monetary policy shocks and security market responses

8/3/2019 Monetary Policy Shocks and Security Market Responses

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Monetary Policy Shocks and Security Market Responses

By

Roger Craine

University of California

Vance Martin

University of Melbourne

First Draft: June 2003

July 2004

Abstract:An old and unanswered question is: how does monetary policy work? This paper contributesto a growing recent literature that tries to quantify the first step of the process. These studies use daily datato estimate the response of security pricesbond yields and equity returnsto exogenous monetary policysurprises. We extend the literature in three directions: (1) theory: we specify a general factor model inwhich security prices respond to multiple sources of systematic riskmonetary policy surprises and othermarket wide information shocksand idiosyncratic risk. (2) Empirical: we use all of the daily data whileother studies use a small sub-sample of less than 10% of the data. And (3) econometric: we estimate avector model and impose the over-identifying restrictions.

Our empirical results show that efficiently estimating a more general model leads to economicallyimportant differences. Our results solve a puzzle and highlight an important neglected short-run channel ofmonetary policy. Cochrane and Piazzesi (2002), the latest of many, found that long maturity bond yieldsincrease in response to a surprise tightening in monetary policya result they properly label a puzzle. Ourresults eliminate the puzzle. The yield curve response to a monetary surprise displays the classical textbookpatternshort maturity yields rise and long maturity yields do nothing. Common information shocks,which most other studies omit, have a level effect on the yield curveall yields increase in response to apositive shock. We also find that the equity market, which is ignored in most studies and textbooks, isquantitatively the most important channel for monetary policy in the short run. The wealth effect from a

monetary surprise in the equity market dwarfs the wealth effect in debt markets.

JEL codes: E44, G12Keywords: Monetary policy, yield curve, stock market, factor model

Contact information: Craine, Economics 3880, University of California, Berkeley, CA USA 94720, email:[email protected]. Martin, Economics, University of Melbourne, Victoria Australia 3010, email:[email protected] thank John Cochrane, Ken Kuttner, Roberto Rigobon, and seminar participants at Berkeley andMelbourne for valuable comments.

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mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Introduction

Economists have attempted to quantify the effect of monetary policy for a long time without much success.

The task is to estimate the change in a policy target caused by the change in policy. It turns out that this is

very hard to do. At least three basic econometric problems plague the effort. First, the policy instrument

in recent years the Fed Funds Target Rateis endogenous. Second, economic variables respond to

anticipated as well as realized changes in monetary policy. And third, economic variables respond to

influences other than monetary policy changes. Figure 2.1 shows the yields on 10 year and 1 year Treasury

bonds and the Fed Funds Target Rate (from now on denoted as the Target). They move together, but with

no clear lead-lag relationship. Market rates respond to changes in the Target and other variables and

policymakers use information in long maturity yields as an indicator of inflationary expectations. Figure

2.2 shows the Target and the 30-day Eurodollar rate for 1999-2001. The Eurodollar rate frequently

anticipates Target changes, but other factors clearly influence the rate. Y2K fears abruptly increased the

Euro rate by % in December of 1999. The increase evaporated in January when the new millennium

arrived without the widely predicted and feared computer glitches.

This paper is part of a growing recent literature that tries to filter exogenous monetary policy surprises from

daily data. The literature uses the fact that monetary policy surprises are only realized on days that the

Federal Reserve changes the Federal Funds Target, or on days that the Federal Open Market Committee

(FOMC) meets and the market expects a change that does not happenso-called event days. On event

days security prices respond to FOMC decisions, but FOMC decisions do not depend on the current days

realizations of security prices. Daily data solve the policy endogeneity problem. Problems two and three

remain. Policy changes must be decomposed into anticipated and unanticipated components and effects of

policy and other influences sorted out. We extend the existing literature in three directions: (1) theory: we

specify a general factor model in which security prices respond to multiple sources of systematic risk

monetary policy surprises and other market wide information shocksand idiosyncratic risk. (2)

Empirical: we use all of the daily data while other studies use a small sub-sample of less than 10% of the

data. And (3) econometric: we estimate a vector model and impose the over-identifying restrictions. These

are the first estimates of an over-identified vector model for monetary surprises that we know of.

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Most of the literature relies on the event study specification. Event study models define the monetary policy

surprise as the change in a specific observable short maturity interest rate on the event day. The notion is

that the short rate reflects the anticipated Target rate, so changes in the short rate reveal the monetary policy

surprise. Cochrane and Piazzesi (2002) chose the change in the 30-day in the Eurodollar rate (see Figure

2.2 for visual support), and Bernanke and Kuttner (2003), Kuttner (2001), and Poole and Rasche (2000)

chose the change in the Federal Funds Futures market rate. The event studies specification implicitly

assumes that problem three, shocks other than monetary surprises, either dont occur on event days or that

they dont affect short maturity rates on event days. If the identification assumption is correct, then

regressing the change in a longer maturity yield or the equity return on the change in the short maturity

yield on event days gives a consistent estimate of the response to a monetary shock.

If, however, the assumption is wrong and other information shocks as well as the monetary policy surprise

affect short maturity rates, then the monetary policy surprise revealed by the change in the short rate is

measured with error. Table 2.1 shows that the standard deviation of the change in the Eurodollar rate is

50% larger on event days than nonevent days. Our factor model attributes roughly 60 to 70%, but not

100%, of the variance in the short rate to monetary shocks on event days. Figure 2.2 shows that other

factors, such as Y2K fears, led to large changes in the short rate.

Poole, Rasche and Thornton (2002) were the first to recognize explicitly that the change in a short maturity

interest rate on the event day measures the monetary policy shock with error. They used an errors in

variables model to estimate the response of yields to the monetary policy surprise on event days. Our factor

model generalizes their errors in variables specification and uses all the daily data.

Event study models can use only the data from event days. And event days are less than 5% of the trading

days since 1988. Rigobon and Sack (2002), in a paper that breaks the mold, specify a model that can use all

the data and includes a common information shock. They specify a bivariate simultaneous equation model

for the change in the short rate and a security price. In their specification the monetary policy shock enters

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through the change in a short yield (as in the event study models) and a common information shock (a very

important generalization) affects both securities. Their model is under-identified. They use the fact that the

monetary policy shock occurs only on event days to identify and estimate the security price response to a

monetary shock. They cannot recover any of the other model parameters. They use a paired sample of event

and nonevent daysonly about 10% of the data. Their identification of the structural parameter rests on the

bivariate specification. In a multivariate specification their procedure only reveals the vector of reduced-

form coefficients, or factor loadings, on the monetary policy shock.

We adopt the popular factor model specification from financial economics, e.g., see Bodie, Kane, and

Marcus, (2002), Chapter 10, or Cochrane (2001), Chapter 6. Security prices (yields and equity returns)

depend on systematic (nondiversifiable) sources of risk and idiosyncratic (diversifiable) sources of risk.

Monetary policy and other information shocks are the factors. We follow Rigobon and Sack and use the

fact the monetary shocks occur only on event days to identify the monetary surprise factor. Our model is

over-identified. We estimate the factor loadings on the monetary policy shocks and the common shocks.

We impose the over-identifying restrictions and use all of the daily data.

Our empirical results show that efficiently estimating a more general model leads to economically

important differences. We solve a long standing puzzle and highlight an important largely neglected short-

run channel of monetary policy. Cochrane and Piazzesi, the latest of many, find that long maturity yields

respond significantly to monetary policy surprises. They properly label this result as a puzzle. Romer and

Romer (2000) conjecture a surprise in the Feds policy action conveys new information to market

participants that causes them to revise their inflationary expectations. The factor model gives a simpler

solution to this puzzle. Our estimated yield curve response to monetary policy shocks fits the classic

textbook description. A Target surprise has a slope effect on yieldsshort maturity yields increase more

than intermediate maturity yields and the long maturity (10 year) yield does nothing in response to a

surprise. Common information shocks have a level effect on yields. Specifications that omit the common

shock find that monetary policy surprises affect the level of the yield curve. We also find that the equity

market, which is not considered as a short run channel of monetary policy in most textbooks or empirical

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studies, is the dominant channel of monetary policy. The equity market is four times as large as the debt

market and the response to a monetary surprise in equity markets is twice the response in debt markets. The

wealth effect in equity markets from a monetary surprise dominates the wealth effect in equity markets.

Bernanke and Kuttner, Guo (2003), and Rigobon and Sack also find large equity market responses to

monetary policy surprises. Bernanke and Kuttner present evidence that monetary surprises affect the equity

risk premium.

The paper is organized as follows: Section 1 presents the details of our factor model specification and

compares it with the other specifications. Section 2 shows the data. Section 3 presents estimates of the

bivariate and multivariate versions of the factor model and compares the results with our estimates of the

event study specification and Rigobon and Sacks specification.

Section 1: Models of Monetary Shocks

A Factor Model

We use a factor model of demeaned yields1, i andy, and the demeaned equity return, r. We distinguish the

shortest maturity yield, i, only because it makes it easier to compare the factor model to the event study and

Rigobon and Sacks model.

We assume that yields and the equity return respond to systematic sources of riskthe monetary policy

surprise, m, a market wide information shock2,s,--plus a security specific idiosyncratic shock, e,

t i t i t

t y t y t y

t r t r t r et

i m s

y m s

r m s e

yte

= +

= + +

= + +

(1.1)

The shocks are independently and identically distributed with zero means and unit variances. The shortest

maturity yield, i, has no idiosyncratic shock3.

1 Here to keep the notation simple we treat the yield vector,y, as a scalar. Generalization to a vector isstraightforward.2 In this section we treats as a scalar to simplify the notation. We allow for multiple sources of systematicrisk, in addition to the monetary shock, below.

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Factor models are common in financial economics. Ross (1976) arbitrage pricing model starts with a

statistical characterization of returns as a factor structure as we do here. Factor models also can be derived

from structural economic models. The CAPM is a single factor model in which the market return is the

factor; Mertons (1973) Intertemporal CAPM generates a multiple factor structure.

Identification

We identify the monetary policy shock by formalizing the notion that monetary policy shocks occur only

on event days. Event days are FOMC meeting days, or on days between FOMC meetings when the Fed

changes the Federal Funds Target rate. The covariance matrix of yields and equity returns on event days

reflects the monetary policy shock and the other shocks,

(1.2)

[ ]

2 2

2 2 2

2 2 2

, E Event t

t

i i

y i y i y y y

r i r i r y r y r r r

i

E y i y r t T

r

+

= + + + + + + +

and on nonevent days when there is no policy shock the covariance matrix is,

(1.3)

2

2 2

Nonevent

2 2

t T

i

NE y i y y

r i r y r r

= +

+

The restriction that monetary policy shocks occur only on event days identifies the monetary shock. The

model is over-identified. In equation 1.2 and 1.3 there are eight unknown parameters,

{ , , , , , , , }i y r i y r y r

=

3 The restriction makes our specification comparable to the event study and R&Ss specification. Therestriction is not rejected, see Section 3 and the Appendix.

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and twelve unique elements of the covariance matrices. The extension to a yield vector with n maturities is

straight-forward and increases the over-identifying restrictions4.

Estimation

Generalized Method of Moments (GMM) is the natural way to estimate this model. We estimate the sample

moments with the observable data. And we use GMM to estimate the unknown parameters and test

hypotheses.

Using the notation in Hamilton (1994) Chapter 14 letg() denote the vector of the deviation of the sample

moments from the population moments (that are functions of the unknown parameter values). For example,

the first two elements ofgare,

2 2 2

1

2

1( ( ))

1( (

Event

Evemt

Event t i i

t TEvent

Event t t y i y i

t TEvent

g iT

g y iT

))

= +

= +

(1.4)

We get consistent estimates of the unknown parameter vector from,

0arg max 'Q g W g = (1.5)

where W0 is any positive definite matrix.

And we get asymptotically efficient estimates using an optimal weighting matrix, see Hamilton.

Comparison with the Literature

Event Study Models

Event study models look only at event days (or windows around the event day) when the Fed changes the

Fed Funds target, and/or when the FOMC meets, t TEvent . Since the FOMC meets only eight times a year

and target changes between meetings are unusual in recent years the event study methodology uses only a

small subset of the daily data. For example, between 1988 and the end of 2001 there are over 3000 trading

4 Increasing the number of factors increases the parameters and reduces the number of over-identifying

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days on the NYSE (observations on yields and returns), but only 144 event days (FOMC meeting dates and

target change dates.)

Identification and Estimation

Event study models define the observed change in the short maturity interest rate on event days as the

exogenous monetary shock. Cochrane and Piazessi use the change in the one-month Eurodollar rate.

Bernanke and Kuttner, Kuttner, and Poole and Rasche use the change in the Fed Funds Futures rate5. The

exogenous monetary shock, defined as the change in the short rate, affects longer maturity yields and

returns,

2 2

; 0;

; 0;

; 0;

;

t t i t

t t Event

t y t y t y yt

y t y yt t Event

t r t r t r rt

r t r rt t Event

t m Event

i m s

m s t y m s e

i e s t T

r m s e

i e s t T

E i t T

T

= +

= = = + +

= + =

= + +

= + =

=

(1.6)

Regressing the change in the yield, or return, on the change in the short rate on event days gives the

response to a monetary surprise.

Comparison

Event study models identify the monetary shock by assuming that the common shocks,s, are zero on event

days. We assume that the variance of the common shock is the same on event and nonevent days and use

the fact that the realization of the monetary shock is zero on nonevent days to identify the monetary shock.

Errors in Variables Model

Poole, Rasche, and Thornton (2002) is the only event study model that explicitly recognizes that changes

in the short maturity interest rate may reflect information surprises as well as the monetary policy surprises.

restrictions.

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They add an information shock to the short maturity interest equation (but not to the longer maturity

yields.) In their specification the observed response, i, is a contaminated measure of the monetary shock,

( )

t t i t

t y t y yt

y t y yt y i t

Event

i m s

y m e

i e s

t T

;

= +

= +

= +

(1.7)

which by construction is correlated with the equation error in their yield equation. They use Wall Street

Journal articles to identify event days with no monetary surprise. On these days the variance ofi is the

variance of the information shock. Given the estimate ofi, they use an errors in variables estimator which

gives consistent estimates of the yield response coefficients, y, for their specification.

Comparison

Our factor model generalizes Poole, Rasche, and Thorntons errors in variables model. Our model gives

consistent estimates when the information shock affects all the security equations and it filters the monetary

policy surprise from all the yields, not just the short rate. In addition, we use a different, and arguably more

objective, identification scheme that allows us to use all the datanot just event days.

Rigobon and Sacks Model

Rigobon and Sack specify a bivariate simultaneous equation model with an unobservable common shock, s

(1.8)t iy t i t t

t yi t t y t

i b y c s m e

y b i s e

= + + +

= + +it

The monetary policy shock enters via the short rate (as in event study models) and spreads to the other

yield through the simultaneous equation specification.

The reduced form of Rigobon and Sacks model is observationally equivalent to a factor model with four

factors and no idiosyncratic shocks,

5 The Fed Funds Futures contract is an unusual contract that depends on the average of the daily Fed Funds

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(1.9)i i i i

t t it

y y y yt

im s e

y

= + + +

yte

E

R&S Identification & Estimation

The model is under-identified.6 R&S cleverly use the fact that the monetary policy shock occurs only on

event days to partially identify the model.7 They call this identification thorough heteroskedasticity. The

difference between the reduced form covariance matrices,

(1.10)2

2

RS RS RS

E N

i

y i y

=

reveals the reduced-form parameters, or factor loadings, on the monetary policy shock.8

R&S use a special feature of a bivariate system that ratios of the elements of the inverse matrix reveal the

structural parameters,

111

11

iy

yiiy yi

bB

bb b

=

(1.11)

to identify the coefficient on the short rate,

2 2/ / yi y i i y y i y ib / = = = (1.12)

in the yield equation.

R&S estimate the identified parameter using an instrumental variable procedure. The advantage of the IV

procedure is that it allows one to estimate the parameters with a canned regression package. The

disadvantage is that it does not impose the over-identifying restriction in equation (1.10).

rates, see Kuttner, and Poole et al, for details.6 Rigobon (2002) Section 3 gives the general conditions for identification of this type of model.7 Actually they assume that monetary policy shocks are larger on event days. The specification in equation(1.8) is equivalent to specifying larger monetary shocks on event days.

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They do not use all the data in their regressions. They chose a paired sampleone nonevent day for each

event day. They use about 10% of the available data. For nonevent days they chose the day before the event

day. Choosing a different nonevent day, e.g., ten days before, can lead to very different point estimates.

Comparison

The reduced form of R&Ss simultaneous model specification is observationally equivalent to a factor

model in which the simultaneous equation structural errors are factors (systematic risk.) In a bivariate setup

one can interpret the ratio of the factor loading on the yield to the factor loading on the short rate as the

structural coefficient on the short rate in the simultaneous equation model. In a multivariate framework all

one can recover is the reduced-form coefficient, or factor loading, vector on the monetary shock, see

Rigobon (2000), proposition 2. Our factor model specification is identified and gives the factor loadings on

the monetary policy shock and the loadings on the common information shocks in a general multivariate

setup.

Section 2: Data

Data Sources

We use data on US bond yields and US equity returns for the period from 10/88 (when Fed Funds Futures

began trading on the CBOE) through 12/01 (the latest CRSP data when we started estimation.) We also

look at a sub-sample starting in 1/94 when the FOMC began to pursue a more transparent policy regime

that made it easier for market participants to forecast policy (Target) changes. The Fed announced changes

in the Target immediately and in 1997 announced the intended federal funds rate and in 1999 started

announcing an intended bias toward changing the Target or keeping it the same. Arguably the most

important move to transparency was limiting Target changes to FOMC meeting dates except for very

unusual events. Prior to 1994 most of the Target changes took place between meetings. Agents had to guess

when the Target would change as well as by how much.

8 Notice that the difference in the sample covariance matrices for a bivariate factor model will yieldestimates of the factor loadings, i,y, that are identical to the reduced form estimates of R&Ss model.

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We use the publicly available data that most of the event study papers use. The yield and Euro$ data come

from the Federal Reserve Boards web site www.federalreserve.gov/releases/. We chose yields for constant

maturity treasury bonds with maturities of 10years, 5years, 3years, 1year, and 3months and the 30-day

Euro$ rate. Figure 2.1 shows the Fed Funds Target and the one and 10year yields. The yields and Target

are measured at annual percentage rates.

Figure 2.1: Yields and Fed Funds Target

1988 1990 1992 1994 1996 1998 2000 20021

2

3

4

5

6

7

8

9

10tcm10y tcm1y FFTarget

tcm10y

FFTarget

tcm1y

The yields and the Target move together, but there are significant departures, even in the one-year yield.

More importantly, there is no clear lead-lag relationship to establish causality.

Event study models define the monetary policy shock on the event day as a change in a short rate. The

choice of a short rate is especially important in these models. Cochrane and Piazzesi equate the change in

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the 30-day Eurodollar rate9 on event days with the monetary policy surprise. Figure 2.2 shows the Euro rate

and the Fed Target.

Figure 2.2: Euro$ rate and FED Funds Target rate

1999 2000 2001 20021

2

3

4

5

6

7Euro1m and Target

Target

Euro

The Euro anticipates most of the increases the Target during 1999 and the first half of 2000, and then most

of the decreases in 2001. Cochrane and Piazzesi use this impressive visual evidence to justify identifying

the monetary policy surprise as the change in the 30-day Euro rate. One should also notice considerable

movements in the Euro rate that are unrelated to the Fed Funds Target. The largest (in the picture) occurred

in December of 1999 when Y2K fears added % to the Eurodollar rate10. The premium disappeared when

the New Millennium arrived without the feared and predicted computer systems failures.

9 Cochrane and Piazzesi use an event window.

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Fed Funds Futures

The Fed Funds futures data comes from Datastream. We used Kuttners (2001) formula to calculate the

change in the futures rate.

Equities

Financial journalists frequently attribute changes in stock prices to changes in Federal Reserve policy, or to

no changes in policy when the market expected a change. It turns out the journalists are right. We find the

largest responses to monetary shocks occur in the equity market. The recent papers by Bernanke and

Kuttner, Hui Guo, and Rigobon and Sack also find large equity market responses to monetary surprises.

We use the return on the value-weighted NYSE from CRSP. The return is calculated as the log difference

of the value-weighted index including distributions. The return is a daily return expressed as a percentage.

Event Days

The FRB website lists meeting days and target changes after 1994. We used Kuttners (2001, 2003) dates

for the early period and a few later dates where the actual announcement time was unclear.

Descriptive Statistics

Table 2.1 gives descriptive statistics for the full sample period. We use every trading day between October

1988 and the end of 2001 when trades occurred on both the NYSE and the Bond market. The only

exception is that we excluded September 17, 200111. On September 17 the NYSE reopened after being

closed for a week following the 9/11 attacks and Fed reduced the target rate. Table 2.2 gives the descriptive

statistics for the sub-sample from 1994-2001.

10 We led the Eurodollar rate by one day to compensate for the six-hour time differential between NewYork and London. In Figure 2.2 leading the Euro makes it appear as if the market also anticipated the NewYear.11 Bernanke and Kuttner also exclude the 9/17/2001 observation.

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Table 2.1

Descriptive statistics for changes in yields and equity returns. The yields are measured

at annual rates in basis points and the equity return is the daily

percentage

Sample: daily 10/1988 through 12/2001.

Asset Std dev Cov-30 day Euro Cov- 1 mth Futures

Event Non-Event Event Non-Event Event Non-Event

30 day Euro

FF Futures

10.561

9.933

7.203

6.499

- - - -

3 mth yield

1 yr yield

3 yr yield

5 yr yield

7 yr yield

10 yr yield

7.718

7.707

7.200

7.216

6.747

6.306

5.392

5.546

6.328

6.313

6.148

5.864

57.988

55.749

38.774

32.294

24.974

18.756

7.723

10.388

11.458

10.150

9.375

8.312

50.809

49.917

32.134

24.507

19.267

13.499

7.366

8.491

7.302

6.640

5.577

4.963

Equity return 0.857 0.852 -3.727 -0.217 -2.765 0.017

No. of days 144 3161 _ _ _ _

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Table 2.2

Descriptive statistics for changes in yields and equity returns. The yields are measured

at annual rates in basis points and the equity return is the daily

percentage

Sample: daily 1/1994 through 12/2001.

Std dev Cov - 30 day Euro Cov - 1 mth FuturesAsset

Event Non-Event Event Non-Event Event Non-Event

30 day Euro FF

Futures

11.008

9.547

5.146

4.528

- - - -

3 mth yield

1 yr yield

3 yr yield

5 yr yield

10 yr yield

7.018

6.440

7.040

7.444

6.417

5.664

5.383

6.359

6.418

6.077

47.129

40.989

25.258

18.043

1.597

7.280

7.700

7.904

6.827

4.815

35.558

27.761

12.109

4.722

-7.546

7.378

6.820

6.228

5.571

3.794

Equity return 0.978 0.927 -6.408 -0.001 -5.119 0.282

No. of days 68 1926

The first two columns give the standard deviations of the variables on event and nonevent days. The event

daysFOMC meeting days or Target change dayshave larger standard deviations. More news arrives

on event days. The first two rows show the standard deviation of the change in the shortest maturity interest

ratethe 30-day Eurodollar, and the Fed Funds Futures rate. Event studies define the change in the short

maturity rate on event days as the monetary shock. The standard deviation of these variables is 50% larger

on event days. But if the variance of the information shock is constant, then 2/3 of the standard deviation of

the short rate comes from other information shocks on event days. Information arrives every day that

changes yields. Sorting information shocks from monetary policy shocks is important.

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The remaining columns give the covariance between changes in a short maturity yield and changes in

longer maturity yields and the equity return.12 The covariance is much larger on event days than on

nonevent days.

3.1 Bivariate Models

In this subsection we present estimates of the bivariate version of the factor model. The next subsection

compares the responses to a monetary shock from the bivariate factor model with our estimates of the

responses from the event study and R&Ss specification.

Table 3.1.1.a shows estimates of the factor model for the long sample of daily data starting in 10/88 and

ending in 12/01 using the Eurodollar rate as the short rate i. Table A.1.b in the appendix shows the

estimates for the sample beginning in 1/94 when Fed policy became more transparent. And Tables A.1.c

and A.1.d in the Appendix show the estimates for the bivariate factor model with the Fed Funds Futures

rate as the short maturity rate for the two sample periods.

The two important results to notice in Table 3.1.a and Tables A.1 in the Appendix are (1) The common

information shock (column 1) is significant in all of the yield equations for both samples. And (2) the

equity response to a monetary shock is large and significant.

The bivariate specification is.

; x (y,r)

t i t i t

t x t x t x t

i m s

x m s e

= +

= + + (1.13)

12 These are proportional to the response coefficients in event studies.

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Table 3.1.1.a

Bivariate Factor Model

i= Eurodollar Rate

Sample 10/88-12/01

GMM standard errors below the coefficients

Common Money Idiosyn. Test

shock () shock () SD (e) (pv)i 6.659 8.740 1.589

(0.656) (1.356) 0.207

3mth 1.159 5.878 5.213

(0.301) (0.816) (0.211)



(0.633) (1.223) 0.466

1 yr 1.500 5.518 5.326

(0.248) (0.963) (0.132)



(0.719) (1.496) 0.900

3 yr 1.593 3.442 6.121

(0.216) (1.048) (0.121)



(0.721) (1.596) 0.7205 yr 1.402 3.219 6.159

(0.188) (1.067) (0.115)



(0.733) (1.689) 0.684

10 yr 1.153 1.694 5.755

(0.126) (1.060) (0.106)



(0.745) (1.572) 0.060

Equity -4.600 -41.700 83.600

(2.500) (12.000) (2.000)

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The last column gives the test of the over-identifying restriction (one for the bivariate model) with the

probability value below the test statistic. Of the twenty-four models only the equity model for the 94

sample, Table A.1.d, rejects the test at the 5% level.

Yield and Equity Responses to a Monetary Shock in Bivariate Models

This subsection compares the yield responses to a monetary shock across modelsthe bivariate factor

model, our estimates of the event study, and Rigobon and Sacks model13and sample periods. Event

study models, and R&S, specify that the monetary shock enters through the short maturity rate and then the

short maturity rate affects other yields and returns, see equation (1.6) and (1.9). In those models a 1%

monetary policy surprise results in a 1% change in the short maturity rate. In the factor model the monetary

shock directly affects all yields and the equity return. Here we normalize the coefficients (factor loadings)

and their standard errors in the factor model so that a 1% monetary policy surprise causes a 1% change in

the short rate.

The important results to notice here are (1) the normalized factor loadings on the monetary shock (columns

1 and 4) and R&Ss structural coefficients measuring the yield response to a monetary shock (columns 3

and 6) are very similar. The factor model and R&Ss specification allow for a common shock. The

responses in the event study specification, which does not include a common shock, are smaller as a simple

errors in variables model predicts.

13 We used the simple instrumental variable procedure in Section 4.1 of R&S.

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Table 3.1.2a

Normalized Yield and Equity Response to a 1% Monetary SurpriseSample 10/1988 - 12/01

Standard errors below coefficient estimates

ASSET 30 day Euro 1mth futures

Factor Event Rig-Sack Factor Event Rig-Sack

3 mth 0.673 0.520 0.778 0.717 0.515 0.639

(0.093) (0.043) (0.095) (0.114) (0.049) (0.078)

1 yr 0.650 0.500 0.674 0.697 0.506 0.554

(0.113) (0.045) (0.084) (0.130) (0.049) (0.069)

3 yrs 0.442 0.348 0.436 0.450 0.326 0.336

(0.134) (0.049) (0.081) (0.137) (0.054) (0.072)

5 yrs 0.439 0.289 0.392 0.422 0.248 0.277

(0.145) (0.052) (0.085) (0.156) (0.057) (0.075)

10 yrs 0.230 0.168 0.223 0.207 0.137 0.113

(0.144) (0.048) (0.078) (0.135) (0.052) (0.069)

Equity -4.923 -3.342 -4.756 -4.298 -2.802 -4.080

(1.422) (0.620) (1.157) (1.564) (0.684) (1.045)

(2) The choice of the short maturity yield30 day Eurodollar or Fed Funds Futuresdoesnt make much

difference. And (3), the standard errors of the factor estimates are larger than the other models. Using all of

the data and imposing the restrictions matters.

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Figure 3.1.2a illustrates the yield responses and the 95% confidence interval with the Euro as the short

ratethe first three columns of Table 3.1.2.a. For maturities longer than one-year the confidence band for

the factor model (in red) contains the confidence bands for the event (in green) and R&Ss specification (in

black).

Figure 3.1.2.a

Sample 88-01

0 2 4 6 8 10 12-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Maturity

Yield Response to 1% Mshock with 95% Confidence Bands

Factor

R&S

Event

The point estimates show the same pattern for the three models, with the event study responses smaller than

the factor and R&S models. The factor model has the largest confidence band. The R&S specification has

the intermediate confidence band. And the event study specification has the tightest confidence band. The

response of the 10-year yield to a shock is insignificant in the factor model and significant in the event

study specification and R&S specification (which allows for another shock but uses a small paired sample).

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Table 3.1.2b gives the estimated responses for the shorter sample starting in 1994.

Table 3.1.2.b

Normalized Yield and Equity Response to a 1% Monetary SurpriseSample 1/1994 - 12/01

Standard errors below coefficient estimates

ASSET30 dayEuro 1mth futures


3 mth 0.421 0.390 0.372 0.453 0.390 0.417

(0.110) (0.062) (0.076) (0.144) (0.077) (0.091)

1 yr 0.352 0.338 0.304 0.318 0.304 0.265

(0.114) (0.059) (0.062) (0.155) (0.074) (0.076)

3 yrs 0.200 0.208 0.166 0.077 0.133 0.084

(0.172) (0.074) (0.075) (0.186) (0.089) (0.088)

5 yrs 0.256 0.149 0.112 0.035 0.052 0.007

(0.201) (0.081) (0.080) (0.244) (0.096) (0.093)

10 yrs -0.018 0.013 -0.030 -0.160 -0.083 -0.137

(0.186) (0.072) (0.075) (0.205) (0.082) (0.085)

Equity -6.915 -5.287 -5.920 -6.898 -5.616 -6.420

(1.220) (0.878) (1.022) (1.967) (1.054) (1.187)

The shorter sample in which Fed policy was more transparent shows far fewer significant responses to

monetary surprises for any of the models and the point estimates show no particular pattern. Note that the

factor model estimates have larger standard errors than the other models.

Response of Equity Returns to a Monetary Policy Surprise

An important, and robust, empirical result is that the equity market response to a monetary surprise

dominates the response in debt markets. Equities show a large, and statistically significant, response to

monetary surprises in all of the models for both sample periods. In Tables 3.1.2 the responses for bonds and

equities are not easy to compare. The yield responses are measured at annual percentage rates and equity

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responses in percent daily (logarithmic) returns. Table 3.1.3.a below shows the responses to a monetary

shock where all of the responses are measured as percent daily (logarithmic) returns.14

Table 3.1.3.a

Bond and Equity Response to a 1% Monetary Surprise

Measured as % daily returnsSample 10/1988 - 12/01

standard errors below coefficient estimates

ASSET30 dayEuro 1mth futures


3 mth -0.168 -0.130 -0.194 -0.179 -0.129 -0.160(0.023) (0.011) (0.024) (0.028) (0.012) (0.019)

1 yr -0.650 -0.500 -0.674 -0.697 -0.506 -0.554

(0.113) (0.045) (0.084) (0.130) (0.049) (0.069)

3 yrs -1.326 -1.044 -1.308 -1.350 -0.978 -1.008

(0.402) (0.147) (0.243) (0.411) (0.162) (0.216)

5 yrs -2.195 -1.445 -1.960 -2.110 -1.240 -1.385

(0.725) (0.260) (0.425) (0.780) (0.285) (0.375)

10 yrs -2.300 -1.680 -2.230 -2.070 -1.370 -1.130(1.440) (0.480) (0.780) (1.350) (0.520) (0.690)

Equity -4.923 -3.342 -4.756 -4.300 -2.802 -4.080

(1.422) (0.620) (1.157) (1.564) (0.684) (1.045)

A positive monetary policy shock causes all security pricesbonds and stockto decline. But the change

in the daily return for equity is more than twice the change in the return on any bond. And this result is not

sensitive to the sample period, or the model specification, see Tables 3.1.2.

t14 The annual yield on a discount bond with maturity n (n years) is ( ) ln( ( ) ) /t y n B n n= , where B is

the bond price. So the daily return is r n( ) ( )t n y n t where we ignored the one day change in thematurity.

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Figure 3.1.3.a shows the response of bond and stock returns and the 95% confidence interval to a 1%

monetary policy shock for the factor, event study, and R&S specification with the 30-day Euro as the short

rate.

Figure 3.1.3.aSample 88-01

0 2 4 6 8 10 12 14 16-8

-7

-6

-5

-4

-3

-2

-1

0

1

Maturity

%returns

Return Responses to 1% Mshock with 95% Confidence Bands

Event

R&S

Factor

Equity

The response to a monetary policy shock measured in the daily return grows with the maturity of the bond

(long maturity bond prices are more volatile). Changes in the return on one-year bonds are less than 1% and

on 10-year bonds are only 2%. Changes in the equity returnshown as a maturity of 15 years in the

figureare ten times as large as the change in the one-year bond return and twice as large as the change in

the five and ten year bond returns.

The wealth effect in the equity market from a monetary surprise dwarfs the wealth effect in debt markets.

The change in wealth due to a monetary shock is the sum of the products of the change in the assets return

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times the capitalized value of the asset15. Market capitalization of equity was roughly $12 trillion at the end

of 2002 while US Treasury securities were only $3.6 trillion. Corporate and mortgage debt push the debt

capitalization close to the equity market, but since most of the reaction in the bond market to a monetary

surprise is at the short end of the maturity structure, no matter how one measures it, the wealth effect in the

debt market is small relative to the equity market.

Our results indicate that the equity market is quantitatively the most important channel of monetary policy

in the short run. Bernanke and Kuttner, Guo, and Rigobon and Sack also find large, significant, response

coefficients of equity returns to monetary surprises.

3.2 Multivariate Factor Models

In theory the monetary shocks and common shocks affect all assets. Estimating a vector model of assets

returns that imposes the over-identifying restrictions gives more efficient estimates. This section extends

the model to a vector of five yields and the equity return. The short rate plays no special role in the factor

model. It is just another yield. We include both the 30-day Euro rate and the change in the Fed Funds

futures in the yield vector. We find four sources of systematic riskthe monetary policy shock, and three

common shocks. There are 19 over-identifying restrictions.

15 i ii

rdW A dm

m

=

where Wdenotes wealth andA the capitalized value of the asset.

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Table 3.2.1a shows the estimates for the long sample from 10/88 through 12/01 and 3.4.1b shows the

estimates for the shorter sample starting in 1/94.

Table 3.2.1a

Multivariate Factor model

10/1988-12/2001

standard errors based on GMM in parentheses

Asset Money Com. 1 Com. 2 Com. 3 Idiosyn.Euro 9.403 2.201 4.625

(1.080) (0.352) (0.372)

FF Fut. 8.163 1.526 1.317 4.843(0.869) (0.242) (0.427) (0.627)

3 mth 5.177 3.721 0.115 3.724(0.700) (0.304) (0.234) (0.153)

3 yrs 3.004 4.740 -3.526 2.190(0.875) (0.265) (0.378) (0.072)

10 yrs 1.167 3.371 -4.778(0.860) (0.416) (0.295)

Equity -30.800 5.600 24.100 -9.700 79.2(9.700) (4.500) (2.100) (2.100) (1.900)

Test 20.859 No. 19(pv) (0.345)

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Table 3.2.1b

Multivariate Factor model

1/1994-12/2001

standard errors based on GMM in parentheses

Asset Money Com. 1 Com. 2 Com. 3 Idiosyn.Euro 11.850 1.871 3.604

(1.321) (0.505) (0.464)

FF Fut. 9.758 1.477 0.160 3.696(0.982) (0.339) (0.205) (0.297)

3 mth 4.211 3.521 -0.541 3.917(0.642) (0.388) (0.227) (0.205)

3 yrs 0.740 3.662 -4.630 2.140(1.015) (0.304) (0.281) (0.079)

10 yrs -1.497 2.303 -5.583(1.144) (0.462) (0.219)

Equity -63.000 13.400 19.700 -8.200 85.000(7.800) (5.200) (2.600) (2.700) (2.600)

Test 23.393 No. 19(pv) (0.220)

In the factor model the coefficients measure the response to a one standard deviation shock in the factor.

Column 1 shows the response of yields or the return to a monetary shock. We examine these in detail

below and normalize the responses to make them comparable to the event and R&Ss model. Here we

concentrate on the common information shocks. The first common shock is a level shock to the yield

curve. All yields increase significantly with the intermediate maturity yields increasing slightly more. The

level common shock has an insignificant effect on the equity return in the long sample, but has a positive

effect on the equity return in the 94 sample. The second common shock twists the yield curve. Long

maturity yields fall (bond prices rise) more than shorter maturity yields and the stock price increases. The

third common shock affects only very short yields and equity. The effect of the third common shock is

similar to the monetary shock, see below. The monetary shock affects short yields and equity.

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3.2.2 Response to a monetary policy shock

Table 3.2.2a and 3.2.2.b show the responses of yields and the equity return to a monetary shock for the

multivariate model, the bivariate factor model, the event study model, and R&Ss specification.

Table 3.2.2a

Yield and Equity Response to a 1% Monetary Surprise

Response of 30-day Euro normalized to 1Sample 10/1988-12/01

Standard Errors below coefficient estimates

Multi-Factor Bi-Factor Event Rig-Sack

AssetEuro 1 1 1 1

(0.114)

FF Fut. 0.868

(0.092)

3 mth 0.550 0.673 0.52 0.778 (0.0744) (0.093) (0.043) (0.095)

1 yr 0.650 0.500 0.674

(0.113) (0.045) (0.084)

3 yrs 0.319 0.442 0.348 0.436

(0.093) (0.134) (0.049) (0.081)

5 yrs 0.439 0.289 0.392

(0.145) (0.052) (0.085)

10 yrs 0.124 0.230 0.168 0.223 (0.091) (0.144) (0.048) (0.078)

Equity -3.275 -4.923 -3.342 -4.756 (1.031) (1.422) (0.620) (1.157)

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Table 3.2.2b

Yield and Equity Response to a 1% Monetary Surprise

Response of 30-day Euro normalized to 1Sample 1/1994-12/2001

Standard Errors below coefficient estimates

Multi-Factor Bi-Factor Event Rig-SackEuro 1 1 1 1 (0.111)

FF Fut. 0.823

(0.083)

3 mth 0.355 0.421 0.389 0.372 (0.054) (0.110) (0.062) (0.076)

1 yr 0.352 0.338 0.304

(0.114) (0.059) (0.063)

3 yrs 0.062 0.200 0.208 0.166 (0.086) (0.172) (0.074) (0.07)

5 yrs 0.256 0.149 0.112

(0.201) (0.081) (0.080)

10 yrs -0.126 -0.018 0.013 -0.030

(0.097) (0.186) (0.072) (0.075)Equity -5.318 -6.915 -5.287 -5.920 (0.654) (1.220) (0.878) (1.022)

The event study model and R&S specify that a 1% monetary shock causes a 1% change in the short maturity

rate (here the 30-day Euro.) The first row in Tables 3.2.2 reflects the normalization to match the event and

R&Ss model.

The factor models display the classic textbook slope effect for the yield curve response to a monetary

shock. The short end of the yield curve shifts up (for a positive shock) and nothing happens to the long

maturity yields. The standard errors of the coefficient estimates are usually smaller in the multivariate

model than in the bivariate modelas one would expect. Notice, however, that the standard error of the

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response for the 10-year yield is larger than the standard error in the event study or R&Ss model, and the

coefficient is insignificant.

Figure 3.2.2 shows the yield curve response to a monetary shock in the multivariate and bivariate factor

models.

Figure 3.2.2

Factor Model Responses to MshockSample 88-01

The yield curve response in the multivariate model to a monetary shock is very similar to the response in

the bivariate model. The confidence intervals overlap. A monetary shock has a slope effect on the yield

curve. Short maturity yields response positively and significantly to a positive monetary shock and the

response of the long maturity yield is insignificant. The 94 sample shows a similar pattern, but all of the

responses are smaller.

Conclusions

This paper estimates the impact of monetary policy surprises on bond yields and on the equity return. We

solve an old puzzle and we discover a quantitatively important, but largely neglected, channel of monetary

policy.

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Cochrane and Piazzesis , Cook and Hahns (1998) , and our estimates of the event study specification

show that long maturity bond yields increase significantly in response to a surprise increase in the Target.

Cochrane and Piazzesi label this a puzzle. We also estimated a more general factor model that allows for

information surprises in addition to monetary shocks. The estimates from our factor model provide a simple

resolution to this puzzle: long maturity bond yields dont respond to monetary surprises, they respond to

common information shocks. Specifications that fail to measure the common shock attribute the impact to

the monetary shock.

Equity returns do respond to monetary surprises. The response in equity markets is larger than the response

in debt marketsequity returns move more that debt returns and the wealth effect is larger in the equity

market. This is an important channel of monetary policy where very little empirical or theoretical research

has been done. Our work only documents a large equity return response to monetary surprises. Bernanke

and Kuttner show most of the response is due to a change in the equity premium. Understanding the

response of equity returns to monetary surprises is a fertile area for future research.

References

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Bernanke, Ben S. and Kenneth N. Kuttner, 2003, What Explains the Stock Markets Reaction to FederalReserve Policy? Federal Reserve Bank of New York.

Bodie, Zvi, Alex Kane and Alan J. Marcus, 2002, Investments, McGraw-Hill.

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Caporale, Barbara and Tony Caporale, 2003, Investigating the effects of monetary regime shifts: The caseof the Federal Reserve and the shrinking risk premium, Economic Letters, 80, 87-91.

Cochrane, John H., 2001, Asset Pricing, Princeton University Press.

Cochrane, John H. and Monika Piazzesi, 2002, The Fed and Interest RatesA

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High Frequency Identification, American Economic Review, 92: 90-101.

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Kuttner, Kenneth N., 2001, Monetary Policy Surprises and Interest Rates: Evidence from the Fed FundsFutures Market, Journal of Monetary Economics, 47: 523-544.

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Poole, William, Rasche, Robert H. and Daniel L Thorton, 2002, Market Anticipations of Monetary PolicyActions, Federal Reserve Bank of St. Louis Review July/August 65-97.

Rigobon, Roberto, 2002, Identification through Heteroskedasticity, forthcoming Review of Economics andStatistics.

Rigobon, Roberto, 2000, A simple test for stability of linear models under heteroskedasticity, omittedvariable, and endogenous variable problems, http://web.mit.edu/rigobon/www/.

Rigobon, Roberto and Brian Sack, 2002, Impact of Monetary Policy on Asset Prices, Finance andEconomics Discussion Series 2002-4. Board of Governors of the Federal Reserve System.

Romer, Christina D. and David H. Romer, 2000, Federal Reserve Information and the Behavior of InterestRates, American Economic Review, 90, 429-457.

Romer, Christina D. and David H. Romer, 2002, A New Measure of Monetary Shocks: Derivation andImplications, mimo University of California at Berkeley.

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Appendix

A.1 Estimates of the bivariate factor model

Table A.1.b

Bivariate Factor Modeli=Eurodollar Rate

Sample 1/94-12/01

GMM standard errors below the coefficients

Common Money Idiosyn. Test(a)

shock () shock () SD (e) (pv)

i 5.145 9.641


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The last column gives the test of the over-identifying restriction (one for the bivariate model) with theprobability value below the test statistic. Only the equity model for the 94 sample rejects the restriction atthe 5% level.

Bivariate Models with Fed Funds Futures as short maturity rate

Table A.1.cSample 10/88-12/01

Common Money Idiosyn. Test (a)


(0.756) (1.377) (0.775)

3mth 1.151 5.556 5.259

(0.254) (0.885) (0.215)

shock () shock () SD (e)

i 6.387 7.702 0.049

(0.726) (1.328) (0.824)

1 yr 1.322 5.370 5.381

(0.208) (0.998) (0.141)

shock () shock () SD (e)i 6.515 7.416 0.005

(0.833) (1.597) (0.942)

3 yr 1.121 3.338 6.229

(0.196) (1.016) (0.127)

shock () shock () SD (e)i 6.601 6.941 0.435

(0.841) (1.676) (0.509)

5 yr 1.009 2.931 6.241

(0.164) (1.082) (0.117)

shock () shock () SD (e)i 6.520 7.210 0.237

(0.864) (1.717) (0.626)

10 yr 0.762 1.496 5.822

(0.122) (0.971) (0.108)

shock () shock () SD (e)i 6.215 8.390 1.747

(0.881) (1.400) (0.186)

Equity -0.400 -36.100 84.200

(2.200) (13.100) (2.000)

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Table A.1.d



(0.656) (1.932) (0.631)

3mth 1.658 3.692 5.459

(0.454) (1.169) (0.279)



(0.657) (1.957) (0.464)

1 yr 1.536 2.566 5.198

(0.359) (1.248) (0.176)



(0.663) (1.956) (0.451)

3 yr 1.401 0.612 6.234

(0.296) (1.484) (0.165)


shock () shock () SD (e) (pv)

i 4.534 7.569 1.203(0.664) (1.995) (0.273)

5 yr 1.249 0.262 6.327

(0.241) (1.849) (0.156)



(0.664) (1.767) (0.847)

10 yr 0.839 -1.304 6.023

(0.148) (1.672) (0.144)



(0.704) (1.791) (0.028)

Equity 0.026 -0.612 0.902

(0.046) (0.174) (0.026)

monetary policy shocks and security market responses

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