noisy information, interest rate shocks and the great moderation

Journal of Macroeconomics 33 (2011) 568–581

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Journal of Macroeconomics

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Noisy information, interest rate shocks and the Great Moderation

Eric Mayer a,1, Johann Scharler b,⇑a University of Wuerzburg, Department of Economics, Sanderring 2, 97070 Wuerzburg, Germanyb University of Linz, Department of Economics, Altenbergerstrasse 69, A-4040 Linz, Austria

a r t i c l e i n f o

Article history:Received 29 September 2010Accepted 22 August 2011Available online 16 September 2011

JEL classification:E32E52E58

Keywords:Great ModerationNew Keynesian modelNoisy data

0164-0704/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.jmacro.2011.08.004

⇑ Corresponding author. Tel.: +43 732 2468 8360E-mail addresses: [email protected]

1 Tel.: +49 931 318 2948; fax: +49 931 8 7275.2 See Giannone et al. (2008) and the references th

a b s t r a c t

In this paper we evaluate the hypothesis that the Great Moderation is partly the result of aless activist monetary policy. We simulate a New Keynesian model in which the centralbank can only observe a noisy estimate of the output gap and find that the less pronouncedreaction of the Federal Reserve to output gap fluctuations since 1979 can account for a sub-stantial part of the reduction in the standard deviation of GDP associated with the GreatModeration. Our simulations are consistent with the empirically documented smaller mag-nitude and impact of interest rate shocks since the early 1980s.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

Since the mid-1980s, the magnitude of fluctuations in economic activity has substantially declined in the US. McConnelland Perez-Quiros (2000) and Blanchard and Simon (2001) were among the first to document this so-called Great Moderation(see also Stock and Watson, 2002; Kim et al., 2004). Although there is little doubt that the business cycle has indeed becomesmoother over time, the sources of the Great Moderation are less clear. Various explanations have been proposed in the lit-erature, including a decline in the volatility of shocks (e.g. Ahmed et al., 2004; Stock and Watson, 2005) and changes in thestructure of the economy (e.g. Blanchard and Simon, 2001; Dynan et al., 2006; Davis and Kahn, 2008).

Other authors claim that better policy was the main source of the Great Moderation. In particular, Clarida et al. (2000)argue that the adoption of an interest rate rule in 1979 that puts a sufficiently large weight on inflation, and thereby satisfiesthe Taylor Principle, has eliminated self-fulfilling expectations which gave rise to instability before the 1980s. More recently,Boivin and Giannoni (2006) and Leduc et al. (2007) provide similar evidence using different empirical methods and data sets.Sims and Zha (2006) and Smets and Wouters (2007), in contrast, find that changes in systematic monetary policy were onlymodest. They conclude that it is mostly the variance of shocks which has declined. Galí and Gambetti (2009) and Canova(2009) argue that the combination of smaller shock variances and a more stabilizing policy is consistent with the lower vol-atility of macroeconomic variables since the mid 1980s.2

Orphanides (2004) estimates an interest rate rule using real time data and finds, in contrast to Clarida et al. (2000), thatmonetary policy has satisfied the Taylor principle before as well as after 1979. Thus, according to these results, self-fulfilling

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; fax: +43 732 2468 9679.(E. Mayer), [email protected] (J. Scharler).

erein for a summary of the empirical literature.

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E. Mayer, J. Scharler / Journal of Macroeconomics 33 (2011) 568–581 569

revisions in inflation expectations were not a source of the macroeconomic instability which characterized the US economybefore the 1980s. However, he proposes an alternative explanation for the higher volatility prior to the 1980s, namely a rel-atively strong response of the Federal Reserve to the output gap in the presence of severe measurement error. More specif-ically, by responding strongly to noisy real time estimates of the output gap, the Federal Reserve amplified the noise in thedata and thereby generated output fluctuations. During the Volcker–Greenspan era, monetary policy was less activist withrespect to output stabilization resulting in smoother business cycles and ultimately the Great Moderation.

The goal of this paper is to quantitatively evaluate this hypothesis. To do so, we simulate the effects of interest rate rulesputting different weights on output stabilization using a New Keynesian model (Woodford, 2003; Clarida et al., 1999) aug-mented with sticky wages and habits and assume that the central bank observes only noisy estimates of the output gap. Ouranalysis is closely related to Orphanides (2003) who shows how an overly activist policy can increase business cycle vola-tility when the output gap and inflation are measured with noise. The novel feature of our paper is to quantitatively inves-tigate this mechanism as an explanation of the Great Moderation.

Based on our simulation results, we conclude that the regime switch in US monetary policy in 1979 to a less activist inter-est rate rule can account for a quantitatively important fraction of the lower standard deviation of detrended real GDP whichwe observe since the mid 1980s. We also find that the magnitude of the increase in macroeconomic stability depends on thespecification of the interest rate rule. If the central bank reacts to the output gap and the inflation rate, as it is usually as-sumed, then the less activist policy pursued after 1979 can account for up to 50% of the lower volatility of the output gapthat characterizes the Great Moderation. If the central bank, in contrast, puts less emphasis on the output gap and reactsto the output growth rate instead, then our simulations indicate that the regime shift towards less activism can explainaround 20% of the Great Moderation. The reason behind this quantitative difference is that measurement errors have onlytransitory effects on the perceived growth rate, even if output itself is measured with persistent noise.

In addition, we explicitly recognize that interest rate shocks are closely related to noise shocks. Empirically, it appearsthat the magnitude as well as the impact of interest rate shocks have declined over time. Our simulations are consistent withthese empirical results. However, according to our interpretation, interest rate shocks do not necessarily represent exoge-nous fluctuations in monetary policy, but result to some degree from the interaction between noisy real time data and sys-tematic monetary policy. Thus, we argue that although a lower variance of interest rate shocks coincides with the decline inoutput volatility, the ultimate source of the smaller disturbances to short-term interest rates is the regime-switch in system-atic monetary policy in 1979. In this sense, noise shocks, as an explanation for the Great Moderation, share some similaritieswith the argument in Giannone et al. (2008) which states that even if a change in the magnitude of the shocks hitting theeconomy appears to be a source of smoother fluctuations, the greater stability may actually be the result of a change in thepropagation mechanism. Our results are also consistent with Sims and Zha (2006) who find that it was mostly the variance ofpolicy shocks which declined whereas systematic monetary policy was subject to small variations only. We find that even asmall change in the parameters of the interest rate rule may give rise to what appears to be a large reduction in the mag-nitude of policy shocks.

The remainder of the paper is structured as follows: Section 2 highlights the close connection between noisy data, activistpolicy and interest shocks. Section 3 outlines the model which forms the basis for our analysis and Section 4 presents ourmain simulation results. A sensitivity analysis is provided in Section 5. Section 6 concludes the paper.

2. The Great Moderation and interest rate shocks

The purpose of this section is threefold: First, we present descriptive statistics for US GDP and inflation to illustrate themagnitude of the reduction in volatility since the mid 1980s. Second, we highlight the close connection between noiseshocks and interest rate shocks. And third, we estimate a vector autogregression (VAR) model to identify reduced-form inter-est rate shocks. In the next section, we will then compare the quantitative implications of a New Keynesian model where thecentral bank can only observe noisy estimates of the output gap to the empirical quantities we present in this section.

Table 1 shows descriptive statistics for real detrended GDP, GDPt, and inflation, Inft, for two subsamples. The first subsam-ple covers 1959:1–1979:3 and the second subsample runs from 1985:1 to 2009:1. The starting date of the first subsample ischosen to match Boivin and Giannoni (2006). The end of the first subsample is motivated by the well documented regimechange in US monetary policy. Although the change in the monetary policy regime occurred abruptly, the beginning of

Table 1Descriptive statistics.

1959Q1–1979Q3 1985Q1–2009Q1

GDP Inf GDP Inf

Mean 0.84 4.29 �0.08 2.46Max 5.87 12.17 4.18 4.79Min �6.74 0.40 �4.96 0.55Stdv 3.29 2.75 1.84 0.97Obs 83 83 97 97

570 E. Mayer, J. Scharler / Journal of Macroeconomics 33 (2011) 568–581

the 1980s was characterized by substantial macroeconomic volatility. Therefore, we do not cover the early 1980s, which weview largely as a transitional period, and take the first quarter of 1985 as the beginning of the Great Moderation period.3 GDPt

is obtained as the residual of a regression of the log of real GDP on a constant, a linear and a quadratic time trend. Inflation ismeasured as the annualized rate of change between two consecutive quarters.4 We see from Table 1 that the standard devia-tions of GDP and inflation have declined substantially after 1985. GDP is about 44% less volatile and the standard deviation ofinflation declined by about two thirds.

We proceed by discussing the close relationship between data noise and interest rate shocks. Suppose that the centralbank conducts monetary policy according to a simple interest rate rule. That is, the central bank sets the interest ratedepending on the output gap, yt , and the inflation rate, pt .5 Also suppose that the central bank cannot observe the outputgap, but only a noisy estimate. More specifically, the central bank observes ~yt ¼ yt þ zt , where zt denotes output gap noise. Thus,monetary policy can be described by the rule

3 Thi4 The5 Hat

bRt ¼ jppt þ jy~yt þ �t; ð1Þ

where jp, jy characterize the responses of the interest rate to fluctuations in inflation and the noisy estimate of the outputgap and �t is a monetary policy shock. Although we will consider more general interest rate rules in the next section, the rule(1) is sufficient to highlight the main intuition.

Using the definition of ~yt , the interest rate rule (1) can be rewritten as

bRt ¼ jppt þ jyyt þ et; ð2Þ

where et ¼ jyzt þ �t . The crucial point is that, in this formulation, et is a convolution of output gap noise, the output coeffi-cient in the interest rate rule and the actual policy shock. Nevertheless, it closely resembles a shock to the interest rate equa-tion analyzed in the large literature using monetary vector-autoregression (VAR) models (see e.g. Christiano et al., 1999).That is, when estimating a VAR with data which may not have been available in real time, the identified policy shock willalso mirror data noise and systematic policy to some extent.

To get some impression about the quantitative magnitudes, we now estimate the interest rate shocks using a VAR. Sincethe shock to the interest rate equation of the VAR may pick up the effects of data noise and its interaction with monetarypolicy, we are not able to identify the actual noise shock. Nevertheless, this exercise still allows us to quantify how the over-all magnitude of interest rate shocks has changed over time and therefore presents another dimension of the data to whichwe can compare our simulation results in the next section.

We estimate the VAR with real GDP, GDPt, disposable income, Ydt, and consumption, Ct, in real terms and per capita, hoursworked, Hourst, the real wage, Waget, the inflation rate, Inft, and the Federal Funds rate, FFt:

Zt ¼ A0 þ AðLÞZt�1 þ ut; ð3Þ

where Zt = (GDPt, Ct, Ydt, Hourst, Wagest, Inft, FFt)0. This ordering of the variables is based on the standard assumption in themonetary VAR literature that monetary policy responds contemporaneously to measures of aggregate economic activityand inflationary pressure, whereas these variables respond only with a one period lag to interest rate innovations.

Fig. 1 shows the impulse responses for the two subsamples. The magnitudes of the responses of output and inflation tointerest rate shocks are generally more pronounced in the first subsample (see also Boivin and Giannoni, 2006). The variancedecomposition, displayed in Table 2 also suggests that the effects of interest rate shocks in the second subsample are sub-stantially reduced. Fig. 2 shows the orthogonalized interest rate shocks obtained for the two subsamples and Table 3 pre-sents descriptive statistics. We see that interest rate shocks have become substantially less volatile over time. This resultis in line with Mojon (2007) who also finds that the size of interest rate shocks declined after 1984.

To summarize, macroeconomic volatility declined substantially after the mid 1980s. At the same time, interest rateshocks, which to some extent mirror the effects of data noise, have become less pronounced and have exerted a smaller influ-ence on macroeconomic variables. In the remainder of this paper we will evaluate the hypothesis that the change in thebehavior of the Federal Reserve resulted in smaller interest rate shocks and ultimately lower macroeconomic volatility.To do so, we calibrate and simulate a New Keynesian business cycle model and compare the simulation results under dif-ferent interest rate rules to the empirical findings presented in this section.

3. Model and calibration

In this section we describe the structure and calibration of a small-scale New Keynesian model which forms the basis forour simulations. As it is standard in the literature, we assume that households supply labor on a monopolistically compet-itive labor market. Household j maximizes E0

P10 btððcjt � hcjt�1Þ1�r

=ð1� rÞ � n1þmjt =ð1þ mÞÞ, where cjt and njt denote con-

sumption and hours worked in period t, r is the coefficient of relative risk aversion and h denotes the degree of externalhabit formation. We denote the inverse of the labor supply elasticity by m. Households supply differentiated types of labor

s dating of the beginning of the Great Moderation is also consistent with evidence presented in, e.g. Smith and Summers (2009).series are obtained from the Federal Reserve Bank of St. Louis Economic Data database.

ted variables are measured as percentage deviations from the steady state values.

Fig. 1. Impulse responses: 1959Q1–1979Q3 and 1985Q1–2009Q1. Notes: This figure shows the responses to an identified monetary policy shock to theFederal Funds Rate FFt along with 95% Hall percentile standard error bands. All time series were drawn from the FRED-II database (acronyms reported inbrackets below). These include, real GDP (GDPC1), GDPt, disposable income (DSPIC96), Ydt, consumption (PCECC96), Ct, hours worked (AWHMAN)multiplied by employment (CE160V), Hours, the real wage in the nonfarm business sector (COMPRNFB), wage, the inflation rate (CPIAUCSL), Inft, and theFederal Funds Rate (FEDFUNDS), FFt along with 95% Hall percentile standard error bands for the two samples 1959Q1–1979Q3 and 1985Q1–2009Q1. All realvariables are expressed in log-levels and normalized by the civilian population over 16.

Table 2Variance decomposition.

Horizion GDP Yd Con Hours Wages Inf FF

1959Q1–1979Q31 0.00 0.00 0.00 0.00 0.00 0.00 82.604 12.07 7.68 14.44 9.15 11.96 14.01 43.928 19.21 11.88 17.37 23.36 12.84 12.49 34.67

12 15.67 10.78 13.55 18.45 10.51 15.66 34.0416 13.50 9.25 11.58 17.87 9.41 14.57 29.57

1985Q1–2009Q11 0.00 0.00 0.00 0.00 0.00 0.00 85.664 0.03 0.08 0.03 0.53 0.35 3.48 75.258 0.78 0.23 1.28 0.52 2.33 5.90 63.65

12 3.74 1.19 4.29 2.61 3.18 5.94 58.3316 6.81 3.00 6.78 6.16 3.12 6.20 56.70


njt and choose their wage to maximize lifetime utility subject to a downward sloping demand equation ndjt ¼ ðwjt=wtÞ�/nt for

their type of labor. The consumption allocation has to satisfy: wjtnjt + bjt�1 Rt = ptcjt + bjt + divjt, where wjt is the nominal wageand bjt�1 denotes nominal bond holdings that household j carries over from period t � 1, which earn a gross, nominal interestrate of Rt. The nominal profits redeemed to household j are denoted by divjt. As households have access to state contingentsecurities, they can insure against variations in household-specific labor income and therefore households are homogeneouswith respect to asset holdings and consumption: bjt = bt and ct = cjt. As in Erceg et al. (2000), we assume a Calvo wage settingscheme and include wage indexation to past inflation rates. (1 � hw) denotes the fraction of households that reset theirwages each quarter. The degree of wage indexation is measured by xw.

Firms operate under monopolistic competition and each firm i hires labor, nit, and produces a differentiated good accord-ing to: yit = nit. Each firm sells its output at a price pit and faces the demand curve yd

it ¼ ðpit=ptÞ��yt , where pt and yt denote the

Fig. 2. Interest rate (FFt) shocks. Notes: This figure shows orthogonalized shocks to the FFt equation for the two samples 1959Q1–1979Q3 and1985Q1–2009Q1.

Table 3Empirical interest shocks.

1959Q1–1979Q3 1985Q1–2009Q1

Mean 0.00 0.00Max 1.84 0.66Min �1.49 �0.88Stdv 0.55 0.30


aggregate price level and aggregate output. As in Calvo (1983), each period, a fraction (1 � hp) of firms is able to adjust itsprice. As an additional feature we include price indexation xp.

We assume that the decisions of firms at time t are predetermined, that is, output, wages and inflation are prevented fromresponding contemporaneously to shocks. This assumption is consistent with the restrictions imposed to identify the inter-est rate shock in Section 2.

The intertemporal optimality condition for the household’s choice problem and goods market clearing give rise to the for-ward-looking IS relationship6:

6 For

yt ¼1

1þ hEt�1ytþ1 þ

h1þ h

yt�1 �1� hð1þ hÞr Et�1ðbRt � ptþ1Þ; ð4Þ

where hatted variables denote percentage deviations from the steady state. Based on the price-setting behavior of firms, weobtain the New Keynesian Phillips Curve:

pt ¼ cf Et�1ptþ1 þ cbpt�1 þ jpEt�1ut; ð5Þ

where cf = (bhp)/[hp + xp(1 � hp (1 � b))],cb = xp/[hp + xp(1 � hp (1 � b))] and jp = [(1 � hp)(1 � bhp)(1 �xp)]/[hp + xp(1 �hp(1 � b))]. Real marginal cost are defined as ut ¼ wt � pt . The evolution of nominal wage setting reads:

Dwt ¼ bv1Et�1Dwtþ1 þxwv1Dwt�1 � bhwv2Et�1pt þ v2pt�1 þ jwEt�1½dmrst � ðwt � ptÞ�; ð6Þ

where v1 = hw/[xw + hw(1 �xw(1 � bhw))], v2 = (xw(1 � hw))/[xw + hw(1 �xw(1 � bhw))] and jw = [(1 � hw)(1 � bhw)(1 �xw)]/[xw + hw(1 �xw(1 � bhw))(1 + m/)]. The marginal rate of substitution is dmrst ¼ ½ðð1� hÞmþ rÞ=ð1� hÞ�ct � ½rh=ð1� hÞ�ct�1.

a detailed derivation see for instance Woodford (2003, p. 332).

Table 4Calibration.

Parameter Calibration

Discount factor b 0.99Coefficient of relative risk aversion r 1.62Inverse of the labor supply elasticity m 2.45Calvo prices hp 0.87Serial correlation of output gap noise qz 0.911Stdv. of measurement noise rz 0.93Monopoly power of households / 5.00Calvo wages hw 0.80Habit formation h 0.69Wage indexation xw 0.64Price indexation xp 0.66


To close the model, we assume that monetary policy follows an interest rate rule. We will simulate the model with twodifferent interest rate rules to see how the amplification of noise shocks depends on the specific type of interest rate rule. Inboth cases, as discussed in Section 2, the central bank observes only a noisy estimate of the output gap when setting interestrates. Specifically, ~yt ¼ yt þ zt , where yt is the true output gap and zt is output gap noise. Output gap noise follows an auto-regressive process:

7 It werrors hshow in

8 How

zt ¼ qzzt�1 þ �zt; ð7Þ

where �zt � N(0, rz) is an i.i.d. noise shock.7

The first rule we analyze is due to Orphanides (2004):

bRt ¼ q1bRt�1 þ q2

bRt�2 þ ð1� q1 � q2Þ jpEt1

1þ iðpt þ . . .þ ptþiÞ þ jy~yt

� �; ð8Þ

where q1 and q2 determine policy inertia, jp and jy are the weights the central bank attaches to expected average inflationand output, respectively, and i indicates the number of periods over which the expected average inflation rate is calculated.The specification with i = 1 corresponds to the case where the central bank responds only to a weighted average of the cur-rent quarterly inflation rate and the inflation rate in the next period. For higher values of i the central bank behaves in anincreasingly forward looking manner. We simulate the model with (8) since it is rather standard in the sense that the centralbank reacts to the output gap and the inflation rate. More importantly, however, Orphanides (2004) provides parameter esti-mates based on real time data.

In addition, we also consider an interest rate rule according to which the central bank puts some weight on output growthin addition to its reaction to the output gap and inflation. When output is measured with persistent noise, output growthshould be subject to measurement error to a lesser extent than the output gap as permanent misperceptions of the levelof output cancel out when calculating growth rates. This point is also noted in Orphanides (2004).8 Thus, the amplificationof noise shocks may be dampened in this case. To see if this intuition holds true, we simulate the model with the interest raterule

bRt ¼ q1bRt�1 þ ð1� q1Þðjppt þ jy~ytÞ þ jDyD~yt ; ð9Þ

where D~yt is output growth. Smets and Wouters (2007) find that the output gap as well as the output growth rate haveexplanatory power for the dynamics of the Federal Funds Rate.

Our evaluation of monetary policy before and after the onset of the Great Moderation will be based on the model sum-marized by Eqs. (4)–(7) and with either Eq. (8) or (9) as the interest rate rule. Note that in this setup, households and firmsobserve the true output gap, whereas the central bank only observes a noisy signal. Thus, we assume that private agents havebetter information concerning the state of the economy than the central bank. In our setting this assumption essentially boilsdown to implying that households know their consumption levels and firms observe the output they produce, whereas thecentral bank has to form estimates. As argued by Orphanides (2003), policymakers may try to infer the information of privateagents through, e.g. consumer sentiment surveys. However, since these data sources are subject to noise, it appears plausiblethat private agents are better informed than policy makers.

To study the quantitative implications of shocks to output gap noise under different interest rate rules, we calibrate andsimulate the model. The calibration is largely standard and described in detail in Table 4. For the noise process (7), we use theparameter estimates from Orphanides (2004). The Orphanides interest rate rule (8) is calibrated according to the parameterestimates reported in Orphanides (2004) and summarized in the first two columns of Table 5 for easy reference. For the

ould be easy to consider inflation noise in addition to output gap noise. However, doing so would have very limited implications since measurementave been less pronounced in the inflation rate and, even more importantly, substantially less persistent according to Orphanides (2003). As we willSection 5 below, it is to a large extent the persistence of noise shocks which drives the results.ever, as Bullard and Eusepi (2005) point out, this need not be the case if the central bank estimates the growth rate directly.

Table 5Calibration of the interest rate rule.

Orphanides rule Smets–Wouters rule

Pre-1979 Post-1979 Pre-1979 Post-1984

i = 0 jp 1.65 1.77jy 0.17 0.08jDy 0.20 0.16q1 0.81 0.84

i = 1 jp 1.49 1.89jy 0.46 0.18q1 0.94 0.85q2 �0.26 �0.08

i = 2 jp 1.54 1.97jy 0.53 0.18q1 0.87 0.82q2 �0.21 �0.06

i = 3 jp 1.59 2.04jy 0.53 0.15q1 0.90 0.78q2 �0.22 �0.04

i = 4 jp 1.48 2.12jy 0.57 0.14q1 0.83 0.77q2 �0.12 �0.04

Notes: This table shows the calibration of the interest rate rule (8) for forecast horizons i = 1, . . . 4 as reported in Orphanides (2004, p. 161) and thecalibration of the rule (9) based on Smets and Wouters (2007, p. 603). Columns labeled ‘pre-1979’ show coefficients estimated for the pre-1979 regime andColumns labeled ‘post-1979’ show the coefficients for the post-1979 regime.


Smets–Wouters rule in (9) we use the parameter estimates from Smets and Wouters (2007), reproduced in the last two col-umns of Table 5. Although they estimate Eq. (9) with revised data, they still report coefficient estimates for two subsamplesthat correspond to the pre and post-1979 periods, and therefore, we are able to calibrate the model accordingly and comparethe results to those obtained with the Orphanides rule.9

Note that it is conceivable that the Fed already internalized problems associated with data noise before the 1980s.10 Sincewe calibrate the model according to empirically estimated interest rate rule coefficients, our simulation results incorporate, inprinciple, the actual reactions to perceived output gaps. Therefore, our simulations take into account that the Fed may alreadyhave been aware of data problems to a certain extent.

4. Activist policy and the Great Moderation

In this section, we quantitatively explore the hypothesis that a less activist monetary policy in the presence of data noiseis partly the source of the Great Moderation. Our analysis is based on counterfactual simulation exercises in which we exam-ine to what extent the switch in the interest rate rule in 1979 has reduced macroeconomic volatility while keeping all otherstructural as well as stochastic characteristics of the model economy constant.

4.1. Noise shocks and output volatility

We conduct the following experiment: we simulate the model and compute asymptotic moments based on a calibrationthat characterizes US monetary policy before 1979. For now, we assume that the stochastic process that governs output gapnoise (7) was stable over time.

The outcome of this experiment is a pair of standard deviations for the inflation rate, rðpÞ, and the output gap, rðyÞ. Next,we simulate the model but re-parameterize the interest rate rule to characterize the post-1979 period. By comparing thesimulated standard deviations across the simulations we are able to quantify the influence of the parameterization of theinterest rate rule on the volatility of the model economy under noisy data.

Note that in our simulations, the noise shock is the only source of volatility. Since we do not explicitly model any othershocks, a comparison of our simulation results with historical data is not straightforward, since the US economy was pre-sumably hit by substantial shocks which were not related to data noise both before and after 1979. In fact, in our simulations

9 The estimation samples in Orphanides (2004) and Smets and Wouters (2007) differ slightly. Orphanides (2004) estimates the rule for 1966:1–1979:2 and1979:3–1995:4 while Smets and Wouters (2007) use the subsamples 1966:2–1979:2 and 1984:1–2004:4.

10 One can argue that this regime shift in monetary policy also moved monetary policy closer to the optimal policy under data uncertainty by putting arelatively lower weight on output gap stabilization (see e.g. Orphanides, 2004; Svensson and Woodford, 2003; Orphanides and Williams, 2007, 2008).

Table 6Volatility relative to the data.

Forecast horizon Post-1979 calibration Pre-1979 calibration except jy

rðyÞ rðpÞ rðyÞ rðpÞ

i = 1 36.55 37.08 32.41 28.65i = 2 41.38 41.57 36.55 32.58i = 3 46.70 45.51 42.01 37.64i = 4 57.24 54.49 47.59 42.13

Notes: This table reports the volatility reduction in the model relative to the data when we simulate the model either with the post-1979 rule or with thepre-1979 rule and jy set to its post 1979 value.


output and inflation are substantially less volatile than in the data, which indicates that the model cannot fully account forthe overall level of macroeconomic volatility. Therefore, to quantify the degree to which the switch in the interest rate rulecan account for the Great Moderation, we report the volatility reduction obtained in our simulations relative to the differencebetween the standard deviations of output and inflation before and during the Great Moderation in the data. Recall fromSection 2 that the standard deviation of output dropped from 3.29 to 1.84. Thus, we observe a change of DrGDP = 1.45 inthe data. Similarly the standard deviation of the inflation rate dropped from 2.75 to 0.97 which corresponds to a changeof DrINF = 1.78. To see for how much of DrGDP and DrINF, the switch to a less activist policy can account, we report thechanges in the standard deviations rðyÞ and rðpÞwhich we obtain with the pre- and post-1979 interest rate rule coefficientsrelative to DrGDP and DrINF respectively.

Table 6 shows the outcome of this exercise using the Orphanides interest rate rule (8) for forecast horizons for the inflationrate ranging from i = 1 to i = 4 periods. The second and the third columns show the relative standard deviations of output andinflation under the pre-1979 interest rate rule. We see that the switch in monetary policy in 1979 can account for 37–57% ofthe lower output volatility associated with the Great Moderation, depending on the forecast horizon. For the inflation rate, theswitch in the interest rate rule can explain 34–57% of the reduction in the standard deviation. To isolate the effect of the out-put coefficient, we set the parameters of the interest rate rule to their pre-1979 values, except for jy, which we set to its post-1979 value. These results are reported in the last two columns of the table. By changing only the coefficient on the output gap,we can still account for 32–48% of the reduction in output volatility associated with the Great Moderation and for 29–42% ofthe reduction in the standard deviation of inflation.

To see how noisy data contribute to business cycle volatility, when the central bank responds to the growth rate of outputin addition to the output gap and the inflation rate, we now repeat the simulations with the Smets–Wouters interest rate rule(9). Intuitively, the effect of noise should be less pronounced since persistent misperceptions are less long-lived whengrowth rates are calculated. Thus, since some of the weight associated with output stabilization is shifted from the outputgap to the output growth rate, noise shocks should remain transitory and should therefore have only a limited impact on thecycle, even if the central bank amplifies noise via an activist policy.

We see from Table 7 that the volatility reductions associated with a less activist policy are still substantial at around 20%for the output gap and 17% for the inflation rate. Nevertheless, they are smaller than those found above using the Orphanidesinterest rate rule. The last two columns of the table show that a large part of the volatility reduction is due to the lower valueof jy in the post-1979 calibration, especially for the reduction in rðyÞ. Overall, these results confirm that reacting to thegrowth rate instead of the output gap amplifies noise shocks to a lesser extent. As a consequence, switching to a less activistpolicy has a quantitatively smaller effect. However, according to the empirical evidence presented by Smets and Wouters(2007), the Federal Reserve still reacted substantially to the output gap itself, prior to 1979, so that we still obtain a non-neg-ligible reduction in business cycle volatility.

In short, although the magnitudes of the volatility reductions depend on the exact specification of the interest rate rule,our simulations suggest that volatility declines by a non-negligible amount in all cases. Using the Orphanides rule (8), themagnitudes of the volatility reductions generally increase with the forecast horizons, that is, for higher values for i. We alsofind that most of the volatility reduction in the output gap, and to a lesser extent also in the inflation rate, is due to the lowercoefficient on the output gap in the interest rate rule. In this sense, the regime switch in US monetary policy to a less activistpolicy in 1979 may indeed have contributed substantially to the reduction in macroeconomic volatility which characterizesthe Great Moderation period.

Fig. 3 shows how the variables in the model respond to a one unit shock in output gap noise. The sub-figures in the leftcolumn show the results for the pre-1979 calibration and the sub-figures in the right column are based on the post-1979calibration. The solid lines correspond to the impulse responses obtained with the Orphanides rule (8), and the broken linesshow the corresponding impulse responses when we use the Smets–Wouters rule (9).11

Qualitatively we obtain the same picture for all calibrations considered here. Since the central bank interprets the positiveinnovation to noise as an increase in the output gap, it tightens monetary policy. Consequently, output gap and inflation

11 When we simulate the model with the Orphanides rule (8) we focus on the forecast horizon of i = 4 period. Shorter forecast horizons produce largely similarresults.

Table 7Relative volatility when the central bank reacts to output growth.

Post-1979 calibration Pre-1979 calibration except jy


19.88 16.85 21.36 22.52

Notes: This table reports the volatility reduction in the model relative to the data when we simulatethe model either with the post-1979 rule or with the pre-1979 rule and jy set to its post-1979 value.

Fig. 3. Impulse responses to a noise shock for different calibrations of jy. Notes: This figure shows impulse responses for the pre-1979 calibration of jy (leftcolumn) and the post-1979 calibration of jy (right column) and a forecast horizon of i = 4 quarters.


decline. The output gap reaches its trough after five quarters and returns subsequently to its baseline level. Due to theassumption of sticky prices and wages, the inflation rate slowly falls along a hump shaped path and reaches its peak response10 quarters after the initial shock.

Although we obtain the same qualitative patterns, the magnitudes of the responses differ substantially across the interestrate rules and also across the calibrations characterizing the different monetary policy regimes. In general, we obtain largerand also more persistent responses when we simulate the model with the Orphanides rule (8).

The reason behind these quantitative differences is the strong amplification of noise shocks, when the central bank reactsto the output gap. Analogous to the discussion in Section 2, the Orphanides rule (8) in the model can be written as

bRt ¼ q1bRt�1 þ q2

bRt�2 þ ð1� q1 � q2Þ jpEt1

1þ iðpt þ . . .þ ptþiÞ þ jyyt

� �þ et ; ð10Þ

where et ¼ ð1� q1 � q2Þjyzt closely resembles an interest rate shock, although it is ultimately data noise which drives thedynamics of the model. The Smets–Wouters rule (9) can be rewritten in a similar way:

bRt ¼ q1bRt�1 þ ð1� q1ÞðjpEtpt þ jy~ytÞ þ jDyD~yt þ ½ð1� q1Þjyzt þ jDyDzt �; ð11Þ

where the last term, ½ð1� q1Þjyzt þ jDyDzt �, again resembles an interest rate shock.The third row of Fig. 3 shows that the interest rate responds stronger in the impact period under the Smets–Wouters rule

(8). However, the response is less persistent than under the Orphanides rule since the effect of the noise shock on et is onlytransitory and essentially disappears in the second period following the shock. Under the Orphanides rule (8), in contrast, theresponse of et turns out to be substantially more persistent.

Comparing the pre-1979 and post-1979 calibrations, we see that regardless of which interest rate rule we use to close themodel, the responses of the output gap and the inflation rate are generally less pronounced under the post-1979 calibrations.Moreover, differences in the impulse responses across simulations with different interest rate rules are smaller under thepost-1979 calibration. Although output gap noise plays only a limited role in the post-1979 calibration, especially with

Fig. 4. Robustness analysis: Orphanides rule. Notes: This figure shows how either ry or rp depends on the parameters of the model for different forecasthorizons i = 1, . . . , 4. All parameters, except for the parameter under consideration, are calibrated as in Table 4.


the Smets–Wouters rule (9), it gives rise to what appear to be substantial, unsystematic changes in monetary policy in thepre-1979 calibration.

Overall, these results are consistent with the empirical observation that interest rate shocks have been less pronouncedsince the onset of the Great Moderation. The results are also consistent with the interpretation that a switch in the system-atic part of monetary policy resulted in a decline in the magnitude of interest rate fluctuations.

In short, the interaction between systematic monetary policy and noisy data gives rise to aggregate volatility if the centralbank pursues an activist output stabilization policy. The regime change in US monetary policy and the resulting lower ampli-fication of noise shocks are in line with empirical evidence concerning the size and impact of interest rate shocks.

4.2. Sensitivity analysis

From the analysis presented in the previous section we conclude that a less activist policy can substantially reduce outputand inflation volatility in the model. We now dig a little deeper and analyze in greater detail how the calibration influencesthe results.

We focus on the parameters of the interest rate rules and the persistence of the measurement error. Figs. 4 and 5 showhow the simulated standard deviations of the output gap rðyÞ and the inflation rate rðpÞ change when we vary the param-eter under consideration, conditioned on all other parameters set to their pre-1979 values. The subplots in the first row ofFig. 4 show the effects of jy and jp and the second row of the figure shows how q1 and qz influence volatility. For the Smetsand Wouters rule (9), we additionally report the influence of the parameter jDy on the relevant statistics.

For the Orphanides rule, Fig. 4 shows that higher values for the output gap coefficient, jy, which we conjecture to be adriving force of the Great Moderation, substantially increase the volatility of the output gap and the inflation rate. In partic-ular the figure reveals that if monetary policy had neglected the output gap, noisy data would have had essentially no impacton the economy. The more activist monetary policy becomes, the more volatility is imputed into the economy. According tothe figure, jy = 1 generates standard deviations between ry = 1.54, for a forecast horizon of i = 1, and ry = 1.57, for i = 4.Accordingly, a reduction of the output coefficient from jy = 1 to jy = 0, while keeping all other parameters constant at theirpre-1979 levels, would be able to explain the complete decline in volatility found in the data which is round aboutDry = 1.45, and would therefore fully account for the Great Moderation.

An increase in the interest rate rule coefficient on inflation, jp, attenuates the adverse effects of noisy information on vol-atility. Intuitively, after a positive noise shock the central bank increases the nominal interest rate which leads to a negativeoutput gap and a decline in the inflation rate. If the central bank is more responsive to fluctuations in the inflation rate, thenmonetary policy quickly counteracts these fluctuations induced by noise shocks. Although quantitatively, jy exerts a stron-ger influence than jp, a stronger response to inflationary pressure still helps to stabilize the economy to a non-negligible

0 0.2 0.4 0.6 0.8 10

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Fig. 5. Robustness analysis: Smets and Wouters rule. Notes: This figure shows how either ry or rp depends on the parameters of the model. All parameters,except for the parameter under consideration, are calibrated as in Table 4.


extent. In this sense, our results are also in line with Clarida et al. (2000), who argue that a stronger reaction of the centralbank to inflationary pressure gave rise to greater stability in the US economy. However, their argument is based on the elim-ination of sunspot fluctuations, whereas we focus on the transmission of a particular fundamental shock.

A more inertial monetary policy, that is, a higher q1, increases output volatility.12 For inflation volatility, the increase is lesspronounced for moderate degrees of policy inertia as the Phillips curve is relatively flat. High inertia implies that noise shockshave a long-lasting influence on the interest rate, despite the fact that the initial response is dampened. In this sense, high policyinertia additionally increases the persistence of the effect of noise shocks. Additionally Fig. 4 also highlights that qualitatively,our results are invariant with respect to the chosen forecast horizon. However, we also see that increasing the forecast horizonfrom i = 1 to i = 4 generally increases the standard deviations. This finding is a natural extension of our previous results. Giventhat the inflation rate is a mean reverting process, the central bank gets effectively less responsive to the inflation rate as theweighted average over a longer forecast horizon of a mean reverting process is likely to be smaller in value than the weightedaverage over a shorter forecast horizon. Thus, reacting to forecasts of the inflation rate operates in a similar way as a reductionof the inflation coefficient jp.

For the Smets–Wouters rule, Fig. 5 shows that we obtain qualitatively similar results with respect to the policy ruleparameters jp, jy. For both policy rules, the figures illustrate that as output gap noise becomes more persistent as measuredby qz, output gap and inflation, both become substantially more volatile. This is due to the fact that persistent noise shockstranslate into persistent fluctuations in the interest rate, which have a large impact on aggregate demand due to the forward-looking nature of the model. While the measured standard deviation of the output gap is between 0.21 and 0.25 for a coef-ficient of qz = 0.5, it sharply increases to 0.62 and 0.70 for qz = 0.8 for the Orphanides rule. Thus, the ability of a less activistpolicy to explain the Great Moderation hinges strongly on the high persistence of output gap noise.

This observation also explains why the interest rate rule (9) was less prone to amplify output gap noise even before 1979and also why we obtain smaller volatility reductions using this interest rate rule. The intuition is straightforward: althoughnoise shocks are highly persistent, their influence on output growth is only transitory by construction, since misperceptionsof output growth rates are less persistent. Thus, even if the shocks are of a similar magnitude, their influence on the interestrate is only short-lived and therefore noise shocks are simply a less important source of volatility. Comparing a scenario ofhighly correlated noise shocks across policy rules with qz = 0.95 the volatility of output is reduced by 37.6% and the volatilityof inflation is reduced by 58.4% compared to the Orphanides rule.

Overall, we see that while the extent to which the central bank reacts to inflationary developments, jp, and the degree ofpolicy inertia, q1, have some influence on macroeconomic volatility in the presence of noisy data, the strength of the feed-back from the output gap to monetary policy, as measured by jy, and the serial correlation of output gap noise, qz, are theparameters that primarily drive our results.

12 We only report results for different values of q1 and set q2 = 0 in all simulations.

Table 8Output gap noise.

Quadratic Trend HP-Filter

1965Q3–1979Q3qz 0.94 0.90rz 1.05 0.89

1985Q1–2009Q1qz 0.99 0.94rz 0.69 0.45

Notes: This table reports the estimated serial correlation, qz, and standard deviation, rz, of noiseshocks, based on either a quadratic trend or the HP filter.


5. Did a reduction in output gap noise contribute to the Great Moderation?

So far, our simulations were based on the assumption that the stochastic process governing output gap noise was stableover time. Clearly, this need not be the case. In fact, it appears plausible that in addition to the switch in systematic policy,the time series properties of output gap noise have also changed. In particular, output gap noise may have declined alongwith the reduction in macroeconomic volatility. In this case our simulations would overestimate the effect of the switchto a less activist policy.

In this section we relax the assumption of a stable process for output gap noise before and during the Great Moderation.We proceed in two steps: first, we construct estimates of historical real time output gaps and characterize the time seriesproperties of the resulting output gap noise series for the samples 1965Q3–1979Q3 and 1985Q3–2009Q1.

To construct proxies for output gap noise we use the real time GDP data provided by the Federal Reserve Bank ofPhiladelphia. The data set consists of different vintages of GDP series which were available in real time ranging from1965Q3 to 2009Q1. All vintage series start in 1947:1. To obtain an estimate of the real time output gap in 1965Q3, we de-trend the GDP series which was available in 1965Q3 and calculate the real time output gap as the deviation from a trend. Werepeat this procedure for each of the following quarters until 2009Q1 and thereby obtain a series of estimated real time out-put gaps. Finally, to obtain an estimate of output gap noise, we calculate another output gap series as the deviation of realGDP from trend based on the final, revised GDP series. The difference between the two series is our measure for output gapnoise. We use two alternative detrending methods: we (i) regress the log of real-time GDP on a constant, a time trend and thesquare of the time trend and (ii) use the Hodrick–Prescott (HP) filter with a smoothing parameter of 1600.

Note that this approach is rather mechanical and does not capture any qualitative aspects, such as judgement, that werepresumably involved when the Federal Reserve generated real time estimates of the output gap. This approach also differsfrom Orphanides (2004), who uses data on the macroeconomic outlook prepared for meetings of the Federal Open MarketCommittee. Nevertheless, Table 8 shows that the time series properties of our mechanically estimated output gap noise ser-ies are remarkably similar to the ones presented in Orphanides (2004) and summarized in Table 4. This is true for both, thequadratic trend as well as the HP filter. Although the standard deviations, rz, of our measures of output gap noise are some-what lower than in Orphanides (2004) we also find that output gap noise is highly persistent as indicated by the high valuesof qz. Comparing the properties of the noise processes across the subsamples shows that the average size of noise shocks, asmeasured by rz, has declined substantially, as expected. We also see, however, that qz remains high or has even increasedslightly. Thus, even though noise shocks have become smaller, they remain highly persistent.

As discussed in Section 2, the empirically estimated interest rate shocks also reflect, among other things, the influence ofoutput gap noise. For the sample 1965Q3–1979Q3, the correlation between the empirical interest rate shock and the noiseinnovation is 0.30. For the sample 1985Q1–2009Q1, in contrast, we find that the correlation is only�0.06.13 Thus, an intimaterelationship between measurement errors in the output gap and identified interest rate shocks from the VAR existed only beforethe 1980s which is consistent with our conjecture that output gap noise was a source behind interest rate fluctuations beforethe onset of the Great Moderation.

To assess how the change in the stochastic process for output gap noise may have interacted with the regime change inmonetary policy, we now repeat our simulations. In particular, we now change the parameters governing the noise processalong with the interest rate rule coefficients. To calibrate the noise process, we use the results obtained using the HP filterreported in the last column of Table 8.

In Table 9 we compare the volatility reductions in the simulated series, based on the Orphanides rule (8), to what weobserve in the data. The switch in the interest rate rule together with the change in the process governing output gap noiseaccounts for 46–62% of the reduction in the volatility of the output gap, and for 28% to slightly below 44% of the lowerinflation volatility associated with the Great Moderation. Hence, taking the reduction in the magnitude of noise shocks intoaccount increases the amount of volatility for which our simulations can account. To isolate the effect of a less activist policy,we calibrate the model to match the noise process and monetary policy prior to 1979, except for jy, which we set to its

13 The correlation coefficients are calculated for the case where the output gap is calculated with a quadratic trend. We obtain similar results for the HP Filter.We also find that the correlation is highly significant in the first subsample with a t-statistic of 2.33 and insignificant in the later subsample (t-statistic = �0.56).

Table 9Relative volatility taking changes in output gap noise into account.

Forecast horizon Post-1979 calibration Pre-1979 calibration except jy


i = 1 46.21 28.09 28.97 21.91i = 2 50.34 32.58 33.10 26.40i = 3 53.79 36.52 37.24 29.78i = 4 62.07 43.82 46.21 30.90

Notes: This table reports the volatility reduction in the model relative to the data when we simulate the model either with the post-1979 rule or with thepre-1979 rule and jy set to its post-1979 value. The process for output gap noise is calibrated according the last column (HP-Filter) in Table 8.

Table 10Relative volatility when the central bank reacts to output growth and the noise process changes.

Post-1979 calibration Pre-1979 calibration except jy


21.43 10.04 19.04 14.73

Notes: This table reports the volatility reduction in the model relative to the data when we simulatethe model either with the post-1979 rule or with the pre-1979 rule and jy set to its post 1979 value.The process for output gap noise is calibrated according the last column (HP-Filter) in Table 8.


post-1979 value. The last two columns show that a less activist policy alone can account for a reduction of output volatilityranging from 29% to 46% of what we observe in the data. Concerning inflation volatility, keeping everything constant exceptfor jy results in volatility reductions ranging from around 22% to around 31% of the more stable inflation rate associated withthe Great Moderation period.

Table 10 shows that we still obtain volatility reductions of around 20% for rðyÞ when we simulate the model with theSmets–Wouters rule (9). Thus, allowing for a change in the process for noise changes little in this respect. We conclude thatalthough smaller noise shocks also contributed to the Great Moderation, the switch to a less activist policy turns out to bequantitatively more important.

6. Conclusions

In this paper we quantitatively evaluate the role of a less activist monetary policy in the presence of data noise as anexplanation for the Great Moderation. Smets and Wouters (2007) state that whether policy has contributed to the reductionof shocks and consequently to the Great Moderation remains an interesting research question. Our simulations suggest thatthe answer to this question is affirmative to a large extent. We argue that interest rate fluctuations partly mirror the re-sponse of monetary policy to noise shocks and therefore a less activist policy dampens the transmission of these shockssubstantially.

Based on a calibrated New Keynesian model, we find that the switch to an interest rate rule that reacts less to fluctuationsin the output gap in 1979, can account for a substantial part of the lower standard deviation of real GDP which we observesince the mid 1980s. Essentially, the high serial correlation of output gap noise implies that noise shocks are a quantitativelyimportant source of macroeconomic fluctuations. Our results are also consistent with the empirical observation that interestrate shocks have become less pronounced since the beginning of the Great Moderation period and that the impact of interestrate shocks on output and inflation has been dampened.

In our analysis, we highlight the interaction between shocks to output gap noise and systematic monetary policy. In thissense we contribute to the literature that emphasizes the role of exogenous shocks as well as policy as the source of theGreat Moderation. According to this branch of the literature, the question is not primarily whether better policy or good luck,in the form of smaller shocks, is the ultimate source of the Great Moderation, but how policy and exogenous shocks togetherresulted in greater macroeconomic stability. In this paper we specifically focus on the interaction between noisy data andmonetary policy. Nevertheless, it remains an interesting topic for future research to identify and explore additional aspectswhere changes in the structure of the economy interacted with exogenous shocks in such a way to result in smoother busi-ness cycles.

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