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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.

Electronic copy available at: https://ssrn.com/abstract=3462101

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=St(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+sp

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[Ztp

t

0]6= 0 (6)

E[Ztq

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.

17

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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

24

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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)

25

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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

30

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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,

32

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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

36

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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

39

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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

s11Σ110Σ21 −

s21

s11Σ11=s12 Qs0

12 (26)

with

Q=s21

s11Σ11 s21

s110

−Σ21 s21

s110

+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

s11Σ110

Q−1Σ21 −

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.

52

Electronic copy available at: https://ssrn.com/abstract=3462101

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<