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Financial Markets Input to Monetary Policy Decision-Making

D I S S E R T A T I O N

of the University of St. Gallen,

School of Management,

Economics, Law, Social Sciences

and International Affairs

to obtain the title of

Doctor of Philosophy in Economics and Finance

submitted by

Nikola Nikodijevic Mirkov

from

Serbia

Approved on the application of

Prof. Paul Söderlind, PhD

and

Prof. Tom Engsted, PhD

Dissertation no. 4196

Print Cuprija, Serbia 2013

The University of St. Gallen, School of Management, Economics, Law, So-

cial Sciences and International Affairs hereby consents to the printing of the

present dissertation, without hereby expressing any opinion on the views herein

expressed.

St. Gallen, March 4, 2013

The President:

Prof. Dr. Thomas Bieger

(Publisher or printer)

Acknowledgments

I enjoy research. I was always inclined towards research. But it was not until

Jovana Zrnic, a very good friend of mine, gave me the idea to do a PhD, that

I could dedicate my full attention to some exciting research. That February

2009 is when this 4-year journey began.

As the idea about the PhD was evolving, the University of St.Gallen (HSG)

came across in a conversation with Slavica Nikodijevic, my mom. The GRE

test was one of the enrollment criteria and I was a bit behind the schedule

in mastering the key tricks. But everything went well, and the next thing I

remember was standing in a queue at Banca Intesa in Milan with Aleksandar

Zdravkovic, my best friend, and discussing about whether I should spend my

last savings on the enrollment fee. “Just do it, so you won’t feel sorry for not

doing it”, he said.

The phenomenal news that I was accepted to the PhD Program at HSG was

thoroughly discussed with my great Italian friends, Mathias Domini, Francesca

Ferri and Angelica Capogna, with my Master thesis advisor, Carlo Favero,

with my boss at BNP Paribas, Andrea Valenti, but especially with Mirko

Nikodijevic, my father, and my mental gurus, Bojana Nikodijevic, my sister,

and Vladimir Stanojlovic, my godfather.

The PhD Program kicked off in September 2009 and it was exactly the time

when I met Gisela Bannerman, Sanna Maarala, Milena Stancheva and Peter

Barta, whom I can’t imagine my time in St. Gallen without. In October 2009,

I started working for my PhD advisor, Paul Söderlind. There are no words to

express my gratitude and appreciation for his invaluable support. Thanks to

Paul, we (his assistents) have always had a vast amount of time for research,

plenty of funding for conferences (very important!) and an advisor with whom

we could always share our thoughts and overly complicated charts. Paul’s

iii

hints for my first paper constituted a signpost for my entire PhD thesis. I

believe I went far further then I would have ever had otherwise.

For instance, it would have been impossible to have almost three papers written

by the end of the fifth semester. As I learned a lot about term structure models

in the first two, I was lucky that Barbara Sutter, a colleague from the Swiss

National Bank, offered me to co-author the third paper and voilá. I met Barbara

at a summer school on monetary policy in Kiel in 2010, where I went together

with Daniel Kienzler, a good friend of mine and a colleague from the Paul’s

chair. I owe to Daniel many pitchers of beer for all his help in practicing

presentations, understanding macroeconomics and especially in catching up

with some very cool phrases in German.

The summer school in Kiel was really an extraordinary event and a great

chance to meet fellow PhD students from around the Europe. We met, among

others, Nina Larsson Midthjell, a colleague and a friend from the University

of Oslo, who deserves a special thanks and here is why. Nina invited me to

a summer shool in Olso one year later, where I met Alfonso Irarrazabal, a

colleague from Norges Bank. Alfonso sent an email to all the participants ex-

plaining that Norges Bank is looking for PhD interns for 2012. So I got the

internship, met Gisle Natvik with whom I wrote the third chapter of this thesis,

met Anders Vredin from the Riksbank, who would later be one of my precious

referees for the job market, spent an amazing time in Oslo with Valent Nikaj

and Alice Ciccone, and met Kevin Lensing, thanks to whom I’ve got a chance

to visit the Federal Reserve Bank of San Francisco for six months.

One of the important conditions for visiting the San Francisco Fed was to

provide a letter of invitation from Monika Piazzesi, a Stanford University pro-

fessor, to whom I wrote from Oslo asking, if I could visit the Econ Department

at Stanford. I learned a lot from Monika and enjoyed her great support while

on the job market, even if we knew each other relatively briefly. Thanks to

Monika, I got the chance to present my research at Stanford and at the Fed,

iv

meet some of the brightest people on the planet and built a solid research net-

work. During my stay in the US, this thesis benefited greatly from insightful

discussions with Glenn Rudebusch, Michael Bauer, Rhys Bidder, Ian Dew-

Becker, Fernanda Necio, Galina Hale, Bart Hobijn, Oscar Jorda, Eric Swan-

son, Jens Christensen, Marius Rodriguez and Sylvain Leduc. I owe a special

thanks to some of you guys for preparing me for the job market, for your

enjoyable company on Wednesday’s at noon (and many weekends too!), but

especially for helping me improve enormously my presentation skills.

None of it would have been as much fun as it was, if there wasn’t for Paolo

Fagiolo, Ermira Mehmetaj, Giovanni Melace, Phillipp der Grosse, Andreas

Steinmayr, Mathias Hübner, Pirmin Meier, Sanja Rikanovic, Stephan Suess,

Nicolas Burckhardt, Daniel Buncic, Santino Centineo, Lu Liu, Jorrit Koop,

Nick Naletov, Tiago Arcolini, Ivan Nikodijevic, Lidia Baca, Dimitri Huttunen,

Juga Demo, Rade Stankovic, Ivica Jovanovic, Olga Karpiankova, Giuseppe

Felicetto, Milos Obradovic, Branko Mihajlovic, Giuseppe Russo, Monika Zla-

tanovska, Lillian Bui, Petra Thieman, Elena Manresa, Andreas Steinhauer,

Raphael el Torero, David Kiss and Guzman Gonzalez-Torres Fernandez.

More importantly, none of it would have been even conceivable, if there wasn’t

for a constant support and unreserved love of (and for) my sister and parents.

Family is the most important thing in the world.

St. Gallen, June 21, 2013

Nikola Mirkov

v


vi

Table of Contents

Executive Summary

page 9

Asymmetries in Interest Rate Response to Monetary Policy Shocks

page 13

Central Bank Reserves and the Yield Curve: Estimating Tobin’sPortfolio Substitution Effect

page 51

Announcements of Interest Rate Forecasts: Do Policymakers Stickto Them?

page 87

Curriculum Vitae

page 131

vii


viii

Executive Summary

The presented research lies at the cross section between financial markets and

monetary policy. As a cumulative thesis, it is made of three separate papers.

The first paper uses the exact timings of policy rate decisions by the Fed-

eral Reserve (Fed) to measure asymmetries in response of interest rates and

risk premia on Treasury securities to those decisions. The analysis shows that

interest rates react asymmetrically to the Fed’s policy actions. Short-term in-

terest rates respond more strongly to expansionary policy decisions, whereas

long-term interest rates rise on average after the Fed’s decisions to decrease

interest rates more than the markets anticipated and the reason might be related

to the fear of future inflation.

The second paper is a co-authored work with Barbara Sutter, and it shows that

the expansion of Central Bank’s balance sheet has a negative effect on long-

term interest rates. We examine the increase in non-borrowed reserves at the

Fed and the increase in total reserves at the Swiss National Bank (SNB) from

December 2008 to December 2012. Independently of whether the increase in

Central Bank reserves occurs because of asset purchases (the Fed) or foreign

currency purchases (the SNB), we find a statistically significant and economi-

cally meaningful effect of increase in Central Bank reserves on the long-term

government bond yields in the two countries.

Finally, the third paper is a co-authored study with Gisle James Natvik, and

it asks whether Central Banks, who publish interest rate forecasts, eventually

stick to their forecasts. We derive and estimate a policy rule for a central bank

that is reluctant to deviate from its forecasts. We find that the Reserve Bank

of New Zealand and the Norges Bank, the two Central Banks with the longest

history of publishing interest rate paths, appear to be constrained by their most

recently announced forecasts.

9


10

Saetak

Tema disertacije obuhvata oblasti monetarne politike i fi-

nansijskih trixta. Istraivaǌe je podeǉeno u tri rada.

Prvi rad istrauje, da li kamatne stope i riziko-premije na

obveznice S.A.D.-a reaguju asimetriqno na odluke Federalne

banke u vezi referentne kamatne stope. Rezultati pokazuju da

je reakcija kratkoroqnih kamatnih stopa na odluke Federalne

Banke vea u sluqaju kada Banka odluquje da umaǌi refer-

entnu kamatnu stopu. U sluqaju kada odluke o umaǌeǌu ka-

matne stope iznenade finansijska trixta, dugoroqne kamatne

stope u proseku rastu.

Drugi rad predstavǉa empirijsku analizu podataka o rezer-

vama centralnih banaka u S.A.D. i Xvajcarskoj, koja ukazuje

na negativni efekat rasta rezervi na dugoroqne kamatne stope

u pomenutim zemǉama. Rezerve banaka su u obraenom vremen-

skom periodu znaqajno porasle, xto je prouzrokovalo statis-

tiqki i ekonomski znaqajan pad prinosa na dugoroqne obveznice

tih zemaǉa. Rad je zajedniqki projekat sa Barbarom Suter.

Konaqno, trei rad istrauje, da li Centralne Banke, koje

redovno objavǉuju prognoze referentne kamatne stope, uzimaju

u obzir prethodno najavǉene prognoze, kada odluquju o sadax-

ǌoj referetnoj stopi. Empirijska analiza koristi podatke o

referentnim kamatnim stopama Rezervne Banke Novog Zelanda

i Norvexke Centralne Banke i ukazuje na to da se obe Cen-

tralne Banke dre svojih najavǉenih prognoza, ali samo onih

kratkoroqnih. Trei rad predstavǉa zajedniqki projekat sa

Gizle-ejms Natvikom.

11


12

Asymmetries in Interest Rate Responseto Monetary Policy Shocks∗

Nikola Mirkov†

Abstract

Interest rates do not respond symmetrically to monetary policy shocksas standard Vector autoregression (VAR) models and Event-study ap-proach would suggest. I use the exact timings of FOMC announcementsto identify monetary policy shocks affecting interest rates and risk pre-mia on the US Treasury bonds, where the shocks are divided accordingto direction of the Fed funds rate change and according to “unantici-pated” fraction of the change, calculated using Fed funds futures data.The direction of the move seem to matter at the short-end of the curve,where the rates and premia react more strongly to interest-rate cuts thaninterest-rate hikes. Introducing the “uncertainty” dimension discovers aclear asymmetric pattern in response of long-term interest rates to Fed’spolicy actions.

Keywords: Interest rates, policy actions, FOMC, risk premia, DTSMJEL Classifications: E43, E52, G12

∗I gratefully acknowledge an invaluable and constant support of my doctoral advisor Paul Söderlind. A greatthanks to Lars Svensson, Charles Engel, Michael Bauer, Hans Dewachter, Martin Brown, Lukas Wäger, An-dreas Steinmayr, Sebastian Schmidt, Kevin Lansing, Dagfinn Rime, seminar and conference participants at theUniversity of St.Gallen, Norges Bank, the 5th CSDA International Conference, the 5th RGS Doctoral Confer-ence in Economics, the 10th Infiniti Conference, 2012 NBS Young Economist Conference and the 27th AnnualCongress of EEA for comments on a previous version of the paper, titled “International Financial Transmissionof the US Monetary Policy: An Empirical Assessment”.

†Nikola Nikodijevic Mirkov, Universität St.Gallen (HSG), Rosenbergstr. 52, 9000 St.Gallen, Switzerland,E-mail: nikola.nikodijevicmirkov@student. unisg.ch, Tel: +41(0)76.22.98.176

13

1 Introduction

Studying the link between the Fed’s policy actions and interest rates is essen-tial for understanding the transmission mechanism of monetary policy to thereal economy. Most of the previous studies use vector autoregression (VAR)1

or event-study approach2 to explore this link, where one of the underlying as-sumptions is that asset prices react symmetrically to monetary expansions andcontractions. This paper offers a high-frequency evidence that the assumptionmight be too strong.

I use the identification strategy from Piazzesi (2005) to estimate monetary pol-icy shocks from daily interest-rates data on US Treasuries and show that theshocks can be different in nature, depending on the direction of the Federalfunds rate change and the portion of the change that was not priced in thenearest-dated Fed funds futures3. A policy shock is a difference between bondprices after the FOMC announced its policy stance and a model-implied ex-pectations of those prices before the announcement. What is new, is that allthe extracted policy shocks are split in various ways, in order to explore asym-metries in interest rate response. The overriding question is whether shocks,arising from different policy actions, have different statistical properties, mostnotably different means. If that is the case, the average reaction of interestrates to one type of policy action is systematically higher or lower in absoluteterms respect to the other.

Few studies explore asymmetries in interest rates response to policy shocksand why there should be an asymmetric response in the first place. Ruge-Murcia (2006) argues that the non-negativity constraint on the values of nom-inal interest rates (i.e. the zero-lower bound) induces a non-linear relationbetween the level of short-term interest rates and long-term interest rates. Themain implication is an asymmetric response of long-term yields to changesin short rates. Choi (1999) argues that an exogenous money supply shock(e.g. change in the amount of reserves balances at the Fed) may have differentliquidity effect on interest rates, depending on whether the shock was expan-

1See Taylor (1995), Christiano, Eichenbaum and Evans (1996), Canova (2005) and Evans and Marshall(1998) among many others.

2See Bernanke and Kuttner (2005) and Ehrmann and Fratzscher (2004).3Federal funds futures contracts are traded on the Chicago Board of Trade and the settlement is based on

average Federal funds rate that prevails over a given month, see Kuttner (2001) and Piazzesi and Swanson(2008).

14

sionary or contractionary4 and estimates an asymmetric response of interestrates to different money supply shocks using a Threshold-VAR.

To the best of my knowledge, this is the first study to use exact timings ofFOMC meetings to explicitly account for asymmetric response of interest ratesto different monetary policy shocks. One clear advantage of using daily data tomeasure future policy expectations, as noted in Cochrane and Piazzesi (2002),is that the omitted-variables problem when estimating policy rules is avoided.The market prices summarise almost all the information used by the Fed insetting policy and used by the Fed watchers to forecast policy. Secondly, themarket expectations adapt to different “tones” in the Fed’s announcementsand thus the time-varying parameters problem is also avoided. Most impor-tantly, high-frequency data surmount orthogonalisation problems when esti-mating policy shocks from monthly or quarterly data, and thus offer a solididentification of interest rates reaction to Fed’s policy actions from the Fed’sreaction to movements in interest rates.

The key results of this paper are two. A decrease in the fed funds rate seemto produce a higher response of short-term interest rates in absolute values,than an increase of the same magnitude. A hypothetical 1% increase in the fedfunds target rises the 3-month Treasury yield by roughly 4 to 6 basis pointson average, while an equivalent cut lowers the yield by 6 to 16 basis pointson average, across different model specifications and sub-samples. The resultis broadly speaking in line with the reported numbers in Ruge-Murcia (2006)(3-month rate response of 12 basis points after hikes and 11 basis points aftercuts) and lower than the ones in Evans and Marshall (1998) (1-month rateresponse of 40 basis points after both hikes and cuts).

Secondly, the average response of long-term interest rates is statistically sig-nificant only after those policy actions where the surprise component of thechange in the fed funds rate was relatively high i.e. when the Fed decreasedthe policy rate more than the market expected. On those occasions, the long-term interest rates reacted positively on average and one possible reason is thata looser policy today means a higher inflation in the future, and thus highernominal interest rates.5 Since the Fed cut more than the markets anticipated,this initial positive reaction of long-term interest rates might point to a “marketconcern” that the future inflationary pressures could be difficult to contain.

4The difference is given by asymmetry in liquidity management of depository institutions at the Fed afterdifferent money supply shocks, see page 409 of Choi (1999).

5And vice versa, see Cochrane (2006).

15

The main findings of the paper stand up to several robustness checks. First,the models using different assumptions regarding the market price of risk and amodel-free approach all seem to indicate the same result. Excluding unsched-uled meetings, which more often resulted in interest rate cuts, does not seemto matter as well. Finally, the reported findings could suffer from endogeneityproblem, if another important macroeconomic news, such as the employmentreport of the Bureau of Labor Statistics, was released on the day of an FOMCstatement. Therefore, I use one-hour changes of selected interest rates aroundthe release of FOMC statements, reported in Fleming and Piazzesi (2005),and show that the main result still holds: short term interest rates react morestrongly to decisions to cut the federal funds rate.

The rest of the paper is organised as follows. Section 2 introduces the dataset,Section 3 explains how the high-frequency identification works, Section 4presents the results of the study and Section 5 concludes.

2 Data

2.1 FOMC Meetings

The identification of monetary policy shocks requires exact timings of theFed funds target rate announcements by the Federal Open Market Committee(FOMC). The dataset includes 126 policy meetings of the FOMC that resultedin an interest rate decision. The starting policy action was an interest rate hikedelivered on the 4th of February 1994. With this particular decision, the Fedstarted communicating the policy rate at the end of each meeting and the pro-cedure has not been changed ever since.6 The last decision in the sample wasmade on the 16th December 2008 in the midst of the post-Lehman financialcrisis, when the Fed decided to cut the reference rate by 75 basis points to thetarget range 0 - 1/4 percent.

The main focus of the paper is on the 60 FOMC decisions from the samplethat resulted in change of the Fed funds target rate and the analysis of mon-etary policy shocks estimated around those decisions are analysed across twodimensions. According to the direction of the change, the 60 decisions aredivided into 31 opting for an interest rate hike and 29 for an interest rate cut.

6See Piazzesi (2005) and Gurkaynak, Sack and Swanson (2005). The starting date in the sample has beenchosen accordingly.

16

Both are equally split across the sample as shown in Table A.1 in the Ap-pendix. Secondly, I follow Kuttner (2001) to calculate the “surprise element”of each of the decisions, namely what is the portion of the delivered targetchange that was unexpected by the markets. Then, the two sub-groups ofpolicy actions (hikes and cuts) are further split depending on the size of thesurprise indicator, as will be explained subsequently.

To begin with, the policy surprise indicator is calculated using Fed funds fu-tures data and in particular, the current 1-month futures contract on (monthly)average federal funds target rate. Even though some previous studies, such asCochrane and Piazzesi (2002) and Rigobon and Sack (2004) use Eurodollarinterest rates and futures to measure policy surprises, Gürkaynak, Sack andSwanson (2006) showed that Federal funds futures are the best predictors oftarget funds rate changes 1 to 5 months ahead.7

The indicator is calculated as follows. For a Fed decision that took place atday d of the month m, the unexpected change in the policy rate, scaled up bythe factor that takes into account the number of days in the month affected bythe change is calculated as:

∆iu = DD−d

(Fm,d −Fm,d−1) (1)

where D is the number of days in the current month and Fm,d is the Fed fundsrate implied by the current-month futures contract value. The closing futuresprice, Fm,d , incorporates all the analysed decisions except from the interestrate cut delivered on the 15th of October 1998, when the FOMC statement wasreleased after the close of the futures market. For this particular policy action,the difference between the opening quote on the 16th and the closing quoteon the 15th is used to calculate the surprise indicator.8 Finally, if the decisionwas widely expected, the above change should be close to zero and the entirechange should be ascribed to the “anticipated element” of the change:

∆ia =∆i−∆iu (2)

In order to minimise the effect of month-end noise, I calculate an unscaledchange for any decisions that came in place in the last 10 calendar days of

7See Bernanke and Kuttner (2005).8See Bernanke and Kuttner (2005).

17

any month.9 Table A.1 reports the surprise indicator for all the decisions inthe sample. As it can be noticed, the market was surprised by different policyactions of the Fed on both upside and downside. Most of the time, the surprisescan be considered as surprises in “magnitude” of the change, i.e. the futuresmarket correctly anticipated the direction of the change but not the size of it.The four selected policy actions in the Table, two target rate hikes and twotarget rate cuts, might be considered as surprises in direction of the change,where the market expected the Fed to leave interest rates unchanged.

Figure 1: Fed Funds Rate and the Surprise Indicator. The Figure reports his-tograms of sizes of the Fed funds rate changes (upper panels) and the surpriseindicator (lower panels). The x-axis is expressed in basis points and the y-axisshows the number of corresponding decisions.

Hikes Cuts

Hikes Cuts

9Kuttner (2001) proposes 3 days for the same purpose. 10 days are chosen to bring the measure closer towhat previous studies using tick-by-tick data produced, most notably Fleming and Piazzesi (2005).

18

Figure 1 illustrates empirical distributions of target changes and the surpriseindicator. Almost all decisions to increase the Fed funds target rate werebrought in 25-basis points sizes, while almost half of the target rate cuts werehalf-a-percentage cuts. The average size of interest rate hikes is thus 29 basispoints, while the average size of the policy rate cuts is 41 basis points. Thismight be one of the reasons for which the distribution of the surprise indicatoraround rate cuts displays a higher dispersion (standard deviation of 18 basispoints) and excess kurtosis (2.34) than the distribution of indicator after theincreases of the target rate (standard deviation of 7 basis points and excesskurtosis of 1.58), see the lower panels of Figure 1. The results presented inthis paper are corrected for the size of changes in the target rate, so that theestimated policy shocks correspond to a 25 basis points hike or cut of the Fedfunds rate. Only then the shocks from different policy actions can be compa-rable.

2.2 Interest Rates

Interest rates used in the analysis stem from off-the-run US Treasury bills andbonds. In particular, I use the 3-month and 6-month secondary market T-billsrates10 and from 1-year to 10-year off-the-run constant maturity yields fromGurkaynak, Sack and Wright (2007)11. Off-the-run treasuries are used to avoidthe treatment of “repo-specialness” implicit in the on-the-run treasuries.12 Allthe yields are continuously compounded, whereas quarterly and semi-annualcompounding is assumed for the 3-month and the 6-month rate, respectively.13

Figure 2 illustrates the entire term structure for the sample period.

A major advantage of this particular dataset of daily interest rates is that thequotes of corresponding T-bills and T-bonds are compiled in a narrow time-window after the FOMC statement is usually published, which is around 2P.M. - 2:15 P.M. Eastern Time. Specifically, the quotes for T-bills are releasedat 2:30 P.M., whereas the quotes for T-bonds from the Gurkaynak et al. (2007)are obtained from the Federal Reserve Bank of New York at 3 P.M. until 1996and from GovPX, Inc. at 5 P.M. from 1996 until the end of the sample.

10Obtained from the Federal Reserve Economic Data base (FRED), under DTB3 and DTB6. The two are notconstant-maturity yields.

11The data can be downloaded from http://www.federalreserve.gov/econresdata/researchdata.htm.

12See Duffie (1996) and Jordan and Jordan (1997).13See Hull (2008).

19

http://www.federalreserve.gov/econresdata/researchdata.htm


Figure 2: Interest Rates. The Figure plots interest rates from US Treasuryyields along with the NBER recessions (grey areas) and fed funds target in-creases (solid green) and decreases (dashed red lines).

Even though interest rates on decision days are released in a short time-frameafter the announcements by the Fed, their first difference “lasts” for one en-tire day. If the policy meeting took place on the day when Bureau of LaborStatistics’ released its employment report, for example, the FOMC membersmight have changed their perspective on the desired level of target rate justhours before the rate announcement.14 Markets might have reacted to the em-ployment report as well. To address this potential endogeneity problem, whereboth policy maker and interest rates react to other information coming out onthe announcement day, I perform a robustness check of the main findings, us-ing one-hour changes of selected interest rates around the FOMC statementreleases, reported in Fleming and Piazzesi (2005).

3 High-Frequency Identification

3.1 Monetary Policy Shocks

3.1.1 Definition

Let us assume there is a term structure model that can well explain both time-series and cross-sectional variation of nominal interest rates (e.g. US Treasuryyields) in a given time period. The model can be used to predict interest rate

14See Bernanke and Kuttner (2005).

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on an n-period zero-coupon bond y(n)t right after the FOMC announced its

policy-rate decision, conditional on all the information available right beforethe FOMC meeting (e.g. a previous day closing quote):

E[

y(n)d |Id−1

]where d is the day when the fed funds target was changed and Id−1 is theinformation set in the previous day. The model-implied forecast error, i.e. thedifference between the ex-post interest rate and the model expectation:

εd = y(n)d −E

[y(n)

d |Id−1

](3)

is considered as monetary policy shock, defined in Piazzesi (2005) and Cochraneand Piazzesi (2002). What is new in the present analysis, is that the estimatedpolicy shocks are split, according to direction of the policy rate change andaccording to the level of corresponding surprise indicator, in order to exploreasymmetries in interest rate response. The big question is whether shocks,arising from different policy actions, have different statistical properties.

3.1.2 Splitting the Shocks according to the Surprise Indicator Value

As shown in Table A.1, some FOMC decisions surprised the Fed funds futuresmarket to much higher extent than the other ones. In response to this largelyunexpected decisions, it might be reasonable to assume that all the interestrates in the term structure moved dramatically. This section explains how thetwo sub-groups of policy actions (hikes and cuts) are further split in order toassess the reaction of interest rates to policy actions with different “levels ofuncertainty”.

To begin with, the empirical distribution of the surprise indicator is used todefine different quartiles15 (expressed in basis points) for both hikes and cuts.For example, the first two quartiles (50th percentile) include all the policyactions after which the surprise indicator was lower than -7.1 and higher than6.8 basis points. These threshold values are then used to isolate from single

15Three values of the surprise indicator that divide the cumulative distribution function of the surprise indi-cator to 4 equal parts.

21

sub-groups of policy actions (e.g. hikes) those that particularly surprised theFed watchers. In such a way, we can analyse not only the average reactionof interest rates to all policy actions, but also to those FOMC announcementsthat might have plausibly resulted in stronger response of interest rates.

3.2 Models

3.2.1 Dynamic Term Structure Model

Setting. The model used in the analysis is an affine Gaussian term structuremodel in the spirit of Duffie and Kan (1996) and Duffee (2002) proposed inJoslin, Singleton and Zhu (2011) (JSZ), where the one-period interest rate isan affine function of a small number of pricing factors Pt:

y(1)t = ρ0 +ρ1Pt (4)

ρ0 is a scalar proportional to the average long-run one-period interest rateand ρ1 is a vector of factor loadings on the one-period rate. The factors areassumed to follow a VAR(1) dynamics under the risk-neutral measure Q:

Pt = KQ

0 +KQ

1 Pt−1 +ΣεQt (5)

where εQt is assumed to be distributed as N(0,Σ). It can be shown that the

equations (4) and (7) generate affine pricing, so that an n-period yield on azero-coupon bond is also an affine function of the pricing factors as:

y(n)t = An +BnPt (6)

where the hyper-parameters An and Bn are complicated non-linear functionsof the underlying parameters. See Appendix A for a detailed derivation.

As it can be noticed, only the Q distribution of the pricing factors Pt is suffi-cient for imposing no-arbitrage condition and obtaining closed-form solutionsfor bond yields of higher maturities. The market prices of risk in the Joslinet al. (2011) setting are thus constructed by using the physical distribution Pof pricing factors:

22

Pt = KP0 +KP

1 Pt−1 +ΣεPt (7)

and in particular, from conditional expectations of the pricing factors under theQ distribution, equation (5), and under the P distribution, equation (7). Startby re-writing the equation (5) as:

Pt = EQ [Pt|I t−1]+ΣεQt (8)

and subtract the conditional expectation of the pricing factors under Q giventhe information in I t−1 from both sides of (7):

Pt −EQ [Pt|I t−1]=(KP

0 −KQ

0

)+

(KP

1 −KQ

1

)Pt−1 +ΣεPt (9)

The equation (9) defines market prices of risk (MPR), the vector(KP

0 −KQ

0

)represents the constant MPR and the matrix

(KP

1 −KQ

1

)shapes the time-varying

part of the MPR. As shown in Joslin et al. (2011), the MPR process can be con-strained by reducing the rank of the matrix

(KP

1 −KQ

1

)to allow for a smaller

number of time-varying “risks” to be priced in yields.16 Specifically, Cochraneand Piazzesi (2008) show that only the level shock should be priced-in and sothe rank of the matrix should be set to 1. On the other side, Duffee (2010)and Joslin, Priebsch and Singleton (2010) argue that both level and slope fac-tors are responsible for driving excess returns in bond yields and thus the rankshould be set to 2. The preferred model specification in this paper is the onewhere MPRs behave in the latter way.

Finally, the pricing factors Pt in the JSZ are linear combinations of (readilyobservable) yields, e.g. the first three principal components of the T ×N ma-trix of yields, where T is the number of observations and N is the number ofmaturities. For this reason, the estimation of the model is fairly easy and astandard maximum-likelihood estimator converges to a global maximum al-most instantaneously.17

16A “more” restrictive constraint would be to impose the number of ranks on the matrix[(KP0 −KQ0

)(KP1 −KQ1

)], and this would constrain the number of both constant and time-varying market prices

of risk. See Joslin et al. (2011) and the Appendix B.3 for details.17Nonetheless, different restrictions need to be imposed on the parameters values, so that the model is well

identified. The details are reported in Appendix B.

23

Policy Shock. Given the explicit separation of parameters governing risk-neutralQ and historical P distribution of yields, the evolution of pricing factorsunder the historical measure is the one relevant for forecasting.18 Let us definea 1-day ahead forecast of the yield on an “n”-periods to maturity bond as:

EP[

y(n)t+1|I t

]= An +BnEP [Pt+1|I t]

The 1-day forecast error around the FOMC statement day:

εJSZd = y(n)

d −EP[

y(n)d |Id−1

](10)

is considered as the monetary policy shock, i.e. the response in the yield thatcan not be explained by the fitted model.

3.2.2 Random Walk

Market prices themselves usually incorporate a vast amount of informationthat can be used to assess an oncoming policy action by the Fed. A naivemodel that forecasts “no-change” in interest rates generates the forecastingerror:

εRWd = y(n)

d − y(n)d−1 (11)

equal to the one-day difference in the yield. These results are reported in orderto have a “model-free” insight into extracted monetary policy shocks.

3.3 Policy Shocks in Other Methods

3.3.1 Standard Vector Autoregression

Standard VAR in reduced form -, structural - or Dynamic Stochastic GeneralEquilibrium models does not account for asymmetries in response of model-

18Notice that a Vector autoregression of pricing factors under P can incorporate further information about theeconomy beyond that contained in the yield curve itself, see Joslin et al. (2010).

24

variables to a monetary policy shock. Some form of regime-switching19 can beestimated in order to obtain different parameters of interest for different policyregimes (e.g. a hiking cycle). Nonetheless, Cochrane and Piazzesi (2002)argue that the identification of a policy shock in a VAR requires some strongassumptions on the contemporaneous relation between monetary policy andinterest rates, namely that one of the two does not react instantaneously to theother. What is more, the orthogonalisation choice completely determines theeffect of the target rate shock on long-term interest rates. For these reasons,Cochrane and Piazzesi (2002) propose the high-frequency identification usedin this paper.

3.3.2 Event-study Approach

In the event-study approach, monetary policy surprises obtained from Fedfunds futures data are related to the first difference in interest rates aroundFOMC meetings using OLS regression.20 As it it shown in the data Section(see 2), the policy surprises can have a different sign for both increases anddecreases of the Fed funds target rate and the Table 1 illustrates why is it so.

Table 1: Surprise Indicator. The Table illustrates how the surprise indicator(rows) shown in Table A.1 can have a different sign for policy actions thatresulted in the same direction of change (columns) of the Fed funds targetrate.

DirectionHikes Cuts

Surprise Element + -e.g. Exp: +25 –» +50 e.g. Exp: -25 –» -50

Surprise Element - +e.g. Exp: +75 –» +25 e.g. Exp: -50 –» -25

If the Fed increased the Fed funds target less than markets expected, the sur-prise indicator will be positive, as much as, when an interest rate cut was deliv-ered and the markets expected a bigger cut. Even though most of the time the

19See for example Choi (1999) for an application of a Threshold-VAR.20See the seminal paper of Kuttner (2001).

25

indicator is positive for hikes and negative for cuts, the presence of negative(positive) revisions after increases (decreases) of the Fed funds rate makes theinterpretation of the slope coefficient in the mentioned regression difficult. Us-ing tick data to obtain more accurate “reading” of the surprise indicator mightnot help as well. The aforementioned study by Fleming and Piazzesi (2005)reports positive and negative changes in the surprise indicator for both hikesand cuts.

4 Results

4.1 Model parameters and pricing errors

Table 2 reports estimated parameters of the preferred model (i.e. level andslope risks priced-in). The first two parameters from the top shape the feed-back matrix under risk-neutral distributionQ. The L• parameters are estimatedlower diagonal elements of the Cholesky-decomposed variance-covariance ma-trix Σ. The rest of the parameters, are the elements of the vector KP

0 and feed-back matrix under historical measure KP

1 . Finally, Table 2 reports asymptoticand bootstrapped21 standard errors for all of the parameters, and bootstrappedstandard errors for the feedback matrix.22

Before moving to estimated monetary policy shocks, we need to make surethat the model fits the data reasonably well. Table 3 reports absolute pricingerrors, i.e. the sum of absolute differences between the cross-section of ob-served and model-generated interest rates. As it can be noticed, all the modelspecifications that accommodate time-varying MPRs perform better than therisk-neutral model, i.e. the model where the rank of the matrix

(KP

1 −KQ

1

)in equation (9) is set to 0. Assuming that the level risk only drives the riskpremia brings the highest marginal improvement in pricing. The performanceof the model is further improved by assuming that the slope risk is priced aswell. Allowing for unconstrained MPR (the “L, S & C” model) adds basicallynothing to the model fit and for this reason, I consider the “L & S” model asthe preferred specification.

21Bootstrapped standard errors are calculated as follows. A starting value for pricing factors is randomlychosen from the dataset. The estimated parameters are then used to simulate a time series of pricing factors with4,000 observations. The parameters and the simulated path of pricing factors produce a simulated yield curve.The model is estimated on such simulated yields for 1,000 times.

22Appendix B.3 shows why this is the case.

26

Table 2: Estimated Parameters. The Table reports the estimated parameters’values (the first column from left), together with asymptotic (the second col-umn) and bootstrapped (the third column) standard errors.

Parameter Estimate Asymptotic S.E. Bootstrapped S.E.λ

Q11 0.997 (0.0031) (0.00524)α 0.813 (0.0110) (0.01741)

L1,1 0.049 (0.0088) (0.01258)L2,1 0.002 (0.0184) (0.01841)L3,1 -0.036 (0.0159) (0.01532)L2,2 0.064 (0.0119) (0.01658)L3,2 0.035 (0.0150) (0.01789)L3,3 0.053 (0.0122) (0.01970)KP

0,1 0.004 - (0.00275)KP

0,2 -0.032 - (0.00356)KP

0,3 0.065 - (0.00770)KP

1,11 0.997 - (0.00046)KP

1,21 0.000 - (0.00096)KP

1,31 -0.004 - (0.00116)KP

1,12 -0.003 - (0.00068)KP

1,22 0.985 - (0.00024)KP

1,32 0.029 - (0.00211)KP

1,13 -0.007 - (0.00114)KP

1,23 -0.005 - (0.00206)KP

1,33 0.977 - (0.00301)

27

Table 3: Pricing Errors. The Table reports pricing errors for selected interestrates (columns) and different model specifications (rows) in basis points. Inparticular, the Q model is the one where the rank of the matrix that shapes thetime-varying MPR in equation (9) is equal to 0. The models L (level), L &S (level and slope) and L, S & C (level, slope and curvature) are those wherethe rank equals to 1, 2 and 3, respectivelly. The negative average value of thelikelihood function is reported in the brackets.

6m 2Y 4Y 6Y 7Y 9YQ (-4.67) 13.9 9.6 8.1 4.1 1.6 7.9L (-9.74) 6.3 7.3 3.0 1.8 1.5 3.1L & S (-14.99) 5.8 6.6 1.6 0.9 1.3 1.1L, S & C (-16.98) 5.7 6.5 1.5 0.9 1.3 0.8

4.2 Interest Rate Responses to Policy Shocks

Table 4 reports the main result of the paper. First, the short end of the USTreasury curve seem to react more strongly to expansionary policy actions.Even though the absolute values of an estimated 25-basis points shock are low(1.5 basis points for hikes and -2.2 basis points for cuts of the Fed funds rate),their relative difference is high and persistent across the robustness checks per-formed, as it is shown in the next Section. Beside the mean, the policy shocksfollowing cuts are also more volatile, with standard deviation of 3-month rateresponse to hikes and cuts of 4.5 and 6.8 basis points, respectively. Distri-butions of both type of responses have fat-tails, with Jarque-Berra statistic of7.05 for hikes and 7.39 for cuts.

Secondly, the average response of long-term interest rates to all the FOMCannouncements to increase (or decrease) the Fed funds rate is not statisticallydifferent from zero. Yet, if one constrains the sample to those policy actionsaround which uncertainty was greater, there seem to be a statistically signifi-cant positive response of long-term interest rates to target rate cuts. One pos-sible explanation of the result is that a looser policy today means a higherinflation in the future, and thus higher nominal interest rates.23

23And vice versa, see Cochrane (2006).

28

Table 4: Interest Rates Reactions. The Table reports estimated policy shocksusing the preferred model for selected maturities of interest rates (columns)and for different quartiles of the empirical distribution of surprise indicator(rows) in basis points. Q j stand for the j-th quartile of the cdf. The valuesin brackets are t-statistics from a two-sample t-test of equal means, where anygiven sample is compared to a sample of one-day forecast errors on non-policydays. Bold fonts denote level of significance of 0.10.

Hikes3m 6m 2Y 5Y 8Y 10Y

Q1 4.1 5.6 5.5 4.5 3.7 3.2(1.62) (1.60) (1.18) (0.97) (0.82) (0.71)

Q2 3.3 4.2 3.2 2.1 1.2 0.7(2.42) (2.14) (1.21) (0.80) (0.49) (0.27)

Q3 1.7 1.8 0.9 0.2 -0.2 -0.5(1.44) (1.05) (0.41) (0.12) (-0.12) (-0.29)

All 1.5 1.1 0.4 -0.1 -0.5 -0.7(1.73) (0.97) (0.27) (-0.12) (-0.43) (-0.67)

Cuts3m 6m 2Y 5Y 8Y 10Y

Q1 -1.2 -0.6 0.4 0.6 0.6 0.7(-0.44) (-0.20) (0.15) (0.26) (0.34) (0.39)

Q2 -0.3 1.1 2.6 2.6 2.4 2.3(-0.19) (0.62) (1.65) (1.87) (1.95) (1.96)

Q3 -1.1 -0.3 0.7 0.9 1.0 1.0(-0.81) (-0.22) (0.45) (0.64) (0.76) (0.84)

All -2.2 -1.9 -0.9 -0.5 -0.3 -0.2(-1.82) (-1.24) (-0.58) (-0.41) (-0.27) (-0.17)

So the reaction of long-term rates is statistically significant and positive onlyafter “surprise” cuts and not all the cuts. It is important to notice that mostof these are surprises on the negative side, i.e. the Fed decreased the policyrate more than the market expected. That said, the initial positive reaction oflong-term interest rates to those particular policy actions might point to a “mar-ket concern” that the move was too large and thus that the future inflationarypressures might be difficult to contain.

29

Table 5: Long-term Interest Rates Reactions to Q2 Cuts. The Table reportsone-day changes in long-term rates with selected maturities (columns) afterevery single policy action to decrease the fed funds rate classified into Q2 sub-group in basis points.

Cuts, Q2

Day Month Year Decision 5Y 8Y 10Y15 10 1998 -25 1.5 1.2 1.317 11 1998 -25 1.0 2.3 2.93 1 2001 -50 21.9 21.9 20.2

18 4 2001 -50 -10.4 -7.7 -6.115 5 2001 -50 2.8 4.2 4.527 6 2001 -25 6.2 2.1 0.017 9 2001 -50 3.9 3.0 3.82 10 2001 -50 -2.5 -2.0 -2.06 11 2001 -50 -4.5 -2.9 -2.26 11 2002 -50 2.1 -1.5 -2.8

25 6 2003 -25 11.9 9.8 9.418 9 2007 -50 -1.8 2.0 3.331 10 2007 -25 9.7 8.0 7.422 1 2008 -75 -21.3 -14.4 -11.118 3 2008 -75 18.2 11.2 8.48 10 2008 -50 27.3 28.4 26.3

29 10 2008 -50 1.1 4.5 6.416 12 2008 -75 -16.3 -17.9 -17.5

For the sake of clarity, Table 5 reports all the policy actions to decrease interestrates, that ended up in the first two quartiles of the distribution, according tothe surprise indicator. The reported is the size of the fed funds rate change andthe corresponding changes in long-term rates.

4.2.1 Robustness Checks

Models. First of all, the main result should hold irrespectively of modellingassumptions. As shown in Table 3, the pricing performance of the “L” and“L&S” models is pretty similar. In addition, the one-day change around policymeetings is also considered, in order to obtain model-free policy shocks. The

30

first two columns of the upper panel in Table 6 show the outcomes of the twochecks. The estimated shock to interest rates are in both cases higher after pol-icy rate cuts, while the mean of the “L” model-estimated shocks after hikes iseven statistically insignificant. The first three rows of the lower panel confirmthe positive reaction of long-term interest rates to FOMC announcements tocut the target rate that were largely unexpected in size.

Sub-samples. The main result for the short end of the Treasury curve holdsafter excluding the financial crisis, started in July 2007 until the end of thesample. On the other side, the series of policy rate cuts delivered by the Fed inthe mentioned period seems to be driving the results on the long end. The mag-nitude of the response in long-term rates falls by half and becomes statisticallyinsignificant.

Finally, the values of the surprise indicator are particularly high after unsched-uled policy meetings. There are arguably six such meetings in the sample, oneinterest-rate hike delivered on the the 18th of April 1994, and five interest-ratecuts from the 15th of October 1998, 3rd of January 2001, 18th of April 2001,17th of September 2001, and the 22nd of January 2008. I exclude those de-cisions and re-calculate the average one-day response to interest rates to theremaining policy actions. The main result holds for both the short rates, andlong rates around interest rate cuts.

Tick Data. As already mentioned in the data Section, daily frequency mightnot be enough to resolve the endogeneity problem of separating interest ratesresponse to monetary policy from the policy response to interest rates. Forthis reason, I use results from Fleming and Piazzesi (2005), who reportedTreasury yield changes of selected maturities to FOMC announcements in aone-hour window around the announcement.24 The analysed period includesall the FOMC decisions from February 1994 until December 2004. In thissense, the results for long-term interest rates around cuts are very similar tothe “RW ex.2008” case - the reaction of 10-year interest rate seem to be sta-tistically insignificant. On the short end, the main result again holds, as the3-month rate reacts much strongly to announced decreases of the Fed fundstarget rate. All the other reported numbers are corrected for the average sizesof increases/decreases of the Fed funds rate mentioned in the data Section.

24The changes are reported in the Appendix B of their paper.

31

Table 6: Robustness Checks. The upper panel reports the responses in basis points of the 3-month rate with t-stats (in(•) brackets from a two-saple t-test) and standard deviations (in • brackets), estimated using the term structure modelwith priced level factor (”L”), the random walk (”RW”), the random walk excluding year 2008 (”RW ex. 2008”) andunscheduled meetings of the FOMC (”RW ex. Un.”) and the random walk estimates from the Fleming and Piazzesi(2005) data (”RW F&P“). The lower panel reports the estimated shocks following Q2 cuts to selected rates (columns)and across different models (rows).

L RW RW ex. 2008 RW ex. Un. RW F&PHikes Cuts Hikes Cuts Hikes Cuts Hikes Cuts Hikes Cuts

Q1 3.7 -1.1 4.6 -1.8 4.6 -1.6 2.4 0.2 8.7 -6.8(1.27) (-0.65) (1.62) (-0.61) (1.62) (-0.81) (1.23) (0.11) 5.75 9.87

Q2 3.3 -0.1 2.1 -0.8 2.1 -0.6 1.6 -0.4 6.5 -5.3(1.88) (-0.51) (1.10) (-0.45) (1.10) (-0.37) (0.98) (-0.21) 5.00 9.14

Q3 2.1 -0.8 1.8 -1.5 1.8 -1.6 1.1 -1.1 2.4 -4.5(1.20) (-1.10) (1.34) (-1.09) (1.34) (-1.35) (1.03) (-0.87) 6.94 7.89

All 1.8 -1.9 1.4 -2.7 1.4 -2.4 1.0 -2.3 0.7 -3.7(1.34) (-2.09) (1.78) (-2.13) (1.78) (-1.73) (1.38) (-1.69) 6.73 10.05

Cuts, Q23m 6m 2Y 5Y 8Y 10Y

L -0.1 1.4 2.8 2.7 2.5 2.3(-0.51) (0.05) (1.12) (1.59) (1.91) (2.11)(-0.19) (0.62) (1.65) (1.87) (1.95) (1.96)

RW -0.8 0.3 2.4 2.4 2.3 2.2(-0.45) (0.23) (1.67) (1.79) (1.86) (1.94)

RW ex. 2008 -0.6 -0.5 1.3 1.3 1.4 1.4(-0.37) (-0.22) (0.61) (0.76) (0.89) (0.98)

RW ex. Unsched. -0.4 -0.5 1.5 2.5 2.5 2.3(-0.21) (-0.27) (0.94) (1.54) (1.69) (1.75)

RW F&P -5.3 -6.5 -3.5 -2.0 - -0.69.14 9.01 10.45 9.63 - 8.04

32

4.3 Decomposing Interest Rate Reactions

This Section explains why the notion of return risk premia25 is used to assesswhether bond risk premia react to FOMC announcements. It does so by show-ing how the usual decomposition of yields and forward rates to expectationsand premia in this setting might provide completely different indications, de-pending on the way, the process for market prices of risk in equation (9) ismodelled.

4.3.1 Definitions

One of the main uses of affine models is to decompose the term structure ofnominal interest rates into expected future short rates and premia.26 The threeknown ways of thinking about yield curve define:27

• Long-term interest rates as the sum of average future one-period ratesplus a risk premium:

y(n)t = 1

nE

[y(1)

t + y(1)t+1 + ...+ y(1)

t+n−1|I t

]+ rp(n)

t (12)

• A long-term forward rate as the sum of expected future one-period rateand the term premium:

f (n)t = E

[y(1)

t+n−1|I t

]+ tp(n)

t (13)

where the instantaneous forward rate reads:

f (n)t = ny(n)

t − (n−1)y(n−1)t

• Expected one-period return on long-term bonds to be equal to the ex-pected return on short-term bond plus a return risk premium:

E[r(n)

t+1|I t

]= y(1)

t + rrp(n)t (14)

25See for example Cochrane and Piazzesi (2005) or Ludvigson and Ng (2009).26See for example Kim and Wright (2005) and Bauer and Rudebusch (2011).27See Cochrane and Piazzesi (2008).

33

Accordingly, the estimated one-day responses of interest rates can be also di-vided into expectation part and premia part. As the data used in this study aredaily and the term structure model includes no explicit variables (e.g. inflation,industrial production, survey data etc.), the described decompositions heavilydepend on modelling choices for market price of risk dynamics. A modellingchoice amounts to setting the rank of the matrix

(KP

1 −KQ

1

)in the MPR pro-

cess (9) to a number lower then the number of pricing factors. By reducingthe rank of that matrix, the VAR matrix in the transition equation (7) underP changes as well,28 and that matrix is essential in estimating the expectationterms in equations (12), (13) and (14).

4.3.2 Return Risk Premia

Let us start by looking at the return risk premia. Expected excess return on ann-periods to maturity bond can be rewritten from (14) as:

rrp(n)t = E

[r(n)

t+1|I t

]− y(1)

t (15)

where E[r(n)

t+1|I t

]is the expected holding-period return from buying an n-

periods bond in t and selling it as an n−1-periods bond in t+1:

rrp(n)t = E

[p(n−1)

t+1 |I t

]− p(n)

t − y(1)t

where p(n)t is the log-price of the bond. That said, model-implied expected

excess return using (6) and (7) is:

rrp(n)t = (An − An−1)+ (BnPt −Bn−1E [Pt+1|I t])− y(1)

t (16)

Equation (15) shows that the longest holding return one needs to calculate,given the interest-rates maturities in the dataset, is one year. From (16) itis therefore clear that the expectation E [Pt+1|I t] is obtained by raising theVAR matrix in (7) to the power of 250. Since interest rates at daily frequencyare highly persistent, the term E [Pt+1|I t] seem to be relatively insensitive

28See the details in the Appendix B.3.

34

to different feedback matrices from the “L” and the “L&S” models. Table 7illustrates this point.

Table 7: Return Risk Premia Reaction for all Hikes and Cuts. The Tablereports the estimated one-day changes in model-generated expected excessreturns for selected maturities (columns) and across modelling assumptions(rows) in basis points. Bold fonts denote level of significance of 0.10.

Hikes(3m,6m) (6m,1Y) (2Y,3Y) (5Y,6Y) (7Y,8Y) (9Y,10Y)

L -2.1 -2.3 -2.3 -1.4 -1.1 -0.8(-3.18) (-2.16) (-1.12) (-0.79) (-0.65) (-0.54)

L & S -1.6 -2.8 -2.9 -2.0 -1.6 -1.4(-3.00) (-3.01) (-1.69) (-1.34) (-1.16) (-1.03)

Cuts(3m,6m) (6m,1Y) (2Y,3Y) (5Y,6Y) (7Y,8Y) (9Y,10Y)

L 2.5 2.9 3.2 2.6 2.4 2.2(2.32) (1.77) (1.14) (1.03) (1.01) (1.01)

L & S 2.4 3.7 3.9 3.3 3.0 2.9(2.74) (2.35) (1.55) (1.50) (1.50) (1.51)

The upper panel of Table 7 shows the one-day average changes of risk pre-mia for all the FOMC announcements that resulted in an increase of the fedfunds rate. As it can be noticed, the reactions of premia across the two mod-elling assumptions is similar and negative. The lower panel of the table reportsequivalent changes following a decrease of the policy rate. As in the case ofinterest rates, risk premia seem to react more strongly to interest rate cuts, andthe sign of the reaction is opposite from the direction of the policy-rate change.This is broadly speaking in line with previous studies29 who argue that premiais on average countercyclical, yet can still go in different directions aroundsingle episodes.30

29See for example Piazzesi and Swanson (2008) and Ludvigson and Ng (2009).30See Bauer and Rudebusch (2011).

35

4.3.3 Yield Risk Premia

The yield risk premia in equation (12) is usually estimated by subtracting theexpectations part from the fitted yields. Differently from obtaining return riskpremia, the VAR matrix from equation (7) used to find the yield risk premiamust be raised to a much higher power. The expected future one-year rate9 years ahead, for instance, is estimated by raising the VAR matrix to thepower of 2250.31 For this reason, small changes in the VAR matrix producecompletely different decompositions of yields, see Figure 3.

Figure 3: Decomposing the 10-year Yield. The Figure plots model implied 10-year Treasury yield (solid blue line), average one-year rate expectation (dashedgreen) and yield risk premium (dashed red) from the model where only leverrisk is priced-in (upper panel) and the preferred model (lower panel), alongwith the NBER recessions (grey areas).

“L” Model

“L&S” Model

31This is why the decomposition of forward rates according to (13) shows that term premia entirely explainthe dynamics of longer-term forward rates, no matter which model specification is used.

36

The upper panel of the figure reports the average future expectations of theshort-rate and the risk premia generated by the “L” (level risk) model and thelower panel reports the same decomposition using the “L&S” (level and sloperisk) model.32 Since the VAR matrix in the “L” model provides a quickerconvergence of factor’s forecasts to the long-run steady state than the “L&S”model, there is almost no persistency in long-term average expectations. Mostof the movement in long-term yields is ascribed to yield risk premia. Conse-quently, the decomposition of yields changes should also point to variation inrisk premia and not the expectations.

Table 8: Decomposing the RW Interest Rates Reactions to Cuts (Q2). TheTable reports the estimated one-day changes in yield risk premia (upper panel)and average short-rate expectations (lower panel) to interest rate cuts fromthe first two quartiles for selected maturities (columns) and across modellingassumptions (rows) in basis points. Bold fonts denote level of significance of0.10.

Yield Risk Premia3m 1Y 4Y 6Y 8Y 10Y

L -1.2 -0.1 1.7 2.1 2.1 2.0(-0.97) (-0.08) (1.33) (1.92) (2.01) (2.01)

L & S -2.1 -1.7 -0.4 0.4 0.6 0.8(-3.24) (-3.10) (-0.83) (0.67) (0.94) (1.08)

Average Short-Rate Expectations3m 1Y 4Y 6Y 8Y 10Y

L 1.0 0.8 0.5 0.3 0.2 0.2(1.41) (1.41) (1.41) (1.41) (1.41) (1.41)

L & S 1.9 2.4 2.6 2.0 1.7 1.4(1.02) (1.29) (1.66) (1.86) (1.91) (1.93)

Table 8 confirms this intuition, where the previously reported reaction of long-term interest rates is decomposed into yield risk premia reaction and averageshort-rate reaction. As it can be noticed, the “L” model estimates that long-term rates increase because the implicit term premia rise. On the other side,the “L&S” model assigns most of the reaction to the increase in average short-rate expectations. Again, the problem might be limited to the models that use

32As the Table 3 reports, the pricing performance of the two models is similar.

37

daily data and no macro-economic33 or survey data34 to better pin down thelong-term interest rate expectations.

5 Conclusion

Using the exact timings of the FOMC announcements, this paper shows thatinterest rates seem to react asymmetrically to Fed’s policy actions. Short-term interest rates respond more strongly to expansionary policy decisions andthe result holds for different modelling assumptions and across different sub-samples. Long-term interest rates rise on average after the Fed’s decisions todecrease interest rates more than the markets anticipated and the reason mightbe related to the fear of future inflation.

Since the estimated policy shocks i.e. model-implied forecast errors aroundFOMC statement releases, are statistically different from zero, the modelsused in the analysis systematically under/overpredict interest rates around pol-icy meetings. An appropriate regime-switching model might provide a betterperformance and a further insight into pricing “seasonalities” around FOMCmeetings mentioned in Piazzesi (2005).

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Bauer, Michael D. and Glenn D. Rudebusch (2011) “The signaling channel forFederal Reserve bond purchases,” Working Paper, No. 2011-21.

Bernanke, Ben S. and Kenneth N. Kuttner (2005) “What Explains the StockMarket’s Reaction to Federal Reserve Policy?” Journal of Finance, Vol. 60,No. 3, pp. 1221–1257, 06.

33See for example Ang, Bekaert and Wei (2008).34See for example Kim and Orphanides (2012).

38

Calvet, Laurent E., Aldai Fisher, and Liuren Wu (2010) “Dimension-InvariantDynamic Term Structures,” Working Paper.

Campbell, John Y and Robert J Shiller (1991) “Yield Spreads and Interest RateMovements: A Bird’s Eye View,” Review of Economic Studies, Vol. 58, No.3, pp. 495–514, May.

Canova, Fabio (2005) “The transmission of US shocks to Latin America,”Journal of Applied Econometrics, Vol. 20, No. 2, pp. 229–251.

Chen, Ren-Raw and Louis Scott (1993) “Multi-Factor Cox-Ingersoll-RossModels of the Term Structure: Estimates and Tests from a Kalman FilterModel,” Journal of Real Estate Finance and Economics, Vol. 27, No. 2.

Choi, Woon Gyu (1999) “Asymmetric Monetary Effects on Interest Ratesacross Monetary Policy Stances,” Journal of Money, Credit and Banking,Vol. 31, No. 3, pp. 386–416, August.

Christiano, Lawrence, Martin Eichenbaum, and Charles Evans (1996) “TheEffect of Monetary Policy Shocks: Evidence from the Flow of Funds,” Re-view of Economics and Statistics, Vol. 78, No. 1, pp. 16–34, 06.

Cochrane, John H. (2006) “Comments on “Macroeconomic Implications ofChanges in the Term Premium” by Glenn Rudebusch, Brian Sack and EricSwanson,” Working Paper.

Cochrane, John H. and Monika Piazzesi (2002) “The Fed and Interest Rates- A High-Frequency Identification,” American Economic Review, Vol. 92,No. 2, pp. 90–95, May.

(2005) “Bond Risk Premia,” American Economic Review, Vol. 95,No. 1, pp. 138–160, March.

(2008) “Decomposing the Yield Curve,” Working Paper.

Duffee, Greg (2010) “Sharpe ratios in term structure models,” EconomicsWorking Paper Archive 575, The Johns Hopkins University,Department ofEconomics.

Duffee, Gregory R. (2002) “Term Premia and Interest Rate Forecasts in AffineModels,” Journal of Finance, Vol. 57, No. 1, pp. 405–443, 02.

Duffie, Darrell (1996) “Special Repo Rates,” The Journal of Finance, Vol. 51,No. 2, pp. pp. 493–526.

39

Duffie, Darrell and Rui Kan (1996) “A Yield-Factor Model Of Interest Rates,”Mathematical Finance, Vol. 6, No. 4, pp. 379–406.

Ehrmann, Michael and Marcel Fratzscher (2004) “Taking stock: monetarypolicy transmission to equity markets,” Working Paper Series 354, EuropeanCentral Bank.

Evans, Charles L. and David A. Marshall (1998) “Monetary policy and theterm structure of nominal interest rates: Evidence and theory,” Carnegie-Rochester Conference Series on Public Policy, Vol. 49, No. 0, pp. 53 – 111.

Fleming, Michael J. and Monika Piazzesi (2005) “Monetary Policy Tick-by-Tick,” Working Paper.

Gurkaynak, Refet S, Brian Sack, and Eric Swanson (2005) “Do Actions SpeakLouder Than Words? The Response of Asset Prices to Monetary PolicyActions and Statements,” International Journal of Central Banking, Vol. 1,No. 1, May.

Gürkaynak, Refet S., Brian Sack, and Eric Swanson (2006) “Market-basedmeasures of monetary policy expectations,”Technical report.

Gurkaynak, Refet S., Brian Sack, and Jonathan H. Wright (2007) “The U.S.Treasury yield curve: 1961 to the present,” Journal of Monetary Economics,Vol. 54, No. 8, pp. 2291–2304, November.

Hamilton, James D. and Jing (Cynthia) Wu (2010) “Identification and Estima-tion of Affine-Term-Structure Models,” Working Paper.

Hull, John C. (2008) Options, Futures, and Other Derivatives with DerivagemCD (7th Edition): Prentice Hall, 7th edition.

Jordan, Bradford D. and Susan D. Jordan (1997) “Special Repo Rates: AnEmpirical Analysis,” The Journal of Finance, Vol. 52, No. 5, pp. pp. 2051–2072.

Joslin, Scott, Marcel Priebsch, and Kenneth J. Singleton (2010) “Risk Premi-ums in Dynamic Term Structure Models with Unspanned Macro Risks.”

Joslin, Scott, Kenneth J. Singleton, and Haoxiang Zhu (2011) “A New Per-spective on Gaussian Dynamic Term Structure Models,” Review of Finan-cial Studies.

40

Kim, Don H. and Athanasios Orphanides (2012) “Term Structure Estimationwith Survey Data on Interest Rate Forecasts,” Journal of Financial andQuantitative Analysis, Vol. 47, No. 01, pp. 241–272, February.

Kim, Don H. and Jonathan H. Wright (2005) “An arbitrage-free three-factorterm structure model and the recent behavior of long-term yields anddistant-horizon forward rates,”Technical report.

Kuttner, Kenneth N. (2001) “Monetary policy surprises and interest rates: Evi-dence from the Fed funds futures market,” Journal of Monetary Economics,Vol. 47, No. 3, pp. 523–544, June.

Ludvigson, Sydney C. and Serena Ng (2009) “Macro Factors in Bond RiskPremia,” Review of Financial Studies, Vol. 22, No. 12, pp. 5027–5067.

Piazzesi, Monika (2005) “Bond Yields and the Federal Reserve,” Journal ofPolitical Economy, Vol. 113, No. 2, pp. 311–344, April.

Piazzesi, Monika and Eric T. Swanson (2008) “Futures prices as risk-adjustedforecasts of monetary policy,” Journal of Monetary Economics, Vol. 55, No.4, pp. 677–691, May.

Rigobon, Roberto and Brian Sack (2004) “The impact of monetary policy onasset prices,” Journal of Monetary Economics, Vol. 51, No. 8, pp. 1553–1575, November.

Ruge-Murcia, Francisco J. (2006) “The expectations hypothesis of the termstructure when interest rates are close to zero,” Journal of Monetary Eco-nomics, Vol. 53, No. 1, pp. 1409 – 1424.

Taylor, John B (1995) “The Monetary Transmission Mechanism: An Empiri-cal Framework,” Journal of Economic Perspectives, Vol. 9, No. 4, pp. 11–26, Fall.

41

Appendix

A.1 Interest Rates

A.1.1 Affine Pricing

Following Duffie and Kan (1996), the one-period interest rate is an affine func-tion of Z-dimensional risk factor X t:

y(1)t = ρ0X +ρ1X X t (17)

where ρ0X is a scalar proportional to the average long-run one-period yield,ρ1X is a 1×Z vector of loadings of state variables on y(1)

t . The state variablesfollow an AR(1) process under the risk neutral measure Q:

X t+1 = KQ

0X +KQ

1X X t +ΣXεQt (18)

where KQ

1X is the feedback matrix, ΣX is the variance-covariance matrix of thenormally distributed error term ε

Qt ∼ N(0,1). Equations (17) and (18) ensure

affine pricing and it can be shown that any n-periods to maturity zero-couponyield is an linear function of the pricing factors as well:

y(n)t = AQ

n,X +BQ

n,X X t (19)

where:

BQ

n,X = KQ

1X BQ

n−1,X −ρ1X

AQ

n,X = KQ

0X BQ

n−1,X + 12

(BQ

n−1,X )′ΣX BQ

n−1,X + AQ

n−1,X −ρ0X

Finally, the pricing factors’ under physical measure P follow also an AR(1)process as:

42

X t+1 = KP0X +KP

1X X t +ΣXεPt (20)

A.1.2 JSZ Rotation

In the spirit of Chen and Scott (1993), let us assume that a Z -number ofinterest rates in the term structure are observed without error and let Pt be avector of those interest rates:

Pt =WYt

where W is a Z × N zero-one matrix, we can refer to as a selection matrix,and Yt is a vector representing the term structure of interest rates at time t.35

Pre-multiply the equation (19) for the entire cross-section of interest rates withthe selection matrix W:

Pt =W AQ

X +WBQ

X X t (21)

and express the latent factors X t in terms of the observable factors and theparameters. Plugging it back into equation (19) yields the rotated measurementequation:

Yt = A+BPt (22)

where:A =

(I−BQ

X

(WBQ

X

)−1W

)AQ

X

and

B = BQ

X

(WBQ

X

)−1

35Needless to say, the selection matrix can accommodate various modelling choices. For instance, it canrepresent loadings of the first Z principal components of a T ×N yield matrix, where T represents the numberof periods in the sample, while N stands for the number of maturities.

43

Applying the same idea to the short rates in (17), to the state variables dynam-ics under the risk neutral measure (18) and under the physical measure (20)yields the JSZ canonical Gaussian dynamic term structure model:

y1,t = ρ0 +ρ1Pt (23)

Pt = KQ

0 +KQ

1 Pt−1 +ΣεQt (24)

Pt = KP0 +KP

1 Pt−1 +ΣεPt (25)

Given the selection matrix W , the invariant transformations of single parame-ters of the model are equivalent to those in Joslin et al. (2011).36

A.2 Econometric Identification and Estimation

A.2.1 Parameter Identification

Solid identification of parameters is an essential part of dynamic term struc-ture models estimation. Before defining the likelihood function and providingestimation details, this section explains the identification strategy used, whichis mostly based on ideas from JSZ work.

Following Hamilton and Wu (2010), Calvet, Fisher and Wu (2010) and Bauerand de los Rios (2012), the KQ

1X matrix is set to be a power law structure, withzero non-diagonal elements and the following power relation on the matrix’diagonal:

λQzz =λQ11α

z−1

where λQ11 is the largest eigenvalue of the matrix KQ

1X , α is a scaling parametercontrolling the distance between the eigenvalues, and finally z = 2, ...Z. Giventhe pricing factors’ dynamics under the risk neutral measure Q in (24), the

36See Appendix B of the article.

44

pricing factors might not be necessarily stationary underQ, i.e. the eigenvaluesof KQ

1 might be equal or larger than one. As noted in Joslin et al. (2011), thelong-run means37 of the one-period rates in such case are not well-definedor negative, respectively. Consequently, the authors propose the followingidentification tactic. The ρ0 is set to zero and the drift of the most persistentfactor P1,t is set to be a constant:

KQ

0X =

kQ∞0...0

where kQ∞ is a derived parameter38. Finally, the scale of the pricing factorsρ1P is set to be a unit vector and the Σ is Cholesky-decomposed to a lowertriangular matrix LΣ with 2Z (2Z+1)/2 parameters to estimate.

That said, the parameters λQ11, α and Σ entirely caracterise the Q distributionof yields. The physical dynamics P, on the other side, is determined by the(KP

0 , KP1 , Σ) parameter set. The complete parameters’ vector is:

Θ=λQ

11,α,KP0 ,KP

1 ,L

A.2.2 Estimation

Let us now define the likelihood function. Following Chen and Scott (1993)and Joslin et al. (2010), it is assumed that the first Z principal componentsPt are observed without error and the remaining (N −Z) components Pu

t aremeasured with error:

Put =Wu A+WuBPt +Σξξt (26)

where Wu is appropriately sliced matrix of principal-components loadings on

37The intercept term in the equation (23).38Calculated in such a way that, a particular value of kQ∞ corresponds to the zero vector ρ0, given KQ1 , see

the appendix of Joslin et al. (2011).

45

the yield matrix and ξt is a vector of normally distributed pricing errors withzero means and the diagonal variance-covariance matrix Σ2

ξ. The conditional

joint density of the state vector and the Put unobserved components is:

pd f(Pt,Pu

t |Pt−1,Θ) = pd f

(Pt|Pt−1,KP

0 ,KP1 ,Σ

)× pd f

(Pu

t |Pt,λQ

11,α,Σ)

(27)

The Q parameters, λ11,α,Σ, are estimated using the maximum likelihood(ML) estimation. In a constrained optimisation39, a standard line-search al-gorithm is used where the descent direction is calculated with Quasi-Newtonmethod. The starting values for the covariance matrix are taken from the un-contrained VAR(1) estimation of the pricing factors. Departing from randomlychosen values of parameters

λQ

11,α, the algorithm converges almost instanta-

neously to the same solution to the 6th decimal. The parameters of the physicaldistribution,

KP

0 ,KP1, are estimated using OLS regression.

A.2.3 Reduced-Rank Regression

As mentioned in Section 3, the market prices of risk can be constrained byreducing the rank of the matrix

(KP

1 −KQ

1

)in equation (9) to a number r. In

that case, the parameters of the P distribution are computed as if they were MLestimates using the reduced-rank regression:

Pt −(KQ

0 +KQ

1 Pt−1

)=β0 +β1Pt−1 +εβt

where β1 is restricted to have a rank lower than the number of pricing factors.As it is shown in Joslin et al. (2011), the solution for β1 is singular valuedecomposition of β1, namely, β1 =UD∗

r V ′, where the matrix D∗r is obtained

by setting to zero all the singular values of D with index larger than r. Giventhe parameters

λQ

11,α,Σ, the ML estimates of the P parameters are then

given by:

39Only the non-negativity constraint on the diagonal elements of the covariance matrix is imposed.

46

KP0 = KQ

0 + β0 and KP1 = KQ

1 + β1

Finally, the base-case market price of risk specification in this study is consid-ered to be the one, where the rank of the β1 is set to r = 2, i.e. both “level” and“slope” risks are priced in yields.40

A.3 Tables

Table A.1: FOMC Meetings. The Table reports the dates of FOMC statementreleases, together with the size of the change of fed funds target rate in basispoints. Columns Surprise and Expected show the split of fed funds targetchanges to unexpected element, extracted from the 1-month fed funds futuresquotes and the “anticipated” element, see equation (1). Finally, the columnSurprise Move indicates policy actions for which the market arguably expected“no change”.

Day Month Year Decision Suprise Expected Surprise(bp) (bp) (bp) Move

4 Feb 1994 25 16 922 Mar 1994 25 11 1418 Apr 1994 25 25 0 Hike17 May 1994 50 12 386 Jul 1994 0 -2 -

16 Aug 1994 50 21 2927 Sep 1994 0 0 -15 Nov 1994 75 11 6420 Dec 1994 0 -23 -1 Feb 1995 50 2 48

28 Mar 1995 0 2 -23 May 1995 0 -1 -6 Jul 1995 -25 -9 -16

22 Aug 1995 0 -4 -26 Sep 1995 0 4 -15 Nov 1995 0 2 -19 Dec 1995 -25 -7 -18

40As in Duffee (2010) and Joslin et al. (2010).

47


31 Jan 1996 -25 -3 -2226 Mar 1996 0 1 -21 May 1996 0 1 -3 Jul 1996 0 -6 -

20 Aug 1996 0 -1 -24 Sep 1996 0 -12 -13 Nov 1996 0 2 -17 Dec 1996 0 0 -5 Feb 1997 0 -2 -

25 Mar 1997 25 2 2320 May 1997 0 -9 -2 Jul 1997 0 -1 -

19 Aug 1997 0 3 -30 Sep 1997 0 0 -12 Nov 1997 0 -3 -16 Dec 1997 0 -2 -4 Feb 1998 0 0 -

31 Mar 1998 0 0 -19 May 1998 0 -5 -1 Jul 1998 0 -2 -

18 Aug 1998 0 3 -29 Sep 1998 -25 4 -2915 Oct 1998 -25 -24 -1 Cut17 Nov 1998 -25 -12 -1322 Dec 1998 0 -4 -3 Feb 1999 0 1 -

30 Mar 1999 0 -1 -18 May 1999 0 10 -30 Jun 1999 25 -8 3324 Aug 1999 25 2 235 Oct 1999 0 6 -

16 Nov 1999 25 11 1421 Dec 1999 0 12 -2 Feb 2000 25 2 23

21 Mar 2000 25 -1 2616 May 2000 50 8 4228 Jun 2000 0 -2 -

48


22 Aug 2000 0 3 -3 Oct 2000 0 2 -

15 Nov 2000 0 0 -19 Dec 2000 0 3 -3 Jan 2001 -50 -24 -26

31 Jan 2001 -50 -5 -4520 Mar 2001 -50 -7 -4418 Apr 2001 -50 -45 -515 May 2001 -50 -22 -2827 Jun 2001 -25 9 -3421 Aug 2001 -25 -3 -2317 Sep 2001 -50 -28 -222 Oct 2001 -50 -14 -366 Nov 2001 -50 -16 -34

11 Dec 2001 -25 -7 -1830 Jan 2002 0 3 -19 Mar 2002 0 -3 -7 May 2002 0 -4 -

26 Jun 2002 0 -9 -13 Aug 2002 0 -7 -24 Sep 2002 0 -2 -6 Nov 2002 -50 -12 -38

10 Dec 2002 0 0 -29 Jan 2003 0 2 -18 Mar 2003 0 4 -6 May 2003 0 -7 -

25 Jun 2003 -25 11 -3612 Aug 2003 0 0 -16 Sep 2003 0 0 -28 Oct 2003 0 -1 -9 Dec 2003 0 1 -

28 Jan 2004 0 3 -16 Mar 2004 0 0 -4 May 2004 0 1 -

30 Jun 2004 25 -8 3310 Aug 2004 25 7 1821 Sep 2004 25 8 18

49


10 Nov 2004 25 1 2414 Dec 2004 25 0 252 Feb 2005 25 1 24

22 Mar 2005 25 29 -4 Hike3 May 2005 25 2 23

30 Jun 2005 25 2 239 Aug 2005 25 0 25

20 Sep 2005 25 7 191 Nov 2005 25 1 24

13 Dec 2005 25 0 2531 Jan 2006 25 1 2428 Mar 2006 25 6 2010 May 2006 25 1 2429 Jun 2006 25 -7 328 Aug 2006 0 -5 -

20 Sep 2006 0 0 -25 Oct 2006 0 -2 -12 Dec 2006 0 -1 -31 Jan 2007 0 0 -9 May 2007 0 1 -

28 Jun 2007 0 2 -7 Aug 2007 0 8 -

18 Sep 2007 -50 -44 -6 Cut31 Oct 2007 -25 9 -3411 Dec 2007 -25 0 -2522 Jan 2008 -75 -63 -1230 Jan 2008 -50 -10 -4118 Mar 2008 -75 -49 -2630 Apr 2008 -25 -7 -1925 Jun 2008 0 -4 -5 Aug 2008 0 -3 -

16 Sep 2008 0 21 -8 Oct 2008 -50 -17 -33

29 Oct 2008 -50 -10 -4016 Dec 2008 -75 -35 -40

50

Central Bank Reserves and the Yield Curve:Estimating Tobin’s

Portfolio Substitution Effect∗

Nikola Mirkov† Barbara Sutter‡

Abstract

If money is an imperfect substitute for other financial assets, a largeincrease in the money supply raises prices and reduces yields on alterna-tive, non-money assets. We refer to this effect as the portfolio substitu-tion effect in the sense of Tobin (1969) and estimate that a $100 billionincrease in Non-borrowed reserves at the Fed reduces the 10-year Trea-suries yield by 5 basis points on average. We use the case of Swiss Na-tional Bank to show that the existence of portfolio substitution channelis independent of whether the expansion of the Central Bank’s balancesheet comes from purchases of Treasury securities (the Fed) or foreigncurrency (the SNB).

Keywords: Interest rates, LSAPs, substitution effect, Bayesian MCMCJEL Classifications: E43, E52, C11, G12

∗We are greatful to Paul Söderlind, Eric Swanson and Glenn Rudebusch for important suggestions at theearlieast stage of the project. A great thanks to Nina Larsson, Ragna Alstadheim, Lars Svensson, Anders Vredin,Francesco Audrino, Ragnar Nymoen and seminar and conference participants at the Norges Bank, University ofOslo, University of St.Gallen, Federal Reserve Bank of San Francisco and the 14th INFER Annual Conference.The views expressed in the paper do not necessarily reflect those of the Swiss National Bank.

†Nikola Nikodijevic Mirkov, Universität St.Gallen (HSG), Rosenbergstr. 52, 9000 St.Gallen, Switzerland,E-mail: nikola.nikodijevicmirkov@student. unisg.ch, Tel: +41(0)76.22.98.176

‡Barbara Sutter, Swiss National Bank, Borsenstrasse 15, 8022 Zurich, Switzerland, E-mail: [email protected], Tel: +41(0)44.63.13.736

51

1 Introduction

In his seminal paper from 1969, James Tobin argues that a change in sup-ply of any asset alters the structure of rates of return on all the assets in theeconomy in a way that induces the public to hold the new supply. Whenthe asset’s own rate of return can change, the adjustment primarily happensthrough the increase or fall in the price of that asset. Yet, if the rate of returnon the asset is fixed (e.g. money), the whole adjustment takes place throughincreases in prices and reduction in yields of all the other assets. The effect ofa large increase in money supply on the long-term interest rates is discussed inBernanke and Reinhart (2004) in the context of monetary policy near the zero-lower bound and the authors refer to it as the “portfolio substitution” effect.This paper assess the empirical relevance of the Tobin’s portfolio substitutioneffect.

In particular, we ask whether the increase in reserves balances at the Fed givenby the large scale asset purchases (LSAPs) has effected the long-term Trea-suries yields beyond producing the well-established supply effect. The supplyeffect arises when the Fed purchases an asset, reduces the supply of it andbids-up its price.1 One possible explanation for the existence of supply effectin Treasury market is offered by the preferred habitat model of interest rates,which assumes imperfect substitutability between securities with similar ma-turities.2 In addition to the supply effect, an outright purchase of the assetby the Fed raises the amount of credit in the form of reserves available in theaggregate. Assuming an unchanged amount of government debt, i.e. Treasurybonds, prices of these bonds should, all else equal, increase as there is moremoney to buy the same amount of assets. Since the short-term governmentbonds constitute a close substitute for money when the Fed funds rate is at thezero lower bound, some of the additional credit might have found its way intolonger-term Treasury bonds and thereby brought down the long-term yields.

1See for example Hamilton and Wu (2010a), Vayanos and Vila (2009), Greenwood and Vayanos (2010),Neely (2010), Kuttner (2006) and D’Amico and King (2010).

2See Li and Wei (2012).

52

To the best of our knowledge, this is the first study to empirically measuresuch substitution effect between the reserve money at the Fed and the Trea-suries. Oda and Ueda (2007) test the “balance sheet expansion” hypothesis ofBernanke and Reinhart (2004) on Japanese data. The closest to our paper isthe study by Krogstrup, Reynard and Sutter (2012) that estimates the “liquidityeffect” of asset purchases on the Treasuries yield curve.

We estimate that an increase in non-borrowed reserves (NBR) at the Fed by$100 billion caused a fall in the 10-Year Treasury yield by 5 basis points onaverage, across different modeling assumptions. The effect is estimated byusing an affine term structure model (ATSM) in which almost entire variationin yields is driven by the information extracted from the yield curve itself andunrelated to the changes in central bank reserves. In such a way, we try tocontrol for different supply effects of the LSAPs found in the previous studies,since the announcement effect,3 the stock effect,4 or any other effect5 of thereduced supply of long-term Treasuries should be priced in the yields them-selves. Therefore, the NBR factor should only explain a marginal variation inyields given by the higher amount of reserves money after the purchases. Mostimportantly, the information in the yield curve should capture changes in ex-pectations regarding the future path of policy that LSAPs might have affected,because any increase in reserve balances above the level necessary to keepthe Fed funds rate at zero implicitly signals a continuation of accommodativemonetary policy stance.6

Finally, we show that the portfolio substitution effect exists independently ofhow the increase in central bank reserves occurs. To this end, we apply ourestimation strategy to the Swiss data, as the reserves at the Swiss NationalBank (SNB) increased seven times since the policy rate has been essentially

3See for example Gagnon, Raskin, Remache and Sack (2010).4See D’Amico and King (2010) and Li and Wei (2012).5See Hamilton and Wu (2010b) and Greenwood and Vayanos (2010) for the effect of change in the maturity

structure of the Treasury debt.6See Bauer and Rudebusch (2011) for the discussion of possible signaling effects that LSAPs could have

had.

53

set to zero and the increase came exclusively from the purchases of foreigncurrency. We estimate a 16 basis points fall in the 10-Year government bondyield associated with an average increase in reserves at the SNB of Sfr.100billion.

The rest of the paper is organized as follows. Section 2 illustrates the dataset.In Section 3, we introduce the term-structure model we use to estimate theportfolio substitution effect and Section 4 provides the details on the modelestimation. Finally, Section 5 presents the results.

2 Data

2.1 United States

We use the Non-Borrowed Reserves (NBR) held at the Fed to measure theeffect of increase in the Fed’s balance sheet i.e. the effect of increase in thesupply of reserves money on the yield curve. The NBR is considered as a nar-row monetary aggregate7 and therefore the one which money demand shocksdo not affect.8 The NBR are calculated by subtracting the borrowed reserves,equal to the sum of credit extended through the Federal Reserve’s regular dis-count window programs and other liquidity facilities, from the amount of totalreserves in the system. The data on aggregate reserves held at the Fed arepublished every Wednesday in the H.3 release by the Federal Reserve Board.

The interest rate data stem from off-the-run US Treasury Bills and Bonds andtheir closing prices on Wednesdays. We use 3-month and 6-month secondarymarket T-bills rates9 and 1- to 10-year off-the-run constant maturity yieldsfrom Gurkaynak, Sack and Wright (2007)10. The yields are continuously

7See Pagan and Robertson (1995).8See e.g. Bernanke and Blinder (1992), Sims (1992), or Christiano and Eichenbaum (1995).9Obtained from the Federal Reserve Economic Data base (FRED), under DTB3 and DTB6. The two are not

constant-maturity yields which is acceptable due to their short maturity.10The data can be downloaded from http://www.federalreserve.gov/econresdata/

researchdata.htm. We use off-the-run treasuries to avoid the treatment of “repo-specialness” implicit

54



compounded, whereas a quarterly compounding is assumed for the 3-monthyield and the semi-annual compounding for the rest of the yields in the yieldcurve.11

The data sample starts from the second week of December 2008, when theFOMC set the target range for the Federal funds rate at 0 - 25 basis points.We do not use the data before the Fed funds rate reached the zero-lower boundin order to empirically assess the effects of “increasing the size of the centralbank’s balance sheet beyond the level needed to set the short-term policy rateat zero” discussed in Bernanke and Reinhart (2004). The upper panel of Figure1 illustrates the US data. The NBR amounted to roughly $540 billion at thetime the Fed funds rate reached the ZLB in December 2008 and continued togrow to roughly $1,500 billion by December 2012.

2.2 Switzerland

We use the data on sight deposit accounts held at the Swiss National Bank(SNB) by both domestic and foreign banks as the measure of supply of reservebalances. Interest rate data are the 3-month and the 6-month Swiss Franc Li-bor rates and 1- to 10-year constant-maturity zero-coupon yields on the SwissConfederation Bonds. The sample starts with the second week of December2008, when the Swiss National Bank (SNB) decreased its targeted level for the3-month Libor from 1% to 0.5%, and ends on the 26th December 2012. Thelower panel of Figure 1 illustrates the Swiss dataset.

in the on-the-run treasuries, see Duffie (1996) and Jordan and Jordan (1997).11See Hull (2008).

55

Figure 1: Interest Rates and Central Bank Reserves. The figure reports se-lected interest rates (left scale) and the central bank reserves (right scale) inthe US (upper panel) and Switzerland (lower panel).

A. The US

B. Switzerland

56

3 The Model

This Section defines the term structure model we use to estimate the portfoliosubstitution effect. We start from the general asset pricing equation, definethe pricing kernel and specify a transition equation for the underlying statefactors. Then, we specify the one-period interest rate and formulate the bondprices across the maturity spectrum.

3.1 General Setting and State Dynamics

The general asset pricing equation12 under the physical probability measure Preads:

Pn,t = E t[Mt+1Pn−1,t+1|I t

], (1)

where Pn,t is the price of an n-periods to maturity zero-coupon bond at timet, Mt+1 denotes the stochastic discount factor, and I t represents the agents’current information set. In a risk-neutral world, where investors request norisk compensation, the price of the bond Pn,t equals:

Pn,t = EQt

[exp(−y1,t)Pn−1,t+1|I t

], (2)

where Q is the risk-neutral probability measure and y1,t is the short-term in-terest rate. The no-arbitrage argument assures that the two prices in (1) and(2) are equal. There exists an equivalent martingale measure Q according towhich (2) holds13 with the stochastic discount factor taking the form:

12See Campbell, Lo and MacKinlay (1997)13See Harrison and Kreps (1979).

57

exp(−y1,t) = E t [Mt+1|I t]

= exp(−y1,t)E t [(dQ/dP)t+1|I t] .

dQ/dP is the Radon-Nykodim derivative14 which follows a log-normal pro-cess, so it reads:

(dQ/dP)t+1 = exp(−1

2(λt)′λt − (λt)′εt+1

)(3)

where λt is the market price of risk associated with the sources of uncertaintyεt

15. Following Duffee (2002), the market price of risk is an “essentiallyaffine” function of the state variables X t, so it can be written as

λt =λ0 +λ1X t. (4)

Equations (3) to (4) jointly define the pricing kernel of the model, where theessentially affine market price of risk constitutes the first fundamental buildingblock of the Gaussian term structure model.

Another fundamental building block of the Gaussian term structure model isthe multivariate state variable X t. It follows a discrete version of the con-stant volatility Ornstein-Uhlenbeck process16. Under the physical probabilitymeasure P, the process is

X t+1 = (I −Ψ)µ+ΨX t +Σεt+1. (5)

14See Dai, Singleton and Yang (2007).15See Ang and Bekaert (2002) and Ang and Piazzesi (2003).16See Phillips (1972).

58

The first term on the right-hand side of equation (5) is a vector of the factors’means. Ψ is the VAR matrix, Σ is the covariance matrix that normalizes theresiduals εt which are assumed to be standard normal i.i.d. shocks.

3.2 Short Rate and Bond Prices

Following Duffie and Kan (1996), the one-period interest rate is an affine func-tion of risk factors X t as:

y1,t = A1 +B1X t

where the coefficient A1 corresponds to the average one-period rate in thesample and B1 is a vector of loadings of the risk factors on y1,t. The riskfactors are:

X t =

l1,t

l2,t

l3,t

Reservest

(6)

The first three factors l it, i = 1,2,3 denote the latent factors backed out from

yields. As commonly in the term structure literature, these factors can be in-terpreted as a level, a slope, and a curvature factor.17 In order to estimate theportfolio substitution effect on the longer-end of the yield curve, this paperadds central bank reserves, as the fourth factor to X t.18 As it can be noticed,the model does not assume that the short rate can reach a zero-lower bound.Yet, as shown in the results Section, the model fits the data reasonably welland thus can be considered as a good approximation.

17See Section 4 for details on how yield-only factors are “backed-out” from yields.18Similarly, Ang and Piazzesi (2003), for instance, are among many studies that use macro-economic vari-

ables as explicit factors.

59

Assuming joint log-normality of bond prices and the pricing kernel in equation(1), the n-periods to maturity nominal bond price is an affine function of thestate variables19 and thus takes the form:

pn,t =−An −Bn X t, (7)

with:

An = An−1 +Bn−1((I −Ψ)µ−Σλ0

)+ 12

Bn−1ΣΣ′B′

n−1 + A1

Bn = Bn−1 (Ψ−Σλ1)+B1

(8)

4 Estimation

In this section we derive the likelihood function used to construct the jointposterior of parameters and data. The model is estimated with a simple versionthe Bayesian Markov-Chain Monte-Carlo (MCMC) method and the sectionprovides the rationale for using MCMC and the description of the algorithm.

4.1 Likelihood Function

Following Chen and Scott (1993), the 6-month, the 5-year and the 10-yearyields are set to be observable, while the rest is measured with error. Let yo,t

be a vector of observed yields i.e. yields perfectly priced by the model:

19See for example: Cochrane and Piazzesi (2009).

60

[yo,t

Reservest

]=

[Ao

01×1

]+

[Bo 03×1

01×3 1

][Xo,t

Reservest

]

where Ao is a 3×1 vector and Bo a 3×3 matrix of factor loadings. Xo,t arethe three latent factors obtained by inverting the above equation as:

[Xo,t

Reservest

]=

[Bo 03×1

01×3 1

]−1 ([yo,t

Reservest

]−

[Ao

01×1

])

The first part of the likelihood function refers to the evolution of the statevariables X t as given in equation (5). The assumption that εt is multivariate-Gaussian implies that the conditional probability density function of X t is

f(X t | yo,t−1,Reservest−1

)= exp(− 1

2ε′t(Σ′Σ

)−1εt

)√

(2π)T |Σ′Σ |. (9)

Let the yu,t be a vector of remaining N−3 yields priced by the model with anerror:

yu,t = Au +Bu X t +ξt

The second part of the likelihood function refers to the pricing errors ξt. Theyare assumed to be distributed as i.i.d. N

(0,ω2I

), with the same variance ω

and zero-correlations across yields, where I is a unity matrix. The conditionaldensity of yu,t is thus given by:

61

f(yu,t | X t

)= exp(− 1

2ξ′t

((ω2I

)′ω2I

)−1ξt

)√

(2π)T∣∣∣(ω2I

)′ω2I

∣∣∣ (10)

The log-likelihood function is just the sum of logarithms of the “time-seriespart” in equation (9) and the “cross-sectional part” in equation (10) and thustakes the form:

lnL (·)= log( f(X t | yo,t−1,Reservest−1

))+ log( f

(yu,t | X t

)) (11)

4.2 Econometric Identification

Solid identification of parameters is an essential part of dynamic term structuremodels estimation. The proposed identification scheme stems mainly from Daiand Singleton (2000) and Hamilton and Wu (2010a).

To begin with, the upper-left block of the VAR matrix Ψ, i.e. the one drivingthe dynamics of the yields-only factors in Xo,t, is set to be a power law struc-ture,20 with zero non-diagonal elements and the following power relation onthe diagonal:

ψzz =ψ11αz−1

where ψ11 is the largest eigenvalue and the AR coefficient of the first latentfactor, α is a scaling parameter controlling the distance between the eigen-values, and z = 2, ...Z, where Z is the number of latent factors. Preliminaryestimation showed that the ψ11 parameter is near one. In line with the near co-

20See also Calvet, Fisher and Wu (2010) and Bauer and de los Rios (2011).

62

integration assumption from previous studies21, we simply set ψ11 to 1,22 andestimate ψzz, where z = 2,3, together with the AR(1) coefficient of the re-serves dynamics. The off-diagonal elements of theΨ are set to zero, as well asvector the µ vector and the off-diagonal elements of matrix Σ in the transitionequation (5).

We impose the usual boundary condition A0 = B0 = 0 on the parameters ofthe pricing equation given in (7). A1 is normalized to average the one-periodinterest rate in the sample23 while B1 is normalized to:24

[1 1 1 bReserves]′

Alternatively, one could set the covariance matrix of the transition equation (5)to a unity matrix and estimate all the elements of B1.25

Lastly, the market price of risk dynamics is restricted to:

λst =

λ0,1

λ0,2

0

0

+

0 0 0 λ1,14

0 0 0 λ1,24

0 0 0 0

0 0 0 0

X t, (12)

so that both “level” and “slope” risks are priced in yields.26 This is the mainmarket price of risk specification of the study. The results are also reported forthe risk-neutral Q measure, where λ0 =λ1 = 0, and for the case where only the“level” shock is being a compensated risk, i.e. where λ0,2 and λ1,24 are set to0.27 It is indeed a restricted set of models, yet previous studies show that many

21See for instance Giese (2008) and Jardet, Monfort and Pegoraro (2011).22As in Diebold and Li (2006), Söderlind (2010) and Bauer (2011).23Following Favero, Niu and Sala (2007).24As in Ang, Bekaert and Wei (2008).25See for instance Ang and Piazzesi (2003).26As in Duffee (2010) and Joslin, Priebsch and Singleton (2010).27We follow exactly this specification from Cochrane and Piazzesi (2009) and add the slope factor.

63

restrictions on the market price of risk are supported by the data.28 In addition,we estimated an unrestricted model with λ1,i j 6= 0 for i = 1,4, j = 1,4 andthe main result holds.29

4.3 Bayesian Inference

The yield curve implied by the model is a complicated non-linear function ofthe underlying parameters. As this non-linearity tend to produce a multi-modallikelihood function30, fitting a yield curve model with a standard maximumlikelihood estimation is a daunting task. Bayesian Markov Chain Monte Carlo(MCMC) method seem to be a powerful alternative, providing both efficiencyand tractability.

4.3.1 Setting

Let Θ be a vector of length K collecting all the parameters of the model to beestimated:

Θ= α,ψReserves,Σ,λ0,λ1,ω,bReserves

The key idea behind Bayesian estimation is to consider the vector as a multi-variate random variable, and use the Bayes’ rule to “learn” about the variablegiven the data:

p (Θ | data)= p (data |Θ) p (Θ)p (data)

(13)

where p (Θ | data) is the posterior density of Θ, p (data |Θ) is the likelihoodfunction and p (Θ) denotes the prior density of the parameters. The term

28See for example Joslin et al. (2010) and Bauer (2011)29We do not report the output from unrestricted model estimation, but the results are available upon request.30See Chib and Ergashev (2009).

64

p (data) is known as "normalising constant" and it is independent of Θ.31 Con-sequently, the rule in (13) can be re-written as:

lnp (Θ | data)∝ lnL + lnp (Θ)

where lnL is the logarithm of the likelihood function defined in (9) and (10):

lnL =T−1∑t=0

lnpdf(X t | yo,t−1, r t−1

)+

T−1∑t=0

lnpdf(yu,t|X t, yo,t−1, r t−1

)(14)

4.3.2 Priors

In the estimation, the priors p (Θ) are set to be non-informative or “flat”, so thatthe posterior density of the model parameters is drawn with equal probabilityfrom the pre-defined support interval. Alternatively, we could derive the priordistributions for parameters Ψ and Σ, given the normality assumption of thestate VAR process,32 and for ω given the assumption of the Gaussian measure-ment error.33 Chib (2001) propose a scaled beta distribution as an alternativeto the uniform distribution. Nevertheless, we choose not to impose lower (orhigher) probability areas from which the candidate values of parameters aredrawn. In such a way, the estimation is almost completely data-driven andproves to be computationally efficient.

The parameters’ suport intervals are specified by following the no-arbitragecondition and previous studies. In particular, the eigenvalues of the VAR ma-

31In particular: p (data)= ∫p(data |Θ)p(Θ)dΘ. See Koop (2003).

32For instance, see Ang, Dong and Piazzesi (2007).33See for example Mikkelsen (2001).

65

trix are set to be positive and less than one and the volatility parameters on thediagonal of Σ are set to be non-negative. The parameter bNBR is constrainedto be inside the unit-circle. The lower bound of the parameters in λ0 vectorand λ1 matrix are set as in Chib and Ergashev (2009).

4.3.3 Markov Chain Monte Carlo

We use a simple version of the “Metropolis within Gibbs” algorithm34 to drawthe parameters from their posterior densities. The parameter candidates aredrawn from continuous uniform distributions U

(Θ,Θ

)where the lower and

the upper boundaries Θ and Θ for each parameter in Θ are specified in Table1. The algorithm can be described in several steps:

Step 1: Set the initial values of parameters Θ0. Two Markov chains withdifferent starting values are set up. The initial values for the VAR parametersin first chain are obtained from OLS and the data descriptive statistics. Thestarting values of the market price of risk parameters and of the second chainare chosen arbitrarily.35

Step 2: Draw a candidate log-posterior density lnp(Θ∗ |Θmc−1,data

)condi-

tional on previously drawn parameters’ values Θmc−1. The number mc de-notes current iteration. The draws are performed separately for every param-eter in Θ. For instance, a proposal for the first element in the vector Θ isgenerated by the following Markov chain:

34The “Metropolis within Gibbs” is a simple method and therefore often used in the literature, as for examplein Gilks (1996), Koop (2003) and Lynch (2007). In particular, this algorithm features two favorable character-istics. First, in standard Metropolis new proposals for the parameter values are drawn all at once, whereas theGibbs sampler draws only one proposal for only one parameter value at a time. Therefore, the Gibbs samplerresults much more efficient, i.e. the estimator converges quicker. Second, the tuning of the estimator is sim-pler, where tuning refers to setting the scale factor in step 2 to different values. In standard Metropolis, onescale factor must “fit all”. The Gibbs sampler is more flexible as it allows for a separate set of values for eachparameter.

35For example, the volatility parameters’ starting values are set to be 3 times larger in the second chain, theΨ matrix parameters are set to 0.8 and the B1 parameter is set to 0.5 and -0.5 in the first and the second Markovchain, respectively.

66

θ∗1 = θmc−11 +ν1U1

where νk is a scaling factor and Uk is an uniformly distributed random numberfrom interval [-1,1]. We initialise νk for parameters α and ψNBR to 0.01, fordiagonal elements of Σ matrix and the market price of risk parameters to 0.1,and for the ω parameter to 0.0000136. The scaling factor is then automaticallyupdated after every 5,000 sweeps37 to obtain the acceptance ratio in step 4 ofapproximately 0.5.

Step 3: For every parameter in Θ∗, calculate the difference between the poste-rior density with the candidate value and the posterior density with the previ-ously drawn parameter value, keeping the other parameter values unchanged.Using again the first element in Θ as an example, the difference reads:

δ = lnp(θ∗1 ,θmc−1

2 , ...,θmc−1K |Θmc−1,data

)− lnp

(θmc−1

1 ,θmc−12 , ...,θmc−1

K |Θmc−1,data)

(15)

Step 4: Draw a random number u ∼ U(0,1) and accept the single parametercandidate from Step 2, whenever the following holds for the difference in Step3:

min(0,δ)> log(u)

Step 5: Repeat the Steps 2 to 5 until the joint posterior density of parametersconverge in distribution.

36Proposed in Ang et al. (2007) so that it roughly corresponds to a 30 basis points bid-ask spread on Trea-suries. An average spread on the OTC plain vanilla swap market might be similar. See also Skarr (2010).

37The algorithm is ran for 100,000 times. The scaling factor is updated starting from the 10,000th iteration tothe 40,000th iteration.

67

The algorithm is ran 100,000 times and the first 40,000 are discarded as theburn-in period. The two Markov chains with different starting values for bothjoint posterior and the single parameters’ posteriors converge to literally thesame posterior distributions. Before estimating the entire model, the proposedparametrization is used to estimate the risk neutral specification. The modelunder Q converges even quicker and thus the algorithm is ran for 50,000 timesand the first 20,000 are discarded as burn-in.38

5 Results

Before coming to our main result, we need to make sure that the estimatedmodel produces reasonable parameter estimates and fits the observed interestrates well. Also, we show that the central bank reserves as a fourth factor inthe term structure model explains only a marginal variation in the fitted yields.Most of the variation is driven by the factors extracted from the yield curveitself and therefore we arguably control for different supply effects reported inthe previous studies.

5.1 Model Performance

5.1.1 Parameters

Table 1 and 2 report the estimated parameters for the US and Switzerland,respectively. Each table illustrates the parameter’s modes and numerical stan-dard errors (in brackets).

38The scaling factor is also automatically adapted until the 20,000th iteration.

68

Table 1: Parameter Estimates for the US. The table reports the estimated pos-terior modes of the parameters for the US together with numerical standarderrors (in brackets). The first two columns provide the support intervals, andthe last two the average acceptance (AccRatio) ratios and inefficiency factors(IF) for the two subsamples. The acceptance ratio is the number of acceptedparameters’ proposals divided by the number of iterations after burn-in. Ineffi-ciency Factor is computed as 1+2

∑Ll=1ρ(l), where ρ(l) is the autocorrelation

at lag l in the Markov chain sequence of a parameter, and L is the lag at whichthe autocorrelation function goes to zero.

aΘ bΘ Θ AccRatio IFα 0.00 0.99 0.93 0.80 1894

(0.00)ψR 0.00 0.99 0.99 0.82 69

(0.00)σ11 0.00 15.0 0.14 0.23 1493

(0.00)σ22 0.00 15.0 0.31 0.55 200

(0.01)σ33 0.00 15.0 0.23 0.23 15

(0.01)σNBR 0.00 15.0 0.07 0.58 21

(0.00)λ01 -100 100 4.89 0.67 2157

(0.22)λ02 -100 100 -2.31 0.32 947

(0.22)λ14 -100 100 -0.13 0.83 328

(0.02)λ24 -100 100 0.21 0.64 503

(0.04)ω 0.00 10.0 0.21 0.19 49

(0.01)bNBR -1.00 1.00 -0.03 0.36 544

(0.18)

The first two columns in the tables provide the support intervals, and the lasttwo the average acceptance ratios39 and inefficiency factors (IF)40 for the twosub-samples. The coefficient estimates are depicted in the third and the fourthcolumn of tables.

39The acceptance ratio is the number of accepted parameters’ proposals divided by the number of iterationsafter the burn-in. The rate between 0.25 and 0.75 is often acceptable, see Lynch (2007) and Koop (2003).

40The Inefficiency Factor measures how well the sampler “mixes” is computed as 1+ 2∑L

l=1 ρ(l), whereρ(l) is the autocorrelation at lag l in the Markov chain sequence of a parameter, and L is the lag at which theautocorrelation function goes to zero. See Chib (2001) for details.

69

Table 2: Parameter Estimates for Switzerland. The table reports the estimatedposterior modes of the parameters for the US together with numerical standarderrors (in brackets). The first two columns provide the support intervals, andthe last two the average acceptance (AccRatio) ratios and inefficiency factors(IF) for the two subsamples. The acceptance ratio is the number of acceptedparameters’ proposals divided by the number of iterations after burn-in. Ineffi-ciency Factor is computed as 1+2

∑Ll=1ρ(l), where ρ(l) is the autocorrelation

at lag l in the Markov chain sequence of a parameter, and L is the lag at whichthe autocorrelation function goes to zero.

aΘ bΘ Θ AccRatio IFα 0.00 0.99 0.92 0.70 294

(0.00)ψSightDepo 0.00 1.00 1.00 0.71 40

(0.00)σ11 0.00 15.0 0.08 0.23 645

(0.00)σ22 0.00 15.0 0.18 0.39 83

(0.01)σ33 0.00 15.0 0.17 0.21 35

(0.01)σSightDepo 0.00 16.0 0.17 0.31 9

(0.01)λ01 -100 100 1.95 0.64 693

(0.21)λ02 -100 100 -1.06 0.27 442

(0.20)λ14 -100 100 -0.04 0.79 308

(0.02)λ24 -100 100 0.10 0.69 433

(0.05)ω 0.00 10.0 0.20 0.21 16

(0.01)bSightDepo -1.00 1.00 0.03 0.28 348

(0.08)

Figure 2 reports the posterior distributions of the parameter estimates for theUS. The estimated factor loadings of the reserves’ factors in the two countrieson the short rate is negative, yet insignificant, which means that any increase inreserves on the long-term yields affects the term premia and not the monetarypolicy expectations embedded in the long-term yields. Put differently, thefactor loading of the NBR factor on the one-period interest rate is basicallyzero and thus has no effect on the expected future one-period rate. The resultis in line with the previous literature showing that the LSAPs lowered the riskpremia on long-term Tresuries.

70

Figure 2: Estimated Posteriors for the US. The Figure illustrates the esti-mated posterior densities for all the parameters of the model where both leveland slope risks are priced in the yield curve (subsequently denoted as “L&Smodel”).

The estimated time-varying prices of risk coefficients, λ14 and λ24, are sta-tistically significant in the two samples. λ14 is associated with the effect ofthe NBR at the Fed (or the sight deposits at the SNB) on the market priceof “level” risk. The significantly negative λ14 suggests that during the ZLBperiod, the discount factor decreases with an expansion in the NBR (or thesight deposits), and so the term premia increases in the level. This could be anevidence of the Fisher effect: expansionary monetary policy eventually leadsto higher inflation rates which, anticipated in the form of increasing inflation

71

expectations and premia, drives up the nominal interest rates. Evidence of thesubstitution effect is found in the market price of risk associated with the slopeof the yield curve. λ24 turns significantly positive at the ZLB, which suggeststhat an increase in the NBR (or the sight deposits) leads to a flattening of theyield curve. Since short-term interest rates are close to zero, the substitutioneffect moves the long-end of the yield curve downwards.41

5.1.2 Pricing

By construction, the 3-month, the 5-year and the 10-year yields are explainedperfectly by the model. Table 3 reports the cross-sectional fit for both coun-tries. Allowing for the time-varying level and slope risks improves the fit abovethe Q model,42 yet, on the whole, the pricing performance is relatively similaracross modeling assumptions.

Table 3: Pricing Errors. Mean absolute pricing errors in basis points acrossdifferent modelling assumptions are reported for selected yields in the US (up-per panel) and Switzerland (lower panel), and for the two subsamples.

USA6M 1Y 3Y 6Y 8Y 9Y

Q 7.8 14.4 10.7 5.7 10.0 7.0L 8.5 16.4 7.8 4.2 8.9 6.7

L & S 7.7 15.0 6.6 4.1 9.0 6.8

CH6M 1Y 3Y 6Y 8Y 9Y

Q 9.5 12.9 8.2 4.1 6.2 4.1L 9.7 13.1 6.0 3.3 5.2 3.4

L & S 9.4 12.5 6.7 3.7 5.7 3.8

41The parameter λ24 is statistically significant and positive even when we estimate an unrestricted version ofthe model, where λ1,i j 6= 0 for i = 1,4, j = 1,4.

42Our preliminary analysis also showed that the reserves factor contribution to pricing performance wasminimal. We do not report this result.

72

5.2 Variance Decomposition and Latent Factor Dynamics

The Table 4 reports the variance decomposition for selected yields and showsthat most of the variance in yields is explained by the three latent factors.43

The contribution of the NBR factor (and the sight deposits factor for the SNB)does not exceed 3.7% (0.4%).

Table 4: Variance Decomposition. The table reports variance decompositionof selected yields in % for the US (upper panel) and Switzerland (lower panel).The variance is decomposed by dividing each single state variable shock j toan n-periods yield: MSE j

n = B′nΣ

jBn +B′nΨΣ

jΨBn, where Σ j is a K ×Kmatrix with zeros and a non-zero j j element corresponding to the volatility ofstate variable j; with the overall Mean Squared Error of forecasting the states1 period ahead: MSEn = B′

nΣBn +B′nΨΣΨBn.

US6M 1Y 3Y 6Y 8Y 9Y

l1 23.2 27.6 43.7 62.0 70.7 74.2l2 47.1 48.4 44.1 30.5 23.1 20.1l3 28.8 22.8 9.7 3.9 2.5 2.1

NBR 0.9 1.2 2.5 3.6 3.7 3.6CH

6M 1Y 3Y 6Y 8Y 9Yl1 43.8 49.8 67.9 82.9 88.2 90.1l2 41.8 40.0 28.9 15.8 10.7 9.0l3 14.0 10.0 3.2 1.1 0.6 0.5

SightDepo 0.3 0.2 0.0 0.3 0.4 0.4

Figure 3 shows the estimated latent factors for the US and the Swiss yieldcurve. The factor l1 is by definition a unit-root process44 and thus drives thelevel of both yield curves, as it can be noticed by comparing the evolution ofthe latent factors with the 5- and 10-year yields in the two countries depictedin Figure 1.

43The result is broadly in line with Litterman and Scheinkman (1991), Ang and Piazzesi (2003) and Joslin,Singleton and Zhu (2011), who all show that almost entire variation in the cross-section of yields can be ex-plained by some three latent factors (or the first three principal components of the yields matrix).

44See Section 4.2.

73

Figure 3: Latent Factors. The figure plots the estimated latent factors for theUS yield curve (upper panel) and the Swiss yield curve (lower panel). Thereported are l1 (solid blue), l2 (solid green), l3 (solid red) factors.

A. The US

B. Switzerland

5.3 The Factor Loadings

5.3.1 The Non-Borrowed Reserves at the Fed

We report our key results in Table 5. The table shows the factor loadings ofthe NBR factor on selected yields under different market price of risk specifi-cations. A factor loading indicates by how much a particular yield changes inresponse to a $100 billion change in the NBR.

74

Table 5: Factor Loadings for the US. The table reports the values of the NBR-factor loadings for selected yields, together with the Z-score from the Z-test(in parenthesis). The levels of significance of 0.1, 0.05 and 0.01 are denotedwith *, ** and ***, respectively.

Q

3M 1Y 3Y 6Y 8Y 10YB -0.01** -0.01* -0.01* -0.01* -0.01* -0.01*

Z-score -(1.92) -(1.92) -(1.92) -(1.92) -(1.92) -(1.92)L

3M 1Y 3Y 6Y 8Y 10YB -0.12*** -0.11*** -0.1*** -0.09*** -0.08*** -0.07***

Z-score -(5.45) -(5.39) -(5.19) -(4.77) -(4.39) -(3.92)L & S

3M 1Y 3Y 6Y 8Y 10YB -0.01 -0.03 -0.06 -0.08** -0.08*** -0.07***

Z-score -(0.22) -(0.60) -(1.55) -(2.57) -(2.89) -(2.94)

We find a statistically and economically significant portfolio substitution effectat the ZLB of an increase in the NBR on the long-term yields. When the NBRrise by $100bn, the 10-year yield falls by 5 basis points on average acrossmodeling assumptions. With the US nominal GDP of roughly $15.1 trillion,the estimates suggest that an increase in the NBR of the size of one percent ofGDP lowers long-term rates by up to 8 basis points. The model under the Qmeasure suggests a smaller effect at long maturities. Our average estimate isalso lower than those reported in Krogstrup et al. (2012) as a liquidity effectof the NBR on long-term yields. The authors estimate a fall of 15 to 20 basispoints in 10-year yield per $100 billion increase in the NBR.

5.3.2 NBR and the Treasury Balances

When the Fed purchases an asset, e.g. a Treasury note, the asset side of theFed’s balance sheet marks an increase in assets that corresponds to the amountof purchased T-notes. Contemporaneously, the liability side of the balancesheet increases by the same amount as the Fed credits the deposit account ofthe asset-seller depository bank with reserves money. This section addresses

75

the balance sheet identity and asks whether our main result is driven by thesupply effect, i.e. the fall in yields of purchased Treasuries given by the fallin their supply available to the public and thus by the increase in Treasurybalances at the Fed.

In particular, we orthogonalize the NBR factor on the amount of purchasedTreasury notes with maturities from 5 to 10 years as:

NBRt =α+βTBt +εt (16)

and then use the residual from the regression εt as the fourth explicit factor inthe estimation. The Figure 4 illustrates the orthogonalised NBR factor and theTable 6 reports the factor loadings for the three modeling alternatives.

Table 6: Factor Loadings for the US with the orthogonal NBR-factor. The tablereports the values of the NBR-factor loadings for selected yields, together withthe Z-score from the Z-test (in parenthesis). The levels of significance of 0.1,0.05 and 0.01 are denoted with *, ** and ***, respectively.

Q

3M 1Y 3Y 6Y 8Y 10YB -0.04*** -0.04*** -0.03*** -0.02*** -0.02*** -0.01***

Z-score -(2.60) -(2.65) -(2.74) -(2.77) -(2.76) -(2.74)L

3M 1Y 3Y 6Y 8Y 10YB -0.07 -0.07 -0.06* -0.05** -0.05** -0.05**

Z-score -(1.35) -(1.44) -(1.69) -(2.01) -(2.17) -(2.26)L & S

3M 1Y 3Y 6Y 8Y 10YB -0.09 -0.1* -0.1** -0.1*** -0.09*** -0.08***

Z-score -(1.51) -(1.77) -(2.29) -(2.71) -(2.84) -(2.91)

The estimated effect on the 10-year yield is essentially unchanged. The Qmodel still measures the smallest effect and the average effect across modelingassumptions is 5 basis points fall in the yield connected to a $100 bn increase inthe NBR orthogonal to the increase in the holdings of 5 to 10-year Treasuries.

76

Figure 4: Orthogonalized NBR-Factor. The figure plots the residuals from theequation (16).

5.3.3 The Sight Deposit Accounts at the SNB

Even though we try to separate the effect of increase in Central Bank reservesfrom asset purchases, the NBR at the Fed increased because the Fed was pur-chasing long-term Treasury and Mortgage-Backed securities. In order to con-firm that the portfolio substitution effect of Tobin (1969) is empirically rele-vant independently of why Central Bank reserves increase, we use the case ofthe Swiss National Bank who has never been engaged in asset purchases. Ta-ble 7 reports the reserves factor loadings across different market price of risksettings and selected yields.

We find a negative and significant effect of increase in reserves held at the SNBon the long term yields according to all the model specifications. The estimatessuggest that the increase in reserves of SFr. 100 billion reduced the 10-yearyield by 16 basis points on average: 11 basis points according to the Q model,27 basis points according to the model in which the level factor is priced, and11 basis points according to the model in which both level and slope risksare priced in yields. In terms of Swiss GDP, which amounts to approximatelySfr.600 billion, an increase of reserves at the SNB of one percent of nominalGDP lowers rates by roughly 1 basis point.

77

Table 7: Factor Loadings for Switzerland. The table reports the values of thereserves factor loadings for selected yields, together with the Z-score from theZ-test (in parenthesis). All the estimates regard the zero-lower-bound subsam-ple. The levels of significance of 0.1, 0.05 and 0.01 are denoted with *, ** and***, respectively.

Q

3M 1Y 3Y 6Y 8Y 10YB -0.11*** -0.11*** -0.11*** -0.11*** -0.11*** -0.11***

Z-score -(4.33) -(4.34) -(4.39) -(4.45) -(4.48) -(4.52)L

3M 1Y 3Y 6Y 8Y 10YB -0.45*** -0.43*** -0.4*** -0.34*** -0.3*** -0.27***

Z-score -(11.14) -(11.04) -(10.70) -(10.00) -(9.36) -(8.59)L & S

3M 1Y 3Y 6Y 8Y 10YB 0.3*** 0.2*** 0.03 -0.08 -0.11** -0.11**

Z-score (3.54) (2.68) (0.56) -(1.60) -(2.24) -(2.36)

5.4 Cumulative Effects

5.4.1 United States

Figure 5 plots the estimated overall effect of an increase in the NBR duringthe ZLB period corresponding to different modeling assumptions. As the 90%confidence bands indicate, the effect is statistically significant only for theyields of long maturities bonds.

The total increase in the NBR of roughly $1 trillion is associated with a fall inthe 10-year yield of 40 basis points on average across the modeling specifica-tions. The model under the Q measure estimates a total decrease of roughly20 basis points for both mid- and long-term yields. The models accounting forthe time-varying level risk and the time-varying level and slope risks estimatea fall in the mid- and long-term yields of approximately 50 basis points as ofDecember 2012.

78

Figure 5: Cumulative Effects for the US. The figure plots cumulative effectof increase in NBR on the 3-month (left-hand side panels) and 10-year (right-hand side panels) interest rates according to the Q-model (top row), the L-model (middle row) and L&S-model (bottom row plots) together with 90 %credible interval (left panels). The credible interval is calculated using theposterior parameters’ distributions, i.e. every 1000th set of parameters alongthe first Markov chain and after burn-in.

5.4.2 Switzerland

According to our estimates, the cumulative effect of the expansion in sightdeposits at the SNB from approximately SFr.26 billion francs in December2008 to SFr.370 billion December 2012 has led to an estimated fall in the 10-year yield of 60 basis points on average across market price of risk settings.Figure 6 shows the estimated cumulative effect as well as the corresponding

79

90%- credible interval. The Q and the L&S models estimate a fall of roughly40 basis points in the yield during the period, whereas the L model points to adrop of around 80 basis points.

Figure 6: Cumulative Effects for Switzerland. The figure plots cumulativeeffect of increase total sight deposits at the SNB on the 3-month (left-handside panels) and 10-year (right-hand side panels) interest rates according tothe Q-model (top row), the L-model (middle row) and L&S-model (bottomrow plots) together with 90 % credible interval (left panels). The credibleinterval is calculated using the posterior parameters’ distributions, specificallyevery 1000th set of parameters along the first Markov chain and after burn-in.

80

6 Conclusion

This study provides evidence of Tobin’s portfolio substitution effect at thelonger end of the yield curve, when the short-term interest rates are near thezero lower bound. Increases in central bank reserves at the Fed and the SwissNational Bank seem to have had a statistically and economically significanteffect on the long-term government bond yields in the two countries. Due tothe sizes of respective secondary markets for those bonds, the average effectin the Swiss case is estimated to be higher relative to the one found in theUS data. The presented analysis might be relevant in the discussion of exitstrategies from the expansionary monetary policy measures, implemented inthe two countries.

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86

Announcements of Interest Rate Forecasts:Do Policymakers Stick to Them?∗

Nikola Mirkov† Gisle James Natvik‡

Abstract

If central banks value the ex-post accuracy of their forecasts, previouslyannounced interest rate paths might affect the current policy rate. We ex-plore whether this “forecast adherence” has influenced the monetary poli-cies of the Reserve Bank of New Zealand and the Norges Bank, the twocentral banks with the longest history of publishing interest rate paths.We derive and estimate a policy rule for a central bank that is reluctantto deviate from its forecasts. The rule can nest a variety of interest raterules. We find that policymakers appear to be constrained by their mostrecently announced forecasts.

Keywords: Interest rates, forecasts, Taylor rule, adherenceJEL Classifications: E43, E52, E58

∗We are most grateful to Francesco Ravazzolo, Dagfinn Rime and Anders Vredin for insightful discussionsat the early stage of the project. A great thanks to Glenn Rudebusch, Francis Diebold, Paul Söderlind, AlejandroJustiniano, Monika Piazzesi, Refet Gürkaynak, Bart Hobijn, Ian Dew-Becker, Rhys Bidder, Paul Hubert, DanielKienzler, Øistein Røisland, Kevin Lansing, Snorre Evjen, Mathis Mehlum and the seminar and conference par-ticipants at the Norges Bank, Universität St.Gallen, Stanford University, Federal Reserve Bank of San Francisco,International Symposium on Forecasting 2012, and the 44th Money, Banking and Finance Conference. Viewsexpressed in this paper are those of the authors, and do not necessarily reflect those of Norges Bank.

†Nikola Nikodijevic Mirkov (corresponding author), Universität St.Gallen (HSG), Rosenbergstr. 52, 9000St.Gallen, Switzerland, E-mail: [email protected], Tel: +1 415 697 41 37

‡Gisle James Natvik, Norges Bank, Bankplassen 2, 0151 Oslo, Norway, E-mail: [email protected], Tel: +47 22 31 63 38

87

1 Introduction

According to economic theory, monetary policy predominantly affects the

economy through expectations regarding the future path of short-term inter-

est rates.1 This insight takes center stage in the debate on “forward guidance”

and has motivated a number of central banks to communicate their policy in-

tentions explicitly by publishing their own forecasts of future interest rates.2

However, the practice of announcing policy intentions has long been somewhat

controversial, and a key issue is whether past announcements could constrain

future policy decisions,3 and what the normative implications of such a con-

straint might be. The reduced flexibility could prevent sufficiently strong pol-

icy responses to macroeconomic shocks. On the other hand, the effectiveness

of forward guidance requires that the central bank eventually implements the

signaled policy and does not simply provide a view on the likely future path of

the economy.4 Importantly, even though there is a rich theoretical debate on

the desirability of announcing interest rate forecasts, the empirical evidence

on whether past announcements actually influence future policy is scarce. Our

paper attempts to close this gap.

We derive a simple policy rule for a central bank that perceives deviations from

its previously announced forecasts to be costly and therefore has an incentive

to stick to them. The specification is sufficiently flexible to nest a broad class

of interest rate rules proposed elsewhere in the literature. We may therefore

use a host of alternative policy formulations to separate the movements in the

central bank’s “preferred” policy rate, i.e. movements in the policy instrument

1See Eggertsson and Woodford (2004) and Woodford (2005).2The Reserve Bank of New Zealand inaugurated the practice (in 1997), followed by the Central Bank of

Norway, Norges Bank, (in 2005), the Swedish Riksbank and the Central Bank of Iceland (in 2007), the CzechNational Bank (in 2008) and the Federal Reserve (in 2012).

3See for instance Svensson (2009), Mishkin (2004), Goodhart (2009) and Kohn (2008). Another debatedissue concerns the merits of informing private agents about the central bank’s reaction pattern, see for exampleMorris and Shin (2002), Svensson (2006), Gosselin, Lotz and Wyplosz (2008) and Rudebusch and Williams(2008).

4See Woodford (2012) and Gersbach and Hahn (2011).

88

driven by the bank’s usual response to changes in the economy, from the effect

of previously published interest rate forecasts. The rules are estimated on the

actual policy rates of the Reserve Bank of New Zealand (RBNZ) and the Cen-

tral Bank of Norway (Norges Bank) to answer the big question: do announced

forecasts influence actual policy decisions? To the best of our knowledge, we

are the first to address this question.

The work that most resembles our analysis is Campbell, Evans, Fisher and

Justiniano (2012), who incorporates qualitative forward guidance (e.g., “con-

siderable period” language) in the reaction function of the Fed and show that

the extended policy rule offers improved empirical predictions. In contrast

to our approach, however, the authors do not examine quantitative forward

guidance and do not assume that the Fed faces costs from deviating from it.

Their assumption is that the public knows that the Fed will renege on such

“promises” in the future, as the policy rule describes its preferred behavior.5

Our main result suggests that both the RBNZ and Norges Bank are reluctant

to deviate from previously announced interest rate forecasts when setting their

policy rates. Specifically, the two central banks appear constrained by their

1-quarter-ahead forecast announced in the quarter before the actual decision

takes place. The forecasts older than one quarter have no effect on the current

policy rate. The result holds both when we model the preferred policy rate

using estimated rules, and when we approximate it using the central banks’

“nowcasts” of the policy rate published in the monetary policy reports. Finally,

we show that policy rules augmented to allow for forecast adherence explain

several episodes in the behaviors of the two banks much better than policy

rules without interest rate forecasts.

We perform two robustness checks of the main result. First, we ask whether

our empirical strategy “cries wolf” i.e., whether simple policy rules tend to5The authors refer to such forward guidance as “Odyssean” forward guidance, as it resembles Odysseus

commanding his sailors to tie him to the ship’s mast, so that he can enjoy the Sirens’ song without jumpingoverboard.

89

indicate forecast adherence, when the policymaker has no such preferences.

To this end, we use a basic New Keynesian model from Gersbach and Hahn

(2011) to simulate the optimal behavior of a central bank that minimizes a loss

function with a weight on forecast errors. The model is simulated for different

values of the weight to mimic different degrees of preference towards forecast

adherence. We then apply our empirical strategy to simulated data and show

that the estimated policy rules do not lead us to commit false positive errors:

the estimated coefficient on forecasts is positive and significant only if the

central bank has a sufficiently strong desire to reduce forecast deviations.

Second, we discuss whether our results can be explained by a completely dif-

ferent assumption regarding policymakers’ preferences, namely that the two

central banks minimize surprises in the policy rate, as suggested by Svens-

son (2003).6 We argue that our results would only be consistent with such

preferences if we assume that: 1) the central bank’s forecasts and market ex-

pectations of future short-rates are perfectly aligned; 2) the central bank adopts

market expectations as its own. We conjecture that the second assumption is

unlikely, given the lack of evidence of such behavior. In addition, we run a

“placebo test” on the Norges Bank data before it began publishing interest rate

forecasts, and show that a previous quarter 3-month forward rate, as a proxy

for market expectations, had no effect on the policy rate.7

The reminder of the paper is organized as follows. In Section 2, we discuss the

dataset and the institutional setting in which the two central banks announce

interest rate forecasts. Section 3 provides details on our estimation strategy.

Section 4 reports the main results and illustrates the robustness checks we

perform.

6For an insightful discussion of such preferences, see Rudebusch (2006).7We are unable to perform the placebo test for the RBNZ, since its operational procedures were significantly

changed at the beginning of our sample in March 1999.

90

2 Dataset on Interest Rate Forecasts

2.1 Reserve Bank of New Zealand

The Reserve Bank of New Zealand (RBNZ) was the first central bank to pub-

lish its own interest rate forecasts, together with projections for CPI inflation

and GDP growth. Beginning in March 1997, the forecasts for the 90-days

Bank Bill rate have been published in the quarterly Monetary Policy State-

ment (MPS), and the upper panel of Figure 1 illustrates an example from the

June 2012 MPS. The RBNZ only publishes the central forecast, and in addi-

tion it provides a qualitative assessment of “what the RBNZ sees as the main

risks and uncertainties around the central forecast.”8 Starting with the MPS

of June 2003, the Bank has published both the current and previous quarter

projections as Figure 1 shows.

The main tool used to produce all of the forecasts is the RBNZ’s core macroe-

conomic model,9 where the policy rate is set according to a forward-looking

Taylor rule. Interest rate forecasts are conditional on the RBNZ’s projections

of future inflation, and the mechanism for producing those forecasts is referred

to as the endogenous policy forecast system.10 Finally, the model-based fore-

casts are subject to a considerable amount of judgment before ultimately being

released in the MPS.11 The Bank’s interest rate forecasts cover an 8-quarter

horizon, and the upper panel of Figure 2 illustrates the 1-, 2- and 3-quarters

ahead forecasts over time against the realized 90-day Bank Bill rate. The start

date for the analysis of the New Zealand data is March 1999, when the RBNZ

adopted the Official Cash Rate (OCR) system, and the operating procedures of

the RBNZ have remained broadly unchanged since.

8See Drew and Karagedikli (2008).9The most recent available documentation on this model is Benes, Binning, Fukac, Lees and Matheson

(2009).10See Ranchhod (2002).11See Drew and Karagedikli (2008).

91

Figure 1: How do Interest Rate Forecasts get Published? The figure reportsexamples of published interest rate forecasts in the Monetary Policy Statementof the Reserve Bank of New Zealand (upper panel) and in the Monetary PolicyReport of the Norges Bank (lower panel).

A. RBNZ

B. Norges Bank

92

2.2 Norges Bank

Three times a year, usually in March, June and October, the Central Bank

of Norway publishes its Monetary Policy Report (MPR), which includes pro-

jections of the future key policy rate, CPI inflation, the output gap and CPI

inflation that excludes changes in tax and energy prices.12 All of the forecasts

are published in the form of fan charts, illustrated in the lower panel of Figure

1. The reason for publishing central forecasts together with confidence bands

is to emphasize the contingency of those forecasts.13

The main tool for producing interest rate forecasts is the core macroeconomic

model of the Norges Bank, NEMO, combined with judgment.14 The model-

generated forecasts are conditional on key macroeconomic projections, vari-

ous exogenous variables (e.g., government spending, oil investments) and fi-

nancial market information, and derived under the condition that the interest

rate is set to minimize a loss function over macroeconomic outcomes. At this

stage, Norges Bank staff follows a set of three criteria for “appropriate” in-

terest rate forecasts: 1) achievement of the inflation target; 2) a reasonable

balance between inflation and capacity utilization; 3) robustness. These crite-

ria are reflected by the loss function that is minimized subject to the NEMO

model equations. Finally, the Executive Board decides on the likely interval

for the policy rate over the next three months (the “strategy interval”), and the

staff produces a forecast for the interest rate path.15 The lower panel of Figure

2 plots the point interest rate forecasts (solid lines) for the period from August

2006 to December 2011 together with the realized key policy rate (dashed

line).12As of 2013, Norges Bank will publish its path four times a year.13See Holmsen, Qvigstad, Røisland and Solberg-Johansen (2008).14The Norwegian Economy Model (NEMO), a medium-size DSGE model, has been used for policy making

since 2008 and details can be found in Brubakk, Husebø, Maih, Olsen and Magne (2006). For a discussion ofthe use of judgment, see Holmsen et al. (2008).

15For further details on the process, see Alstadheim, Bache, Holmsen, Maih and Røisland (2010).

93

Figure 2: Time-Series of Interest Rate Forecasts. The figure plots monthlyseries of realized interest rates (dashed black lines) in New Zealand (up-per panel) and Norway (lower panel) together with previously announced1-quarter (solid blue), the 2-quarters (solid green) and 3-quarters (solid red)ahead forecasts for that period.

A. RBNZ

B. Norges Bank

94

3 Model of Interest Rate Adherence

3.1 Deriving the Reaction Function

Consider a policymaker who at each time t sets the current interest rate i t and

announces a future path of that rate. The path consists of interest rate forecasts

for a number of consecutive periods in the future, given the central bank’s

expectations regarding future macroeconomic variables, such as inflation or

unemployment. We assume that the central bank only publishes two such

interest rate forecasts, a short-horizon forecast ipt,t+s (e.g., 1 quarter) and a

long-horizon forecast ipt,t+l (e.g., 8 quarters). In this way, we attempt to keep

the exposition simple, while mimicking the cross-section of published interest

rate forecasts. The Bank sets i t, ipt,t+s and ip

t,t+l in every t to minimize the

expected discounted sum of future per period losses:

Lt = 12

E t

∞∑k=0

δk

(i t+k − i∗t+k

)2 +ϕ (i t+k − i t+k−1)2

+κs

(i t+k − ip

t+k−s,t+k

)2 +κl

(i t+k − ip

t+k−l,t+k

)2

(1)

The first term in the loss function represents the costs of deviating from an

implied target level of the policy rate. The target rate i∗t summarizes the cen-

tral bank’s preferences and the state of the economy in period t, and can be

any non-inertial Taylor rule with arbitrarily numerous forward- and backward-

looking variables. Note that this method of deriving a policy rule is different

from characterizing the policy that minimizes a loss function over intermediate

targets such as inflation and output. The latter strategy requires the specifica-

tion of an economic model, which implies that the resultant policy formulation

will be model dependent, and any estimation based on it will be sensitive to

model misspecification. Our approach is less model-specific, as it allows us to

estimate a variety of i∗t .

95

The second term in the per-period loss function captures policymakers’ pref-

erence for interest rate smoothing. The parameter ϕ results in policy inertia.16

Our key objects of interest are the last two terms in the loss function, where

κs and κl capture the policymaker’s preference for adhering to previously an-

nounced interest rate forecasts. If either of these weights is positive, the poli-

cymaker perceives forecast deviations as costly and tries to minimize the dis-

tance between the current interest rate and the previously announced forecasts

for the current period. In this respect, our setting is similar to Gersbach and

Hahn (2011). The difference is that we allow for a cross-section of forecasts,

as the central banks publish multiple period forecasts, and more importantly ,

might value the accuracy of forecasts from different horizons differently.

The first order condition for the optimal interest rate i t is given by:

i t − i∗t+ϕ (i t − i t−1)−δϕ(

E t iot+1 − i t

)+κs

(i t − ip

t−s,t

)+κl

(i t − ip

t−l,t

)−E t

∑∞k=0δ

k[(

i t+k − i∗t+k) ∂i∗t+k

∂i t

]= 0

(2)

The term E t∑∞

k=0δk [•] implies that deviations from the target rate might af-

fect the target rate itself, by affecting the macroeconomic variables contained

in i∗t . Yet, as monetary policy influences the economy with a lag , the cur-

rent policy rate decisions have a negligible effect on the i∗ in the short term,

i.e.,∂i∗t+k∂i t

≈ 0 when k is small. For a sufficiently large k, the actual policy rate

should converge to the target rate, and thus E t(i t+k − i∗t+k

)≈ 0 when k is large.

Approximatively, the product E t(i t+k − i∗t+k

) ∂i∗t+k∂i t

≈ 0 for all k = 1,2, ...,T.

Imposing these approximations and solving the equation (2) for the current

interest rate yields a testable specification of the reaction function:

16See for instance Clarida, Galí and Gertler (2000) and Bache, Røisland and Torstensen (2011).

96

i t =Ω∗[

1 ϕ δϕ κs κl

]

i∗ti t−1

E t i t+1

ipt−s,t

ipt−l,t

, (3)

where

Ω∗ = 11+ϕ(1+δ)+κs +κl

measures the responsiveness of the actual policy rate i t to changes in the

macroeconomic environment. Intuitively, the reluctance to deviate from previ-

ously published interest rate forecasts, i.e. a positive κ j for j = s, l, reduces

the impact of changes in i∗t on the actual policy rate in a manner similar to the

effect of interest rate smoothing. Therefore, forecast adherence will dampen

the responsiveness to macroeconomic innovations. When κ j = 0 for j = s, l,

equation (3) collapses to:

i t = (1−ρb −ρ f )i∗t +ρb i t−1 +ρ f E t i t+1, (4)

where

ρb = ϕ(1+ϕ(δ+1)) , ρ f = δ ϕ

(1+ϕ(δ+1)) ,

and a preference for interest rate smoothing implies both partial adjustment

from the previous policy rate, and adjustment to the anticipated policy rate in

the next period, as shown in Bache et al. (2011). Accounting for the forward-

looking aspect of interest rate smoothing is essential in our setting, where we

attempt to isolate the adherence to previously announced forecasts from the

policymaker’s effort to anticipate the next policy rate level.

97

We next proceed from the general formulation of the reaction function in equa-

tion (3) to establish various policy rules that can be estimated for the two cen-

tral banks, the RBNZ and the Norges Bank, to identify the adherence prefer-

ences κ j for j = s, l.

3.2 Policy Rules

The main challenge in identifying κ j for j = s, l is to capture the empirical

counterpart of the implied target rate i∗t . We follow the available documen-

tation provided by the two banks, staff memos and the general literature on

simple policy rules to ensure a solid fit of the i∗t before adding the interest rate

forecasts. The following section describes the reaction functions we estimate.

3.2.1 Institution-specific Rules

For each central bank, we follow the documentation on simple policy rules that

describes the actual policy reasonably well. Both policymakers are assumed

to apply a partial adjustment to the target rate.

For the RBNZ, we follow the definition of the target rate from the last available

macro-model used for policy purposes, the so called K.I.T.T.17 The target rate

is defined as

i∗t = γπ (E tπt+1 −E tπt+1) , (5)

where E tπt+1 is the next period inflation expectation and E tπt+1 is the ex-

pected target inflation rate. The terms on the right-hand side are demeaned.

For the inflation expectations, we use the RBNZ survey of inflation expecta-

tions 2 years ahead.18 For the Norges Bank, we follow Bernhardsen (2008),

17Kiwi Inflation Targeting Technology, see Benes et al. (2009).18Great thanks to Ashley Lienert from the RBNZ for providing these data. We should also mention at this

98

who argues that the following target rate is both policy-relevant and fits the

historical record well:

i∗t = γππt +γint iintt +γwwt +γy yt. (6)

Here πt is core inflation, and the series is constructed by averaging the year-on-

year monthly increase in the CPI index adjusted for energy and taxes within

each quarter. The series is also seasonally adjusted. Further, iintt is the in-

ternational interest rates index (quarterly average). The index is constructed

by weighting the interest rate levels of Norway’s main trading partners us-

ing trade data weights.19 The next term, wt, is year-on-year wage growth in

Norway (quarterly average) generated by NEMO, the macroeconomic model

used by the Norges Bank for policy-making.20 Finally, yt is the output gap

from NEMO (quarterly average). The output gap is constructed by deducing

potential growth, as determined by NEMO, from the Norges Bank’s mainland

GDP growth forecast, as published in the Monetary Policy report. All of the

variables on the right-hand side, except the wage growth series, are real-time

variables, available at the time of actual policy rate decisions.21 This might be

particularly important for our purposes, as the published interest rate forecasts

added to the rules are also real-time variables.

Finally, a comment on the actual timing of the publication of interest rate fore-

casts by the Norges Bank is warranted. As mentioned above, the Norges Bank

only announces interest rate forecasts three times a year, namely in March,

point that we attempted to use the one-quarter-ahead inflation forecasts from the Monetary Policy Statementas inflation expectations. As the forecasts consider headline inflation, the series is noisy and the γπ coefficientturns out to be insignificant.

19Namely: Sweden, the US, Germany, the UK, Japan, Canada, Poland, Denmark, Czech Republic and Hun-gary.

20In contrast to the data in the US, for instance, the wage growth series seem to be less noisy in the Norwegiandata and, as it will be seen in the results section, explains a non-trivial portion of the movement in the key policyrate.

21See Orphanides (2001) for a discussion on the importance of using real-time vs. historical data whenestimating policy rules.

99

June and October. To obtain quarterly data, we consider forecasts published

in June third-quarter observations, i.e., interest rate forecasts produced in the

third quarter. By doing so, the September forecasts are “slided” cross-sections

of June forecasts by one quarter.22

3.2.2 Generalized Taylor Rule

The extended Taylor Rule of Clarida, Galí and Gertler (1999) is used for both

countries as an alternative to the country-specific ones. According to the rule,

the actual policy rate is partially adjusted to the target rate and the target rate,

is defined as:

i∗t = γπE tπt+1 +γyE t yt+1 (7)

where E tπt+1 and E t yt+1 denote expected inflation and output gap, respec-

tively. For New Zealand, we use the previously mentioned 2-year inflation

expectations from the RBNZ survey. The expected inflation data for Norway

and the expected output gap data for both countries are published in the mon-

etary policy reports of the RBNZ and the Norges Bank.

We use the following specification to test whether κ j = 0 for j = s, l for both

the institution-specific and the generalized Taylor rule of Clarida et al. (1999):

i t =Ω∗partial

[1 ϕ κs κl

]

i∗ti t−1

ipt−s,t

ipt−l,t

, (8)

where Ω∗partial term is equal to:

22The 2-quarters-ahead forecast from June becomes the 1-quarter-ahead forecast in September for the (same)average key policy rate in December and so on.

100

Ω∗partial =

11+ϕ+κs +κl

,

and where i∗ is the appropriate target rate for an individual central bank,

institution-specific or the one proposed in Clarida et al. (1999).

3.2.3 “Calvo-Rule”

Finally, we consider a policy rule with a weight on the expected future inter-

est rate. We denote this a “Calvo-Rule”. The term was introduced by Levine,

McAdam and Pearlman (2007) to describe a policy that weights a discounted

sum of future inflation, while Bache et al. (2011) derive such a policy from the

perspective of optimal interest rate smoothing and show that it can be repre-

sented as a policy rule with a weight on the expected future interest rate. Note

that by adding the interest rate forecasts to the rule, the specification is iden-

tical to the most general one from equation (3). The target rate i∗t we model

as in Clarida et al. (1999), with the expected interest rate E t i t+1 approximated

by the 1-quarter ahead forecast published by the two central banks.

3.3 Estimating the Model

Without loss of generality, let us consider the reaction function defined in (8)

for the target rate according to Clarida et al. (1999). For both central banks,

we estimate:

i t = 11+ϕ+κs +κl

[1 ϕ κs κl

]γπE tπt+1 +γyE t yt+1

i t−1

ipt−s,t

ipt−l,t

+εit (9)

where εit is modeled as an AR(1) process in line with Rudebusch (2002):

101

εit =λεi

t−1 +ζt (10)

and ζt is assumed to be i.i.d N(0,σζ). Accordingly, we allow for separation

between the policy inertia, i.e. the preference for interest rate smoothing, and

the persistence of the shock itself. The null hypothesis is that estimated coeffi-

cients κs and κl are not significantly different from zero, i.e., the policymakers

do not adhere to previously announced interest rate forecasts. The equations

(9) (the reaction function) and (10) (autocorrelated error) are estimated by

maximizing the appropriate likelihood function.23 Our key result refers to the

policy rule with the short-horizon forecast s = 1 only, i.e. the forecast added

to the rule is the 1-quarter-ahead forecast announced one quarter before the

policy rate is set. Adding longer-horizon forecasts and estimating policy rules

with s = 1 and l = 2,3, ...8 yields identical results as the s = 1 case, see sec-

tion 4.3.

In all of the reaction functions we estimate, the announced forecasts are or-

thogonal to the lagged policy rate.24 We regress the forecasts on the policy

rate as follows:

ipt,t+h =β0 +β1 i t−1 +εp,h

t (11)

and use the residuals from the regression, instead of the original forecast series,

in the interest rate rules. In such a way, the forecast variables added to differ-

ent rules include only information beyond the general level of interest rates.

Interestingly, when the original forecast series are included in rules, the lagged

policy rate, and not the forecasts, become insignificant due to collinearity.25

23A standard line-search algorithm is used to estimate the system, where the descent direction is calculatedusing the Quasi-Newton method.

24 Additionally, we correct the RBNZ forecasts for the spread between the 90-day Bank Bill rate and thepolicy rate by subtracting the time varying (quarter average) spread from the forecasts.

25In all the augmented specifications we estimate for the RBNZ, and in the “Calvo” specification we estimate

102

4 Results

Our main results are reported in tables 1 and 2, where we test for adherence

to 1-quarter-ahead forecasts announced in the quarter before the actual policy

rate is set. We discuss the findings for each country separately, beginning with

New Zealand.

4.1 Estimated Reaction Functions

4.1.1 RBNZ

The first column from the left in table 1 reports the estimated coefficients of

the policy rule from the K.I.T.T. model, with inflation expectations and lagged

interest rate as the only arguments. The second column reports the estimated

coefficients for the same interest rate rule when the forecast of the 1-quarter-

ahead Bank Bill rate announced in a previous quarter is added. Similar pair-

wise exercises are performed for the Clarida et al. (1999) rule in columns 3

and 4 and for the forward-looking Calvo-type rule in columns 5 and 6. For

each coefficient, the t-statistic is reported in brackets. Our main parameter of

interest is κs, the weight on past forecasts.

The main insight from table 1 is that for all three specifications, κs is positive

and statistically significant. Therefore, the RBNZ seem to have adhered to its

own forecasts. Furthermore, adding these forecasts to the reaction functions

makes the AR(1) element of the error terms in the KITT and the “Calvo” rules

become insignificant. In other words, previously published forecasts seem to

explain some of the systematic deviation of the actual policy rate from the “tar-

get” rate implied by the conventional simple rule without forecasts. However,

this is not the case for all of the estimated reaction functions.

for the Norges Bank, we constrain the coefficient ϕ in front of the lagged policy rate to be equal to its valuefrom the rule without interest rate forecasts. When we exclude the constraint, the algorithm does not convergeto a finite solution.

103

Table 1: Policy Rules for the RBNZ from 1999 - 2011 (1Q Forecasts). Ta-ble reports the estimated parameters of the rule from the RBNZ documenta-tion (column KITT), the rule by Clarida et al. (1999) (column CGG) and theCalvo-type rule by Levine et al. (2007) (column Calvo). All specifications areestimated without and with the 3-month-ahead interest rate forecast. Reportedt-statistics (in brackets) are calculated using asymptotic standard errors. Theremaining rows report F-statistic (F-stat), Durbin-Watson statistic (DW) andadjusted R-squared, and the number of observations is 51.

KITT CGG Calvo- s = 1 - s = 1 - s = 1

γπ 3.350 3.983 3.754 4.986 3.202 2.269(8.547) (1.900) (11.93) (1.523) (23.79) (3.328)

γy 1.619 1.204 0.800 0.365(8.914) (0.602) (17.40) (1.263)

ϕ 2.256 2.256 5.084 5.084 2.140 1.907(7.290) (1.069) (20.99) (1.177) (15.25) (1.693)

δ 0.467 0.524(3.943) (0.380)

κs 1.552 2.513 1.145(2.956) (1.738) (2.613)

λ 0.895 0.982 0.607 0.939 0.970 0.995(6.095) (2.181) (5.966) (1.808) (23.758) (3.605)

F-stat 3.156 1.219 19.28 4.39 13.847 18.96F-stat (CV) 4.218 3.747 3.747 3.444 3.444 3.232

DW Statistic 1.518 1.739 1.634 1.995 1.443 1.554Adjusted R2 0.997 0.995 0.999 0.997 0.999 0.999

104

We also see that the 2-years-ahead inflation expectations seem to explain a sig-

nificant amount of the variation in the actual policy rate. This is reasonable, as

the RBNZ is a strict inflation targeter. Yet it is somewhat puzzling that the in-

flation expectations variable is not statistically significant in all specifications,

especially when the interest rate forecast is added to the rule. As a robustness

check, we therefore extended the analysis by adding the forecast term to the

rule that is orthogonal to both the lagged policy rate and expected inflation.

The results did not change, and we therefore do not report the outcome of this

exercise.26

The in-sample fit of all the rules without the forecast terms is relatively high,

so the forecasts are less likely to capture some other (forward-looking) in-

formation omitted in the original rules. However, the forecasts do explain a

statistically significant portion of the actual policy rate variation. The upper

panel of Figure 3 plots the estimated residuals from the Clarida et al. (1999)

rule without (red bars) and with (solid blue line) the 1-quarter-ahead forecast

in the rule. We see that the interest rate forecasts seem to play an important

role in the policymaker’s reaction pattern, as the residuals from the augmented

rule on average are lower than those of the original rule.27

Moreover, augmenting the standard policy rules with the forecast terms identi-

fies some episodes in the actual policy rate setting, where the rate differed from

what the original rule suggested. For instance, the RBNZ increased the policy

rate two times during the second quarter of 2002, from 5 to 5.5%. The CGG

rule suggests the average policy rate for the quarter of 4.91% as appropriate

and the 1-quarter ahead forecast for the 90-day Bill rate that the RBNZ pub-

lished in the previous quarter was 5.41%. Another example would be March 9,

2006 when the RBNZ decided to leave the OCR unchanged at 7.25%, whereas

the policy rule suggests a cut to 7% and the previously announced 1-quarter

26The results are available on request.27The original rule residuals have a mean of -1.6 and standard deviation of 30 basis points, versus the -1 basis

point mean and 20 basis point standard deviation of the augmented rule residuals.

105

ahead forecast for the 90-day Bill rate was 7.6%. On September 16, 2010, the

RBNZ’s OCR rate was at 3%, while the Taylor rule suggests 2.5% as appro-

priate, and the 1-quarter ahead interest rate forecast announced in June of the

same year was 3.28%. It took another 3 policy meetings before the policy rate

was cut to 2.5% in March 2011, and the 1-quarter forecast for the 90-day Bank

bill rate was lowered to 2.86%.

Figure 3: Estimated Policy Shocks. The figure plots residuals from the esti-mated Clarida et al. (1999) rule from the equation (8) without the 1-quarter-ahead interest rate forecast (red bars), together with residuals from the samerule that includes the previously announced forecast iP

t−1,t (solid blue line),estimated for the RBNZ (upper panel) and the Norges Bank (lower panel).

A. RBNZ

B. Norges Bank

106

4.1.2 Norges Bank

Table 2 reports the corresponding results for the estimated reaction function of

the Norges Bank. Coefficients and t-statistics are calculated using asymptotic

standard errors (in brackets).

Similar to the case of the RBNZ, the Norges Bank seems to adhere to the

1-quarter-ahead interest rate forecast, as κs is estimated to be significant in

all specifications. The expected output gap is another important variable in

the estimated policy rules, whereas the coefficient of inflation is significantly

different from zero only when the Clarida et al. (1999) rule is used. The im-

provement of the fit due to the inclusion of the interest rate forecasts is again

marginal, but helpful in explaining some of the estimated policy shocks from

the original rules.

The lower panel of Figure 3 again plots the residuals from the estimated Clar-

ida et al. (1999) rule without the forecasts terms (red bars) and including the

1-quarter-ahead forecasts (blue solid line).28 The rule augmented with adher-

ence apparently explains several policy decisions better than the original rule,

which indicates that these decisions might have been particularly strongly af-

fected by the previously announced forecasts. For example, the key policy rate

in the third quarter of 2008 was 5.75%, whereas the estimated policy rule sug-

gests 5.5% as the appropriate level and the 1-quarter ahead forecast for the key

policy rate, published in June 2008, was 5.75%. Another example is the sec-

ond quarter of 2010, when the previously announced 1-quarter-ahead forecast

stood at 1.9% and the policy rate was set to 2% at the end of the quarter, while

the original Clarida et al. (1999) rule suggests 1.75%. As the figure shows,

there are other episodes where the forecasts added no additional information

to the original rules, yet on average policy seems to have adhered to previously

announced short-horizon forecasts.28Similar to the RBNZ case, augmenting the original rule reduces the mean of the estimated shocks from -1.3

basis points to 0.2 and the standard deviation from 21 basis points to 12.

107

Table 2: Policy Rules for the Norges Bank from 2005 - 2011 (1Q Fore-casts). The policy rules reported are Bernhardsen (2008) (column B), Claridaet al. (1999) (column CGG) and the Calvo-type rule by Levine et al. (2007)(column Calvo). Reported t-statistics (in brackets) are calculated using asymp-totic standard errors and the number of observations is 25.

B CGG Calvo- s = 1 - s = 1 - s = 1

γπ 0.242 0.615 0.831 1.595 1.093 1.438(0.804) (1.305) (6.416) (2.250) (3.699) (3.192)

γint 0.832 0.121(2.137) (0.565)

γw -0.049 1.272(-0.087) (3.948)

γy 0.468 0.524 0.961 1.309 1.264 1.128(1.270) (3.053) (4.043) (4.298) (1.894) (6.504)

ϕ 0.351 0.796 0.627 1.303 0.824 0.824(0.686) (1.387) (5.976) (1.613) (1.506) (2.571)

δ 0.382 0.006(1.195) (0.041)

κs 0.915 0.799 0.518(3.267) (1.898) (2.075)

λ 0.923 0.240 0.367 0.086 0.367 0.138(3.083) (0.237) (1.821) (0.089) (0.586) (0.152)

F-stat 7.68 114.96 45.70 95.17 33.96 70.80F-stat (CV) 4.015 3.927 4.431 4.171 4.171 4.015


108

4.2 The Preferred Policy Rates

In this section we approach our empirical question from a slightly different

angle. We consider two different proxies for what the interest rate would have

been without adherence, referred to as the “preferred” rate, and thereafter eval-

uate whether adherence is significant after controlling for the preferred rate.

4.2.1 Using the Estimated Rules

We “construct” the preferred policy rate series for the two central banks from

the estimated interest rate rules without the previously announced forecasts.

There are three such estimates for each central bank, namely the fitted policy

rate according to the institution-specific rules (the KITT model documentation

for the RBNZ and Bernhardsen (2008) for the Norges Bank), the generalized

Taylor rule (Clarida et al. (1999)) and the “forward looking” rule (Levine et al.

(2007)). Once we obtain the fitted policy rates, we perform the following two

regressions:

i t = Ω i t + Å1 ipt−1,t +εt (12)

and

i t = Ω i t + Å1εp,1t +εt (13)

where i t is the preferred policy rate, ipt−1,t is the 1-quarter-ahead forecast an-

nounced in a previous quarter and εp,1t is the residual from the regression (11),

i.e., the 1-quarter-ahead forecast orthogonal to the lagged policy rate. We use

the 2-step General Least Squares (GLS) model of Hoffman (1987) to estimate

the regression coefficients and therefore account for the so called “generated

regressor” problem. Table 3 reports the parameter estimates.

109

Table 3: Fitted Policy Rules as the Preferred Policy Rate. Table reportsthe estimated parameters from the equation (12) (upper panel) and (13) (lowerpanel) where the preferred policy rate i t is estimated using the previously men-tioned policy rules for the two central banks. The coefficients are calculatedusing the 2-step GLS estimator of Hoffman (1987). Reported t-statistics (inbrackets) are calculated using Newey-West standard errors. The remainingrows report Durbin-Watson statistic (DW) and adjusted R-squared.

ipt,t+1

RBNZ Norges BankKITT CGG Calvo B CGG Calvo

Ω -0.312 0.488 0.974 0.130 0.522 0.623(-2.416) (-1.507) (-0.272) (-8.554) (-3.523) (-4.352)

Å1 1.230 0.557 0.187 0.834 0.458 0.377(27.46) (11.21) (4.652) (6.265) (5.615) (5.537)

DW 0.576 0.849 1.337 1.309 1.300 1.551R2 0.916 0.957 0.996 0.966 0.975 0.989

εp,1t

RBNZ Norges BankKITT CGG Calvo B CGG Calvo

Ω 1.253 0.992 0.981 0.748 0.937 1.003(0.433) (-0.025) (-0.185) (-3.039) (-0.525) (0.034)

Å1 0.461 0.259 0.070 0.138 0.128 0.028(9.264) (4.770) (2.596) (1.046) (1.645) (0.991)

DW 0.576 0.849 1.507 1.309 1.300 1.711R2 0.916 0.957 0.994 0.966 0.975 0.989

The “weight” the RBNZ places on the 1-quarter ahead interest rate forecasts

is significantly different from zero in all the estimated equations, independent

of whether we use the original time-series of the forecast or that orthogonal

to the lagged policy rate (the residual term from the equation (11)). The esti-

mates for the Norges Bank are similar, whereas the forecast series orthogonal

to the lagged policy rate is only marginally significant. Overall, the main result

holds.

110

4.2.2 Using “Nowcasts” as the Preferred Policy Rate

Interest rate rules provide a simplistic description of monetary policy. Deci-

sions regarding the appropriate policy rate can be systematically influenced by

the omitted factors such as financial market conditions, house prices or judg-

ment. All of these factors could in principle be correlated with past interest

rate forecasts. In addition to the omitted variable problem, it could also be

the case that the 1-quarter-ahead forecasts are simply “good” forecasts of the

policy rate, which we misinterpret as forecast adherence.

We address these potential issues by using the two central banks’ “nowcasts”

of the policy rate as the preferred policy stance in a current quarter.29 The

nowcasts are produced by the core macroeconomic models of the central banks

and combined with judgment before being released in the monetary policy

reports.30 It is therefore likely that these nowcasts capture the factors that have

systematically influenced monetary policy in the two countries. Moreover, the

information content from past forecasts is embedded in the current information

set. If the announced paths are merely forecasts, they should have no predictive

power on the policy rate over and above the nowcasts.

Table 4 reports the estimated coefficients from equations (12) and (13) where

we use the nowcasts as the preferred policy rate i t. The key insight remains

intact: the two central banks appear constrained by their most recently an-

nounced forecasts. When we use the orthogonalized series of forecasts, the

result remains the same for the RBNZ and we obtain a marginally significant

Å1 for the Norges Bank. As the nowcasts contain the most up-to-date informa-

tion about the current state of the economy and the two central banks’ judg-

ments about the appropriate policy, it is unlikely that our main result reflects a

superior forecasting ability of past interest rate forecasts.29The nowcasts published by the Norges Bank concern the key policy rate, while as previously explained, the

RBNZ announces the nowcasts of the 90-day Bank Bill rate. We adjust the latter for the spread between theBank Bill rate and the policy rate.

30See Drew and Karagedikli (2008) and Holmsen et al. (2008).

111

Table 4: Central banks’ Nowcasts as the Preferred Policy rate. Table re-ports the estimated parameters from the equation (12) (the columns ip

t,t+1) and

the equation (13) (the columns εp,1t ). Reported t-statistics (in brackets) are

calculated using Newey-West standard errors. The statistics tell us whetherthe coefficients Ω and Å1 are statistically different from 1 and 0, respectively.The remaining rows report F-statistic (F-stat), Durbin-Watson statistic (DW),adjusted R-squared and the number of observations (N.Obs.).

RBNZ Norges Bankip

t,t+1 εp,1t ip

t,t+1 εp,1t

Ω 1.065 1.001 0.875 1.010(2.545) (0.404) (-1.667) (2.301)

Å1 -0.063 0.108 0.133 0.018(-2.594) (2.264) (1.681) (1.601)

DW Statistic 1.548 1.715 1.723 2.207Adjusted R2 0.998 0.998 0.994 0.993

N.Obs. 55 55 24 24

4.3 Longer Horizon Forecasts

The actual policy rate seems to be affected by the interest rate forecast an-

nounced in the preceding quarter, but not by the forecasts announced before

that. This is clear from tables 5 and 6, which illustrate the results for s = 1

(1 quarter) and l = 2 (2 quarters ahead), for the RBNZ and the Norges Bank,

respectively.

We have also estimated the rules using forecast horizons from 3 to 8 quarters

ahead. The mid- and long-range forecast above 1-quarter ahead do not add any

information to the estimated rules.

112

Table 5: Policy Rules for the RBNZ from 1999 - 2011 (1Q & 2Q Forecasts).Table reports the estimated parameters of the rule from the RBNZ documen-tation (column KITT), the rule by Clarida et al. (1999) (column CGG) and theCalvo-type rule by Levine et al. (2007) (column Calvo). All specifications areestimated without and with interest rate forecasts, whereas the short-horizonforecast is s = 1 (3 months) and the long-range forecast is l = 2 (6 months).Reported t-statistics (in brackets) are calculated using asymptotic standard er-rors and the number of observations is 50.

KITT CGG Calvos = 1, l = 2 s = 1, l = 2 s = 1, l = 2

γπ 3.764 4.003 1.940(3.867) (4.211) (2.906)

γy 1.307 0.270(2.519) (0.711)

ϕ 2.237 5.095 1.536(3.772) (4.468) (2.135)

δ 0.584(1.633)

κs 1.462 1.906 0.953(1.307) (7.275) (1.833)

κl -0.306 -1.155 0.177(-0.136) (-1.011) (0.524)

λ 0.978 0.824 1.000(3.527) (2.953) (3.181)

F-stat 1.36 11.49 16.87F-stat (CV) 3.454 3.243 3.087

DW Statistic 1.739 1.932 1.413Adjusted R2 0.995 0.999 0.999

113

Table 6: Policy Rules for the Norges Bank from 2005 - 2011 (1Q & 2QForecasts). Table reports the estimated parameters from the policy rule inBernhardsen (2008) (column B), the rule by Clarida et al. (1999) (columnCGG) and the Calvo-type rule by Levine et al. (2007) (column Calvo). Re-ported t-statistics (in brackets) are calculated using asymptotic standard errorsand the number of observations is 23.

B CGG Calvos = 1, l = 2 s = 1, l = 2 s = 1, l = 2

γπ 0.558 1.507 1.092(1.036) (1.997) (1.622)

γint 0.950(2.413)

γw 0.598(1.069)

γy 0.200 1.409 0.748(0.522) (4.589) (2.578)

ϕ -0.055 1.668 2.898(-0.115) (2.129) (6.682)

δ -0.577(-5.493)

κs 0.250 1.017 1.064(1.135) (4.205) (3.281)

κl 0.527 -0.213 1.050(1.567) (-0.480) (2.558)

λ 0.872 0.051 -0.028(2.278) (0.129) (-0.043)

F-stat 16.98 94.87 128.95F-stat (CV) 4.004 4.102 4.026

DW Statistic 1.669 1.932 1.824Adjusted R2 0.995 0.999 0.999

114

4.4 Does Our Empirical Strategy “Cry Wolf”?

We specify policy in terms of simple rules rather than the minimization of an

explicit objective function. A natural concern is that our findings falsely indi-

cate a preference for adherence, when in reality no such preference exists. To

address this issue, we apply our empirical approach to data that are artificially

generated from an environment where the central bank’s true preferences are

known.

4.4.1 The Model

We simulate data from the standard 3-equation New Keynesian model used in

Gersbach and Hahn (2011), where the central bank optimally sets policy to

minimize a loss function over output and inflation, and potentially is also con-

cerned about deviations from the previously announced 1-period-ahead fore-

casts of the policy rate. As explained in the Data Section, both the RBNZ and

the Norges Bank announce interest rate forecasts conditional on future infla-

tion and output gap forecasts. In principle, these forecasts might also carry a

weight. We thus incorporate the costs of deviating from inflation projections,

as in Gersbach and Hahn (2011).

The Phillips curve, determined by forward-looking price-setters, reads:

πt = δE t[πt+1]+λyt +χt,

where χt is an AR(1) cost-push shock:

χt = ρχχt−1 +εχt .

The dynamic IS curve is given by:

115

yt = E t[yt+1]+σ(io

t −E t[πt+1])+ωt,

where ωt is an AR(1) demand shock:

ωt = ρωωt−1 +εωt .

In every period t, the central bank sets the current interest rate i t, the 1-quarter-

ahead inflation forecast πPt+1,t, and the 1-quarter-ahead interest rate forecast

iPt+1,t to minimize the following loss function:

Lt = 12

E t

∞∑k=0

δ j(π2

t+k +ay2t+k +b(πt+k −πP

t−1+k,t+k)2 + c(i t+k − iPt−1+k,t+k)2

)(14)

The parameters a, b and c describe the central bank’s preference for stabiliz-

ing output and minimizing the costs of deviating from previous inflation- and

interest rate forecasts, respectively. The three weights are all normalized by

the weight on inflation. Note that the central bank internalizes how its choice

of interest rate forecast affects future policy and thereby future output and in-

flation. In this sense, the interest rate path becomes a “commitment device”,

allowing the central bank to affect private expectations, because reneging on

these “promises” is costly.

4.4.2 Model Simulation and Estimated Policy Rule

As the central bank re-optimizes in every period, by setting the current policy

rate and announcing the optimal policy rate in the next period, the policy-

maker’s reaction function can not be expressed in a closed form (in terms of a,

116

b and c). To relate our empirical approach to the optimal policy in this specific

environment, we first simulate the model, assuming different values of devia-

tion costs b and c, and then estimate the following non-inertial Taylor rule on

simulated data samples:

isimt = γππsim

t +γy ysimt +ρ1 iP,sim

t−1,t +ϑt (15)

where ϑt is an AR(1) process. The higher we set the coefficient c in the loss

function, the higher the estimate of coefficient ρ1 in the rule should be. The

model is solved for optimal policy under discretion using the algorithm of

Söderlind (1999). We generate 3,000 samples of data, where each sample

contains 60 observations. We then estimate the equation (15) on each sample

and report the means of estimated parameters in table A.1 in the Appendix,

together with t-statistics (in brackets) calculated using the standard deviation

of those estimates. The upper panel provides the model parametrization that

we employ, which consists of the same values as in Clarida et al. (2000).

The lower panel illustrates the key takeaway from the exercise: our estimated

simple policy rules do not commit false positive errors. The coefficient on the

interest rate forecast ρ1 is only significantly different from zero if the “true”

reluctance to deviate from previous forecasts is relatively strong. In our exer-

cise, the empirical strategy implies adherence when c is above 0.2, i.e. when

the weight on deviations from the announced interest rate forecasts is equal to

one-fifth of the weight on inflation. In the other two cases, when c = 10−7 i.e.

practically zero,31 and c = .1, previous interest rate forecasts appear unimpor-

tant in the reduced-form reaction function.32

31With c = 0, the interest rate deviation term from the loss function vanishes and the interest rate forecasts arenot determined.

32The variation in the values of the estimated inflation coefficient γπ is in line with Cochrane (2007), whoargues that the Taylor rule parameter γπ cannot be identified by regressing the policy rate on inflation.

117

Most important, this result is independent of whether the policy rule we es-

timate on the simulated data is misspecified. Excluding the output gap term

from equation (15) will still not lead us to commit false positive errors when

measuring forecast adherence with the interest rate rules, see table A.2 in the

Appendix.

4.5 Policy Rate Surprises

Our interpretation of the empirical findings is that the two central banks find it

costly to deviate from their own forecasts. Such costs introduce an additional

adjustment term in the banks’ reaction functions, and constrain policymak-

ing over and above the desire to smooth the policy rate itself. In this section

we discuss whether our results might be explained by a completely different

assumption, namely that the central banks aim to minimize surprises in the

policy rate, as suggested by Svensson (2003).33

Suppose that the central bank’s optimization problem can be described by the

following loss function:

Lt = 12

E t

∞∑k=0

δk

[ (i t+k − i∗t+k

)2 +ϕ (i t+k − i t+k−1)2

κE1 (i t+k −E t+k−1 i t+k)2

], (16)

where the first two terms describe, as previously explained, the central bank’s

objectives to set the actual policy rate according to the state of the economy,

in a gradual fashion, respectively. The parameter κE1 captures the bank’s pref-

erences for minimizing the difference between the current policy rate i t and

the expected policy rate one period before the decision, E t−1 i t. If the future

short-rate expectations of the central bank and the public are perfectly aligned,

and if we further assume that the public and not the central bank “dictates”

33See also Rudebusch (2006).

118

those expectations, our empirical strategy captures the policymaker’s effort to

reduce surprise movements in the policy rate and not to stick to its promises.

Let us consider the two assumptions individually. As we have shown, our

main result concerns the shortest-horizon forecasts announced a quarter be-

fore the actual policy rate is set. Over the course of any three-month period,

we might indeed assume that the uncertainty around a policymaker’s decisions

is relatively low (with respect to medium- or long term outlook) and thus the

expectations of the central bank and the markets are broadly aligned. The

better the proxy for market expectations one has, the closer the results of es-

timating the reaction function of the policymaker in (16) are going to be to

our results. Yet, the central banks we consider publish their own interest rate

forecasts, and thus a positive and significant κE1 coefficient de facto means that

the two central banks adhere to their own forecasts, irrespective of whether

the underlying motive is to avoid the loss of reputation or minimize surprises

in the policy rate. The two explanations are complementary and empirically

indistinguishable.

Only if the second assumption holds, does our explanation that the central

banks adhere to their own short-horizon forecasts fail. As the market expec-

tations are those that guide the central banks’ short-rate expectations, the esti-

mates of κs that we report in tables 1 and 2 measure the policymaker’s effort to

reduce policy surprises. Nevertheless, the assumption is quite strong. It means

that the RBNZ and the Norges Bank publish their own forecasts by relabeling

market expectations. There might be some anecdotal evidence that the central

banks that publish interest rate forecasts occasionally adjust those forecasts to

appear similar to the observed forward rate curve on the day prior to the an-

nouncement, but it is unlikely that this relabeling is done in a systematic way,

without discussing it openly in monetary policy reports.

Finally, if our results are entirely driven by a preference for conforming to

market expectations, this preference should also have influenced policy before

119

the practice of publishing paths was introduced. This is testable, and we turn

to such a test in the next section.

4.6 Placebo Test

We ask whether the Norges Bank “adhered” to market expectations and run

our regressions on the Norges Bank data before it began announcing interest

rate forecasts in November 2005.34 We approximate market expectations with

the 3-month forward rate. As explained in the previous section, this is not

simply a “placebo test” of our strategy, but it also indicates whether our main

findings are driven by preferences for avoiding policy surprises. If we find

that the Norges Bank had no such incentives prior to 2005, it is reasonable

to believe that no such preferences existed after 2005 either. To appreciate

the potential importance of aversion to policy surprises, we consider a central

bank that might have been concerned in the past about disappointing market

expectations, namely the Bank of England (BoE).35

We solve the optimization problem in equation (16) with respect to i t, and

estimate the following reaction function for the BoE from 2001 to 2009 and

for the Norges Bank from 1999 to 2004:

i t =Ω∗E

[1 ϕE κE

1

]γπE tπt+1 +γyE t yt+1

i t−1

E t−1 i t

+εEt (17)

where

Ω∗E = 1

1+ϕE +κE1

,

34Since 1999, monetary policy in Norway has been conducted in pursuit of low and stable inflation and itsoperational procedures have remained broadly unchanged. However, the monetary policy implemented by theRBNZ was substantially different before the beginning of the sample used, see for example the Reserve BankBulletin from March 1999.

35See Appendix for a brief description of policymaking at the BoE and some anecdotal evidence of prefer-ences towards reducing surprises in the policy rate.

120

http://www.rbnz.govt.nz/research/bulletin/1997_2001/1999mar62_1archerbrookesreddell.pdf

http://www.rbnz.govt.nz/research/bulletin/1997_2001/1999mar62_1archerbrookesreddell.pdf

and where the target rate is defined as in Clarida et al. (1999), E t−1 i t is the

3-month forward rate orthogonal to the lagged policy rate and εEt is again

allowed to have an AR(1) component. For the 1-period-ahead inflation and

output gap expectations in the BoE case, we use the forecasts published in the

Inflation Report.36 Table 7 reports the results.

Table 7: Placebo Test. Table reports the estimated parameters from the policyrule specified in equation (17) for the Bank of England (2001 - 2009) and theNorges Bank (1999 - 2004). In both cases, the rule is estimated without andwith the 3-month forward rate. t-statistics (in brackets) are calculated usingasymptotic standard errors. The remaining rows provide F-statistic (F-stat),Durbin-Watson statistic (DW) and adjusted R-squared.

Bank of England Norges Bankwithout with without with

γπ 0.043 1.013 3.717 4.426(0.283) (0.304) (12.76) (3.141)

γy 0.875 2.200 0.717 0.574(9.425) (1.609) (6.283) (0.934)

ϕ 1.954 1.954 2.721 2.721(8.590) (1.234) (12.54) (1.546)

κE1 3.064 0.395

(1.621) (0.997)λ 0.163 0.584 0.128 0.098

(1.115) (0.723) (0.658) (0.087)F-stat 14.18 6.81 54.90 52.87

F-stat (CV) 4.018 3.725 4.500 4.248DW Statistic 1.950 1.965 1.641 1.673Adjusted R2 0.998 0.996 0.999 0.999

N.Obs. 34 34 23 23

36The BoE publishes forecasts for GDP growth and not the output gap, as the RBNZ and the Norges Bankdo. We use the demeaned GDP growth forecast for the Et yt+1 variable in the rule.

121

Our empirical strategy passes the placebo test for the Norges Bank: The 3-

month forward rate has no explanatory power for the policy rate in Norway.

This adds credibility to the interpretation of our main results. Moreover, it

implies that the Norges Bank did not “adhere” to the market forecasts and

apparently did not have a preference for minimizing surprises in the policy rate

over and above what the interest rate smoothing might imply. Moreover, we

also observe that our estimation finds adherence to market expectations where

we a priori would expect that such preferences exist: We report a positive yet

marginally significant κ1 coefficient in the policy rule for the BoE, which is

known to emphasize market expectations when setting its interest rate.

5 Conclusion

The practice of explicitly announcing future monetary policy intentions has

been widely recommended in the theoretical literature and increasingly im-

plemented by several central banks, including the Federal Reserve. Our find-

ings indicate that the actual policy decisions of the two central banks with

the longest history of publishing interest rate forecasts might have been con-

strained by those forecasts. Once the future interest rate paths are announced,

the two central banks appear reluctant to deviate from their short horizon pro-

jections.

Normatively, the question of whether forecast adherence is beneficial remains

an open question. Adherence might indicate that policymakers use published

interest rate paths as a commitment device to increase policy effectiveness.

However, reluctance to deviate from past forecasts might prevent policymakers

from reacting sufficiently strongly to unexpected shocks. Addressing these

arguments requires further theoretical and empirical work.

122

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Appendix

Bank of England

Starting from November 2004, the Bank of England (BoE) uses forward rates

implied by market yields to condition its key macroeconomic projections of

future inflation and GDP growth. The forward rate curve extracted from gov-

ernment bonds (GLC - Government Liability Curve) and the macroeconomic

projections are published regularly in the Bank’s Inflation Report every Febru-

ary, May, August and November. Such policymaking is well described by the

statement of the BoE’s Chief Economist, Spencer Dale: “[...] the Committee’s

preferred approach is to describe its assessment of the outlook for output and

inflation, and allow the public and markets to make their own assessment of

the likely future path of interest rates.”37

Even before 2004, the BoE dedicated particular attention to the forward rate

curve in its Inflation Report, but the conditioning assumption for inflation and

GDP forecasts was “no change” in the Bank Rate.38 The BoE has regularly

commented on the market expectations implicit in the forward curve since the

May 2001 Inflation Report, and we therefore use this starting date to estimate

the policy rule specified in (17), for which results were reported in Table 7.

Interestingly, the BoE sometimes made comments on the published forward

rate curve, which might indicate that these forward rates could matter for the

actual policy decisions. Two examples are the following:

” On 6 November, the Monetary Policy Committee increased the repo rate by

0.25 percentage points to 3.75%; in the previous three months official interest

rates had not been changed. On 5 November, the general collateral (GC)

repo/gilt forward curve suggested that market participants expected interest

37See Andersson and Hofmann (2009).38See Goodhart (2009).

127

rates to rise in 2004 and 2005.”39

”The Monetary Policy Committee (MPC) has left official interest rates un-

changed during the past three months. [...] The forward curve indicates that

in the run up to the MPC’s meeting on 8-9 February, market participants ex-

pected official interest rates to remain broadly unchanged over the next few

years.“ 40

39See the BoE Inflation Report from November 2003.40See the BoE Inflation Report from February 2006.

128

Table A.1: Estimated Taylor Rule on Simulated Data. Table illustrates thecalibration of the model in Section 4.4.1 (upper panel) and the estimated pa-rameters of the policy rule (15) without and with the interest rate forecast term(lower panel), whereas t-statistics (in brackets) are calculated using standarderrors from the Monte Carlo simulation. The average values of Durbin-Watsonstatistic (DW) and adjusted R-squared are also reported, whereas every gener-ated sample contains 60 observations and we simulate the model 3,000 times.

CalibrationNK Phillips Curve: δ= 0.99

λ= 0.3

IS curve: σ= 1

Cost-Push Shock: ρχ = 0.9σχ = 1

Demand Shock: ρω = 0.9σω = 1

Loss-Function: a = 0.3b = 0.2

c = 10−7 c = 0.1 c = 0.2without with without with without with

γπ 1.394 1.393 0.196 0.240 0.691 0.620(1.241) (1.231) (0.852) (0.948) (4.247) (3.271)

γy 0.566 0.564 0.605 0.635 0.075 0.032(0.616) (0.609) (5.000) (4.677) (1.202) (0.413)

ρ1 -0.016 0.100 0.120(-0.113) (1.212) (1.677)

λ 0.888 0.889 0.928 0.938 0.920 0.934(12.77) (12.64) (20.88) (24.95) (18.77) (22.95)


129

Table A.2: Estimated Taylor Rule on Simulated Data when the Rule isMisspecified. Table illustrates the calibration of the model in Section 4.4.1(upper panel) and the estimated parameters of the policy rule (15) when theoutput gap term is excluded (lower panel). t-statistics (in brackets) are calcu-lated using standard errors from the Monte Carlo simulation. The average val-ues of Durbin-Watson statistic (DW) and adjusted R-squared are also reported,whereas every generated sample contains 60 observations and we simulate themodel 3,000 times.

CalibrationNK Phillips Curve: δ= 0.99

λ= 0.3

IS curve: σ= 1

Cost-Push Shock: ρχ = 0.9σχ = 1

Demand Shock: ρω = 0.9σω = 1

Loss-Function: a = 0.3b = 0.2

c = 10−7 c = 0.1 c = 0.2without with without with without with

γπ 0.715 0.716 0.639 0.637 0.578 0.570(5.844) (5.792) (5.741) (5.656) (5.135) (5.064)

ρ1 -0.017 0.061 0.125(-0.115) (0.711) (2.071)

λ 0.888 0.889 0.918 0.925 0.919 0.935(13.18) (12.78) (17.15) (19.07) (17.17) (21.39)


130

Nikola Nikodijevic MirkovUniversität St.Gallen (HSG)

Swiss Institute of Banking and FinanceRosenbergstrasse 52, 9000 St.Gallen

RESEARCH INTERESTS

Term structure models, Monetary policy, Forecasting

EDUCATION2012 - 2013 Visiting Student Researcher, Stanford University

2009 - 2013 PhD, Universität St.Gallen (HSG)

2006 - 2009 MSc, Università Commerciale Luigi Bocconi

2001 - 2006 BSc, Univerzitet u Beogradu

PROFESSIONAL EXPERIENCE (RECENT)

2012 - 2013 Federal Reserve Bank of San Francisco, Economic Research

Visiting Scholar

2012 Norges Bank, Monetary Policy Research

PhD Intern

2009 - 2013 Universität St.Gallen (HSG), SBF

Research & Teaching Assistant

2008 Citigroup, CitiFX Milan

Junior FX salesman

REFERENCES

Paul Söderlind Monika Piazzesi

Universität St.Gallen (HSG) Stanford University

[email protected] [email protected]

Francesco Audrino Anders Vredin

Universität St.Gallen (HSG) Sveriges Riksbank

[email protected] [email protected]

131

PAPERS

Asymmetries in Interest Rate Response to Monetary Policy Shocks

Working Paper, July 2012

Announcements of Interest Rate Forecasts: Do Policymakers Stick to Them?

Joint with Gisle James Natvik, Working Paper, March 2012

Central Bank Reserves and the Yield Curve: Estimating Tobin’s Substitution

Portfolio Effect, Joint with Barbara Sutter, Working Paper, November 2011

International Financial Transmission of US Monetary Policy: An Empirical

Assessment, HSG SoF Working Paper Series No. 141, January 2012

US Term Premia around FOMC Decisions

HSG SoF Working Paper No. 139, September 2011

CONFERENCES AND SEMINARS

2013: Walking the Talk? Challenges for Monetary Policy Actions and Com-

munication in Uncertain Times, Canada; 28th Annual Congress of the Euro-

pean Economic Association, Sweden; 28th Annual Congress of the European

Economic Association, Sweden; 17th ICMAIF Conference, Greece; FRBSF;

UC Berkeley (invited talk); 2012: FRBSF; Stanford University; 44th Annual

Money, Macro and Finance Conference, Ireland; 27th Annual Congress of the

European Economic Association, Spain; 32nd Annual International Sympo-

sium on Forecasting, US; National Bank of Serbia 2012 Young Economists

Conference, Serbia; Infinity Conference on International Finance, Ireland;

14th INFER Annual Conference, Portugal; 16th ICMAIF Conference, Greece;

Norges Bank; 5th RGS Doctoral Conference in Economics, Germany; Univer-

sity of St.Gallen; Campus for Finance Research Conference, Germany; 2011:University of St.Gallen; 6th End-Of-Year Conference of Swiss Economists

Abroad, Switzerland; 5th CSDA Conference on Computational and Financial

Econometrics, UK; 28th GdRE Annual Symposium on Money, Banking and

Finance, UK 2010: University of Konstanz

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