the conference on “John Taylor’s Contributions to Monetary Theory andPolicy” at the Federal Reserve Bank of Dallas, October 2007. We have also benefited from seminarpresentations at U.C. Santa Cruz, U.C. Davis, FU Berlin, Birkbeck College, the European Central Bank, theKiel Institute as well conferences at the Bundesbank, the University of Cambridge and the Center for FinancialStudies. We would also like to thank Ignazio Angeloni, Joshua Aizenman, John Driffill, Tim Cogley, AlexCukierman, Mark Gertler, Stefan Gerlach, Robert Hall, Otmar Issing, Robert Lucas, Ronald McKinnon, John B.Taylor, Peter Tinsley, Carl Walsh, John C. Williams and Michael Woodford for useful comments. The usualdisclaimer applies.

Submitted 21 August 2008

1 Introduction

John Taylor’s research on monetary policy rules changed theeconomics profession’s focus from

monetary aggregates to the interest rate as the appropriateinstrument for monetary policy.1

Even the late Milton Friedman, in his last published writing, studied Taylor’s rule for interest

rate policy, though he tried to reclaim a role for money on itsright-hand side.2 Recent theo-

retical advances in New-Keynesian macroeconomics building on microeconomic foundations

with monopolistic competition and price rigidity have further de-emphasized the role of money

in monetary policy. As shown by Kerr and King (1996), Svensson (1997) and Clarida et al.

(1999) optimal interest rate policy in models with price rigidities is conducted with reference

to inflation forecasts and output gaps but without direct concern for monetary aggregates—

not unlike Taylor’s rule.3 Some macroeconomists, however, have expressed concern about the

disappearance of money from monetary theory and policy. Lucas (2007), for example, writes:

“New-Keynesian models define monetary policy in terms of a choice of money mar-

ket rate and so make direct contact with central banking practice. Money supply

measures play no role in the estimation, testing or policy simulation of these mod-

els. A role for money in the long run is sometimes verbally acknowledged, but

the models themselves are formulated in terms of deviationsfrom trends that are

themselves determined somewhere off stage.

1Taylor (2006) writes on his progression from money to interest rates: “Taylor (1979) showed that a fixedmoney growth rule - a Friedman rule - would have led to better performance than actual policy in the post WorldWar II period ... (but) a money growth rule which responded toeconomic developments could do even better. Sincethen I have found that policy rules in terms of interest rateshave worked better as practical guidelines for centralbanks.”

2Friedman (2006) notes at first that he always preferred a monetary aggregate for a policy instrument but thentakes the perspective of Taylor’s rule with the federal funds rate as instrument: “The Taylor rule is an attempt tospecify the federal funds rate that will come closest to achieving the theoretically appropriate rate of monetarygrowth to achieve a constant price level or a constant rate ofinflation. Suppose the federal funds target rate is equalto a Taylor rule that gives 100 percent weight to inflation deviations. That may not be the right rate to achievethe desired inflation target because other variables such asoutput or monetary growth are not at their equilibriumlevels. On this view, additional terms in the Taylor rule would reflect variables relevant to choosing the right targetfunds rate to achieve the desired inflation target.”

3The New-Keynesian model as laid out by Rotemberg and Woodford (1997) and Goodfriend and King (1997)and developed in detail in Woodford (2003) and Walsh (2003) has quickly become the principal workhorse modelin monetary economics. The case against money is perhaps made most vigorously by Woodford (2006).

1

It seems likely that these models could be reformulated to give a unified account

of trends, including trends in monetary aggregates, and deviations about trend but

so far they have not been. This remains an unresolved issue onthe frontier of

macroeconomic theory. Until it is resolved, monetary information should continue

to be used as a kind of add-on orcross-check.”

We address Lucas’s request for a unified account of trends anddeviations, including mone-

tary aggregates, and provide a formal analysis of his proposal to use monetary information as a

cross-check for policy. The central bank’s beliefs regarding trends and deviations play a central

role in the analysis, specifically its estimates of the economy’s potential output and the implied

output gap that drives inflation forecasts in Keynesian-style models.

Research on optimal monetary policy design under uncertainty usually has to rely on a-

priori modeling assumptions regarding unobservable variables such as potential output (cf.

Svensson and Woodford (2003) and Wieland (2006)). These assumptions are needed to de-

termine the optimal, model-based estimates of potential output, on which policy is then condi-

tioned. Orphanides (2003) has provided an alternative approach for evaluating policies under

uncertainty that avoids these particular a-priori assumptions by using instead historical, real-

time estimates of potential output. The true value of potential output at any point in time is

assumed to be equal to the central bank’s final estimate on thebasis of information available

many years later. We use historical series of central banks’output gap estimates for the United

States and Germany from Orphanides (2003) and Gerberding etal. (2005) respectively. Both

series indicate very persistent misperceptions regardingpotential output.

Model simulations indicate that historical output gap misperceptions induce an inflation-

ary bias in interest rate policies that the central bank considered optimal conditional on its

model and associated forecasts. As a result, the central bank induces trends in money growth

and inflation even though it pursues a constant inflation target. Thus, as requested by Lucas,

Keynesian-style models built to explain inflation deviations from trend are able to provide an ac-

count of money growth and inflation trends. This finding complements recent empirical studies

that have identified proportional movements in money growthand inflation at low frequencies

2

using a variety of filters4 and provides a structural explanation.

Next, a general definition of a policy with cross-checking that formalizes Lucas (2007)

proposal is presented. The cross-check is characterized bya first-order condition that in-

corporates expected trend inflation, which is estimated from a simple monetary model. The

cross-check is triggered in a nonlinear-fashion whenever astatistical test on the basis of the

monetary model signals a trend shift. An earlier note, Beck and Wieland (2007), presented

an interest rate rule that incorporates such a shift5 and simulated a counterfactual example in

the traditional Keynesian-style model with backward-looking dynamics of Svensson (1997),

Orphanides and Wieland (2000) and Orphanides (2003). The present paper shows how to de-

rive an interest rate rule with cross-checking from an optimization problem and proceeds to

implement cross-checking in the benchmark New-Keynesian model.6

The advantage of the Keynesian model with backward-lookingdynamics is that it fits the

historical persistence in output and inflation and arguablyembodies central bankers’ beliefs

on policy tradeoffs and monetary policy transmission in the1970s and 1980s quite well. It

may be the better candidate for modeling central bank perceptions and describing historical

outcomes and was used for this purpose by Orphanides (2003).While the New-Keynesian

model is an unlikely description of central bank perceptions in the 1970s and 1980s, it has the

advantage of microeconomic foundations in optimal decision-making of households and firms.

Thus, it accounts for forward-looking, optimizing decision-making by market participants and

constitutes an important testing ground for policy strategies currently recommended to central

banks. For this reason, the subsequent analysis is carried out in both models in parallel.

The policy with cross-checking against money-based estimates of trend inflation is found

to substantially improve inflation control in the event of persistent policy mistakes due to his-

torical output gap misperceptions. Furthermore, monetarycross-checking remains effective in

4See Gerlach (2004), Benati (2005), Pill and Rautananen (2006) and Assenmacher-Wesche and Gerlach(2007).

5Beck and Wieland (2007) point out that such an interest rate rule captures key elements of the ECB’s descrip-tion of its two-pillar policy strategy. However, the ECB hasnever published a formal, mathematical exposition ofits strategy.

6Our definition of monetary cross-checking is different fromanother interesting strategy proposed byChristiano and Rostagno (2001) and Christiano et al. (2006)that combines monetary targeting with Taylor-styleinterest rate rules.

3

the event of sustained velocity shifts—the Achilles heel oftraditional monetary targeting—if

standard recursive money demand estimation is applied. Thenonlinear nature of interest-rate

adjustments due to cross-checking turns out to be essential. Linear policies with money-based

estimates of trend inflation perform substantially worse than cross-checking, whether central

bank estimates of the output gap are correct, on average, or not. Finally, cross-checking can also

be implemented successfully using inflation-based estimates of trend inflation but money-based

estimates would dominate if money leads inflation as indicated by recent empirical studies.

The remainder of this paper is structured as follows. Section 2 presents the optimal interest

rate policy under uncertainty and explains how we introducehistorical central bank misper-

ceptions into the analysis. Section 3 describes the relationship between trend money growth

and trend inflation and shows that central bank misperceptions represent an important source

of such trends in Keynesian-style models. Section 4 introduces the general definition of cross-

checking. Section 5 applies cross-checking in the event of central bank misperceptions. Section

6 subjects the policy with cross-checking to further sensitivity analysis and section 7 concludes.

An appendix provides further details on the models and theirsolution under cross-checking.7

2 Output gap misperceptions and optimal policy

Keynesian-style models of inflation determination assign acentral role to the output gap, that is

the difference between actual output and the economy’s potential. For example, the model used

by Svensson (1997), Orphanides and Wieland (2000) and Orphanides (2003) to study monetary

policy incorporates an accelerationist Phillips curve that relates current inflation,πt , to the gap

between current and potential output (in logs),yt − zt , lagged inflation,πt−1, and a cost-push

shock,ut :

πt = λ(yt −zt)+πt−1+ut (1)

The slope parameterλ determines the trade-off between output and inflation.

Similarly, the New-Keynesian model of Rotemberg and Woodford (1997) and Goodfriend

7Software for replicating the quantitative analysis in thispaper is available from the authors upon request.

4

and King (1997) that was used by Clarida et al. (1999) to studythe design of monetary policy

assigns center stage to the output gap in determining deviations from steady-state inflation,π,

next to expected future inflation,πet+1, and cost-push shocks:

πt −π = λ(yt −zt)+β(πet+1−π)+ut , whereπe

t+1 = Et [πt+1] (2)

Since this Phillips curve is derived from microeconomic foundations, the parameters have a

clear economic interpretation.β refers to the discount factor of optimizing households and

firms. λ is a function of the probability that firms are allowed to adjust prices according to

Calvo (1983). Furthermore, expectations regarding futureinflation are formed in a rational,

forward-looking manner. Potential output,zt , which is an unobservable and model-dependent

variable, corresponds to the level of output that would be realized if prices were completely

flexible.8 In the following, the Keynesian-style model associated with equation (1) is referred

to as theK-Modeland the New-Keynesian model associated with (2) as theNK-Model.

2.1 Optimal interest rate policy under uncertainty

Optimal policy in the above-mentioned models prescribes that the central bank conditions its

policy decisions on its best estimate of potential output. This recommendation applies even

if the central bank’s objective focuses exclusively on stabilizing inflation without any explicit

concern for output fluctuations. The objective function of such a strictly inflation targeting

central bank is given by:9

−12

Et

{

∞

∑i=0

βi [(πt+i −π∗)2]}

. (3)

π∗ denotes the central bank’s inflation target. In the following, it is normalized at zero along with

steady-state inflation,π. The rational expectationEt [.] of the objective function is conditional

8Traditional Keynesian models have typically related the measure of potential in the accelerationist Phillipscurve, equation (1), more loosely to the output implied by a standard model of long-run growth.

9Our analysis can be extended to an objective function that includes output deviations from potential andhas welfare-theoretic foundations in the New-Keynesian model. Here, we focus on strict inflation targeting toemphasize that our findings regarding the consequences of output gap misperceptions do not rely on including thegap in the objective function. Thus, we are more likely to understate than overstate their negative implications.

5

on the particular model of inflation determination preferred by the central bank.

The optimal monetary policy that maximizes the above objective must satisfy the following

first-order condition:10

E[πt+i | t,K/NK] = π∗ = 0 ∀i = {0,1,2, ..,∞}. (4)

The output level that would achieve this optimum at timet is given by

K-Model: yt = zt −λ−1(πt−1+ut) (5)

NK-Model: yt = zt −λ−1ut (6)

Thus, the central bank aims for an output level above (or below) potential to the extent nec-

essary to offset inflationary pressures from cost-push shocks and—in the K-Model—inherited

inflation.

In practice, however, the central bank cannot observe potential output or particular shocks

with any certainty and needs to rely on estimates. We use the superscripte to refer to the

central bank’s estimates or perceptions of such unobservable variables. Thus,zet|t refers to the

central bank’s estimate of potential output in periodt given the information available at that

point in time anduet|t to the cental bank’s estimate of the cost-push shock. We assume that

these perceptions represent the best available estimates of the unobservable variables from the

perspective of the central bank. Similarly, we use the superscript e as a short-hand for the

rational expectations of output and inflation. For example,πet|t = E[πt |t] represents the central

bank’s best forecast of inflation at the point in periodt when it decides on its policy, i.e. before

it can observe the joint consequences of potential output, the cost-push shock and its policy

choice on inflation.

Fortunately, the optimal policy under uncertainty can be determined quite easily if the fol-

10See Svensson (1997) for the K-Model and Clarida et al. (1999)for the NK-Model. In the NK model thequestion arises whether to consider the optimal policy under discretion or commitment. Note, however, that forstrict inflation targeting the optimal policies under discretion and commitment are identical. If output were to beincluded in the loss function we would analyze optimal policy under discretion.

6

lowing conditions are fulfilled: the model is linear, the parameters are known and uncertainty

is additive. In this case, certainty-equivalence applies,i.e. the optimal policy must satisfy the

first-order condition, equation (4), in expectation (see, for example, Svensson and Woodford

(2003) for the NK-Model and Wieland (2006) for the K-Model).11 Then, the expected optimal

output level corresponds to:

K-Model: yet|t = ze

t|t −λ−1(πt−1+uet|t) (7)

NK-Model: yet|t = ze

t|t −λ−1uet|t (8)

The conditions for certainty-equivalence—linearity, known parameters and additive uncertainty—

require making importanta-priori assumptionsregarding the processes that determine unob-

servable variables. Svensson and Woodford (2003), for example, assume that potential output,

zt, in the NK-model follows an auto-regressive process,

zt = νzt−1+ εzt , (9)

with known persistence parameter,ν, and known variance,σεz.12 Wieland (2006) makes a simi-

lar assumption regarding the natural rate in a version of theK-Model. Under these assumptions

the central bank can solve the estimation problem separately from the optimal policy problem.

Svensson and Woodford (2003) and Wieland (2006) show how to derive the optimal estimate

of potential output,zet|t, using the Kalman filter. Conditional on this estimate the optimal policy

implies setting the nominal interest rate,it , so as to achieve the expected output level defined

by equations (7) or (8), respectively. This value of the interest rate may be inferred from the IS

11Certainty-equivalence fails if multiplicative parameters such asλ are unknown. Then, the central bank faces acomplex control and estimation problem. Examples are studied by Wieland (2000), Beck and Wieland (2002) andWieland (2006).

12We are referring to equation (43) in Svensson and Woodford (2003). In addition, the authors assume thecentral bank observes a signal regarding potential output that is correct up to an i.i.d. normal noise term.

7

equations:

K-Model: yt = yt−1−ϕ(it −πt−1)+gt (10)

NK-Model: yt = yet+1−ϕ

(

it −πet+1

)

+gt (11)

Thus, the optimal interest rate setting is given by:

K-Model: it = πt−1+(ϕλ)−1(πt−1+uet|t)+(ϕ)−1(yt−1−ze

t|t +get|t) (12)

NK-Model: it = (ϕλ)−1(uet|t)+(ϕ)−1(ze

t+1|t −zet|t +ge

t|t) (13)

This characterization of optimal interest rate policies can be simplified further by exploiting

modeling assumptions regarding the economic shocks. In particular, we assume that(gt ,ut) are

i.i.d. normal with zero-mean and known variances(σg,σu). With regard to the K-Model we

follow common practice (cf. Svensson (1997), Orphanides and Wieland (2000)) and assume

that the central bank has no information on periodt shocks when settingit , i.e. get|t,K = 0 and

uet|t,K = 0. With regard to the NK-Model we follow Clarida et al. (1999)and assume that the

central bank has some information on current shocks. Specifically, we assume that the central

bank receives a signal(get ,u

et ) that is correct up to an additive noise term(εg

t ,εut ) with zero

mean. Thus,get|t,NK = ge

t , anduet|t,NK = ue

t .13

Consequently, the optimal interest rate policies correspond to:

K-Model: iKt = πt−1+(ϕλ)−1(πt−1)+(ϕ)−1(yt−1−zet|t) (14)

NK-Model: iNKt = (ϕλ)−1(ue

t )+(ϕ)−1(zet+1|t −ze

t|t +get ) (15)

The optimal policy in the K-Model is a version of the famous Taylor rule, yet its coefficients

on inflation and the output gap need not coincide with the values of 0.5 that Taylor (1993)

used to match federal funds rate choices by the FOMC from 1988to 1993. As to the optimal

13More specifically, we assume that the true value of the demandand cost-push shocks, denoted bygt andut

respectively, are given bygt = get + εg

t whereεgt ∼ i.i.d. N

(

0,σεg

)

andut = uet + εu

t whereεut ∼ i.i.d. N(0,σεu).

Shocks to money demand are modeled in a similar fashion.

8

policy under the NK model, Clarida et al. (1999) already pointed out that it can be interpreted

as a forward-looking Taylor rule that responds to expected inflation and a measure of aggregate

demand disturbance.

It is important to note that we have followed Svensson and Woodford (2003) in adopting

the assumption of symmetric information in the NK-Model. Thus, the central bank, price-

setting firms and households share the same information regarding potential output and eco-

nomic shocks and form identical expectations regarding future output and inflation.14

2.2 The irrelevance of monetary aggregates

So far, we have not discussed monetary aggregates because they are not needed to characterize

the transmission of interest rate changes to inflation in Keynesian-style models. In these models

changes in the nominal interest rate influence the real interest rate due to the presence of price

rigidities; the real interest rate determines the level of output; and the gap between actual and

potential output drives inflation. Of course, the models maybe extended to include a standard

money demand equation15 such as:

mt − pt = γyyt − γi it +st . (16)

whereγy denotes the income elasticity of money demand,γi the semi-interest rate elasticity and

st an i.i.d. normal money demand shock. While the central bank controls interest rates via open-

market operations that also affect the money supply, the equilibrium level of money balances

is determined recursively from the money demand equation. For this reason, money does not

14Svensson and Woodford (2004) also provide certainty-equivalence results under the assumption of asymmet-ric information. In this case, which arises under a consistent application of the representative agent assumption,households and firms know the true value of potential output.In our view, however, the assumption of symmetricinformation is more appropriate for the policy problem at hand. In practice, individual private agents are unlikelyto know more about aggregate potential output than the central bank. If some individuals are particularly good atestimating aggregate potential output, central banks willbe eager to hire them or to buy their inflation forecasts.One might even argue that it is more realistic to assume that the private sector is less knowledgeable about macroe-conomic aggregates. Interestingly, however, the Bundesbank’s potential output estimates that we use later on weremade public in the 1970s and 1980s consistent with our assumption of symmetry (cf. Bundesbank (1973, 1981)).

15This specification can be derived from the optimization problem of a household that values money holdingsaccording to a utility function that is separable in real balances and consumption goods (see Walsh (2003)).

9

appear in the optimal interest rate policies defined by equations (14) and (15). The quantity of

money adjusts so as to achieve the interest rate prescribed by the optimal policy. Technically,

mt is determined by equation (16) conditional on the desired interest rate and the current values

of real income and the price level.

What about the information value of monetary aggregates? Since we treat actual output and

inflation as observable variables, monetary aggregates have no additional information value.

The estimate of potential output,zt|t, discussed by Svensson and Woodford (2003) and Wieland

(2006) is obtained by means of the Kalman filter from past observations of output and inflation.

Monetary aggregates provide no relevant information as long as money balances do not appear

directly in the Phillips curve or the IS equation.16 In practice, initial values of GDP, the GDP

deflator and monetary aggregates are revised for a few quarters. While GDP is only available

on a quarterly basis, monetary aggregates are available on amonthly frequency and tend to

be revised less. Thus, monetary aggregates may provide information that helps improve initial

estimates of actual output. This information role of monetary aggregates is investigated by

Coenen et al. (2005). They show that initial GDP estimates for the euro area are revised more

substantially than monetary aggregates. Using an estimated model of the euro area with rational

expectations they find that optimal estimates of current GDPassign some weight to monetary

aggregates, but this weight is very small.17

2.3 Evaluating policy performance with historical central bank misper-

ceptions

We have already pointed out that the optimal policy depends importantly on the central bank’s

estimate of potential output,zt|t. A possible route for further analysis would be to follow

Svensson and Woodford (2003) and Wieland (2006) in studyingpolicy performance using cal-

16Ireland (2004) and Andres et al. (2006) investigate the direct role of money balances in output and inflationdetermination. They suggest that such direct effects are ofminor importance.

17Coenen et al. (2005) assume that the central bank and the private sector have symmetric information and applythe same filtering techniques as in Svensson and Woodford (2003). An interesting paper by Dotsey and Hornstein(2003) investigates this question in a calibrated model of the U.S. economy under the assumption of asymmetricinformation as in Svensson and Woodford (2004). Their findings regarding the information value of money areeven more negative.

10

culations that make use ofa-priori assumptions concerning the unobservable process determin-

ing potential output, i.e. equation (9). Instead, we choosea different research strategy following

the influential study of Orphanides (2003). Orphanides usedhistorical output gap estimates to

argue that the Taylor rule would not have been able to preventthe “Great Inflation” of the 1970s.

Orphanides (2003) collected real-time data on U.S. inflation and output including real-time

estimates of potential output obtained by the Council of Economic Advisers (1966-1980) and

the Federal Reserve (1980-1994).18 On this basis, we denote the difference between the real-

time estimate of potential output and the final estimate as of1994 aset :

et = zet|t −ze

t|1994 (17)

et provides a lower-bound on the extent of the central bank’s misperception of potential output

since estimates may still have been revised after 1994. Thus, Orphanides (2003) proposed to

analyze policy treating the final estimate in 1994,zet|1994, as the true value of potential output,

zt:

zet|t = zt +et (18)

The resulting series of real-time U.S. output gap misperceptions,Et [yt −zt ]−(yt −zt), is shown

by the solid line in Figure 1.

Critics have argued that the potential GDP measures constructed by the CEA were politi-

cized maximum measures not taken seriously by Federal Reserve decision makers. Therefore,

we contrast the U.S. CEA-FRB output gap misperceptions provided by Orphanides (2003) with

a similar series from Gerberding et al. (2005) for Germany from 1974 to 1999. This series is

shown by the dashed line in Figure 1. In this case, the underlying production potentials are the

Bundesbank staff’s estimates.19 The Bundesbank started to produce its own estimates of poten-

18The output gap data for the 1980s and 1990s of Orphanides (2003) was constructed from the Greenbook, theFederal Reserve document summarizing the Board staff’s analysis of economic developments distributed to theFOMC members a few days before each FOMC meeting. For the 1960s and 1970s Orphanides could not recovera complete time series for potential output estimates from Federal Reserve sources but notes that discussion ofoutput gap measures appeared in the FOMC Memorandum of Discussion throughout this period. Thus, he usesreal-time estimates of potential output that were producedby the Council of Economic Advisers (CEA) in thoseyears and available at FOMC meetings.

19The data were reconstructed from official Bundesbank publications and from internal documents such as the

11

tial output in the early 1970s. Its methods are described in detail in Bundesbank (1973). The

Bundesbank made clear that it aimed to construct a measure consistent with price stability—not

a maximum measure.

Both series of historical output gap revisions indicate very persistent misperceptions by the

respective central bank. This persistence arises primarily from the estimates of unobservable

potential output, since revisions to actual output declinemuch more rapidly than those to the

output gap. Both series indicate that the production potential of these economies was over-

estimated through the 1970s and well into the 1980s. U.S. andGerman policy makers taking

into account these estimates were led to believe that their respective economies suffered a very

deep recession from 1974 to 1976. In retrospect, however, this period appears as a mild reces-

sion in the United States and as a decline from excessive levels towards potential in Germany.

To the extent the Federal Reserve or the Bundesbank based their inflation forecasts on the

output gap estimates available at the time, they must have concluded that inflation would soon

decline. In retrospect, such a forecast would have been wrong. Using an estimated variant of

the K-Model for the United States Orphanides (2003) showed that if interest rates had been

set according to Taylor’s rule with historical output gap estimates, inflation would have risen

dramatically. Thus, he concluded that Taylor’s rule would not have helped the FOMC avoid the

“Great Inflation” of the 1970s, as long as it believed the output gap estimates.

3 Money and inflation trends due to historical output gapmisperceptions

In the following, Orphanides (2003)’ findings regarding theeffect of historical central bank

misperceptions on inflation under Taylor’s rule are shown toextend to the optimal interest rate

policies in the K- and NK-Model. Furthermore, it is shown that central bank misperceptions

constitute an important source of common trends in money growth and inflation similar to

the low-frequency co-movements identified by recent empirical studies. Thus, Keynesian-style

models with central bank misperceptions can provide a unified account of short-run deviations

briefing material for the Council’s discussions on the monetary target for the year to come.

12

from trend as well as long-run movements in money growth and inflation as requested by Lucas

(2007).

In a first step, the long-run equilibrium values of money growth and inflation are derived.

To this end, the money demand equation (16) is re-arranged and first-differences are taken to

obtain a short-run relationship between money growth and inflation:

πt = ∆pt = ∆mt − γy∆yt + γi∆it −∆st . (19)

Here,∆ denotes the first-difference operator. In the long run, money demand shocks will av-

erage to zero; the nominal interest rate will converge to itsconstant steady-state level and its

first-difference to zero;20 and output growth will converge to the steady-state growth rate of

potential,∆y = ∆z. Thus, long-run inflation is proportional to long-run moneygrowth adjusted

for trend output growth and trend velocity21 :

π = ∆m− γy∆y = µ. (20)

Recent empirical studies confirm the long-run proportionalrelationship between inflation and

money growth (cf. Gerlach (2004), Benati (2005), Pill and Rautanen (2006) and Assenmacher-

Wesche and Gerlach (2007). These studies use various types of filters. Gerlach (2004), for

example, defines filtered money growth as

∆mft = ∆mf

t−1+ω(

∆mt −∆mft−1

)

. (21)

Accordingly, we obtain a filtered measure of adjusted money growth from equation (20):

µft = ∆mf

t − γy∆yft . (22)

20The steady state level of the nominal interest rate corresponds to the sum of the equilibrium real interest rateand the inflation target.

21Specifically, with velocity defined asvt ≡ −mt + pt +yt and money demand determined by equation (16) thelong-run trend in velocity corresponds to∆v = (1− γy)∆y.

13

Interestingly, the empirical studies cited above report that filtered measures of money growth

tend to lead filtered inflation by several quarters. This property would renderµft a particularly

useful forecast of impending movements in trend inflation. However, the timing assumptions of

the Keynesian-style models with money demand presented in section 2, preclude such a leading

indicator role of filtered money growth. This question is discussed further in section 6.

The next step is to introduce central bank misperceptions. Thus, the perceived potential out-

put,zet|t , in the optimal interest rate policies (equations (14) and (15)) is replaced with the histor-

ical, real-time estimates for the U.S.A. and Germany, respectively. Similarly, the true value,zt ,

in the Phillips curves (equations (1) and (2)) is replaced with the final estimates (U.S.A.: 1994,

Germany: 1999). The difference between real-time and final estimates constitutes the output

gap misperception,et . Then, the models are simulated by drawing from the shock distributions

and parameter values posited in Table 1. Thus, a-priori assumptions regarding the true structural

process driving unobservable potential (cf. equation (9))are avoided and policy performance is

evaluated with data on historical misperceptions. It is straightforward to show that inflation will

inherit the persistence properties of historical output gap misperceptions:

K-Model: πt = λet +λgt +ut (23)

NK-Model: πt = λet +λεgt + εu

t (24)

Thus, actual inflation will persistently deviate from the zero inflation target even though the

central bank aims to offset all forecasted deviations conditional on its preferred Keynesian-style

model and associated gap estimate.

Figure 2 reports simulations with U.S. and German output gapmisperceptions in the K-

model for a given draw of exogenous shocks and noise terms.22 The first row of two panels

shows the rate of inflation,πt , and the filtered measure of adjusted money growth,µft , with U.S.

output gap misperceptions. From period 15 onwards till period 135 the difference between the

true and the perceived output gap corresponds to the difference between real-time and 1994

22The sequence of shocks is arbitrary but we obtain similar results for many alternative draws and will discussaverages later on in this section.

14

estimates from Orphanides (2003). The persistent over-estimate of potential output induces the

central bank to set interest rates too low to maintain price stability. Thus, money growth and

inflation increase and inherit the serial correlation of thecentral bank’s misperceptions regarding

potential output. Over time, also the filtered measure of adjusted money growth,µft , increases as

shown in the second panel of the first row. The lower two panelsof Figure 2 report a simulation

with the Bundesbank misperceptions from Gerberding et al (2005). Again, the misperceptions

start in period 15. From then on, policy is too accommodativeand (adjusted) money growth and

inflation increase up to a peak of around 5 percent in spite of the central bank’s constant target

of zero inflation. This peak is somewhat smaller than in the case of the U.S. misperceptions

that trigger an increase up to an inflation rate of 6 percent. In both cases, filtered money growth

provides a good mirror image of the trend movement in inflation.

Why does the central bank accept this sustained increase in inflation? The reason is that

it conducts a policy that is believed to be very effective in stabilizing inflation. Its forecast of

inflation that is based on its preferred estimate of the output gap indicates a recession. Con-

sequently, the central bank continuously predicts an imminent decline in the rate of inflation.

If it were to raise interest rates further its forecast wouldsignal a worsening of the recession

and an undershooting of its inflation target. Ex-post, the estimation procedure that is employed

by the central bank to obtain its potential estimate,zet|t , attributes the persistent forecast misses

to a sequence of unfavorable shocks. Such a reconciliation of potential output estimates and

observed inflation performance is not without historical parallel. Many accounts of the 1970s

attribute the stagflation in the United States and Germany primarily to inflationary and reces-

sionary consequences of oil price shocks.23

We obtain similar results with the New-Keynesian model (notshown). Rather than report-

ing more individual simulations, we turn to a summary overview in Figure 3 on the basis of

averages over 1000 simulations with U.S. and German output gap misperceptions in the K- and

NK-Model, respectively. For each of the four possible combinations, we show two panels that

23Orphanides (2003) describes how potential output estimates for the U.S.A. were eventually revised downwardsfollowing the sustained increase of inflation. Similarly, the Bundesbank learned from its mistakes. However, theserevisions occurred in several steps and after a substantialperiod of time.

15

report the cross-simulation averages of inflation,πt , and the filtered measure of adjusted money

growth,µft . A comparison of these panels indicates that filtered money growth matches low-

frequency movements in inflation very well. Thus, the monetary model derived from the quan-

tity theory explains trend inflation very well. Money and inflation trends are due to the same

source, namely persistent central bank misperceptions with regard to potential output. These

misperceptions provide a structural explanation of the trends identified in recent empirical stud-

ies by Gerlach (2004), Benati (2005), Pill and Rautanen (2006) and Assenmacher-Wesche and

Gerlach (2007). In other words, the introduction of imperfect knowledge and persistent cen-

tral bank misperceptions in Keynesian-style models is sufficient to provide a unified account

of trends and deviations, including monetary trends—the unresolved issue on the frontier of

macroeconomic theory emphasized by Lucas (2007). An alternative explanation of common

trends in money growth and inflation would be an on-going shift in the central bank’s infla-

tion target, i.e. upwards in the 1970s and downwards in the 1980s. However, there exists no

direct evidence of such a change in central bank objectives.Our explanation with a constant

inflation target but persistent policy mistakes offers an alternative that is grounded in empirical

observation in terms of historical output gap revisions.

4 A general definition of cross-checking

In light of the empirical evidence on concurring trends in money growth and inflation, Lucas

(2007) proposed to use monetary information as an add-on or cross-check in interest rate policy.

In this section, we provide a formal interpretation of his proposal. We start by reiterating the

first-order condition that describes the optimal policy derived under certainty-equivalence:

E[πt+i −π∗| t] = 0 ∀i = {0,1,2, ..,∞} (25)

It implies that trend inflation equals the inflation target inexpectation. Specifically,E[πt+N|t]→

E[π] asN → ∞, and consequently:

E[π] = π∗ (26)

16

Thus, a policy maker who trusts that the Keynesian-style model correctly describes the

economy, expects that trend inflation will turn out to match the target as long as policy is set to

stabilize expected inflation in every period.24

However, such confidence in model-based forecasts and estimates of unobservable variables

may be misplaced. The simulations of historical output gap misperceptions conducted in the

preceding section provide an example that sustained trend deviations from target may occur

even under policies that aim to stabilize inflation as close to target as seems feasible on the

basis of model forecasts. Following Lucas’s recommendation, a sceptical policy maker may

instead prefer a simpler model of trend inflation based on monetary information. In fact, the

preceding section offers a simple candidate model derived from the quantity equation:

E[π] = E[µf ] (27)

This relationship holds in the Keynesian-style models of section 2, but would also remain valid

if the true structure of the economy were to correspond to a real business cycle model without

any price rigidities. Thus, a policy maker in the monetaristtradition, who distrusts short-run

inflation forecasts, may instead focus on controlling trendinflation. Such a monetarist policy

maker would conduct open-market operations in periodt so that trend inflation as estimated by

the most recent observation on filtered adjusted money growth is expected to equal the inflation

target:

E[π|µft ] = π∗ = 0 (28)

Sinceµft is constructed from money growth and actual output growth observations, it may be

monitored without relying on model-based estimates of potential output. As a result, the mon-

etary strategy can succeed in stabilizing trend inflation inspite of output gap misperceptions.25

Clearly, such a monetarist approach may appeal to a central banker who gives priority to

managing first-order risks. In our view, however, it goes toofar in abandoning any attempt at

24Similarly, a flexibly inflation targeting central bank that aims to stabilize inflation and output gap would expectthat trend inflation equals the target since the trend outputgap equals zero in expectation.

25Of course, a natural question concerns the implications of sustained velocity shifts for this strategy of stabiliz-ing trend inflation. We return to this question in section 6.

17

short-run inflation stabilization. After all, Keynesian-style models may not be that far off the

mark and potential output estimates need not always be utterly wrong. Instead, we follow Lucas

(2007) and investigate how to use monetary information as a cross-check rather than as a policy

prescription that is applied in every period.

We formalize the idea of cross-checking in the following manner. In every period, the

central bank checks whether filtered money growth is still consistent with attaining the inflation

target, or whether money growth trends have shifted, by monitoring the test statistic,

κt =µf

t −π∗

σµf, (29)

and comparing it to a critical valueκcrit . Here,σµf denotes the standard deviation of the filtered

money growth measure. It can be determined under the null hypothesis that the central bank’s

preferred Keynesian-style model is correct.

As long as the test statistic does not signal a sustained shift in filtered money growth, the

central bank implements the optimal policy under the preferred Keynesian-style model, i.e. the

policy that satisfies the first-order condition (4). Thus, inthe absence of persistent output gap

misperceptions it can stabilize short-run inflation variations very effectively.

Once the central bank receives successive signals of a shiftin trend inflation as estimated by

filtered money growth, i.e.(κt > κcrit for N periods) or (κt < −κcrit for N periods), policy is

adjusted so as to control trend inflation.26 The policy with cross-checking may be characterized

with a first-order condition that includes trend inflation:

E[πt |zet|t,K/NK] = −E[π|µf

k ] (30)

This condition guarantees that the central bank acts to offset any significant shift in trend in-

flation as estimated on the basis of monetary information.µfk denotes the most recent significant

26The two parametersκcrit andN play different roles.κcrit reflects the probability that an observed deviation ofµf from π⋆ is purely accidental (for example a 5% or 1% significance level). N defines the number of successivedeviations in excess of this critical value. Thus, the greater N the longer the central bank waits to accumulateevidence of a sustained policy bias.

18

estimate of a trend shift in periodk, i.e. (κk > κcrit , ..,κk−N > κcrit ) or (−κk <−κcrit , ..,−κk−N <

−κcrit ). Following a significant cross-check, the interest rate is set according to:

K-Model: it = (1+(ϕλ)−1)πt−1+(ϕ)−1(yt−1−zet|t)+(ϕλ)−1µf

k (31)

NK-Model: it = (ϕλ)−1(uet )+(ϕ)−1(ze

t+1|t −zet|t +ge

t )+(ϕλ)−1µfk (32)

This policy implies that the expectation of periodt inflation on the basis of the respective

Keynesian-style model corresponds to−µfk as prescribed by the first-order condition, equation

(30).27

The interest rate policy with cross-checking consists of two components,

it = iK/NKt + iCC

t , whereiCCt = (ϕλ)−1µf

k , (33)

the optimal interest rate policy conditional on the preferred Keynesian-style model and gap

estimates denoted byiK/NKt and the (occasional) adjustment in interest rate levels dueto cross-

checking,iCCt . iCC

t changes in a non-linear fashion whenever a new significant trend shift in

money growth is detected.

5 Monetary cross-checking succeeds in stabilizing inflation

trends due to historical output gap misperceptions

We now turn to exploring the performance of interest rate policy with monetary cross-checking

as defined by equations (31) and (32). The cross-checking parameters,N andκcrit , are calibrated

such that the central bank considers the likelihood that cross-checking will come into play in

the foreseeable future as negligible conditional on its preferred Keynesian-style model.28

Figures 4 and 5 report stochastic simulations of monetary cross-checking in the K- and

27The derivation for the NK model is presented in more detail inthe appendix that is made available on theScienceDirect website.

28Givenκcrit = 2.575, the 1% critical value for the normal distribution, andN = 4, the probability of a cross-check under the null hypothesis is less than 10−8.

19

NK-models. Comparing inflation in the top left panel of Figure 4, i.e. for the case of US mis-

perceptions in the K-Model, to the outcome without cross-checking given the same draw shocks

shown previously in Figure 2, we find that it evolves quite differently. The sustained upward

trend observed previously is broken. The policy with cross-checking responds to an increase in

filtered money growth,µft , fairly quickly after the output gap misperceptions have induced an

inflationary policy bias, and succeeds in reversing the inflation surge. The policy response is

not driven by an improved gap estimate. Rather, the central bank responds to monetary trends

over and above what is prescribed by the model-specific output-gap based inflation forecast.

To illustrate the interest rate adjustment from cross-checking we have added a panel that

compares the interest rate effect of the current output gap misperception,(ϕ)−1et , to the cross-

checking adjustment,iCCt = (ϕλ)−1µf

k . Once the monetary test statisticκ signals a trend shift in

periodk, it triggers an adjustment in the overall level of interest rates. This new level is main-

tained until the next significant trend shift is detected. Since output gap misperceptions increase

further and continue to induce an inflationary policy bias the test statistic triggers two more up-

ward adjustments in the level of interest rates. Cross-checking also works “on the way down” as

output gap misperceptions subside and inflation and adjusted money growth decline below tar-

get. Consequently, monetary cross-checking triggers three successive downward adjustments.

In sum, the cross-checks, on average, offset the inflationary or disinflationary consequences of

sustained output gap misperceptions.

The lower set of three panels in Figure 4 reports the simulation with German output gap

misperceptions. Again, monetary cross-checking serves tooffset the inflationary trends arising

from mistaken beliefs and policies. However, one large upward shift and two smaller downward

shifts turn out to broadly match the contours of the inflationary bias arising from central bank

misperceptions. Figure 5 confirms that cross-checking alsoworks in the New-Keynesian model

with interest rate setting defined by equation (32).

It is confirmed that the above findings hold true on average by simulating 1000 draws of

shocks of 150 periods length from the respective normal distributions. The results (not shown)

indicate that cross-checking effectively reduces the duration of the policy bias arising from

20

persistent output gap misperceptions. Of course, the simulations are still characterized by infla-

tionary or disinflationary trends lasting for shorter periods. These movements serve to signal a

trend shift and trigger the interest rate adjustment due to cross-checking.

6 Three questions concerning cross-checking

In this section, the effectiveness of cross-checking is investigated in further detail. Three ques-

tions are considered, namely how to account for velocity shifts, how important is the nonlinear

nature of cross-checking and what alternative estimates oftrend inflation may be considered.

6.1 How would you account for velocity shifts in monetary cross-checking?

It is well-known that a strategy of strict monetary targeting would transmit variations in the

velocity of money to output and inflation fluctuations. For example, the money-demand equa-

tion (16) implies that short-run changes in money demand arise from three sources: shocks,st ,

changes in interest rates,γi∆it and changes in real income,γy∆yt . While such fluctuations render

a strict monetary targeting strategy undesirable, they do not inhibit monetary cross-checking as

shown in the preceding section. A more interesting questionconcerns the performance of mon-

etary cross-checking in the event of sustained changes in trend velocity, for example due to

financial innovations. Two interesting examples regardingU.S. money demand have been doc-

umented by Orphanides and Porter (2000, 2001) , and Reynard (2004).29 Orphanides and Porter

point out that M2 velocity increased substantially in the mid 1990s. They report a sustained in-

tercept shift in their estimated velocity equation occurring over a period of several years. They

also show that this shift was identified in real time by recursive estimation techniques allowing

for intercept shifts. Such a shifting intercept may be included in the money demand equation:

mt − pt = γ0,t + γyyt − γi it +st . (34)

29Reynard (2004) notes an apparent increase in the interest-rate elasticity of money demand, i.e.γi , in the early1970s from the perspective of time-series analysis. He emphasizes the usefulness of cross-sectional analysis forobtaining improved estimates of the true structural parameters of money demand.

21

We use the NK model to simulate a fairly dramatic shift in the intercept,γ0,t , that generates

a velocity trend of 2 percentage points for 75 periods.30 As the intercept increases, velocity de-

clines and equilibrium money growth rises to accommodate increased demand at a given level

of the interest rate. First, we assume that the central bank sticks to the original estimate of the

intercept, never re-estimates and never considers the possibility of a structural shift. The result-

ing simulation is reported in the top two panels of Figure 6. The observed, sustained increase in

money growth due to shifting velocity triggers a cross-check and thus a policy tightening. As a

result, inflation declines below target by 2 percentage for the duration of the downward trend in

velocity. Once velocity stabilizes, another cross-check brings inflation back to target.

Alternatively, we allow the central bank to recursively estimate money demand and consider

the possibility of structural shifts.31 The resulting simulation is reported in the lower two panels

of Figure 6. We find that recursive estimation can detect the velocity shift considered and ensure

the usefulness of monetary cross-checking. This finding underscores the importance of money

demand analysis at the central bank.

6.2 Why does the cross-check take a nonlinear form rather than a linear

feedback coefficient?

Cross-checking takes the form of an occasional adjustment of the model-dependent optimal

interest policies derived from the first-order condition (4). This adjustment is triggered in period

k when the test-statistic,κ, defined by equation (29), has exceeded the critical valueκcrit for N

successive periods.32 A seemingly simpler alternative would be to augment the linear interest-

rate equations with an additional linear feedback on filtered money growth,µft , that applies at

30Again, this is an a-priori assumption regarding the structural process determining an unobservable variable.In future work, we aim to collect real time estimates of moneydemand and velocity trends to be able to analyzevelocity trends in the same manner as output gap estimates insections 3 and 5.

31Orphanides and Porter (2001) propose regression tree methods as a new approach to identify such shifts inreal time. Here, we consider a more traditional tool of moneydemand analysis in form of recursive least squareswith time-varying parameters or recursive least-squares with forgetting (see Harvey (1990), Chapter 4).

32Similarly, N successive negative realizations ofκ smaller than the negative ofκcrit trigger a symmetric down-ward adjustment. Note, the counter forN is reset to zero after every significant cross-check. The first-ordercondition, equation (30) based onµf

k then applies till the next adjustment is triggered.

22

all times. Including such a linear feedback in the K-Model implies:

it = (1+(ϕλ)−1)πt−1+(ϕ)−1(yt−1−zet|t)+(ϕλ)−1µf

t−1 (35)

Here, the time subscript onµft−1 refers to the most recent observation prior to the policy decision

from periodt −1, rather than from periodk, that was the most recent period with a significant

cross-check.

We compare the rule with linear feedback to the optimal interest rate policy conditional on

the gap estimate, equation (14), and the policy with cross-checking, equation (31). Since central

bank loss is measured by squared deviations of inflation froma zero inflation target we evaluate

policies by the simulation outcomes forE(π2). Table 2 reports the average central bank loss

over 1000 simulations under three different scenarios: no output gap misperceptions,et = 0,

U.S. output gap misperceptions,eUSt , and German output gap misperceptions,eDE

t .

By default, the model-dependent optimal policy (equation (14)) is the best performing pol-

icy when implemented under the assumption that the central bank’s estimate of the output gap

is correct. However, the policy with cross-checking performs just as well in that scenario. Its

nonlinearity ensures that in times when the central bank’s preferred Keynesian-style model and

associated output gap estimates deliver reliable inflationforecasts, the model-dependent opti-

mal policy is implemented. Thus, as long as the central bank’s beliefs regarding the appropriate

macroeconomic model, the implied concept of potential output, and the appropriate estimation

method do not imply sustained misperceptions, monetary cross-checking will not trigger pol-

icy adjustments. Policy is only adjusted according to the first-order condition (30) when the

simple monetary model of trend inflation, equation (27), strongly signals a trend shift. The

policy with linear feedback, however, always responds to variations in trend money growth, and

consequently causes more than twice the mean-squared errorof inflation.

In the case of U.S. output gap misperceptions, the policy without cross-checking generates

a mean squared error of inflation of 5.39. The rule with linear feedback to trend money growth

responds more aggressively and improves inflation performance in terms of a mean squared

23

error of 3.36. In this horse race, however, the policy with cross-checking again performs best

by generating a lower mean-squared error of 2.07. A similar ranking, but with smaller abso-

lute values, is obtained with German output gap misperceptions. Thus, the nonlinear policy

response implied by the occasional adjustments triggered via cross-checking promises to be a

useful approach when the central bank is uncertain about theappropriate model of the economy

and would like to revert to a simple fall-back option when outcomes persistently deviate from

model-based forecasts.

6.3 Why cross-check with money instead of other variables?

So far, the focus of the analysis has been on the two points raised by Lucas (2007), namely,

to provide an explanation of the joint trends in money growthand inflation observed empiri-

cally, and to develop a formal approach for cross-checking Keynesian-style interest rate policies

against information from monetary aggregates. However, there are other variables that may be

used as trend inflation estimates in cross-checking. Since central bank policy is considered to

be the source of sustained money and inflation trends, it is important to use variables that are

affected by policy even in the long run, that is nominal variables. Two candidates, in addition

to filtered money-growth, are long-run nominal interest rates and filtered measures of inflation

itself.

Nominal interest rates are difficult to read with regard to implications for trend inflation

because of the interaction of the short-run negative liquidity effect and the long-run positive

Fisher effect. As to filtered inflation,π ft , our analysis in section 5 suggests that it should per-

form at least as well as filtered money growth, because our modeling assumptions imply that

money growth and inflation move contemporaneously and that money growth is more noisy

than inflation. Table 3 confirms this conjecture with simulations of German and US output gap

misperceptions. In the K-Model, cross-checking with filtered inflation performs about as well

as with filtered money growth. In the NK-Model it performs slightly better.

However, the timing assumptions in the K- and NK-Model that are behind this result are at

odds with the recent empirical literature, which finds that money growth leads inflation at low

24

frequencies by several quarters.33 If the timing assumptions were to be modified to replicate

this leading indicator role of money at low frequencies, filtered money growth would gain a

competitive advantage over filtered inflation as a forecast of trend inflation.

We also note two other reasons that would motivate a preference for cross-checking against

long-run money growth measures. First, the Keynesian-style models we use preclude direct

effects of money and credit beyond those captured by the interest rate on output and inflation. If

these modeling assumptions fail to hold then cross-checking with filtered money growth would

be preferable to filtered inflation. The second reason is concerned with the use of models in the

political decision-making process at the central bank. A central bank staff that relies exclusively

on a Keynesian-style model and the associated output gap estimates interprets the sustained

increase in inflation induced by output gap misperceptions as a consequence of unfavorable

shocks. From this perspective, the staff will recommend against an additional policy response

to past filtered measures of inflation, because it would implyforecasting a deflation. Policy

makers may therefore find it preferable to request policy recommendations derived from a set of

competing models and may want to give special attention to monetary models of trend inflation.

7 Conclusions

In Keynesian-style models sustained trends in money growthand inflation can be explained by

successive policy mistakes due to central bank misperceptions. Using historical measures of

output gap misperceptions for the U.S. and German economiesfrom the 1970s to the 1990s we

have provided a unified treatment of money growth and inflation trends along with short-run

deviations in Keynesian models as requested by Lucas (2007). This result is obtained without

relying on undocumented shifts in central bank inflation targets.

Central bankers today, might argue that they would not make such mistakes in estimating

potential output since they employ sophisticated filteringtechniques. However, this optimism

may be unfounded. Orphanides and van Norden (2002) have shown that a variety of modern

33See Gerlach (2004), Benati (2005), Pill and Rautananen (2006) and Assenmacher-Wesche and Gerlach(2007).

25

filtering techniques lead to persistent output revisions similar to the Federal Reserve’s historical

estimates when applied to real-time data on U.S. output and inflation without a-priori assump-

tions. Also, central banks in the 1970s already had very sophisticated techniques at their dis-

posal. Federal Reserve researchers in the 1970s knew how to use the Kalman filter and solve

complex models (cf. Kalchbrenner and Tinsley (1977)) and economists at the Bundesbank used

fairly sophisticated production functions to calculate potential output (see the monthly reports

in October 1973 and October 1981).

Furthermore, we have provided a formal implementation of Lucas’s proposal to use mone-

tary information as an add-on or cross-check to the model-based interest rate policy. An earlier

note, Beck and Wieland (2007), posited an interest rate rulewith monetary cross-checking. In

this paper, a more general definition of cross-checking has been provided by deriving such

interest rate policies from a central bank objective function and first-order condition that incor-

porate trend inflation. A further innovation has been to analyze central bank misperceptions and

cross-checking in the New-Keynesian model. Following Orphanides (2003) alternative policy

strategies under output gap uncertainty have been evaluated without a-priori assumptions re-

garding the structure of the process driving potential output by using instead historical real-time

and final estimates of the output gap. Monetary cross-checking has been shown to substantially

improve inflation performance relative to the policy that would be optimal conditional on the

Keynesian model and the a-priori assumptions on potential output.

Finally, we have addressed three additional questions regarding cross-checking. Firstly,

monetary cross-checking is found to remain effective in thepresence of long-lasting velocity

shifts if standard recursive estimation techniques allowing for such shifts are used in money

demand analysis. Secondly, cross-checking has been compared with a policy that incorporates

linear feedback on filtered money growth. The linear feedback rule was shown to be dominated

by cross-checking whether persistent output gap misperceptions occur or not. Thirdly, filtered

inflation is found to constitute a good alternative to filtered money growth for cross-checking

as long as the timing assumptions of the benchmark Keynesian-style models hold up. If these

assumptions were modified such that money leads inflation as indicated by the recent empirical

26

literature, filtered money growth would gain an advantage over filtered inflation. We aim to

explore the role of timing assumptions and the optimal choice of estimate of trend inflation in

future research.

For practical central bank policy we recommend to use the gap-based Keynesian models

of inflation regularly for policy design, but consider the quantity-theory based model of trend

inflation as a fall-back option. We suggest to implement the quantity-theory based policy rec-

ommendation in circumstances when policies based on the Keynesian models have persistently

under-performed, i.e. when trend inflation is better captured by the monetary models. In fu-

ture research, we aim to collect historical money demand estimates for the United States and

Germany to study whether monetary cross-checking would have helped preventing double-digit

inflation in the United States in the 1970s and 1980s, and whether Germany escaped double-

digit inflation, because the Bundesbank gave more weight to monetary models of trend inflation.

27

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30

Table 1: Parameter Values

Parameter Value Economic interpretation

β 0.99 Discount factor of the policy maker.−ϕ -1 Real interest rate elasticity of aggregate demand (in

line with Andres et al. (2006) and Ireland (2004)).λ 0.5 Elasticity of Phillips curve w.r.t. output gap (broadly

in line with Gerlach (2004)).34

γy 0.1 Income elasticity of money demand (in line with An-dres et al. (2006) and Ireland (2004)).

−γi -0.4 Interest rate elasticity of money demand (in line withAndres et al. (2006) and Ireland (2004)).

ω 0.2 Weighting parameter of filter (broadly in line inGerlach (2004))

∆y, π,π⋆ 0 Equilibrium real interest rate, potential outputgrowth, steady-state inflation and inflation target

σg,σu,σs 0.8 Standard deviation of cost-push, demand and moneydemand shocks

σεg,σεu 0.4 Standard deviation of noise of aggregate demandand cost-push shocks

σεs 0.1 Standard deviation of money demand shocksκcrit 1.96 5% critical value for the cross-checking rule.N 4 Number of periods required for a sustained deviation

in the cross-checking rule.σµf Standard deviation ofµf is not exogenous but deter-

mined consistently with model and policy

Notes: Table 1 provides an overview of the parameter values that we have used in our model

simulations.

31

Table 2: Linear Feedback vs Nonlinear Cross-Checking

Policy Central bank loss(K-Model)

et = 0 eUSt eDE

t

No cross-checking 0.79 5.39 2.67Cross-checking withµf

t 0.79 2.07 1.79Linear feedback withµf

t 1.73 3.36 2.60

Notes: Central bank loss corresponds to the mean squared deviations,E[(π)2],

and is measured by averages over 1000 simulations of 150 periods length as in

Figure 3. eUSt refers to U.S. output gap misperceptions andeDE

t to German

output gap misperceptions.

32

Table 3: Filtered Money Growth vs Filtered Inflation

Policy Central bank lossK-Model NK-Model

eUSt eDE

t eUSt eDE

t

No cross-checking 5.39 2.67 5.10 2.32Cross-checkingµf

t 2.07 1.79 1.85 1.57Cross-checkingπ f

t 2.06 1.75 1.72 1.50

Notes: Central bank loss corresponds to the mean squared deviations,E[(π)2], and is

measured by averages over 1000 simulations of 150 periods length.eUSt refers to U.S.

output gap misperceptions andeDEt to German output gap misperceptions.

33

Figure 1: Output Gap Misperceptions in the United States andGermany

1965 1970 1975 1980 1985 1990 1995 2000−2

0

2

4

6

8

10

12

Time

e(t)

USGerman

Note: Figure 1 plots historical U.S. and German output gap misperceptions. The data for the U.S.output gap misperceptions were provided by Orphanides (2003), the German output gap misperceptiondata were provided by Gerberding et al. (2005).

34

Figure 2: Money Growth and Inflation Trends in the K-Model

U.S. Output Gap Misperceptions

50 100 150

−2

0

2

4

6

π

50 100 150

−2

0

2

4

6

µf

German Output Gap Misperceptions

50 100 150

−2

0

2

4

6

π

Time

50 100 150

−2

0

2

4

6

µf

Time

Notes:Figure 2 reports simulations with U.S. and German output gapmisperceptions in the K-modelfor a given draw of exogenous shocks and noise terms. The upper two panels show the inflation rate,π,and the filtered measure of adjusted money growth,µf , with U.S. output gap misperceptions, the lowertwo panels show the corresponding series with German outputgap misperceptions.

35

Figure 3: Money Growth and Inflation Trends - Averages of 1000Draws of Shocks

50 100 150

−2

0

2

4

6

π (US,K)

50 100 150

−2

0

2

4

6

µf (US,K)

50 100 150

−2

0

2

4

6

π (US,NK)

50 100 150

−2

0

2

4

6

µf (US,NK)

50 100 150

−2

0

2

4

6

π (DE,K)

Time

50 100 150

−2

0

2

4

6

µf (DE,K)

Time

50 100 150

−2

0

2

4

6

π (DE,NK)

Time

50 100 150

−2

0

2

4

6

µf (DE,NK)

Time

Notes:Figure 3 reports averages of 1000 simulations with U.S. and German (DE) output gap misper-ceptions in the K- and NK-model. For each of the four possiblecombinations two panels are shown thatreport the cross-simulation averages of the inflation rate,π, and the filtered adjusted money growth rate,µf .

36

Figure 4: Monetary Cross-Checking in the K-Model

U.S. Output Gap Misperceptions

50 100 150

−2

0

2

4

6

π

50 100 150

−2

0

2

4

6

µf

50 100 150−2

0

2

4

6

8

10

12

iCC,e

iCC

e

German Output Gap Misperceptions

50 100 150

−2

0

2

4

6

π

Time

50 100 150

−2

0

2

4

6

µf

50 100 150−2

0

2

4

6

8

10

12

iCC,e

Time

iCC

e

Notes: Figure 4 reports simulations of monetary cross-checking inthe K-model for U.S. (upper threepanels) and German (lower three panels) output gap misperceptions. In each case the inflation rate,π, thefiltered measure of adjusted money growth,µf , the output gap perception error,e, and the cross-checkingadjustment,iCC, are plotted.

37

Figure 5: Monetary Cross-Checking in the NK-Model

U.S. Output Gap Misperceptions

50 100 150−4

−2

0

2

4

6

π

50 100 150−4

−2

0

2

4

6

µf

50 100 150−2

0

2

4

6

8

10

12

iCC,e

iCC

e

German Output Gap Misperceptions

50 100 150−4

−2

0

2

4

6

π

Time

50 100 150−4

−2

0

2

4

6

µf

Time

50 100 150−2

0

2

4

6

8

10

12

iCC,e

Time

iCC

e

Notes:Figure 5 reports simulations of monetary cross-checking inthe NK-model for U.S. (upper threepanels) and German (lower three panels) output gap misperceptions. In each case the inflation rate,π, thefiltered measure of adjusted money growth,µf , the output gap perception error,e, and the cross-checkingadjustment,iCC, are plotted.

38

Figure 6: Monetary Cross-Checking and Velocity Shifts in the NK-Model

Central Bank Never Considers the Possibility of Shifts

50 100 150

−2

0

2

4

6

π

50 100 150

−2

0

2

4

6

µf

Central Bank Uses Recursive Least Squares with Possibilityof Shifts

50 100 150

−2

0

2

4

6

π

Time

50 100 150

−2

0

2

4

6

µf

Time

Notes:Figure 6 reports simulations with U.S. and German output gapmisperceptions in the NK-modelfor a given draw of exogenous shocks and noise terms when changes in trend velocity occur. The upperthree panels show the inflation rate,π, and the filtered measure of adjusted money growth,µf , for the casethat the central bank sticks to the original estimate of the intercept,γ0, in the money demand equation andnever considers the possibility of a structural shift. The lower three panels plot the same series for thecase that the central bank recursively estimates money demand and considers the possibility of structuralshifts.

39

A Model Equations

Table A1: Model Equations

Description Model Equation

Common equations

Central bank objective −12Et

{

∞∑

i=0βi

[

(πt+i −π∗)2]

}

, π∗ = 0

Perceived potential zet|t = zt +et

Money demand mt − pt = γyyt − γi it +vt , vt ∼ i.i.d. N(0,σv)

K-ModelPhillips curve πt = πt−1+λ(yt −zt)+ut , ut ∼ i.i.d. N(0,σu)IS Curve yt = yt−1−ϕ(it −πt−1)+gt , gt ∼ i.i.d. N(0,σg)

NK-ModelPhillips curve πt − π = β(πe

t+1− π)+λ(yt −zt)+ut,ut ∼ i.i.d. N(0,σu) , π = π∗ = 0

IS Curve yt = yet+1−ϕ

(

it −πet+1

)

+gt , gt ∼ i.i.d. N(0,σg)

Demand signal/noise gt = get + εg

t , εgt ∼ i.i.d. N

(

0,σεg

)

Cost-push signal/noise ut = uet + εu

t , εut ∼ i.i.d. N(0,σεu)

Money-demand vt = vet + εv

t , εvt ∼ i.i.d. N(0,σεv)

signal/noise

Notes:

Table A provides an overview of the equations, parameters and assumptions regarding the traditional Keynesian

and New-Keynesian models used in “Central Bank Misperceptions and the Role of Money in Interest Rates Rules”.

40

B Cross-checking in the NK-Model: Detailed derivations

In the following two subsections a detailed derivation of the optimal monetary policy under

uncertainty in the NK-model without and with cross-checking is provided.

B.1. Optimal policy under uncertainty without cross-checking

We start by deriving the optimal policy under uncertainty given symmetric information be-

tween the central bank and market participants. Thus, the central bank and market participants

share the same information regarding central bank objectives, potential output estimates and

expectations regarding future inflation and output. In principle, the derivation is for the case of

optimal policy under discretion, but given a strictly inflation targeting central bank it turns out

that the policies under discretion and commitment are identical.

The policy maker’s objective under strict inflation targeting is to maximize the following

loss function

max−12

Et

{

∞

∑i=0

βi [(πt+i −π∗)2]}

(36)

subject to the Phillips curve and the IS curve (see Table A1).The inflation target is normalized

at zero,π∗ = 0. The associated first-order condition is

E[πt+i| t] = π∗ = 0 ∀i = {0,1,2, ..,∞} (37)

whereπt+i depends on the output gap,yt+i − zt+i , according to the New-Keynesian Phillips

curve. It follows that the central bank and market participants expect future inflation to be equal

to the zero inflation target:

πet+1|t = 0 (38)

Furthermore, since we have assumed that the cost-push shocks ut are serially uncorrelated, the

expected future output gap is also equal to zero, consistentwith the expected future inflation

rate:

xet+1|t = 0⇐⇒ ye

t+1|t = zet+1|t . (39)

Solving the Phillips curve foryt and applyingπet+1|t = 0 yields the level of output compatible

with the expected inflation rate for periodt:

yet|t = ze

t|t −1λ

uet|t . (40)

41

Using the IS curve, which corresponds to the log-linear version of the household Euler equation,

yt = yet+1−ϕ

(

it −πet+1

)

+gt (41)

we can determine the optimal interestit as

it = πet+1|t −

1ϕ

yet|t +

1ϕ

yet+1|t +

1ϕ

get|t (42)

=1

λϕue

t,t +1ϕ

(

zet+1|t −ze

t|t +get|t

)

.

In the derivation ofit we have made use of the above-mentioned expressions foryet|t , ye

t+1|t and

πet+1|t.

B.2 Optimal policy with cross-checking using µfk as estimate of trend inflation

The policy with cross-checking may be characterized by a first-order condition that includes

trend inflation:

E[πt|zet|t ] = −E[π|µf

k ] (43)

This condition guarantees that the central bank acts to offset any significant shift in trend infla-

tion as estimated on the basis of monetary information.µfk denotes the most recent significant

estimate of a trend shift. Thus, in periodk the test statisticκ defined by

κt =µf

t −π∗

σµf, (44)

satisfies the condition(κk > κcrit , ..,κk−N > κcrit ) or (−κk < −κcrit , ..,−κk−N < −κcrit ).

To determine the interest rate setting induced by a significant cross-check in the NK model

it is important to consider the effect of cross-checking on market participants’ expectations of

future inflation. First, we note that conditional on the NK model and the associated estimate of

potential output neither the central bank nor market participants expect cross-checking to kick

in. Recall, that the probability that the test statisticκ exceeds the critical value is negligible,

and even more so the probability that it exceedsκcrit for N periods. Thus, in the absence of a

significant cross-check the expectations for inflation in period t under the null hypothesis of the

New-Keynesian model and the potential output estimatezet|t are

πet|t = 0 (45)

Once a significant cross-check occurs, the first-order condition with the monetary estimate of

42

trend inflation governs policy. As a consequence:

πet|t = −µf

k (46)

Thus, under symmetric information the central bank and market participants will expect current

inflation–conditional on the New-Keynesian model and potential output estimate–to fall below

the target by the extent of the trend inflation estimate provided by filtered money growth.

To solve the New-Keynesian Phillips curve for the expected output level that the central

bank should aim at according to the policy with cross-checking, it is necessary to characterize

market participants’ expectation of inflation in periodt +1. In the baseline case it is assumed

that market participants expect future inflation to return to the zero inflation target of the central

bank, i.e. πet+1|t = 0. This assumption is standard for the optimal policy under discretion.

It implies that the central bank cannot manipulate market participants’ inflation expectations

by promising to commit to delivering future inflation outcomes different from the objective

function with its long-run target.

Next, the Phillips curve is solved for the level of output that the central bank expects to

achieve in periodt, yet|t . Usingπe

t+1|t = 0 andπet|t = −µk

f one obtains

yet|t = ze

t|t +1λ

πet|t −

βλ

πet+1|t −

1λ

uet|t ⇐⇒ (47)

yet|t = ze

t|t −1λ

uet|t −

1λ

µkf .

In the next step, the IS curve is solved for the interest rateit that achieves the expected optimal

level of output, that is, the level of output consistent withthe central bank’s first-order condition.

To this end, it is necessary to characterize market participants’ expectation of output in period

t + 1. Consistent with the expectation that inflation will be equal to the target in periodt + 1,

market participants expect output to be equal to potential output in periodt +1:

yet+1|t = ze

t+1|t . (48)

Solving the IS equation forit given the expressions foryet|t , ye

t+1|t andπet+1|t yields the interest

rate policy with cross-checking:

it = 0−1ϕ

[

zet|t −

1λ

uet|t −

1λ

µkf

]

+1ϕ

zet+1|t +

1ϕ

get|t (49)

=1

λϕue

t|t +1ϕ

(

zet+1|t −ze

t|t +get|t

)

+1

λϕµk

f .

For the sake of completeness, we have also investigated the policy with cross-checking

43

under the assumption that the central bank is able to credibly commit to maintaining the disin-

flationary stance implied by the policy with cross-checkingfor a finite number of periods,T,

in the future. In this case, the central bank is able to influence future inflation expectations s.t.

πT|t = πT−1|t = .. = πt|t = −µfk . Thus, future inflation expectations move in a way that will

help offsetting the apparent increase in trend inflation. The implied expected path of output and

interest rates can be solved for recursively by starting in period T + 2 and solving backwards

for expected inflation, output and interest rates. The interest rate level expected for periodT

coincides with the expectation of equation (49):

iT|t =1ϕ

(

zeT+1|t −ze

T|t

)

+1

λϕµk

f . (50)

The interest rate level set in periodt, however, incorporates the response of market participants

expectation of future inflation to the central bank’s announcement of the policy with cross-

checking:

it =1

λϕue

t|t +1ϕ

(zet+1|t −ze

t|t +get|t)−µf

k . (51)

We have simulated this policy under historical U.S. and German output gap misperceptions in

the New-Keynesian model. The simulation results are similar to the baseline case discussed

in the paper concerning the success of cross-checking in offsetting the inflationary bias due to

persistent central bank misperceptions. Of course, due to the response of inflation expectations

to the announcement of cross-checking, the particular interest rate path followed by the central

bank differs from the baseline case.

44

NBB WORKING PAPER No. 147 - OCTOBER 2008 45

NATIONAL BANK OF BELGIUM - WORKING PAPERS SERIES

1. "Model-based inflation forecasts and monetary policy rules" by M. Dombrecht and R. Wouters, ResearchSeries, February 2000.

2. "The use of robust estimators as measures of core inflation" by L. Aucremanne, Research Series,February 2000.

3. "Performances économiques des Etats-Unis dans les années nonante" by A. Nyssens, P. Butzen,P. Bisciari, Document Series, March 2000.

4. "A model with explicit expectations for Belgium" by P. Jeanfils, Research Series, March 2000.5. "Growth in an open economy: some recent developments" by S. Turnovsky, Research Series, May 2000.6. "Knowledge, technology and economic growth: an OECD perspective" by I. Visco, A. Bassanini,

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Research Series, May 2000.10. "Monetary union and economic growth" by J. Vickers, Research Series, May 2000.11. "Politique monétaire et prix des actifs: le cas des Etats-Unis" by Q. Wibaut, Document Series, August

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Documents Series, November 2001.18. "The interest rate and credit channels in Belgium: an investigation with micro-level firm data" by

P. Butzen, C. Fuss and Ph. Vermeulen, Research series, December 2001.19. "Openness, imperfect exchange rate pass-through and monetary policy" by F. Smets and R. Wouters,

Research series, March 2002.20. "Inflation, relative prices and nominal rigidities" by L. Aucremanne, G. Brys, M. Hubert, P. J. Rousseeuw

and A. Struyf, Research series, April 2002.21. "Lifting the burden: fundamental tax reform and economic growth" by D. Jorgenson, Research series,

May 2002.22. "What do we know about investment under uncertainty?" by L. Trigeorgis, Research series, May 2002.23. "Investment, uncertainty and irreversibility: evidence from Belgian accounting data" by D. Cassimon,

P.-J. Engelen, H. Meersman, M. Van Wouwe, Research series, May 2002.24. "The impact of uncertainty on investment plans" by P. Butzen, C. Fuss, Ph. Vermeulen, Research series,

May 2002.25. "Investment, protection, ownership, and the cost of capital" by Ch. P. Himmelberg, R. G. Hubbard,

I. Love, Research series, May 2002.26. "Finance, uncertainty and investment: assessing the gains and losses of a generalised non-linear

structural approach using Belgian panel data", by M. Gérard, F. Verschueren, Research series,May 2002.

27. "Capital structure, firm liquidity and growth" by R. Anderson, Research series, May 2002.28. "Structural modelling of investment and financial constraints: where do we stand?" by J.- B. Chatelain,

Research series, May 2002.29. "Financing and investment interdependencies in unquoted Belgian companies: the role of venture

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NBB WORKING PAPER No. 147 - OCTOBER 200846

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33. "Investment, R&D and liquidity constraints: a corporate governance approach to the Belgian evidence"by P. Van Cayseele, Research series, May 2002.

34. "On the Origins of the Franco-German EMU Controversies" by I. Maes, Research series, July 2002.35. "An estimated dynamic stochastic general equilibrium model of the Euro Area", by F. Smets and

R. Wouters, Research series, October 2002.36. "The labour market and fiscal impact of labour tax reductions: The case of reduction of employers' social

security contributions under a wage norm regime with automatic price indexing of wages", byK. Burggraeve and Ph. Du Caju, Research series, March 2003.

37. "Scope of asymmetries in the Euro Area", by S. Ide and Ph. Moës, Document series, March 2003.38. "De autonijverheid in België: Het belang van het toeleveringsnetwerk rond de assemblage van

personenauto's", by F. Coppens and G. van Gastel, Document series, June 2003.39. "La consommation privée en Belgique", by B. Eugène, Ph. Jeanfils and B. Robert, Document series,

June 2003.40. "The process of European monetary integration: a comparison of the Belgian and Italian approaches", by

I. Maes and L. Quaglia, Research series, August 2003.41. "Stock market valuation in the United States", by P. Bisciari, A. Durré and A. Nyssens, Document series,

November 2003.42. "Modeling the Term Structure of Interest Rates: Where Do We Stand?, by K. Maes, Research series,

February 2004.43. "Interbank Exposures: An Empirical Examination of System Risk in the Belgian Banking System", by

H. Degryse and G. Nguyen, Research series, March 2004.44. "How Frequently do Prices change? Evidence Based on the Micro Data Underlying the Belgian CPI", by

L. Aucremanne and E. Dhyne, Research series, April 2004.45. "Firms' investment decisions in response to demand and price uncertainty", by C. Fuss and

Ph. Vermeulen, Research series, April 2004.46. "SMEs and Bank Lending Relationships: the Impact of Mergers", by H. Degryse, N. Masschelein and

J. Mitchell, Research series, May 2004.47. "The Determinants of Pass-Through of Market Conditions to Bank Retail Interest Rates in Belgium", by

F. De Graeve, O. De Jonghe and R. Vander Vennet, Research series, May 2004.48. "Sectoral vs. country diversification benefits and downside risk", by M. Emiris, Research series,

May 2004.49. "How does liquidity react to stress periods in a limit order market?", by H. Beltran, A. Durré and P. Giot,

Research series, May 2004.50. "Financial consolidation and liquidity: prudential regulation and/or competition policy?", by

P. Van Cayseele, Research series, May 2004.51. "Basel II and Operational Risk: Implications for risk measurement and management in the financial

sector", by A. Chapelle, Y. Crama, G. Hübner and J.-P. Peters, Research series, May 2004.52. "The Efficiency and Stability of Banks and Markets", by F. Allen, Research series, May 2004.53. "Does Financial Liberalization Spur Growth?" by G. Bekaert, C.R. Harvey and C. Lundblad, Research

series, May 2004.54. "Regulating Financial Conglomerates", by X. Freixas, G. Lóránth, A.D. Morrison and H.S. Shin, Research

series, May 2004.55. "Liquidity and Financial Market Stability", by M. O'Hara, Research series, May 2004.56. "Economisch belang van de Vlaamse zeehavens: verslag 2002", by F. Lagneaux, Document series,

June 2004.57. "Determinants of Euro Term Structure of Credit Spreads", by A. Van Landschoot, Research series,

July 2004.58. "Macroeconomic and Monetary Policy-Making at the European Commission, from the Rome Treaties to

the Hague Summit", by I. Maes, Research series, July 2004.59. "Liberalisation of Network Industries: Is Electricity an Exception to the Rule?", by F. Coppens and

D. Vivet, Document series, September 2004.60. "Forecasting with a Bayesian DSGE model: an application to the euro area", by F. Smets and

R. Wouters, Research series, September 2004.61. "Comparing shocks and frictions in US and Euro Area Business Cycle: a Bayesian DSGE approach", by

F. Smets and R. Wouters, Research series, October 2004.

NBB WORKING PAPER No. 147 - OCTOBER 2008 47

62. "Voting on Pensions: A Survey", by G. de Walque, Research series, October 2004.63. "Asymmetric Growth and Inflation Developments in the Acceding Countries: A New Assessment", by

S. Ide and P. Moës, Research series, October 2004.64. "Importance économique du Port Autonome de Liège: rapport 2002", by F. Lagneaux, Document series,

November 2004.65. "Price-setting behaviour in Belgium: what can be learned from an ad hoc survey", by L. Aucremanne and

M. Druant, Research series, March 2005.66. "Time-dependent versus State-dependent Pricing: A Panel Data Approach to the Determinants of

Belgian Consumer Price Changes", by L. Aucremanne and E. Dhyne, Research series, April 2005.67. "Indirect effects – A formal definition and degrees of dependency as an alternative to technical

coefficients", by F. Coppens, Research series, May 2005.68. "Noname – A new quarterly model for Belgium", by Ph. Jeanfils and K. Burggraeve, Research series,

May 2005.69. "Economic importance of the Flemish maritime ports: report 2003", F. Lagneaux, Document series, May

2005.70. "Measuring inflation persistence: a structural time series approach", M. Dossche and G. Everaert,

Research series, June 2005.71. "Financial intermediation theory and implications for the sources of value in structured finance markets",

J. Mitchell, Document series, July 2005.72. "Liquidity risk in securities settlement", J. Devriese and J. Mitchell, Research series, July 2005.73. "An international analysis of earnings, stock prices and bond yields", A. Durré and P. Giot, Research

series, September 2005.74. "Price setting in the euro area: Some stylized facts from Individual Consumer Price Data", E. Dhyne,

L. J. Álvarez, H. Le Bihan, G. Veronese, D. Dias, J. Hoffmann, N. Jonker, P. Lünnemann, F. Rumler andJ. Vilmunen, Research series, September 2005.

75. "Importance économique du Port Autonome de Liège: rapport 2003", by F. Lagneaux, Document series,October 2005.

76. "The pricing behaviour of firms in the euro area: new survey evidence, by S. Fabiani, M. Druant,I. Hernando, C. Kwapil, B. Landau, C. Loupias, F. Martins, T. Mathä, R. Sabbatini, H. Stahl andA. Stokman, Research series, November 2005.

77. "Income uncertainty and aggregate consumption, by L. Pozzi, Research series, November 2005.78. "Crédits aux particuliers - Analyse des données de la Centrale des Crédits aux Particuliers", by

H. De Doncker, Document series, January 2006.79. "Is there a difference between solicited and unsolicited bank ratings and, if so, why?" by P. Van Roy,

Research series, February 2006.80. "A generalised dynamic factor model for the Belgian economy - Useful business cycle indicators and

GDP growth forecasts", by Ch. Van Nieuwenhuyze, Research series, February 2006.81. "Réduction linéaire de cotisations patronales à la sécurité sociale et financement alternatif" by

Ph. Jeanfils, L. Van Meensel, Ph. Du Caju, Y. Saks, K. Buysse and K. Van Cauter, Document series,March 2006.

82. "The patterns and determinants of price setting in the Belgian industry" by D. Cornille and M. Dossche,Research series, May 2006.

83. "A multi-factor model for the valuation and risk management of demand deposits" by H. Dewachter,M. Lyrio and K. Maes, Research series, May 2006.

84. "The single European electricity market: A long road to convergence", by F. Coppens and D. Vivet,Document series, May 2006.

85. "Firm-specific production factors in a DSGE model with Taylor price setting", by G. de Walque, F. Smetsand R. Wouters, Research series, June 2006.

86. "Economic importance of the Belgian ports: Flemish maritime ports and Liège port complex - report2004", by F. Lagneaux, Document series, June 2006.

87. "The response of firms' investment and financing to adverse cash flow shocks: the role of bankrelationships", by C. Fuss and Ph. Vermeulen, Research series, July 2006.

88. "The term structure of interest rates in a DSGE model", by M. Emiris, Research series, July 2006.89. "The production function approach to the Belgian output gap, Estimation of a Multivariate Structural Time

Series Model", by Ph. Moës, Research series, September 2006.90. "Industry Wage Differentials, Unobserved Ability, and Rent-Sharing: Evidence from Matched Worker-

Firm Data, 1995-2002", by R. Plasman, F. Rycx and I. Tojerow, Research series, October 2006.

NBB WORKING PAPER No. 147 - OCTOBER 200848

91. "The dynamics of trade and competition", by N. Chen, J. Imbs and A. Scott, Research series, October2006.

92. "A New Keynesian Model with Unemployment", by O. Blanchard and J. Gali, Research series, October2006.

93. "Price and Wage Setting in an Integrating Europe: Firm Level Evidence", by F. Abraham, J. Konings andS. Vanormelingen, Research series, October 2006.

94. "Simulation, estimation and welfare implications of monetary policies in a 3-country NOEM model", byJ. Plasmans, T. Michalak and J. Fornero, Research series, October 2006.

95. "Inflation persistence and price-setting behaviour in the euro area: a summary of the Inflation PersistenceNetwork evidence ", by F. Altissimo, M. Ehrmann and F. Smets, Research series, October 2006.

96. "How Wages Change: Micro Evidence from the International Wage Flexibility Project", by W.T. Dickens,L. Goette, E.L. Groshen, S. Holden, J. Messina, M.E. Schweitzer, J. Turunen and M. Ward, Researchseries, October 2006.

97. "Nominal wage rigidities in a new Keynesian model with frictional unemployment", by V. Bodart,G. de Walque, O. Pierrard, H.R. Sneessens and R. Wouters, Research series, October 2006.

98. "Dynamics on monetary policy in a fair wage model of the business cycle", by D. De la Croix,G. de Walque and R. Wouters, Research series, October 2006.

99. "The kinked demand curve and price rigidity: evidence from scanner data", by M. Dossche, F. Heylenand D. Van den Poel, Research series, October 2006.

100. "Lumpy price adjustments: a microeconometric analysis", by E. Dhyne, C. Fuss, H. Peseran andP. Sevestre, Research series, October 2006.

101. "Reasons for wage rigidity in Germany", by W. Franz and F. Pfeiffer, Research series, October 2006.102. "Fiscal sustainability indicators and policy design in the face of ageing", by G. Langenus, Research

series, October 2006.103. "Macroeconomic fluctuations and firm entry: theory and evidence", by V. Lewis, Research series,

October 2006.104. "Exploring the CDS-Bond Basis" by J. De Wit, Research series, November 2006.105. "Sector Concentration in Loan Portfolios and Economic Capital", by K. Düllmann and N. Masschelein,

Research series, November 2006.106. "R&D in the Belgian Pharmaceutical Sector", by H. De Doncker, Document series, December 2006.107. "Importance et évolution des investissements directs en Belgique", by Ch. Piette, Document series,

January 2007.108. "Investment-Specific Technology Shocks and Labor Market Frictions", by R. De Bock, Research series,

February 2007.109. "Shocks and frictions in US Business cycles: a Bayesian DSGE Approach", by F. Smets and R. Wouters,

Research series, February 2007.110. "Economic impact of port activity: a disaggregate analysis. The case of Antwerp", by F. Coppens,

F. Lagneaux, H. Meersman, N. Sellekaerts, E. Van de Voorde, G. van Gastel, Th. Vanelslander,A. Verhetsel, Document series, February 2007.

111. "Price setting in the euro area: some stylised facts from individual producer price data", byPh. Vermeulen, D. Dias, M. Dossche, E. Gautier, I. Hernando, R. Sabbatini, H. Stahl, Research series,March 2007.

112. "Assessing the Gap between Observed and Perceived Inflation in the Euro Area: Is the Credibility of theHICP at Stake?", by L. Aucremanne, M. Collin, Th. Stragier, Research series, April 2007.

113. "The spread of Keynesian economics: a comparison of the Belgian and Italian experiences", by I. Maes,Research series, April 2007.

114. "Imports and Exports at the Level of the Firm: Evidence from Belgium", by M. Muûls and M. Pisu,Research series, May 2007.

115. "Economic importance of the Belgian ports: Flemish maritime ports and Liège port complex - report2005", by F. Lagneaux, Document series, May 2007.

116. "Temporal Distribution of Price Changes: Staggering in the Large and Synchronization in the Small", byE. Dhyne and J. Konieczny, Research series, June 2007.

117. "Can excess liquidity signal an asset price boom?", by A. Bruggeman, Research series, August 2007.118. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary

policy operations", by F. Coppens, F. González and G. Winkler, Research series, September 2007.119. "The determinants of stock and bond return comovements", by L. Baele, G. Bekaert and K. Inghelbrecht,

Research series, October 2007.

NBB WORKING PAPER No. 147 - OCTOBER 2008 49

120. "Monitoring pro-cyclicality under the capital requirements directive: preliminary concepts for developing aframework", by N. Masschelein, Document series, October 2007.

121. "Dynamic order submission strategies with competition between a dealer market and a crossingnetwork", by H. Degryse, M. Van Achter and G. Wuyts, Research series, November 2007.

122. "The gas chain: influence of its specificities on the liberalisation process", by C. Swartenbroekx,Document series, November 2007.

123. "Failure prediction models: performance, disagreements, and internal rating systems", by J. Mitchell andP. Van Roy, Research series, December 2007.

124. "Downward wage rigidity for different workers and firms: an evaluation for Belgium using the IWFPprocedure", by Ph. Du Caju, C. Fuss and L. Wintr, Research series, December 2007.

125. "Economic importance of Belgian transport logistics", by F. Lagneaux, Document series, January 2008.126. "Some evidence on late bidding in eBay auctions", by L. Wintr, Research series, January 2008.127. "How do firms adjust their wage bill in Belgium? A decomposition along the intensive and extensive

margins", by C. Fuss, Research series, January 2008.128. "Exports and productivity – comparable evidence for 14 countries", by The International Study Group on

Exports and Productivity, Research series, February 2008.129. "Estimation of monetary policy preferences in a forward-looking model: a Bayesian approach", by

P. Ilbas, Research series, March 2008.130. "Job creation, job destruction and firms' international trade involvement", by M. Pisu, Research series,

March 2008.131. "Do survey indicators let us see the business cycle? A frequency decomposition", by L. Dresse and

Ch. Van Nieuwenhuyze, Research series, March 2008.132. "Searching for additional sources of inflation persistence: the micro-price panel data approach", by

R. Raciborski, Research series, April 2008.133. "Short-term forecasting of GDP using large monthly datasets - A pseudo real-time forecast evaluation

exercise", by K. Barhoumi, S. Benk, R. Cristadoro, A. Den Reijer, A. Jakaitiene, P. Jelonek, A. Rua,G. Rünstler, K. Ruth and Ch. Van Nieuwenhuyze, Research series, June 2008.

134. "Economic importance of the Belgian ports: Flemish maritime ports, Liège port complex and the port ofBrussels - report 2006" by S. Vennix, Document series, June 2008.

135. "Imperfect exchange rate pass-through: the role of distribution services and variable demand elasticity",by Ph. Jeanfils, Research series, August 2008.

136. "Multivariate structural time series models with dual cycles: Implications for measurement of output gapand potential growth", by Ph. Moës, Research series, August 2008.

137. "Agency problems in structured finance - a case study of European CLOs", by J. Keller, Documentseries, August 2008.

138. "The efficiency frontier as a method for gauging the performance of public expenditure: a Belgian casestudy", by B. Eugène, Research series, September 2008.

139. "Exporters and credit constraints. A firm-level approach", by M. Muûls, Research series, September2008.

140. "Export destinations and learning-by-exporting: Evidence from Belgium", by M. Pisu, Research series,September 2008.

141. "Monetary aggregates and liquidity in a neo-Wicksellian framework", by M. Canzoneri, R. Cumby,B. Diba and D. López-Salido, Research series, October 2008.

142 "Liquidity, inflation and asset prices in a time-varying framework for the euro area, by Ch. Baumeister,E. Durinck and G. Peersman, Research series, October 2008.

143. "The bond premium in a DSGE model with long-run real and nominal risks", by Glenn D. Rudebusch andEric T. Swanson, Research series, October 2008.

144. "Imperfect information, macroeconomic dynamics and the yield curve: an encompassing macro-financemodel", by H. Dewachter, Research series, October 2008.

145. "Housing market spillovers: evidence from an estimated DSGE model", by M. Iacoviello and S. Neri,Research series, October 2008.

146. "Credit frictions and optimal monetary policy", by V. Cúrdia and M. Woodford, Research series,October 2008.

147. "Central bank misperceptions and the role of money in interest rate rules", by G. Beck and V. Wieland,Research series, October 2008.