1. No category

Monetary News Shocks
Nadav Ben Zeev∗
Christopher Gunn†
Hashmat Khan‡
Ben-Gurion University of the Negev
Carleton University
Carleton University
March 17, 2015
Abstract
We pursue a novel empirical strategy to identify monetary news shocks and determine their effects on the US economy during the Greenspan-Bernanke era of
Federal Reserve Chairmanship. We first construct a monetary policy residual as
gap between the observed federal funds rate and a policy rule. Using the maximumforecast error variance (MFEV) approach, we identify a monetary news shock as
the linear combination of reduced form innovations orthogonal to current policy
residual which maximizes the sum of contributions to policy residual’s forecast error variance over a finite horizon. Real GDP declines in a hump-shaped manner
after a positive monetary news shock. This contraction in economic activity is
accompanied by an immediate fall in inflation and a rapid increase in the nominal
interest rate. By contrast, we highlight that in most DSGE models the nominal
interest rate falls after a positive monetary news shock. Our findings suggest caution in interpreting the effects of forward guidance for the path on nominal interest
rates.
JEL classification: E32, E52, E58
Key words: Monetary News Shocks, Monetary Policy Residual, Federal Funds Rate, New Keynesian DSGE Models
∗
Department of Economics, Ben-Gurion University of the Negev, Beer-Sheva, Israel. E-mail: nadavbz@bgu.ac.il.
†
Department of Economics, Carleton University, Ottawa, Canada. E-mail: chris.gunn@carleton.ca.
‡
Department of Economics, Carleton University, Ottawa, Canada.
E-mail:
hashmat.khan@carleton.ca.
1
Introduction
Monetary news shocks refer to deviations from a central bank’s policy rule that are anticipated
by private agents. Although the policy rule is not observed it is typically described by a
Taylor Rule (Taylor (1993)) or its variants. A potential source of monetary news shocks is the
practice of ‘forward guidance’ through which a central bank provides information about the
future course of monetary policy (Rudebusch and Williams (2008), den Haan (2013), Svensson
(2014)). In an attempt to quantify the impact of forward guidance in dynamic stochastic
general equilibrium (DSGE) models, recent work has included anticipated components to the
exogenous (non-systematic) portion of the policy rule, similar to the news shock approach of
Beaudry and Portier (2006).1 Moreover, central banks are also currently using this approach
for policy analysis.2 There is, however, little work on identifying monetary news shocks in the
data in parallel to the vast literature on identifying unanticipated monetary shocks.3 The main
objective of this paper is to fill this gap.
We pursue a novel empirical strategy to identify monetary news shocks and determine their
effects on the US economy during the Greenspan-Bernanke era of Federal Reserve Chairmanship. We first construct a monetary policy residual. This policy residual measures deviations
from an interest rate rule that tracks the observed federal funds rate well during this period.
Next, we propose a restriction to identify monetary news shocks using the maximum-forecast
error variance (MFEV) approach within the structural vector autoregression (SVAR) framework similar to Barsky and Sims (2011), Francis et al. (2012), and Ben Zeev and Khan (2012).
Specifically, a monetary news shock is identified as the linear combination of reduced form
innovations orthogonal to current policy residual which maximizes the sum of contributions to
policy residual’s forecast error variance over a finite horizon.
1
See, for example, Lasseen and Svensson (2011), Milani and Treadwell (2012), Gomes et al. (2013),
Harrison (2014), De Graeve et al. (2014), McKay et al. (2015), among others.
2
See, for example, the ‘FRBNY DSGE Model’ (Negro et al. (2013)) and the ‘Chicago FED DSGE
model’ (Brave et al. (2012))
3
Some examples of the literature on identifying unanticipated monetary shocks are Bernanke and
Mihov (1998), Christiano et al. (1999), Romer and Romer (2004), and Barakchian and Crowe (2013).
1
There are at least four advantages of our approach. First, by imposing orthogonality with
respect to the current policy residual we can isolate a pure news component that defines a
monetary news shock. Second, relative to an event-study approach that identifies the effects of
specific policy announcements (Gurkaynak et al. (2005)), our approach allows for forward guidance to be communicated to private decision makers via all channels available to the FOMC.
Third, the approach allows for a more general view of anticipated monetary policy beyond just
forward guidance. In particular, we allow that monetary news shocks may comprise both forward guidance via central bank communications about future policy positions as well as signals
received by market participants that are unrelated to formal central bank communications. For
example, an announcement in the news-media (or comments by a key observer of monetary
policy in the financial sector) about the increased likelihood of a monetary authority of leaning
against asset prices in the future might constitute news about future monetary policy, and one
that is unrelated to forward guidance if the monetary authority chose not to address it in its
formal regular communications. Fourth, the impulse responses to monetary news shocks that
we report are a useful benchmark to compare with those obtained from DSGE models that
include these shocks. To our knowledge, our empirical approach is first in identifying monetary news shocks in the tradition similar to that of identifying unanticipated shocks (see, for
example, Christiano et al. (1999)).
Our paper is related to Campbell et al. (2012) who identify forward guidance shocks at the
quarterly data frequency.4 The main similarity is that, like their work, we also consider the
monetary policy residual based on an interest rate rule as the starting point for identifying monetary news shocks. The identification approaches, however, are completely different. Campbell
et al. (2012) use quarterly aggregates of Blue Chip forecasts and interest rate futures prices
in an interest rate rule with two lags of the interest rates and measures of the unemployment
gap and inflation. The monetary policy residual has both an unanticipated contemporaneous
component and a forward guidance component that is anticipated by the public up to four
4
Campbell et al. (2012) distinguish between Odyssean and Delphic central bank communications.
The former implies public commitment to action whereas the latter do not.
2
quarters before the change in interest rate. The four quarter ahead forward guidance shock is,
for example, constructed as a gap between two expectations: the four-period ahead expected
interest rate minus the four-period ahead expected interest rate implied by the interest rate
rule, given values of the parameters in the rule. They use a Generalized Method of Moments
(GMM) approach to estimate the parameters. By contrast, we construct a policy residual conditional on calibrated values of the interest rate rule parameters, and identify monetary news
shocks via the MFEV approach imposing orthogonality with the contemporaneous residual.
The monetary news shocks that we identify may capture not only Odyssean commitments in
the sense of Campbell et al. (2012), but also changes in private sector expectations’ about
future monetary policy not communicated formally by the central bank, information to the
public about the Federal Reserve’s objectives, and beliefs about the long-run natural rate of
unemployment. Calomiris (2012) has stressed the importance of these latter two aspects of
forward guidance. Moreover, our identification allows for the possibility of capturing the effects
of forward guidance and/or changes in expectations about monetary policy that may last for
more than four quarters. A prominent example of long-term forward guidance is the phrase
‘...policy accommodation can be maintained for a considerable period ’ in the August 12, 2003
FOMC statement. More recently, the February 18, 2015 press release suggest a potential longterm forward guidance ‘Based on its current assessment, the Committee judges that it can be
patient in beginning to normalize the stance of monetary policy.’.5
Our main empirical findings are as follows. There is an immediate and persistent decline
in real GDP after a positive monetary news shock. The response is hump-shaped reaching its
trough after about 10 quarters. This contraction in economic activity is accompanied by an
immediate fall in inflation, and recovers within about two years. The federal funds rate responds
very little initially but then rises rapidly in subsequent periods, peaking after about 5 quarters.
Over a two year horizon, monetary news shocks account for approximately 50 percent of the
forecast variance in the policy residual, and approximately 20 percent of the forecast variance
5
http://www.federalreserve.gov/newsevents/press/monetary/20150128a.htm
3
in output, federal funds futures, and the federal funds rate. They account for about 10 percent
of the variance in inflation. Relative to DSGE models with monetary news shocks, the striking
finding is the response of the interest rate. In New Keynesian model with a Taylor rule, a
positive monetary news shock (i.e., anticipated contractionary monetary policy) always leads
to a contemporaneous fall in the nominal interest rate. This result is a robust feature of any
contemporary DSGE model with monetary news shocks. By contrast, our empirical results
suggest a hump-shaped increase in nominal interest rate to a monetary news shock identified
in the data.
In the remainder of the paper we proceed as follows. In Section 2, we construct the monetary
policy residual and examine its properties. In Section 3 we introduce our empirical approach and
identification methodology, and present the main results. In Section 4 we present a canonical
New Keynesian DSGE model to illustrate the responses of variables to monetary news shocks.
Section 5 concludes.
2
Monetary policy residual
Consider a policy rule
it = g(Ωt ) + εt ,
(1)
where it is the nominal interest rate, Ωt is the time t information set of the policymaker, g(Ωt )
is a function of the variables in the information set and denotes the unobserved systematic
component of policy, and εt is a collection of both unanticipated and anticipated shocks to the
interest rate. Specifically, εt is given as
εt = ε0t +
P
X
εjt−j
(2)
j=1
where ε0t denotes the unanticipated shock at time t, and terms for 1 < j ≤ P are anticipated
shocks, up to an including some horizon P periods in the future, such that the εjt−j is a shock
4
received j periods in advance of period t but that impacts the interest rate process in period t.
We consider a linear approximation of g(Ωt ) in (1) given as
g˜(it−1 , πt , ut ) ≡ 0.8it−1 + 0.2 2 + πt + 0.5 πt − 2 + 2 6 − ut ,
(3)
where πt is the inflation rate, and ut is the unemployment rate. The intercept of 2 captures
the normal level of the real interest rate, the inflation target is assumed to be 2 percent, and
the long-run normal level of unemployment is 6 percent. This modified ‘Taylor rule’ is similar
to that considered in Clark (2012). A policy rule like (3) with unemployment gap in place of
the output gap is appealing for two reasons. First, it is often argued, as in (Clark (2012)), that
unemployment is a better reflection of the maximum employment element of the Federal Open
market Committee’s dual mandate. Indeed, Campbell et al. (2012) also consider a policy rule
with unemployment. Second, in the theoretical literature the output gap is a model-specific
notion. It is typically defined as the gap between actual and the unobservable flexible price
level of output (see Woodford (2003)). Determining an appropriate empirical counterpart to
the output gap implied by theory is thus wrought with issues.6 In this regard, using the
unemployment gap serves as a practical empirical proxy for the economic ‘slack’ implied by the
output gap of many theoretical models. Indeed Gal´ı (2011) uses a New Keynesian model with
unemployment to show that one can construct unemployment-based measures of the modelimplied output gap. Moreover, he shows that a simple policy rule that responds to price
inflation and the unemployment rate can not only approximate the optimal policy rule, but
better capture movements in the Federal Funds rate from 1987 to 2008 than a similar policy
rule using a more traditional HP-Filtered measure of the output gap.
We then define our policy rate process as
it = g˜(it−1 , πt , ut ) + vt ,
6
See Gal´ı (2011) for additional discussion.
5
(4)
and refer to the term vt as the policy residual. That is, the residual obtained from netting
out an assumed policy rule parameterized as in (3) from the nominal interest rate using time
series observations on it , πt and ut to construct (3). In effect, our policy rule is a structural
element analogous to the Solow Residual obtained from netting out a parameterized aggregate
production function from real output, using the appropriate time series observations. Since
equation (4) is not a regression model, we allow at least in principal that vt may be correlated
with g˜(·), such that it may contain both endogenous or systematic elements of policy as well
as exogenous shocks. For example, if in the data the central bank targets asset markets in
addition to inflation and the output gap, or, responds to inflation more aggressively than the
response implied by the simple policy rule g˜(·), then vt would include systematic components
capturing the central bank’s reaction function to asset prices (which is not captured in (3) or
its additional inflation response).
Thus, the policy residual is
vt = it − g˜(it−1 , πt , ut ) ≡ f (Ωt ) + ε0t +
P
X
εjt−j ,
(5)
j=1
where f (Ωt ) is some linear function of variables of the information set that captures all the
deviations between the systematic components of the unobserved policy rule and its approximation.
2.1
Properties of the Baseline Policy Residual
Figure 1 shows a plot of vt using quarterly data observations of the federal funds rate it , the
inflation rate πt , and the employment rate ut from 1960Q1 to 2014Q2.7 As is clear from the
figure, the policy rule (3) tracks quite closely the federal funds rates for much of the sample,
even before the modern inflation-targeting era.
7
The data were obtained from FRED Database at the Federal Reserve Bank of St. Louis (with
mnemonics in brackets). The effective federal funds rate (F F ) is a quarterly average. The inflation rate is
measured as annualized percentage of the growth in the GDP deflator (GDP DEF ). The unemployment
rate is the quarterly average of the civilian unemployment rate (U RAT E).
6
Figure 2 shows the policy residual vt over this same era, constructed as in (3). Note that the
policy residual appears to move systematically in and out of recessions, reflecting movements
in either the systematic components of vt responding to realized or anticipated changes in the
fundamentals of the economy, or, movements in the realized or anticipated exogenous variation
in vt .
3
Identifying monetary news shocks
In this section we present our empirical results for identifying the macroeconomic impact of
anticipated monetary policy shocks. We begin by first providing an overview of our empirical
approach before presenting our identification and estimation methodology in detail. Following this, we discuss the impulse responses and forecast error variance decompositions of the
identified shocks, and as well, explore the robustness of these results over several dimensions.
In the context of our interest rate process defined previously, it = g˜(it−1 , πt , ut ) + vt , where
P
vt = it − g˜(it−1 , πt , ut ) ≡ f (Ωt ) + ε0t + Pj=1 εjt−j , we wish to identify the macroeconomic impact
P
of the anticipated exogenous shocks Pj=1 εjt−j , interpreted as a pure change in expectations.
We use a VAR-based procedure using quarterly time series on the monetary policy residual
(MPR), the Federal Funds Rate (FF), the log of the Federal Funds Rate futures index (FFF),
CPI inflation, and the log of output (real GDP) per capita. The Federal Funds Rate futures is a
contract for the average daily federal funds rate during the particular month of the contract (in
our case, 6 months in the future). We include this futures data to exploit its forward-looking
nature to capture variation due to changes in expectations about future monetary policy, much
in the same way that the original news shock literature such as Beaudry and Portier (2006)
used stock prices to capture unobserved changes in expectations about future productivity.
One may argue that an analogous approach to that taken by Beaudry and Portier (2006)
to identifying TFP news shocks as innovations in stock prices orthogonalized with respect to
TFP can be taken in our setting by identifying monetary news shocks as innovations in FFF
7
orthogonalized with respect to MPR. Yet while such a restriction partitions out the impact of
the unanticipated monetary shock ε0t and potential impact policy-change f (Ωt ), nothing assures
us that monetary news shocks are the only shocks not affecting MPR on impact and impacting
the FFF, effects that would manifest themselves through f (Ωt+p ) for p > 0. For example, if in
the presence of a news shock about future TFP agents expect (correctly) the Federal Reserve to
alter its future policy-response, f (Ωt+p ) would change in the future and show up in the future
policy residual. As such, we propose to identify these expectational shocks using the maximumforecast error variance (MFEV) framework. Specifically, a monetary news shock is identified
as the linear combination of reduced form innovations orthogonal to the current policy residual
which maximizes the sum of contributions to policy residual’s forecast error variance over a
finite horizon that is thought to correspond to the operative horizon of monetary policy. The
following section details this approach.
3.1
Methodology
We now show in more more detail our identification methodology. Let yt be a kx1 vector of
observables of length T . Let the reduced form moving average representation in the levels of
the observables be given as
yt = B(L)et
(6)
where B(L) is a kxk matrix polynomial in the lag operator, L, of moving average coefficients
and et is the kx1 vector of reduced-form innovations. We assume that there exists a linear
mapping between the reduced-form innovations and structural shocks, εt , given as
et = Aεt .
8
(7)
Equation (6) and (7) imply a structural moving average representation
yt = C(L)εt ,
(8)
where C(L) = B(L)A and εt = A−1 et . The impact matrix A must satisfy AA0 = Σ, where Σ
is the variance-covariance matrix of reduced-form innovations. There are, however, an infinite
number of impact matrices that solve the system. In particular, for some arbitrary orthogonale (we choose the convenient Choleski decomposition), the entire space of permissible
ization, A
e where D is a k x k orthonormal matrix (D0 = D−1 and
impact matrices can be written as AD,
DD0 = I, where I is the identity matrix ).
The h step ahead forecast error is
yt+h − Et yt+h =
h
X
e t+h−τ ,
Bτ ADε
(9)
τ =0
where Bτ is the matrix of moving average coefficients at horizon τ . The contribution to the
forecast error variance of variable i attributable to structural shock j at horizon h is then given
as
Ωi,j =
h
X
0
e 0A
e0 Bi,τ
Bi,τ Aγγ
,
(10)
τ =0
e is a kx1 vector corresponding with the jth column of
where γ is the jth column of D, Aγ
a possible orthogonalization, and Bi,τ represents the ith row of the matrix of moving average
coefficients at horizon τ . We put MPR in the first position in the system and index the unanticipated MPR shocks as 1 and the monetary news shock as 2. Monetary news shocks identification
requires finding the γ which maximizes the sum of contribution to the forecast error variance of
MPR over a range of horizons, from 0 to H (the truncation horizon), subject to the restriction
that these shocks have no contemporaneous effect MPR. Formally, this identification strategy
9
requires solving the following optimization problem
argmax
γ
H
X
Ω1,2 (h) = argmax
γ
h=0
H X
h
X
e 0A
e0 B 0
B1,τ Aγγ
1,τ
(11)
h=0 τ =0
e j) = 0 ∀j > 1
subject to A(1,
(12)
γ(1, 1) = 0
(13)
γ 0 γ = 1.
(14)
The first two constraints impose on the identified news shock to have no contemporaneous effect
on MPR. The third restriction that imposes on γ to have unit length ensures that γ is a column
vector belonging to an orthonormal matrix. This normalization implies that the identified
shocks have unit variance. We follow the conventional Bayesian approach to estimation and
inference by assuming a diffuse normal-inverse Wishart prior distribution for the reduced-form
VAR parameters. Our benchmark choice for the truncation horizon is H=5, a horizon that
generally corresponds to an operative period of monetary policy of less than two years in the
future. We explore the sensitivity of our identification to changes in this horizon length later
in the paper.
3.2
Impulse response functions
Figure 3 depicts the median and 84th and 16th percentiles of the posterior distribution of
impulse responses to a positive one standard deviation monetary news shock (that is, an anticipated tightening of policy). The posterior distribution was constructed by taking 2000 draws
from the posterior distribution of the VAR parameters.
Following a positive monetary news shock there is an immediate and persistent decline in
real GDP. The response is hump-shaped, reaching its trough after about 10 quarters. This
contraction in economic activity is accompanied by an immediate fall in inflation, which then
recovers within about two years. The policy residual does not change in the initial period by
construction because of our orthogonality restriction. It rises quickly however in subsequent
10
periods, peaking after about 5 quarters. The Federal Funds Rate - which is left unrestricted
- inherits much of the dynamics of the policy residual, changing very little initially, and then
peaking about the same time as the policy residual. To the extent that in reality the Federal
Funds Rate is a function of both a systematic rule (which in this instance would loosen monetary
policy in the face of the drop in output and inflation) and the policy residual, this suggests that
the monetary news shock is playing a critical role in driving behavior of the federal funds rate.
Moreover, the fact that the Federal Funds Rate does not move in the initial period when the
policy residual also does not move suggests there is no significant systematic effect of monetary
policy in the initial period. Finally, the Federal Funds Rate Futures rises immediately, consistent
with the eventual rise in the Federal Funds Rate itself.
3.3
Forecast error variance decompositions
Figure 4 shows the median forecast error variance decompositions along with the 68% posterior
probability bands. Over a one year horizon, monetary news shocks account for 56% of the
forecast variance in the policy residual, and 8%, 32%, and 29% of the forecast variance in output,
federal funds futures, and the federal funds rate, respectively. Furthermore, they account for
12% of the one year variation in inflation.
A very important element of these results is that the monetary news shock explains a
considerable share of the variation in the policy residual, indicating that monetary news shocks
are strongly present in the data. The large shares explained of the variation in the federal
funds futures and the federal funds rate are also interesting in that they suggest that i) market
participants’ expectations about the stance of monetary policy are strongly affected by signals
about future monetary policy and that ii) an important component of the Fed’s determination
of the interest rate is anticipated in advance.
11
3.4
Robustness
We now explore the robustness of our results to an alternate specification of the policy rule
and a change in the truncation horizon, and as well, we investigate the extent to which our
identification shocks may be related to news shocks about fundamentals.
3.4.1
Alternative monetary policy residual
Proceeding as before when constructing our baseline residual, we now repeat that exercise, this
time using a ‘Taylor rule’ that is exactly identical to that considered in Clark (2012), i.e., one
that uses the lagged unemployment rate rather than the current unemployment rate. We view
this as a less appealing specification as it is reasonable to assume that the Fed responds within
the quarter to variations in the unemployment rate. That said, it is still an informative exercise
to run; results are shown in Figure 5. Impulse responses for all variables apart from output
are quite similar to the benchmark ones. In contrast to the immediate decline observed in the
benchmark VAR, output now goes down only with a delay of about two years. This is likely
the result of the omission of the current level of the unemployment rate from the ‘Taylor rule’
which generates a bias in the identified monetary policy residual.
3.4.2
Longer truncation horizons
Figures 6(a) and 6(b) show the median and 84th and 16th percentiles of the posterior distribution of impulse responses to a positive one standard deviation monetary news shock obtained
from setting the truncation horizons to H=10 and H=15, respectively. These figures indicate
that our results are robust to having longer truncation horizons than H=5, both qualitatively
and quantitatively.
3.4.3
Relation with other news shocks
To assess whether our monetary news shock is related to two other important types of news
shocks identified in the literature using a similar approach to ours - the TFP news shock identi-
12
fied in Barsky and Sims (2011) and the investment-specific technology (IST) news shock recently
identified in Ben Zeev and Khan (2012) - we report the correlation of our recovered shock series
with these other shocks recovered independently. Table 1 shows the median correlations of our
monetary news shock with the two news shock series from Barsky and Sims (2011) and Ben
Zeev and Khan (2012), along with the 16th and 84th percentiles. It is apparent that our shock
is largely unrelated to these news shocks having low correlations with both shocks. We can
therefore be fairly confident that we are not picking up news shocks about fundamentals other
than the monetary policy residual.
Table 1: Correlation between monetary news shocks and TFP and IST news
shocks.
Correlation
TFP news shocks
IST news shocks
-0.11 [-0.16,-0.07]
0.03 [-0.05,0.11]
Notes: This table presents the median correlation between the monetary news shocks
identified in this paper and the TFP and IST news shocks identified in Barsky and
Sims (2011) and Ben Zeev and Khan (2012), respectively. The 16th and 84th percentile
correlations are shown in parenthesis.
4
Implications for DSGE models
We now illustrate the impact of monetary news shocks in a standard small-scale New Keynesian
model without capital based on the model used by Milani and Treadwell (2012). The model
consists of an infinitely-lived representative household, a measure of imperfectly competitive
intermediate goods producers, and a single final goods producer that nonetheless acts competitively. Household preferences are defined over sequences of consumption and leisure, where the
period utility function is separable in consumption and leisure and includes habit-formation in
consumption. Nominal variables into into the model in a cashless manner. Nominal rigidities
are based on a Calvo pricing mechanism for intermediate goods prices. The monetary policy
rule is standard Taylor-rule whereby the central bank adjusts the nominal interest rate in re-
13
sponse to variations in the inflation rate and the output gap, but only partially each period
such that there is interest-rate inertia built into the policy rate. For simplicity, we limit the
shocks in the model to unanticipated and news shocks to the monetary policy rule. Moreover,
for illustrative purposes we assume that agents receive a single news shock 4 periods in advance.
The resulting linearized system representing the model equilibrium is giving by
xt =
πt =
1
φ
σ −1 (1 − φ)
Et xt+1 +
xt−1 −
(it − πt+1 )
(15)
1+φ
1+φ
1+φ
σ −1
γ
(1 − θ) (1 − βθ)
β
ωxt +
Et πt+1 +
πt−1 +
(xt − φxt−1 ) (16)
1 + βγ
1 + βγ
θ (1 + βγ)
(1 − φ)
it = ρit−1 + (1 − ρ) (χπ πt + χx xt ) + νt
(17)
νt = ρν νt−1 + ενt + εν,4
t−4 ,
(18)
where xt , πt and it are the output gap, inflation rate and nominal interest rate respectively, and
νt is the exogenous (non-systematic) component of the monetary policy rule which is comprised
of unanaticipated and anticipated shocks ενt and εν,4
t−4 respectively.
Equation (15) is the household’s Euler equation, where φ parameterizes the degree of consumption habits, σ is the intertemporal elasticity of consumption, and χ is the Frisch elasticity
of labour supply. Equation (16) is the New Keynesian Phillip’s curve, where θ is the Calvo
probability of no price adjustment, β is the household’s rate of time discount, γ is the indexation
to past inflation, and ω depends on two structural parameters, namely, the intertemporal elasticity of labour supply (χ) and the elasticity of output with respect to labour (α), and is given
as ω = (χ + 1 − α)/α. Equation (17) is the monetary policy rule, where ρ governs the degree
of interest rate inertia due to partial adjustment, χπ and χx govern the systematic response
of the monetary authority to inflation and the output gap respectively. Finally, equation (18)
describes the process for the non-systematic portion of the monetary policy rule, where ρν is
the persistence parameter. Table 2 shows the calibrated values of the parameters taken from
Milani and Treadwell (2012).
Figure 7 shows the response of the model economy to a monetary news shock. Specifically,
14
Table 2: Parameterization
β
φ
χ
γ
θ
α
ρ
χπ
χx
ρν
ρµ
0.99
0.9
2
0.88
0.7
0.89
0.88
1.52
0.5
0.23
0.03
agents receive as news in period 1 about a positive shock to the interest rate that will hit
4 periods later. Both output and inflation fall in the present. These responses appear to
be consistent with the conventional effects on unanticipated monetary shocks. By contrast,
however, we now see that the fall in output is accompanied by a fall in the nominal interest rate
in the present. To understand this result, note that agents looking forward from period 1 know
that the shock will drive up the real interest rate in period 5, and thus they lower consumption
in the present to smooth the drop in consumption over time. The drop in consumption in
the present leads to downward pressure on inflation and the output gap in the present, and as
a result the monetary authority systematically lowers the interest rate, softening the drop in
consumption. As the interest rate panel clearly shows in the figure, all variation in the nominal
interest rate from periods 1 to 4 is due to the systematic response of the monetary authority,
whereas in period 5 the exogenous non-systematic portion counteracts this and results in a small
overall rise the interest rate in the future. Additionally, we can see from the figure that the
systematic portion of policy continues to dominate the behaviour of the interest rate even after
the exogenous shock hits, such that at its peak in period 6 the interest rate rises only slightly
above steady state before again dropping below steady state. Figure 8 shows the response to
the same shock, except this time assuming a persistent shock process. As the figure clearly
shows, the systematic portion of the policy rule dominates even more than in the previous case,
such that at no point does the interest rate every move above steady state.
Curiously then, in the baseline model we see that expectations of tight monetary policy in
the future result in loose monetary policy in the present, and that the systematic portion of
the monetary policy rule dominate the dynamics of the interest rate both before and after the
15
exogenous shock hits 8 . This lies in stark contrast with our empirical results from earlier. Recall
those results suggest that the Federal Funds Rate barely moves initially given anticipation of
future tightening, and then rises to a peak significantly above steady state over several quarters,
such that the dynamics of the rate are dominated by the policy residual rather than than the
systematic simple rule as in this structural New Keynesian model.
As a result of this tendency in New Keynesian models for the interest rate in the present
to move in the opposite direction of the expected future monetary policy shock, recent structural work seeking to capture forward-guidance has often specified shock processes that allow
for pure news shocks combined with contemporaneous unanticipated monetary policy shocks.
Such specifications effectively allow the exogenous shock in the present, working in the same
direction of the expected exogenous shock in the future, to dominate the effect of the systematic response in the present. Our empirical results have a lot to say with regard to this
approach, since we identify anticipated shocks that are orthogonal to monetary policy shocks in
the presents, but still, the federal funds rate moves in the same direction as the policy residual,
such that an expected future tightening indeed leads to a gradual tightening. Thus our empirical results suggest that the approach of combining contemporaneous shocks with news shocks
about monetary policy only masks a more fundamental problem of associated with anticipated
monetary policy shocks in New Keynesian models.
5
Conclusion
We pursue a novel empirical strategy to identify monetary news shocks and determine their effects on the US economy during 1988-2008 period. Starting with a parameterized policy rule we
construct a policy residual. Using the maximum-forecast error variance (MFEV) approach, we
identify a monetary news shock as the linear combination of reduced form innovations orthog8
This result holds up in larger scale versions of the New Keynesian model that incorporate variable
capital, investment adjustment costs and other real rigidities present in typical DSGE models used in
policy. Impulse response functions for these larger scale models are available from the authors upon
request.
16
onal to current policy residual which maximizes the sum of contributions to policy residual’s
forecast error variance over a finite horizon. Real GDP declines in a hump-shaped manner after
a positive monetary news shock. This contraction in economic activity is accompanied by an
immediate fall in inflation and a rapid increase in the nominal interest rate. By contrast, we
highlight that in most DSGE models the nominal interest rate falls after a positive monetary
news shock. Our findings suggest caution in interpreting the effects of forward guidance for the
path on nominal interest rates.
17
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20
Figure 1: Federal Funds Rate and Simple Policy Rule, 1960-2007.
18
MP Rule
FFR
16
Nominal Interest Rate
14
12
10
8
6
4
2
0
Q1-55 Q1-60 Q1-65 Q1-70 Q1-75 Q1-80 Q1-85 Q1-90 Q1-95 Q1-00 Q1-05 Q1-10
Q1-Year
21
Figure 2: Baseline Policy Residual, 1960-2007.
6
MP Residual
5
4
Policy Residual
3
2
1
0
-1
-2
-3
-4
Q1-55 Q1-60 Q1-65 Q1-70 Q1-75 Q1-80 Q1-85 Q1-90 Q1-95 Q1-00 Q1-05 Q1-10
Q1-Year
22
Figure 3: Impulse Responses to a Monetary News Shock: Baseline case.
Federal Funds Rate
60
Basis Points
Basis Points
20
10
0
−10
0
10
Horizon
Inflation
20
0
−40
20
10
20
Horizon
Federal Funds Futures
0.6
Percentage Points
Percentage Points
40
−20
0.2
0.1
0
−0.1
−0.2
−0.3
Percentage Points
Policy Residual
30
0
10
Horizon
20
0
Output
0.2
0
−0.2
−0.4
−0.6
−0.8
0
10
Horizon
20
0.4
0.2
0
−0.2
−0.4
0
10
Horizon
20
Notes: This figure shows the median and 16th and 84th posterior percentiles of the
impulse responses to the monetary news shock from the benchmark VAR.
23
0.6
0.4
0.2
0
5
10 15 20
Horizon
Inflation
1
0.8
0.6
0.4
0.2
0
5
10 15 20
Horizon
Federal Funds Rate
1
0.8
0.6
0.4
0.2
0
5
Proportion of Forecast Error
0.8
Proportion of Forecast Error
Policy Residual
1
Proportion of Forecast Error
Proportion of Forecast Error
Proportion of Forecast Error
Figure 4: Forecast Error Variance Decomposition of Monetary News Shocks: Baseline
case.
10 15 20
Horizon
Federal Funds Futures
1
Output
1
0.8
0.6
0.4
0.2
0
5
10 15 20
Horizon
0.8
0.6
0.4
0.2
0
5
10 15 20
Horizon
Notes: This figure shows the median and 16th and 84th posterior percentiles of the
contributions of the monetary news shock to the forecast error variance of the variables
from the benchmark VAR.
24
Figure 5: Robustness to monetary policy rule: using lagged unemployment instead of
current unemployment.
Federal Funds Rate
60
Basis Points
Basis Points
20
10
0
−10
0
10
Horizon
Inflation
20
0
−40
20
10
20
Horizon
Federal Funds Futures
0.6
Percentage Points
Percentage Points
40
−20
0.2
0.1
0
−0.1
−0.2
Percentage Points
Policy Residual
30
0
10
Horizon
20
0
Output
0.4
0.2
0
−0.2
−0.4
−0.6
0
10
Horizon
20
0.4
0.2
0
−0.2
−0.4
0
10
Horizon
20
Notes: This figure shows the median and 16th and 84th posterior percentiles of the
impulse responses to the monetary news shock identified using a monetary policy residual
based on a monetary policy rule that includes lagged unemployment instead of current
unemployment.
25
26
0
0
10
Horizon
10
Horizon
Inflation
20
20
0
−0.4
−0.2
0
0.2
0.4
0
10
Horizon
20
10
20
Horizon
Federal Funds Futures
0.6
−40
−20
0
20
Federal Funds Rate
40
−0.8
−0.6
−0.4
−0.2
0
0
10
Horizon
Output
20
−0.2
−0.1
0
0.1
0.2
−10
0
10
20
30
0
0
10
Horizon
10
Horizon
Inflation
20
20
Policy Residual
0
−0.4
−0.2
0
0.2
0
10
Horizon
20
10
20
Horizon
Federal Funds Futures
0.4
−40
−20
0
20
Federal Funds Rate
40
−1
−0.8
−0.6
−0.4
−0.2
0
0
10
Horizon
Output
20
Notes: Panel (a): This figure shows the median and 16th and 84th posterior percentiles of the impulse responses to the
monetary news shock identified using a truncation horizon of H=10. Panel (b): This figure shows the median and 16th
and 84th posterior percentiles of the impulse responses to the monetary news shock identified using a truncation horizon
of H=15.
(a) Impulse Responses to a One Standard Deviation Mon- (b) Impulse Responses to a One Standard Deviation Monetary News Shock (H=10).
etary News Shock (H=15).
−0.3
−0.2
−0.1
0
0.1
−10
0
10
20
Policy Residual
Percentage Points
Percentage Points
30
Basis Points
Figure 6: Robustness to truncation horizon: (a) H=10; (b) H=15
Basis Points
Percentage Points
Basis Points
Percentage Points
Basis Points
Percentage Points
Percentage Points
Figure 7: Anticipated 1 S.D. positive shock to MP rule in period 5: baseline parameterization.
Interest rate
Output gap
0
0
−0.02
−0.01
−0.04
−0.02
−0.06
−0.08
−0.1
−0.03
2
4
6
8
10
12
2
4
6
8
10
12
Real interest rate (i−Etpit+1)
Inflation
0
0.06
−0.02
0.04
−0.04
−0.06
0.02
−0.08
0
−0.1
2
4
6
8
10
12
2
4
6
8
10
12
Notes: The blue and red shading in the Interest rate panel indicate the systematic and
exogenous components of the interest rate respectively.
27
Figure 8: Anticipated 1 S.D. positive shock to MP rule in period 5: persistent shock
parameterization.
Interest rate
Output gap
0
0
−0.1
−0.05
−0.2
−0.3
−0.1
−0.4
−0.5
−0.15
−0.6
2
4
6
8
10
2
4
6
8
10
Real interest rate (i−Etpit+1)
Inflation
0
−0.1
0.4
−0.2
0.3
−0.3
−0.4
0.2
−0.5
0.1
−0.6
0
2
4
6
8
10
2
4
6
8
10
Notes: The blue and red shading in the Interest rate panel indicate the systematic and
exogenous components of the interest rate respectively.
28