Long-term rate and interest rate volatility in monetary policy transmission

Abstract

As monetary policy tools exert increasing impacts on the longer end of the yield curve, this paper considers a long-term real rate as an alternative policy indicator in a structural VAR framework. Based on an event study of FOMC announcements, we advance a measure of the unexpected policy influence on long-term interest rate volatility. Monetary policy shocks identified by this volatility measure as an external instrument drive significant swings in credit market sentiments and real output, while the policy shocks motivated by unexpected policy rate changes lead to muted responses. Our results support the validity of the risk-taking channel, in which risk perception in financial markets plays an indispensable role in monetary policy transmission.

Full text

The Long-term Rate and Interest Rate Volatility
in Monetary Policy Transmission∗
Zhengyang Chen
St. Cloud State University
First Draft: September 5, 2017
This Draft: October 14, 2021
Abstract
Abstracts:
As monetary policy tools exert increasing impacts on the
longer end of the yield curve, this paper considers a long-term real rate as
an alternative policy indicator in a structural VAR framework. Based on
an event study of FOMC announcements, we advance a measure of the
unexpected policy influence on long-term interest rate volatility. Monetary
policy shocks identified by this volatility measure as an external instrument
drive significant swings in credit market sentiments and real output, while
the policy shocks motivated by unexpected policy rate changes lead to
muted responses. Our results support the validity of the risk-taking channel,
in which risk perception in financial markets plays an indispensable role
in monetary policy transmission.
Keywords:
Monetary Policy Transmission; Risk-Taking Channel; Structural
VAR; High-Frequency Identification
JEL classification codes: E3, E4, E5
∗Acknowledgments deferred for review.
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1 Introduction
Conventionally, monetary economists use changes in short-term interest rates,
e.g., the federal funds rate for the United States, to gauge monetary policy
stances and identify monetary policy shocks. The Taylor rule, in its various
iterations, provides theoretical support for these practices. However, from
December 2008 to November 2015, when the federal funds rate was essentially
lowered to its zero lower bound (ZLB), the measurement of monetary policy
incurred two challenges: first, short-term rates became uninformative; second,
those unconventional monetary policy tools were designed to affect longer-term
interest rates. Both of these impose question marks on the validity of a Taylor
rule strategy in monetary policy identification.
One potential solution is to construct measures sensitive to policy rate
changes during the non-ZLB period and otherwise unconstrained by the ZLB.
For instance, Krippner (2013), Lombardi and Zhu (2014) and Wu and Xia (2016)
use parametric estimations from a factor approach to construct ”shadow policy
rates” that can accommodate negative values and may give insight on how far the
nominal short-term rate would reach if unconstrained by the ZLB. alternatively,
Freedman (1994) proposes the Monetary Conditions Index, which is derived
from a linear combination of short-term interest rates and exchange rates, to
infer monetary policy action.
Those alternative measures are based on the common wisdom that monetary
policy only exerts influence through short-term rates. However, unconventional
monetary policy tools extensively applied during the ZLB period may have
affected longer-term interest rates. For instance, the Federal Reserve increasingly
relies on communication, such as forward guidance, to implement monetary policy,
particularly since the possibilities to steer the economy via short-term rate policy
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has been limited by the effective zero lower bound (refer to Cœur´e (2017) and
Blinder (2018)). Woodford (2012) and Swanson and Williams (2014) show that
the forward guidance strategy affects the two-year–and even longer maturity–
Treasury yields through guiding expectations on future policy rates. Another
example of these unconventional tools is a series of large-scale asset purchases
(LSAP) programs between late 2008 and October 2014. These programs expanded
the Federal Reserve’s balance sheet with direct purchases of longer-term Treasury
securities and mortgage-backed securities in private markets. The explicit
intention, evident by empirical findings, was to depress longer-term interest rates.
(Gagnon, 2010; Gagnon et al., 2011; d’Amico et al., 2012; Rosa, 2012; Swanson,
2015).
Former FOMC Chair Bernanke summarized that
”Forward rate guidance affects longer-term interest rates primarily by in-
fluencing investors’ expectations of future short-term interest rates. LSAPs, in
contrast, most directly affect term premiums.” Bernanke (2013)
In light of those challenges, we suggest the 10-year real interest rate (i.e.,
the 10-year TIPS bond yield) as an alternative monetary policy indicator with
three main considerations. First, we expect this measure to be sensitive to
variations in short-term rates and the real economy. Second, this measure should
be unrestricted by the ZLB. Third, it should reflect the non-negligible impact of
unconventional monetary policy tools on the longer end of the yield curve.
Admittedly, quantifying monetary policy actions through longer-term rates
is a relatively new approach, though it has been gradually gaining attention.
In an SVAR model, Wright (2012) identifies the impact of LSAPs through
heteroskedasticity of the reduced-from residual from the 10-year Treasury yield.
Weale and Wieladek (2016) include the 10-year Treasury yield in an SVAR
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model to show how purchases of government bonds by the Bank of England
and the Federal Reserve affect long-term yields. Gurkaynak et al. (2004) and
Swanson (2017) extract factors from prices of financial assets, including a variety
of long-term securities, to measure the effects of policy rate changes, forward
guidance, and LSAPs. They specifically identify the factor most closely related
to LSAPs as the only one that affects long-term interest rates.
Considering a long-term interest rate—such as the 10-year real yield—as the
policy indicator imposes a challenge in the identification of exogenous monetary
policy shocks. Specifically, which part of fluctuation in the long-term rate should
contribute to the impact of monetary policy shocks? And which component
may be due to the contemporaneous responses of the long-term rate to other
structural shocks?
Our identification approach in the structural VAR model stems from that
in Gertler and Karadi (2015). They advance a VAR identification strategy
with external instrumental variables in which unexpected changes in the Fed
Funds futures contracts, captured by an event-study approach, facilitate the
identification of monetary policy shocks from movements in the policy indicator
(the one-year Treasury yield). However, simply applying the aforementioned
strategy to identify policy shocks in a long-term rate could be counterproductive.
Figure 1 highlights that the 10-year rate seems to be considerably more volatile
than the federal funds rate and the one-year Treasury yield. It may be conjectural
to assert that unexpected funds rate changes should reflect the overall impacts of
FOMC announcements on a long-term rate. In the alternative, we seek after the
second-moment variation in interest rate to instrument the structural monetary
policy shocks.
Empirically, we notice that the Federal Reserve seems to maintain different
degrees of intention on the two ends of the yield curve. Interest rate volatility is
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Figure 1: The Federal funds rate, the one- and ten-year Treasury yields
frequently under-explored in the context of monetary policy transmission.
As to the short end of the yield curve, it might be reasonable to allow for
a level change of the short-term rate, within a tight window around FOMC
announcements, to fully represent the exogenous monetary policy actions. This
could be an appropriate mechanism because of the Federal Reserve’s explicit
commitment to the policy rate target. The near-term expectation of the federal
funds rate may immediately adjust to a newly announced target if the Federal
Reserve constantly fine tunes the discrepancy of the policy rate from its target
range via open market operations. As a result, the fluctuation of the policy rate,
ex-post an FOMC meeting, may be marginal in assessing the effects of policy
actions and is often ignored in the measurement of monetary policy. Not until
recent exploratory work of Bundick et al. (2017) and Bauer et al. (2019) do we
realize that even the volatility of short rates conceives important information of
monetary policy for asset pricing and real activities 1.
For the other end of the yield curve, the Federal Reserve does not explicitly
express and maintain a target for any long-term rates. After an FOMC press
release, the new information content in the statement may induce heteroskedastic
1
Bundick et al. (2017) include their measure in a SVAR model and incur the price puzzle,
in which the price abnormally reacts in the same direction as the monetary policy shocks.
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variation in long-term rate fluctuations around ex-post steady states. In other
words, the investigation of event study should not be restricted to changes in
the expected levels of long rates, but also shed light on shifts in conditional
volatility.
Theoretically, recent developments in the topic of risk-taking channel of
monetary policy transmission reconfirm our focus on the critical but less explored
role of interest rate volatility. Borio and Zhu (2012) formally propose the
concept of the risk-taking channel and review how monetary policy affects
banks’ perceived risk. The countercyclical nature of perceived risk in the risk-
taking channel is isomorphic to the external financing premium in a financial
accelerator model (Bernanke et al., 1999). Difference also exists. Rather than the
physical constraint in borrowers’ balance sheets which is centered in the financial
accelerator models, risk perception and risk tolerance of financial intermediaries
in the risk-taking channel contribute to their commitment to lending behavior
and in turn affect economic activities. Utilizing data in banking sector, Adrian
and Shin (2008),Altunbas et al. (2009), Gambacorta (2009), Delis et al. (2012),
Bruno and Shin (2015) and Dell’Ariccia et al. (2017) supply evidence for the
impact of monetary policy on the risk-taking behavior of financial intermediaries.
As to the measurement of risk, it is not rare to utilize the volatility implied by
options prices to gauge the perceived risk in a given market. Fleming et al. (1995),
Fleming (1998) and Christensen and Prabhala (1998) evaluate the perceived risk
in stock market, and Carlson et al. (2005), Emmons et al. (2006) and Swanson
(2006) indicate the perceived uncertainty in the policy rate. Several market-based
measures of interest rate volatility – such as the MOVE index, the TIV index of
Choi et al. (2017) and TYVIX index of the Chicago Mercantile Exchange – are
focused on expected volatility of longer-term interest rates and provide us access
to this analysis.
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Responding to monetary policy announcements, the unrestricted fluctuation
of long-term rates and varying risk perception of financial intermediaries suggests
a novel and probably viable venue to identify monetary policy shocks from
the risk-taking channel, encompassing the diversified information and actions
announced in FOMC press releases.
In detail, our econometric model considers the 10-year TIPS yield as the
policy indicator in a structural VAR model with a financial variable. Monetary
policy shocks are identified via high-frequency (i.e., daily) external instruments.
We capture two monetary policy surprises via an event-study approach and adopt
them as external instruments for identification. One, borrowed from Gertler and
Karadi (2015), is based on an event study of policy-induced changes in the three
month ahead Fed Funds futures. It is ideal to identify the exogenous monetary
policy impact in the state-of-art interest rate channel. Another monetary policy
surprise specifically designed for the risk-taking channel is the volatility surprise.
It intercepts the jumps of expected volatility of the 10-year Treasury bond price
around policy announcements. Unlike the conditional volatility calculated from
GARCH-type models, this options-implied volatility is model free and market
based, offering the real time variation in the risk percieption in a longer-term
bond market. We convert those two event-specific series into monthly frequency
and instrument for two monetary policy shocks in different transmission channels
in a Gertler and Karadi (2015)-type SVAR model.
The impulse responses show that contractionary policy shocks motivated
by both surprises can stimulate reasonable surge in the long-term real rate
and decline in the price level without incurring the price puzzle put forth by
Eichenbaum (1992), but only the policy shocks transmitting through risk-taking
channel drives swings of financial frictions and real output. Policy shocks driven
by unexpected policy rate changes exert neglegible influence in credit market
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constraint and real activities. Our findings corroborate the financial accelerator
models (Bernanke et al., 1999) in which financial intermediation amplify the
policy impact on economic activity. Besides, Banks’ risk evaluation seems play
a central role, triggering the soar of credit premium and the decline of lending
activities. Our findings also question the validity of cost-of-capital effect in
Neoclassical theory of investment as interest rate hikes make no difference in
industrial production.
This paper extends a typical SVAR model identifying with external instrument
to examine the validity of two different monetary transmission channels within a
comparable framework. Furthermore, we are the first to utilize high-frequency
options data to gauge the exogenous impact of monetary policy on expected
volatility of a long-term interest rate
2
. This measure has the potential to be an
alternative monetary policy shock to indicate the risk-side impact of monetary
policy.
The rest of the paper proceeds as follow. Section 2 presents our econometric
framework of structural VAR model and identification strategy. Section 3
introduce our measure of monetary-policy-induced difference in the uncertainty
of long-term rate and its role in identifying monetary policy shocks in the risk-
taking channel. Section 4 describes the data and sample period in the SVAR
model. Section 5 lays out the empirical results, and Section 6 discusses their
implications on the monetary policy transmission. Section 7 concludes.
2 Econometric Framework
Our econometric analysis is based on an SVAR model encompassing a high-
frequency identification (HFI) scheme to identify monetary policy shocks.
2
An array of papers study policy impacts on realized interest rate volatility via observing
model-based conditional variance (see Arnold and Vrugt (2010), Abad and Chuli´a Soler (2013),
and more). We focus on model-free options-implied expected volatility.
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The HFI approach is developed based on Stock and Watson (2012) and
Mertens and Ravn (2013). It identifies monetary policy shocks with the assis-
tance of external instrumental variables. This method is originally designed
to deal with the sensitivity of the included endogenous financial variables to
structural shocks (Bagliano and Favero, 1999; Cochrane and Piazzesi, 2002;
Faust et al., 2004; Mertens and Ravn, 2013). In an SVAR model with financial
variables, recursive timing restrictions in the conventional Cholesky identification
could be questionable. It is arduous to justify that those financial variables,
given their high-frequency fluctuations, do not contemporaneously respond to
certain structural shocks. In contrast, HFI does not restrict the timing of
contemporaneous responses.
The distinguishing feature of the identification scheme via external instru-
ments is the separation of policy instruments and policy indicators. A policy
instrument is captured in the high-frequency financial data, such as the Fed
Funds futures or the option-implied volatility of the 10-year rate, by imposing
an “adequately small” time window on each FOMC meeting announcement.
Policy instruments produced by this event study manner measure the unexpected
impact of monetary policy caused by FOMC announcements and carry relevance
to monetary policy shocks. If time windows are appropriately designed to cope
with the impact of economic news, those instruments should be orthogonal to
other structural economic shocks. A policy indicator is one of the endogenous
variables in the lower-frequency VAR. It reflects the impact of monetary policy
actions and represents monetary policy stances. The challenge in identification
is that a contemporaneously unexpected movement in the policy indicator may
be attributed to monetary policy shocks as well as accommodative policy actions
or other structural shocks. To tease out the exogenous monetary policy effects,
we utilize policy instruments as instrumental variables to estimate the unbiased
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contemporaneous responses of the policy indicator to structural monetary policy
shocks. This method combines the features of event study with the structural
identification in VAR models.
In general econometric representation, let
Yt
be a vector of n economic and
financial variables.
A
and
Cj∀j>
1 are conformable coefficient matrices,
while
t
is a vector of structural white noise shocks. Matrix
A
denotes the
contemporaneous interactions among endogenous variables. The structural
shocks are orthogonal to each other and normalized to one standard deviation.
Then the general structural form of the VAR model is given by
AYt= Σp
j=1CjYt−j+t(1)
The straightforward OLS estimation of structural form VAR may incur the
endogeneity issue. Pre-multiplying both sides of the equation with
A−1
derives
the reduced form representation
Yt= Σp
j=1BjYt−j+ut(2)
where
ut
is the vector of reduced form residuals. Parameters in reduced form
VAR can be estimated by equation-by-equation ordinary least square regressions.
Since the structural shocks are of the concern, the reduced form residuals are
related to the structural shocks in the following mapping function
ut=St(3)
with
Bj
=
A−1Cj
and
S
=
A−1
. Matrix
S
is the mapping from structural shocks
to reduced form residuals. By normalizing structural shocks
t
to an identity
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matrix, the reduced form variance-covariance matrix is
Et[utu
0
t] = SS
0= Σ (4)
Consider
yp
t∈Yt
as the policy indicator and
p
t
as the associated structural
policy shock. Then, let s (
n×
1) denote the column in matrix S that corresponds
to the impact of structural policy shocks
p
t
(1
×
1) on elements in the vector
of reduced form shocks
ut
. Since our primary question is how economic and
financial variables in
Yt
respond to monetary policy shocks, we thus need to
estimate parameters in the following equation. We only identify the monetary
policy shocks and impose no restrictions on other structural parameters.
Yt= Σp
j=1BjYt−j+sp
t(5)
The difficulty of identification lies in the estimation of the mapping vector
s
that is related to monetary policy shocks. The reduced form residual of policy
indicator
up
t
is estimable via OLS regression in the policy indicator equation,
but it requires restrictions to identify the portion of
up
t
driven by structural
monetary policy shocks and exogenous to other economic shocks.
Identification by external instrument considers monetary policy surprises
constructed through an event study method in high-frequency data as the exoge-
nous component of monetary policy. Event-study monetary policy surprises are
qualified as policy instruments
Zt
if they are strongly correlated with monetary
policy shocks
p
t
(relevance condition), but orthogonal to other structural shocks
q
t(exogeneity condition).
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E[Ztp
t
0]6= 0 (6)
E[Ztq
t
0] = 0 (7)
The two-stage identification process is similar to the 2-stage least square
regression in univariate analyses. The reduced form residual in the policy
equation
up
t
is endogenously related to other reduced form residuals
uq
t
due
to the contemporaneous interactions among variables in
Yt
. In the first stage
regression, we adopt externally identified monetary policy surprises as policy
instruments to tease out the component of
up
t
affected by contemporaneous
monetary policy shocks p
t.
‘up
t=γZt+t(8)
In the second stage, we obtain the relationship between responses of other
included variables and that of policy indicator to a unit increase of monetary
policy shocks by equation (9).
sq
link the contemporary variation of non-policy
variables uq
tto a unit of monetary policy shock p
tand spdenote how the VAR
residual in the policy indicator equation react to one unit of
p
t
. Since the
reduced form residual
up
t
may be partially endogenous to
uq
t
, we make use of the
exogenous component
γZt
(
ˆ
up
t
) derived from the first stage to acquire unbiased
estimation of relative changes of
uq
t
to
up
t
in response of a unit increase of
monetary policy shock sq
sp.
uq
t=sq
sp
ˆ
up
t+et(9)
With the estimated
sq
sp
, reduced form residuals
ut
and the reduced form
variance-covariance matrix Σ, we thus derive the estimation of spand sq.3
Importantly, this econometric framework imposes no restrictions that the
3See Appendix A for more details about the algorithm for identification.
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policy indicator must be a short-term rate, and that policy instrument should
be a variable describing behavior of the policy rate.
3 Measuring the Exogenous Impact of Mone-
tary Policy in the Risk-Taking Channel
To identify the monetary policy shocks in the risk-taking channel in the afore-
mentioned SVAR model, we propose a new measure of monetary policy impact
on the risk perception of interest rate in financial markets. Apart from other
options-price-based monetary policy uncertainty measures like those introduced
by Bundick et al. (2017) and Lakdawala et al. (2019), our measure takes into
account the expected volatility of a longer-term interest rate; it reflects the
risk-side impact of monetary policy on the farther end of the yield curve.
3.1 Risk perception in the long-term rate
We evaluate the risk perception in long-term rates through the conditional
volatility inferred from derivatives of the 10-year Treasury bond. There are two
advantages of this options-implied volatility over the typical GARCH-model-
based measures. First, it is model free and directly converted from real-time
options prices so that no model uncertainty involves. Second, consistent with
the definition of risk, our approach measures the expected volatility rather than
the volatility realized in the history.
The volatility of concern is the expected 30-day volatility of 10-year Treasury
note futures. The 10-year Treasury note futures are contracts with payoffs tied
to the 10-year Treasury note price. These future contracts are the most liquid
exchange-traded medium- to long-term interest rate derivatives in the world.
Denoting by
P(120)
t,T
the time-t value of a 10-year (i.e., 120 periods in monthly
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frequency) T-note future expiring at
T
. Option contracts are tied to futures
contracts, with payoff
max
(
P(120)
T,T −K,
0) for call options, and
max
(
K−P(120)
T,T ,
0)
for put options, where
K
is the strike price. These 10-year T-note options are
effectively options on 10-year Treasury yield, since the nominal yield on a T-note
maturing in 10 years is inversely mapped with the T-note price.
log(y(120)
t) = −1
nlog(P(120)
t) (10)
For a given trading date
t
and an expiration date
T
we can estimate the T-t
day variance of an asset (VAR) with the forward value of a portfolio of at- and
out-of the-money options on the asset expiring at T. The conditional variance
of future 10-year T-note can be calculated from a portfolio of out-of-the-money
10-year T-note puts and calls:
V ARt(P(120)
t,T )=[erτ {X
Ki
2∆Ki
K2
i
pt,T (Ki) + X
Kj
2∆Kj
K2
j
ct,T (Kj)} − (F
K∗−1)2]
(11)
where
pt,T
(
Ki
) (and
ct,T
(
Kj
)) are prices of out-of-money put (call) options
with strike
Ki≤K∗≤Kj
.
K∗
is the at-the-money strick, which is theoretically
equal to the future price
P(120)
t,T
. 2
∆Kj
K2
j
is the number of options at strike K
included in the portfolio.
erτ
is a discount factor that converts the price of
each option to a future value. The term (
F
K∗−
1)
2
compensates for the error
introduced by the substitution of
K∗
for the future price. It is larger than zero
when no listed strike price is equal to the future value.
Applying Equation (11) to options data, the Cboe Global Markets, Inc.
(Cboe) calculates the annualized options-implied 30-day standard deviation of
10-year T-note futures, which is referred to as the CBOE/CBOT 10-year U.S.
Treasury Note Volatility Index (ticker:
T Y V I X
). It is denoted monthly as
follows in such 10 years is equal to 120 months:
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T Y V I X = 100 ∗r365
30 V ARt(P(120)
t,t+1 ) (12)
The TYVIX is denoted as a percentage of foward 10-year T-note price and
subject to changes in price level. As per Swanson (2006), I convert it into the
TYVIX in basis points (TYVIXBP) by multiplying it with the spot month
10-year T-note future price:
T Y V I X B P =P(120)
t,t+1 ∗T Y V I X (13)
TYVIXBP is not subject to the forward price changes and is thus comparable
at different time points in a sample with considerable T-note price fluctuation.
Figure 2:
The TYVIX index in basis points and three month Fed funds futures
(Daily)
Figure 2 plots the TYVIX in basis points. In the long-run, it shows a
negative relationship with the short-term interest rate. It soared to a peak at
the outbreak of the financial crisis and experienced a gradual decline during the
zero-lower-bound period. Its two peaks are coincided with two local troughs of
the federal funds future rate in August 2003 and December 2008. These inverse
movements may suggest that the turns of expansionary monetary policy paths
introduce more uncertainty in the long-term interest rate.
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3.2 Four-day time window
We adopt a four-day time window around each FOMC announcement to capture
the surprise of monetary policy in terms of interest rate volatility. It is because
a wider time window, compared with the typical one-day window in previous
studies, sometimes better capture the policy impact.
For illustration, the security price movement around a policy announcement
can be segmented into two phases, such as the formation phase and verifica-
tion phase. The formation phase refers to the price shift shortly before the
announcement date. In this phase, investors trade securities because of the
upcoming announcement without actual knowledge of the unannounced policy.
The verification phase refers to the price shift right after the announcement.
Investors verify their beliefs based on the realized policy decision; cash the gain
when they get right and, otherwise, suffer a loss.
We notice that the dramatic price change on an announcement date not only
reflects the exogenous policy impact but also results from mean reversion to the
price variation during the formation phase. This mean-reverting movement is
often associated with the event-driven trading activities instead of the reaction
to policies.
Table 1 summarizes three typical scenarios of price movement around an
event: only the first one does not have the mean reverting pattern. First, some
investors may have insider information or collect sufficiently adequate information
to make a winning bet on a given policy decision before the official news release.
Their rational bets may lead the security price to gradually approach the ex-post
level ahead of the official statement. Second, event-driven trading activities
- trading on rumors, hedging, speculation, etc. - may boost the demand for
certain securities, such as options, and push up their prices before an event.
The increase (decrease) in trading volume before (after) an announcement could
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result in a hump shaped reaction in a security price. Third, some investors
may avoid uncertainty by selling off a security prior to a foreseeable event
and then buy it back later. In this case, its price may demonstrate a crater
shape response. Unlike the other two, the first scenario is the only one that
fits for a one-day window. It is because, although information may leak to the
public before the announcement, the same-day price movement is still mainly
driven by the information of the policy actions rather than event-specific trading
activities. This argument may not be applied to the other two scenarios, in
which event-specific trading is non-negligible.
Table 1: Summary of price patterns around policy events
E(rF
−rV) Pattern around events Senario Suitable window
Zero Accelerating trend Information leak One day
Positive Hump shape Increased volume Four day
Negative Crater shape Uncertainty avoidance Four day
Note:
E
(
rF
−rV
) is the expected difference between the return in the formation phase
and that in the verification phase.
We test for the necessity of a wider time window by examining the mean rever-
sion behavior. We regress the difference between the formation and verification
phases on a constant. An assumption is that expansionary and contractionary
monetary policy actions are announced in a random manner. If no apparent
event-driven trading activities present, the price movements in the formation
and verification phases should be irrelevant or positively correlated and thus the
expected value of the difference between the two phases,
E
(
rF−rV
), is zero.
Merely in this case should a one-day window be adequate. In contrast, when
E
(
rF−rV
) is equal to a non-zero figure, a turning kink emerges between the
two phases, suggesting that the security price is affected by the trading due to
the event occurrence. Then the shift on the announcement date is polluted and
may not truely reflect the policy effect.
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Table 2: Test for the neccessity of a wider time window on security prices
(rF
−rV) MP1 FF4 10Y TYVIXBP MOVE
C 0.29 0.49 0.10 5.06∗∗∗ 1.81∗∗∗
(0.58) (0.60) (0.28) (0.48) (0.63)
Obs. 158 158 158 158 158
Durbin Watson 1.96 1.89 2.24 2.36 2.25
F-Stat. 0.25 0.65 0.12 110.38 8.15
Note: *
p <
0
.
05, **
p <
0
.
01, ***
p <
0
.
001. HAC-robust standard
deviation in parentheses.
E
(
rF−rV
) is the expected difference between the return in the forming
phase and that in the verifying phase. Cis the constant term.
Table 2 shows the test results for various security prices. Interest rate levels,
such as spot month, three month funds future rate, and ten-year Treasury yield,
demonstrate price trend consistent with the ”information leak” scenario. As to
the second-moment variation of interest rates, such as the TYVIXBP and MOVE
indexes, a hump shape price reaction is identified around FOMC announcements.
Figure 3 particularly plots the fluctuation of the TYVIXBP, the variable of
concern, around a ”typical” FOMC announcement. The point values are averaged
from 158 FOMC news releases from 2003 to 2020. This hump-shape price pattern
may be due to an elevated volume of trading predicated on rumors and on the
hedging of uncertainty as the official press release approaches. Since we aim to
capture the impact of monetary policy rather than the FOMC-event-driven fixed
effect, a four-day window should be more appropriate than a one-day one. If we
take the plot in Figure 3 as the price reaction around one particular statement,
our proposed event-study measure on TYVIXBP captures the difference between
the dash lines B and A. In Appendix C, we provide additional institutional
explanation for selecting this four-day window.
Figure 4 exhibits the proposed event-study volatility surprise, whose naming
is analogous to the monetary policy surprise in Kuttner (2001). Data points
in the volatility surprise represent changes in the TYVIXBP during the unified
18
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Figure 3: Averaged TYVIXBP index from -7D to +7D of FOMC decisions
4-day time windows around FOMC announcements. A positive volatility surprise
indicates that a policy announcement induces an increase in the expected volatil-
ity of long-term rate and vice versa. To fit the volatility surprise in our monthly
SVAR model, we convert it into a monthly time series following a procedure
discussed in Appendix B (The monthly series is also shown in Figure 4).
Figure 4: The volatility surprise (Event study & Monthly)
In the next two subsections, we evaluate whether this volatility surprise is
relevant to monetary policy actions and empirically examine its impacts on
Treasury yields.
19
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3.3 Volatility Surprise and Unconventional Policy Actions
To identify monetary policy shocks as an external instrument, the volatility
surprise should be relevant to monetary policy actions even during the zero lower
bound period.
Table 3 summarizes the monetary policy narratives, actions and the volatility
surprise. In general, changing forward guidance communication style and switch-
ing the direction of large-asset purchases seem to be associated with a positive
volatility surprise. This consist with the observation that the public perceive
more uncertainty in the long term when the Fed sees new development of the
economy and switches gear for its monetary policy. Investors also doubt the
effectiveness of adopting novel policy actions in depressing the further end of the
yield curve. Excluding those announcements that introduce directional changes
to policy tools, forward guidance and large-scale asset purchases, in general,
generate a negative volatility surprise and enhance the stability of longer-term
rates.
As a robustness check for the four-day time window, we further look at the
relationship between volatility surprises captured by different time windows and
unconventional monetary tools (Table 4). In detail, we regress volatility surprises
captured by different time windows on the dummy variables of announcements
related to LSAPs and forward guidance. The dummies of unconventional policy
tools are based on narratives in FOMC statements. To retain consistency with the
literature, we adopt identical narratives as Swanson (2017). Because almost all
FOMC announcements since the ZLB period contain sentences regarding forward
guidance, we only mark those announcements that change the communication
styles in the forward guidance dummy, for instance, the switch from a calendar
threshold to an outcome-based threshold. Since the Federal Reserve primarily
implements those unconventional tools during the ZLB period, we truncate the
20
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Table 3: Event study of quantitative easing and forward guidance
Dates Policy actions VOL mpu
∆LASP
direction
∆FG
Language
Description
2008/11/25 QE1 0.81 -3.33 Y
The Fed began buying $600 billion in mortgage-backed securities and $100
billion in other debt.
2008/12/16 QE1/FG -0.78 -4.33
ZLB is reached and the Fed introduce clear forward guidance phrase: excep-
tionally low levels of the federal funds rate for some time.”
2009/0 3/18 QE1/FG 1.44 -2.67 Y
Change in language about low rates to ”for an extended period” from previous
statement which said ”for some time”
2010/11/03 QE2 -1.66 -1.00
the Fed announced it would buy $600 billion of Treasury bills, bonds, and
notes by March 2011.
2011/08/09 FG 2.98 -4.67 Y
Introduction of calendar based forward guidance: ”exceptionally low levels
for the federal funds rate at least through mid-2013.”
2011/09/21 MEP -1.12 0.00
The Fed sold or redeemed a total of $667 billion of shorter-term Treasury
securities and used the proceeds to buy longer-term Treasury securities.
2012/01/25 FG -1.19 -0.67 The fed funds rate is likely to stay near zero ”at least through late 2014.”
2012/09/13 QE3/FG 0.03 -0.67 Hold the fund rate near zero ”at least through mid-2015”.
2012/12/12 FG 0.15 0.00 Y
Adopt outcome-based threshold on employment and projected inflation be-
tween and two years ahead.
2013/06/19 Taper Tantrum 1.21 0.33 Y
the Fed’s announcement of future tapering of its policy of quantitative easing.
2014/12/17 FG -0.98 -0.33
The Fed replaces the ”considerable time” language with a vow to be ”patient”
in raising interest rates.
2015/03/18 FG 0.03 -1.33
The FOMC replaces the indication that ”it can be patient” with the indication
that an increase in the target range ”remains unlikely at the April FOMC
meeting”.
Std. Dev (full sample) 1 1
Note: VOL is the volatility surprise and mpu is the market-based monetary policy uncertainty proposed by Lakdawala et al. (2019).
Both event-study series are normalized to unit standard error.
The fifth column marks the initiation and the taper tantrum of large-scale asset purchases. The sixth column marks changes in forward guidance languages.
21
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Table 4:
Comparison of the time windows for volatility surprises (Event study)
VOL 1D 2D 3D 4D 5D
FG 27.07 54.644 68.64∗∗ 73.92∗∗ 73.92∗∗
(22.40) (37.30) (34.06) (34.17) (34.17)
LASP −68.66∗∗∗
−72.66∗∗∗
−74.98∗∗∗
−71.46∗∗∗
−71.46∗∗∗
(16.60) (22.76) (22.16) (22.27) (22.27)
Obs. 88 88 88 88 88
R2-0.228 0.061 0.100 0.112 0.107
*p < 0.05, ** p < 0.01, *** p < 0.001
Note: HAC Robust standard errors in parentheses
sample to that period.
Table 4 shows the superiority of the four-day time window, as volatility
surprises captured by this window has the highest correlation with announcements
of unconventional monetary policy tools than those measured in other time
windows. It confirms our hypothesis that the pre-FOMC-announcement drift in
the volatility are mostly consisted of noise, rather than the informational effect
of monetary policy.
3.4 Volatility Surprise and Term Premium
How does the volatility surprise, a second-moment measure, affect a long-term
interest rate? Based on a simple model and some empirical evidence, we verify the
conjecture in Woodford (2012) that ”term premia are affected by expectations
about the short-rate process (in particular, the degree of uncertainty about
future short rates)”. This subsection lays the foundation for our identification
strategy – utilizing the volatility surprise to identify the policy-induced exogenous
movement in a long-term interest rate.
Similar to Bundick et al. (2017) stylized model, the representative household
chooses
Ct+s
and
b(n)
t+s+1
for all bond maturities nand all future periods sby
22
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solving the problem:
maxEt
∞
X
s=0
βslog(Ct+s) (14)
subject to the intertemporal household budget constraint in each period,
Ct+
N
X
n=1
p(n)
t
b(n)
t+1
Pt
≤et+
N
X
n=1
p(n−1)
t
b(n)
t
Pt
(15)
The first order conditions are derived as
1
Ct
=λt(16)
p(1)
t=Et{βλt+1
λt
Pt
Pt+1
}(17)
p(n)
t=Et{βλt+1
λt
Pt
Pt+1
p(n−1)
t+1 }(18)
Prices are fixed
Pt
=
P
, for simplicity and model tractability. The price of a
n-period bond at time tis given by:
p(n)
t=Et{mt+1p(n−1)
t+1 }(19)
where the stochastic discount factor
Etmt+1 =Et{βλt+1
λt
}
After methmetical substitution and manipulation, the bond price and risk-
neutral bond price are:
log(p(n)
t) = −[Et
n−1
X
i=0
rt+i+1
2V ARt
n−1
X
i=0
rt+i−COVtct+n
n−1
X
i=0
rt+i] (20)
log(q(n)
t) = −[Et
n−1
X
i=0
rt+i−1
2V ARt
n−1
X
i=0
rt+i] (21)
23
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where
rt+i
and
ct+n
are the logarithms of gross interest rate and consumption.
The second moment of expected future short rates represents the compounded
loss due to fluctuations in the expected short rate path.
So how the volatiltiy surprise affects the term premium? As shown in
Equation (22), the term primium is equal to the difference between the bond
yield and the yield of its risk-neutral counterpart. When
n
increases,
ct+n
approaches permanent income, which is unlikely to vary with the path of rates.
Therefore, the covariance term COVtct+nPn−1
i=0 rt+ishould be small.
T P (n)
t=−1
n(p(n)
t−q(n)
t) = 1
n[V ARt
n−1
X
i=0
rt+i−COVtct+n
n−1
X
i=0
rt+i] (22)
Based on the expression of bond price in Equation (20), variance of the price
of a n-period bond at time t is calculated as follow if we retain the first and
second moments.
V ARt(p(n)
t) = Et(p(n)
t)2−(Etp(n)
t)2
=V ARt
n−1
X
i=0
rt+i(23)
Note that the uncertainty of the interest rate path dominates the variation
in bond price. Combining Equations (22) and (23), the volatility surprise, which
measures the impact of FOMC announcements on the volatility of the long-term
bond price, should have direct influence on the term premium of long-term
interest rates. The empirical evidence supports this argument.
We evaluate that to what extend the term premium reacts to the volatility
surprise (shown in Table 5). The accumulated daily changes within the 30 days
after a FOMC announcement is of our concern. To control for the influence of
policy rate targeting and forward guidance, we include first differences of the
spot month and three month federal funds future rates in the regression. We
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Table 5:
Impact of the volatility surprise on term premiums (Event study,
Daily)
∆MT Pi=α+βV OLi+γ1∆MFFRi+γ2∆MFFRi+2 +ei
i denotes the ith FOMC announcement since 2003:01. ∆MFFRi+2 represent 30-day
changes in the three-month (approx. two scheduled meetings) ahead funds futures.
∆MACM Term Premium
5 year 10 year
∆MMP1 −0.47∗∗∗
−0.48∗∗∗
−0.50∗∗∗
−0.51∗∗
−0.54∗∗∗
−0.57∗∗
[-3.62] [-4.23] [-3.98] [-2.26] [-2.76] [-2.50]
∆MFF4 0.11 0.15 0.17 -0.07 -0.01 0.02
[0.95] [1.35] [1.49] [-0.35] [-0.04] [0.10]
VOL 0.08∗∗ 0.15∗∗
[2.46] [2.49]
VOL 1d 0.08 0.12
[1.21] [1.04]
R2 0.178 0.240 0.207 0.155 0.233 0.181
∆MKW Term Premium
5 year 10 year
∆MMP1 −0.53∗∗∗
−0.53∗∗∗
−0.54∗∗∗
−0.67∗∗∗
−0.69∗∗∗
−0.74∗∗∗
[-6.75] [-7.09] [-6.77] [-5.38] [-6.27] [- 6.39]
∆MFF4 0.48∗∗∗ 0.50∗∗∗ 0.51∗∗∗ 0.52∗∗∗ 0.56∗∗∗ 0.62∗∗∗
[6.88] [6.82] [6.34] [4.75] [5.33] [5.56]
VOL 0.05∗∗ 0.10∗∗∗
[2.06] [2.78]
VOL 1d 0.04 0.14∗∗∗
[1.06] [3.35]
R20.216 0.252 0.230 0.166 0.241 0.242
Note: Robust t-statistics in parentheses.
ACM and KM term premium are respectively estimated according to Adrian et al.
(2013) and Kim and Wright (2005).
∆
M
indicates the 30-day change after event announcements. MP1 and FF4 are spot
month and three month ahead federal funds futures.
VOL (or VOL 1d) is the volatility surprise captured by the four-day (or one-day) time
window.
Sample excludes the period from July 2007 to June 2009 containing the Global Financial
Crisis.(Bauer et al., 2019)
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consider two estimates of the term premium and two long-term maturities to
show the robustness.
Three points in Table 5 worth noting. First, adding the volatility surprise
to the regression improves the explanatory power (
R2
). Second, the volatility
surprise captured by the four-day window demonstrates more significant impact
on the term premium than that captured by the one-day window, with the
only exception that the Kim and Wright (2005) term premium of the ten-year
Treasury is considered. Lastly, the information content in the volatility surprise
is irreplaceable by measures of policy rate changes or forward guidance.
In conclusion, the volatility surprise is constructed based on real-time and
high-frequency financial data. It shows relevance to monetary policy actions and
exerts influence to the term premia of longer-term rates. We will utilize those
properties of the volatility surprise to identify monetary policy shocks in the
risk-taking channel.
4 Data in the SVAR Model
Our sample ranges from January 2003 to January 2020. It includes 158 FOMC
meetings, both scheduled and unscheduled. The sample covers the entire ZLB
period as well as two periods at the beginning and the end with the normalized
federal funds rate.
In the SVAR model, we include four endogenous variables, such as the PCE
chain-type price index, the industrial production, a monetary policy indicator,
and a measure of financial frictions.
The PCE chain-type price index is a measure of final good prices of all
domestic personal consumption
4
. The Federal Reserve emphasizes its role in
4
A detailed comparison between CPI and PCE price index is provided by McCully, C. P., et
26
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measuring price inflation as it ”covers a wide range of household spending”
5
. The
industrial production is a sensitive indicator of real production activities, and
is released in monthly frequency. We follow the practice of Gertler and Karadi
(2015) and use the excess bond premium (Gilchrist and Zakrajˇsek, 2012) as a
measure of financial frictions. The excess bond premium captures the difference
in yields between the corporate and Treasury bonds with identical maturities
after statistically purging the impact of firm-specific indicators of default and
bond characteristics. Empirically, it is a viable indicator of the credit market
sentiment and the degree of financial friction in financial markets.
The policy indicator that we select is a long-term real interest rate, i.e., the
10-year Treasury inflation-protected securities (TIPS) yield. Hanson and Stein
(2015) and Nakamura and Steinsson (2018) suggest that TIPS yields reflect
virtually all the responses of nominal interest rates to monetary policy surprises
on FOMC dates. Furthermore, a real yield is theoretically connected with the
real activities and the policy transmission to the real economy.
We generate two event-study monetary policy surprises as the policy instru-
ments. The first monetary policy surprise, the policy rate surprise, is used in
G¨urkaynak et al. (2005) and Gertler and Karadi (2015). It captures changes in
the three month Federal Funds futures (FF4) on FOMC announcement days.
Fluctuation of Fed Funds futures, as they claim, captures impacts produced
by policy rate changes and forward guidance. It is a common practice that
assesses exogenous monetary policy actions in light of the Taylor rule. The
other monetary policy surprise that we innovate for the risk-taking channel
is the volatility surprise. We generate the volatility surprise by capturing the
unexpected change of near-term expectation in long-term rate volatility (i.e.,
al. (2007). ”Comparing the consumer price index and the personal consumption expenditures
price index.” Survey of Current Business 87(11): 2633.
5
See the official website of the Federal Reserve: https://www.federalreserve.gov/faqs/economy
14419.htm
27
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the TYVIXBP index) around each FOMC meeting announcement. We select
the interest rate volatility of 10-year Treasury yield in order to match with the
maturity of our policy indicator. Both surprises are converted into monthly
time series to fit into the monthly SVAR model. The conversion procedure is
summarized in Appendix B.
When considering the volatility surprise as the policy instrument, we are not
intended to presume that the Federal Reserve attempts to control or manipulate
the expected volatility of an interest rate. Instead, we strive to recognize the
fact that the Federal Reserve’s unconventional policy tools and innovations in
communication may contribute to the exogenous impact of monetary policy on
financial markets. In the SVAR model, the communication and other unintended
consequences of FOMC announcements may have an impact on the real economy
that originates from the monetary authority. This impact may thus constitute
a portion of exogenous monetary policy shocks to the SVAR system. The two
monetary policy surprises demonstrate two distinctive and orthogonal dimensions
of the impact of monetary policy announcements, such as its influence on
short rate level versus its influence on long rate volatility. The policy rate
surprise narrow focus to changes in the policy rate, while the volatility surprise
comprehensively evaluates monetary policy announcements in terms of its impact
on the risk perception. We simulate monetary policy shocks with the policy
rate surprise in the the interest rate channel, which is characterized by a Taylor
rule type of monetary policy reaction function. The risk-taking channel instead
accepts a broader definition of monetary policy and emphasizes the influence on
interest rate volatility. Therefore, the volatility surprise is ideal for motivating
the monetary policy shocks in the risk-taking channel so that we can investigate
the risk-side of monetary policy transmission.
28
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4.1 First-stage regression and the relevance of external
instruments
A common issue of the estimations with instrumental variables is the weak instru-
ment. If the covariance between an endogenous regressor and its instrumental
variable is low, the IV estimator is severely biased toward the OLS estimator. In
this case, the instrumental variable is considered as a weak instrument. We adopt
Stock and Yogo (2005) criteria (an F-statistics larger than 10) to determine
the relevance of instrumental variables. In various specifications, the policy
indicator is either the one-year Treasury yield or 10-year TIPS yield. And the
policy instrument is either the volatility surprise or policy rate surprise. In the
first-stage regression, we regress the reduced form VAR residual of either policy
indicator on each monetary policy surprise. Table 6 shows the results. The
F-statistic is computed with heteroskedasticity and autocorrelation consistent
(HAC) standard deviation.
Table 6: Results of the first-stage regression (Monthly)
Channels Risk-taking Interest-rate Credit
Policy Indicator 10Y TIPS(1) 10Y TIPS(1) 1Y 1Y
VOL 0.077∗∗∗ 0.019∗
(0.014) (0.011)
PRATE 1.425∗∗∗ 0.659∗∗∗
(0.299) (0.169)
Obs. 203 203 203 203
Robust F-Stat. 26.97 22.73 15.3 3.04
Note: *
p <
0
.
05, **
p <
0
.
01, ***
p <
0
.
001. Robust standard errors in
parentheses.
The dependent variable is the reduced form VAR residual of the policy
indicator specified in the second row. VOL and PRATE are the volatility
surprise and policy rate surprise converted into monthly time series.
In models similar to Gertler and Karadi (2015), which consider the one-year
Treasury yield as the policy indicator, the coefficient of policy rate surprise is
highly significant. This indicates that unexpected policy rate changes constitute
29
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a strong instrumental variable for the monetary policy as projected by short-term
rates. In contrast, the volatility surprise is barely correlated with shifts in the
short-term rate. As to the timing, the reactions of the one-year yield to both
monetary policy surprises are instantaneous.
When considering the 10-year real rate as the policy indicator, the volatility
surprise and policy rate surprise are both strong instruments with higher than 10
F-statistics. the volatility surprise is more significant as an instrumental variable
for the long-term real rate than the policy rate surprise is. The explanation power
is higher as well. This evidence reveals the difficulty of utilizing variation in the
funds rate or other short-term rates to explain the more volatile fluctuations in
long-term rates.
However, the strong correlation only exists between the lagged VAR residual
of 10-year TIPS yield and the two monetary policy surprises. Our evidence in
Table 7 and 8 suggest that this mismatch may be because these monetary policy
surprises have a more persistent impact on the long-term real rate than what
they do on the short-term rate. This lagged matching can also be attributed to
the conversion of monetary policy surprises from daily to monthly time series,
a process that unavoidably extend the persistence of surprises. Matching the
lagged residual of policy indicator with current monetary policy surprises may
better reconcile monetary policy actions with reactions of financial markets.
One concern about the non-contemporaneous matching is that historical
values of the policy indicator seem predictive for volatility surprises. Thus,
identified monetary policy shocks might reflect a systematic component of the
impact of monetary policy. However, we find no evidence to support this
argument in the daily date analysis and Granger causality test.
Table 7 shows that volatility surprises do not predict 10-year TIPS yield
movements within one week before 4-day time windows. In contrast, volatility
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surprises motivate significant fluctuations in long-term TIPS yield and the impact
is relatively persistent.
Table 7:
Real yield effects of volatility surprises (Event study, Daily, 2003-2020)
Week 1-w before 1-week 2-week
Maturity 10Y 2Y 5Y 10Y 2Y 5Y 10Y
VOL -1.231 0.051 0.043∗∗ 0.041∗∗∗ 0.137∗∗∗ 0.074∗∗∗ 0.057∗∗∗
[-0.882] [1.448] [1.898] [2.717] [2.068] [2.630] [2.308]
R2 0.014 0.066 0.088 0.116 0.156 0.133 0.112
Note: * p < 0.05, ** p < 0.01, *** p < 0.001. Robust t-statistic in parentheses.
Cumulative changes of Treasury real yields in the weeks before announcements as well as
those changes in one week (or two weeks) after announcements.
The standard deviation of volatility surprise is normalized to 1.
The volatility surprise is the dependent variable in the second colume, while it is the
explaining variable for the remaining columns.
Table 8 exhibits the Granger causality between volatility surprises and the
reduced-form VAR residual in the policy indicator equation at monthly frequency.
Importantly, we pair volatility surprises with contemporaneous policy indicator
residuals. It is shown that the monetary-policy-induced volatility surprise
can help in predicting innovations in the 10-year TIPS yield but historical and
current innovations in this yield render limited explanatory power to the volatility
surprise. The result strongly supports the unidirectional impact of volatility
surprises on policy indicator residuals.
Table 8: Pairwise Granger causality test (Monthly)
Null Hypothesis Obs. F-statistic Prob.
VOL does not GC Policy Indicator Residual 200 6.001 0.001
Policy Indicator Residual does not GC VOL 0.308 0.820
The VAR model used to generate the policy indicator residual includes four
variables, such as industrial production, the PCE price index, the 10-year TIPS
yield (policy indicator) and the excess bond premium.
Three lags are included in the test. VAR residuals of the policy indicator are
contemporaneous with volatility surprises.
Consequently, we attribute the mismatching to the conversion procedure from
daily to monthly times series and the persistent impact of volatility surprises on
31
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the long-term real yield.
In summary, we construct a four-variable SVAR model with a financial variable
that measures financial frictions. Departing from the literature’s stylized short-
term rates, we adopt a long-term real rate to indicate the monetary policy
impact on the whole yield curve. To properly identify the monetary policy
shocks in the risk-taking channel, we generate a new high-frequency, event-study
measure of perceived risk in long-term rates. Thus, we can analyze how monetary
policy influence the economy through the risk perception in the financial sector.
In adherence with the literature, we retain the policy rate surprise that is
theoretically consistent with the discretionary policy actions under a Taylor rule.
In the next section, we correspond the two policy instruments with two monetary
policy transmission channels and evaluate their effects on the economy.
5 Empirical Results
This section present the impulse responses of economic variables to monetary
policy shocks respectively identified in the interest rate channel and the risk-
taking channel.
5.1 Transmission in the interest rate channel
The Keynesian-type interest rate channel is the textbook view of the monetary
policy transmission mechanism in which long-term rates play a role.
This channel may be partitioned into two stages of propagation, such as the
transmissions to the yield curve and to the economy. The former, in general,
characterizes three suppositions. First, the monetary policy is measured by
changes in the policy rate. Second, changes in short-term rates pass through
to long-term rates given to expectations theory of the term structure. Third,
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nominal and real rates move synchronously due to the sticky price setting
in Keynesian-type models. Statistically, we test the validity of those three
hypotheses jointly by observing whether policy rate surprises can stimulate
fluctuations in a long-term real rate.
In terms of the transmission to economic activities, the interest rate channel
works through a cost-of-capital effect typically discussed as the neoclassical theory
of investment. Accordingly, changes in the cost of capital affect real activities
through their impact on consumption of durable goods and fixed investment.
To examine the monetary transmission in the interest rate channel, we
consider the 10-year TIPS yield as the policy indicator and adopt the policy rate
surprise to identify monetary policy shocks.
In the first stage regression, if the transmission to the yield curve is valid,
the coefficient in the first stage regression should be positive and statistically
significant, which is confirmed by our results in Table 6. Furthermore, the
F-statistics is significantly higher than 10. In the second stage, we estimate the
mapping vector between the monetary policy shocks and reduced form residuals
of endogenous variables under the restriction that monetary policy affects long-
term rates primarily through unexpected variation in the policy rate (i.e., the
policy rate surprise).
Figure 5 plots impulse responses of endogenous variables to the monetary
policy shocks identified in the interest rate channel. In comparison, we also
show the impulse responses from the conventional Cholesky identification scheme
in the right column. Both columns show impulse responses to a one standard
deviation structural monetary policy shock. In the right column, the reactions
in the VAR model with the conventional Cholesky identification are insignificant
for all variables. In the left column, monetary policy shocks are identified as the
systematic movements of a long-term real rate in responses to unexpected policy
33
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Figure 5:
The impulse responses to the monetary policy shocks identified in
the interest rate channel
rate changes on FOMC announcement dates. Influenced by a contractionary
policy shock, the price level gradually slides for roughly eight months and remains
at a low level for an extended period. The reaction of output is silent to this
shock and the confidence band is wide. The muted response in production
provides opposing evidence to the cost-of-capital effect and implies the failure
of the interest rate channel in transmitting to the economy. Furthermore, the
typically countercyclical excess bond premium reacts ,but only mildly, to the
shock.
34
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5.2 Transmission in the risk-taking channel
Risk is a critical factor for asset pricing in finance studies, but it is less explored
at the aggregate level, especially in the studies of monetary policy transmission
(related work includes Bekaert et al. (2013), Baker et al. (2016), Husted et al.
(2020)). Borio and Zhu (2012) first shed light on the role of risk percieved by
financial markets in monetary policy transmission and officially propose the
risk-taking channel. Specifically, the monetary policy may affect risk perceptions
or risk tolerance of financial intermediaries and then have a first-order impact
on economic activity. This paper is the first empirical attempt to identify the
monetary policy shocks through influence of monetary policy on the aggregate
risk perception in bond markets, which monetary policy primarily exert impact
on.
We consider the 10-year TIPS yield to indicate the monetary policy actions
and the volatility surprise to instrument the identification of monetary policy
shocks. The volatility surprise incorporates the impact of all the components of
monetary policy, notably including effects of unconventional monetary policy
tools. Monetary policy shocks in the risk-taking channel are identified as variation
in a long-term real rate driven by monetary-policy-induced changes in perceived
fluctuations of monetary policy shocks in the long run. For instance, if financial
markets expect less volatility of monetary policy shocks in the future ten years due
to an FOMC announcement, we consider this monetary policy as expansionary.
The Figure 6 shows the impulse responses to monetary policy shocks identified
in the risk-taking channel. A one-standard-deviation contractionary monetary
policy shock leads to a significant and persistent drop in price level, a similar
result as the “interest rate channel” SVAR model. What interests us is the strong
reactions of the excess bond premium and output. Under a tightening shock
transmitting through the perceived risk, the credit environment immediately
35
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Figure 6:
The impulse responses to monetary policy shocks identified in risk-
taking channel
aggravates, and excess credit costs hike up for ten basis point for approximately a
year. The same shock also leads to 50 basis point decline in output. Additionally,
we observe close interaction between financial frictions and industrial production.
The trough of production coincides with the time point as the soaring excess
bond premium recovers from the peak.
The impulse responses of aggregate variables suggest the viability of the
risk-taking channel. FOMC statements somehow influence the expected volatility
of future interest rate path in the long run. This aspect of monetary policy
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shows strong implication for long-term real rates, financial frictions, and real
activity.
6 Discussion
In this section, we compare the empirical results among those three monetary
transmission channels and provide preliminary explanations based on existing
findings in the literature.
6.1 Quiescent financial markets and illusive cost-of-capital
effect
When considering a long-term rate as a node of monetary policy transmission,
the linkage between the policy rate and long-term rates seems marginally drive
economic activity. We delve into the literature in search of theoretical or
institutional clues for the muted responses of the excess bond premium and real
output in the interest rate channel model.
The reaction of real output is consistent with Blinder and Maccini (1991),
Chirinko (1993), among others, which find the difficulty in identifying a quanti-
tatively significant effect of the cost-of-capital variable in ”interest-rate sensitive”
components of aggregate spending.
Whereas, due to the multidimensionality of monetary policy, it should be
premature to conclude the disfunction of monetary policy. The FOMC statements
may include some components of monetary policy other than the policy rate
targeting that influence both long-term rates and economic activity. As a
complement, by identifying the risk-taking channel via the volatility surprise, we
suggest a more comprehensive identification strategy of monetary policy shocks.
The unresponsiveness of the excess bond premium may attribute to two
37
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explanations, respectively center around the two components of a long-term
yield, such as the expected path of future short-term rates and the term premium.
One possible avenue is that financial intermediaries may passively adjust
their expectations in future short-term rates and their baseline long-term lending
rates when encountering exogenous policy rate changes. That is to say a policy
rate movement may be unexpected, but the adjustment of long-term real rates
to a policy rate change could be systematic. An increase in the banks’ cost of
capital due to a policy rate change may thus pass through to borrowers. In a
competitive market, a bank may have no incentive to augment excess credit
premium on baseline long-term rates as long as the information of the expected
path of future short rates is publicly available in financial markets. In fact,
the Federal Reserve periodically releases the estimated expected yield and term
premium data of Treasury bonds with a full spectrum of maturities based on
approaches of Kim and Wright (2005) and Adrian et al. (2013). This information
offers limited arbitrage space for a bank to implement a heterogeneous premium
on baseline rates from other banks.
Another potential explanation is a story of yield-searching investors proposed
by Hanson and Stein (2015), among others. This story aims to justify their
finding that unexpected policy rate changes are highly associated with significant
changes in term premia on distant real forward rates. This short-lived variation
in term premia due to demand shocks in the bond market is well observed not
only by empirical research but also in the institutional behaviors of commercial
banks (Stein, 1989). The response of the excess bond premium in the interest
rate channel indicates that these demand shocks in financial tradings may be too
trivial and transitory to affect banks’ lending decisions and the credit premium.
In combination, the muted reaction of the excess bond premium may be justified
from the perspectives of interest rate pass-through and short-lived drifts in term
38
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premia. However, our results may be insufficient to distinguish between those
explanations.
Lastly, the flat impulse responses of financial frictions and output to policy
shocks in the interest rate channel motive us to explore the content of monetary
policy beyond policy rate changes.
6.2 Comprehensive identification and role of credit supply
We notice that systematic changes of a long-term rate responding to policy rate
decisions do not trigger sways of the excess bond premium and output. Whereas,
changes in the long-term real rate caused by shifts in perceived interest rate risk
do.
The synchronization of the responses of excess bond premium and real output
corroborate financial accelerator models first proposed by Bernanke et al. (1999).
They feature amplifier effects of credit market frictions on monetary policy
transmission. Their claim is in accordance with our results. The increase in
excess credit costs demonstrates the aggravation in information asymmetry
and the increase of agency costs in the credit generating process, leading to
widespread real effects. Meanwhile, our evidence opposes the Modigliani and
Miller (1958) Theorem, which implies that financial structure is irrelevant to
real economic outcomes.
The Fed’s private information may also play a role in the transmission.
Campbell et al. (2012) and Nakamura and Steinsson (2018) demonstrate that
market participants may update their expectations about economic fundamentals
in response to Federal Reserve’s announcements. The Federal Reserve also
signals information about the state of the economy to the public (Romer and
Romer, 2000; Melosi, 2016). These effects may be sourced from the private
information held by the Federal Reserve and exogenous to financial markets. In
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order to evaluate the exogenous impact of entire information content in FOMC
announcements, we do not specially tease out these effects in the volatility
surprise and instead incorporate them in the monetary policy shock identification.
Therefore, facing a policy shock stimulated by a volatility surprise, financial
intermediaries’ update of economic prospects may influence their perception
in future monetary policy actions. Thus lead to variation in the excess bond
premium.
Furthermore, we shed light on the monetary policy impact on the supply of
long-term capital than the demand. The cost-of-capital effect focuses on the
demand side in credit markets and seems pale in explaining how monetary policy
pull out the economy from mud of recessions. The risk-taking channel shift our
attention to the supply side of long-term capital. Financial intermediaries may
keep an eye on the uncertainty of future monetary policy path. An unexpected
soar of the volatility may aggravate information asymmetry, boost monitor costs
of borrowers’ balance sheets, and require additional loss provision for future
deterioration. These real costs may render banks with incentives to charge an
excess credit premium and, more likely, to reduce risk-taking lending behaviors.
Our finding call for further exploration and theoretical development related to
the banks’ reaction to second-moment movements in interest rates.
7 Conclusion
Monetary policy is multi-dimensional, and it contains more information than what
may be explicit by policy rate movements. The introduction of unconventional
monetary policy tools shifts our attention to policy influences in longer-term
interest rates. To incorporate the entire policy impact on the whole yield curve,
we introduce a long-term interest rate as the policy indicator into an otherwise
standard monetary SVAR. In order to distinguish monetary policy shocks from
40
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endogenous long-term rate fluctuations, we consider an instrumental variable
identification strategy. Our innovation is to construct an event-study monetary
policy surprise from the variation of interest rate volatility around each FOMC
announcement and utilize it as an external instrument for identification.
We estimate an empirical SVAR model to evaluate the validity of the conven-
tional Keynesian interest rate channel and the less-explored risk-taking channel
within a single framework.
We gather evidences that the interest rate volatility is a critical ingredient in
identifying monetary policy shocks from movements in the long-term real interest
rate. While the transmission through the conventional Keynesian interest rate
channel is insignificant, we empirically witness the transmission through the
risk-taking channel.
Admittedly, our analysis does not constitute a call for a different new instru-
ment of monetary policy, especially given the difficulty of accurately targeting
the public’s perception of interest rate volatility. Instead, we provide a tool for
market participants including the Fed to analyze the potential impact of policy
on long-term rates from a bank’s risk-taking channel perspective. This paper
underscores the need for further exploration on the role that long-term interest
rates and their volatility play in the transmission mechanism of monetary policy.
41
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A Algorithm for Identification
Considering partitioning the mapping matrix between reduced-form residuals and
structural shocks as
S=s Sq=


s11 s12
s21 s22


(24)
and the reduced-form variance-covariance matrix as
Σ = 


Σ11 Σ12
Σ21 Σ22


(25)
Since structural shocks are normalized,
E
[
utu0
t
] =
E
[
SS0
] = Σ and Σ is symmetric.
Therefore,
Σ21 −
s21
s11Σ110Σ21 −
s21
s11Σ11=s12 Qs0
12 (26)
with
Q=s21
s11Σ11 s21
s110
−Σ21 s21
s110
+s21
s11Σ0
21+ Σ22 (27)
The contemporaneous response of the policy indicator to a unit increase of monetary
policy shocks spis derived from the underlying closed form solution.
(sp)2=s2
11 = Σ11 −s12s0
12,(28)
where the portion of reduced-form variance of the policy indicator attributed to other
structural shocks
s12s0
12 =Σ21 −
s21
s11Σ110
Q−1Σ21 −
s21
s11Σ11(29)
With the estimated
s21
s11
in the second-stage regression and Σ in reduced form VAR,
we obtain the estimate of s vector.
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B Conversion of the Event-study Series to Monthly
Time Series
Most macro-economic variables are measured in monthly or lower frequencies. In
order to infer with macroeconomic variables in our monthly SVAR model, we convert
the event-study time series into a monthly series in three steps. First, we arrange
all event-study volatility surprises on a daily time axis according to their respective
announcement dates. As the TYVIX index measures the 30-day implied volatility of
the long rate, a volatility surprise shows the difference of investors’ expectation of long
rate volatility measured for the future 30 days due to an FOMC announcement. Thus,
we set the impact horizon of a volatility surprise as 30 days to match the time length
of the expectation. Second, in case of the 30-day impacts of two volatility surprises
partially overlapped, we integrate the two surprises based on their respective FOMC
announcement dates and sum up the overlapped portion. This circumstance may incurs
between an unscheduled and a scheduled FOMC meetings, or between two unscheduled
meetings. Third, we add up the impacts of volatility surprises on each day of a month
and divide the sum with number of days in a month (i.e. 30 days).
Figure 7: The volatility surprise (monthly & event study)
Overall, the monthly volatility surprise retains the features of the event-study
time series, such as the timing of peaks and troughs, the mean reverting property,
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etc. However, in monthly series, we notice that one positive spike on October 2008,
which amounts to more than 8 times of sample standard deviation, is more prominent
than its counterpart in event-study series. As shown in Figure 7, we truncate the
data on October 2008 to the same level as that on September 2008 to diminish the
distortion. The distinctive spike is due to the different ways of recording volatility
surprise impacts in the two series. Near the October 2008, two emergent unscheduled
FOMC meetings were held on September 29th and October 7th. Both meetings induce
large positive volatility surprises, indicating the policy actions announced after those
meetings aggravate the long-term perceived risk in interest rates. Those meetings are
less-than-30-day apart. In the event-study series, the impacts of those meetings are
parallelly registered on their respective dates and do not intervene with each other.
In contrast, the monthly time series lengthen the impacts of volatility surprises to
30 days and adds up the overlapped impacts of two meetings with less than 30-day
interval. Therefore, if two or more FOMC meetings are closely adjoined and generate
volatility surprises in an identical sign, the monthly time series may be distorted by
the resulting extremely large spike. This phenomenon is prominent in October 2008
and a truncation is applied to restore the distortion.
Admittedly, this conversion approach may fall short in identifying the timing of
events. For example, if an FOMC announcement is made at the end of month t. In
event-study time series, this volatility surprise is in the month t. However, in monthly
conversion, since the 30 days after the meeting majorly locate in month
t
+ 1, the
principle volatility surprise is recorded in month
t
+ 1, rather than in the month when
it actually happens. This shortcoming partially explains why the monthly volatility
surprise matches better with the lagged VAR residual of the policy indicator.
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C Institutional Explanation for the Four-day Win-
dow
We further investigate the institutional mechanism of this pre-FOMC-event drift in
the volatility that roughly starts from 4 days prior to an FOMC announcement. We
find its association with the timing of an FOMC announcement in a week. In Table
9, we list the weekday distribution of FOMC announcement dates. In the whole
sample from 2003 to 2018, the majority of FOMC decisions (92%) are announced on
Tuesday, Wednesday, and Thursday. Four days before those weekdays are respectively
Friday, Saturday and Sunday. As weekends are non-trading days for major exchanges,
the data on Saturdays and Sundays are identical with closing quotes on the nearest
precedent Fridays. Therefore, the TYVIX data in four days before the 93% of FOMC
announcements points to closing quotes on Fridays in preceding weeks. In other words,
the 4-day time window essentially takes the difference of the ending quote on Friday
preceding one announcement and the ending quote on the announcement date.
Table 9: Weekday Convention of FOMC Announcements
Mon Tue Wed thu Fri, Sat, Sun Total
Sample Counts 5 40 97 11 5 158
Percent 3% 25% 61% 7% 4% 100%
However, why do Fridays before announcement weeks become turning points of
the TYVIX index? Chordia et al. (2001) among others investigate weekday effects
of trading activities and indicate that Fridays often feature a significant decrease in
trading volume and liquidity. Chen and Singal (2003) and Jones and Shemesh (2010)
address a “Friday effect” with the reduction in demand and price of call and put
options due to the downside risk of holding securities during weekends. The TYVIX
index is calculated with the Treasury note options prices via Black-Sholes non-arbitrage
formula. Therefore, decline in demand for call and put options leads to a lower figure
of the TYVIX index on Fridays.
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For our purpose, we attempt to capture the exogenous impact of monetary policy
rather than the effects of upcoming FOMC meetings. Therefore, we strive to mini-
mize the noise introduced by the event-driven, pre-FOMC-announcement drift. The
utilization of this Friday effect facilitates this practice.
In detail, the trading positions of options established after a weekend are more or
less related to two types of short-term trading activities. First is the short-term hedge
for the interest rate volatility caused by an FOMC event. An approaching FOMC
meeting<