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REVIEW
FEDERAL RESERVE BANK OF ST. LOUIS
SECOND QUARTER 2019
VOLUME 101 | NUMBER 2
Gauging Market Responses to Monetary Policy Communication
Kevin L. Kliesen, Brian Levine, and Christopher J. Waller
International Trade Openness and Monetary Policy:
Evidence from Cross-Country Data
Fernando Leibovici
The Real Term Premium in a Stationary Economy
with Segmented Asset Markets
YiLi Chien and Junsang Lee
Racial Gaps, Occupational Matching, and Skill Uncertainty
Limor Golan and Carl Sanders
REVIEW
Volume 101 • Number 2
President and CEO
James Bullard
Director of Research
Christopher J. Waller
Chief of Staff
Cletus C. Coughlin
Deputy Directors of Research
iii
In Memoriam: Keith M. Carlson
B. Ravikumar
David C. Wheelock
Review Editor-in-Chief
Carlos Garriga
Research Economists
David Andolfatto
Subhayu Bandyopadhyay
YiLi Chien
Riccardo DiCecio
William Dupor
Maximiliano Dvorkin
Miguel Faria-e-Castro
Sungki Hong
Kevin L. Kliesen
Julian Kozlowski
Fernando Leibovici
Oksana Leukhina
Fernando M. Martin
Michael W. McCracken
Alexander Monge-Naranjo
Christopher J. Neely
Michael T. Owyang
Paulina Restrepo-Echavarría
Juan M. Sánchez
Ana Maria Santacreu
Don Schlagenhauf
Guillaume Vandenbroucke
Yi Wen
Christian M. Zimmermann
69
Gauging Market Responses to
Monetary Policy Communication
Kevin L. Kliesen, Brian Levine, and Christopher J. Waller
93
International Trade Openness and Monetary Policy:
Evidence from Cross-Country Data
Fernando Leibovici
115
The Real Term Premium in a Stationary Economy
with Segmented Asset Markets
YiLi Chien and Junsang Lee
135
Racial Gaps, Occupational Matching,
and Skill Uncertainty
Limor Golan and Carl Sanders
Managing Editor
George E. Fortier
Editors
Jennifer M. Ives
Lydia H. Johnson
Designer
Donna M. Stiller
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
i
Review
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© 2019, Federal Reserve Bank of St. Louis.
ISSN 0014-9187
ii
Second Quarter 2019
Federal Reserve Bank of St. Louis REVIEW
In Memoriam: Keith M. Carlson
For several decades, the St. Louis Fed was known as
the “Monetarist Fed.” Several St. Louis Fed economists—
and a few Bank presidents—were instrumental in developing and burnishing this reputation. Keith M. Carlson,
who passed away on January 22, 2019, was one of those
economists.
Most economists familiar with this history likely knew
Keith through his important work on the St. Louis equation.
His most famous article was “A Monetarist Model for
Economic Stabilization,” co-authored with Leonall (Andy)
Andersen and published in the St. Louis Fed Review in
1970 (Andersen and Carlson, 1970). This article described
the first version of the St. Louis model used to assess how
monetary policy affects macroeconomic activity through
Keith M. Carlson
changes in the money stock.
1934-2019
For at least 25 years, the St. Louis model guided St. Louis
Fed Bank presidents and their research directors as they
prepared for Federal Open Market Committee meetings. Moreover, the model was central to
the debate in the 1970s and 1980s over the relative effectiveness of monetary and fiscal policy.
As with any economic model, though, it went through numerous iterations. Keith would
publish the final version of the model in 1986 (Carlson, 1986).
Although best known for his work on the St. Louis model, Keith’s earliest contributions
focused on fiscal and federal budget policy. He studied the “crowding out” effects of budget
deficits; developed a measure of the “high employment budget” (Carlson, 1967); and elaborated on a key result in the Anderson-Jordan equation with St. Louis Fed colleague Roger W.
Spencer (Carlson and Spencer, 1975).
Keith was also known as a great teacher. His Review articles span a variety of topics and
explain difficult material in a manner that is accessible to students of economics and the lay
public alike. A few articles stand out. In 1988, Keith discussed variables that influence the
natural rate of unemployment, a topic that remains highly relevant today for anyone trying
to understand the perils facing a central bank that gauges the stance of policy by comparing
the unemployment rate to the unknown natural rate (Carlson, 1988). A year later, a Review
article on price indexes revisited the role that asset prices should play in a cost of living index
(Carlson, 1989).
Keith was known for his friendly ease, openness, honesty, and sense of humor. He always
had an excellent and timely smile and a one-liner suitable for the moment. He was extremely
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
iii
In Memoriam: Keith M. Carlson
helpful in giving of his time and attention to his colleagues in the support of their data, economic
theories, econometric findings, and policy and institutional history.
Not everyone knew this, but he was also a walking encyclopedia of Major League Baseball,
especially the St. Louis Cardinals. He spent much of his free time studying and honing his
knowledge of the game through statistical analysis. At one point, a request came from the leading authorities in this field to collect obscure data for their compilation of baseball statistics.
Keith methodically went through old issues of the St. Louis Globe-Democrat to assemble hitby-pitch data from the 1890s. He was duly thanked for his contribution and added another,
unexpected accomplishment: Keith reported that his life felt full now that he had shaken
hands with both Milton Friedman and Pete Palmer.1
Keith was born in Mitchell, South Dakota, on July 3, 1934. He received his undergraduate
degree from Gustavus Adolphus College and his M.A. in economics from the University of
Nebraska. After graduation, he moved back to Minnesota to teach at St. Olaf College. In 1963,
he moved to St. Louis to take a position at the Federal Reserve Bank of St. Louis that would
serve as the culmination of his career. He will be missed. n
NOTE
1
Pete Palmer co-authored The Hidden Game of Baseball, which is generally viewed as creating the foundation for
sabermetrics, a tool used to evaluate a player’s ability and featured in the movie “Moneyball.”
REFERENCES
Carlson, Keith M. “Estimates of the High-Employment Budget: 1947-1967,” Federal Reserve Bank of St. Louis Review,
June 1967, pp. 6-14.
Andersen, Leonall C. and Keith M. Carlson, “A Monetarist Model for Economic Stabilization,” Federal Reserve Bank
of St. Louis Review, April 1970, pp. 7-25; https://doi.org/10.20955/r.68.45-66.djw.
Carlson, Keith M. and Roger W. Spencer, “Crowding Out and its Critics,” Federal Reserve Bank of St. Louis Review,
December 1975, pp. 2-17.
Carlson, Keith M. “A Monetarist Model for Economic Stabilization: Review and Update,” Federal Reserve Bank of
St. Louis Review, October 1986, pp. 18-28; https://doi.org/10.20955/r.68.18-28.yls.
Carlson, Keith M. “How much lower can the unemployment rate go?” Federal Reserve Bank of St. Louis Review, July
1988, pp. 44-57; https://doi.org/10.20955/r.70.44-57.fgu.
Carlson, Keith M. “Do Price Indexes Tell us about Inflation? A Review of the Issue,” Federal Reserve Bank of St. Louis
Review, November 1989, pp. 12-30; https://doi.org/10.20955/r.71.12-30.hhd.
iv
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Federal Reserve Bank of St. Louis REVIEW
Gauging Market Responses to
Monetary Policy Communication
Kevin L. Kliesen, Brian Levine, and Christopher J. Waller
The modern model of central bank communication suggests that central bankers prefer to err on
the side of saying too much rather than too little. The reason is that most central bankers believe
that clear and concise communication of monetary policy helps achieve their goals. For the Federal
Reserve, this means to achieve its goals of price stability, maximum employment, and stable longterm interest rates. This article examines the various dimensions of Fed communication with the
public and financial markets and how Fed communication with the public has evolved over time.
We use daily and intraday data to document how Fed communication affects key financial market
variables. We find that Fed communication is associated with changes in prices of financial market
instruments such as Treasury securities and equity prices. However, this effect varies by type of
communication, by type of instrument, and by who is doing the speaking. (JEL E52, E58, E61, G10)
Federal Reserve Bank of St. Louis Review, Second Quarter 2019, 101(2), pp. 69-91.
https://doi.org/10.20955/r.101.69-91
KEYNES: Arising from Professor Gregory’s questions, is it a practice of the Bank of England never to
explain what its policy is?
HARVEY: Well, I think it has been our practice to leave our actions to explain our policy.
KEYNES: Or the reasons for its policy?
HARVEY: It is a dangerous thing to start to give reasons.
KEYNES: Or to defend itself against criticism?
HARVEY: As regards criticism, I am afraid, though the Committee may not all agree, we do not admit
there is a need for defense; to defend ourselves is somewhat akin to a lady starting to defend her virtue.
Exchange between John Maynard Keynes and Bank of England Deputy Governor Sir Ernest Harvey,
December 5, 1929.1
Kevin L. Kliesen is a business economist and research officer, Brian Levine was a senior research associate, and Christopher J. Waller is executive
vice president and director of research at the Federal Reserve Bank of St. Louis.
© 2019, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses,
and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
69
Kliesen, Levine, Waller
INTRODUCTION
Central bank communication has come a long way since the Bank of England’s motto
ostensibly was “Never explain, never apologize.”2 Today, the motto of central bankers might
instead be “Can you hear me now?” The modern model of central bank communication suggests that central bankers prefer to err on the side of saying too much rather than too little. In
this vein, central bank communication takes many forms, from economic forecasts and official
reports, to speeches, interviews, testimonies before governmental bodies, and policy statements
and press conferences immediately after policy meetings. In the United States, enhancements
in central bank communication are most pronounced in the realm of speeches and other
remarks (e.g., television interviews) by Federal Reserve (hereafter, Fed) governors and Reserve
Bank presidents. These forms of communication have become more prominent since the
recession and Financial Crisis. In an era of increased communication by Federal Open Market
Committee (FOMC) participants, one may ask whether additional information is useful for
financial market participants who carefully monitor monetary policy developments. Indeed,
some economists and analysts have argued that Fed officials talk too much.3 There are many
nuances to this argument, but the primary claim is that more information increases the probability of market mispricing. Shin (2017) discusses some of these issues.
There are at least two counterarguments to the market mispricing view. The first, as
enunciated by Kocherlakota (2017), is that the price of an independent central bank is a set
of independent voices to insure against group think. The second counterargument is that the
pricing of financial instruments in markets is more efficient with more, not less, information.
Regardless, central bank communication is important because individuals’ economic decisions
are based on expectations of future policies. Thus, clear communication of its policies and
actions may help the Fed achieve its mandated goals of stable prices, maximum employment,
and moderate long-term interest rates.
The purpose of this article is twofold. The first part examines the various dimensions of
Fed communication with the public and financial markets. This includes documenting how
communication with the public has evolved over time. The second part empirically analyzes
the economic effects of Fed communication on key financial market variables. Our analysis
uses daily and intraday data. We find that Fed communication can affect prices of financial
market instruments such as equities and Treasury securities. However, this effect varies by
type of communication, by type of instrument, and by who is doing the speaking. We also
find that larger financial market reactions tend to be associated with communication from
the Fed Chair, non-Chair Fed governors, and FOMC meetings without an associated press
conference. We further find that financial market reactions following press conferences after
FOMC meeting statements are not significant.
HOW DOES THE FED COMMUNICATE?
As the exchange between John Maynard Keynes and Bank of England Deputy Governor
Sir Ernest Harvey demonstrated, the principles of central bank communication have evolved
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Kliesen, Levine, Waller
Table 1
Types of Fed Communication
Type
Communicator
Frequency
Release timing
Policy statement
FOMC
8 times per year
After each FOMC meeting, ~2 PM EST
Minutes
FOMC
8 times per year
3 weeks after each FOMC meeting, ~2 PM EST
Press conference
Chair
8 times per year*
After designated FOMC meeting, ~2:30 PM EST
Summary of Economic Projections
FOMC
4 times per year
After designated FOMC meeting, ~2 PM EST
Monetary Policy Report to Congress
Chair
2 times per year
~February and July of each year
Speeches and other public remarks
FOMC
Continuous†
NA
Statement of Longer-Run Goals
and Policy Strategy
FOMC
1 time per year
Reaffirmed each January
Policy Normalization Principles
and Plans‡
FOMC
Updated periodically
After associated FOMC meeting, ~2 PM EST
NOTE: Table reflects the present-day FOMC procedure. The timing and frequency of each event has changed over the past 20 years. ~Indicates
times are approximations and may differ slightly from event to event. *During the period analyzed, press conferences were held only four times
per year. Beginning in January 2019, press conferences are held after every FOMC meeting. †Excludes FOMC “blackout periods,” which begin the
second Saturday preceding an FOMC meeting and end the Thursday following the meeting. ‡Initially released in September 2014. An addendum
was adopted in March 2015 and augmented in June 2017. For a history of revisions, see https://www.federalreserve.gov/monetarypolicy/timeline-policy-normalization-principles-and-plans.htm.
over time. A modern comparison describing the evolution of Fed communication was noted in
2003 by then Fed Governor Janet Yellen when she said that the FOMC “had journeyed from
‘never explain’ to a point where sometimes the explanation is the policy.”4 Some have termed
this policy “open-mouth operations.”5 Although views may differ between policymakers and
across central banks, the fundamental principles of central bank communication are founded
on the dual notions that increased transparency enhances the effectiveness of policy and the
accountability of policymakers in a democratic society.6 In this article, we focus on Fed communication, though the principles and practices are similar among many of the world’s central
banks.
When analyzing central bank communication, the following questions come to mind: First,
who should do the talking; second, what should the central bank talk about; and, third, who
should the central bank talk to? There is a vast economic literature that attempts to answer
these questions. One notable early effort was a cross-country study by Blinder et al. (2001), who
surveyed communication methods and tactics, among other things. A subsequent article by
Blinder et al. (2008) argued that there was large variation in strategies but no consensus on the
best-practice approach to communicating monetary policy to the public. Woodford (2001)
was an early proponent of using communication to influence market expectations. This view
influenced several subsequent Fed officials, most notably former Fed Chairman Ben Bernanke.7
Finally, in the aftermath of the Financial Crisis of 2008, several event studies were published
that analyzed the FOMC’s unconventional policy actions on prices of financial market instruments, macroeconomic outcomes, and the expectations about future monetary policy actions.8
Federal Reserve Bank of St. Louis REVIEW
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Kliesen, Levine, Waller
In sum, the academic literature offers more support for the modern view of central bank
communication: More is generally better. Table 1 lists the primary methods that the Fed uses
to communicate its policies, procedures, and policy expectations to the public.9 These methods
include the policy statement released at the end of the eight regularly scheduled FOMC meeting,
the minutes released three weeks after each of the eight regularly scheduled FOMC meetings,
the Chair’s quarterly press conference, along with speeches, testimonies, and media interviews
by Fed governors and Reserve Bank presidents. Some of these innovations are long standing,
such as the FOMC minutes, while others are more recent, such as the Chair’s press conferences.10
Given the prominence of FOMC policy statements as a communication instrument, the following discussion will first briefly focus on their history and role.
Policy Statements: Length and Readability
The Fed’s principle medium of communication is the policy statement released after each
FOMC meeting. The policy statement has evolved over time. From 1967 to 1992, the FOMC
issued a “Record of Policy Actions” (ROPA), which were initially released with a 90-day lag.11
Beginning under Chairman Alan Greenspan, the FOMC began to issue policy statements
immediately after the February 4, 1994, meeting. The first policy statement was rather short,
at 99 words, and made no mention of the intended federal funds target rate. Instead, the
inaugural statement indicated that the Committee decided to “increase slightly the degree of
pressure on reserve positions” in financial markets. In taking this action, the FOMC noted
that they expected an “associated small increase in short-term money market interest rates.”12
Following the release of the inaugural statement, the FOMC released a post-meeting statement four additional times in 1994. Three post-meeting statements were released in 1995,
including the statement released after the July 6, 1995, meeting, which was the first instance
that the FOMC specifically mentioned the federal funds rate. The FOMC continued to issue
post-meeting statements over the next few years, but only at meetings where a policy change
occurred. However, beginning with the May 18, 1999, meeting, statements were released after
each FOMC meeting.13 The public focus on the policy statement was such that the financial
press developed a “briefcase barometer.”14
The post-meeting FOMC statements have evolved over time. Prior to the Financial Crisis,
the post-meeting policy statement mostly focused on the state of the economy and the Com
mittee’s rationale for raising or lowering the policy rate or reasons why the policy rate was not
changed. In general, less was said about the future path of interest rate changes. The policy
statement evolved to take on a larger role in communicating the stance of monetary policy
during the Financial Crisis after the federal funds rate reached the zero lower bound (ZLB)
on December 16, 2008.15 Figure 1 shows that the word count of the policy statements began
to increase steadily in 2007 during the early stages of the Financial Crisis. The word count
continued to increase during the adoption of quantitative easing (QE) policies that both
increased the size of the balance sheet and changed its composition. Prior to the ZLB period,
the number of words in each statement averaged 223. During the ZLB period, the count was
more than twice as much, averaging 580 words.
After the nominal federal funds target rate reached the ZLB in December 2008, the Fed provided the largest amount of monetary accommodation through balance sheet adjustments and
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Kliesen, Levine, Waller
Figure 1
FOMC Statement Word Count
Number of Words in Each Statement
1,000
900
800
700
600
500
400
300
200
100
0
1994
1999
2001
2002
QE1
2004
2006
2008
QE2 MEP QE3
2009
2011
2013
2015
2017
NOTE: Shaded area indicates the period of the FOMC’s unconventional monetary policy with interest rates at the effective ZLB. MEP, Maturity
Extension Program. Under the MEP, the Fed sold or redeemed shorter-term Treasury securities and used the proceeds to buy longer-term
Treasury securities, thereby extending the average maturity of the securities in the Fed’s portfolio. Updated through 2017.
SOURCE: Board of Governors of the Federal Reserve System.
other unconventional policies.16 But as the U.S. economy transitioned from recession to a
slower-than-average recovery, the Fed’s policy approach also changed. The new approach
focused instead on influencing the public’s expectations of the future direction and level of the
federal funds target rate. This approach, in its current form, is referred to as forward guidance.17
For example, following the August 9, 2011, meeting, the policy statement stated the following:
The Committee currently anticipates that economic conditions—including low rates of
resource utilization and a subdued outlook for inflation over the medium run—are likely
to warrant exceptionally low levels for the federal funds rate at least through mid-2013.
In this case, the FOMC’s intent was to signal to the public that its policy rate would remain
low for a long time in order to spur the economy’s recovery. This signal was meant to be taken
as a public commitment, what Campbell et al. (2012) termed “Odyssean” policy. Using language from Greek mythology, Odyssean policy is meant to convey a public commitment not
to change policy for a certain period—in this case, for more than two years. Instead, the public
appeared to view this statement as a forecast, what Campbell et al. (2012) termed “Delphic”
policy. In effect, the Delphic statement strongly suggested that, in the FOMC’s view, the economic weakness would persist for more than two years. However, at the June 2011 meeting
two months earlier, the Summary of Economic Projections (SEP) indicated that real gross
domestic product (GDP) would increase by 3.5 percent in 2012 and by 3.9 percent in 2013
(each measure is the midpoint of the central tendency).18 Thus, by August, the Committee
appeared to have concluded that it, like most private sector forecasters, had been much too
optimistic about the pace of real GDP growth during the early stages of the expansion. Indeed,
by the January 2012 meeting, forecasts for real GDP growth in 2012 and 2013 had been marked
down to 1.7 percent and 2.5 percent, respectively.
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Kliesen, Levine, Waller
Figure 2
FOMC Statement Complexity
Flesch-Kincaid Reading Grade Level
24
QE1
QE2 MEP QE3
22
20
18
16
14
12
10
8
6
1994
1999
2001
2002
2004
2006
2008
2009
2011
2013
2015
2017
NOTE: Shaded area indicates the period of the FOMC’s unconventional monetary policy with interest rates at the effective ZLB. MEP, Maturity
Extension Program. Under the MEP, the Fed sold or redeemed shorter-term Treasury securities and used the proceeds to buy longer-term
Treasury securities, thereby extending the average maturity of the securities in the Fed’s portfolio. Updated through December 2017.
SOURCE: Board of Governors of the Federal Reserve System (FOMC statements) and Educational Testing Service (word count).
To accomplish the Fed’s goals and objectives in a slow-growth economy, the post-meeting
statement changed in two dimensions. The first change, as noted above, was that the length
increased. The statements included more discussion of the economic situation and its implication for the near-term direction of policy (changes in the federal funds target rate).19 Second,
the statements incorporated more complex economic terms and analysis. This is shown in
Figure 2, which uses text evaluation software to measure the Flesch-Kincaid reading grade
level of the policy statement. A higher grade level is assumed to reflect increased complexity
of the statement. Prior to the ZLB period, the median grade level was 13.5, indicating comprehension accessible to someone reading at a college undergraduate level. But by late 2013,
when the FOMC was in the midst of increasing the size of its balance sheet through asset purchases, the grading level rose to 20, which is commensurate to a graduate school reading level.
For the entire ZLB period, the grade level rose to 16 (median), but then fell to 15 (median)
during the post-ZLB period.20 Researchers find that the readability of central bank policy
statements and remarks are an important factor in how they are received by financial markets.
Not surprisingly, clearer statements lead to lower volatility.21
This section has highlighted how the FOMC changed the length and composition of the
policy statement during the period of unconventional monetary policy. But the policy statement is only one form of central bank communication. Speeches and other public remarks
are another form of communication that policymakers have deployed to increase the public’s
knowledge of the prevailing monetary policy regime. The next two sections will delve into
monetary policy communication strategies by Fed officials, both old and new.
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Kliesen, Levine, Waller
Figure 3
Number of Public Remarks by Type of Fed Official
Total Remarks Per Year
250
ZLB Period Begins
(December 2007)
200
Bank Presidents
150
100
Non-Chair Governors
50
0
FOMC Chair
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
NOTE: Through 2017.
SOURCE: Board of Governors of the Federal Reserve System, the 12 Federal Reserve Banks, Bloomberg, and authors’
calculations.
Public Remarks by Fed Officials
Fed officials have long used other forms of public communication besides policy statements.22 Public remarks can take many forms, including formal speeches, Congressional
testimonies, interviews with the financial media, or published articles and commentaries.
Sometimes, Fed officials do not comment on monetary policy issues that may be discussed at
recent or upcoming FOMC meetings. In those instances, policymakers may instead choose
to focus on other issues, such as local economic conditions, economic education, community
development, or banking and financial market regulation.
The ZLB period witnessed an unprecedented rate of spoken and written communication
with the public by Fed governors and Reserve Bank presidents. Figure 3 shows the annual
number of public remarks by the Fed Chair, non-Chair governors, and Reserve Bank presidents since 1998.23 From 1998 to 2004, the total number of public remarks by Reserve Bank
presidents remained roughly constant at about 150 per year. A slightly different pattern
occurred with governors and the Fed Chair. Total remarks over this period steadily fell, but
then rebounded, so that the numbers of public remarks in 2004 were close to the 1998 totals.
Beginning in 2005, the total number of public remarks by Reserve Bank presidents began to
increase, reaching a peak in 2013 of a little more than 220 public remarks. Interestingly, though,
the FOMC Chair and governors delivered public remarks slightly less frequently over the
ZLB period. Some of the reduced frequency of public remarks by members of the Board of
Governors (excluding the Chair) reflects the fact that the Board has rarely operated with a
full complement of Governors (seven). From 1998 to 2017, there has only been four years
when there were seven governors present at the last formal meeting of the year. Indeed, at
the end of 2017, there were only four governors at the December meeting. At the March 2018
meeting, the number of governors had dwindled to three.
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Kliesen, Levine, Waller
Figure 4
Number of Times More Than One Bank President or Governor Spoke on the Same Day, 1998-2017
Frequency
80
70
Bank Presidents
60
60
50
40
30
20
Governors
10
0
3
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
SOURCE: Board of Governors of the Federal Reserve System, Bloomberg, and authors’ calculations.
Speeches have become important communication events. Chairman Greenspan’s new
economy speech in 1995 and his “irrational exuberance” speech in 1996 were among his more
notable speeches. Chairman Ben Bernanke also gave notable speeches during his tenure. Two
that standout are his “Deflation: Making Sure ‘It’ Doesn’t Happen Here” speech in 2002 and
his global saving glut speech in 2005. Days with multiple Fed communication events have
become more numerous over time—particularly since the Financial Crisis. Figure 4 shows
the increase in multiple Fed communication events on the same day stems from an increase
in more than one Reserve Bank president speaking on the same day. For example, in 2017,
there were 60 days when more than one Reserve Bank president spoke. In 2004, it was about
half as much. By contrast, in 2017 there were only three days when more than one Fed
governor spoke publicly on the same day. This is down sharply from 2003, when there were
19 days when multiple Fed governors spoke on the same day.24
In separate analysis, we looked at the annual number of public remarks by Reserve Bank
presidents from January 1998 to December 2017. We separated the sample into roughly two
10-year periods: January 1998 to August 2008 (pre-Financial Crisis) and September 2008 to
December 2017 (post-Financial Crisis). The number of public remarks by Reserve Bank
presidents increased in all but three Fed Districts (Chicago, New York, and Richmond). The
average increase in volume across these nine Districts was 46 percent. We did not examine
whether the nature of the remarks by Reserve Bank presidents has changed over time. We did,
however, analyze the number of speeches and public remarks given by presidents of the Fed
Bank of St. Louis since January 1929. We have documented this in the boxed insert.
Other Forms of Fed Communication
In the past several years, chiefly under the Bernanke regime, the FOMC has adopted
several new forms of communication to further increase transparency. As noted earlier, the
Chair’s quarterly press conference, beginning under Chairman Bernanke’s term in January
76
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Kliesen, Levine, Waller
Volume and Subject Matter Across Time: An Example Using St. Louis Fed Presidents
The table lists the number of speeches (including public remarks) given by presidents of the Federal Reserve Bank of St. Louis
since January 1929. The table also lists the primary subject matter of the speeches under three broad headings: The economic
outlook (which includes monetary policy related topics), banking and finance, and all other subjects. In general, St. Louis Fed
presidents prior to the 1960s tended to give fewer speeches than presidents after the 1960s. Moreover, presidents prior to the
1960s tended to talk more about non-economic outlook topics and proportionately more about banking and finance issues relative to their modern-era counterparts.
Speeches by St. Louis Fed Presidents, 1929 to 2017
Other
% of total
speeches
about
economic
outlook
% of total
speeches
about
banking
and finance
% of total
speeches
about
other
Average
number of
speeches
per year
Start
End
Months
in office
Total
speeches
Economic
outlook
Banking
and
finance
William McChesney
Martin Sr.
Jan-1929
Feb-1941
145
4
0
3
1
0
75
25
0.3
Chester C. Davis
Apr-1941
Feb-1951
118
64
38
11
15
59
17
23
6.5
Delos C. Johns
Feb-1951
Feb-1962
132
25
15
8
2
60
32
8
2.3
Harry A. Shuford
Oct-1962
Jan-1966
39
9
4
5
0
44
56
0
2.8
Darryl R. Francis
Jan-1966
Feb-1976
121
110
94
11
5
85
10
5
10.9
Lawrence K. Roos
Mar-1976
Jan-1983
82
37
33
4
0
89
11
0
5.4
Theodore H. Roberts
Feb-1983
Dec-1984
22
8
6
2
0
75
25
0
4.4
Thomas C. Melzer
Jun-1985
Jan-1998
151
100
82
17
1
82
17
1
7.9
William Poole
Mar-1998
Mar-2008
120
140
133
4
3
95
3
2
14.0
James Bullard
Apr-2008
Dec-2017*
116
179
173
5
1
97
3
1
18.5
President
NOTE: *End date for President Bullard reflects our window for analysis rather than his tenure in office.
SOURCE: Presidents prior to Poole, FRASER®, Federal Reserve Bank of St. Louis. Poole and Bullard, Bloomberg.
As shown in the table, the focus in recent years has shifted toward a greater emphasis on the economic outlook, which includes
macroeconomic conditions and monetary policy developments. Indeed, the economic outlook (and monetary policy related
topics) comprised a very large percentage (more than 95 percent) of the speeches of the most recent two St. Louis Fed presidents—William Poole and James Bullard. Finally, consistent with the findings of Figure 3, the last column of the table shows that
these two St. Louis Fed presidents have given the highest number of speeches per year of all St. Louis Fed presidents.
2012, is one key innovation. Current Chairman Jerome Powell expanded on this innovation,
announcing that press conferences will be held after every FOMC meeting beginning in January
2019. Other innovations include the FOMC’s “Statement of Longer-Run Goals and Monetary
Policy Strategy,” “Policy Normalization Principles and Plans,” and “Summary of Economic
Projections” (SEP). These are also listed in Table 1. The first two are meant to provide clarity
on the Fed’s dual mandate and balance sheet, respectively, while the SEP conveys projections
for four key macroeconomic variables. In addition, the SEP conveys each FOMC participant’s
assessment of appropriate monetary policy, as indicated by their federal funds rate projections
over short-, medium-, and longer-term horizons.
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Grading Fed Communication
The Hutchins Center on Fiscal and Monetary Policy at Brookings conducted a survey of
academics and private sector Fed watchers to assess the effectiveness of different forms of
Fed communication.25 Survey participants viewed the FOMC policy statement, speeches by
the FOMC Chair, and quarterly press conferences as the most useful forms of Fed communication. On net, academics generally found these forms of communication more useful than
did the private sector economists and Fed watchers.
One of the key communication innovations during the Bernanke tenure was the public
release of individual FOMC participants’ expectations of the future level of the federal funds
rate. Once a quarter, with the release of the SEP, each FOMC participant—anonymously—
indicates their preference for the level of the federal funds rate at the end of the current year,
at the end of the next two to three years, and over the “longer run.” According to the survey,
these projections are often termed the FOMC “dot plots.” Both academics and those in the
private sector found the dot plots of limited use as an instrument of Fed communication
(more “useless” than “useful”). One-third of the respondents found the dot plots “useful or
extremely useful,” 29 percent found them “somewhat useful,” and 38 percent found them
“useless or not very useful.”
The limited usefulness of the dot plots probably reflects many factors. First, each participant’s projection is conditioned on the highly restrictive assumption of “appropriate monetary
policy.” Each participant’s appropriate monetary policy stance is conditioned on their view
of the outlook for real GDP growth, inflation, and the unemployment rate over the medium
term. Moreover, the range of participants’ views may not dovetail with the policy path outlined in the FOMC statement, which can further complicate the communicated outlook and
diminish the tool’s effectiveness. The regular presence of dissents suggests that appropriate
policy can differ sharply across the Committee.
Second, the participants may have other vastly different assumptions that influence their
outlook, such as the equilibrium real interest rate, the future path of crude oil prices, the foreign exchange value of the dollar, or their outlook for foreign economic growth. For these
reasons and more, FOMC participants persistently over-projected the federal funds target
rate path during the early years of the current expansion. [See earlier discussion on page 73.]
These persistent one-sided forecast errors may have impaired the credibility of the dot plots to
the extent that the projections were important inputs in establishing expectations about future
monetary policy.
Finally, the Brookings study revealed that survey participants believe that Reserve Bank
presidents’ speeches are slightly less useful than the dot plots, but still more useful than Fed
reports to Congress, such as the semi-annual Monetary Policy Report.26 This finding is perhaps striking given that the number of public remarks by Reserve Bank presidents has been
trending up over time, especially during the ZLB period, while the number of public remarks
by the Chair and non-Chair governors has been trending down.
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EMPIRICAL ANALYSIS
The final section of the article assesses how financial market participants respond to various forms of Fed communication. Admittedly, this is a difficult empirical exercise for many
reasons. First, public remarks by Fed senior officials are often context- and perspectivedependent. Each individual brings their own perspective, model of the economy, and view of
the monetary policy transmission mechanism. These views naturally inform their assessments
of appropriate monetary policy going forward, which are then conveyed in public remarks.
For their part, financial market participants may become familiar with a given policymaker’s
view or assume a given outcome for a particular FOMC meeting. If so, markets may react only
to views that are sufficiently different from expectations. Past research has demonstrated that
monetary policy surprises can have significant effects on high-frequency asset prices.27 We
acknowledge the importance of monetary policy surprises, but use a different approach to
assess the significance of Fed communication events.
Second, when attempting to gauge the significance of public remarks, markets do not
usually assign equal weights to all FOMC participants. Certainly, markets carefully parse
remarks by the Chair, who is typically viewed as the public voice of the FOMC and the one
who sets the policy agenda. Moreover, while the Chair’s views often convey the consensus view
of the Committee, the Chair nonetheless also has a policy preference. Although the Chair’s
preference invariably prevails, dissents still occur periodically. Indeed, Reserve Bank presidents
sometimes use their public remarks, or dissents, with the intention of signaling future policy
preferences or advocating for alternative frameworks.28 Still, markets may discount the views
of the presidents, on average, because they believe their views unnecessarily distort market
signals or future policy intentions. For example, Lustenberger and Rossi (2017) claim that
remarks by Reserve Bank presidents worsen the accuracy of private sector forecasts.
With these caveats in mind, we adopt a two-pronged empirical exercise. The first exercise
uses daily data to examine whether Fed communication events are associated with significant
movements in key financial market variables. Admittedly, this approach has some drawbacks.
First, daily financial market data tend to be more volatile compared with monthly or quarterly
data. Second, this volatility arises, in part, because financial markets trade on many types of
information, such as macroeconomic data or global financial or geopolitical developments.
Thus, while Fed communication comprises one set of information the market uses to price
assets, there are potentially many other sources of information that the market uses that we
can’t readily account for. Our intent is to assess market reactions to Fed communication
events and not to model changes in asset price movements at a high frequency.
The second empirical exercise uses intraday data at 5-minute frequencies. Using intraday data allows us to more closely match the timing of Fed communication events with the
responses in financial markets. This is the approach adopted by most of the aforementioned
event studies. Our intent is to determine if the empirical results using the daily data are consistent with those from the intraday data. Before presenting the results, we provide a detailed
description of our data sources and approach.
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Data Sources and Approach
We study the effects of seven types of Fed communication events: FOMC meeting statements;29 FOMC minutes; Fed Chair press conferences; public remarks by the Fed Chair,
non-Chair Fed governors, and Reserve Bank presidents; and unconventional monetary policy
announcements.30 Five of the seven categories are included in the Brookings study. It is
important to note that there is an overlap between FOMC meetings and six of the seven
unconventional policy announcements we include.31 Initially, our data set included public
remarks made after market hours and on weekends. Consistent with some of the literature,
we initially moved an after-hours communication event to the following trading day to gauge
the market’s reaction to the remark. However, this approach ended up producing large reactions that were probably not tied to the public remark itself. For example, many key data
releases are often issued before the market opens.32 In this case, it is difficult to determine
whether the market is responding to the public remarks by a Fed official or to economic data
releases that may be a surprise.33
Empirical Analysis: Daily Data
We create a series of dummy variables for the Fed communication events. Because the
Brookings study found that survey participants viewed the Fed Chair press conferences as a
useful form of communication, we identify regularly scheduled FOMC meetings with and
without an associated press conference. In recent years, FOMC press conferences have
occurred after the March, June, September, and December meetings. Since the liftoff from
the ZLB at the December 2015 meeting, increases in the FOMC’s federal funds target rate
have occurred at meetings with an associated press conference by the Fed Chair. Our sample
period is January 6, 1998, to December 29, 2017. There are nine types of communication
events:
•
•
•
•
•
•
•
•
•
Non-press conference FOMC meeting statements
Press conference FOMC meeting statements
Releases of FOMC minutes
Remarks by the FOMC Chair
Remarks by all other Fed governors
Remarks by Reserve Bank presidents
Days when there are multiple Fed communication events (e.g., speeches)
Unconventional policy actions (e.g., large-scale asset purchases)
Key macroeconomic data releases (e.g., industrial production)
We evaluate the market reaction for three financial instruments: the absolute value of
the daily change in the yield on 2-year Treasury notes, the yield on 10-year Treasury notes,
and the Chicago Board Options Exchange equity market volatility index (VIX). Changes in
2-year Treasury yields are widely viewed as being sensitive to expected changes in FOMC
policy. The 10-year Treasury yield is the most liquid, long-term, risk-free interest rate in the
financial markets. It is also sensitive to changes in inflation expectations and longer-term
expectations about short-term interest rates. Finally, the VIX, which is often termed the mar80
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ket’s “fear gauge,” is sometimes viewed as signaling changes in economic uncertainty. This
exercise can be represented by the following equation:
ΔYi ,t = α + β1ΔYi ,t−1 + β 2 NPCi ,t + β3 PCi ,t + β 4 MIN i ,t + β5CHAIRi ,t + β6GOVi ,t
+ β7 PRESi ,t + β8 MULTi ,t + β9UNCONVi ,t + β10 MACROi ,t ,
where ∆Yi,t represents the absolute value of the daily change in financial variable i (either the
2-year Treasury yield, 10-year Treasury yield, or VIX) on day t. The independent variables
include a constant, a one-day lag of the dependent variable, and a series of dummy variables
(specified earlier in this section) that take the value of 1 if that event occurs on day t or are
zero if the event does not occur on day t.
We analyze daily data with three ordinary least-squares regressions. We use the absolute
value of the daily changes because some communication events will cause yields to increase
or decrease, while others will generate no market response. Using absolute values are a more
effective way to gauge the effects of communication events on financial market activity.34 We
also include another dummy variable (MACRO) on days when key economic statistics are
released. The motivation for this is that the market trades on information contained in these
reports. Our economic statistic dummy variable takes the value of 1 when the following
monthly economic reports are released (and is zero on all other days): the consumer price
index, monthly employment situation, industrial production, retail sales, the Institute for
Supply Management Report on Manufacturing, and the three GDP releases (advance, second,
and third estimates).
Table 2 shows the results of our analysis using daily data. Daily data allow us to make a
few noteworthy observations. First, for the change in the 2-year Treasury yield, markets react
significantly (at the 1 or 5 percent level) to Fed Chair and Fed governor communication events
and also to FOMC statements at non-press conference meetings. Table 2 further indicates that
changes in 2-year Treasury securities do not react significantly on days when one Reserve
Bank president speaks, but they do react significantly on days when there are multiple Fed
speakers. (Recall from Figure 4 that the number of days with multiple Fed speakers has increased
since the Financial Crisis). Finally, 2-year yields also react significantly to macroeconomic
data releases. Unconventional policy actions are marginally significant (at the 8 percent level).
With the exception of days with multiple Fed speakers, the signs of the coefficients on the
significant variables are positive.
The second and third sets of regressions in Table 2 show results for the change in the
10-year Treasury yield and in the VIX. Traders of longer-term Treasury securities react broadly
similarly to Fed communication events and data releases as traders of 2-year Treasury securities. For instance, 10-year yields react significantly to the Fed Chair’s remarks, on days when
there are multiple Fed speakers, and to macroeconomic data releases; the coefficients generally
have the same signs and magnitudes as those from the regression using 2-year yields. However,
there are some differences between the 2-year and 10-year responses. For example, the change
in the 10-year yield is significantly associated with unconventional policy actions. Moreover,
10-year yields do not react significantly to remarks by Fed governors or to non-press conference FOMC statements.
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Table 2
Federal Reserve Communication Events and Financial Market Responses Using Daily Data
Dependent variables
Independent variables
2-year Treasury
10-year Treasury
VIX
Constant
0.023
(0.000)**
0.035
(0.000)**
0.641
(0.000)**
Lagged dependent variable
0.248
(0.000)**
0.132
(0.000)**
0.321
(0.000)**
Non-press conference FOMC meetings
0.013
(0.001)**
0.006
(0.187)
0.059
(0.588)
Press conference FOMC meetings
0.004
(0.594)
0.001
(0.880)
0.092
(0.626)
FOMC minutes
0.004
(0.154)
0.004
(0.309)
–0.078
(0.315)
FOMC Chair remarks
0.006
(0.001)**
0.005
(0.012)*
0.018
(0.787)
Fed governor remarks
0.004
(0.003)**
0.001
(0.347)
0.020
(0.645)
Fed president remarks
0.000
(0.775)
0.000
(0.877)
0.093
(0.111)
Multiple Fed speakers
–0.004
(0.032)*
–0.004
(0.018)*
–0.068
(0.265)
Unconventional policy actions
0.036
(0.080)
0.044
(0.021)*
0.626
(0.176)
Macroeconomic data releases
0.009
(0.000)**
0.009
(0.000)**
0.077
(0.031)*
Adjusted R-squared
0.089
0.040
0.109
Durbin-Watson statistic
2.107
2.043
2.264
NOTE: p-values listed in parentheses. The sample period is January 6, 1998 to December 29, 2017.
* and ** indicate significance at the 5 percent and 1 percent levels, respectively. Dependent variables are
expressed as the absolute value of their one-day changes.
Column 3 presents the results for the change in the VIX. Equity market volatility does
not react significantly to Fed communication events. The closest variable of significance
(p = 0.11) are remarks by Reserve Bank presidents. Equity market volatility does, however,
react significantly to macroeconomic data releases. Finally, in all three regressions, the constant and the lagged dependent variable are significant at the 1 percent level.
Figure 5 provides some visual evidence for the behavior of equity market volatility around
FOMC meetings: From January 1994 to December 2017, the VIX begins to rise about a week
before an FOMC meeting. The VIX then drops relatively sharply (nearly 3 percent) on the
day the FOMC statement is released. This finding suggests that equity markets appear to be
increasingly uncertain about the meeting outcome, or its effects on financial markets, in the
run-up to FOMC meetings.35 Likewise, we see a noticeable reduction in market volatility
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Kliesen, Levine, Waller
Figure 5
Relative Changes in the VIX Near FOMC Announcement Days
VIX = 100 on FOMC Announcement Day
104
103
102
101
100
99
98
97
Mean drop in VIX on day of FOMC
Statement release: 2.8%
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1 FOMC 1
2
3
4
5
6
7
8
9
10
NOTE: Sample includes all regularly scheduled FOMC meetings between January 1994 and December 2017.
SOURCE: Haver Analytics and authors’ calculations.
after the policy announcement (statement), perhaps indicating a decline in uncertainty and
clearer understanding of the Fed’s reaction function. Finally, other than the lagged dependent
variable, the dummy variable that accounts for the release of key economic reports is the only
other independent variable that is statistically significant.
We now turn to the second approach of our empirical exercise, namely, examining the
effects of communication events on financial market outcomes using intraday data.
Empirical Analysis: Intraday Data
We use intraday data to estimate the effects of Fed communication on key financial market
variables. Many researchers have used intraday data to gauge market reactions to monetary
policy surprises or to the Fed’s announcements of unconventional polices after the Financial
Crisis. These event studies, as they are often called, are intended to measure the financial
market’s response to news at intervals measured in minutes. Our analysis of the market’s
response to Fed communication events generally follows the form and practice of the event
study literature.
Event studies can be criticized for many reasons. First, the studies gauge only the initial
announcement responses rather than the responses across time. Second, the results can be
sensitive to the choice of window size—that is, responses evaluated over a 1-minute window
versus a 5- or 10-minute window. Third, responses could be affected by non-announcement
effects, such as from economic data releases or geopolitical events. In view of these concerns,
we tested several different window sizes for robustness and used minute-by-minute asset price
data for the S&P 500 stock prices and 10-year Treasury futures prices.36 For FOMC meeting
statements, FOMC minutes, and unconventional policy announcements (non-speaker events),
a window of plus or minus 15 minutes is used. For FOMC press conferences and other public
remarks (speaker events), a window of 15 minutes before to 60 minutes after the event is used.
We do not find that the interpretation of the results meaningfully changes when the event
window is adjusted.37
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Since these two variables are both prices, we calculate the percent change in each series
over each event window.38 We then summarize this information via two metrics: mean
absolute change and cumulative change. For non-speaker events, where the event window is
+/–15 minutes, the mean absolute change can be represented as
j
MACNon-Speaker
=
j
1 N ⎛ Yi ,t+15 ⎞
−1⎟ * 100 ,
∑
j
N i=1 ⎜⎝ Yi ,t−15
⎠
where Yi,tj represents, for each non-speaker event category j, the asset price associated with
observation i at time t, and N represents the total number of observations for each nonspeaker event category j over the sample.
Likewise, for speaker events, where the event window is –15/+60 minutes, the mean
absolute change can be represented as
j
MACSpeaker
=
j
1 N ⎛ Yi ,t+60 ⎞
−1⎟ * 100 ,
∑
j
N i=1 ⎜⎝ Yi ,t−15
⎠
using the same notation as before.
The cumulative change is calculated similarly, but we are now summing (instead of
averaging) over our sample, and we are not taking the absolute value beforehand. We represent
this as
and
N ⎡⎛ Y j
⎤
⎞
j
CCNon-Speaker
= ∑ ⎢⎜ i ,t+15
−1⎟ * 100 ⎥
j
i=1 ⎢
⎥⎦
⎣⎝ Yi ,t−15 ⎠
N ⎡⎛ Y j
⎤
⎞
j
CCSpeaker
= ∑ ⎢⎜ i ,t+60
−1
*
100
⎥
j
⎟
i=1 ⎢
⎥⎦
⎣⎝ Yi ,t−15 ⎠
for non-speaker and speaker events, respectively, again using the same notation as before.
The results are shown in Figure 6A, Figure 6B, and Figure 7. The grouping on the left
side of Figure 6A shows the mean absolute changes in the S&P 500 index in response to Fed
communication events not associated with an individual Fed official (non-speaker events),
while the grouping on the right side of Figure 6A shows those is response to events with public
remarks by a Fed official (speaker events).39 On the left side, we find that stock prices react
most strongly to unconventional policy actions—indeed, twice as strong as the next-largest
event (FOMC meeting statements). This finding appears consistent with the event study literature cited earlier. On the right side, stock prices react the most to the Chairs’ press conferences
and their remarks. In contrast, stock price changes in response to Fed communication events
by Reserve Bank presidents and Governors are similar in magnitude.
Figure 6B shows the same calculation for 10-year Treasury bond futures prices. The results
in Figure 6B are broadly similar to those in Figure 6A. In particular, responses to unconventional policies are substantially larger than to other forms of Fed communication, such as
FOMC meeting statements. As with stock prices, bond markets appear to react more strongly
84
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Kliesen, Levine, Waller
Figure 6A
Mean Absolute Changes in S&P 500 Index
Percent
0.70
0.7
Non-Speakers
0.6
Speakers
0.5
0.4
0.35
0.35
0.3
0.21
0.2
0.33
0.28
0.26
0.25
0.16
0.1
#2
ts
ts
en
en
id
Ev
es
n-
Pr
ai
Go
rR
ve
em
rn
ar
or
s
ks
es
No
Ch
sC
es
Pr
Un
No
co
n-
on
Ev
fe
en
re
ts
nc
#1
es
ut
in
tin
gs
ee
M
nv
M
en
tio
na
l
0.0
NOTE: Underlying data are expressed as a percent change in the S&P 500 index over an event window of –15/+15
minutes (non-speaker events) or of –15/+60 minutes (speaker events). The absolute values of these percent changes
are then averaged, for each event category, over the full sample. Non-event days are days with no Fed communication
event. Non-speaker events and speaker events have different non-event day controls because they are associated with
different window sizes.
Figure 6B
Mean Absolute Changes in 10-Year Treasury Futures Prices
Percent
0.7
0.68
Non-Speakers
0.6
Speakers
0.5
0.4
0.3
0.22
0.2
0.18
0.09
0.1
0.14
0.12
0.05
0.10
0.08
Ev
en
t
n-
es
id
Pr
s#
2
ts
s
or
ve
rn
Go
en
No
Ch
ai
rR
em
ar
ks
es
on
sC
es
Pr
No
n-
Ev
e
nt
fe
re
nc
s#
1
es
ut
in
M
ee
t
M
Un
co
nv
en
tio
na
in
gs
l
0.0
NOTE: Underlying data are expressed as a percent change in 10-year Treasury futures price over an event window of
–15/+15 minutes (non-speaker events) or of –15/+60 minutes (speaker events). The absolute values of these percent
changes are then averaged, for each event category, over the full sample. Non-event days are days with no Fed communication event. Non-speaker events and speaker events have different non-event day controls because they are
associated with different window sizes.
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Kliesen, Levine, Waller
Figure 7
Cumulative Changes for Fed Communication Events
Percentage Points
4.0
S&P 500
10-Year Treasury Futures
2.0
3.19
1.32
1.32
0.0
–0.54
–2.0
3.39
1.76
–0.07
–1.38
Meetings
Minutes
Press Conferences
Unconventional
NOTE: Underlying data are expressed as a percent change in the index (S&P 500) or price (10-year Treasury futures) over
the event window. These percent changes are then summed, by category, over the full sample. For FOMC meetings,
minutes, and unconventional policy measures, the window is –/+15 minutes. For press conferences, the window is
–15/+60 minutes. For illustrative purposes, other public remarks were removed from the figure because of very high
cumulative change values.
to meeting statements than the release of FOMC minutes. The right side of Figure 6B shows
that the bond market’s responses to the Chair’s press conferences and the Chair’s remarks
are appreciably larger than to non-Chair Fed governors and Reserve Bank presidents.
Figure 7 plots the cumulative changes for FOMC meeting statements, minutes, press
conferences, and unconventional monetary policy announcements. We exclude other events
for illustrative purposes, as they exhibit very high cumulative change values. Similar to the
findings in Figures 6A and 6B, unconventional policies are associated with large stock and
bond market responses during our sample. The cumulative change in stock prices associated
with FOMC press conferences is also relatively large and positive. However, for FOMC meeting
statements and the release of FOMC minutes, the cumulative response of stock prices is negative, with the response of the latter more than double the former. The response of bond futures
prices to FOMC meeting statements is of the same magnitude as the minutes, but, again, far
smaller than to unconventional policies. For Chair press conferences, the near-zero cumulative change is not a function of the bond futures market ignoring this information; rather, it
is the result of large, positive price reactions negating large, negative price reactions over the
sample. In summary, the empirical analysis presented in this article suggests that stock and
bond markets respond to a variety of Fed communication events, especially FOMC meeting
statements, FOMC press conferences, and remarks by the Fed Chair.
CONCLUSION
Clear and concise communication of monetary policy helps the Fed achieve its congressionally mandated goals of price stability, maximum employment, and stable long-term
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interest rates. It does so by helping to reduce uncertainty about the future direction of policy.
This helps to reduce distortions in market pricing, thereby improving the efficient allocation
of resources by firms, households, and governments. This article has examined the various
dimensions of Fed communication with the public and financial markets. This includes documenting how the Fed’s communication with the public has evolved over time. Using both
daily and intraday data, our empirical analysis documents how Fed communication affects
key financial market variables. We find that Fed communication is associated with changes
in prices of financial market instruments such as Treasury securities and equity prices. How
ever, this effect varies by type of communication, by type of instrument, and by who is doing
the speaking. Perhaps not surprisingly, we find that the largest financial market reactions tend
to be associated with communication by Fed Chairs rather than by other Fed governors and
Reserve Bank presidents and with FOMC meeting statements rather than FOMC minutes. n
NOTES
1
The occasion was a hearing of the Committee on Finance and Industry. According to Ahamed (2009), this was a
select committee to investigate the British banking system in the aftermath of the 1929 collapse in stock prices
and the poor performance of the British economy. See Ahamed (2009, pp. 371-72).
2
Ahamed (2009, p. 371).
3
For example, see Cochrane (2017), Cogan and Shultz (2017), and Derby (2017).
4
From a 2003 speech by Governor Yellen, as quoted in Holmes (2013). Holmes argues that central bankers, both in
the United States and elsewhere, have increasingly (even before the Financial Crisis) moved away from traditional
instruments, such as interest rates or exchange rates, toward “communicative experiments” designed to influence
public sentiments and expectations.
5
For an early discussion of this phenomenon applied to the Reserve Bank of New Zealand and the FOMC, see
Guthrie and Wright (2000) and Thornton (2004), respectively.
6
See Blinder et al. (2001).
7
See Bernanke, Reinhart, and Sack (2004). A synthesis of Bernanke’s views was presented in a 2013 speech,
“Communication and Monetary Policy.”
8
See, for example, Neely (2015) or Bauer and Rudebusch (2014).
9
We define the public as anyone who uses expectations about future monetary policy actions as an input into
their decisionmaking process.
10 Current Chairman Jerome Powell expanded on this innovation, announcing that press conferences will be held
after every FOMC meeting beginning in January 2019.
11 For example, the ROPA for the January 15, 1970, meeting was released on April 15, 1970, a three-month lag. The
FOMC ceased publication of the ROPA after the December 22, 1992, meeting. Beginning in 1993, the ROPA was
effectively folded into the FOMC minutes and released with a much shorter lag. For more historical detail, see
https://www.federalreserve.gov/monetarypolicy/fomc_historical.htm.
12 This statement, and subsequent policy statements, can be found on the Board of Governors of the Federal Reserve
System website: https://www.federalreserve.gov/monetarypolicy/fomc_historical_year.htm.
13 Wynne (2013) provides a short history of the FOMC’s communication practices.
14 See Gavin and Mandal (2000).
15 The ZLB is the period when the target range for the intended federal funds rate was 0 percent to 0.25 percent.
The ZLB period ended at the December 2015 FOMC meeting.
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16 The monetary easing commenced in August 2007, when the Board of Governors voted to reduce the discount
rate by 50 basis points. See https://www.stlouisfed.org/financial-crisis/full-timeline.
17 Wynne (2013) documented that the Fed used forward-looking language to shape expectations before the Financial
Crisis. For example, in 2003, the FOMC noted that “policy accommodation can be maintained for a considerable
period” in its post-meeting statement. Most economists and policymakers, though, would probably agree that
the use was most pronounced during the ZLB era. The FOMC’s forward guidance policy was influenced importantly
by Woodford (2001) and Eggertsson and Woodford (2003).
18 The midpoint of the central tendency excludes the three highest and three lowest projections for each variable in
each year.
19 Moreover, following the November 3, 2010, meeting, the policy statements crafted under the leadership of Chair
man Bernanke began to emphasize the economy’s current performance and expected outcome relative to the
Fed’s “statutory mandate” of price stability and maximum employment. This was a departure from the Greenspan
era, when the statement rarely—if ever—mentioned the Fed’s statutory mandate. The November 2010 statement
was also noteworthy because it announced the second round of the large-scale asset purchase program (QE2).
20 The average Flesch-Kincaid scores during this period were very close to the reported medians.
21 See also Jansen (2011). Others have found similar findings for other major central bank communications. See
Coenen at al. (2017), Haldane (2017), and Ehrmann and Talmi (2017).
22 Meltzer (2009) documents a 1962 FOMC meeting where communication with the public was discussed. Then-
Chairman Martin favored increased communication with the public as a way to counter academic critics of Fed
policy who he believed were mistaken in their analysis. However, Martin opposed regular (quarterly) policy reviews
because there were instances where the FOMC would not wish to explain its decision. See discussion on p. 337 of
Meltzer (2009).
23 The source of this repository is Bloomberg. More detail on this source, and its limitations, is provided in the
empirical analysis section.
24 As noted above, the declining number of Fed governors speaking on the same day reflects to some extent the
dwindling number of years when there was full complement of governors (seven) serving on the FOMC.
25 See Olson and Wessel (2016).
26 See https://www.federalreserve.gov/monetarypolicy/mpr_default.htm.
27 See Fawley and Neely (2014).
28 See Bullard (2016), Evans (2017), and Kashkari (2017).
29 Conference calls and unscheduled FOMC meetings were excluded from the analysis.
30 For simplicity, we only focus on announcements directly related to a large-scale asset purchase program. These
include the following: QE1 announcement and expansion, QE2 announcement, Maturity Extension Program
announcement and expansion, and QE3 announcement and expansion.
31 The initial QE1 announcement, which was made on November 25, 2008, did not coincide with an FOMC meeting.
32 For example, the release of nonfarm payroll employment, CPI inflation, and GDP (advance, second, and third esti-
mates) all occur before or at the market open.
33 As previously mentioned, our database for public remarks comes from Bloomberg; it begins in 1998. For consis-
tency, we start all Fed communication event categories at this date, where applicable. Only public remarks made
during market hours are included in the event study. If Bloomberg did not provide a time for an event, and this
time could not be identified by other sources, the event was removed from the sample. We considered merging
Bloomberg’s repository with other databases, but since there was not a consistent time horizon or speaker overlap,
we did not proceed with this approach. In particular, we examined databases from the Board of Governors of the
Federal Reserve System and the Federal Reserve Bank of St. Louis’s “FOMC Speak.” The Board’s database does not
include public remarks made by Bank presidents, while “FOMC Speak” only begins in 2010. Merging either database with Bloomberg’s would result in an upward estimate of governors’ remarks (for the former scenario) or an
upward estimate of remarks over the 2010-17 period (for the latter scenario), which would also affect Figure 3.
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Nevertheless, we acknowledge that the Bloomberg database is only a proxy for public remarks when presenting
this analysis.
34 Our dependent variable is very similar to the approach used by Andersson (2010), who used intraday data to
analyze financial market responses to Federal Reserve and European Central Bank monetary policy decisions.
35 Andersson (2010) studied intraday volatility in the bond futures market and in the equity market (S&P 500 index)
around FOMC statement releases from April 1999 to May 2006. He found that intraday volatility rises sharply at
the time of the release of FOMC meeting statements.
36 TickWrite is the source for the intraday data used in this analysis.
37 The one exception is for press conferences, where expanding our event window noticeably increased the market
reaction relative to other events. One possible explanation is that press conferences are often more than an hour
long. However, a closer inspection reveals that the press conferences driving this jump in magnitude are those on
June 22, 2011, and June 19, 2013. The latter was noteworthy because this is when Chairman Bernanke discussed
the so-called taper tantrum that had developed in the markets in response to his Congressional testimony a month
earlier. In that testimony, he raised the possibility of the FOMC beginning to taper asset purchases later that year.
38 It is not our intent to examine whether stock and bond prices may react differently to Fed communication events.
We refer the reader to numerous studies on the effects of these dynamics in the interactions with monetary policy
actions. For example, see Campbell and Ammer (1993), Bernanke and Kuttner (2005), Andersen et al. (2007), and
Connolly, Stivers, and Sun (2005).
39 The non-event day controls in Figures 6A and 6B are constructed to have similar response windows to the events
they are compared with. For example, in Figure 6A, we use a rolling event window of 30 and 75 minutes to calculate a benchmark for non-speakers and speakers, respectively. Windows that either include an event or overlap
days are removed before calculating the benchmark mean absolute changes. We follow the same procedure for
Figure 6B.The authors thank Chris Neely for helpful comments in this regard.
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International Trade Openness and Monetary Policy:
Evidence from Cross-Country Data
Fernando Leibovici
This article studies the extent to which open economies conduct monetary policy differently from
economies that are relatively closed to international trade. I first estimate country-specific Taylor
rules for 26 economies, following the approach of Clarida, Galí, and Gertler (1998 and 2000). Then,
I examine the extent to which open economies assign systematically different weights to changes in
economic outcomes, such as inflation and the output gap, than their closed economy counterparts
do. I find that open economies respond less strongly to changes in expected inflation than relatively
closed economies do and that the response to changes in the output gap is independent of the degree
of trade openness. Moreover, I find that this difference between closed and open economies may be
accounted for by the higher weight open economies give to changes in the real exchange rate, whereby
these economies are more likely to decrease the nominal interest rate when the real exchange rate is
relatively appreciated. (JEL E5, F1, F41)
Federal Reserve Bank of St. Louis Review, Second Quarter 2019, 101(2), pp. 93-113.
https://doi.org/10.20955/r.101.93-113
1 INTRODUCTION
Open economies are typically exposed to different sources of shocks than economies relatively closed to international trade1: To the extent that a country trades goods with the rest
of the world, economic conditions in its trade partners and changes in international relative
prices may affect domestic economic activity. Insofar as central banks design monetary policy
to moderate business cycle fluctuations, the different nature of business cycles in open economies has led many to ask, to what extent should central banks in open economies conduct
monetary policy differently from their closed-economy counterparts?
In a recent study, Leibovici and Santacreu (2015) find that openness should indeed be an
important consideration for the design of monetary policy. In particular, we show that international trade fluctuations play a key role in accounting for the optimal monetary policy that
central banks in open economies should conduct. This finding suggests that trade openness
should be a key factor in optimal monetary policy design.
Fernando Leibovici is an economist at the Federal Reserve Bank of St. Louis. The author thanks Jonas Crews for excellent research assistance and
Ana Maria Santacreu for helpful discussions.
© 2019, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses,
and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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Leibovici
More generally, while theoretical studies have also largely concluded that open economies
should indeed conduct monetary policy differently, studies differ in their policy recommendations. On the one hand, Clarida, Galí, and Gertler (2002) and Corsetti, Dedola, and Leduc
(2010) show that in a specific class of economic models the design of monetary policy in open
economies is “isomorphic” to the conduct of monetary policy in a closed economy: Central
banks should only respond to changes in inflation and the output gap, but they may respond
differently to these depending on the degree of trade openness. On the other hand, morerecent studies have shown that this need not necessarily be the case in more realistic environments (Faia and Monacelli, 2008, De Paoli, 2009, and Lombardo and Ravenna, 2014) in which
central banks in open economies may also want to respond to changes in other variables such
as the real exchange rate.
Yet, while much work has been devoted to understanding the normative question about
whether and how central banks in open economies should design monetary policy differently
from their closed-economy counterparts, much less is known about the positive question on
whether they do indeed conduct policy differently. Therefore, in this article I ask, to what
extent do central banks of open economies conduct monetary policy differently from those
of closed economies?
The answer to this question has important implications. To the extent that the relationship
between trade openness and monetary policy observed in the data differs from the relationship implied by the optimal policy analysis of structural economic models, this may suggest
that some countries are indeed conducting monetary policy suboptimally. Alternatively, to
the extent that central banks of open economies conduct monetary policy differently from
that implied by standard models, this may reflect economic channels or concerns of policymakers that may not be explicitly considered in the economic models, but which may yet be
important for understanding the link between trade openness and monetary policy.
The goal of this article is, thus, to investigate the empirical relationship between trade
openness and the design of monetary policy using cross-country time-series data for the
period 1980 to 2006. In the first step of the analysis, I compute empirical measures that allow
me to characterize and compare the nature of monetary policy across different countries over
this period. Then, I use these empirical measures to examine whether open economies conduct monetary policy differently from closed economies.
My starting point to characterizing the nature of monetary policy across countries is the
standard Taylor rule (1993), which specifies a link among nominal interest rates, inflation,
and the output gap. While an increasing number of countries use the nominal interest rate as
their preferred instrument for the conduct of monetary policy combined with some sort of
inflation and/or output-related targets, the approach I take here is more broad. In particular,
in this article I do not interpret the Taylor rule coefficients as structural parameters that govern
the response of interest rates to changes in inflation and output but, instead, use the Taylor
rule as a device to summarize the statistical properties of how interest rates, inflation, and
output behave in the time series across countries regardless of the particular underlying monetary policy instruments, outcome-targeting regimes, or exchange rate regimes in place in
each country.
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Leibovici
The goal of this approach is to characterize monetary policy across countries through a
common lens in order to facilitate cross-country comparability. This advantage comes at the
cost of forcing the analysis to abstract from differences in monetary policy across countries
not captured by differences in the empirical Taylor rule coefficients.
Thus, I first estimate country-specific Taylor rules for 26 countries with differing degrees
of openness to international trade (as measured by the ratio of aggregate exports to gross
domestic product [GDP]) using time-series data on interest rates, inflation, and output. I follow the generalized method of moments (GMM) approach of Clarida, Galí, and Gertler (1998
and 2000), which allows me to obtain estimates of the explicit or implicit response of interest
rates to changes in inflation and the output gap. Then, I examine whether the statistical relationship among interest rates, inflation, and output differs systematically based on the degree
of trade openness.
I begin the analysis by considering a baseline specification of the Taylor rule, which specifies the relationship among nominal interest rates, expected inflation, and the current output
gap. In addition, I include lagged nominal interest rates, following a large literature that has
observed that central banks adjust interest rates gradually over time. I find considerable dispersion across countries in the empirical relationship between nominal interest rates and
expected inflation, as well as between nominal interest rates and the output gap. Moreover, I
find that these relationships differ systematically across countries based on their degree of
international trade openness: Nominal interest rates in open economies respond systematically
less to changes in expected inflation than they do in closed economies. I find no systematic
relationship between the response of a country’s nominal interest rate to changes in its output
gap and the degree of the country’s openness.
While the lower response of nominal interest rates in open economies to changes in inflation may reflect that such countries are less concerned about inflation, it may also reflect that
these countries actually respond to changes in variables other than inflation. To investigate
this possibility, I reconduct the analysis, extending the Taylor rule to include a trade-related
variable that may affect how open economies conduct monetary policy, as suggested by previous studies (Faia and Monacelli, 2008, and De Paoli, 2009, among others)—the real exchange
rate. I find that, indeed, open economies are systematically more likely to adjust their nominal
interest rate in response to changes in the real exchange rate.
These findings suggest that open economies do conduct monetary policy differently from
their closed-economy counterparts. First, I find that open economies respond relatively less
to changes in inflation. Second, I find that open economies respond relatively more to changes
in the real exchange rate. And, finally, I find that the degree of interest rate smoothing and
the response of nominal interest rates to changes in the output gap do not vary systematically
with the degree of international trade openness.
This article contributes to a growing empirical literature that studies the relationship
between trade openness and monetary policy, such as Lubik and Schorfheide (2007), Berument,
Konac, and Senay (2007), and Basilio (2013). This article is also related to empirical papers
aimed at estimating Taylor rules across countries. I follow very closely the estimation approach
of Clarida, Galí, and Gertler (1998 and 2000), who apply it to the United States, Japan, Germany,
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Leibovici
France, Italy, and the United Kingdom. Also related are Torres (2003), Hayo and Hofmann
(2006), Yazgan and Yilmazkuday (2007), and Kahn (2012).
More broadly, this article is also related to a large theoretical and quantitative literature
that investigates the extent to which open economies should conduct monetary policy differently. Corsetti, Dedola, and Leduc (2010) provide a broad discussion of many of the studies
in this literature. More recently, Faia and Monacelli (2008), De Paoli (2009), Lombardo and
Ravenna (2014), and Leibovici and Santacreu (2015) investigate this question in richer and
more realistic economic environments.
The rest of this article is structured as follows. Section 2 presents the economic framework,
and Section 3 presents my approach to estimating it. Section 4 presents the data that I use to
estimate the economic framework and describes the details of the implementation. Sections
5 and 6 present the results, and Section 7 concludes.
2 THE TAYLOR RULE
The starting point of the analysis is the Taylor rule, an equation that specifies the nominal
short-term interest rate target as a function of three variables: (i) the long-run equilibrium
nominal rate, (ii) deviations of inflation from an inflation target, and (iii) deviations of output
from a target level of output. In addition, I consider an extension of the standard Taylor rule
to allow for the possibility that nominal interest rates also respond to other variables. Mathe
matically, we have
(1)
Rt* = R + β ⎡⎣ E (π t+1 | Ωt ) − π * ⎤⎦ + γ ⎡⎣ E ( yt | Ωt ) − yt* ⎤⎦ + ξ z t ,
–
where R is the long-run equilibrium nominal rate; πt+1 is the rate of inflation between periods t
and t+1; yt is real output; π* is the target level of inflation; yt* is the target level output; and zt is
a vector of additional variables that the monetary authority may respond to. Moreover, E is
the expectation operator and Ωt is the information set available to the central bank at the time
it sets interest rates. A variety of specifications of the Taylor rule have been considered in the
literature; here, I focus on the specification studied by Clarida, Galí, and Gertler (1998 and
2000).
I assume that, every period, the effective short-term nominal interest rate Rt adjusts partially to the nominal interest rate target Rt* according to the following AR(2) process:
(2)
Rt = (1− ρ1 − ρ 2 ) Rt* + ρ1Rt−1 + ρ 2 Rt−2 + ν t ,
where ρ1 (0,1) and ρ2 (0,1) capture the degree of interest rate smoothing, vt is a zeromean independent and identically distributed (i.i.d.) shock to the nominal interest rate, and
ρ1 + ρ2 < 1.
Then, given the above expressions for the target short-term nominal interest rate (equation (1)) and the nominal interest rate (equation (2)), the actual nominal short-term interest
rate can be expressed as
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{
Rt = (1− ρ1 − ρ 2 ) R + β ⎡⎣ E (π t+n | Ωt ) − π * ⎤⎦ + γ ⎡⎣ E ( yt | Ωt ) − yt* ⎤⎦ + ξ z t
+ ρ1Rt−1 + ρ 2 Rt−2 + ν t .
(3)
}
Thus, to the extent that a country’s nominal interest rate follows equation (3), its evolution is
characterized by
–
(i) a long-run value R for the nominal interest rate,
(ii) a set of outcome variables X t = E (π t+1 | Ωt ) − π *, E ( yt | Ωt ) − yt* , Rt−1, Rt−2,z t on
which the nominal interest rate target depends, and
(iii) a set of coefficients θ = {β ,γ , ρ1, ρ 2 , ξ } that dictate the response of the nominal interest
rate target to changes in the outcome variables Xt .
{
}
Throughout the rest of the article, I use this framework as a lens to characterize differences
in the design of monetary policy across countries. In particular, given a set of outcome variables X t = E (π t+1 | Ωt ) − π *, E ( yt | Ωt ) − yt* , Rt−1, Rt−2,z t on which the nominal interest rate is
assumed to depend, I estimate the set of coefficients θ = {β ,γ , ρ1, ρ 2 , ξ } that dictates its response
to changes in the outcome variables. From the lens of this approach, differences in the design
of monetary policy across countries boil down to differences in the set of estimated coefficients
θ. Then, I examine the extent to which open economies conduct monetary policy differently
from closed ones by investigating whether the set of coefficients θ varies systematically with
the degree of international trade openness across countries.
Importantly, note that while I use the framework above to characterize differences in the
design of monetary policy across countries, I do not necessarily restrict attention to countries
with explicit interest rate targeting rules. In particular, I do not interpret the Taylor rule coefficients θ as structural parameters that govern the response of nominal interest rates to changes
in inflation and output but, instead, use the specification above as a device to summarize the
statistical properties of how interest rates, inflation, and output behave in the time series across
countries regardless of the particular underlying monetary policy instruments, outcome-
targeting regimes, or exchange-rate regimes in place in each country.
{
}
3 ESTIMATION APPROACH
To estimate the Taylor rule described above (equation (3)) for a given country, I follow
the approach of Clarida, Galí, and Gertler (1998 and 2000). The objective is to estimate the
vector of coefficients θ = {β ,γ , ρ1, ρ 2 , ξ } that dictates the response of the nominal interest rate
to changes in the outcome variables Xt .
The first problem I face in estimating θ using equation (3) is that E (π t+1 | Ωt ) and E ( yt | Ωt )
are unobservable. While inflation and output are regularly measured by statistical agencies
across countries, this is not typically the case for the expected value of inflation and output at
the time that monetary policy decisions are made.
To address this challenge, I rewrite equation (3) in terms of observable variables, following
Clarida, Galí, and Gertler (1998 and 2000):
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(
)
(
)
Rt = (1− ρ1 − ρ 2 ) ⎡⎣ R − βπ * + βπ t+1 + γ yt − yt* + ξ z t ⎤⎦ + ρ1Rt−1 + ρ 2 Rt−2 + ε t ,
(4)
where I refer to yt – yt* as the output gap and the error term εt is now given by
ε t = vt − (1− ρ1 − ρ 2 ) β ⎡⎣π t+1 − E (π t+1 | Ωt ) ⎤⎦
(5)
{
}
− (1− ρ1 − ρ 2 )γ ⎡⎣ yt − yt* ⎤⎦ − ⎡⎣ E ( yt | Ωt ) − yt* ⎤⎦ .
Having addressed the first challenge, the question now is how to estimate equation (4) given
data on inflation πt+1 and the output gap yt – yt*. Estimating it by ordinary least squares (OLS)
would result in biased estimates since we would be violating the exogeneity assumption, which
in this case requires that E ⎡⎣ε t | π t+1,yt − yt* , z t ,Ωt ⎤⎦ = 0. To see this, note that even though vt may
be a mean-zero i.i.d. variable, equation (5) implies that
E ⎡⎣ε t | π t+1 , yt − yt* , z t ,Ωt ⎤⎦ = − (1− ρ1 − ρ 2 ) β ⎡⎣π t+1 − E (π t+1 | Ωt ) ⎤⎦
{
}
− (1− ρ1 − ρ 2 )γ ⎡⎣ yt − yt* ⎤⎦ − ⎡⎣ E ( yt | Ωt ) − yt* ⎤⎦ .
That is, E ⎡⎣ε t | π t+1,yt − yt* , z t ,Ωt ⎤⎦ is a function of the forecast errors for inflation and the output
gap, which generically need not be equal to zero in all states of the world.
The violation of the exogeneity assumption required by OLS to produce unbiased estimates
can equivalently be expressed as
{
(
)
(
}
)
% | Ω ≠ 0,
E ⎡ Rt − (1− ρ1 − ρ 2 ) ⎡⎣ R − βπ * + βπ t+1 + γ yt − yt* + ξ z t ⎤⎦ − ρ1Rt−1 − ρ 2 Rt−2 ⎤ X
⎣
⎦ t t
{
}
% t = π t+1,yt − yt* ,z t ,Rt−1,Rt−2 .
where X
To address this second challenge, I follow Clarida, Galí, and Gertler (1998 and 2000) in
pursuing an instrumental-variables approach. This approach requires one to find a vector of
% t but that are uncorrelated with ε or, equivalently,
variables ut that are correlated with X
t
uncorrelated with νt , π t − E (π t | Ωt ), and ⎡⎣ yt − yt* ⎤⎦ − ⎡⎣ E ( yt | Ωt ) − yt* ⎤⎦ . In other words, the
objective of this approach is to find variables ut such that the following two properties are
satisfied:
{
}
% t ut | Ωt ≠ 0,
(i) non-zero correlation between instruments and outcome variables: E X
and
(ii) zero correlation between instruments and the error term εt :
{
(
)
(
)
}
(6) E ⎡ Rt − (1− ρ1 − ρ 2 ) ⎡⎣ R − βπ * + βπ t+1 + γ yt − yt* + ξ z t ⎤⎦ − ρ1Rt−1 − ρ 2 Rt−2 ]ut | Ωt = 0.
⎣
Following Clarida, Galí, and Gertler (1998), possible elements of ut include any lagged variable
that may help to forecast inflation or the output gap. Why? By definition, the forecast error
consists of the difference between the realization of a variable and its expected value conditional on the information set at the time that the nominal interest rate is determined. Then,
to the extent that one identifies a lagged variable that may help to forecast either πt+1 or yt – yt*,
such a variable should not be associated with the forecast error. Other candidate instruments ut
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include any contemporaneous variables that are uncorrelated with the current interest rate
shock vt .
Given a set of instruments ut that satisfy conditions (1) and (2) above, I estimate equation
(4) following a GMM approach. Let j = 1,…,J index the different instruments in vector ut .
First, I define the population moment corresponding to instrument j as
{
(
)
(
}
)
M j = E ⎡ Rt − (1− ρ1 − ρ 2 ) ⎡⎣ R − βπ * + βπ t+1 + γ yt − yt* + ξ z t ⎤⎦ − ρ1Rt−1 − ρ 2 Rt−2 ⎤ ut,j | Ωt = 0.
⎣
⎦
Second, I construct its empirical counterpart:
{
}
T
% j = 1 ∑ Rt − (1− ρ1 − ρ 2 ) ⎡ R − βπ * + βπ t+1 + γ yt − yt* + ξ z t ⎤ − ρ1Rt−1 − ρ 2 Rt−2 ut,j .
M
⎣
⎦
T t=1
(
)
(
)
Third, I construct the moment condition mj corresponding to instrument j:
% j − Mj
mj = M
% j −0
=M
% .
=M
j
Fourth, I stack all moment conditions mj for j = 1,…,J into a vector m.
Finally, given a symmetric positive-definite weighting J×J matrix W,2 the GMM estimator
is given by the vector θ = {β ,γ , ρ1, ρ 2 , ξ } of parameters that solves the following problem:
min
{β ,γ , ρ1, ρ2 ,ξ }
m T Wm,
where a variable with superscript T denotes the transpose of the variable.
4 DATA
To implement the estimation procedure described in the previous section, I use quarterly
cross-country time-series data collected by the International Monetary Fund (IMF) and the
Organisation for Economic Co-operation and Development (OECD) and accessed through
Haver Analytics.3
I select the variables and sources used as well as the details of the specification that I estimate under two guiding principles. First, my goal is to obtain country-specific estimates of
the Taylor rule coefficients θ that can be compared across countries. Therefore, I restrict attention to variables and data sources that maximize the number of countries available while ensuring that variables are measured under a methodology that is as similar as possible across
countries.4 My second goal is, to the extent possible, to follow the estimation approach of
Clarida, Galí, and Gertler (1998 and 2000), with the intention of maximizing the comparability of my findings with previous estimates from the literature.
In this section, I present the data used to estimate equation (3) under the constraint
ξ = zt = 0, which is the standard Taylor rule formulation. I present the corresponding results
in Section 5 and consider extensions of this specification in Section 6.
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4.1 Taylor Rule Variables
I measure the nominal interest rate Rt using data on central bank policy rates collected
by the IMF (Haver code: C###IC@IFS). As described by the IMF (n.d.), “The central bank
policy rate (CBPR) is the rate that is used by the central bank to implement or signal its monetary policy stance. It is most commonly set by the central banks’ policy making committees
(e.g., the Federal Open Market Committee).”5
I measure the realized inflation rate πt+1 as the quarterly log change in the GDP deflator
between period t+1 and period t; I obtain data on the GDP deflator from the IMF and OECD
(Haver codes: C###GJ@IFS for the IMF series and C###GPI@OECDNAQ for the OECD
series).6
To measure the output gap yt – yt*, I compute the log difference of real GDP from its
country-specific quadratic trend.7 I obtain data on real GDP from the IMF and OECD (Haver
codes: C###GDPC@IFS for the IMF series and E###GDPC@OECDNAQ for the OECD series).
4.2 Instruments
Following Clarida, Galí, and Gertler (1998 and 2000), the set of instruments that I use
consists of two types of variables. On the one hand, I include the first four lags of each of the
Taylor rule variables as part of the instrument set. In particular, I include the following variables as instruments:
(
)(
)(
)(
)
*
*
*
*
*
*
*
*
Rt−1,Rt−2,Rt−3,Rt−4, yt−1 − yt−1
, yt−2 − yt−2
, yt−3 − yt−3
, yt−4 − yt−4
,π t−1
, π t−2
, π t−3
, π t−4
.
On the other hand, I include lags of other variables that may forecast changes in the Taylor
rule variables but that are unlikely to be correlated with forecast errors. Specifically, I include
lags of two variables not included in the baseline specification of the Taylor rule: an index of
world commodity prices ωt and country-specific effective real exchange rates Qt . To measure
world commodity prices, I use the S&P Goldman Sachs Commodity Index (S&P GSCI Com
modity Nearby Index; Haver code GSCI@USECON). To measure country-specific effective
real exchange rates, I use data from the IMF and OECD (Haver codes: C###EIRC@IFS for
the IMF series and C###FXEF@OECDMEI for the OECD series) and the Bank for International
Settlements (BIS).8 In particular, I include the following variables as instruments:
ΔlnQt−1,ΔlnQt−2,ΔlnQt−3 ,ΔlnQt−4,Δlnω t−1,Δlnω t−2,Δlnω t−3,Δlnω t−4 ,
where Δlnxt−k = lnxt−k − lnxt−k−1 for any variable x and integer k.
I adopt the convention throughout that real exchange rates are measured as the relative
price of a domestic consumption basket relative to a foreign consumption basket (both in
domestic units), so that an increase in the real exchange rate consists of a real appreciation.
4.3 Cleaning Up the Data
Before using these variables to estimate country-specific Taylor rules following the GMM
approach described in the previous section, I apply a few filters to ensure that there is sufficient
data available for each country as well as to clean the variables used.
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First, I restrict attention to the period 1980:Q1
to 2006:Q4.9 For each of the variables that has data
available from both the OECD and the IMF, I examine for each country whether there are data available
from the OECD for at least 36 consecutive quarters.
If so, then I use data from the OECD for that country.
Otherwise, I examine whether there are data available from the IMF for at least 36 consecutive quarters.
If so, then I use data from the IMF for that country;
otherwise, I exclude the country from the analysis.10
Second, I seasonally adjust the level of all of
these variables except Rt, using the X13 seasonal
adjustment procedure developed by the U.S. Census
Bureau. I adjust this procedure to avoid controlling
for U.S.-specific seasonality patterns that may not
be applicable to other countries (e.g., U.S. holidays).
Finally, I restrict attention to countries with at
least 36 consecutive quarters of data in which all of
the Taylor rule variables and instruments are available (Rt ,yt ,πt ,ωt ,Qt ). The countries and time periods
used throughout the analysis are displayed in Table 1.
4.4 Trade Openness and GDP Per Capita
Table 1
Countries and Periods
Country
First period
Last period
Australia
1980:Q2
2006:Q4
Austria
1980:Q2
1998:Q4
Bolivia
1996:Q2
2006:Q4
Canada
1993:Q1
2006:Q4
Chile
1995:Q1
2006:Q4
Czech Republic
1996:Q1
2006:Q4
Denmark
1980:Q2
2006:Q4
Germany
1980:Q2
1998:Q4
Hungary
1995:Q2
2006:Q4
Iceland
1994:Q1
2006:Q4
India
1997:Q2
2006:Q4
Indonesia
1990:Q2
2006:Q4
Israel
1995:Q2
2006:Q4
Italy
1980:Q2
1998:Q4
Japan
1980:Q2
2006:Q4
Latvia
1995:Q2
2006:Q4
Netherlands
1980:Q2
1993:Q4
Norway
1980:Q2
2006:Q4
Poland
1998:Q1
2006:Q4
Portugal
1980:Q2
1998:Q4
In order to examine the extent to which monetary
Slovenia
1996:Q4
2006:Q4
policy in open economies is systematically different,
South Africa
1980:Q2
2006:Q4
I measure openness to international trade as the
Spain
1984:Q1
1998:Q4
average ratio of nominal exports to nominal GDP
Switzerland
1980:Q2
2006:Q4
across the sample period (Haver codes: C###GE@IFS
and C###GDP@IFS for the IMF series and
United Kingdom
1980:Q2
2006:Q4
A###X@OECDNAQ and A###GDP@OECDNAQ
United States
1982:Q4
2006:Q4
for the OECD series), both in domestic units. How
ever, all the findings are robust to alternative measures
of trade openness, such as the average ratio of nominal exports plus nominal imports to
nominal GDP.
In the next section, I also sometimes control for the level of economic development, as
proxied by GDP per capita, which I obtain from Penn World Tables 9.0 (output-side real GDP,
purchasing-power-parity adjusted, in 2011 U.S. dollars).
4.5 Implementation
Throughout the next sections, I execute the GMM estimation approach described above
by applying the two-step GMM estimator implemented by Stata’s “gmm” command with correction for heteroskedasticity and serial correlation. That is, first I obtain parameter estimates
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based on an initial weighting matrix. Then, I compute a new weighting matrix based on those
estimates. Finally, I reestimate parameters based on that weighting matrix. I correct for hetero
skedasticity and serial correlation using the Newey-West kernel with four lags.
5 BASELINE TAYLOR RULE
In this section, I begin to analyze the extent to which open economies conduct monetary
policy differently from their closed-economy counterparts. To do so, I use the Taylor rule as
the lens to measure differences in the conduct of monetary policy across countries. In particular, in this section I restrict attention to a Taylor rule where the nominal interest rate responds
to changes in expected inflation, the output gap, and lagged values of the nominal interest rate
(as in Clarida, Galí, and Gertler, 1998 and 2000).
5.1 Taylor Rule Coefficients
The first step of the analysis consists of following the estimation approach described above
to estimate a Taylor rule for each of the countries in the sample. Table 2 presents the estimated
Taylor rule coefficients corresponding to equations (3) and (4). In addition, I also report the
average degree of international trade openness as measured by the aggregate exports-to-GDP
ratio.
5.1.1 Validation: Estimates for the United States. To begin with, I contrast my estimated
Taylor rule coefficients for the United States with estimates from previous studies in the literature. Consistent with previous studies, I find that monetary policy in the United States places
a higher weight on changes in inflation than on the output gap, and nominal interest rate
adjustments are smoothed over time. For instance, in the specification that uses data series
closest to the ones that I use, Clarida, Galí, and Gertler (2000) estimate a weight on expected
inflation equal to 1.97 (vs. 1.35), a weight on the output gap equal to 0.55 (vs. 0.62), and an
impact of lagged interest rates equal to 0.76 (vs. 0.93).11
Importantly, I find that most differences between my estimates and those of Clarida, Galí,
and Gertler (2000) are explained by differences in the data series used. Using exactly the same
data series used by Clarida, Galí, and Gertler (2000) to estimate the second row of Table II
(their baseline estimates) in their paper, I estimate a weight on expected inflation equal to 2.17
(vs. 2.15), a weight on the output gap equal to 1.23 (vs. 0.93), and an impact of lagged interest
rates equal to 0.80 (vs. 0.79 ). While these data series lead to estimates that are closest to those
in Clarida, Galí, and Gertler (2000), some of them are not available across a large number of
countries, preventing me from conducting the cross-country analysis using these particular
series.
Recall that, in this article, my choice of data series is significantly driven by my twofold
goal of conducting the analysis for as many countries as possible and simultaneously using
data series that are as comparable across countries as possible. An implication of this approach
is that the data series that I use need not always line up exactly with the variables that the
central bank in each country responds to, leading to estimated Taylor rule coefficients different
from those estimated under the best possible data, as illustrated above for the United States.
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Table 2
Taylor Rule Coefficients: The Baseline Taylor Rule
Taylor rule coefficients
Country
Australia
Austria
Bolivia
Canada
Chile
Czech Republic
Denmark
Germany
Hungary
Iceland
India
Indonesia
Israel
Italy
Japan
Latvia
Netherlands
Norway
Poland
Portugal
Slovenia
South Africa
Spain
Switzerland
United Kingdom
United States
Expected
inflation
1.486***
(0.268)
0.135
(0.187)
0.326***
(0.111)
0.088
(0.138)
–0.163**
(0.083)
1.078***
(0.129)
0.195
(0.538)
0.394
(0.311)
0.531***
(0.075)
1.004***
(0.287)
–0.165***
(0.027)
0.876***
(0.334)
–1.543
(1.247)
1.244***
(0.214)
1.466***
(0.181)
0.0637***
(0.016)
0.735***
(0.082)
–0.629
(0.471)
–0.427***
(0.111)
1.223***
(0.253)
1.267***
(0.110)
0.354
(0.253)
1.672***
(0.195)
0.614***
(0.172)
0.873***
(0.337)
1.354**
(0.584)
Output gap
0.612
(0.430)
1.033***
(0.251)
3.354***
(0.466)
1.072***
(0.173)
0.904***
(0.105)
1.985***
(0.485)
0.677
(0.620)
0.678***
(0.159)
–2.010*
(1.157)
0.574*
(0.333)
0.281***
(0.037)
–0.735***
(0.268)
–1.218
(0.956)
2.031***
(0.766)
–0.257**
(0.114)
0.0221
(0.039)
1.248***
(0.203)
1.927**
(0.770)
6.484***
(0.526)
0.964**
(0.435)
0.621
(0.491)
1.006***
(0.327)
–0.205
(0.145)
0.494***
(0.170)
0.903*
(0.545)
0.621***
(0.228)
Lagged
interest rates
0.893***
(0.016)
0.919***
(0.019)
0.901***
(0.018)
0.851***
(0.016)
0.758***
(0.036)
0.942***
(0.008)
0.976***
(0.008)
0.887***
(0.022)
0.890***
(0.010)
0.942***
(0.015)
0.823***
(0.013)
0.788***
(0.052)
0.962***
(0.020)
0.915***
(0.030)
0.919***
(0.013)
0.753***
(0.021)
0.841***
(0.024)
0.970***
(0.011)
0.855***
(0.014)
0.920***
(0.034)
0.874***
(0.018)
0.897***
(0.022)
0.822***
(0.036)
0.915***
(0.012)
0.903***
(0.022)
0.932***
(0.016)
Constant
1.673
(1.204)
4.287***
(0.540)
5.628***
(0.939)
3.819***
(0.396)
5.509***
(0.424)
–0.123
(0.583)
4.208**
(1.769)
3.470***
(0.863)
5.877***
(0.600)
6.493***
(1.004)
6.931***
(0.157)
5.307*
(3.101)
8.186***
(2.785)
2.844
(1.754)
1.619***
(0.225)
3.254***
(0.133)
4.726***
(0.232)
10.25***
(2.216)
7.930***
(0.438)
–1.327
(3.639)
1.444*
(0.737)
9.633***
(2.771)
1.619
(1.063)
1.860***
(0.366)
3.846***
(1.305)
1.707
(1.610)
Overidentification
test
Trade openness
X/GDP
J = 11.77, χ 2(16)
p-value = 0.760
J = 10.30, χ 2(16)
p-value = 0.851
J = 7.63, χ 2(16)
p-value = 0.959
J = 8.47, χ 2(16)
p-value = 0.934
J = 6.81, χ 2(16)
p-value = 0.977
J = 7.46, χ 2(16)
p-value = 0.963
J = 10.68, χ 2(16)
p-value = 0.829
J = 10.10, χ 2(16)
p-value = 0.862
J = 7.82, χ 2(16)
p-value = 0.954
J = 7.49, χ 2(16)
p-value = 0.963
J = 6.21, χ 2(16)
p-value = 0.986
J = 6.72, χ 2(16)
p-value = 0.978
J = 7.97, χ 2(16)
p-value = 0.950
J = 10.37, χ 2(16)
p-value = 0.847
J = 11.43, χ 2(16)
p-value = 0.782
J = 8.12, χ 2(16)
p-value = 0.945
J = 6.76, χ 2(16)
p-value = 0.978
J = 11.73, χ 2(16)
p-value = 0.762
J = 6.73, χ 2(16)
p-value = 0.978
J = 8.38, χ 2(16)
p-value = 0.937
J = 6.88, χ 2(16)
p-value = 0.976
J = 11.98, χ 2(16)
p-value = 0.745
J = 9.30, χ 2(16)
p-value = 0.901
J = 12.68, χ 2(16)
p-value = 0.696
J = 7.61, χ 2(16)
p-value = 0.960
J = 10.83, χ 2(16)
p-value = 0.820
0.172
0.339
0.249
0.377
0.328
0.490
0.390
0.220
0.567
0.338
0.146
0.299
0.334
0.205
0.115
0.384
0.548
0.396
0.304
0.257
0.521
0.260
0.196
0.463
0.235
0.093
NOTE: *, **, and *** denote 10 percent, 5 percent, and 1 percent statistical significance, respectively. The coefficients on expected inflation, the
–
output gap, and lagged interest rates correspond to β, γ, and ρ1 + ρ2 , respectively, from equation (4). The constant corresponds to R – βπ *.
Standard errors are in parentheses.
Federal Reserve Bank of St. Louis REVIEW
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103
Leibovici
Therefore, throughout the rest of the article, I interpret the Taylor rule coefficients as moments
that characterize salient features of monetary policy in each country rather than as structural
parameters.
5.1.2 Cross-Country Estimates. I now examine salient features of my estimated Taylor
rule coefficients across countries (Table 2). First, I find that there is substantial heterogeneity
across countries in the Taylor rule coefficient on expected inflation. This coefficient is estimated
to be negative for three countries (Chile, India, and Poland), not statistically different from
zero12 for seven countries (Austria, Canada, Denmark, Germany, Israel, Norway, and South
Africa), statistically higher than zero but lower than 1 for seven countries (Bolivia, Hungary,
Indonesia, Latvia, the Netherlands, Switzerland, and the United Kingdom), and higher than
1 for nine countries (Australia, the Czech Republic, Iceland, Italy, Japan, Portugal, Slovenia,
Spain, and the United States).13
Second, I find that there is a similar degree of heterogeneity across countries in the Taylor
rule coefficient on the output gap. This coefficient is estimated to be negative for three countries (Hungary, Indonesia, and Japan), not statistically different from zero for six countries
(Australia, Denmark, Israel, Latvia, Slovenia, and Spain), statistically higher than zero but
lower than 1 for eight countries (Chile, Germany, Iceland, India, Portugal, Switzerland, the
United Kingdom, and the United States), and higher than 1 for nine countries (Austria, Bolivia,
Canada, the Czech Republic, Italy, the Netherlands, Norway, Poland, and South Africa).
Third, I find that the sum of the coefficients on lagged interest rates is statistically significant for all countries, suggesting that all countries engage in some degree of nominal interest
rate smoothing. Therefore, while countries differ in the response to changes in expected inflation and the output gap, in all cases lagged interest rates are an important factor in determining current interest rates.
Finally, the last column of Table 2 reports the average degree of trade openness, measured
through the exports-to-GDP ratio across the 26 countries under analysis. I find that there is
substantial heterogeneity in the degree of trade openness across these countries, ranging
from relatively closed economies such as the United States and Japan, with exports-to-GDP
ratios equal to 0.093 and 0.115, respectively, to relatively open economies such as Hungary,
the Netherlands, and Slovenia, with exports-to-GDP ratios equal to 0.567, 0.548, and 0.521,
respectively.
5.2 Taylor Rule Coefficients and Trade Openness
I now ask, to what extent do open economies conduct monetary policy differently from
closed economies? To answer this question, I examine the relationship between the cross-
country Taylor rule coefficients reported in Table 2 and the countries’ degree of openness to
international trade.
5.2.1 Expected Inflation. The top panel of Table 3 reports the results of regressing the
country-specific Taylor rule coefficients on each country’s aggregate exports-to-GDP ratio.
The first two columns of the table report the results from conducting the analysis using the
expected- inflation Taylor rule coefficients for all countries regardless of the degree of statistical
significance obtained in the previous section. The last two columns of this table report the
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Table 3
Monetary Policy and Trade Openness: The Baseline Taylor Rule
With Taylor rule coefficient
significant at 10%
All countries
(1)
(2)
(3)
(4)
–0.895
(0.826)
–1.182**
(0.529)
Dependent Variable: The Taylor Rule Coefficient on Expected Inflation
X/GDP
–1.284
(1.033)
–1.471
(0.955)
0.184
(0.159)
GDP per capita
0.434***
(0.115)
Constant
0.947**
(0.358)
–0.799
(1.523)
R2
0.049
0.082
0.046
0.372
26
26
19
19
–0.963
(2.745)
–0.91
(2.943)
No. of countries
1.071***
(0.333)
–3.034**
(1.165)
Dependent Variable: The Taylor Rule Coefficient on the Output Gap
X/GDP
–0.806
(2.039)
–0.674
(2.134)
–0.13
(0.408)
GDP per capita
–0.0396
(0.437)
Constant
1.142
(0.682)
2.374
(4.075)
1.428
(0.877)
1.796
(4.261)
R2
0.005
0.009
0.006
0.006
26
26
20
20
No. of countries
Dependent Variable: The Taylor Rule Coefficient on Interest Rate Lags
X/GDP
0.000228
(0.0668)
–0.0434
(0.0546)
0.000228
(0.0668)
0.0428***
(0.0139)
GDP per capita
–0.0434
(0.0546)
0.0428***
(0.0139)
Constant
0.886***
(0.0220)
0.482***
(0.140)
0.886***
(0.0220)
0.482***
(0.140)
R2
0.000
0.284
0.000
0.284
26
26
26
26
No. of countries
NOTE: *, **, and *** denote 10 percent, 5 percent, and 1 percent statistical significance, respectively. Standard errors
are in parentheses. GDP per capita denotes the natural logarithm of the GDP per capita variable.
results when restricting attention to the subset of expected-inflation Taylor rule coefficients
that are statistically significant at the 10 percent level.14
I find that all specifications imply that there is a negative relationship between the degree
of a country’s trade openness and the Taylor rule coefficient on expected inflation: In open
economies the nominal interest rate responds relatively less to changes in inflation. This relationship, however, is only statistically significant when one controls for GDP per capita while
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
105
Leibovici
restricting attention to countries with significant Taylor rule coefficients. That is, among the
set of countries that respond to changes in expected inflation, they seem to respond relatively
less if they are open.
As observed in Table 2, the Taylor rule coefficient on expected inflation is not statistically
significant for all countries. This is because either their Taylor rule coefficients are very close
to zero or because the coefficients are estimated with a significant amount of error. Therefore,
in columns 3 and 4, I restrict attention to countries in which the Taylor rule coefficients are
significant at the 10 percent level.
Yet, only once I control for the countries’ level of GDP per capita does the relationship
between trade openness and the Taylor rule coefficient on expect inflation become significant.
This is not necessarily very surprising, given developed economies are simultaneously more
likely to be open as well as to be inflation targeters in their conduct of monetary policy.
To quantify the economic importance of this relationship, consider the average Taylor
rule coefficient on expected inflation is equal to 0.54. Then, changing the aggregate exportsto-GDP ratio from its lowest to highest value across countries (from 0.093 to 0.567) is associated with a decrease in the value of the Taylor rule coefficient equal to 0.56. This evidence
suggests that open economies assign a lower weight on expected inflation when conducting
monetary policy, a relationship that is both statistically and economically significant.
5.2.2 Output Gap. The middle panel of Table 3 reports the results of regressing the
country-specific output-gap Taylor rule coefficients on each country’s aggregate exports-toGDP ratio. I find that there is no systematic relationship between the degree of a country’s
trade openness and the weight it assigns to changes in the output gap for the conduct of monetary policy. This finding is robust to restricting attention to Taylor rule coefficients that are
statistically significant at the 10 percent level as well as to controlling for GDP per capita (see
columns 1 to 4). In all cases, the relationship between trade openness and the weight on the
output gap is negative, but the degree of error is substantial, making these coefficients statistically insignificant. This evidence suggests that monetary policy in open and closed economies
responds similarly to changes in the output gap.
5.2.3 Lagged Interest Rates. Finally, the bottom panel of Table 3 reports the results of
regressing the country-specific sum of the interest rate lags of the Taylor rule on each country’s
aggregate exports-to-GDP ratio. As with the output gap, I find that there is no systematic relationship between the degree of a country’s trade openness and the extent to which that country
smooths its interest rate adjustments over time. This finding is robust to restricting attention
to Taylor rule coefficients that are statistically significant at the 10 percent level as well as to
controlling for GDP per capita (see columns 1 to 4). Yet, what I do find is that richer economies
smooth their nominal interest rate adjustments relatively more than poorer ones, suggesting
that richer economies conduct their monetary policy decisions in a more predictable way.
6 TAYLOR RULE WITH REAL EXCHANGE RATE
The evidence presented in the previous section suggests that monetary policy in open
economies is conducted differently from monetary policy in closed economies, but only along
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Federal Reserve Bank of St. Louis REVIEW
Leibovici
certain dimensions. In particular, while open economies typically assign a lower weight to
changes in expected inflation, they respond to changes in the output gap to a similar extent
as closed economies do.
I now examine whether, in addition to inflation, open economies also respond differently
to changes in other variables not included in the baseline specification of the Taylor rule.
Following previous studies from the literature, in this article I restrict attention to the real
exchange rate as an additional variable that central banks in open economies may respond to
when conducting monetary policy.
6.1 Taylor Rule Coefficients
As in the previous section, I begin by estimating a Taylor rule for each of the countries in
the sample. In this section, however, I extend the Taylor rule by including the real exchange
rate as an additional variable that nominal interest rates may respond to.15 In particular, I compute the real exchange rate variable that nominal interest rates respond to as the log difference
of the real exchange rate from its country-specific quadratic trend.16 Table 4 presents the estimated Taylor rule coefficients corresponding to this extended specification of the Taylor rule.
I find that there is significant heterogeneity in the estimated Taylor rule coefficients on the
real exchange rate. This coefficient is estimated to be negative for eight countries (the Czech
Republic, Germany, Hungary, Indonesia, Japan, the Netherlands, Poland, and Switzerland),
not statistically different from zero for 13 countries (Australia, Austria, Chile, Denmark,
Iceland, India, Israel, Italy, Norway, Slovenia, South Africa, the United Kingdom, and the
United States), and statistically higher than zero for five countries (Bolivia, Canada, Latvia,
Portugal, and Spain).17
Moreover, I also find that including the real exchange rate as an additional variable in
the Taylor rule significantly affects the estimated coefficients on expected inflation and the
output gap, as can be readily observed by comparing Tables 2 and 4.
These findings suggest that the real exchange rate is a variable that many central banks
across the world might respond to when executing monetary policy decisions, even if they
sometimes respond to it to different extents and in qualitatively different ways.
6.2 Taylor Rule Coefficients and Trade Openness
I now ask, to what extent do open economies conduct monetary policy differently from
closed economies once the real exchange is included as an additional variable in the Taylor
rule? To answer this question, I examine the relationship between the cross-country Taylor
rule coefficients reported in Table 4 and the countries’ degree of openness to international
trade.
6.2.1 Expected Inflation. The top panel of Table 5 reports the results of regressing the
country-specific expected-inflation Taylor rule coefficients on each country’s aggregate
exports-to-GDP ratio. I find that, while the relationship between trade openness and the
weight on expected inflation is negative, as in the previous section, this relationship is statistically insignificant in all the specifications considered. In particular, note that I no longer
find that open economies assign a lower weight on expected inflation once I restrict attention
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
107
Table 4
Taylor Rule Coefficients: The Baseline Taylor Rule
Taylor rule coefficients
Country
Australia
Austria
Bolivia
Canada
Chile
Czech Republic
Denmark
Germany
Hungary
Iceland
India
Indonesia
Israel
Italy
Japan
Latvia
Netherlands
Norway
Poland
Portugal
Slovenia
South Africa
Spain
Switzerland
United Kingdom
United States
Expected
inflation
1.569***
(0.286)
–0.0278
(0.342)
0.208*
(0.121)
0.0427
(0.132)
–0.178*
(0.095)
0.960***
(0.153)
0.0876
(0.586)
0.176
(0.373)
0.635***
(0.116)
1.294**
(0.503)
–0.184***
(0.039)
0.266***
(0.092)
–1.245
(1.287)
1.336***
(0.239)
1.309***
(0.194)
0.0686***
(0.019)
0.554***
(0.082)
–0.651
(0.516)
–1.803***
(0.407)
0.985***
(0.136)
1.267***
(0.111)
0.239
(0.294)
1.528***
(0.238)
0.925***
(0.203)
0.846**
(0.343)
1.701
(1.035)
Output
gap
0.614
(0.460)
1.020***
(0.283)
2.408***
(0.498)
1.260***
(0.211)
1.404***
(0.250)
1.691**
(0.843)
0.755
(0.755)
0.810***
(0.262)
0.364
(1.616)
0.481
(0.383)
0.256***
(0.060)
1.101**
(0.441)
–0.690
(1.241)
2.717**
(1.222)
–0.220**
(0.110)
0.0801
(0.058)
1.221***
(0.183)
1.939**
(0.841)
10.91***
(1.449)
0.313
(0.215)
0.578
(0.619)
1.038***
(0.383)
–2.405***
(0.462)
0.197
(0.148)
0.909
(0.579)
0.491
(0.359)
Real
exchange rate
–0.0799
(0.148)
–0.415
(0.337)
1.173***
(0.272)
0.186***
(0.066)
–0.186
(0.132)
–0.984***
(0.298)
–0.705
(0.552)
–0.355**
(0.159)
–0.654***
(0.191)
0.270
(0.212)
0.0546
(0.071)
–0.874***
(0.227)
–0.410
(0.610)
–0.203
(0.222)
–0.0939**
(0.041)
0.128***
(0.022)
-0.346***
(0.065)
–0.178
(0.716)
–0.653***
(0.177)
0.421***
(0.158)
–0.00940
(0.152)
–0.110
(0.153)
1.154***
(0.220)
–0.489***
(0.138)
0.00500
(0.123)
0.0587
(0.059)
Lagged
interest rates
0.898***
(0.015)
0.932***
(0.020)
0.892***
(0.025)
0.846***
(0.021)
0.799***
(0.032)
0.951***
(0.008)
0.976***
(0.010)
0.916***
(0.029)
0.913***
(0.013)
0.953***
(0.018)
0.820***
(0.012)
0.733***
(0.032)
0.959***
(0.023)
0.927***
(0.029)
0.916***
(0.015)
0.759***
(0.020)
0.828***
(0.022)
0.972***
(0.014)
0.898***
(0.016)
0.848***
(0.055)
0.873***
(0.019)
0.904***
(0.027)
0.832***
(0.030)
0.908***
(0.018)
0.905***
(0.022)
0.931***
(0.016)
Constant
1.330
(1.342)
4.537***
(1.060)
6.457***
(1.355)
3.781***
(0.327)
5.376***
(0.530)
–0.349
(0.935)
4.605**
(1.801)
3.787***
(0.864)
4.182***
(1.020)
5.767***
(0.212)
7.042***
(0.237)
13.38***
(1.748)
7.569**
(3.116)
1.959
(2.000)
1.458***
(0.304)
3.262***
(0.148)
4.929***
(0.190)
10.30***
(2.380)
10.08***
(0.894)
2.792*
(1.627)
1.454**
(0.737)
10.84***
(3.143)
2.126*
(1.148)
1.529***
(0.517)
3.950***
(1.326)
0.846
(2.688)
Overidentification
test
Trade openness
X/GDP
J = 11.61, χ 2(15)
p-value = 0.708
J = 10.65, χ 2(15)
p-value = 0.777
J = 7.55, χ 2(15)
p-value = 0.951
J = 8.33, χ 2(15)
p-value = 0.910
J= 6.59, χ 2(15)
p-value = 0.968
J = 7.81, χ 2(15)
p-value = 0.931
J = 9.89, χ 2(15)
p-value = 0.827
J = 9.09, χ 2(15)
p-value = 0.873
J = 7.51, χ 2(15)
p-value = 0.942
J = 7.00, χ 2(15)
p-value = 0.958
J = 5.95, χ 2(15)
p-value = 0.981
J = 8.83, χ 2(15)
p-value = 0.886
J = 7.94, χ 2(15)
p-value = 0.926
J = 10.10, χ 2(15)
p-value = 0.814
J = 11.15, χ 2(15)
p-value = 0.742
J = 7.38, χ 2(15)
p-value = 0.946
J = 6.68, χ 2(15)
p-value = 0.966
J = 11.69, χ 2(15)
p-value = 0.703
J = 6.39, χ 2(15)
p-value = 0.972
J = 7.30, χ 2(15)
p-value = 0.949
J = 6.86, χ 2(15)
p-value = 0.962
J = 11.22, χ 2(15)
p-value = 0.74
J = 8.53, χ 2(15)
p-value = 0.901
J = 9.53, χ 2(15)
p-value = 0.848
J = 7.68, χ 2(15)
p-value = 0.936
J = 10.73, χ 2(15)
p-value = 0.772
0.172
0.339
0.249
0.377
0.328
0.490
0.390
0.220
0.567
0.338
0.146
0.299
0.334
0.205
0.115
0.384
0.548
0.396
0.304
0.257
0.521
0.260
0.196
0.463
0.235
0.093
NOTE: *, **, and *** denote 10 percent, 5 percent, and 1 percent statistical significance, respectively. The coefficients on expected inflation, the
–
output gap, and lagged interest rates correspond to β, γ, and ρ1 + ρ2 , respectively, from equation (4). The constant corresponds to R – βπ *. Standard
errors are in parentheses.
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Table 5
Monetary Policy and Trade Openness: The Taylor Rule with the Real Exchange Rate
With Taylor rule coefficient
significant at 10%
All countries
(1)
(2)
(3)
(4)
–0.332
(0.992)
–1.123
(0.642)
Dependent Variable: The Taylor Rule Coefficient on Expected Inflation
X/GDP
–1.200
(1.163)
–1.541
(1.042)
0.335**
(0.140)
GDP per capita
0.574***
(0.0940)
Constant
0.837*
(0.418)
–2.331*
(1.280)
0.751
(0.442)
R2
0.033
0.118
0.003
0.302
26
26
18
18
4.148
(3.288)
4.731
(3.831)
No. of countries
–4.509***
(0.906)
Dependent Variable: The Taylor Rule Coefficient on the Output Gap
X/GDP
0.919
(1.611)
1.269
(1.655)
–0.343
(0.303)
GDP per capita
–0.234
(0.371)
Constant
0.834
(0.790)
4.080
(3.256)
0.440
(1.291)
2.505
(3.072)
R2
0.003
0.016
0.031
0.036
26
26
15
15
No. of countries
Dependent Variable: The Taylor Rule Coefficient on the Real Exchange Rate
X/GDP
–1.630***
(0.579)
–1.548**
(0.558)
–2.480**
(1.113)
–0.0808
(0.175)
GDP per capita
–2.348*
(1.083)
–0.122
(0.356)
Constant
0.389
(0.229)
1.154
(1.765)
0.746
(0.512)
1.877
(3.494)
R2
0.171
0.185
0.251
0.268
26
26
13
13
No. of countries
Dependent Variable: The Taylor Rule Coefficient on Interest Rate Lags
X/GDP
0.0109
(0.0732)
–0.0396
(0.0648)
0.0109
(0.0732)
0.0496***
(0.0163)
GDP per capita
–0.0396
(0.0648)
0.0496***
(0.0163)
Constant
0.885***
(0.0241)
0.415**
(0.164)
0.885***
(0.0241)
0.415**
(0.164)
R2
0.001
0.348
0.001
0.348
26
26
26
26
No. of countries
NOTE: *, **, and *** denote 10 percent, 5 percent, and 1 percent statistical significance, respectively. Standard errors
are in parentheses. GDP per capita denotes the natural logarithm of the GDP per capita variable.
Federal Reserve Bank of St. Louis REVIEW
Second Quarter 2019
109
Leibovici
to countries with Taylor rule coefficients that are statistically significant at the 10 percent level
and control for GDP per capita. This evidence shows that including the real exchange rate as
part of the Taylor rule fundamentally affects the differential response to changes in expected
inflation between open and closed economies estimated in the previous section. This evidence
also suggests that differences in the responses to the real exchange rate may be a fundamental
dimension along which these economies differ in the conduct of monetary policy.
6.2.2 Output Gap. The second panel of Table 5 reports the results of regressing the
country-specific output gap Taylor rule coefficients on each country’s aggregate exports-toGDP ratio. In contrast to the results presented in the previous section, I now find that open
economies are estimated to assign a relatively higher weight on changes in the output gap;
however, these estimates are statistically insignificant at the 10 percent level in all the specifications considered. Thus, I conclude that open economies do not systematically respond differently from closed economies to changes in the output gap.
6.2.3 Real Exchange Rate. The third panel of Table 5 reports the results of regressing
the country-specific real exchange rate Taylor rule coefficients on each country’s aggregate
exports-to-GDP ratio. First, I find that open economies assign a lower (or more negative)
weight on changes in the real exchange rate than closed economies do. And, moreover, I find
that this relationship is statistically significant in all the specifications considered.
To quantify the economic importance of this relationship, I restrict attention to the
results reported in column 4, where I control for GDP per capita and consider only Taylor
rule coefficients that are statistically significant at the 10 percent level. On the one hand, consider that the average Taylor rule coefficient on the real exchange rate in this specification is
equal to –0.11. On the other hand, note that changing the aggregate exports-to-GDP ratio
from its lowest to highest value across countries (from 0.093 to 0.567) is associated with a
decrease in the value of the Taylor rule coefficient equal to –1.11. This decrease suggests that
open economies respond to a significantly larger extent to deviations of the real exchange rate
from its trend than closed economies do. In particular, open economies are more likely to
decrease the nominal interest rate when the real exchange rate is relatively appreciated (that
is, when the real exchange rate is above trend).
6.2.4 Lagged Interest Rates. Finally, the bottom panel of Table (5) reports the results of
regressing the country-specific sum of the interest rate lags of the Taylor rule on each country’s
aggregate exports-to-GDP ratio. As in the previous section, I find that there is no systematic
relationship between the degree of a country’s trade openness and the extent to which that
country smooths interest rate adjustments over time in any of the specifications considered.
Yet, as in the previous section, I find that richer economies smooth their nominal interest
rate adjustments relatively more than poorer ones.
7 CONCLUSION
In this article, I study the extent to which open economies conduct monetary policy
differently from closed economies. To do so, I apply the estimation approach of Clarida, Galí,
and Gertler (1998 and 2000) to estimate country-specific Taylor rules for 26 economies and
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Federal Reserve Bank of St. Louis REVIEW
Leibovici
then examine whether open economies assign systematically different weights to changes in
inflation and the output gap than their closed-economy counterparts do. I find that, indeed,
open economies respond less strongly to changes in expected inflation than closed economies
do; in contrast, I find that the response to changes in the output gap is independent of the
degree of trade openness.
Moreover, I find that this difference between closed and open economies may be
accounted for by the higher response of open economies to changes in the real exchange
rate. Recomputing the analysis by extending the Taylor rule to allow nominal interest rates
to respond to movements in the real exchange rate, I find that open economies no longer
assign a systematically lower weight to inflation as closed economies do. Instead, I find that
open economies respond more strongly to deviations of the real exchange rate from its trend.
It is important to remark that the analysis conducted in this article is subject to several
caveats. An important one is that I restrict attention to differences in monetary policy as
measured from the lens of the Taylor rule. To the extent that central banks may conduct
monetary policy using instruments and targets that have no impact on the joint time-series
dynamics of nominal interest rates, inflation, and the output gap, such policies would not be
captured by my approach.
One question raised by these findings concerns the optimality of these differences in policymaking. To what extent should open economies indeed conduct monetary policy differently
from closed economies along the dimensions documented in this article? And, if the observed
differences in monetary policy are indeed suboptimal, then to what extent can open economies
achieve better economic outcomes by conducting monetary policy in an optimal fashion?
These are important questions left for further research. n
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NOTES
1
Practically no country in the world can be accurately described to be a fully closed economy, since most countries
trade with other countries to some extent. Nevertheless, throughout the rest of the paper, I sometimes loosely
refer to economies that trade relatively less than others as “closed economies.”
2
A symmetric J × J matrix W is positive definite if the scalar xTWx is positive for every non-zero vector x, where xT is
the transpose of x.
3
All variables used are based on the latest revised data; that is, the analysis is not conducted using real-time data
and is subject to the limitations discussed in Orphanides (2001). Similarly, all filters (e.g., seasonal adjustment,
detrending) applied to the data are based on the full sample and are not estimated on a real-time basis.
4
Thus, the variables that I use need not correspond exactly to the variables targeted by each of the country-specific
central banks, even for countries in which monetary policy may be characterized as following a Taylor rule.
5
For more information, see IMF (n.d.).
6
The GDP deflator is typically not the main variable used by central banks across the world, such as the Federal
Reserve or European Central Bank, to measure inflation. Yet, in this article I restrict attention to measuring inflation based on the GDP deflator to maximize the cross-country comparability of the inflation measure.
7
Results are robust to other detrending procedures, such as computing the output gap as the cyclical deviation of
real GDP from a Hodrick-Prescott trend with a smoothing parameter of 1,600.
8
Downloaded directly from the BIS website: https://www.bis.org/statistics/eer.
9
While there are data available extending beyond 2006, I restrict attention to the pre-Great-Recession period to
abstract from the measurement and modeling issues that would be introduced by having to deal with monetary
policy at the zero lower bound.
10 For each country, I select the real exchange rate series used in the analysis as follows: (i) I use IMF data if there are
at least 36 consecutive quarters available; (ii) otherwise, I use the BIS narrow real exchange rate data if there are at
least 36 consecutive quarters available, (iii) otherwise, I use the OECD data if there are at least 36 consecutive
quarters available; (iv) otherwise, I use the BIS broad real exchange rate data if there are at least 36 consecutive
quarters available, and (v) otherwise, I exclude the country from the analysis.
11 These values correspond to the estimates from the second row of Table III in Clarida, Galí, and Gertler (2000).
12 Throughout the rest of the paper I refer to “not statistically different from zero” if a coefficient is not statistically
significant at the 10 percent level.
13 I interpret the estimated Taylor rule coefficients as empirical moments informative about the comovement
among nominal interest rates with expected inflation, the output gap, and lagged nominal rates. Thus, for
instance, I interpret negative and insignificant values of the Taylor rule coefficients as informative about the way
in which a country conducts monetary policy, regardless of whether the country follows a Taylor rule or some
other monetary policy regime.
14 Note that the Taylor rule coefficients estimated in the previous section are estimated with uncertainty. I abstract
from this source of uncertainty when computing the standard errors reported in Table 3.
15 I measure the real exchange rate using the variables described in Section 4.2.
16 I also include four lags of this variable as additional instruments.
17 Note that a negative coefficient on the real exchange rate implies that a depreciated real exchange rate (a low
value of the real exchange rate relative to trend) is associated with a higher nominal interest rate; similarly, a positive coefficient implies that a depreciated real exchange rate is associated with a lower nominal interest rate.
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REFERENCES
Basilio, J.R. “Empirics of Monetary Policy Rules: The Taylor Rule in Different Countries.” Ph.D. thesis, University of
Illinois at Chicago, 2013.
Berument, H.; Konac, N. and Senay, O. “Openness and the Effectiveness of Monetary Policy: A Cross-Country
Analysis.” International Economic Journal, 2007, 21(4), pp. 577-91; https://doi.org/10.1080/10168730701699018.
Clarida, R.; Galí, J. and Gertler, M. “Monetary Policy Rules in Practice Some International Evidence.” European
Economic Review, 1998, 42(6), pp. 1033-67; https://doi.org/10.1016/S0014-2921(98)00016-6.
Clarida, R.; Galí J. and Gertler, M. “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.”
Quarterly Journal of Economics, 2000, 115(1), pp. 147-80; https://doi.org/10.1162/003355300554692.
Clarida, R.; Galí J. and Gertler, M. “A Simple Framework for International Monetary Policy Analysis.” Journal of
Monetary Economics, 2002, 49(5), pp. 879-904; https://doi.org/10.1016/S0304-3932(02)00128-9.
Corsetti, G.; Dedola L. and Leduc, S. “Optimal Monetary Policy in Open Economies,” in B.M. Friedman and M.
Woodford, eds., Handbook of Monetary Economics. Volume 3. North-Holland, 2010, pp. 861-933;
https://doi.org/10.1016/B978-0-444-53454-5.00004-9.
De Paoli, B. “Monetary Policy and Welfare in a Small Open Economy.” Journal of International Economics, 2009,
77(1), pp. 11-22; https://doi.org/10.1016/j.jinteco.2008.09.007.
Faia, E. and Monacelli, T. “Optimal Monetary Policy in a Small Open Economy with Home Bias.” Journal of Money,
Credit, and Banking, 2008, 40(4), pp. 721-50; https://doi.org/10.1111/j.1538-4616.2008.00133.x.
Hayo, B. and Hofmann, B. “Comparing Monetary Policy Reaction Functions: ECB versus Bundesbank.” Empirical
Economics, 2006, 31(3), pp. 645-62; https://doi.org/10.1007/s00181-005-0040-7.
International Monetary Fund. “What Is the Central Bank Policy Rate?” N.d.; http://datahelp.imf.org/knowledgebase/articles/484375-what-is-the-central-bank-policy-rate, accessed December 10, 2018.
Kahn, G.A. “Estimated Rules for Monetary Policy.” Federal Reserve Bank of Kansas City Economic Review, 2012, p. 5;
https://www.kansascityfed.org/publicat/econrev/pdf/12q4Kahn.pdf.
Leibovici, F. and Santacreu, A.M. “International Trade Fluctuations and Monetary Policy.” Working paper, 2015.
Lombardo, G. and Ravenna, F. “Openness and Optimal Monetary Policy.” Journal of International Economics, 2014,
93(1), pp. 153-72; https://doi.org/10.1016/j.jinteco.2014.01.011.
Lubik, T.A. and Schorfheide, F. “Do Central Banks Respond to Exchange Rate Movements? A Structural Investigation.”
Journal of Monetary Economics, 2007, 54(4), pp. 1069-87; https://doi.org/10.1016/j.jmoneco.2006.01.009.
Orphanides, A. “Monetary Policy Rules Based on Real-Time Data.” American Economic Review, 2001, 91(4), pp. 964-85;
https://doi.org/10.1257/aer.91.4.964.
Taylor, J.B. “Discretion versus Policy Rules in Practice.” Carnegie-Rochester Conference Series on Public Policy, 1993,
39, pp. 195-214; https://doi.org/10.1016/0167-2231(93)90009-L.
Torres, A. “Monetary Policy and Interest Rates: Evidence from Mexico.” North American Journal of Economics and
Finance, 2003, 14(3), pp. 357-79; https://doi.org/10.1016/j.najef.2003.08.001.
Yazgan, M. Ege and Yilmazkuday, H. “Monetary Policy Rules in Practice: Evidence from Turkey and Israel.” Applied
Financial Economics, 2007, 17(1), pp. 1-8; https://doi.org/10.1080/09603100600606206.
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The Real Term Premium in a Stationary Economy
with Segmented Asset Markets
YiLi Chien and Junsang Lee
This article proposes a general equilibrium model to explain the positive and sizable term premia
implied by the data. The authors introduce a slow mean-reverting process of consumption growth
and a segmented asset-market mechanism with heterogeneous trading technologies into an otherwise
standard heterogeneous agent general equilibrium model. First, the slow mean-reverting consumption
growth process implies that the expected consumption growth rate is only slightly countercyclical
and the process can exhibit near-zero first-order autocorrelation, as observed in the data. This slight
countercyclicality suggests that long-term bonds are risky, and hence the term premia should be positive. Second, the segmented asset-market mechanism amplifies the magnitude of the term premia
because aggregate risk is highly concentrated in a small fraction of marginal traders who demand
high compensation for taking risk. For sensitivity analysis, the role of each assumption is further
investigated by removing each factor one at a time. (JEL G11, G12, E30)
Federal Reserve Bank of St. Louis Review, Second Quarter 2019, 101(2), pp. 115-34.
https://doi.org/10.20955/r.101.115-34
1 INTRODUCTION
The positive and sizable term premia observed in the data have been hard to reconcile
using a standard structural macroeconomic model. Backus, Gregory, and Zin (1989) demonstrate the failure of a standard model in accounting for the sign and the magnitude of real
bond risk premia. Campbell (1986), Donaldson, Johnsen, and Mehra (1990), and den Haan
(1995) also experience the same difficulty with standard macroeconomic models.1
Although equilibrium models are difficult to work with and have limited success, it is
still important to try to understand the fundamental mechanisms behind positive and sizable
term premia. For macroeconomists, the disconnect between the observed term premia in the
data and what a standard structural macroeconomic model predicts is often referred to as
the “term premium puzzle.” The issue is also important to central bankers. As pointed out by
YiLi Chien is an economist and research officer at the Federal Reserve Bank of St. Louis. Jungsang Lee, the corresponding author, is an associate
professor at Sungkyunkwan University, Seoul, Korea.
© 2019, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses,
and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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Wright (2011), the term premia represent the relationship between the short rate, which is
controlled by central banks, and the long rate, which relates more deeply to real economic
activities. Hence, understanding the term premia helps central bankers evaluate the effectiveness of monetary policy and the mechanism behind its effects on the real economy. Finally,
for investors, it is of utmost importance to understand term premia—to hedge against interest
rate risk.
A standard macroeconomic model with the pricing kernel or the stochastic discount factor
derived from a utility maximization problem generally has great difficulty matching the slope
and the level of the term structure. Campbell (1986) shows that the term premium depends
on the nature of the consumption growth process. If the consumption growth process is positively autocorrelated, then the expected future growth rate falls and bond prices rise in a
recession. The long-term bond then becomes a good hedge, and hence the term premium is
negative. On the other hand, if the consumption growth rate is negatively autocorrelated,
then the model predicts a positive term premium since the long-term bond becomes risky
because of its procyclical pricing. This intuition together with near-zero autocorrelation of
consumption growth, that is, a random walk in empirical studies, implies that the term premium should be close to zero when the pricing kernel is derived from a standard macroeconomic model.
In addition, it is also well known that the pricing kernel of a standard model, which relies
purely on the expected aggregate consumption growth rate, is not volatile enough to deliver
a high market price of risk. Therefore, the standard model not only fails to match the sign of
the term premium but also fails to generate the correct magnitude of the term premium.
In this article, we assume that the aggregate consumption process is trend stationary
with a long memory process, which shows near zero but slightly negative autocorrelation of
the consumption process. This consumption process alone generates positive term premia
but with very small magnitude. This process is not easily statistically distinguished from a
difference-stationary process such as the random walk. This view is supported by Christiano
and Eichenbaum (1990,) who argue that no clear statistical evidence exits to support either a
trend-stationary or a difference-stationary process of aggregate consumption. More specifically, we consider a slow trend-reverting aggregate consumption process in our model economy and hence the level of consumption can be well above or below its long-run trend for an
extended period. With this process, when a bad shock is realized, the expected growth rate of
consumption is only slightly higher because of its slow mean-reverting property. Therefore,
the expected growth rate of consumption is only slightly countercyclical and the autocorrelation of consumption growth between two consecutive periods could be very close to zero but
slightly negative (only –0.02 in our calibrated model), which is consistent with the randomwalk-like consumption process in the data.
Following Chien, Cole, and Lustig (2011), there is a segmented asset-market mechanism
in our model. Specifically, the model features a large fraction of households who do not participate in the equity market and hence do not bear any aggregate risk. There is, however, a
small fraction of households who do participate in the equity market and hence bear a great
amount of aggregate risk, which in this article results in a high market price of risk. In equi116
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librium, those households demand high risk compensation. As a result, high risk premia are
obtained not only in equities but also reflected onto long-term bonds. Therefore, the segmented
market mechanism amplifies the size and the magnitude of the term premia.
Our calibrated model considers not only the segmented asset-market mechanism but also
the asymmetric bond positions of U.S. households. The data on U.S. households show that a
large fraction of households carry long-term mortgage loans but save in short-term risk-free
assets, such as checking or savings accounts. In other words, these households essentially
borrow in long-term bonds by using housing as a collateral and save in short-term bonds. In
our calibrated model, we also evaluate the extent to which this asymmetric bond position of
households matters for term premia quantitatively.
The assumptions in our model are built with solid support from empirical evidence. The
first assumption, of a mean-reverting consumption growth process, is prevalent in the macro
economics literature. The growth of aggregate variables, such as output or consumption, is
often decomposed into trend components and cyclical components (business cycles). Such a
decomposition is consistent with the mean-reverting assumption. The second assumption,
of a segmented market mechanism, is firmly grounded in empirical evidence from the household finance literature. The evidence shows that most households do not purchase most of
the assets available to them (Guiso and Sodini, 2012). In fact, the composition of household
asset holdings varies greatly across households, even in a developed country such as the United
States. Only 50 percent of U.S. households participate in the equity market, according to the
2010 Survey of Consumer Finance (SCF hereafter) data. Moreover, even among the participants in the equity market, many investors still hold low-risk portfolios and do not adjust
their portfolios frequently.2 On the other hand, a small fraction of households actively adjust
their portfolios and earn a higher return by taking more aggregate risk. The SCF data also show
that a large fraction of households carry mortgage loans and save in short-term safe assets.
These households effectively have a long position in short-term bonds and a short position in
long-term bonds. As the data also show, wealthier households, a relatively small fraction of
all households, tend to hold a higher fraction of long-term bonds in their portfolios.
Only a handful of structural models in the literature are able to deliver an average upward-
sloping nominal and/or real yield curve. Many of them modify household preferences into
various forms in the standard macroeconomic model. Piazzesi and Schneider (2007) demonstrate that the nominal yield curve can be upward sloping even with a flat or downward-sloping
real yield curve since a low-frequency negative correlation between consumption growth
and the inflation rate causes inflation risk. They assume a recursive preference, and hence
agents are very willing to substitute consumption over time even though they are risk averse.
The recursive preference plays a critical role in the low-frequency correlation mattering for
the current price. Bansal and Shaliastovich (2013) also generate a positive nominal term premium with inflation risks and recursive preferences. Rudebusch and Swanson (2012) further
extend the endowment economy model to a production economy general equilibrium model.
By introducing inflation ambiguity into a representative agent model, Ulrich (2013) explains
the upward-sloping nominal yield curve with a log utility function. Our work is complementary to the existing papers discussed above since we focus on the real term premia rather than
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the nominal premia. Wachter (2006) uses a habit-persistence model to explain both the positive real and nominal bond premia. To maintain the consumption level, investors tend to sell
long-term bonds during recessions and vice versa during expansions. Namely, the demand
for long-term bonds is procyclical, which makes the bond price procyclical and hence the longterm bond itself a risky asset. Rudebusch and Swanson (2012) find that the habit-formation
mechanism in Wachter (2006) fails to generate a sizable term premia without distorting the
behavior of other macroeconomics variables.
Our benchmark model generates a high and volatile equity premium with a 7.26 percent
mean and a 15.63 percent standard deviation, as well as a low and stable risk-free return with
a 0.95 mean and a 1.45 percent standard deviation—estimates quite close to those in the asset-
pricing literature. Most importantly, our quantitative result also predicts a high real term
premium: 1.92 percent for 30-year zero-coupon bonds. This article delivers a reasonable term
premium result, with a risk aversion coefficient of 4. For the sensitivity analysis, we further
investigate the role of our assumptions by removing each factor one by one.
Our main contribution to the literature is to provide a simple and intuitive story that can
reconcile the puzzling disconnect between asset prices, equity and term premia in particular,
and aggregate macroeconomic variables. The model in this article integrates the empirical
facts of heterogeneous portfolios across households, as found in the household finance literature, and a mean-reverting aggregate consumption process, as found in the macroeconomics
literature, to explain the real term-premia puzzle. Our model successfully delivers a positive
sign for and significant magnitude of the real term premia. Specifically, we demonstrate the
importance of the household portfolio heterogeneity documented in the macro-finance literature, while the majority of asset-pricing models rely on a representative agent framework
with modifications to preferences.
2 THE MODEL
We consider an endowment economy in which households sequentially trade assets and
consume. Two features distinguish our model from the standard model. First, our endowment
(consumption) growth follows a slow mean-reverting process. After the realization of a bad
endowment shock, the expected consumption growth rate edges up only slightly because of
the trend-reverting property, which makes the autocorrelation of the consumption growth
process slightly negative but very close to zero. Hence, our shock process is consistent with
the empirical fact that consumption growth is well approximated by the random walk.
The second key feature of our model is that it exhibits ex-ante heterogeneity in the trading
technologies. The trading technologies are modeled on the menu of assets, specifically by
exogenously restricting the portfolios a household can trade and hold. The goal of these
restrictions is to capture the observed portfolio behavior of most households. In our calibrated
model, this form of ex-ante heterogeneity delivers a high market price of risk and hence helps
to deliver sizable term premia.
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2.1 The Environment
There is a unit measure of households subject to both aggregate endowment growth risks
and idiosyncratic income shocks. Households are ex-ante identical except for the trading
technologies that they are endowed with. Ex post, these households differ in terms of their
idiosyncratic income-shock realizations. All households face the same stochastic process for
idiosyncratic income shocks, and all households start with the same present value of wealth.
In the model, time is discrete, infinite, and indexed by t = 0,1,2,… The first period, t = 0,
is a planning period in which all trading takes place. We assume constant average growth of
the endowment process and a transitory shock that makes the actual level of aggregate consumption deviate from its long-term trend. More specifically, let mt be the percentage deviation
of aggregate endowment from the growth trend. Then, the total endowment in period t,
denoted by Yt , is
lnYt = tln g + mt ,
where g– is the average growth rate of the endowment. The output growth process is therefore
affected by the evolution of mt, which is assumed to follow an AR(1) process:
(
)
mt+1 = ρmt + ε t+1 , ε t+1 ∼ N 0,σ ε2 .
With this specification of the endowment shock process, the growth rate of output, denoted
Y
by g t+1 ≡ t+1 , is therefore given by
Yt
(1)
ln
Yt+1
≡ ln g t+1 = ln g + ( ρ −1)mt + ε t+1 .
Yt
If ρ is 1, then the endowment process follows a random walk with drift, a difference-stationary
process. If ρ is less than 1 but close to 1, then the endowment slowly reverts to trend, a trend-
stationary process (a long-memory property). As mentioned in the Introduction, there is no
clear evidence in favor of either a trend-stationary or difference-stationary process for macro
economic variables, such as consumption or output. Our model follows the view of a trend-
stationary endowment process with long memory. Hence, the value of ρ is set to 0.95 in the
calibration.
Let zt denote the history of aggregate states up to period t, and hence let Yt(zt ) denote the
aggregate endowment is period t. In addition, aggregate endowment each period is divided
into two parts: diversifiable income and nondiversifiable income. Claims to diversifiable
income can be traded in financial markets, while claims to nondiversifiable income cannot.
We assume a constant share of nondiversifiable income, denoted by γ (0,1). The nondiversifiable component is subject to idiosyncratic stochastic shocks, denoted by ηt . Nondiversifi
able household income is denoted by γYt(zt )ηt .
Similarly, let ηt denote the history of idiosyncratic shocks up to period t. In addition, we
use π(zt ,ηt ) to denote the unconditional probability of state (zt ,ηt ) being realized. The idioFederal Reserve Bank of St. Louis REVIEW
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syncratic shock events are governed by a first-order Markov process, and their probabilities
are assumed independent between z shocks and η shocks:
(
)
π z t+1 ,η t+1 z t ,η t = π ( zt+1 z t )π (ηt+1 η t ) .
Since we can appeal to the law of large numbers, π(ηt ) also denotes the fraction of agents
in state zt that have drawn the history ηt . We introduce some additional notation: z t+1 zt or
η t+1 ηt means that the left-hand-side node is a successor node to the right-hand-side node.
We denote by {zτ zt } the set of successor aggregate histories for zt , including those many
periods in the future; ditto for {ητ η t }. When we use , we include the current nodes zt or
η t in the set.
All households live for infinite periods and rank a stream of consumption according to
the following criterion:
(2)
U ({c}) =
1
∞
∑ β t 1− α ct ( z t ,η t ) π ( z t , η t ) ,
(
t ≥1, z t , η t
1−α
)
where α denotes the coefficient of relative risk aversion, β denotes the time discount factor,
and ct(zt ,η t ) denotes household consumption in state (zt ,η t ).
In this economy, there are four type of assets available: state-contingent claims on aggregate shocks, a long-term bond (consol) with a constant stream of payments, risky equities,
and one-period risk-free bonds. Note that the market is incomplete in our environment since
there is no state-contingent claims available for idiosyncratic shocks. Equity is assumed to be
a leveraged aggregate output process, with dividend growth determined by
ΔlnDt+1 = Et ( ΔlnYt+1 ) + φ ⎡⎣ ΔlnYt+1 − Et ( ΔlnYt+1 ) ⎤⎦ ,
where ϕ is the leverage ratio, which is assumed constant over time. Finally, we denote the
value of total equity by Vt (zt ). The gross returns of leveraged equity, or Ret,t–1(zt ), are given by
(3)
e
Rt,t−1
( z ) = (V )( z () ) .
t
Dt z t +Vt z t
t−1
t−1
2.2 Heterogeneity in Trading Technologies
To match the size of the term premium, we introduce the segmented market mechanism,
in particular portfolio heterogeneity at the household level. As mentioned in the Introduction,
heterogeneity in portfolio choices is widely supported by the data. As we demonstrate later,
the concentration of a large portion of aggregate risk in a relatively small fraction of households amplifies the price of risk in the calibrated model. Without such a mechanism, the model
fails to match the size of the term premium quantitatively. To capture such portfolio heterogeneity, we adopt the approach by Chien, Cole, and Lustig (2011), which exogenously imposes
different restrictions on investors’ portfolio choices. These restrictions apply to the menu of
assets that households can trade as well as to the composition of households’ portfolios.
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There are two classes of investors in terms of their asset-trading technologies: Mertonian
traders and non-Mertonian traders. Mertonian traders face no restrictions on their portfolio
choices and hence a menu of tradable assets. Specifically, they are capable of trading a complete set of contingent claims on the aggregate endowment. They optimally adjust their portfolio choices in response to changes in the set of investment opportunities. Therefore, they
act as market arbitrageurs and price aggregate risk in our model.
Non-Mertonian traders face restrictions on their portfolio choices. Specifically, their
portfolio composition is restricted to be constant over time. There are two types of non-
Mertonian traders: The first type, non-Mertonian equity investors, can trade equities, riskfree bonds, and long-term bonds but not state-contingent claims on aggregate shocks. The
second type, nonparticipants, do not hold equity but invest only in risk-free bonds and console bonds. Even though the portfolio composition of non-Mertonian traders is exogenously
given, they can still choose how much to save and consume.
Non-Mertonian investors deviate from the optimal portfolio choice in two dimensions:
First, they cannot change the share of equities, long-term bonds, or short-term bonds in their
portfolios in response to changes in the market price of risk, which indicates missed market
timing. Second, their portfolio share in each asset might deviate from the optimal share on
average, implying that their average exposure to aggregate risk might not be optimal. We
denote the measure of different types of households by μj , where j {me,et,np} represents
Mertonian investors, non-Mertonian equity investors, and non-Mertonian nonparticipants,
respectively.
2.3 The Household’s Problem
2.3.1 Budget Constraints of Mertonian Traders. Consider a Mertonian trader entering
the period with net financial wealth at(zt ,η t–1) given the event history (zt ,η t–1). Note that net
financial wealth is not spanned by the realization of idiosyncratic shocks, ηt , since there are
no contingent claims on idiosyncratic shocks. At the end of the period, Mertonian traders
buy shares of equities st(zt ,η t ), one-period risk-free bonds bt(zt ,η t ), long-term consol bonds
bct (zt ,η t ), and state-contingent claims, ât(zt ,η t–1) in financial markets, and consumption
ct(zt ,η t ) in the goods markets is subject to the following one-period budget constraint:
(4)
(
) ( ) (
)
(
)
(
) (
) (
st z t ,η t Vt z t + bt z t ,η t + btc z t ,η t + ∑ Q z t+1 z t ât+1 z t+1 ,η t + ct z t ,η t
(
)
( )
z t+1
)
≤ at z t ,η t−1 + γ Yt z t η t , for all z t ,η t ,
where Q(z t+1|zt ) denotes the state-contingent price of a unit contingent claim to the consumption good in aggregate state z t+1 acquired in aggregate state zt . The agent’s net financial wealth,
at(zt ,η t–1), in state (zt ,η t ) is given by the payoff from the agent’s portfolio last period:
(5)
(
) (
( z )b ( z
) ( ) ( )
) + â ( z ,η ),
( ) (
f
at zt ,η t−1 = st−1 z t−1 ,η t−1 ⎡⎣ Dt z t +Vt z t ⎤⎦ + Rt,t−1
z t−1 bt−1 z t−1 ,η t−1
c
+Rt,t−1
t
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t−1
t−1
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t
t
)
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f
where Rct,t–1(zt ) and R t,t–1
(zt–1) denote the return of a long-term consol bond and a one-period
risk-free bond in period t, respectively. Note that the total equity share of this economy,
st(zt ,η t ), is normalized to 1.
2.3.1 Budget Constraints of Non-Mertonian Traders. The non-Mertonian traders have
no access to state-contingent claims on aggregate shocks and are restricted to fixed portfolio
weights among the equity, short-term risk-free bonds, and long-term consol bonds. At the
end of period t, the households buy equity shares, one-period risk-free bonds, and long-term
consol bonds, subject to a fixed target portfolio equity share and long-bond share, denoted
–e and ω
–c, respectively. As a result, in addition to equations (4) and (5), their constraints
by ω
also include a portfolio restriction,
) ( )
s ( z ,η )V ( z ) + b ( z ,η ) + b ( z ,η )
b ( z ,η )
=
,
s ( z ,η )V ( z ) + b ( z ,η ) + b ( z ,η )
t
t
ω
c
(
st z t ,η t Vt z t
ωe =
t
t
t
t
c
t
t
t
t
t
t
t
t
t
t
c
t
t
t
t
c
t
t
t
t
t
and no access to state-contingent claims
(
)
ât z t ,η t−1 = 0 for all z t and η t−1 .
–e – ω
–c.
The portfolio share of short-term bonds is therefore 1 – ω
Alternatively, we can simplify the budget constraint of non-Mertonian traders as follows:
(
) (
)
( ) (
)
( )
p
ŝt z t ,η t + c z t ,η t ≤ Rt,t−1
z t ŝt−1 z t−1 ,η t−1 + γ Yt z t ηt ,
p
where ŝt denotes the asset holdings at the end of period t. R t,t–1
(zt ) represents the gross return
on the fixed portfolio imposed on the non-Mertonian traders and is given by
(
)
( )
( ) (
)
( )
p
f
e
c
Rt,t−1
z t ,η t = ω e Rt,t−1
z t + ω c Rt,t−1
z t + 1− ω e − ω c Rt,t−1
zt .
–e is zero.
In the case of nonparticipants, ω
Finally, all households are subject to nonnegative net wealth constraints, given by
at(zt ,η t–1) ≥ 0 for Mertonian and ŝt(zt ,η t ) ≥ 0 for non-Mertonian traders. The details of the
household problem and its associated optimal conditions are provided in Appendix A.1.
2.4 The Competitive Equilibrium
The competitive equilibrium for this economy is defined in the standard way. It consists
of a consumption allocation, allocations of state-contingent claims, one-period risk-free bonds,
long-term consol bonds, and equity choices as well as a list of prices such that (i) given these
prices, households’ assets and consumption choices maximize the households’ expected utility
subject to the budget constraints, the solvency constraints, and the constraints on their portfolio choices and (ii) all asset markets clear.
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3 QUANTITATIVE RESULTS
This section performs a quantitative exercise of our model. The next two subsections
explain how we calibrate idiosyncratic shocks and aggregate shocks as well as the pool of
traders in the benchmark case. Next, we briefly describe the real Treasury yields observed in
the data. Finally, we report our benchmark asset-pricing quantitative results, especially the
size of the real term premia, in Subsection 3.4.
3.1 Calibration
The calibration of aggregate shocks is critical to our results. The aggregate endowment
process is assumed to have a constant growth trend and an innovation term that makes the
realization of output deviate from its trend:
lnYt = t ln g + mt ,
where g– is the average growth rate of the endowment and the deviation from trend is captured
by a variable m, which is assumed to follow the AR(1) process
(
)
mt+1 = ρmt + ε t+1 , ε t+1 ∼ N 0,σ ε2 .
We use a two-state Markov process to approximate the independent and identically distributed innovation εt . More specifically, since expansions occur more often than recessions, the
probability of a good innovation shock is set to 27.4 percent, as in Alvarez and Jermann (2001).
However, the expected endowment growth rate in each period depends on how far the current
consumption level has deviated from its trend, which depends on the whole past history of
innovation shocks. In computation, we therefore have to keep track of one extra state variable,
m, in order to compute the conditional expected growth rate.
Our model operates at an annual frequency. The average aggregate consumption growth
rate g– is set to 1.8 percent with a standard deviation of 3.15 percent. Given that the aggregate
consumption growth data are well approximated by the random walk in the short run, the
persistency of m has to be high. We set ρ = 0.95, which makes the consumption growth autocorrelation of –0.02 sufficiently close to zero.
We also consider a two-state first-order Markov chain for idiosyncratic shocks. The first
state is low and the second state is high. Following Alvarez and Jermann (2001) and Storesletten,
Telmer, and Yaron (2004), we calibrate the shock process by two moments: the standard
deviation of idiosyncratic shocks and the first-order autocorrelation of the shocks, except we
eliminate the countercyclical variation in idiosyncratic risk. The Markov process for the log
of the nondiversified income share, lnη, has a standard deviation of 0.71 and an autocorrelation of 0.89. The transition probability is denoted by
⎡ 0.945 0.055 ⎤
π (η ′ η ) = ⎢
⎥.
⎣ 0.055 0.945 ⎦
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The two states of the idiosyncratic shock, for which the mean is normalized to 1, are
ηL = 0.3894 and ηH = 1.6106.
All households have the identical constant relative risk aversion preference. In our calibration, there are strong incentives for household to save because of idiosyncratic shocks in
an incomplete-market environment, which causes the risk-free rate to be lower than the reciprocal of the preference discount factor β, even in a growing economy As a result, we set the
time discount factor to β = 0.95 to match the low risk-free rate in our benchmark model. The
risk-aversion rate α is set to 4 to produce a high risk premium in our benchmark calibration.
Following Mendoza, Quadrini, and Rios-Rull (2009), the fraction of nondiversifiable output is set to 88.75 percent. As shown in Section 2, equity in our model is simply a leveraged
claim to the diversifiable income process. Following Abel (1999) and Bansal and Yaron (2004),
the leverage ratio parameter is set to 3.
3.2 The Composition of Traders
In the model, 50 percent of U.S. households are stock market nonparticipants, as in the
2010 SCF data. The remaining 50 percent do hold equities, and we divide them into non-
Mertonian equity traders and Mertonian traders as discussed. To match the high risk premia, a
small fraction of Mertonian traders must absorb a large amount of aggregate risk. We therefore
set the fraction of Mertonian traders to 5 percent for our benchmark economy. The remaining
fraction of households, 45 percent, are classified as non-Mertonian equity traders, who can
own constant portfolio shares in short risk-free bonds, long-term risky bonds, and equities.
In addition to the equity market participation rate, the portfolio shares of non-Mertonian
traders are also important parameters. Again, we use the 2010 SCF data to calibrate the portfolio share of non-Mertonian equity traders and non-participants in our model, which account
for 45 percent and 50 percent of the population, respectively.
To identify the portfolio choice of the non-Mertonian equity traders, we must first sort by
equity position the 50 percent of households in the data that hold equities and then compute
the average equity share excluding the top 5 percent of equity holders. The average computed
equity share is 21.1 percent, which we use as the equity share of non-Mertonian equity traders
in the benchmark case. This calibration reflects the observations both from the data and from
our model that more sophisticated households tend to hold larger amounts of equities.
3.3 The Real Yield Curve in the Data
Using the constructed international data on zero-coupon yields, Wright (2011) demonstrates that nominal term premia are estimated to be positive among 10 industrialized countries.
However, we do not observe the real term premium directly from the data and the positive
nominal term premia do not necessarily imply positive real term premia, because of inflation
risk. Strong empirical evidence supporting the real term premia comes from the real Treasury
yield. The average real Treasury yields for 5-year, 7-year, and 10-years maturities are listed in
Table 1 for different sample periods. For 2003 to 2007, the average 5-year, 7-year, and 10-year
real Treasury yields are 1.646 percent, 1.871 percent, and 2.061 percent, respectively, which
indicates a positive real term premium. The real yield data decrease after 2009 as the sample
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Table 1
The Real Treasury Yield
Period/Maturity
5-year
7-year
10-year
2003 to 2007
1.646
1.871
2.061
2003 to 2009
1.513
1.757
1.962
2003 to 2011
1.160
1.452
1.715
2003 to 2013
0.772
1.082
1.367
2003 to 2015
0.658
0.968
1.226
SOURCE: U.S. Department of Treasury; https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realyield.
Table 2
Quantitative Results
Case
Benchmark
No mortgage
No NME
No HTT
RA economy
Mertonian
5%
5%
50%
100%
100%
Non-Mertonian equity
45%
45%
0%
0%
0%
Nonparticipant
50%
50%
50%
0%
0%
ωet
(0.211,–0.195)
(0.211,0)
NA
NA
NA
ωnp
(0,–0.537)
(0,0)
NA
NA
NA
E(R zc30 – R f )
1.924
1.713
0.678
0.427
0.532
σ (Q )
E (Q )
0.475
0.464
0.204
0.135
0.133
⎛ σ (Q ) ⎞
Std ⎜ t
⎝ Et ( Q ) ⎟⎠
9.766
9.494
1.077
0.033
0.000
E(R e – R f )
7.262
6.937
2.602
1.697
1.741
σ (Re − Rf )
E (Re − Rf )
0.465
0.455
0.204
0.135
0.132
E(R f )
0.949
1.206
3.485
3.923
11.714
σ(R f )
1.449
1.296
1.326
1.365
2.049
NOTE: Parameter settings: risk aversion rate, γ = 4; discount factor, β = 0.95; nondiversifiable share of income, γ =0.885;
and leverage ratio: ф = 3. NME, non-Mertonian equity trader. HTT, heterogeneous trading technologies. RA, representative agent. The simulation results are generated by an economy with 3,000 agents and 10,000 periods.
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Figure 1
The Average Real Yield Curve in the Benchmark Case, the Zero-Coupon Bond
Percent
3.5
3.0
2.5
2.0
1.5
1.0
0.5
5
10
15
20
25
30
35
40
45
50
Year
periods become longer. This is because the short-term real rate becomes negative. However,
the sizable positive real term premia implied by the data should remain robust to the different
sample periods.
3.4 Benchmark Results
The benchmark asset-pricing results are shown in the “Benchmark” column in Table 2.
First, we report the real term premia of our model, defined as the average yield difference
between a 30-year and a 1-year zero-coupon bond, denoted by E(R zc30 – R f ). In addition,
Table 2 also includes the market price of risk, σ(Q)/E(Q); the conditional standard deviation
of the market price of risk, std(σ(Q)/E(Q)); the equity premium E(R e – R f ), the Sharpe ratio
on equity returns E(R e – R f )/σ(R e – R f ); the average risk-free rate E(R f ); and the standard
deviation of the risk-free rate σ(R f ).
As explained earlier, the long bond is risky because its price tends to fall during recessions,
which is simply a result of higher expected growth after recessions. In our benchmark case,
the average term premium of a 30-year zero-coupon bond is 1.924 percent. To illustrate the
upward-sloping real yield curve, Figure 1 plots the yield curve of zero-coupon bonds.
In addition, our benchmark economy produces a high and volatile market price of risk
as well as a low and stable risk-free rate. These asset-pricing statistics are hard to match in
standard macroeconomic model, as indicated by Mehra and Prescott (1985). In the benchmark
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case of Table 2, the market price of risk is high, 0.475, and volatile, with a standard deviation
of 9.766 percent. The equity premium reaches 7.262 percent, and the Sharpe ratio on equity
is 0.465. The average risk-free rate is low at 0.949 percent, and its volatility is only 1.449 percent.
Hence, our calibrated model is capable of producing reasonable asset-pricing results. In our
model, the success of matching high-risk premia and low risk-free rates relies on two key
frictions. The first friction is the incomplete market with respect to idiosyncratic risk. It is
well known that incomplete-market models can produce reasonable risk-free rates in a growing economy. The second friction, which is limited participation combined with a relatively
small fraction of Mertonian traders, produces a high equity premium by concentrating aggregate risk on Mertonian traders.
Our results show the mechanism of our model is able to deliver positive term premia of
sufficient magnitude. This success comes from imposing the trend-reverting consumption
process and heterogeneous portfolio choices into an otherwise standard macroeconomic
model. In the next section, we explore the relative importance of these assumptions.
4 TREND REVERTING VERSUS A RANDOM WALK
The trend-reverting endowment process is important to our results. If the endowment
growth process truly follows a random walk, then long-bond returns do not necessarily fall
during recessions and hence the standard model might fail to generate even a positive bond
premium. In this subsection, we demonstrate this point analytically in the representative
agent economy.
Given the assumption of our shock process, the following lemma describes the expression for the term premia as well as its property in a representative agent economy.
Lemma 1. The unconditional expectation of the term premium for a k-period zero-coupon bond is
(6)
⎡ 1 1− ρ 2k ⎤ α 2σ ε2
E ⎡⎣rtk − rt1 ⎤⎦ = ⎢1−
.
2 ⎥
⎣ k 1− ρ ⎦ 2
In addition, the term premium, E[r tk – rtl ] is increasing in k given 0 < ρ < 1.
Proof. Please refer to Appendix Section A.2.
With 0 < ρ < 1 in the representative agent economy, Lemma 1 not only shows a positive
term premium but also shows that the term premium is increasing in k, an indication of an
upward-sloping real yield curve. However, if ρ = 1, the random-walk case, the average term
premium shown in equation (6) becomes zero and independent of k. The independence
implies a flat yield curve.
This result is not surprising in the sense that the autocorrelation of the consumption
growth rate is negative when 0 < ρ < 1 and becomes zero when ρ = 1. This can be seen clearly
⎛ 1− ρ ⎞ 2
from the fact that cov ( ln g t+1, ln g t ) = − ⎜
σ < 0 if ρ < 1. However, if ρ is sufficiently close
⎝ 1+ ρ ⎟⎠
to 1, then the consumption growth correlation is close to zero, which is not far from what we
observe in the data.
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The quantitative results of a representative agent economy with a trend-reverting process
are reported in the “RA economy” column of Table 2. The term premium is positive, as shown
in this subsection. However, the term premium is not sizable, at only 0.487 percent, because
of the absence of a high market price of risk, which drops significantly to only 0.133 from
0.475 in our benchmark economy.
5 INSPECTION OF THE MECHANISM
In our benchmark economy, two features quantitatively contribute to the sizable real term
premia: the heterogeneous trading technologies and the mortgage effects. In this section, we
decompose the contribution of each feature by removing each one from our benchmark
economy.
5.1 No Mortgage Effects
Part of the real bond risk premia could be from the asymmetric bond portfolio holdings
across households, which is motivated by the heterogeneous amounts of mortgages held across
households. Here, we simply shut down this channel by assuming that both nonparticipants
and non-Mertonian equity holders do not have a position on long-term bonds. The “No
mortgage” column of Table 2 reports the results. We find that this asymmetric bond portfolio
channel has minor effects on the market price of risk and equity risk premia. The market price
of risk decreases slightly, from 0.475 to 0.464, as does the standard deviation of the market
price of risk, from 9.766 percent to 9.494 percent. The equity premium decreases 32.5 basis
points to 6.937 percent. The risk-free rate increases to 1.206 percent from 0.949 percent, and
the standard deviation of the risk-free rate decreases to 1.296 percent from 1.449 percent.
As for the impact on the real term premia, the 30-year term premium drops by 21 basis
points. This exercise revels that the asymmetric portfolios in terms of bond maturity play only
a minor role in increasing bond risk premia.
5.2 No Non-Mertonian Equity Traders
In this subsection, we highlight the importance of distinguishing between Mertonian
traders and non-Mertonian equity traders. Both types of traders hold equity, and hence it is
not easy to distinguish between them in the data. In fact, most of the work in the segmented
market literature does not consider the possibility of different types of equity market participants. We remove the differences between these two types of equity market participants and
assume all are Mertonian traders. The assumption of a trend-reverting process for the endowment growth rate remains unchanged. The results are reported in the “No NME” column of
Table 2.
With half of total households now Mertonian traders and able to absorb the residual risk
created by nonparticipants, aggregate risk is not concentrated enough quantitatively. The
market price of risk and the term premium are greatly reduced. Quantitatively, the market
price of risk drops significantly to 0.204 from 0.475. The equity premium is only 2.602 percent,
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and the term premium for a 30-year zero-coupon bond drops significantly, to only 0.678
percent.
This sensitivity analysis suggests that a high market price of risk is essential to our results.
The large fraction of nonparticipants and few equity market participants not only helps to
match the high and volatile equity risk premia, but also goes a long way to increasing the real
bond risk premia.
5.3 No Heterogeneous Trading Technologies
In this subsection, we remove totally the heterogeneous trading technologies assumed in
the model. All households are now Mertonian traders and face no restriction on their portfolio
choices. The results are reported in the “No HTT” column of Table 2. With the force of hetero
geneous risk loading completely absent, the model acts similar to a Bewley-type model and
exhibits low risk premia. The market price of risk, the equity premium, and the term premium
are all small and close to those in a representative agent model.3
6 CONCLUSION
We find that a slow mean-reverting shock process of consumption growth and a segmented asset-market mechanism with a heterogeneous trading technology can quantitatively
account for the positive and sizable term premium for bonds as suggested by the data. The
slow mean-reverting consumption process explains the positive term premia, although the
size of the premia is still very small quantitatively. Our quantitative exercise shows that with
this slight modification of the aggregate shock process, the long-term bond is risky because
the risk-free rate is slightly countercyclical, even in the representative agent model. The segmented market mechanism with a heterogeneous trading technology and an asymmetric bond
position across households can amplify the size and magnitude of the term premia while
raising the market price of aggregate risk.
We think our model is the first step in resolving the inconsistency between theoretical
macroeconomic models and the empirical asset-pricing findings of the yield curve, with no
modification of preferences. There are two obvious directions for future research that can
improve the model. For the asset-pricing literature, one can enrich the model by additionally
introducing a long-term consumption growth shock in order to match more properties of
real bond premia found in the empirical literature. For macroeconomics, our mechanism does
not rely on the modification of preferences, and the behavior of asset pricing is pinned down
by a relatively small set of marginal investors in a segmented market mechanism. Therefore,
the consumption and saving behaviors of most households stay close to those in a standard
macroeconomic model. It is more likely that our results extend to a general equilibrium production economy without comprising dynamics of other macroeconomic variables. n
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APPENDIX
A.1 THE TIME-ZERO TRADING HOUSEHOLD PROBLEM
This appendix describes an equivalent version of this economy in which all households
trade at time zero. The time-zero price of a claim that pays one unit of consumption in node
zt can be constructed recursively from the one-period-ahead Arrow prices:
( ) ( ) (
) (
)
(
)
P z t π z t = Q zt z t−1 Q zt−1 z t−2 …Q z1 z 0 Q ( z0 ) .
The net financial wealth position of any trader given the trader’s history can be stated as
(
)
−at z t , η t = ∑
(
) (
(
s
s
∑
)(
t
s≥t z , η ± z , η
t
(
)
( )
(
)
P% z s , η s ⎡⎣γ Y z s ηs − c z s , η s ⎤⎦ ,
)
) ( )
where P% z t , η t = π z t , η t P z t . From the above equation, we are able to write the household
problem in the form of a time-zero trading problem, as shown in the next subsection.
A.1.1 The Household Optimization Problem
Following Chien, Cole, and Lustig (2011), we state the household problem in this Arrow-
Debreu economy.
We start with the Mertonian traders’ problem in the home country. There are two constraints. Let χ denote the multiplier on the present value budget constraint and φ(zt ,η t ) denote
the multiplier on debt constraints. The saddle-point problem of a Mertonian trader can be
stated as follows:
∞
max
t
L = {min
χ ,υ ,ϕ } {c} ∑ β
t=1
1
∑ 1− α c ( z t , η t ) π ( z t , η t )
1−α
z t ,η t
⎫⎪
⎧⎪ ∞
+ χ ⎨∑ ∑ P% z t , η t ⎡⎣γ Y z t ηt − c z t , η t ⎤⎦ + a0 z 0 ⎬
t t
⎪⎭
⎩⎪ t=1 ( z ,η )
(
( )
(
⎪
∑ ϕ t ( z t , η t ) ⎨∑
t=1 z t ,η t
(
)
( )
⎫⎪
P% z s , η s ⎡⎣γ Y z t ηs − c z s , η s ⎤⎦ ⎬.
⎪⎩ s≥t ( z s ,η s )±( z t ,ηt )
⎪⎭
⎧
∞
−∑
)
)
∑
(
)
( )
(
)
The first-order condition with respect to consumption is given by
(7)
t
(
β c z t ,ηt
)
−α
(
) ( )
(
)
= ζ z t , η t P z t for all z t , η t ,
where ζ(zt ,η t ) is defined recursively as
(
)
(
)
(
ζ t z t , η t = ζ t−1 z t−1, η t−1 − ϕt z t ,η t
)
with initial ζ 0 = χ. It is easy to show that this is a standard convex constraint maximization
problem. Therefore, the first-order conditions are necessary and sufficient.
Non-Mertonian traders face additional restrictions on their portfolio choices. Let vt(zt ,η t )
denote the multiplier on portfolio restrictions. Given the same definition of other multipliers
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as in the active-trader problem, the saddle-point problem of a nonparticipant trader whose
assets at the end of the period are ât–1(zt–1,η t–1) can be stated as
∞
max
t
L = { min
χ ,υ ,ϕ } {c, ŝ} ∑ β
t=1
1
∑ 1− α ct ( z t , η t ) π ( z t , η t )
1−α
z t , ηt
⎫⎪
⎧⎪ ∞
χ ⎨∑ ∑ P% z t , η t ⎡⎣γ Y z t ηt − c z t , η t ⎤⎦ + a0 z 0 ⎬
t t
⎪⎭
⎩⎪ t=1 ( z , η )
⎧ Σ s≥t Σ s s t t P% z s , η s ⎡γ Y z s ηs − c z s , η s ⎤ ⎫
∞
⎣
⎦⎪
( z , η )±( z , η )
t
t ⎪
+ ∑ ∑ νt z ,η ⎨
⎬
p
t=1 ( z t , η t )
⎪⎩
⎪⎭
z t ŝt−1 z t−1, η t−1
+ P% z t , η t Rt,t−1
∞
⎫⎪
⎧⎪
− ∑ ∑ ϕ t z t , η t ⎨∑
P% z s , η s ⎡⎣γ Y z s ηs − c z s , η s ⎤⎦ ⎬.
∑
s s
t t
t=1 ( z t , η t )
⎩⎪ s≥t ( z , η )±( z , η )
⎭⎪
(
)
(
)
(
)
( )
(
)
( )
(
(
)
( )
( ) (
)
(
)
(
)
( )
(
)
)
The first-order condition with respect to consumption is given by
t
(
)
β c z t ,ηt
−α
(
) ( )
(
)
= ζ z t , η t P z t for all z t , η t ,
where ζ(zt ,η t ) is defined as
(
)
(
) (
)
(
)
ζ t z t , η t = ζ t−1 z t−1, η t−1 + ν t z t , η t − ϕt z t , η t .
Therefore, the first-order condition with respect to consumption is independent of trading
restrictions. The first-order condition with respect to total asset holdings at the end of period
t–1, ŝt–1(zt–1,η t–1) is
p
( z t ) v t ( z t , η t ) P ( z t )π ( z t , η t ) = 0
∑ Rt,t−1
t
z ,η
t
for all z t , η t .
This condition varies according to the different trading restrictions.
A.1.2 Stochastic Discount Factor
By summing the first-order condition with respect to consumption, equation (7), across
all domestic households at period t, we obtain the consumption sharing rule as follows:
(
c z t ,ηt
( )
C z
( )
t
)= (
where ht(zt ) is defined as ht z t ≡ ∑ζ ( z t , η t )
η
t
)
h (z )
ζ z t ,ηt
t
−
1
α
t
−
1
α
,
( )
π η t . In addition, by plugging the consump-
tion sharing rule back into to the first-order condition with respect to consumption, equation
(7), we obtain the price of the home consumption basket at state zt :
( )
P z t = β t C ( z t ) ht ( z t ) .
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Therefore, the stochastic discount factor is given by the Breeden-Lucas stochastic discount
factor with a multiplicative adjustment:
(
Qt+1 z t+1
( ) = β ⎛ C(z )⎞
z )≡
⎜
⎟
P(z )
⎝ C(z ) ⎠
P z t+1
t
t+1
t
t
−α
( )
( )
α
⎛ ht+1 z t+1 ⎞
⎜
⎟ .
t
⎝ ht z ⎠
A.2 PROOF OF LEMMA 1
Given that our assumed growth rate of output is g t+1 = ge ( ρ −1)mt +εt+1 the one-period-ahead
− α ρ −1 m − αε
pricing kernel is Mt,t+1 = β g −α e ( ) t e t +1 . The price of a one-period bond is therefore
Pt1
= Et Mt,t+1 = β
2
2σ ε
− α − α ( ρ −1)mt α 2
g e
e
,
which is a function of the current deviation from trend mt. The one-period yield is then
rt1 = −lnPt1 = −ln β + α ln g + α ( ρ −1)mt −
α 2σ ε2
.
2
We derive the price of a k-period zero-coupon bond and its yields as follows:
⎡ k−1
⎤
Ptk = Et ⎡⎣ Mt,t+k ⎤⎦ = Et ⎢ ∏ Mt+τ ,t+τ +1 ⎥
⎣τ +0
⎦
k
α 2σ ε2
k=1 τ
⎡ k−1 2 τ ⎤
−kα − α ( ρ −1)⎡⎣ ∑τ =0 ρ ⎤⎦mt ⎣ ∑τ =0 ρ ⎦ 2
g e
e
=β
1
rtk = lnPtk
k
= −lnβ + α ln g + α ( ρ −1)
,
1 1− ρ k t 1− ρ 2k α 2σ ε2
m −
.
1− ρ 2 2
k 1− ρ
The term premium at period t for a k-period zero-coupon bond is
⎡ 1 1− ρ k ⎤ t ⎡ 1 1− ρ 2k ⎤ α 2σ ε2
rtk − rt1 = α (1− ρ ) ⎢1−
⎥ m +1 ⎢1− k 1− ρ 2 ⎥ 2 ,
⎣ k 1− ρ ⎦
⎣
⎦
which is again a function of mt. Taking the unconditional expectation of rtk – rtl gives equation
(6) because of E(mt ) = 0.
Moreover, we want to show that the term premium is increasing with k, that is, for
∂E ⎡⎣rtk − rt1 ⎤⎦
> 0 for k > 1. First, notice that ρ 2k 1− ln ρ 2k <1 because (i)
∂k
lim ρ 2 k →1ρ 2k 1− ln ρ 2k = 1 and (ii)
(
(
)
)
(
)
∂ ⎡⎣ ρ 2k 1− ln ρ 2k ⎤⎦
= −ln ρ 2k > 0 if ρ 2k <1.
∂ ρ 2k
τ
Second, by using the fact that ∑τk−1
=0 ρ =
132
Second Quarter 2019
1− ρ 2k
, the average term premium can be rewritten as
1− ρ 2
Federal Reserve Bank of St. Louis REVIEW
Chien and Lee
E ⎡⎣rtk − rt1 ⎤⎦ =
α 2σ ε2
α 2σ ε2
1− ρ 2k
−
×
2
k
2 1− ρ 2
(
)
and hence the derivative of E[rtk – rtl ] with respect to k is
∂E ⎡⎣rtk − rt1 ⎤⎦
∂k
=
1− ρ
α 2σ ε2
×
2
2 1− ρ
(
)
2k
(1− ln ρ )
2k
k2
> 0 if ρ < 1 and k >1.
The last inequality uses the fact that ρ2k(1 – lnρ2k) < 1 if ρ2k < 1.
NOTES
1
The standard equilibrium macroeconomic model refers to the classical representative agent complete-market
model, such as the one in Mehra and Prescott (1985). See also Grkaynak and Wright (2012) for a review of issues
related to term premia.
2
In this article, the terms “household,” “trader,” and “investor” are used interchangeably.
3
The statistics for the representative agent economy are reported in the “RA economy” column of Table 2.
REFERENCES
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https://doi.org/10.1016/S0304-3932(98)00039-7.
Alvarez, F. and Jermann, U. “Quantitative Asset Pricing Implications of Endogenous Solvency Constraints.” Review
of Financial Studies, 2001, 14, pp. 1117-52; https://doi.org/10.1093/rfs/14.4.1117.
Backus, D.K.; Gregory, A.W. and Zin, S.E. “Risk Premiums in the Term Structure: Evidence from Artificial Economies.”
Journal of Monetary Economics, 1989, 24(3), pp. 371-99; https://doi.org/10.1016/0304-3932(89)90027-5.
Bansal, R. and Shaliastovich I. “A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets.”
Review of Financial Studies, 2013, 26(1), pp. 1-33; https://doi.org/10.1093/rfs/hhs108.
Bansal, R. and Yaron A. “Risks for the Long Run: A Potential Resolution of Asset Prizing Puzzles.” Journal of Finance,
2004, 59, 1481-509; https://doi.org/10.1111/j.1540-6261.2004.00670.x.
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Finance.” Review of Economic Studies, 2011, 78(1), pp. 199-234; https://doi.org/10.1093/restud/rdq008.
Christiano, L.J. and Eichenbaum M. “Unit Roots in Real GNP: Do We Know, and Do We Care?” Working Paper Series,
Macroeconomic Issues 90-2, Federal Reserve Bank of Chicago, 1990.
den Haan, W.J. “The Term Structure of Interest Rates in Real And Monetary Economies.” Journal of Economic
Dynamics and Control, 1995, 19(5-7), pp. 909-40; https://doi.org/10.1016/0165-1889(94)00813-W.
Donaldson, J. B.; Johnsen, T. and Mehra, R. “On the Term Structure of Interest Rates.” Journal of Economic Dynamics
and Control, 1990, 14(3-4), pp. 571-96; https://doi.org/10.1016/0165-1889(90)90034-E.
Grkaynak, R.S. and Wright, J.H. “Macroeconomics and the Term Structure.” Journal of Economic Literature, 2012,
50(2), pp. 331-67; https://doi.org/10.1257/jel.50.2.331.
Guiso, L. and Sodini, P. “Household Finance. An Emerging Field.” EIEF Working Paper, 2012.
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Mehra, R. and Prescott E.C. “The Equity Premium: A Puzzle.” Journal of Monetary Economics, 1995, 15(2), pp. 145-61;
https://doi.org/10.1016/0304-3932(85)90061-3.
Mendoza, E.G.; Quadrini, V. and Rios-Rull, J.-V. “Financial Integration, Financial Development, and Global Imbalances.”
Journal of Political Economy, 2009, 117(3), pp. 371-416; https://doi.org/10.1086/599706.
Piazzesi, M. and Schneider, M. “Equilibrium Yield Curves,” in NBER Macroeconomics Annual 2006. Volume 21. National
Bureau of Economic Research, Inc., 2007, pp. 389-472.
Rudebusch, G.D. and Swanson, E.T. “The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks.”
American Economic Journal: Macroeconomics, 2012, 4(1), pp. 105-43; https://doi.org/10.1257/mac.4.1.105.
Storesletten, K.; Telmer, C.I. and Yaron, A. “Cyclical Dynamics in Idiosyncratic Labor Market Risk.” Journal of Political
Economy, 2004, 112(3), pp. 695-717; https://doi.org/10.1086/383105.
Ulrich, M. “Inflation Ambiguity and the Term Structure of U.S. Government Bonds.” Journal of Monetary Economics,
2013, 60(2), pp. 295-309; https://doi.org/10.1016/j.jmoneco.2012.10.015.
Wachter, J. “A Consumption-Based Model of the Term Structure of Interest Rates.” Journal of Financial Economics,
2006, 79, pp. 365-99; https://doi.org/10.1016/j.jfineco.2005.02.004.
Wright, J.H. “Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset.”
American Economic Review, 2011, 101(4), pp. 1514-34; https://doi.org/10.1257/aer.101.4.1514.
134
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Federal Reserve Bank of St. Louis REVIEW
Racial Gaps, Occupational Matching,
and Skill Uncertainty
Limor Golan and Carl Sanders
White workers in the United States earn almost 30 percent more per hour on average than Black
workers, and this wage gap is associated with large racial differences in occupational assignments. In
this article, we theoretically and empirically examine the Black-White disparity in occupations. First,
we present a model based on Antonovics and Golan (2012) that relates occupational assignments to
the incentives workers face while learning about their own unknown ability. Second, we document
differences between Black and White workers in both the complexity of skills required in their initial
occupations and the growth rates of this complexity over time. To do this, we match panel data from
the National Longitudinal Survey of Youth 1979 with the Dictionary of Occupational Titles measures
of occupational characteristics and find that, compared with White workers, Black workers start in
occupations requiring less-complex skills, see slower growth in job complexity over time, and are
relatively more likely to transition to jobs with lower complexity. Finally, we consider the relationship
between our model and our empirical findings; for example, discrimination in hiring early in the
career can have long-term consequences on the ability of Black workers to learn their best occupa
tional match and explains part of their lower wage growth. We conclude with suggestions for policy
and future research directions. (JEL J01, J24, J31)
Federal Reserve Bank of St. Louis Review, Second Quarter 2019, 101(2), pp. 135-53.
https://doi.org/10.20955/r.101.135-53
1 INTRODUCTION
The labor market experiences of Black and White workers in the United States are dramati
cally different. A first-order difference is the well-documented racial wage gap: The average
hourly wage for White workers is 30 percent higher than for Black workers. This racial wage
gap has been shown to reflect differences in both socioeconomic backgrounds and discrimina
tory practices in the labor market and has created a sizable literature across multiple disciplines.
But differences in earnings do not exhaust the racial differences in labor market experiences.
In this article, we consider racial gaps in workers’ occupations, that is, differences in what
Limor Golan is an associate professor at Washington University in St. Louis and a research fellow at the Federal Reserve Bank of St. Louis.
Carl Sanders is an assistant professor at Washington University in St. Louis.
© 2019, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses,
and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
Federal Reserve Bank of St. Louis REVIEW
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Golan and Sanders
White and Black workers do rather than what they earn. Even the most basic descriptive
statistics show large differences between Black and White workers in the types of work they
perform. For example, Black workers were 12 percent of the working population in 2016 and
made up 26 percent of the occupation “truck and tractor operators,” while making up only 3
percent of “chief executives.” White workers showed the opposite pattern, making up 45 per
cent of the working population in 2016 and 85 percent of chief executives.1
Our focus on racial differences in occupations is consistent with recent work in empirical
labor economics, which links differences in occupations and occupational mobility to workers’
wage growth. It is often more informative to know someone’s occupational title than their
current wage: taking two young workers who each earn $15 an hour, the knowledge that one
has the occupation “accountant” and the other “refrigeration mechanic” helps to make the
(on average correct) prediction that the accountant will make significantly more than the
mechanic 10 years later. Understanding the reasons Black and White workers take different
occupations can provide insight into differences in wage levels and wage growth.
The primary contribution of this article is documenting and interpreting the differences
in the relative occupational assignments of Black and White workers. In the first part of the
study, we present an economic model to use as a framework for interpreting our empirical
results on occupational choice, occupational turnover, and wage growth. In the second section,
we document the racial gaps in occupational choice in representative U.S. data, looking both
at aggregate trends in occupational choice within a worker’s career and at occupation-tooccupation transition rates. Finally, in our empirical results, we compare the predictions of
the model to our descriptive findings and discuss the implications of the underlying economic
mechanisms for policy and future research.
Section 2 of our article gives a framework to interpret occupational mobility across races
as the result of different economic circumstances. Our model is a learning model following
Antonovics and Golan (2012) that is capable of generating occupational mobility and wage
growth across the career. For simplicity, we present analysis of a two-period model. Each
period, workers choose an occupation to maximize the expected present discounted value of
lifetime income, but occupational choice is complicated by the fact that workers do not know
their own ability and thereby their best occupational match. Working allows a worker to learn
about his ability over time, but different jobs give information about the worker’s skills at
different rates.
The amount that workers learn about their skills depends on the intensity of their job.
Different jobs require performance of tasks that require varying intensities of unobservable
skills. The more output depends on the unobserved skills, the more information the job
reveals about those skills. For example, workers learn more about their ability as a manager
in management jobs. Information about skill levels may increase future earnings because it
allows a better assignment of workers to jobs. Thus, workers experiment, forgoing expected
current-period output in order to learn about their skills by taking jobs they would not take
otherwise. Antonovics and Golan’s (2012) results show that the optimal level of experimen
tation is initially small, increases as workers gain experience, and then declines as workers
become increasingly certain about their skills.
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Golan and Sanders
Mapping the theoretical concept of “occupational intensity” to the data requires nonstandard measures, since in Census-like data sets only the occupational title is recorded rather
than any specific on-the-job activities. To overcome this data limitation, we use data on occu
pational characteristics from the Dictionary of Occupational Titles (DOT) merged with worker-
level panel data from the National Longitudinal Survey of Youth 1979 (NLSY79). We use the
detailed occupation-level characteristics from the DOT to reduce the unordered list of occu
pational titles into a single-dimensional index that ranks occupations by the degree to which
output depends on skills that are difficult to observe directly, e.g., creativity. This index ranks
occupations with respect to the dependence of output on skills that are hard to observe, which
we call “complexity” throughout for brevity.2
In Section 3, we analyze the merged data sets and show that, as expected, the average
White worker’s first occupation tends to be more-complex than the average Black worker’s
first occupation. Moreover, over a career, the average White worker’s occupational complexity
grows faster than the average Black worker’s. Further empirical analysis considers whether
these differences are driven by rates of occupational switching, differences in the promotion
rates of less- versus more-complex occupations, and the role of demographic characteristics
and education in explaining these occupational gaps.
When we look more closely at the rates of occupational switching, we find that the slower
pattern of occupational upgrading by Black workers relative to White workers is not driven
by lower occupational mobility. Rather, Blacks are marginally more likely to switch occupa
tions than Whites, but a greater proportion of Black occupational transitions are “downgrades,”
that is, switches toward occupations characterized by lower levels of complexity. Given an
occupational switch, White workers make an occupational upgrade 54 percent of the time,
compared with 51 percent for Black workers.
Regarding potential average demographic differences between races, we examine to what
extent differences in workers’ first occupations and the growth rate of occupational complexity
are driven by race alone rather than other explanations. For example, Black workers may
begin in less-complex occupations on average more often than White workers due simply to
average differences in education levels. We find that racial differences in the speed of occupa
tional upgrading persist even if we consider White and Black workers who are originally in
the same occupation. This finding suggests that race-specific factors such as discrimination
might partially explain differences in occupational transition rates.
Additionally, we consider the first job that workers have and find that controlling for
measurable demographics such as education level and test scores does not eliminate the effect
of race on the initial occupational assignment: Black workers with seemingly very similar skills
as White workers tend to work in less-complex occupations. Our economic model suggests
that if Black workers are discriminated against in hiring for high-complexity occupations, it
can have long-term effects on their occupational complexity and wage growth relative to
White workers.
From a policy perspective, one of the major issues surrounding racial labor market gaps
is the question of mismatch. Workers may not always be well matched to their job or occu
pation, and if demographic background differences and racial discrimination make this problem
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Golan and Sanders
more severe, there may be large productivity gains by improving the match of Black workers
with their best occupations. In this article, we focus on the role of mismatch induced by infor
mational frictions in the Black-White wage gap. Even if there were no barriers to hiring or
finding jobs, workers and employers do not always have complete information about the
worker’s skills or the suitability of those skills to the tasks required by the job. Over time, as a
worker comes to know his or her own skills and the employer observe the worker’s performance,
both the worker and the employer both could learn about the worker’s ability and compara
tive advantage. Based on this information, workers change jobs and, over time, wages grow
because workers work in occupations and jobs in which they are better matched. Policies that
aim to improve the information available to both workers and employers could potentially
reduce the costs of mismatch and, and if discrimination in occupational attainment leads to
Black workers receiving less information about their skills over their careers, it may be nec
essary to target these policies to Black workers.
The remainder of the article is organized as follows: In Section 2 we review the literature
on labor learning models and racial labor market gaps; in Sections 3 and 4 we set up and solve
the two-period learning model; in Section 5 we describe worker and occupational data con
struction; in Section 6 we present the empirical results; and in Section 7 we present conclusions.
2 RELATED LITERATURE
The theoretical and empirical literature on uncertainty in the labor market primarily
focuses on models of matching (see, for example, Jovanovic, 1979, and Miller, 1984) and
models of learning (see, for example, Farber and Gibbons, 1996; Gibbons and Waldman,
1999; Neal, 1999; and Gibbons et al., 2005). There is also a set of empirical labor papers that
analyze how workers and firms learn about unobserved ability and how quickly this happens
(see Miller, 1984; Pastorino, 2009; Papageorgiou, 2014; James, 2012; Sanders, 2017; and
Golan et al., 2017).
There is a large literature on Black-White pay gaps as well as other racial differences in
labor market outcomes. The economics literature emphasizes the importance of pre-market
factors in these differences in outcomes. See Altonji and Blank (1999), Cameron and Heckman
(2001), Carneiro et al. (2005), and Fryer (2011) for surveys of economic analyses of racial
labor market gaps, including the empirical relationships between pre-market characteristics
such as education, test scores, and family background, with a variety of labor market outcomes.
There has been less recent focus on the role of post-market entry differences in the experiences
of Black and White workers. The fact that similar Black and White workers are employed at
different rates was originally discussed in the context of long-term trends in racial wage gaps:
Brown (1984), Chandra (2000), Juhn (2003), and Western and Pettit (2005) all found evidence
that more Black workers than White workers dropped out of the labor force between 1940
and 1990, and higher-wage Black workers were more likely to drop out than higher-wage
White workers, increasing the measured wage gap. In the context of a single cohort, Eckstein
and Wolpin (1999) emphasize the difference between actual and potential wage-offer distribu
tions, making the point that observed wages can either under- or over-estimate discrimination.
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Golan and Sanders
Antecol and Bedard (2004) find that including measures of actual (rather than potential)
labor market experience closes even more of the gap in the Neal and Johnson (1996)-type
wage specification.
There are other economic theories of racial wage gaps that do not require systematic
differences in average skills. For example, Oettinger (1996) develops and tests a model of
statistical discrimination, where assuming Blacks have less-precise signals of ability predicts
an increasing wage gap with experience, even if both races have equal mean ability. He finds
that Blacks have lower gains to mobility, which causes the Black-White wage gap to rise with
experience. Altonji and Pierret (2001) develop a test for statistical discrimination and do not
find evidence supporting the hypothesis that employers discriminate based on easily observed
characteristics such as education.
This article focuses on describing the patterns in the occupational choices and job transi
tions of Black and White individuals. While there is a growing literature relating occupational
choices of workers, tasks performed, and data on occupational skill requirements (see Sanders
and Taber, 2012, for a review of the literature on heterogeneous/multidimensional human
capital, which often uses task-based data), the labor literature on job tasks has not typically
focused on cross-race differences in labor force outcomes. Golan et al. (2017), a complemen
tary paper, develops a generalized life-cycle model that includes occupational sorting, job
turnover, multidimensional skill gaps, and taste differences, and quantifies the magnitude of
the different factors accounting for the life-cycle racial gaps in earnings, participation, and
occupational choices.
3 MODEL
The model presented was developed in Antonovics and Golan (2012). We consider a
two-period economy with risk-neutral workers and firms with a common discount factor δ.
Workers differ in the sets of skills they possess. We examine a simple scenario in which each
worker has only two skills: a known skill, k, and an unknown skill, θ, both of which are time
invariant. For simplicity we assume that each firm offers one job. Each job differs in the extent
to which output depends on k and θ. There is a continuum of jobs, j, each completely charac
terized by a given value of α j [0,1], where α denotes the degree to which output depends on θ
relative to k. Thus, choosing a job in period t is equivalent to choosing a value of α. Given this
choice, we assume output in period t is given by
(1)
yt = α tθ + (1− α t ) k + ε t ,
where εt are independent and identically distributed productivity shocks and αt is the value
of α chosen by the worker at time t. Note that there is one job in which output is sensitive
only to θ(α = 1) and one job in which output is sensitive only to k(α = 0). For the rest of the
jobs, the higher is α j, the more output depends on θ.
Information in the model is symmetric; firms and workers have common priors on θ,
k is known to everyone, and output is commonly observed. Workers and firms acquire addi
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Golan and Sanders
tional information about a worker’s unknown skill through successive observations of output.
Thus, having observed output, workers and firms calculate
xt =
(2)
yt − (1− α t ) k
ε
=θ + t ,
αt
αt
where xt serves as a signal of the worker’s unobserved skill, θ. The noise in xt is not indepen
dent of a worker’s job choice. In particular, the higher is αt , the higher is the signal-to-noise
ratio and the more information about θ the market is able to extract from xt. Under the
assumption that the prior distribution of θ at time t is normal with mean μt and variance σt2
and the distribution of εt is normal with mean zero and variance σε2, the posterior distribution
2
of θ is known to be normal with mean μt+1 and variance σt+1
, where
µt+1 =
(3)
and
σ
(4)
2
t+1
µtσ ε2%,t + xtσ t2
σ ε2%,t + σ t2
σ ε2%,tσ t2
= 2
σ t + σ ε2%,t
σ ε2
. In addition, μt+1 is itself normally distributed with mean mt+1 and
α t2
variance st2+1 given by
and where σ ε2%,t =
mt+1 = µt
(5)
2
st+1
=
(6)
σ t4
.
σ t2 + σ ε2%,t
Thus, the posterior mean of θ follows a martingale and the more information xt reveals about
θ (the higher is α), the higher is the variance of the posterior mean.
We assume competitive markets and free entry into the labor market. Thus, wages are
the expected productivity in each period.
Workers’ current-period utility is given by Ut = wt so workers choose αt to maximize the
expected present discounted value of lifetime wages.
3.1 Optimal Job Choice
Workers work for two periods and then retire. Thus, the worker’s problem can be written as
(7)
(
)
V µ1 ,σ 12 = max α 1µ1 + (1− α 1 ) k + δ E1 ⎡⎣α 2 µ2 + (1− α 2 ) k ⎤⎦ ,
α t∈[ 0,1]
which we can solve recursively beginning from the second period.
The second-period optimal choice of job is given by
(8)
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⎧⎪ 1, if µ2 ≥ k,
α 2 ( µ2 ) = ⎨
⎩⎪ 0, otherwise.
Federal Reserve Bank of St. Louis REVIEW
Golan and Sanders
The second-period job assignment is simply to choose the job in which the wage is the highest.
Solving backwards, we first solve for the optimal assignment in period one. Note that
expected productivity in period two depends on the second-period belief, μ2, which in turn
depends on α1 through x1 (see equations (2) and (3)). We therefore rewrite the first-period
problem as
(9)
(
)
∞
V µ1 ,σ 12 = max α 1µ1 + (1− α 1 ) k + δ ⎡ Φ ( r ) k + ∫k µ2 f ( µ2 )d µ2 ⎤ ,
⎣
⎦
α1∈[ 0,1]
k − µ1
, Φ(.) is the standard normal cumulative density function and f is the normal
s2
α 2σ 4
probability density function with mean m2 = μ1 and variance s22 = 2 1 2 1 . The above equation
α 1 σ 1 +1
makes clear that when μ1 < k, there is a cost associated with selecting α1 > 0 since expected
current-period output will be less than k. Thus, when μ1 < k, workers must weigh the benefit of
increasing α1 in terms of expected second-period output against the cost in terms of expected
current-period output.
The second-period output is increasing in α1. The expected value of any left-truncated
normal random variable is increasing in the variance of that random variable. Thus, since s22
is increasing in α1, we know that expected second-period output must also be increasing in α1.
Intuitively, information is valuable because workers can truncate the loss if they receive a
negative signal about θ by selecting future jobs with α = 0, but can take advantage of the arrival
of positive information about θ by selecting jobs with α = 1.
We say that a worker experiments if a worker chooses to forego expected current-period
wages in order to gain information about θ, that is, if a worker with μ1 < k chooses α1 > 0.
Proposition 2 in Antonovics and Golan (2012) establishes that for every value of beliefs μ1 < k,
there exists a prior variance σ 2, so it is optimal to choose α > 0. That is, experimentation is
beneficial if there is sufficient uncertainty about a worker’s skill. Intuitively, even when θ is
believed to be very low, if there is sufficient uncertainty about θ, then the probability that θ > k
is high enough that it is worth foregoing current-period output to gain additional information
about θ’s true value.
The first-order necessary condition for an interior solution is
where r =
(10)
∂φ ( r )
∂s
∂Φ ( r ) k − µ1
s2 + 2 φ ( r ) + ( k − µ1 )
=
,
∂α 1
∂α 1
∂α 1
δ
where ϕ(r) is the standard normal probability density function.
Thus, in an interior solution, the marginal benefit of experimenting with α in terms of
second-period output is equal to the marginal cost in terms of first-period output. Note that
when μ1 > k, the cost of increasing α is negative (the right-hand side of equation (10) is nega
tive). Thus, when μ1 > k, both first-period and second-period expected output are increasing
in α1, and there will be a corner solution at α1 = 1. As shown in Antonovics and Golan (2012),
the optimal level of experimentation is increasing in μ; however, it is non-monotonic in the
variance σ. This non-monotonicity is counterintutitive: We would expect that if you had less
information you would always want to experiment more, but that is not the case.
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Golan and Sanders
To understand why there is a non-monotonic relationship between α1 and σ1, note that
current-period expected output does not depend on σ12; this finding implies that the nonmonotonic relationship between σ12 and the optimal choice of α1 must depend solely on how
increases in α1 affect expected future output. In particular, the effect of increasing α1 on
expected future output must be low both when σ12 is small and when σ12 is large. When σ12 is
small, the option value of new information is low because new information on θ is unlikely
to have a large impact on the posterior mean of θ. Moreover, the expected loss of output due
to incorrect future job assignments is small because the likelihood that θ is much different
from μ1 is small. To see why the benefit of increasing α1 is also small when σ12 is large, recall
that an increase in α1 increases expected future output through its effect on s22, the spread of
μ2. As is clear from equation (6), however, s22 is also increasing in σ12 and the marginal effect of
an increase in α1 on s22 is small when σ12 is large. Thus, when there is considerable uncertainty
about a worker’s skill, the spread of μ is large and experimentation has little value on the margin
since increased information has little effect on the optimal job assignment in the second period.
While the two-period model cannot be generalized directly to a life-cycle model, intui
tively, over the life-cycle the uncertainty about a worker’s skill decreases, which implies, hold
ing μ constant, that experimentation may initially increase and then decrease (for some values
of μ and σ) based on expectations (see details and analysis of a full dynamic problem in Section 4
of Antonovics and Golan, 2012).
In our empirical work, we will use the intuition gained from the model to understand
patterns of occupational choices and transitions in the data.
4 DATA AND EMPIRICAL IMPLEMENTATION
In our empirical work, we merge the occupational work histories from the NLSY79 to
occupational characteristics from the DOT in order to construct patterns of occupational
complexity and wages over workers’ careers.
4.1 The Dictionary of Occupational Titles
The model relates the occupational returns to unobservable skills to worker experimen
tation; however, these returns are typically not directly observable. To create an empirical
analogue of these returns, the α from the model, we use an index derived from occupationlevel characteristics that ranks occupations by the degree to which output depends on unob
served skills. This index was derived in Antonovics and Golan (2012) and here corresponds
to our idea of occupational “complexity.”
The construction of α relies on information in the DOT. The DOT provides information
on the primary tasks performed in a given occupation and the worker characteristics necessary
for successful job performance. The occupational characteristics given in the DOT are linked
to the 1970 Census three-digit occupation codes in an augmented version of the April 1971
Current Population Survey compiled by the Committee on Occupational Classification and
Analysis at the National Academy of Sciences. The data in the DOT are both comprehensive
and detailed, describing over 12,000 occupations along 44 dimensions.
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It is important to use a list of job characteristics that captures the importance of the
unknown (hard-to-observe) skill to job performance. In our model, there are several key fea
tures that characterize the unknown skill: First, there must be uncertainty about the skill prior
to a worker’s entry into the labor market. Second, observing output only gradually reveals a
worker’s skill and the more important the unobservable skill is to successful job performance,
the more quickly the skill is revealed. In order to identify occupations in which hard-toobserve skill is important to job performance, we select occupational characteristics that
indicate the importance of complex tasks. We define complex tasks as those for which it is
hard to write down an explicit algorithm for successful completion. This is similar to the
definition of “nonroutine” tasks in Autor et al. (2003).
The reasoning is that if a task can be broken into an ordered list of well-defined actions,
then a worker’s ability can be quickly learned by observing how the worker performs each
separate action. In contrast, if it is difficult to explicitly describe how to successfully complete
a task, then it will be difficult to determine a worker’s skill without observing his or her on-thejob performance.3 Using this list of variables, the index is created using principal component
analysis. To ease comparison with the theoretical model, the index is converted into percent
ages. Each normalized predicted score takes on a value between zero and 1, with higher values
indicating a higher level of required skill. The index is then matched to the occupation data
from the NLSY79.
4.2 The National Longitudinal Survey of Youth 1979
In order to construct this occupational work history, we use the NLSY79, which follows
individuals born between 1957 and 1964. We focus our empirical analysis on males in the
cross-sectional sample. Although the NLSY79 contains information on individuals’ labor force
activities for each week from 1978 through the most recent year in which a respondent was
interviewed, we rely only on labor market data from 1978 through 2000 because of a switch
in occupational coding that occurred after 2000. If a respondent is not interviewed in a given
year (or years), then at the next interview date, the respondent is asked to go back and retro
spectively report their labor force activities. As a result, the NLSY79 allows us to construct
relatively complete work histories. The work history data include information on each of up
to five jobs a respondent may have held in a given week, and we define an individual’s occu
pation in a given week to be their occupation in the job at which they worked the most hours.
We follow individuals’ occupational histories starting with their first transition to full-time
work after the completion of their highest degree. In particular, following completion of a
degree, we identify the first week in which an individual works at least 10 hours per week and
from which he continues to work at least 10 hours per week for at least 39 of the next 52 weeks.
We then keep a running tab of the individual’s actual labor market experience and occupation
in each week in which he works.4 In our empirical analysis, we focus on the first 350 weeks
(about 6.7 years) of each individual’s actual experience in the labor force because attrition
from the sample makes it difficult to construct complete work histories for longer horizons.
We take as our initial sample the cross-sectional sample of White males and the crosssectional plus supplemental sample of Black males. We lose 829 respondents because we
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Table 1
Summary Statistics
Whites mean
Standard
deviation
Blacks mean
Standard
deviation
AFQT
62
(26)
29
(23)
Percent with only high school or below
56
(.)
77
(.)
Hourly wage ($)
14.58
(7.95)
11.86
(7.05)
Occupational α
0.54
(0.27)
0.42
(0.27)
Total no. of workers
1,601
Whites
1,048
Blacks
553
NOTE: AFQT, Armed Forces Qualification Test.
cannot identify either their highest degree or the date at which they received their highest
degree. We additionally drop 420 respondents who completed their highest degree prior to
the start date of the work-history record and 305 respondents who completed their highest
degree relatively late in life, because we worry that these workers already may have accumu
lated substantial labor market experience that could influence employers’ beliefs about skills.
We also drop 36 respondents who lack information on their first week in the labor market as
well as 370 respondents whose occupational histories are relatively incomplete. In particular,
we drop those who either have more than 150 weeks in which they did not work or have miss
ing occupation information during the first 500 weeks following the transition to full-time
work. In other words, we give individuals 500 weeks in which to accumulate 350 weeks of
valid occupation information, otherwise we drop them from the sample. We additionally drop
72 respondents who ever reported an hourly wage of either over $100 or under $2 and 38
respondents with missing Armed Forces Qualification Test (AFQT) scores. After these restric
tions, we are left with 1,601 individuals: 553 Black and 1,048 White. Relative to the initial
sample, these individuals are young and have strong attachment to the labor force.
5 EMPIRICAL ANALYSIS
5.1 Racial Wage and Occupation Gaps Over the Career
Sample summary statistics are shown in Table 1. The left (right) two columns contain
mean and standard deviations for White workers’ (Black workers’) scores on the AFQT, the
percentage of those workers with only a high school diploma or below, their hourly wages,
the percentile rank of their occupation in terms of α, and the complexity of tasks performed
there. Black workers’ socioeconomic background characteristics fall below White workers’
for both the AFQT score and completed years of education. Black workers earn around 25
percent lower hourly wages than White workers, and controlling for education and the AFQT
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Figure 1
Wage as a Function of Experience
Mean Wage (in 2000 dollars)
16
14
12
10
Black
8
0
50
100
150
200
250
White
300
350
Actual Experience (in weeks)
Figure 2
Occupational Complexity as a Function of Experience, By Race
Mean Alpha
0.6
0.5
0.4
Black
0.3
0
50
100
150
200
250
300
White
350
Actual Experience (in weeks)
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score reduces (but does not eliminate) this wage gap (see Neal and Johnson, 1996, and Lang
and Modove, 2011). Less documented in the literature, Black workers tend to work in lesscomplex occupations, with the average Black worker’s occupation about 10 percentage points
lower in the occupation distribution than the average White worker’s. As a reference point,
note that the modal occupational category near the α = 0.42 average for Black workers is
“trade, industrial, and technical teachers” and near the α = 0.54 average for White workers is
“salesmen and sales clerks.”
Differences between White and Black average wages are driven by both cross-sectional
differences (at one point in the careers) and different growth rates of wages across the careers.
Figure 1 shows wage levels of White and Black workers as a function of their actual labor
market experiences; that is, we take the average wages of workers who we have observed in a
job for exactly 50 weeks regardless of their age, the time since labor market entry, etc. As the
figure shows, White workers start with hourly wages around $10.30 compared with around
$9.00 for Black workers; and by 350 weeks of work, White workers are earning nearly $16.00,
compared with slightly less than $13.00 for Black workers.5
Figure 2 summarizes a less well-known pattern in labor force outcomes: Black workers
begin their careers in less-complex occupations, and even by 350 weeks, the average Black
worker is not even at the same job complexity as the average White worker in his first job. As
in the wage-gaps graph (see Figure 1), there are differences between races in both the levels
and growth rates of occupational complexity: White workers both perform higher levels of
complex tasks and move over time to higher levels of complex tasks more quickly than Black
workers do.
5.2 Patterns in Occupational Mobility
There are many possible explanations for the faster occupational-upgrading rates of
White workers relative to Black workers. First, consider explanations within the class of racial
discrimination: White and Black workers could face the same potential promotions and out
side offers, but Black workers could be passed over more often due to discrimination at the
screening phase; White and Black workers could get the same total number of opportunities
to move, but White workers move up more at each transition; or Black workers could be more
likely to be fired than White workers. An explanation that doesn’t require any racial discrim
ination motive at all is simply that the growth rate of occupational complexity for workers in
less-complex jobs is lower, and the lower average level of job complexity for Black workers
also then explains the lower growth rate.
To get some idea about the relative merits of some of these potential explanations for the
racial gap in occupational complexity, we first decompose complex-task growth over time
into (i) occupation and wage changes conditional on moving jobs and (ii) the probability of
moving jobs. Table 2 summarizes our results. In Panels A and B of the table, we take every
week-to-week occupational transition of White workers and Black workers, respectively, and
divide these into those who “move down” (move to an occupation with a lower α), those who
“stay” (do not change occupations or move to an occupation with an identical α), and those
who “move up” (move to an occupation with a higher α). We also then split these weeks into
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Table 2
Occupation and Wage Changes by Mover Category
A. Whites
Weeks 1-50
51-100
101-150
151-200
201-250
251-300
310-350
–0.22
–0.21
–0.21
–0.22
–0.21
–0.21
–0.21
E[ΔW] ($)
1.38
1.11
1.38
1.52
1.37
1.33
1.15
σΔW ($)
4.28
5.60
4.52
6.65
6.91
5.50
5.67
Count
309
318
317
296
264
262
238
Move down
E[Δα]
Stay
E[ΔW] ($)
0
0
0
0
0
0
0
σΔW ($)
0.42
0.47
0.48
0.59
0.76
0.54
0.60
44,455
46,837
47,205
47,355
47,779
47,657
47,764
E[Δα]
0.25
0.24
0.24
0.22
0.21
0.20
0.21
E[ΔW] ($)
1.98
1.04
1.28
1.11
1.74
1.92
0.56
σΔW ($)
4.80
4.91
4.87
4.70
4.68
6.38
4.67
Count
344
385
352
338
301
303
251
Weeks 1-50
51-100
101-150
151-200
201-250
251-300
310-350
–0.20
–0.21
–0.21
–0.21
–0.23
–0.22
–0.24
E[ΔW] ($)
0.58
1.10
0.30
0.18
0.68
1.19
0.81
σΔW ($)
3.20
3.59
4.63
4.14
7.23
4.57
3.82
Count
164
209
174
152
174
172
141
Count
Move up
B. Blacks
Move down
E[Δα]
Stay
E[ΔW] ($)
0
0
0
0
0
0
0
σΔW ($)
0.34
0.54
0.74
0.73
0.51
0.67
0.90
23,256
24,494
24,805
24,704
25,116
25,089
24,925
E[Δα]
0.23
0.22
0.23
0.21
0.24
0.21
0.22
E[ΔW] ($)
1.48
0.46
1.31
1.03
0.75
0.15
0.86
σΔW ($)
6.12
7.72
4.04
4.38
7.58
6.00
3.58
Count
220
244
196
205
155
166
134
Count
Move up
NOTE: For White workers, the weekly probability of a move is 1.20 percent: 0.64 percent upward and 0.56 percent
downward. For Black workers, the weekly probability of a move is 1.25 percent: 0.65 percent upward and 0.60 percent
downward.
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bins based on total experience: workers in weeks 1-50, 51-100, etc. The “move down” category
in the respective panels contains the average size of α for workers that make a downward occu
pational move (to a lower α, which must by construction be negative), the average change in
wages for downward occupational moves, and the standard deviation of wages for the down
ward occupational moves. The same statistics are computed for those who stayed in the same
occupation and those who moved to a higher occupation.
Comparing Black and White workers, the two panels of Table 2 are surprisingly similar
in terms of occupational moves: Given a downward occupational move, both White and Black
workers move down an average of about –.20 α (20 percentage points) regardless of their
career stage. Similarly, for those who move to a higher α, the average size of an occupational
change is about 0.21. However, the two tables do differ in terms of the wage changes from
occupational moves. Even for downward occupational moves, White workers see an average
increase of around $1.30, compared with $0.80 for Black workers. For upward occupational
moves, White workers see an average increase in wages of about $1.50, compared with $1.00
for Black workers. Given that the sizes of the occupational moves are the same, Black workers’
wages are seemingly less sensitive to the complex tasks in a job.
The types of occupational moves Black and White workers make are similar, and the factor
that explains the differences in life-cycle patterns of occupational moves is noted with Table 2:
Black and White workers have almost identical weekly probabilities of switching occupations
(1.20 percent for Whites and 1.25 percent for Blacks), but the relative rates of upward and down
ward moves differ dramatically: Given a move, White workers are 14 percent more likely to move
up versus down, while Black workers are only 8 percent more likely to move up versus down.
To examine the upward versus downward mobility rates of Black and White workers in
more detail, we consider transition tables across occupations, conditional on moves. Table 3
is constructed to show these rates: We take every occupational transition (and ignore “stayers”),
group the “pre-move” and “post-move” occupations into 10 bins, and calculate the conditional
probability of a worker being in in some post-move bin given the worker’s pre-move occu
pation. So by construction, the rows sum to 1 and reading across a row gives the probabilities
of moving into that bin given the row. This table helps deal with differences in the average
occupations between White and Black workers: Now we can compare the occupational moves
of a White worker and a Black worker who begin in the same occupation, which will help
control for potential demographic and unobserved differences between them.
The overall results from Table 3 show that conditional on a worker’s current occupation,
the race of the worker matters strongly when predicting to which occupations he will move
to next. Take a White worker and a Black worker both in the occupation “sales,” which has
0.42 α, putting them in the “0.5” row. At his next move, the White worker ends up in a morecomplex-task job 37 percent of the time. The Black worker, however, ends up at a higher-α job
only 25 percent of the time.6 This pattern is repeated across almost every row: low-occupation
White workers move up faster than low-occupation Black workers, and high-occupation
White workers downgrade less than high-occupation Black workers.
Interpreting these transition matrices within our model, given a worker is in a particular
occupation in one period, there are two reasons he can be in a different occupation the next
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Table 3
Transition Matrices
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Count
0.1
0.18
0.16
0.14
0.16
0.17
0.07
0.06
0.04
0.01
0.02
539
0.2
0.20
0.12
0.17
0.14
0.14
0.09
0.08
0.04
0.02
0.01
406
0.3
0.16
0.13
0.15
0.09
0.16
0.09
0.11
0.06
0.02
0.02
418
0.4
0.16
0.11
0.10
0.09
0.16
0.12
0.09
0.11
0.03
0.04
448
0.5
0.15
0.12
0.12
0.11
0.14
0.10
0.12
0.09
0.03
0.03
485
0.6
0.08
0.05
0.08
0.10
0.12
0.13
0.09
0.15
0.11
0.09
415
0.7
0.06
0.05
0.09
0.07
0.07
0.13
0.12
0.19
0.08
0.15
430
0.8
0.06
0.01
0.05
0.06
0.09
0.13
0.13
0.21
0.11
0.16
467
0.9
0.03
0.01
0.02
0.04
0.05
0.12
0.09
0.22
0.14
0.28
292
1.0
0.01
0.02
0.01
0.02
0.03
0.10
0.17
0.19
0.19
0.27
378
0.1
0.27
0.14
0.19
0.12
0.14
0.05
0.03
0.04
0
0.01
560
0.2
0.29
0.11
0.20
0.13
0.10
0.03
0.07
0.06
0
0.01
269
0.3
0.28
0.11
0.15
0.14
0.12
0.08
0.07
0.03
0.01
0.01
375
0.4
0.17
0.09
0.12
0.16
0.19
0.09
0.05
0.07
0.03
0.03
329
0.5
0.23
0.14
0.19
0.15
0.07
0.06
0.05
0.07
0.03
0.02
296
0.6
0.16
0.08
0.13
0.18
0.10
0.05
0.09
0.11
0.08
0.02
171
0.7
0.10
0.06
0.19
0.06
0.11
0.05
0.13
0.11
0.14
0.06
145
0.8
0.09
0.04
0.07
0.14
0.10
0.09
0.09
0.17
0.07
0.14
162
0.9
0.02
0.02
0.05
0.09
0.10
0.13
0.13
0.15
0.15
0.16
93
1.0
0.02
0.03
0.05
0.04
0.04
0.07
0.10
0.16
0.16
0.34
106
Whites
Blacks
NOTE: Bolded entries represent the conditional median of post-move α given pre-move α.
period: First, he learned that another occupation is a better fit, and/or second, the value of
experimentation has changed after learning in the first period. For example, if Black workers
in high-complexity occupations are in those occupations because they are informative, whereas
they are the best matches for the average White worker, you are more likely to see Black
workers leave those occupations as they learn more and have less incentive to experiment
further. Discrimination adds a further level of complexity because Black workers may be
restricted from entering their preferred occupations, so the incentives to learn may be the
same but they may be being restricted from finding their best match as quickly as White
workers. Using a structural life-cycle model, we further investigate the roles of productivity,
learning, and discrimination in Golan et al. (2017).
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Table 4
Table 5
The Relationship Between Wage Growth and Initial
Job Assignment
Determinants of an Initial Job Assignment
(1)
Blacks
(2)
Whites
Initial wage
0.596***
(0.044)
0.674***
(0.038)
Initial α
Initial α
0.880
(0.747)
0.358
(0.634)
Years of schooling (0 to 7)
0.057***
(0.004)
0.572***
(0.111)
Actual experience (in years)
0.508***
(0.149)
0.954***
(0.127)
Age
0.014***
(0.002)
0.168***
(0.055)
Initial wage × actual
experience
–0.032**
(0.016)
–0.045***
(0.015)
Black
–0.026*
(0.015)
–0.312
(0.324)
Initial α × actual experience
1.267***
(0.264)
1.130***
(0.190)
AFQT
0.068***
(0.008)
0.440***
(0.175)
AFQT
1.532***
(0.286)
1.330***
(0.185)
Constant
–0.128
(0.049)
3.340***
(1.070)
Constant
2.320***
(0.346)
0.805***
(0.410)
Dependent variable: wages
Observations
R2
181,424
343,620
0.310
0.347
Dependent variable: wages
(1)
Initial α
(2)
Initial wage
3.477***
(0.555)
Observations
1,593
1,593
R2
0.376
0.189
NOTE: Robust standard errors are in parentheses. *** p < 0.01 and
* p < 0.1.
NOTE: Robust standard errors are in parentheses. *** p < 0.01 and
** p < 0.05.
5.3 Initial Job Assignment
In the context of a learning model, the initial job assignment has an outsized effect on
the career path. If workers start their careers in a job or occupation where they learn nothing
about themselves, their wages would grow only as a result of human capital growth or other
factors. On the other hand, workers beginning in very informative jobs will see their wages
grow on average as they become better matched. If more-complex jobs also reveal more about
a worker’s innate ability, there should be a positive relationship between the measure of com
plexity in a worker’s initial job and future wage growth.
In Table 4 we consider the relationship between characteristics of a worker’s first job and
future wage growth. The dependent variable is the pooled cross section of wages in all jobs
after the first job, while the independent variables include both initial wages and initial α, actual
labor market experience, and interactions between initial job characteristics and actual expe
rience. The model has no particular predictions for the relationship between the initial α and
wages, but it predicts that the coefficient on the interaction of the initial α and experience will
be positive, which is what the data show. To interpret the estimates, relative to the wage growth
of a worker at the Black-worker sample average of α = 0.42, a worker at the White-worker
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sample average of α = 0.54 would see faster average wage growth of about $0.13 per year.
That is, there is around a 1 percent difference in the average yearly rates of wage growth that
can be attributed to racial differences in occupational characteristics.
Differences in information about one’s own ability can be reflected as well in the choice
of initial occupation: Workers with more to learn about themselves would tend toward occu
pations that provide more information. In Table 5 we document the relationship between
worker characteristics and the complexity measure α and the wage of the worker’s first job.
In the first column, the dependent variable is the complexity of the initial occupation, and
we condition on education, age, race, and AFQT score. Even after the controls for ability,
provided by controlling for education and the AFQT score, we find that Black workers start
their careers in about 2 percentage point less-complex-task occupations. While this may seem
small, it can be compared with the effect of lowering a worker’s AFQT score by 1/3 of a stan
dard deviation, which is a substantial drop. On the other hand, in the second column of Table 5
we find little evidence of a direct effect of race on the wage of the initial job once α and the
ability measures have been controlled for.
The finding that Black workers end up in less-complex jobs than comparable White
workers all while earning effectively the same as those White workers can be interpreted in
multiple ways consistent with our model of worker learning. For one, say discrimination is
the reason that Black workers don’t have access to more-complex jobs. This will reduce the
amount of learning Black workers have about themselves relative to what White workers—
in more-informative occupations—have about themselves. The long-run effect of the initial
discrimination would be that Black workers’ wage growth is lower relative to White workers’
wage growth than it would otherwise be if both races were assigned the same α jobs initially.
6 CONCLUSION
This article documents racial gaps in occupational assignment, turnover, and wages. We
use a learning model in which there is uncertainty about skills early in a worker’s career to
interpret the empirical evidence on the economic forces behind occupation mobility and the
Black-White pay gap and its evolution over a worker’s career.
We first document that both wage and occupation racial gaps increase with worker expe
rience. Occupational turnover is on average associated with an increase in pay. This is true
even for transitions from high- to low-skill-requirement occupations. Our learning model is
consistent with this pattern because it implies that workers sort into jobs that better match
their skills. This pattern holds for both Black and White individuals. Furthermore, we find
no significant differences in the number of occupational moves for Black and White workers.
However, Black workers are more likely to transition into occupations with lower skill require
ments than White workers and therefore experience smaller wage growth. This pattern is
also consistent with the widening gap in occupational skill requirements between Black and
White workers.
To further explore the Black-White wage gaps, we focus on differences in initial occupa
tional assignments. The learning model presented predicts that workers assigned initially to
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more-complex jobs will experience faster wage growth than those assigned initially to less-
complex jobs, because those in more-complex jobs will have more ability to learn about their
best occupation. Again, our analysis demonstrates that this pattern empirically holds for both
Black and White individuals. However, Black workers are assigned initially to jobs with lower
complexity partly because they have different demographic characteristics when they enter
the labor market, such as lower educational attainment and lower AFQT scores. Nevertheless,
we show that AFQT scores and educational attainment do not explain the entire gap in initial
occupational assignments. This finding can be interpreted both as differences in beliefs and
learning, but can at the same time be consistent with discriminatory hiring practices.
For future research, we suggest that further analyses should focus on understanding the
interaction between discrimination and learning, since restricting workers from entering their
preferred occupation as young workers can have lifetime effects on earnings and potentially
be an important source of racial inequality. n
NOTES
1
2016 Current Population Survey, Bureau of Labor Statistics.
2
This index was created in Antonovics and Golan (2012).
3
For details and examples, see Antonovics and Golan (2012).
4
In this tabulation, after making the sample selection rules discussed below, we treat individuals with missing
occupation information as being out of the labor force.
5
An alternative specification of these graphs uses worker age on the horizontal axis, which makes the gaps marginally larger and increasing over time, since differences in actual experience between White and Black workers
grow over time. See Golan et al. (2017) for a discussion of the effects of labor market participation rates on wage
and occupation gaps.
6
This calculation is done by summing all elements of the row to the right of the “0.5” column.
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