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מאמרים על הזעזועים המניעים מחזורי עסקים
חיבור לשם קבלת תואר דוקטור לפילוסופיה
מאת
נדב בן זאב
בירושלים, הוגש לסנט האוניברסיטה העברית
12/2011
מאמרים על הזעזועים המניעים מחזורי עסקים
חיבור לשם קבלת תואר דוקטור לפילוסופיה
מאת
נדב בן זאב
בירושלים, הוגש לסנט האוניברסיטה העברית
12/2011
:של ועבודה זו נעשתה בהדרכת
פרופסור יוסף זעירא
קצירת
? אילו זעזועים מניעים מחזורי עסקים: אחת משאלות המחקר החשובות ביותר במדע המקרו כלכלה הינה
קיימים עדיין כיום חילוקי דעות רבים וחוסר , מענה לשאלה זולמרות המחקר הרב שנעשה על מנת למצוא
עבודת הדוקטוראט שלי משתייכת לספרות . הסכמה לגבי סוגי הזעזועים אשר מניעים מחזורי עסקים
בעוד . הרחבה של מחזורי עסקים בעצם יכולתה לתרום להבנתנו בסוגי הזעזועים המניעים מחזורי עסקים
ים עדות אמפירית על זעזועי אינפורמציה לגבי טכנולוגיה בסקטור שני המאמרים הראשונים מספק
המאמר השלישי מפתח מסגרת , וזעזועי היצע אשראי כזעזועים המניעים מחזורי עסקים) IST(ההשקעה
.תיאורטית של משק קטן ופתוח אשר מאפשרת לחקור את השפעתם של זעזועי אינפורמציה ורעש
לאחרונה הוצעהאשר אינפורמציה זעזועי לזיהוי אמפירית מתודולוגיה מרחיב הראשון המאמר
.הכלכלה של האמיתי המודל סוג לגבי ההנחה על מגבלה הטלת ללא ל"הנ הזעזועים את לזהות שמטרתה
זעזועי שתזהה מתודולוגיה מציע אלא מסוים מבני מודל של מבנית אמידה אומד לא אני, כלומר
המתקיימות זיהוי הנחות באמצעות השפעתם ואת שקעההה בסקטור הטכנולוגיה על אינפורמציה
כי להראות בכדי, בפרט. אינפורמציה זעזועי הכוללים כללי למשק שיווי של כלכליים מקרו במודלים
- ניו מבני ממודל נתונים ייצרתי בהן קרלו הטמונ סימולציות ביצעתי, טוב זיהו מבצעת המתודולוגיה
הממצאים. המלאכותיים הנתונים על האמידה אלגוריתם את יויישמת פעמים של רב מספר יאניסקיינ
מעודדת עדות אכן זו טוב לזיהוי הוכחה לא זו כי ולמרות, טוב זיהוי מבצעת המתודולוגיה אכן כי מראים
כדי ב"ארה כלכלת על בנתונים שימוש עשיתי, מכך ביתרה. טוב זיהוי לבצע מסוגלת שהמתודולוגיה לכך
התיאורטיים אלו עם עקביים האמפיריים הממצאים. ל"הנ הזעזועים של יריתהאמפ ההשפעה את לבחון
את מגדילה בעתיד IST על חיובית אינפורמציה, כלומר. מוצג במאמרש התיאורטי מהמודל שנובעים
זעזועי האינפורמציה , בנוסף. לדפלציה מביאה בעת ובו מיידית וצריכה השקעה, תעסוקה, התוצר
המיתונים עשרתמתוך תשעהל ותרמו בפועל ל"תיות קצרת הטווח במשתנים הנמהתנוד 70% -מסבירים כ
מחזורי לייצר מסוגלים רק לא האינפורמציהזעזועי כי מראות התוצאות, לסיכום. ב"האחרונים בארה
60 - ב האמריקאי המשק של העסקים במחזורי בשישה ומרכזי חשוב תפקיד שיחקו שהם גם אלא עסקים
רומה המרכזית של מאמר זה מתבטאת בעדות האמפירית החזקה כי זעזועי הת. האחרונות השנה
.מהווים את הגורם המשמעותי מאחורי מחזורי עסקים ISTאינפורמציה על
מציע שאני הזיהוי שיטת. עסקים במחזורי ובתפקידם אשראי היצע בזעזועי עוסק השני המאמר
זה שזעזוע המגבלה תחת החיצוני המימון ייתפרמ את ביותר הטובה בצורה מסביר אשר הזעזוע את מזהה
ברמת תלויים בלתי הינם אשר הזעזועים קבוצת מתוך, כלומר. במשק הטכנולוגיה ברמת תלוי בלתי הינו
. החיצוני המימון פרמיית את טוב הכי שמסביר בזעזוע בוחר אני, בעתיד והן בהווה הן במשק הטכנולוגיה
הממצאים. החיצוני המימון פרמיית את טוב הכי מסביר אשר קושהבי זעזוע את מוצא בעצם אני, למעשה
זה וזעזוע החיצוני המימון בפרמיית השונות רוב את שמסביר ביקוש זעזוע שישנו מראים אכן האמפיריים
במיתון מרכזי תפקיד ושיחק עסקים מחזורי לייצר מסוגל הוא, בפרט. אשראי היצע זעזוע כמו מתנהג
דומה באופן מתנהגים אשר אשראי היצע זעזועי הכולל תיאורטי מודל מפתח םג אני. ב"בארה האחרון
היצע זעזועי את לזהות מסוגלת שלי הזיהוי שיטת כי מראה אני, לבסוף. מזהה שאני האמפיריים לזעזועים
התרומה העיקרית ש מאמר .התיאורטי המודלי "בהתבסס על נתונים מלאכותיים המיוצרים ע האשראי
למרות שאינם הגורם הדומיננטי המסביר של , עדות האמפירית כ זעזועי היצע אשראיזה מתבטאת ב
, בתקופות שבהן ישנם זעזועי היצע אשראי גדולים, בפרט. מסוגלים לייצר מחזורי עסקים, מחזורי עסקים
ביחד עם התוצאות של המאמר הראשון. סביר כי ייווצר מיתון רציני ביותר, כמו במיתון העולמי האחרון
של מאמר זה מספקות תמונת מצב התוצאות , אשר זוהו במאמר הראשון ISTעל זעזועי האינפורמציה על
.מעניינת המצביעה על שני זעזועים אשר מסוגלים לייצר מחזורי עסקים
עם אינפורמציה מבנה של הרחבה ופתוח הכולל קטן משק של יאניסקיינ- ניו מודל מפתחהשלישי המאמר
זעזועי מולידה זו הרחבה. במשק הפרטים מקבלים אותם העתידי הכולל לפריון בנוגע רעש בעלי סיגנלים
את ממדל שאני לציין יש. העסקים במחזור תפקידם בחינת את ומאפשרת המודל לתוך ורעש אינפורמציה
של הולדה המאפשר דומה אינפורמציה מבנה עם סגור משק של יאניסקיינ- ניו כמודל העולם שאר כלכלת
הינה ורעש אינפורמציה בזעזועי העוסקת לספרות שלי התרומה. העולמית הכלכלה ברמת ל"הנ עיםהזעזו
הכלכלה ברמת והן המקומי המשק ברמת הן, ורעש אינפורמציה זעזועי של ההשפעה את בוחן שאני בכך
עיקרב כה עד שהתמקדה בספרות נעשה לא זה מסוג ניתוח, ידיעתי למיטב. ופתוח קטן משק על, העולמית
התמקדו פתוחים משקים בחנו שכן מאמרים של םצמוצהמ המספר, בנוסף. סגור משק של במודלים
שזעזועי כך על מצביעות המאמר של המרכזיות התוצאות. רעש זעזועי של בחינה ללא אינפורמציה בזעזועי
אינפורמציה זעזועי, לדפלציה וגורמים הכלכלית הפעילות את מרחיבים מקומיים חיוביים אינפורמציה
רעש וזעזועי בדפלציה המלווה מיידית אינפלציה ומייצרים הכלכלית הפעילות את מרחיבים כן גם עולמיים
ומייצרים הכלכלית הפעילות את המרחיבים טהורים ביקוש כזעזועי מתנהגים ועולמיים מקומיים
פוטנציאלי תפקיד רעשו אינפורמציה זעזועיל יש התיאורטית ברמה לפחות כי הינה המסקנה. אינפלציה
.פתוח קטן משק של העסקים במחזור חשוב
Essays on The Sources of Business Cycles
Thesis submitted for the degree of
“Doctor of Philosophy” (Economics)
By
Nadav Ben Zeev
Submitted to the Senate of the Hebrew University
12/2011
Essays on The Sources of Business Cycles
Thesis submitted for the degree of
“Doctor of Philosophy” (Economics)
By
Nadav Ben Zeev
Submitted to the Senate of the Hebrew University
12/2011
This work was carried out under the supervision of:
Prof. Joseph Zeira
1
Acknowledgements
I would like to thank my committee members - Joseph Zeira, Zvi Hercowitz, Bob
Barsky, and Michael Beenstock. I am especially grateful to my chair, Joseph Zeira,
without whom I would not have had the opportunity to pursue my research interests
and become part of the PhD program at Hebrew U. I enjoyed our discussions and
learned a lot from them. He was also the main reason behind my three months visit at
the University of Michigan which had a very positive effect on my dissertation.
A special thanks is also due to Bob Barsky with whom I was fortunate enough
to spend a semester at the University of Michigan during which time I benefited a lot
from numerous discussions with him. Bob's work on news shocks influenced me a
great deal and was the main reason for which I started to do independent work in the
field of news shocks. I also benefited from discussions with Zvi Hercowitz, who
introduced the concept of investment specific technology in the framework of an
otherwise standard macro model over 20 years ago. This concept has turned out to be
one of the main themes of my dissertation. Furthermore, I am very grateful to
Michael Beenstock who taught me a lot of what I know about time series
econometrics and was always patient and willing to read and discuss my work.
Lastly, I am greatly indebted to my parents for their love and support. They
have played a crucial part in my being able to pursue my academic goals. I am also
very grateful to my brother for always being there for me. I would also like to express
my deep gratitude to my girlfriend and best friend, Lori, for her love, support, and
patience during my PhD studies.
2
Abstract
The quest for understanding the driving forces behind business cycles has been a
prominent feature of modern macroeconomic research. The role of several candidate
shocks as business cycle drivers has been studied, leaving much debate and lack of
consensus on the types of shocks that drive business cycles. This dissertation belongs
to the vast business cycle literature in that it tries to contribute to our understanding of
the types of shocks that drive the business cycle. While the first two papers in the
dissertation provide empirical evidence on news shocks about future investment
specific technology and credit supply shocks as business cycle drivers, the third paper
is a theoretical contribution that models the role of news and noise shocks in an open
economy setting.
The first paper focuses on the empirical role of news shocks about future
investment specific technology (IST), i.e. technology that is specific to the investment
goods sector, and provides robust evidence that IST news shocks constitute a
significant force behind the business cycle. Extending a recent empirical approach to
identifying news shocks, I find robust evidence that IST news shocks induce positive
comovement, i.e., raise output, consumption, investment, and hours of work, explain
70% of their business cycle variation, and have played an important part in nine of the
last ten U.S recessions. I also show that the empirical method I employ is indeed
capable of identifying IST news shocks from data generated by a standard DSGE
model. Overall, the main contribution of the paper is the robust evidence that IST
news shocks are the major force behind the business cycle. Hence, the paper offers a
potential resolution for the debate about which shocks actually drive business cycles.
The second paper studies the role of credit supply shocks in the business cycle,
an issue that has received considerable attention in light of the recent financial crisis
3
and great recession in the U.S. Extending Uhlig's (2003) method, I identify the
demand shock that explains the most of the movements in the external finance
premium (EFP). This demand shock induces business cycle comovement and has
played an important part in the recent recession. Impulse response functions provide
an interpretation of this shock as a credit supply shock. Monte Carlo simulation
results based on a DSGE model with a financial accelerator, in which credit supply
shocks generate impulse responses consistent with the observed empirical responses,
indicate that the identification method does a good job of identifying these shocks
from model generated data. The results indicate that even though credit supply shocks
are not a dominant source behind the business, they have the potential of generating
business cycles. Moreover, as is evident from the recent recession, large adverse
credit supply shocks are likely to cause a serious recession.
The third paper studies the potential role of domestic and foreign news and
animal spirits shocks in a small open economy using a calibrated small open economy
new Keynesian model. The main contribution of the paper lies in proposing a setting
in which the effect of both foreign and domestic news and animal spirits shocks can
be studied. The news shock is a permanent but not immediate innovation to the level
of technology as it is an anticipation of a future technology shock. I only allow
domestic and foreign households to observe a noisy signal of domestic and foreign
news, respectively, and interpret a pure noise innovation as an animal spirits shock, as
it is associated with erroneous consumer optimism or pessimism. I find that foreign
news are expansionary and induce inflation on impact followed by deflation at longer
time horizons, while domestic news are expansionary and deflationary. Domestic
animal spirits are expansionary and inflationary playing the role of aggregate demand
4
shocks whereas foreign animal spirits are expansionary and lead to deflation on
impact and inflation afterwards.
5
Table of Contents
Acknowledgements ........................................................................................................ 1
Abstract .......................................................................................................................... 2
List of Figures ............................................................................................................... 8
List of Tables ............................................................................................................. 10
Chapter I. Introduction ................................................................................................ 11
Chapter II. News Shocks about Future Investment Specific Technology and Business
Cycles .......................................................................................................................... 14
1. Introduction ................................................................................................... …14
2. Empirical Strategy ............................................................................................. 17
2.1 Identification Strategy ................................................................................ 18
2.2 Simulation Evidence ................................................................................. 20
3. Empirical Evidence ............................................................................................ 27
3.1 Data ............................................................................................................ 27
3.2 Benchmark Results .................................................................................. 29
3.3 Sensitivity Analysis ................................................................................... 35
3.4 Relation with Previous Work ..................................................................... 37
4. Conclusion ......................................................................................................... 40
III. The External Finance Premium and Business Cycles............................................ 58
1. Introduction ......................................................................................................... 58
2. Empirical Strategy .............................................................................................. 61
3. Empirical Evidence ............................................................................................ 64
6
3.1 Data ............................................................................................................ 64
3.2 Benchmark Results .................................................................................. 65
3.3 Sensitivity Analysis ................................................................................... 69
4. A DSGE Model with a Financial Accelerator .................................................... 72
4.1 Model ......................................................................................................... 72
4.2 Estimation ................................................................................................ 75
4.3 Results ........................................................................................................ 77
4.4 Simulation Evidence .................................................................................. 78
5. Conclusion ........................................................................................................ 80
IV. The Role of Domestic and Foreign News and Animal Spirits Shocks in a Small
Open Economy............................................................................................................. 97
1. Introduction ........................................................................................................ 97
2. Small Open Economy Model ........................................................................... 101
2.1 Households .............................................................................................. 101
2.1.1 The real exchange rate and the terms of trade ..................... 103
2.1.2 The Foreign Economy and International risk sharing .......... 104
2.1.2 Uncovered interest parity ...................................................... 105
2.2 Firms ....................................................................................................... 106
2.2.1 Technology and News Shocks .............................................. 106
2.2.2 Perceptions and Animal Spirits ............................................. 108
2.2.3 Price-Setting .......................................................................... 110
3. Equillibrium ..................................................................................................... 112
3.1 The Demand Side: Aggregate demand and output determination .......... 112
7
3.2 The Trade Balance ................................................................................... 113
3.3 The Supply Side: Marginal Cost and Inflation Dynamics ....................... 114
3.4 Closing the Model: Domestic monetary policy rule and Foreign Economy
Equilibrium .............................................................................................. 115
4. Numerical Results .......................................................................................... 116
4.1 Calibration .............................................................................................. 116
4.2 Impulse Responses to the Structural Shocks ........................................ 117
4.3 Variance Decomposition ........................................................................ 120
4.4 Robustness ............................................................................................. 121
5. Conclusion ....................................................................................................... 124
V. Conclusion .......................................................................................................... 137
8
List of Figures
Figure 2.1 : Model and Monte Carlo Estimated Impulse Responses to IST News
Shock............................................................................................................................ 50
Figure 2.2 : Model and Monte Carlo Estimated Impulse Responses to Unanticipated
IST Shock..................................................................................................................... 51
Figure 2.3 : Empirical Impulse Responses to IST News Shock ................................. 52
Figure 2.4 : Share of Forecast Error Variance Attributable to identified shocks ........ 53
Figure 2.5 : Identified News Shock Time Series and U.S Recessions ........................ 54
Figure 2.6 : Empirical Impulse Responses to Unanticipated IST Shock .................... 55
Figure 2.7 : Impulse responses to IST News shock: Alternative investment price
measure ........................................................................................................................ 56
Figure 2.8 Impulse responses to IST News shock: Larger VAR ................................. 57
Figure 3.1 : Empirical Impulse Responses to EFP Shocks .......................................... 89
Figure 3.2 : Share of Forecast Error Variance Attributable to identified shocks ........ 90
Figure 3.3 : Identified News Shock Time Series and U.S Recessions ........................ 91
Figure 3.4 : Impulse responses to EFP shocks: Smaller Sample ................................. 92
Figure 3.5 : Impulse responses to EFP shocks: Alternative measure of EFP .............. 93
Figure 3.6 : Impulse responses to EFP shocks: Including Credit Quantity ................. 94
Figure 3.7 : Impulse responses to Credit Supply shock for DSGE model ................... 95
Figure 3.8 : Model and Monte Carlo Estimated Impulse Responses to Credit Supply
shocks ........................................................................................................................... 96
Figure 4.1 : Impulse Responses to Technology Shocks ............................................ 127
Figure 4.2 : Impulse Responses to News Shocks ...................................................... 128
9
Figure 4.3 : Impulse Responses to Animal Spirits Shocks ........................................ 129
Figure 4.4 : Forecast Error Variance Decomposition ................................................ 130
Figure 4.5 : Impulse Responses to Domestic Technology Shocks under Alternative
Policy Rules ............................................................................................................... 131
Figure 4.6 : Impulse Responses to Foreign Technology Shocks under Alternative
Policy Rules ............................................................................................................... 132
Figure 4.7 : Impulse Responses to Domestic News Shocks under Alternative Policy
Rules .......................................................................................................................... 133
Figure 4.8 : Impulse Responses to Foreign News Shocks under Alternative Policy
Rules .......................................................................................................................... 134
Figure 4.9 : Impulse Responses to Domestic Animal Spirits under Alternative Policy
Rules .......................................................................................................................... 135
Figure 4.10 : Impulse Responses to Foreign Animal Spirits under Alternative Policy
Rules .......................................................................................................................... 136
10
List of Tables
Table 2.1: The Variables and Equations of the model ................................................. 45
Table 2.2 : Description of the Parameters of the Model and Bechmark Values .......... 47
Table 2.3 : Correlation Estimates................................................................................. 48
Table 2.4 : Historical Contribution of IST News Shocks to Output per Capita Loss in
U.S Recessions ............................................................................................................. 49
Table 3.1: Correlation Estimates.................................................................................. 84
Table 3.2 : Historical Contribution of EFP Shocks to Output per Capita Loss in U.S
Recessions .................................................................................................................... 85
Table 3.3: The Variables and Equations of the Model ................................................ 86
Table 3.4 : Description of the Parameters of the Model and Bechmark Values .......... 88
11
Chapter I
Introduction
The field of macroeconomics has long been devoted to studying the sources of
business cycles. Though significant research has been conducted on identifying the
specific types of shocks that generate business cycles, we are still left with much
debate and lack of consensus on which shocks actually drive the business cycle. This
dissertation contributes to the business cycle literature by providing evidence
regarding the types of shocks that drive the business cycle.
Chapter II extends a recent empirical approach to the identification of news
shocks and applies this extended method to identify news shocks about future
investment specific technology (Henceforth IST) using U.S postwar data. These
shocks do not affect IST contemporaneously but rather portend future changes in it
and thus are defined as news shocks. The method is VAR based and essentially
identifies the IST news shock as the shock that is orthogonal to current IST and that
maximally explains future variation in IST over a finite horizon. Chapter II finds
robust evidence that IST news shocks induce positive comovement, i.e., raise output,
consumption, investment, and hours of work, explain 70% of their business cycle
variation, and have played an important part in nine of the last ten U.S recessions.
These novel findings suggest that business cycles are broadly generated by IST news
shocks hence offering a potential resolution for the debate about the types of shocks
drive business cycles.
While chapter II deals with technology related shocks, chapter III is concerned
with the identification of credit supply shocks, an issue that has received considerable
attention in light of the recent financial crisis and great recession in the U.S.
Extending Uhlig's (2003) VAR based method, I identify the demand shock that
explains the most of the movements in the external finance premium (EFP).
12
Specifically, the identified shock is attained by finding the shock that maximally
explains future variation in the external finance premium under the restriction that it
has no effect on both neutral and investment specific technology at all horizons. It is
found that this demand shock induces business cycle comovement and has played an
important part in the recent recession. Impulse response functions provide an
interpretation of this shock as a credit supply shock. Even though credit supply shocks
are not the dominant force behind business cycles in general, the results indicate that
they are indeed capable of generating business cycles especially when large negative
shocks realize, as was clearly demonstrated by the recent recession.
Chapters II and III follow recent work which used monte carlo simulations
based on DSGE models to check the suitability of a given identification method (e.g.
Francis et al., Chari et al. (2008), and Barsky and Sims (2010a)). Accordingly, it is
verified in both papers that the identification strategy is capable of recovering the IST
news shock and credit supply shock as well as their dynamic effects from data
simulated from DSGE models. For each paper, a different DSGE model is used so
that a proper modeling framework is chosen. In chapter II, On the basis of simulations
from a state-of-the-art DSGE model that incorporates IST news shocks, it is shown
that the identification method is likely to perform well at identifying IST news shocks
in practice. In chapter III, Monte Carlo simulation results based on a DSGE model
with a financial accelerator, in which credit supply shocks generate impulse responses
consistent with the observed empirical responses, indicate that the identification
method does a good job of identifying these shocks from model generated data.
Chapter IV formulates a theoretical small open economy New Keynesian
model that incorporates domestic and foreign news shocks and animal spirits (noise)
shocks and allows an examination of the implications of these shocks for a small open
economy. The news shock is a permanent but not immediate innovation to the level of
technology as it is an anticipation of a future technology shock. I only allow domestic
and foreign households to observe a noisy signal of domestic and foreign news,
13
respectively, and interpret a pure noise innovation as an animal spirits shock, as it is
associated with erroneous consumer optimism or pessimism.
The main contribution of the paper lies in proposing a setting in which the
effect of both foreign and domestic news and animal spirits shocks can be studied.
The reason such an extended setting is interesting is twofold. First, it is appealing to
examine whether the effects of domestic news and animal spirits shocks are different
for a small open economy model relative to a closed economy model. The findings
indicate that the effects are similar to the closed economy model as domestic news are
expansionary and deflationary while domestic animal spirits are expansionary and
inflationary playing the role of aggregate demand shocks. Second, it is interesting to
study how the effects of foreign news and animal spirits shocks differ from their
domestic counterparts. The findings indicate a difference with respect to the response
of inflation which is attributable to exchange rate behavior. In particular, it is found
that foreign news are expansionary and induce inflation on impact (due to currency
depreciation) followed by deflation at longer time horizons which is imported by the
deflation in the foreign economy, while foreign animal spirits are expansionary and
lead to deflation on impact (due to currency appreciation) and inflation afterwards as
the demand side effects of the shocks become more dominant than the exchange rate
effect.
The introduction of noise into the news signals arguably renders a more
realistic setting than one in which news shocks are perfectly observed and known in
advance. Chapter IV demonstrates that news shocks can be important even if they are
imperfectly observed as noisy signals. Nevertheless, as the news signals become
noisier their importance diminishes. Given that the VAR based identification method
used in chapter II is also suitable for the case in which news signals contain noise, it
can be deduced that IST news shocks are not dominated by noise even though it is
fairly reasonable to assume that they are not perfectly known in advance.
Chapter V presents concluding remarks and binds the various themes of the
dissertation together. It also discusses possible avenues for future related research.
14
Chapter II
News Shocks about Future Investment Specific
Technology and Business Cycles
1. Introduction
This paper contributes to the vast literature that has strived to comprehend which
forces drive business cycles by providing robust evidence that IST news shocks are a
significant force behind business cycles. I identify IST news shocks by extending the
VAR based method for the identification of news shocks that was recently proposed
by Barsky and Sims (2010a),1 which in turn builds upon the maximum forecast error
variance (MFEV) identification approach developed by Uhlig (2003). Whereas the
former identified TFP news shocks as the shocks that maximally explain future
variation in TFP over a finite horizon orthogonalized with respect to unanticipated
TFP shocks, thus adding one identifying restriction to the MFEV optimization
problem, I add two identifying restrictions for the identification of IST news shocks.
In particular, the IST news shock is identified as the linear combination of reduced
form innovations orthogonal to both unanticipated TFP and IST shocks which
maximizes the sum of contributions to IST forecast error variance over a finite
horizon.2 As discussed in section 2.2, the main reason for including TFP and the
corresponding additional orthogonality restriction is that the monte carlo simulation
results, using DSGE model generated data, showed that it significantly improves the
identification of IST news shocks. The main virtue of this identification approach to
1 They focus on TFP news shocks and find the latter to be associated with an increase in consumption
and decrease in output, investment and hours worked on impact thus suggesting an unimportant role of
these shocks in the business cycle. 2 It's important to note here that TFP is a measure of exogenous neutral technology, as opposed to labor
productivity, and it is therefore appropriate to impose on IST news shocks to be orthogonal to it
contemporaneously.
15
IST news shocks is that it does not impose a specific model structure on the data as in
the empirical DSGE literature but rather exploits two common assumptions in IST
news driven DSGE models that (i) only a limited number of shocks ever affect IST
and (ii) IST news shocks do not affect IST contemporaneously but rather portend
future changes in it. After it is shown that this identification procedure performs well
on DSGE model generated data in terms of identifying IST news shocks and their
business cycle effects, I apply it on postwar U.S data.3 I find robust evidence that IST
news shocks induce positive business cycle comovement, i.e., raise output,
consumption, investment, and hours of work, explain 70% of their forecast error
variance at business cycle frequencies, and have played an important part in nine of
the last ten U.S recessions. Overall, it can be deduced that IST news shocks are not
only capable of generating business cycles but also that they have played an important
role as drivers of U.S business cycles over the last sixty years.
The role of several candidate shocks as business cycle drivers has been
studied, leaving much debate and lack of consensus on the types of shocks that drive
business cycles. Such candidate shocks include total factor productivity (TFP) shocks
(e.g. Gali (1999) and Basu, Fernald, and Kimball (2006; Henceforth BFK)),
investment specific technology (IST) shocks (e.g. Greenwood, Hercowitz, and Krusell
(2000; Henceforth GHK), Fisher (2006), Justiniano et al. (2010a, 2010b), and Khan
and Tsoukalas (2011)), and news shocks about future TFP, i.e. shocks that portend
future changes in TFP (e.g. Beaudry and Portier (2006), Beaudry and Lucke (2009),
and Barsky and Sims (2010a)).
The few papers that have tried to assess the role of IST news shocks in the
business cycle did so using estimated dynamic stochastic general equilibrium (DSGE)
models (i.e. Davis (2007), Schmitt-Grohé and Uríbe (2008), and Khan and Tsoukalas
(2010)). The main advantage of the DSGE approach is that it provides a structural
interpretation of the mechanisms transmitting the shocks. The disadvantage, however,
3 I follow GHK (1997, 2000), Fisher (2006), Schmitt-Grohé and Uríbe (2008), Beaudry and Lucke
(2009), and Liu et al. (2011) and use a real investment price measure to gauge IST (see section 3.1 for
data descriptions).
16
is that model based inferences often depend upon the assumed structure which could
be different from the true one. Therefore, imposing a certain structure on the data
could lead to incorrect inferences. Davis (2007) introduces news shocks in the
Christiano et al. (2005) model and finds that IST news shocks account for about 52%
of the variation in output growth.4 By contrast, Schmitt-Grohé and Uríbe (2008)
estimate a flexible price-wage DSGE model with TFP and IST news shocks and find a
strong role for TFP news compared to a negligible role for IST news. Lastly, Khan
and Tsoukalas (2010) estimate a DSGE model with both real and nominal frictions,
including TFP and IST news shocks, and find a relatively weak role for news shocks
as drivers of the business cycle. That the above DSGE literature arrived at different
conclusions about the relative importance of each type of news shock suggests that
some features of the model structure may themselves have an effect on the
quantitative assessments. Overall, the empirical DSGE literature has not found robust
evidence in support of a strong role for IST news shocks as business cycle drivers.
The empirical findings of this paper stand in contrast to the findings of the
DSGE literature on IST news shocks. While the results from this literature depend on
the type of structure of the model, my results are derived from a model-free
identification approach that does not impose any structure on the data but is still
capable of identifying IST news shocks and their business cycle effects from a variety
of model structures. Nevertheless, it's important to understand what type of model
structure is needed in order for IST news shocks to be at the very least capable of
generating business cycles. In the next section, which provides monte carlo simulation
evidence that confirms that the proposed identification approach works fairly well on
DSGE model generated data, I present a state-of-the-art DSGE model that is capable
of providing the structure that is needed for IST news shocks to be drivers of business
cycles. The model is a standard New-Keynesian DSGE model (e.g. Smets and
Wouters (2007)) augmented with the recently popularized Jaimovich and Rebelo
4 Nevertheless, it is unclear whether or not IST news shocks produce business cycle comovement in his
paper as the impulse responses are not shown.
17
(2009) preference structure and a specification of the cost of utilization in terms of
increased depreciation of capital, as originally proposed by Greenwood, Hercowitz
and Huffman (1988; Henceforth GHH) in a neoclassical setting. The model
essentially contains the three elements that are needed for IST news shocks to be
capable of generating business cycles, as shown by Jaimovich and Rebelo (2009):
preferences with a small wealth effect on labor supply, investment adjustment costs,
and variable capital utilization.
The remainder of the paper is organized as follows. In the next section the
details of the empirical strategy are laid out and simulation evidence that the
identification procedure performs well on data generated from a state-of-the-art
DSGE model is provided. Section 3 begins with a description of the data, after which
it presents the main empirical evidence and provides a sensitivity analysis of the
results as well as a discussion on their relation to earlier work. The final section
concludes.
2. Empirical Strategy
It is assumed that IST is well-characterized as following a stochastic process driven
by two shocks. The first is the traditional unanticipated IST shock of the IST
literature, first introduced in the pioneering work of GHH (1988), which impacts the
level of IST in the same period in which agents observe it. The second is the news
shock, which is differentiated from the first shock in that agents observe the news
shock in advance and it portends future changes in IST. The following is an example
process that incorporates both unanticipated and IST news shocks:
1 1
is is is is
t t t tgε ε η− −= + + (1)
1
is is is
t t tg g eκ −= + (2)
Here log IST, denoted by is
tε , follows a unit root process where the drift term itself
1
is
tg − follows an AR(1) process. Parameterκ describes the persistence of the drift
term. is
tη is the conventional unanticipated IST shock. Given the timing
assumption, is
te has no immediate impact on the level of IST but portends future
18
changes in it. Hence, it can be defined as an IST news shock. In a VAR including
empirical measures of TFP, IST and several macroeconomic aggregates, the IST news
shock is identified as the shock that best explains future movements in IST over a
horizon of fifteen years and that is orthogonal to both TFP and IST unanticipated
shocks. The restriction with respect to IST is important for identification as it imposes
on the identified shock to have no contemporaneous effect on IST, which complies
with the definition of a news shock. I include TFP in the VAR and impose the
corresponding additional orthogonality restriction because monte carlo simulation
evidence indicated that doing so significantly improves identification. In practice, this
identification strategy involves finding the linear combination of VAR innovations
contemporaneously uncorrelated with TFP and IST innovations which maximally
contributes to IST's future forecast error variance.
The remainder of this section is organized as follows. Section 2.1 introduces
terminology and lays out the identification strategy more formally. This paper follows
recent work which used monte carlo simulations based on DSGE models to check the
suitability of a given identification method (e.g. Francis et al., Chari et al. (2008), and
Barsky and Sims (2010a)). Thus, it is verified in Section 2.2 that the identification
strategy is capable of recovering the IST news shock and its dynamic effects from
data simulated from DSGE models. On the basis of simulations from a state-of-the-art
DSGE model, it is shown that the identification method is likely to perform well at
identifying IST news shocks in practice.
2.1 Identification Strategy
The identification method pursued in the paper will now be presented in detail.
Let ty be a k x1 vector of observables of length T. Estimating a stationary vector error
correction model (VECM) or an unrestricted VAR in levels can generate the reduced
form moving average representation in the levels of the observables:
ty B(L)ut = (3)
Where L is the lag operator and0
B(L) B Lτττ
∞
=
=∑ . It is assumed there exists a linear
mapping between innovations and structural shocks:
19
t tu Aε= (4)
This implies the following structural moving average representation:
t ty C(L)ε= (5)
Where C(L) B(L)A= and 1At tuε −= . The impact matrix A must satisfy 'AA = Σ ,
whereΣ is the variance-covariance matrix of innovations. However, there's an infinite
number of impact matrices that solve the system 'AA = Σ . In particular, for some
arbitrary orthogonalization, A (e.g. a Choleski decomposition), the entire space of
permissible impact matrices can be written as AD , where D is a k x k orthonormal
matrix ( 'DD I= ).
The h step ahead forecast error is:
t+h t t+h t+h-
0
y -E y = B ADh
τ ττ
ε=∑ (6)
The contribution to the forecast error variance of variable i attributable to structural
shock j at horizon h is then:
'
' '
i,j , ,
0
(h) B A A Bh
i iτ ττ
γγ=
Ω =∑ (7)
γ constitutes the jth column of D. Aγ is then a k x 1 vector corresponding with the jth
column of a possible orthogonalization and ,Bi τ represents the ith row of the matrix of
moving average coefficients at horizonτ . Let TFP and IST occupy the first and
second positions in the system, respectively, and let the unanticipated TFP and IST
shocks be indexed by 1 and 2, respectively. Finally, the news shock is indexed by 3
and is identified as the shock that is orthogonal to unanticipated TFP and IST shocks
and that maximally explains movements in IST not accounted for by its own
innovations and TFP innovations. In particular, the IST news shocks is identified by
finding theγ which maximizes the sum of contribution to the forecast error variance
of IST at horizons from 0 to H subject to the restriction that this shock have no
contemporaneous effect on TFP and IST. This implies solving the following
optimization problem:
20
'* ' '
2,3 2, 2,
0 0 0
'
arg max ( ) B A A B
A(1, ) 0 1
A(2, ) 0 2
. (1,1) 0
(2,1) 0
1
H H h
h h
h
j j
j j
s t
τ ττ
γ γγ
γγγ γ
= = =
= Ω =
= ∀ >
= ∀ >
=
=
=
∑ ∑∑
H is some finite truncation horizon. The first four constraints impose on the identified
shock to have no contemporaneous effect on TFP and IST. The fifth restriction that
imposes onγ to have unit length ensures thatγ is a column vector belonging to an
orthonormal matrix. Following Uhlig (2003), this maximization problem can be
rewritten as a quadratic form in which the non-zero portion ofγ is the eigenvector
associated with the maximum eigenvalue of the lower (k-2) x (k-2) sub-matrix of the
following matrix S:
( ) ( ) ( )'
2, 2,
0
S 1 B A B AH
H τ ττ
τ=
= + −∑
Hence, this procedure constitutes an application of principle components.
Specifically, it identifies the IST news shock as the first principal component of the
lower (k-2) x (k-2) sub-matrix of matrix S orthogonalized with respect to IST and
TFP innovations.
2.2 Simulation Evidence
Simulation evidence which confirms that the above proposed empirical strategy is
indeed capable of doing a good job of identifying IST news shocks will now be
presented. I consider the by now classic Smets and Wouters (2007) model augmented
with three elements, along the lines of Khan and Tsoukalas (2010, 2011): the recently
popularized Jaimovich and Rebelo (2009) preferences that allow for an arbitrarily
weak wealth effect on labor supply,5 specification of the cost of utilization in terms of
increased depreciation of capital, as originally proposed by GHH (1988) in a
5 These preferences nest two polar specifications that have featured prominently in the business cycle
literature: the one used in King et al. (1988) and the one introduced by GHH (1988).
21
neoclassical setting,6 and finally the model also includes TFP and IST news shocks.
TFP news shocks are also included in the model in order to be consistent with the
news shocks literature. Prior to presenting the simulation evidence I will first present
the model used to simulate the data.
The preference structure suggested by Jaimovich and Rebelo (2009), which
conveniently nests two special cases which we describe below, is assumed.
Specifically, the utility function of household [0,1]j∈ is
1 1
0
0
( ( ) ) 1
1
lbt t t t t
t c
C L j XE
σ σε χβ
σ
+ −∞
=
− − −
∑ (8)
Where 1t t tX C Xω ω−= and agents internalize the dynamics of tX in their maximization
problem. E0 denotes the expectation conditional on the information available at time
zero, 0 < β < 1, lσ > 1, χ > 0, Cσ > 0, 0 <ω < 1, and b
tε is the preference shock.
When 1ω = the preferences are the same as in King et al.(1988) with the implication
that intertemporal substitution effect influences labor effort. When 0ω = the
preferences are the same as in Greenwood et al.(1988), with the implication that
intertemporal consumption-saving choice does not affect labor effort.
The budget constraint and the capital accumulation equation are given as
1 1( ) ( ) k
t t t t t t t tt t t
t t t t t t
B B W j L j R Z K DivC I T
R P P P P P
− −+ + − ≤ + + + (9)
[ ]1 1(1 ( )) 1 ( / )i
t t t t t t tK Z K S I I Iδ ε− −= − + − (10)
respectively, where tI is investment, is
tε is investment specific technology, tB are
nominal government bonds, tR is the gross nominal interest rate, tP is the price level,
tT is lump-sum taxes, Wt(j) is the nominal wage, k
tR is the rental rate on capital, tZ is
the utilization rate of capital, ( )tZδ is an increasing and convex function of the
utilization rate as in GHH (1988), and tDiv the dividends distributed to the
households from labor unions. The left hand side of (9) represents real expenditures at
6 Traditionally, the cost of utilization is specified in terms of forgone consumption following
Christiano et al. (2005), who studied the effects of monetary policy shocks. I follow Khan and
Tsoukalas (2011) who use the capital depreciation specification and show that it has a superior fit with
the data relative to the Christiano et.al (2005) specification. This specification is also used in Jaimovich
and Rebelo (2009).
22
time t net of taxes on consumption, investment, and bonds. The right hand side of (9)
indicates real receipts from wage income, earnings from supplying capital services net
of cost, and dividends. In (3), 1( / )t tS I I − is a convex investment adjustment cost
function. In the steady state it is assumed that S=S'=0, and S''>0. The aggregate
resource constraint is
t t t tC I G Y+ + = (11)
The first-order condition for optimal utilization of capital is given by the
following equation
'( )k
tt t
t
RQ Z
Pδ= (12)
where tQ is the shadow value of installed capital in consumption units, given by the
ratio of the marginal value of installed capital and the marginal value of
consumption.
The equilibrium conditions of the model log-linearized about the balanced
growth path, along with the definition of the variables, are presented in table 2.1.
Equation (T.1) is the aggregate resource constraint; Eq. (T.2) is the Euler equation for
consumption where the coefficients 1c and 2c depend on the underlying model
parameters and the steady state level of hours worked;7 Eq. (T.3) is the Euler equation
for investment; Eq.(T.4) depicts the dynamics of Tobin’s q; Eq.(T.5) is the aggregate
production function; Capital services used in production are a function of capital
installed in the previous period and capital utilization, as described by eq. (T.6); Eq.
(T.7) expresses the optimal capital utilization rate as a function of the value of capital
and rental rate on capital; Eq. (T.8) is the capital accumulation equation; The price
mark up is defined by Eq. (T.9); Inflation dynamics are described by the New-
Keynesian Phillips curve in Eq. (T.10); Cost minimization by firms implies that the
capital-labor ratio is inversely related to the rental rate of capital and positively related
to the wage rate, as described by eq. (T.11); The wage markup is given by Eq. (T.12);
7 The reader is referred to Khan and Tsoukalas (2010, 2011) for the exact expressions for these
parameters.
23
The wage inflation dynamics are described by Eq. (T.13); Lastly, Eq. (T.14) describes
the monetary policy rule.
The news processes, given by eq. (T.16) and (T.21), are simply a smooth
version of the news process studied in Beaudry and Portier (2004) and Jaimovich and
Rebelo (2009) where the news shock portends a future permanent change in
technology j periods into the future. This smooth specification is consistent with the
smooth gradual news processes employed in Leeper et.al (2009) and Leeper and
Walker (2011). Identification also performs well when the more standard
specification of Beaudry and Portier (2004) and Jaimovich and Reblelo (2009) is
used. Nevertheless, I choose the smooth version specification because it seems to be
more consistent with the data, as indicated by the empirical results in section 3.
Labels, definitions and benchmark values of the parameters are in Table 2.2.
The benchmark values of the discount factor, intertemporal elasticity, capital share
and capital utilization elasticity are set in accordance with Jaimovich and Rebelo
(2009). The wealth elasticity parameter is set at 0.1.8 The values for the news
persistence parameters follow Barsky and Sims (2010b) while those of the monetary
policy rule are consistent with the empirical estimates of Coibion and Gorodnichenko
(2007), Fernandez-Villaverde and Rubio-Ramirez (2007), Erceg, Guerrieri, and Gust
(2006), and Ireland (2004). The standard deviation of the news shocks is set in
accordance with Khan and Tsoukalas (2010) while all remaining parameters' values
by and large follow the estimates of Smets and Wouters (2007).9
I simulate 2000 sets of data with 240 observations each, drawing all eight
exogenous shocks from normal distributions. The sample size of 240 observations
matches in size the empirical postwar sample employed in section 3 which spans the
8 The value chosen here is bigger than the estimate of Schmitt-Grohé and Uríbe (2008) (0.007) though
significantly smaller than the estimate of Khan and Tsoukalas (2011) (0.53) and Khan and Tsoukalas
(2010) (0.85). While bigger values have no noticeable effect on the simulation results, I prefer to use a
smaller value as it generates a robust increase in hours on impact in response to IST news shocks. 9 I follow Fisher (2006), Schmitt-Grohé and Uríbe (2008), Fernandez-Villaverde (2009), and Jaimovich
and Rebelo (2009) and assume that TFP and IST follow a unit root process (see eq. T.15 and eq. T.21
in table 1). This implies that TFP and IST news shocks have a permanent effect on TFP and IST,
respectively. The identification results are robust to assuming stationary processes for TFP and IST as
in Smets and Wouters (2007) and Khan and Tsoukalas (2010, 2011).
24
period 1951:Q1-2010:Q4. So as to make the simulated data as close as possible to
actual data, the simulated series are transformed by adding back in trend growth
where applicable.10
For each simulation, I estimate a four-lag VAR with a constant
that includes the levels of TFP, IST, output, investment, consumption, hours, nominal
interest rate, and inflation, which coincides with the benchmark empirical VAR in
Section 3. The truncation horizon is set at H=60. In other words, the IST news shock
is identified as that shock orthogonal to current TFP and IST which maximally
explains IST over a horizon of fifteen years. A truncation horizon of fifteen years,
which is also used for the empirical VAR in section 3, is both long enough to account
for potentially strong long run effects of IST news shocks on IST and short enough to
provide reliable results. Following the identification procedure outlined above the
estimated impulse responses and identified time series of IST news shocks for each
simulation are collected.
Figure 2.1 depicts both theoretical and estimated impulse responses of IST,
output, consumption, investment, hours, and inflation averaged over the simulations
to a favorable IST news shock. The theoretical responses are represented by the solid
lines and the average estimated responses over the simulations are depicted by the
dashed lines, with the dotted lines depicting the 10th
and 90th
percentiles of the
distribution of estimated impulse responses. It is apparent that the business cycle
effects of IST news shocks are well identified. In particular, the estimated empirical
impulse responses are unbiased on impact and for a number of quarters thereafter
while being downward biased at long horizons. Nevertheless, the unbiasedness of the
estimated responses at short horizons coupled with the observation that the confidence
intervals do not include zero are especially important since my focus is not on the
long horizon implications of IST news shocks, but rather on their ability to generate
business cycles. Figure 2.2 depicts the results for identification of unanticipated IST
shocks. Overall, the identification performs well at short horizons while being
10
Following Fernandez-Villaverde (2009), quarterly trend growth rates of 0.28% and 0.34% are added
to TFP and IST, respectively, and in accordance with the balanced growth path 0.63% is added to
output, investment and consumption.
25
downward biased at long horizons. The identification of the effects of TFP shocks
(not shown) also performs well, in particular at short run horizons.
The average correlation between the identified IST news shock and the true
IST news shock across simulations is 0.81, with the median correlation 0.82 and the
10th and 90th percentile correlations 0.71 and 0.88, respectively. The mean
correlation between identified unanticipated TFP and IST shocks and their
corresponding true shocks is higher reaching 0.90 and 0.91, respectively.
A similar simulation exercise in which TFP was not included in the VAR was
conducted as well. The results from this simulation indicate that on top of a
significantly lower mean correlation (48%), the confidence interval of the empirical
distribution of the estimated impulse responses is considerably wider. For example,
the confidence interval for the output, consumption, and investment responses is more
than three and a half times as large on impact and more than twice as large for the six
quarters thereafter when TFP is excluded compared to the benchmark case, after
which the difference is also considerable. This implies that estimation is much more
precise, as measured by the confidence bands, when TFP and the corresponding
orthogonality restriction are included in the estimation procedure.11
Therefore, it is
found that excluding TFP from the VAR is inferior to the benchmark case.
My series of simulation results also indicate that the issue of VAR non-
invertibility is not a major concern for my identification strategy. VAR invertiblity
pertains to the case in which DSGE models produce moving average representations
in the observables which can be inverted into a VAR representation in which the VAR
innovations correspond to economic shocks (see Fernandez-Villaverde, Rubio-
Ramirez, Sargent, and Watson (2007) for the conditions needed for VAR
invertibility). Invertibility problems potentially arise when there are unobserved state
variables which do not enter the estimated VAR (Watson (1986)). Hence, having
news shocks in the model generates invertibility problems as the latter constitute both
shocks and unobserved state variables. I also experimented with news specifications
11
Similar results obtain when the standard deviations of the estimated responses are compared.
26
in which news shocks affect IST with a lag of several periods as opposed to one
period as in the benchmark case, thus exacerbating VAR invertibility problems due to
the introduction of additional unobserved state variables, and found that identification
still performs well despite a slight decline in the mean correlation between identified
shocks and true shocks. Nevertheless, the empirical results of the next section provide
evidence in favor of a news process in which there is a gradual increase in future IST
starting with a lag of one period.
It is also important to note that the identification method is robust to assuming
signal extraction problems facing agents. Blanchard, L'Hullier, and Lorenzoni (2009)
consider a framework in which agents receive news about productivity that is
contaminated with noise and conclude that it is not possible to employ long run
restrictions to separately identify the noise shock. Nevertheless, similarly to the
Barsky and Sims (2010a) identification method, the identification strategy pursued in
this paper is still capable of identifying news shocks in the presence of noise since the
introduction of noise into the news signals merely weakens the effect of news shocks
on agents' actions while not altering any of the identifying assumptions as the IST and
news processes themselves remain unaffected.
The suitability of the identification strategy appears robust to alternative
calibrations of the model. Since the identification algorithm mechanically picks out
from all the shocks that are orthogonal to current IST and TFP the shock that
maximally explains future variation in IST, the method naturally performs better in
calibrations in which there is more variation in IST directly attributable to the IST
news shock. It is therefore encouraging that the empirical results, which will be
presented in the next section, indicated that IST news shocks drive a considerable
share of IST variation accounting for 83% of the latter at the fifteen year horizon.
Furthermore, taking into account that the estimated effects of IST news shocks on IST
at long horizons most likely understate the true effects, as demonstrated in figure
27
2.1,12
suggests that we can be fairly confident that the identification method has
performed well in practice. Overall, the monte carlo simulations suggest that the
identifying strategy is capable of doing a good job of identifying both IST news
shocks and their business cycle effects on macroeconomic aggregates.
3 Empirical Evidence
In this section the main results of the paper are presented. The findings indicate that
favorable IST news shocks generate a rise in output, investment, consumption, and
hours worked, explain 70% of their business cycle variation, and have played an
important role as drivers of U.S business cycles over the last sixty years. Before
proceeding, a brief discussion of the data is given. Then, section 3.2 presents the main
empirical results in detail followed by a sensitivity analysis section which will provide
evidence that the above results are robust. Finally, section 3.4 compares this paper to
previous work in the literature.
3.1 Data
Proper identification of IST news shocks requires an appropriate gauge of IST. I
follow GHK (1997, 2000), Fisher (2006), Schmitt-Grohé and Uríbe (2008), Beaudry
and Lucke (2009), and Liu (2011) and use a real investment price measure to gauge
IST. This price is measured as a consumption deflator divided by an investment
deflator. The consumption deflator corresponds to nondurable and service
consumption, derived directly from the National Income and Product Accounts
(NIPA). The investment deflator corresponds to equipment and software investment
and durable consumption, also derived directly from the NIPA. Some authors, such as
GHK (1997, 2000) and Fisher (2006), preferred to use Gordon’s (1990) price series
for producer durable equipment (henceforth the GCV deflator), as later updated by
Cummins and Violante (2002), so as to better account for quality changes. More
recently, Liu et al. (2011) used an updated GCV series constructed by Patrick Higgins
at the Atlanta Fed that spans the period 1959:Q1:2010:Q4. I prefer to use the NIPA
12
It is apparent that there is a relatively big downward bias at long horizons for the effect of the IST
news shock on IST, as manifested in the failure of the confidence bands to contain the true response.
28
deflators since they allow for a larger sample size. Furthermore, as Justiniano et al.
(2010b) note, the NIPA deflators include quality adjustments that generate price
declines in accordance with other studies based on micro data (e.g. Landefeld and
Grimm, 2000). Nonetheless, it is shown in section 3.3 that the results are robust to the
use of the recently updated GCV deflator used by Liu et al. (2011).13
For the TFP series, I employ the real-time, quarterly series on total factor
productivity (TFP) for the U.S. business sector, adjusted for variations in factor
utilization - labor effort and capital’s workweek, constructed by Fernald (2009) and
available for downloading from his website. The utilization adjustment follows BFK
(2006).
The output measure used is the log of real GDP at a quarterly frequency. The
consumption series is the log of real non-durables and services. The hours series is log
of total hours worked in the non-farm business sector. These series are converted to
per capita terms by dividing by the civilian non-institutionalized population aged
sixteen and over. The output, investment, and consumption data are taken from the
BEA; hours and population data are taken from the BLS. The population series in raw
form is at a monthly frequency. It is converted to a quarterly frequency using the last
monthly observation of each quarter. The measure of inflation is the percentage
change in the CPI for all urban consumers. Use of alternative price indexes generates
similar results. The three month Treasury Bill is used as the measure of the interest
rate. Similar results obtain when the federal funds rate is used instead. I prefer to use
the former because it is a better gauge of the theoretical interest rate in standard
DSGE models where the time period is quarterly. The inflation and interest rates
series are at a monthly frequency. As with the population data, these series are
converted to a quarterly frequency by taking the last monthly observation from each
quarter. My benchmark data series span the period 1951:Q1-2010:Q4.14
13
I thank Patrick Higgins at the Atlanta Fed for providing me with this series. The reader is referred to
the appendix in Liu et al. (2011) for a description of the methods used to construct the series. 14
Similar results obtain when the entire postwar sample is used. Nevertheless, I prefer to start the
sample in 1951 due to the Treasury-Fed Accord announced on March 3, 1951which restored
independence to the Fed and therefore constituted a potentially important structural shift.
29
3.2 Benchmark Results
Eight variables are included in the benchmark system: TFP, IST, nominal interest
rates, inflation, output, investment and durables, non-durables and services
consumption, and total hours worked. As a benchmark, the system is estimated as a
VAR in levels. This system is identical to the one that was used in section 2.2 for the
monte carlo simulations. The levels specification is preferred over a VECM because it
produces consistent estimates of the impulse responses while being robust to
cointegration of unknown form. In particular, it avoids making potentially invalid
assumptions concerning common trends which can yield misleading results (e.g.
Fisher (2010)). Furthermore, as was noted in section 2.2, the benchmark identification
method is also valid in the presence of unit roots. The Akaike, Hannan-Quinn
information and Schwartz criteria favor two lags, while the likelihood ratio test
statistic chooses eight lags. Given the large number of variables in the VAR, a middle
ground of four lags is chosen. Robustness to the levels specification and to alternative
lag lengths will be considered in section 3.3.
In terms of the identification strategy outlined in the previous section, the
truncation horizon is set at H=60. In words, then, the IST news shock is identified as
that shock orthogonal to current TFP and IST which maximally explains movements
in IST over a fifteen year horizon. As with lag length, robustness along this dimension
is discussed below.
Table 2.3 presents estimates of both unconditional and conditional correlations
between the growth rate of output and the growth rates of consumption, investment,
and hours. The conditional correlations estimates are based on the benchmark VAR
model and computed in accordance with Gali's (1999) formula where the conditioning
is made with respect to IST news shocks. These estimates can be used to infer the
extent of the capability of IST news shocks to generate business cycles. As the first
column of table 2.3 shows, the unconditional correlations, which are computed
directly from the data, are high, as expected, reflecting the well known feature of the
business cycle that output, consumption, investment, and hours move in tandem. As
30
the second column of the table demonstrates, the conditional correlations of output
with consumption, investment, and hours are very high at 91%, 97%, and 94%,
respectively, all being statistically significant at the one percent level.15
That the
conditional correlations are at such high levels is an indication that IST news shocks
have the potential of generating business cycles.
Figure 2.3 shows the estimated impulse responses of IST, output, investment,
consumption, hours, and inflation to a favorable IST news shock from the benchmark
VAR, with the dashed lines representing 1st and 99
th percentile confidence bands.
These bands are constructed from a residual based bootstrap procedure repeated 2000
times. I use the Hall confidence interval (see Hall (1992)) which attains the nominal
confidence content at least asymptotically under general conditions and was also
shown to have relatively good small sample properties by Kilian (1999). Following a
favorable IST news shock, IST does not change on impact, by construction, after
which it grows gradually and persistently increasing by 1.34 percent after ten years
and eventually peaking after 27 years at 2.07 percent higher than its pre-shock value.
Output, investment, consumption, and hours all jump up on impact, with the
responses being both statistically and economically significant at 0.29, 0.27, and 0.26
percent for output, consumption, and hours, respectively, and 1.07 percent for
investment, after which they all keep growing where output, investment, and hours
reach their peak after six quarters while consumption peaks after thirteen years. The
significant positive conditional comovement among aggregate variables on impact is
compatible with IST news shocks being an important source of fluctuations.
Moreover, the identified IST news shock series significantly raises the three month T-
Bill rate with a lag of one period while it significantly reduces inflation on impact and
has an insignificant effect on TFP. The responses of inflation, interest rate, and real
macroeconomic aggregates are broadly consistent with the DSGE model presented in
the previous section. As the primary focus of this paper is the business cycle
15
The confidence bands (not shown) for the conditional correlation estimates were constructed from a
residual based bootstrap procedure repeated 2000 times.
31
relevance of IST news shocks, the impulse responses of TFP and interest rates are
omitted.
Figure 2.4 depicts the share of the forecast error variance of several of the
variables in the VAR attributable to the IST news shock and unanticipated IST and
TFP shocks over a range of five years. IST news shocks account for 47 percent of the
forecast error variance share of IST at the five years horizon and 72 percent at the ten
year horizon (not shown). The IST news shock and the unanticipated IST innovation
combine to account for 91 percent or more of the forecast error variance of IST at
frequencies up to ten years. At the five year horizon, 91 percent of IST fluctuations
are explained by the two shocks. That such a small portion of IST remains
unexplained at both short and long horizons validates the assumption underlying
identification that most of the movements in IST can be attributed to only two shocks,
and suggests that the identification method has done a good job at identifying the IST
news shock.
IST news shocks account for a large share of the forecast error variance of
macroeconomic aggregates at business cycle frequencies. In particular, they explain
60 percent of output fluctuations at the one year horizon and 72 percent at the two
year horizon. IST news shocks account for 74 percent of consumption and hours
forecast error variance at the two year horizon, and 65 percent of investment forecast
error variance. Overall, the results indicate that IST news shocks are a substantial
source of the business cycle.
Figure 2.5 plots the time series of identified IST news shocks from the
benchmark VAR. The shaded areas represent recession dates as defined by the NBER.
So as to make the figure more readable, the one year moving average of the identified
shock series is shown as opposed to the actual series. Negative IST news shocks are
associated with nine of the last ten U.S recessions, the exception being the 1981-1982
recession.16
Furthermore, a series of positive IST news shocks is prevalent in the mid
16
Given that the average quarterly growth rate of IST in the sample period is 0.55%, it should be
emphasized that negative IST news shocks do not imply an expected decline in IST in the future but
rather that IST is expected to grow less than its steady state growth rate (i.e. 0.55%).
32
to late 1990's confirming the view that the ten year long 1990's expansion was in part
induced by positive news about IST. The story that emerges from figure 2.5 is
consistent with the results from the historical decomposition discussed below which
indicate that IST news shocks were an important driver of U.S business cycles in the
last sixty years.
Table 2.4 shows the historical contribution of IST news shocks to the ten
NBER determined U.S recessions since 1951. In particular, for each recession the
contribution of IST news to the percentage change in output per capital from peak to
trough (in deviation from trend growth) is calculated. A 1.7% output per capita steady
state annual growth is assumed, which is consistent with the average growth rate of
output per capita over the sample. The results indicate that IST news were a driving
force behind nine of the last ten U.S recessions, where the only recession in which
IST news had no role was the 1981-1982 recession. The recent recession, in which
output loss was 7.8 percent, seems to have been driven in part by IST news shocks
which contributed 3.8 percent of that accumulated decline. IST news shocks also
contributed 1.6 percent and 5.1 percent of the accumulated 2.7 percent and 7.9 percent
output per capita loss during the 1990-1991 and 1973-1975 recessions, respectively.
Moreover, that 1.1 percent of the 1.5 percent output loss in the 2001 recession is
attributed to IST news shocks is consistent with the view that a downward revision of
expectations about future IST took place after the IST news driven boom of the mid to
late 1990's. One may be concerned that the above results for the recent recession and
some of the prior recessions (e.g. 1973-1975, 1980, 1990-1991) may be driven in part
by credit market shocks and oil price shocks, respectively. Robustness along this
dimension is discussed below in the next section where it is shown that these results,
as well as the other results in the paper, are not driven by oil shocks or financial
shocks. Overall, the historical decomposition results point to a central role of IST
news shocks as a driving force of the business cycle.
Figure 2.6 shows the impulse responses of aggregate variables to the
unanticipated IST shock. IST's response to its own innovation is large and significant
33
on impact and also quite persistent. Output rises for the first three quarters following
the shock, after which it starts to decline. Investment rises significantly for the first
five quarters and then starts to fall though this negative response is insignificant.
Hours follow a similar pattern as investment whereas consumption falls significantly
on impact and thereafter as well. The negative response of consumption is consistent
with a modified version of the DSGE model of the previous section in which the cost
of utilization is specified in terms of forgone consumption as in Christiano et al.
(2005) (see Khan and Tsoukalas (2011)). Taken as a whole, the results indicate that
unanticipated IST shocks are not an important source of the business cycle, a finding
that may appear surprising in light of a growing recent literature arguing that this type
of shock represents an important driver of aggregate activity (e.g. Fisher (2006),
Justiniano et al. (2010a), and Khan and Tsoukalas (2010)). Nevertheless, Schmitt-
Groh'e and Uribe (2008) include the real price of investment as an observable in their
structural estimation procedure and find that unanticipated IST shocks have a
negligible role as drivers of the business cycle. They argue that, at least in the context
of structural DSGE models estimated using Bayesian methods, this discrepancy is
explained to a large extent by whether the set of observables used for estimation
includes or not the price of investment. Furthermore, Beaudry and Lucke (2009), who
combine short and long run restrictions in an SVECM framework, also find that
unanticipated IST shocks have a negligible role as business cycle drivers.
Given the stark contrast between the responses to unanticipated shocks
compared to IST news shocks, a brief discussion should be made on the normalization
of the shocks. In accordance with the SVAR literature, figures 3 and 6 present the
impulse responses to a one standard deviation unanticipated shock and one standard
deviation IST news shock, respectively. Hence, one may be concerned that once the
shocks are normalized such that their long term effect on IST is equalized, the
aforementioned contrast between the effects of the two shocks will be greatly
diminished. The IST news shock raises IST in the long run by nearly three times as
much than the unanticipated IST shock. However, even if one were to triple the
34
effects of the unanticipated IST shock, IST news shocks would still have a bigger
effect on the other variables. For example, IST news shocks have a peak on output of
one percent whereas that of the unanticipated shock is two tenths of a percent.
Moreover, the latter effects go in opposite directions as the effect of IST news shocks
is positive whereas that of the unanticipated shock is negative. Hence, changing the
normalization will not change the main result of the paper regarding the business
cycle effects implications of IST news shocks as well as the stark contrast in the
responses to IST news shocks versus IST news shocks.
An additional concern regarding the results from figure 6 is that the Monte
Carlo simulations indicated that there is a bigger downward bias for the response of
output and consumption to unanticipated shocks compared to IST news shocks.
Hence, it may be the case that the true effect of unanticipated IST shocks on
consumption and output is underestimated more so than that of IST news shocks. It is,
however, apparent that the size by which the downward bias in the unanticipated
shock is larger than that in the news shocks is significantly smaller than the size by
which the estimated responses in figure 6 is smaller than those in figure 3. For
example, while the downward bias at the two year horizon for output in response to
the unanticipated shock is twice as much relative to that in response to the news
shock, the estimated response of output at the corresponding horizon to the news
shock is more than ten time as much than the estimated response to the unanticipated
shock. Hence, one can be fairly confident in the result that IST news shock have a
much bigger effect on the variables than unanticipated shocks.
Lastly, the impulse responses of aggregate variables to the unanticipated TFP
shock (not shown) indicate that positive TFP shocks generate an increase in output,
investment, and consumption and a decline in hours. These results are consistent with
the findings of Gali (1999) and BFK (2006) which indicate that TFP shocks are not
important drivers of business cycle fluctuations.
35
3.3 Sensitivity Analysis
The main result that IST news shocks are an important force behind business cycles is
robust to alternative lag structures, different truncation horizons for the maximization
problem underlying identification, alternative real investment price measure, larger
systems containing additional variables as well as estimation of a VECM which
accounts for a potential long run relationship between non stationary variables in the
model.
At all tested lag lengths, output, investment, consumption and hours rise on
impact in response to a favorable IST news shock with the effect being similar both
qualitatively and quantitatively. With more lags in the reduced form system there is
more evidence of reversion in the series at long horizons, but the basic qualitative
nature of the responses is unchanged. The qualitative and quantitative nature of the
responses is also unaltered with different truncation horizons, both shorter ones such
as H=40 and longer ones such as H=80. The results are also similar across sub-
samples (e.g. estimating the VAR only post 1984). In the interest of space, these
figures are omitted from the paper.
The main results are also robust to using a different measure of the real
investment price. I estimated the benchmark system with the real price of investment
measured by the GCV deflator instead of the NIPA deflators, as used by Liu et al.
(2011). Figure 2.7 presents the impulse responses from this system. Both the
quantitative and qualitative nature of the results remains unchanged as IST news
shocks continue to induce business cycle comovement. Moreover, news shocks are
deflationary as in the benchmark case.
Robustness to the levels specification was also considered. While estimation
of a VAR in levels will in general produce consistent estimates of the impulse
responses and variance decomposition, estimation of a vector error correction model
(VECM) will result in an efficiency gain in finite samples if the non-stationary
variables in the VAR share a common stochastic trend. Nevertheless, as discussed in
Section 3.2, the levels specification is preferred because it produces consistent
36
estimates of the impulse responses while being robust to cointegration of unknown
form. In particular, it avoids making potentially invalid assumptions concerning
common trends which can yield misleading results (e.g. Fisher (2010)). Impulse
responses from an estimated VECM (not shown) in which I allowed for two
cointegrating vectors between TFP, IST, consumption, output, and investment, while
imposing that interest rates, inflation, and hours are stationary, indicate that the effects
of IST news shocks are both quantitatively and qualitatively similar to the benchmark
results. Similar results also obtain when a different number of cointegrating vectors is
allowed for. The only difference lies in the estimated long-run responses, with more
evidence of reversion evident in the levels specification.
Furthermore, the IST news shock was also identified in a larger system. In
addition to the eight variables in the benchmark system, measures of stock prices and
consumer confidence were also included. The measure of stock prices used is the log
of the real S&P 500 Index, taken from Robert Shiller's website. This series is
converted to a quarterly frequency by taking the last monthly observation from each
quarter. The results are insensitive to dividing the stock price data by the population.
The consumer confidence data are from the Michigan Survey of Consumers, and
summarize responses to a forward-looking question concerning aggregate
expectations over a five year horizon. This series is available from 1960:Q1 hence
dictating 36 fewer observations compared to the benchmark sample. There are several
reasons for including these additional variables. Stock prices and consumer
confidence are naturally forward-looking, and previous research has shown them to be
prognostic of future movements in economic activity in general and TFP in particular
(e.g. Beaudry and Portier (2006) and Barsky and Sims (2010b)). Thus, it is reasonable
to presume that these variables also contain information about future IST. Moreover,
as stressed by Watson (1986), the inclusion of forward-looking variables mitigates the
impact of potential non-invertibilities even if these variables do not fully reveal the
missing state(s). Furthermore, it is of interest in and of itself to examine the responses
of these forward-looking variables to IST news shocks. Figure 2.8 depicts the
37
responses of the six benchmark variables as well as stock prices and consumer
confidence to a favorable IST news shock. It is apparent that the main results are left
unchanged; favorable IST news shocks generate positive comovemnent and are
deflationary. Moreover, IST news shocks are associated with a significant positive
increase in both stock prices and consumer confidence, a finding which is consistent
with the view that these variables contain important information about the future
value of IST.
Finally, as noted in the previous section, it was also confirmed that the results
in the paper are not driven by either financial shocks originating in credit markets or
shocks to the real price of oil. In relation to the issue of a possible connection between
the identified IST news shocks and credit market shocks, it was found that the results
are robust to adding to the VAR a risk premium variable, measured by the spread
between the expected return on medium-grade bonds and high-grade bonds (Moody's
seasoned Baa corporate bond yield and Aaa corporate bond yield, respectively), and
imposing on the identified IST news shock to be orthogonal to the risk premium
innovation. This robustness is an indication that the results regarding IST news shocks
reported in section 3.2 are not driven by pure financial shocks that originate in the
financial system. Moreover, so as to verify that the results are not driven by oil
shocks, an extended identification procedure was also applied to larger systems
including the real price of oil where the identified IST news shock was imposed upon
to be orthogonal to oil innovations. The results obtained were similar to the
benchmark results, both qualitatively and quantitatively.
3.4 Relation with Previous Work
The robust evidence found in this paper that IST news shocks are important drivers of
business cycles contrasts with the mixed evidence provided by the relatively small
number of papers that estimated DSGE models which contain IST news shocks.
Given that there is no clear agreement on what the true structure of the economy is,
and that inferences regarding the role of IST news shocks based on different structural
models differ, it seems worthwhile to use an identification method that does not
38
impose any structural model on the data but rather imposes identifying assumptions
that are common to different IST news driven DSGE models. This is precisely what is
done in this paper, thus offering new insights regarding the business cycle
implications of IST news shocks.
The results in this paper indicate that unanticipated IST shocks are not an
important source of the business cycle as opposed to IST news shocks. Fisher (2006)
identified unanticipated IST shocks in an SVAR framework with long run restrictions
and found that IST shocks are important drivers of the business cycle. Since his
identification procedure allows IST shocks to raise IST on impact while imposing that
they are the only shocks to affect IST in the long run, it really identifies a combination
of unanticipated IST shocks and IST news shocks, thus offering a potential
reconciliation with the results presented here. So as to further shed light on the
difference between my results and Fisher's, I applied both my identification method as
well as Fisher's using the same variables he used in his paper and found that the
correlations between my identified IST news shocks and unanticipated shocks and
Fisher's identified unanticipated IST shocks are 0.8 and 0.25, respectively. This
evidence indicates that Fisher's method identifies a combination of unanticipated IST
shocks and IST news shocks, though his identified shock is more strongly associated
with IST news shocks than unanticipated IST shocks.17
Even though there has not been an attempt in the literature to identify IST
news shocks along the lines of the identification approach presented in this paper,
Beaudry and Lucke (2009) employ a method that, at least to some extent, resembles
the one used in this paper. They use a combination of short and long run restrictions
in an SVECM framework for the identification of news shocks. In particular, in
systems featuring TFP, IST and other variables their identified news shock is
identified by postulating zero effects on both types of technology on impact, but
17
It's interesting to note that this result is sensitive to whether hours enter the VAR in levels, as in
Fisher's baseline specification, or in first differences in accordance with Fisher's alternative
specification. In particular, when hours enter the VAR in first differences the correlations between my
identified IST news shocks and unanticipated shocks and Fisher's identified IST shocks are 0.66 and
0.58, respectively.
39
allowing for unrestricted long-run effects. Thus, under their identification scheme
news can be news about both TFP and IST. In contrast, the identification approach in
this paper is aimed at identifying specific news shocks, namely IST news shocks. In
fact, as was shown in section 2.2, my identification method performs well on data
generated from a DSGE model that contains both TFP and IST news shocks, in which
case the Beaudry and Lucke (2009) identification method would not be appropriate as
it does not impose any restriction on the type of news shocks being identified. In
particular, Schmitt-Grohé (2010) shows that their SVECM identification method fails
to identify both IST news shocks and TFP news shocks once the true model contains
both news shocks. Nevertheless, Beaudry and Lucke (2009) do report results in favor
of news shocks being an important driver of business cycle while interpreting their
identified news shock as TFP news because these shocks explain about 60% of TFP
forecast error variance in the long run.
From a methodological standpoint, even though the identification method used
in this paper builds on the one employed by Barsky and Sims (2010a), there is a
difference worth noting. In their work, the identified TFP news shock is orthogonal
only to the unanticipated TFP shock. I extend their identification method by imposing
upon the IST news shock to be orthogonal to both IST and TFP shocks thus enabling
me to identify both unanticipated IST and TFP shocks in addition to IST news shocks.
As was reported in section 2.2, adding TFP to the system and imposing the
corresponding orthogonality restriction improves the identification of IST news
shocks. Furthermore, that the identified IST news shock has an insignificant and
negligible effect on TFP confirms that the identified IST news shocks are not related
to TFP news shocks.
Lastly, while this paper has mainly focused on presenting empirical evidence
on the strong role of IST news shocks in the business cycle, it is also important to
comprehend the mechanism by which IST news drive the business cycle. As
Jaimovich and Rebelo (2009) show, endogenous capital utilization is an important
element that must be contained in standard DSGE models so that they are able to
40
generate IST news shocks that are business cycle drivers. The empirical results of this
paper provide evidence in favor of the importance of the capital utilization channel for
transmitting the effect of IST news shocks on macroeconomic variables. Given a
capital share of 0.36, which is what is assumed in Jaimovich and Rebelo (2009) and
also in the theoretical model of section 2, the empirical result of this paper that output
rises on impact by 0.29 percent while hours do by 0.26 percent implies a rise in the
capital utilization rate of 0.34 percent, which is larger than all of the variables apart
from investment.18
In the theoretical model of section 2, capital utilization rises by
one percent, indicating the importance of the capital utilization channel in a
theoretical context as well, as was discussed in detail by Jaimovich and Rebelo
(2009). Overall, it can be deduced that an important mechanism at play here is the
capital utilization channel, which could provide valuable information for builders of
future DSGE models in constructing models that are capable of matching the results
of this paper.
4 Conclusion
This paper has closely examined the hypothesis that IST news shocks are important
drivers of business cycles. While the few papers that have examined the role of IST
news shocks employed fully specified estimated DSGE models to do so, this paper
used a different identification approach that does not impose a structural model on the
data but rather exploits identifying assumptions that are common to a variety of IST
news driven DSGE models. Specifically, I extended the empirical VAR based
approach to identifying news shocks that was recently proposed by Barsky and Sims
(2010a), which is directly based on the implications of theoretical models of
expectations driven business cycles, and showed that this approach performs well on
model generated data in terms of identifying IST news shocks and their business cycle
effects on macroeconomic aggregates.
18
This computation merely relies on the production function equation. Since hours rise by 0.26 percent
and their weight is 0.64 the remaining contribution to the change in output is 0.29-0.64*0.26=0.12.
Given that capital is a predetermined variable and hence does not change on impact, the change in the
capital utilization rate is 0.12/0.36=0.34.
41
Applying this empirical procedure on postwar U.S data, I found robust
evidence that IST news shocks induce positive comovement, i.e., raise output,
consumption, investment, and hours of work, and explain 70% of their forecast error
variance at business cycle frequencies. Furthermore, the historical decomposition
results indicate that IST news played an important part in nine of the last ten U.S
recessions. Overall, it can be deduced that IST news shocks are not only capable of
generating business cycles but also that they have played an important role as drivers
of U.S business cycles over the last 50 years.
The empirical results of this paper with respect to IST news shocks are
broadly consistent with the state-of-the-art DSGE model presented in section 2.2,
which extends the by now classic Smets and Wouters (2007) model via the addition of
two elements, along the lines of Khan and Tsoukalas (2011): the recently popularized
Jaimovich and Rebelo preferences that allow for an arbitrarily weak wealth effect on
labor supply and specification of the cost of utilization in terms of increased
depreciation of capital, as originally proposed by GHH (1988) in a neoclassical
setting. Nevertheless, this model does not match the empirical results found by Barsky
and Sims (2010a) that TFP news shocks are associated with a contemporaneous
decline in output, investment, and hours and an increase in consumption thus
indicating an unimportant role for these shocks in the business cycle. Hence, it seems
interesting and important for future research to focus on formulating a DSGE model
that fits both Barsky and Sims' (2010a) results and this paper's results.
42
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45
Table 2.1
The Variables and Equations of the Model
(a) The variables of the model; (b) the equations of the model
a)
L a b e l D e f in i t io n
O u tp u t
In v e s tm e n t
C o n s u m p tio n
H o u r s
In s ta l le d c a p i ta l
C a p i ta l s e r v ic e s
In f la t io n r a te
T o b in 's q
R e a l c a p i ta l r e n ta l r a te
N o m in a l r a te
U ti l i z a t io n r a te
P r ic e m a r k - u p
W a g e m a r k -u p
t
t
t
t
t
s
t
t
t
k
t
t
t
p
t
w
t
y
i
c
l
k
k
q
r
r
z
u
u
π
b)
t y t y ty = (1-i -g )c + i i + g
y tε (T.1)
1
t t t+1 1 t t 1 2 t t+1 t 2 t t+1 tc = E c + c (r - E + ) + c E (l - l ) + c (1 ) E (x - x ) b
t t lπ ε σ −+ + (T.2)
1
t t-1 t t+1 t1 2
1 1i = i + E i + (q + )
1c
c
is
t
σσ β ε
β ϕ−
−
γ + γ γ
(T.3)
*t t t t+1 t t+1 t t+1
* *
r (1 )q = (r -E + ) + E r + E q
r (1 ) r (1 )
kb k
t k k
δπ ε
δ δ−
−+ − + −
(T.4)
t ty = ( k + (1- )l + )s a
p t tφ α α ε (T.5)
t-1 tk = k + zs
t (T.6)
z (r )k
t t tqψ= − (T.7)
'
*t t-1 t
(1- ) (1- ) (1- )k = k + 1- i + 1- is
t t
Zz
δ δ δ δε
ν ν ν ν −
(T.8)
t t(k -l ) + p s a
t t tu wα ε= − (T.9)
1 1
t t-1 t t+11 1 1
(1- )(1 ) = + E -
1 1 (1 )(1 ( 1) )
c c
c c c
p p p p p
t
p p p p p p
u
σ σ
σ σ σ
ι β ι β ξ ξπ π π
β ι β ι β ι φ ε ξ
− −
− − −
γ γ −
+ γ + γ + γ + − (T.10)
46
t t tr (k -l ) + wk s
t = − (T.11)
( )( )( )
(1 ) (1 ) (1 )( 1)/ 1 ( 1)/ ( 1)/
t * * *
(1 ) (1 ) (1 )( 1)/ 1 ( 1)/ ( 1)/
* * *
(1 ) (1 )( 1)/ 1 ( 1)/
* *
u = w (1 ) (1 )
(1 ) (1 )
(1 ) )
l l l
l l l
l l
w
t l l t
l t
t
L L L l
L L L x
L L c
σ σ σω ω ω ω ω ω
σ σ σω ω ω ω ω ω
σ σω ω ω ω
χω χω σ χω σ
χω χω χω σ
χω χω
+ + +− − − −
+ + +− − − −
+ +− − −
− − γ − γ + γ
+ − γ − γ + γ
− − γ γ
(T.12)
1
t t-1 t t+1 t t+1 t t-11 1 1 1
1
1
1 1 1 = + 1 (E +E )
1 1 1 1
(1- )(1 ) ((1 ) )(( 1) 1)
c
c c c c
c
c
w
w ww wt t
w w w
w w w
u
σ
σ σ σ σ
σ
σ
β ιπ π π
β β β β
β ξ ξε
β ξ φ ε
−
− − − −
−
−
+ γ− − + + γ + γ + γ + γ
γ −− +
+ γ − +
(T.13)
1 (1 )( ) r
t r t r t y t tr p r p yππ ε−= + − Θ +Θ ∆ + (T.14)
1 1
a a a a
t t t tgε ε η− −= + + (T.15)
1
a a a
t t tg g eκ −= + (T.16)
1
b b b
t b t tε ρ ε η−= + (T.17)
1
g g g
t g t tε ρ ε η−= + (T.18)
1 1
w w w w
t w t t w tε ρ ε η κ η− −= + − (T.19)
1 1
is is is is
t t t tgε ε η− −= + + (T.20)
1
is is is
t t tg g eκ −= +
(T.21)
Notes: This table presents the equations of the DSGE model of section 2.2. tx is an index
variable that makes preferences non-time-separable in consumption and hours worked (see
Jaimovich and Rebelo (2009)). The eight disturbances are: TFP unanticipated shocka
tε ; TFP
news shocka
te ; monetary policy shockr
tε ; preference shock b
tε ; government spending
shockg
tε ; wage mark-up shockw
tε ;IST unanticipated shockis
tε ; IST news shockis
te . In
particular, news processes 1
a
tg − and 1
is
tg − are stochastic drift terms that follow AR(1) processes
(T.16) and (T.21), respectively. Following Barsky and Sims (2010a, 2010b), the
corresponding i.i.d shocksa
te andis
te in (T.16) and (T.21) are defined as TFP and IST news
shocks as they portend future changes in TFP and IST, respectively.
47
Table 2.2
Description of the Parameters of the Model and Benchmark
Values
L a b e l D e f in it io n B e n c h m a r k V a lu e
In v e r s e in te r te m p o r a l e la s t ic i ty 1
W e a lth e la s t ic i ty 0 .1
C a lv o w a g e s 0 .7
In v e r s e la b o r e la s t ic i ty 1 .8 3
C a lv o p r ic e s 0 .6 6
W a g e in d e x a t io n 0 .5 8
P r ic e in d e x a t io n 0 .2 4
C a p i t
c
w
l
p
w
p
σ
ωξσ
ξιι
ψ a l u t i l iz a tio n e la s t ic i ty 0 .1 5
F ix e d c o s t s h a r e 1 .2 5
S te a d y s ta te la b o r m a r k e t m a rk -u p 1 .2 5
G o o d s m a r k e t c u r v a tu r e 1 0
L a b o r m a r k e t c u r v a tu r e 1 0
M o n e ta r y P o l ic y ru le in f la t io n 4 .5
M o n e ta r y P o l ic y ru le
p
w
p
w
rp
π
φ
φεε
Θ
*
in f la t io n 0 .7 5
M o n e ta r y P o l ic y ru le o u tp u t g r o w th 1
In v e s tm e n t a d ju s tm e n t c o s t 5 .8 8
D e te r m in is t ic o u tp u t g r o w th 0 .0 0 6 3
D e te r m in is t ic c a p i ta l g r o w th 0 .0 0 9 2
D is c o u n t f a c to r 0 .9 8 5
L S te a d y s ta te h o u r s 0 .5 3
C a p
y
ϕγν
β
α
Θ
i ta l s h a r e 0 .3 6
R is k p r e m iu m p e r s is te n c e 0 .2 2
G o v e r n m e n t s p e n d in g p e r s is te n c e 0 .9
W a g e m a r k -u p p e r s is te n c e 0 .9
W a g e m a r k -u p M A 0 .9
N e w s s h o c k p e r s is te n c e 0 .8
T F P s h o c k s t . d e v . 0 .0 0 4 5
T F P
b
g
w
w
a
a
e
ρρρ
κκ
σσ n e w s s h o c k s t . d e v . 0 .0 0 0 9
R is k p re m iu m s h o c k s t . d e v . 0 .0 0 2 3
G o v e r n m e n t s p e n d in g s h o c k s t . d e v . 0 .0 0 0 1 6
M o n e ta ry p o l ic y s h o c k s t . d e v . 0 .0 0 2 3
IS T s h o c k s t . d e v . 0 .0 0
b
g
r
is
σσ
σσ 4 5
IS T n e w s s h o c k s t . d e v . 0 .0 0 1 9i s
eσ
Notes: This table presents a description of the parameters of the DSGE model of section 2.2
as well as their benchmark values.
48
Table 2.3
Correlation Estimates
Unconditional Conditional
Output 1 1
Consumption 0.54 0.91
Investment 0.84 0.97
Hours 0.73 0.94
Notes: Table 3 reports estimates of both unconditional and conditional correlations between
the growth rate of output and the growth rates of consumption, investment, and hours. The
unconditional correlations are computed directly from the data whereas the conditional
correlations estimates are based upon the benchmark VAR model where it is assumed that
IST news shocks are the only shocks hitting the economy.
49
Table 2.4
Historical Contribution of IST News Shocks to Output per
Capita Loss in U.S Recessions
Recession Percentage Change in
Output per Capita (deviation
from trend growth)
Contribution of IST News Shocks
1953:2-1954:2 -5.5 -1.9
1957:3-1958:2 -5.4 -1.9
1960:2-1961:1 -2.8 -1.2
1969:4-1970:4 -4.1 -1.2
1973:4-1975:1 -7.9 -5.1
1980:1-1980:3 -3.9 -1.4
1981:3-1982:4 -6.3 1.6
1990:3-1991:1 -2.7 -1.6
2001:1-2001:4 -1.5 -1.1
2007:4-2009:2 -7.8 -3.8
Notes: Table 4 reports estimates of the contribution of IST news shocks to each of the
recessions in my sample period. The first column presents the percentage change from peak to
trough of output per capita, relative to trend growth, in every recession. The second column
reports the contribution of IST news shocks, based on the benchmark VAR model, to the
corresponding output loss. A 1.7% output per capita annual trend growth is assumed, which is
consistent with the average growth rate of output per capita over the sample.
50
Figure 2.1
Model and Monte Carlo Estimated Impulse Responses to IST
News Shock
The solid lines show the theoretical impulse response to an IST news shock from the model of
section 2.2. The dashed lines depict the average estimated impulse responses over 2000
Monte Carlo simulations, with the dotted lines representing the 10th and 90
th percentiles of the
distribution of estimated impulse responses.
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1IST
Horizon
Pe
rce
nta
ge
De
via
tio
n
Model
Estimated
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1
1.5Output
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1
1.5Consumption
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1
1.5
2
2.5Investment
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.4
-0.2
0
0.2
0.4
0.6Hours
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.08
-0.06
-0.04
-0.02
0
0.02
0.04Inflation
Horizon
Pe
rce
nta
ge
Po
int
De
via
tio
n
51
Figure 2.2
Model and Monte Carlo Estimated Impulse Responses to
Unanticipated IST Shock
The solid lines show the theoretical impulse response to an unanticipated IST shock from the
model of section 2.2. The dashed lines depict the average estimated impulse responses over
2000 Monte Carlo simulations, with the dotted lines representing the 10th and 90
th percentiles
of the distribution of estimated impulse responses.
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8IST
Horizon
Pe
rce
nta
ge
De
via
tio
n
Model
Estimated
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1Output
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1Consumption
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1
1.5Investment
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.2
0
0.2
0.4
0.6Hours
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.04
-0.02
0
0.02Inflation
Horizon
Pe
rce
nta
ge
Po
int
De
via
tio
n
52
Figure 2.3
Empirical Impulse Responses to IST News Shock
The solid lines are the estimated impulse responses to the IST news shock from the
benchmark VAR. Dashed lines represent 1st and 99
th percentile Hall (1992) confidence bands
generated from a residual based bootstrap procedure repeated 2000 times.
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5IST
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2Output
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-0.6
-0.4
-0.2
0
0.2Inflation
Horizon
Pe
rce
nta
ge
Po
ints
53
Figure 2.4
Share of Forecast Error Variance Attributable to Identified
Shocks (IST News, Unanticipated IST and TFP)
The above bar diagrams show the share of forecast error variance of each variable attributable
to the identified IST news, unanticipated IST and unanticipated TFP shocks from the
benchmark VAR. As the identification pursued in the paper is a partial one, the sum of
relative contributions of all three shocks do not necessarily add up to one as there are
potentially additional unidentified shocks also accounting for part of the forecast error
variance.
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
IST
IST News
Unanticipated IST
Unanticipated TFP
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Output
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Consumption
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
rInvestment
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Hours
2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Inflation
54
Figure 2.5
Identified News Shock Time Series and U.S Recessions
Smoothed IST News Shock Series
This figure plots the time series of identified IST news shocks from the benchmark VAR. U.S
recession are represented by the shaded areas. So as to render the figure more readable, the
plotted data is smoothed using a one year moving average. Specifically, it is calculated
as 3 2 1( ) / 4s
t t t t tε ε ε ε ε− − −= + + + . The series begins in 1952:4 and ends in 2010:4.
55
Figure 2.6
Empirical Impulse Responses to Unanticipated IST Shock
The solid lines are the estimated impulse responses to the unanticipated IST shock from the
benchmark VAR. Dashed lines represent 1st and 99
th percentile Hall (1992) confidence bands
generated from a residual based bootstrap procedure repeated 2000 times.
0 2 4 6 8 10 12 14 16 18 200.2
0.4
0.6
0.8
1
1.2IST
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-1
-0.5
0
0.5Output
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-0.6
-0.4
-0.2
0
0.2Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-2
-1
0
1
2Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-1
-0.5
0
0.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-0.2
0
0.2
0.4
0.6Inflation
Horizon
Pe
rce
nta
ge
Po
ints
56
Figure 2.7
Empirical Impulse Responses to IST News Shock: Alternative
Investment Price Measure
The solid lines are the estimated impulse responses to the IST news shock from the
benchmark VAR with the real price of investment measured by the GCV deflator instead of
the NIPA deflators, as used in Liu et al. (2011). Dashed lines represent 1st and 99
th percentile
Hall (1992) confidence bands generated from a residual based bootstrap procedure repeated
2000 times.
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
1
1.5
2
2.5IST
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2Output
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 2 4 6 8 10 12 14 16 18 20-0.6
-0.4
-0.2
0
0.2Inflation
Horizon
Pe
rce
nta
ge
Po
ints
57
Figure 2.8
Empirical Impulse Responses to IST News Shock: Larger VAR
The solid lines are the estimated impulse responses to the IST news shock from a larger VAR
that includes stock prices and consumer confidence in addition to the eight benchmark
variables. The consumer confidence series starts in 1960:Q1, hence dictating 36 fewer
observations for the larger system compared to the benchmark system. Dashed lines represent
1st and 99
th percentile Hall (1992) confidence bands generated from a residual based bootstrap
procedure repeated 2000 times.
0 5 10 15 200
0.5
1
1.5
2IST
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 200
0.5
1
1.5
2Output
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 200
0.5
1
1.5
2Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 200
1
2
3
4
5
6Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 200
0.5
1
1.5
2
2.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-0.6
-0.4
-0.2
0
0.2Inflation
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 202
4
6
8
10
12Stock Prices
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 200
2
4
6
8
10
12Consumer Confidence
Horizon
Pe
rce
nta
ge
Po
ints
58
Chapter III
The External Finance Premium and Business
Cycles
1. Introduction
The recent financial crisis and great recession in the U.S have generated a new wave
of interest in research on the role of the external finance premium (EFP) in the
business cycle. The empirical literature on EFP has well established that credit
spreads, which proxy for the external finance premium, are valuable in predicting
economic growth (Stock and Watson (1989), Gertler and Lown (1999), Mueller
(2007), Gilchrist, Yankov and Zakrajsek (2009)). The DSGE literature has illustrated
that EFP is a central variable in the business cycle both in terms of propagating other
shocks (Bernanke, Gertler and Gilchrist (1999; Henceforth BGG), De Graeve (2008),
Christensen and Dib (2008), and Queijo von Heideken (2008)) and in terms of
mirroring exogenous changes in credit supply (Gilchrist, Ortiz and Zakrajsek (2009;
Henceforth GOZ), Christiano, Motto, and Rostagno (2009; Henceforth CMR), and
Hirakata et.al (2010)). Nevertheless, it still unclear, at least empirically, which shocks
drive EFP and in turn, even more importantly, what is their role in the business cycle?
This paper tries to provide an answer to this question by providing robust evidence
that credit supply shocks are important drivers of EFP and have the potential of
generating business cycles. Specifically, the empirical findings suggest that these
shocks explain 87%, 77%, and 70% of EFP variation at the one year, two year, and
three year horizons, respectively, and generate business cycle comovement while
reducing inflation and interest rates. Even though these shocks are not the dominant
source of business cycle fluctuations on average, explaining 13% and 11% of the
business cycle variation in output and investment, respectively, 5% of that in
consumption and 23% of hours' business cycle variation, the historical decomposition
59
results show that they have played a crucial part in the recent great recession. Namely,
periods in which large credit supply shocks are realized are likely to transform into
serious recessions.
Initially, I identify the demand shock that explains the most of the movements
in EFP via an extension of Uhlig's (2003) maximum forecast error variance (MFEV)
method. In particular, the identified demand shock is a shock which has no effect on
both neutral (TFP) and investment specific technology (IST) at all horizons and which
maximizes the sum of contributions to EFP forecast error variance over a finite
horizon. The impulse response functions (IRF's) for this shock lead me to interpret it
as a credit supply shock of the kind studied by GOZ (2009), CMR (2009), and
Hirakata et.al (2010).1 This interpretation is confirmed by presenting a New
Keynesian DSGE model with a financial accelerator in which credit supply shocks
generate IRF's that are consistent with the observed empirical responses to the
identified demand shock. Furthermore, following the recommendation of the recent
work by Chari, Kehoe, and McGrattan (2008), which questioned the ability of VARs
to effectively identify shocks from DSGE models, I provide Monte Carlo simulation
results, based on such a model, which indicate that the identification method does a
good job of identifying credit supply shocks and their dynamic effects from model
generated data.
The identification approach taken in this paper is similar to the one pursued in
Uhlig (2003) and more recently in Kurmann and Otrok (2010). The former tried to
identify the shocks that drive real GNP while the latter aimed to identify the shocks
that drive the term premium. Both papers employed Uhlig's (2003) MFEV method to
identify the shocks and then tried to give them economic interpretation based on
1 CMR (2009) provided a structural interpretation of the credit supply shock in their model as a shock
that signifies an increase in the variance of idiosyncratic shocks affecting the firm’s profitability, which
aggravates the costly-state verification problem faced by entrepreneurs. They argue that this shock,
referred to as a 'risk shock', largely originates in the credit market in that it reflects changes in the
perceptions about borrowers' creditworthiness. In the BGG model, a credit supply shock may also
mirror an increase in the monitoring costs (i.e., a decline in recovery rates in the case of default).
Hirakata et.al (2010) introduce an additional risk shock which represents an increase in the variance of
idiosyncratic shocks affecting the profitability of the financial intermediary (FI) and find that the
effects of the two shocks are qualitatively similar, though the FI shock has a stronger effect.
60
economic theory. I offer an extension of this method in that it is imposed that the
identified shock have no effect on TFP and IST, thus restricting it be a pure demand
shock, as opposed to the above two papers which placed no restrictions on the
identified shocks other than having them maximally explain a target variable's FEV.
Imposing these restrictions allows an identification of shocks that are orthogonal to
both unanticipated TFP and IST shocks and TFP and IST news shocks, which
separates this paper from the vast literature that studied the role of these shocks in the
business cycle.2
Moreover, as noted above, the demand shock identified in this paper explains
a considerable share of EFP, though this share declines with the time horizon from
87% at the one year horizon to 70% at the three year horizon. These shares are lower
than the ones obtained in Boivin et.al (2010), for instance, who employed factor
augmented VAR's (FAVAR) for the identification of credit supply shocks using
monthly data and recursive restrictions, where they exceed 90%. These differences
can be explained by the identifying restrictions that are imposed in order to identify a
pure demand shock.
The identification approach pursued in this paper might not be very useful if
there are many demand shocks that drive EFP of which no shock is truly dominant.
Nevertheless, under the null hypothesis that credit supply shocks are important drivers
of EFP, in relation to the other demand shocks in the economy, this identification
method will do a good job of identifying credit supply shocks and their dynamic
effects, as shown in sub section 4.4. In the theoretical model presented in sub section
4.1 credit supply shocks drive a considerable part of EFP fluctuations, though the
share declines with the time horizon from 99% at the two year horizon to 83% and
70% at the five year and ten year horizons, respectively. This is mainly due to an
2 For example, Gali (1999) and Basu, Fernald and Kimball (2006) studied unanticipated TFP shocks,
Greenwood, Hercowitz and Krusell (2000; Henceforth GHK), Fisher (2006), Justiniano et al. (2010a,
2010b), and Khan and Tsoukalas (2009) studied unanticipated IST shocks, Beaudry and Portier (2006),
Beaudry and Lucke (2009), and Barsky and Sims (2010) studied TFP news shocks, and Davis (2007),
Schmitt-Grohé and Uríbe (2008), Khan and Tsoukalas (2010) and Ben Zeev (2010) studied IST news
shocks.
61
increasing share attributed to unanticipated TFP shocks. Overall, the main conclusion
of the monte carlo simulation evidence from sub-section 4.4 is that as long as credit
supply shocks drive a considerable share of EFP in relation to the other demand
shocks in the model, the proposed identification method will do a good job of
identifying credit supply shocks and their effects on macroeconomic variables.
The remainder of the paper is organized as follows. In the next section the
details of the empirical strategy are laid out. Section 3 presents the main empirical
evidence and provides a sensitivity analysis of the results. In section 4 I present a
DSGE model augmented with the financial accelerator ˋa la BGG (1999) in which
credit supply shocks generate impulse responses consistent with the observed
empirical responses obtained in section 3. Simulation evidence that the identification
procedure performs well on data generated from this model in terms of identifying
credit supply shocks and their dynamic effects is also provided. The final section
concludes.
2. Empirical Strategy
The identification method pursued in the paper is now presented in detail. Let ty be a
k x1 vector of observables of length T. One can form the reduced form moving
average representation in the levels of the observables either by estimating a
stationary vector error correction model (VECM) or an unrestricted VAR in levels:
ty B(L)ut =
(1)
Where L is the lag operator and0
B(L) B Lτττ
∞
=
=∑ . Assume there exists a linear mapping
between innovations and structural shocks:
tu A tε= (2)
This implies the following structural moving average representation:
y C(L)t tε= (3)
Where C(L) B(L)A= and 1At tuε −= . The impact matrix A must satisfy 'AA = Σ ,
whereΣ is the variance-covariance matrix of innovations. However, there's an infinite
number of impact matrices that solve the system 'AA = Σ . In particular, for some
62
arbitrary orthogonalization, A (e.g. a Choleski decomposition), the entire space of
permissible impact matrices can be written as AD , where D is a k x k orthonormal
matrix ( 'DD I= ).
The h step ahead forecast error is:
t+h t t+h t+h-
0
y -E y = B ADh
τ ττ
ε=∑ (4)
The contribution to the forecast error variance of variable i attributable to structural
shock j at horizon h is then:
'
' '
i,j , ,
0
(h) = B A A Bh
i iτ ττ
γγ=
Ω ∑ (5)
γ constitutes the jth column of D. Aγ is then a k x 1 vector corresponding with the jth
column of a possible orthogonalization and ,Bi τ represents the ith row of the matrix of
moving average coefficients at horizonτ . Let TFP and IST occupy the first and
second positions in the system, respectively. Without loss of generalization, let EFP
occupy the third position in the system. System (1) can now be written equivalently as
follows:
1 111 12
2 221 22
B(L) B(L)
B(L) B(L)
t t
t t
y u
y u
=
(6)
The group of variables 1y consists of TFP and IST while group 2y consists of
the rest of the variables. The shocks are partitioned in a corresponding manner. The
identified demand shock is identified as the shock that has no effect on TFP and IST
at all horizons and that maximally explains movements in EFP. In particular, this
shock is identified by finding theγ which maximizes the sum of contribution to the
forecast error variance of EFP at horizons from 0 to H subject to the restriction that
this shock has no effect on TFP and IST at all horizons. The latter restriction is
imposed via the constraint that 12( ) 0B L = , i.e. TFP and IST are assumed to be block-
exogenous with respect to the rest of the variables (see Hamilton (1994)), coupled
with the constraints that (1, ) 0 1, (2, ) 0 2A j j A j j= ∀ > = ∀ > , namely that TFP
and IST are also contemporaneously exogenous with respect to the rest of the
63
variables. For the identification of the demand shock, I first apply maximum
likelihood estimation of the VAR under the assumption of block exogeneity of TFP
and IST to arrive at consistent estimates of ( )B L , as detailed in Hamilton (1994), after
which the following optimization problem is solved:
'* ' '
3,3 3, 3,
0 0 0
'
arg max ( ) B A A B
A(1, ) 0 1
A(2, ) 0 2
. (1,1) 0
(2,1) 0
1
H H h
h h
h
j j
j j
s t
τ ττ
γ γγ
γγγ γ
= = =
= Ω =
= ∀ >
= ∀ >
=
=
=
∑ ∑∑
H is some finite truncation horizon. The first four constraints impose that the
identified shock has no contemporaneous effect on TFP and IST. Note that the block
exogeneity restriction is already imposed through the B matrices in the objective
function. The fifth restriction that imposes onγ to have unit length ensures thatγ is a
column vector belonging to an orthonormal matrix. Following Uhlig (2003), this
maximization problem can be rewritten as a quadratic form in which the non-zero
portion of γ is the eigenvector associated with the maximum eigenvalue of the lower
(k-2) x (k-2) sub-matrix of the following matrix S:
( ) ( ) ( )'
3, 3,
0
1 B A B AH
S H τ ττ
τ=
= + −∑
Hence, this procedure constitutes an application of principle components.
Specifically, it identifies the demand shock as the first principal component of the
lower (k-3) x (k-3) sub-matrix of matrix S under the restriction of block exogeneity of
TFP and IST.3
3 Similarly, the second, third, etc. principle components determine the second, third, etc. most
important shocks in terms of explaining EFP FEV. Since these shocks explain a negligible amount of
EFP variation, I focus only on the first shock identified via the first principle component which
explains a considerable amount of EFP FEV.
64
3 Empirical Evidence
In this section the main results of the paper are presented. It is found that the
identified demand shocks (Henceforth: EFP shocks) are associated with a decline in
output, investment, consumption and hours worked, explain 13% and 11% of the
business cycle variation in output and investment, respectively, 5% of that in
consumption and 23% of hours' variation, and have played an important role as
drivers of the recent recession. Before proceeding I begin with a brief discussion of
the data.
3.1 Data
Two critical data series needed to proceed are the IST and TFP series. These variables
need to be measured in an accurate manner so as to properly identify a pure demand
shock. I follow GHK (1997, 2000), Fisher (2006), Schmitt-Grohé and Uríbe (2008)
and Beadry and Lucke (2009) and use a real investment price measure to measure
IST. This price is measured as a consumption deflator divided by an investment
deflator. The consumption deflator corresponds to nondurable and service
consumption, derived directly from the National Income and Product Accounts
(NIPA). The investment deflator corresponds to equipment and software investment
and durable consumption, also derived directly from the NIPA. For the TFP series, I
employ the real-time, quarterly series on total factor productivity (TFP) for the U.S.
business sector, adjusted for variations in factor utilization - labor effort and capital’s
workweek, constructed by Fernald (2009). The utilization adjustment follows Basu,
Fernald, and Kimball (BFK, 2006).4
The external finance premium variable (EFP) is measured by the spread
between the yield to maturity on Moody's Baa bonds and 10 year government bonds.
The robustness of the results to using the Baa-Aaa spread is discussed in sub-section
3.3. I also include a measure of firms' leverage ratio gauged by total market value of
assets of nonfarm nonfinancial corporate business divided by their total market value
4 I downloaded the series from John Fernald's website.
65
of net worth. The leverage ratio variable is added to the system being that it's a central
variable in the theory of financial frictions in macro models. Moreover, it will help to
give a structural interpretation of the identified shock. The output measure used is the
log of real GDP at a quarterly frequency. The consumption series is the log of real
non-durables and services. The hours series is total hours worked in the non-farm
business sector. These series are converted to per capita terms by dividing by the
civilian non-institutionalized population aged sixteen and over. The output,
investment, and consumption data are taken from the BEA; hours and population data
are taken from the BLS. The population series in raw form is at a monthly frequency.
It is converted to a quarterly frequency using the last monthly observation of each
quarter. The measure of inflation is the percentage change in the CPI for all urban
consumers. Use of alternative price indexes produces similar results. The three month
Treasury Bill is used as the measure of the interest rate. The inflation, EFP and
interest rates series are at a monthly frequency. As with the population data, these
series are converted to a quarterly frequency by taking the last monthly observation
from each quarter. The 10 year government bonds yield series is available from
1953:Q2; all other series begin in 1948. Hence, the benchmark data series span the
period 1953:Q2-2010:Q2.
3.2 Benchmark Results
Ten variables are included in the benchmark system: TFP, IST, EFP, leverage ratio,
interest rates, inflation, output, investment and durables, non-durables and services
consumption and total hours worked. As a benchmark, the system is estimated as a
VAR in levels. The levels specification is preferred to a VECM for three main
reasons. First, it produces consistent estimates of the impulse responses and is robust
to cointegration of unknown form.5 Second, the monte carlo simulation evidence from
section 4.4 confirmed that the levels specification continues to produce good
identification results in the presence of unit roots in TFP and IST. Third, invalid
5Standard unit root tests overwhelmingly fail to reject the hypotheses that TFP, IST, consumption,
investment and GDP are I(1); the tests are inconclusive for EFP, inflation, interest rates and hours.
66
assumptions concerning common trends can yield misleading results (Fisher (2010)).
Nevertheless, the results are unchanged when a cointegrated VAR that accounts for
the long run relationship between the non stationary variables of the model is
estimated. The Hannan-Quinn information and Schwartz criteria favor two and one
lags, respectively, while the likelihood ratio test statistic chooses five lags. Given the
large number of variables in the VAR, a middle ground of two lags for each variable
is chosen. Robustness to the levels specification and to alternative lag lengths will be
considered in the next subsection.
In terms of the identification strategy outlined in the previous section, the
truncation horizon is set at H = 20. In words, then, the EFP shock is a shock that is
orthogonal to current TFP and IST and which maximally explains movements in EFP
over a five year horizon. A truncation horizon of five years is both long enough to
capture potential medium run forces and short enough to provide fairly reliable
results. As with lag length, Robustness along this dimension is discussed below.
Table 3.1 presents estimates of both unconditional and conditional correlations
between the growth rate of output and the growth rates of consumption, investment
and hours. The conditional correlations estimates are based on the benchmark VAR
model and computed in accordance with Gali's (1999) formula where the conditioning
is made with respect to the identified EFP shocks. These estimates can be used to
infer the extent of dominance of EFP shocks as business cycle drivers. As the first
column shows, the unconditional correlations, which are computed directly from the
data, are high, as expected, reflecting the well known feature of the business cycle
that output, consumption, investment and hours move in tandem. As the second
column demonstrates, the conditional correlations are very high exceeding 92% and
are statistically significant at the one percent level.6 That the conditional correlations
are at such high levels is an indication that EFP shocks have the potential of
generating business cycles.
6The confidence bands for the conditional correlation estimates were constructed from a residual based
bootstrap procedure repeated 2000 times.
67
Nevertheless, for the interpretation of the identified shock to be reliable,
comprehensive information with respect to the dynamic effects of the EFP shocks
needs to be examined. Figure 3.1 shows the estimated impulse responses of EFP,
leverage, output, investment, consumption, hours, interest rates and inflation to a
positive EFP shock from the benchmark VAR, with the dashed lines representing 5th
and 95th percentile confidence bands. These bands are constructed from a residual
based bootstrap procedure repeated 2000 times. I use the Hall confidence interval
(See Hall (1992)) which attains the nominal confidence content at least asymptotically
under general conditions and was also shown to have relatively good small sample
properties by Kilian (1999). Following the EFP shock, EFP jumps on impact and
stays higher for about two years prior to returning to its pre shock level. Leverage
increases for four years following the EFP after which it begins to decrease signifying
the beginning of a persistent deleveraging process.
Output, investment, consumption and hours all decline on impact, with the
responses being both statistically and economically significant, after which they all
keep declining where output, investment and hours reach their dip after one year
while consumption dips after four years. The conditional comovement among
aggregate variables on impact demonstrates that EFP shocks have the potential of
driving business cycles. Moreover, the EFP shock series is negatively and
significantly correlated with the three month T-Bill rate and inflation. The finding that
EFP shocks are deflationary while inducing an interest rate decline is consistent with
their characterization as demand shocks. Note that the fact that EFP shocks reduce
interest rates while decreasing economic activity helps to negate an interpretation of
the identified shock as a monetary policy shock. Moreover, it is straightforward to
negate an interpretation of EFP shocks as being related to oil shocks given that the
former are both contractionary and deflationary whereas oils shocks are
contractionary and inflationary.
The above IRF's can be also used to refute an interpretation of EFP shocks as
the net worth shocks recently studied by GOZ and CMR. The finding that the EFP
68
shock first increases leverage for the first four years after which the deleveraging
process starts to take place is consistent with the GOZ findings with respect to adverse
credit supply shocks. In contrast, GOZ show that adverse net worth shocks are
associated with an immediate and persistent increase in leverage. These results are
also consistent with the DSGE model I present in section 4. Therefore, it is unlikely
that EFP shocks represent net worth shocks but rather embody credit supply shocks.
Figure 3.2 depicts the share of the forecast error variance of several of the
variables in the VAR attributable to the EFP shock and unanticipated IST and TFP
shocks over a range of five years. EFP shocks account for 87 percent of the forecast
error variance share of EFP at a horizon of one year and 65 percent at the five year
horizon. While IST shocks account for 9% of the variation in EFP on impact with this
share declining with the time horizon, TFP shocks explain less than 3% of EFP
variation at all time horizons. Therefore, even though TFP, IST and EFP shocks
explain at least 95 percent of EFP fluctuations from impact to the one year horizon,
15% and 21% of the variation are left unexplained at the two and three year horizons,
respectively. My identification method cannot explain which specific shocks are
responsible for these unexplained shares though it does indicate that that these shocks
are unrelated to both neutral and investment specific technology.
EFP shocks explain 13 percent of output fluctuations at the one year horizon
and 10 percent at the two year horizon while accounting for 11 and 5 percent of
investment and consumption forecast error variance at the one year horizon,
respectively. While the latter shares are quite small, EFP shocks seem to play a bigger
role as drivers of hours' fluctuations explaining 22% of the variation in hours at the
one year horizons. Nevertheless, these results indicate that EFP shocks are not a
substantial source of the business cycle though they have the potential of generating
business cycles.
Figure 3.3 plots the time series of identified EFP shocks from the benchmark
VAR. The shaded areas represent recession dates as defined by the NBER. So as to
make the figure more readable, the one year moving average of the identified shock
69
series is shown as opposed to the actual series. Positive EFP shocks, representing
adverse credit supply shocks, are associated with the first three recessions, the 1982
recession, and the two recent recessions. Nevertheless, it is apparent that the biggest
role was played in the most recent recession. Furthermore, a series of negative EFP
shocks is prevalent in the mid 2000's to late 2007 just prior to the start of the recent
recession, confirming the view that a credit bubble may have been formed during
these years. Overall, the story that emerges from figure 3.3 is consistent with the
results from the historical decomposition discussed below; EFP shocks played a
relatively modest part as drivers of U.S business cycles in the last fifty five years,
apart from the recent recession in which they played a dominant part.
Table 3.2 shows the historical contribution of EFP shocks to the nine NBER
determined U.S recessions since 1954. In particular, for each recession the
contribution of EFP to the percentage change in output per capita from peak to trough
(in deviation from trend growth) is calculated.7 The results indicate that EFP shocks
contributed a modest portion of the 1957-1958 recession, 1960-1961 recession, 1969-
1970 recession, 1981-1982 recession, 2001 recession, while constituting a dominant
force behind the recent recession. This recession, in which output loss was 8.3
percent, seems to have been driven considerably by EFP shocks which contributed 4.7
percent of that accumulated decline.
3.3 Sensitivity Analysis
My main result that EFP shocks have the potential of generating business cycles is
robust to alternative lag structures, different truncation horizons for the maximization
problem underlying identification, estimation of a cointegrated VAR that accounts for
the long run relationship between the non stationary variables of the model, different
sample sizes, alternative measures of EFP, and a system that includes a measure of the
quantity of credit as opposed to the leverage ratio.
7 I assume a 2% output per capita steady state annual growth, which is consistent with the average
growth rate of output per capita over the sample.
70
For space reasons, only three of the above robustness checks are reported here.
First, in light of the known argument that structural change occurred in the U.S
economy following Volcker's appointment as Fed chairman in 1979 and the great
moderation that started in 1984, the robustness of the results to using a sub-sample
starting in 1984 is confirmed. Figure 3.4 presents the IRF's to an EFP shock for this
sub-sample. It is apparent that the qualitative nature of the results is left unchanged
whereas all of the responses are significantly stronger quantitatively. This is
especially evident when looking at the variance decomposition results (not shown);
EFP shocks account for 40 percent and nearly 50 percent of output and hours business
cycle variation, respectively.
This interesting result could be explained by the period of significant financial
deregulation that commenced in the early 1980's up until the crisis of 2008. Note that
the latter crisis is not likely to be the driver of the strong sub sample results given that
the period of the crisis is included in both the large sample and the sub sample.
Nevertheless, it is outside the scope of this paper to directly test the hypothesis that
financial deregulation caused EFP shocks to be more important in the business cycle.
A structural model that explicitly models the aspect of financial regulation and its
impact on the model's behavior would be an interesting avenue of future research that
could address the financial regulation hypothesis in the context of my results.
Second, I examine the IRF's to an EFP shock replacing the benchmark EFP
measure with the Baa-Aaa spread. The latter measure is inferior to the benchmark
measure in that the Aaa yield does not represent the risk free rate as well as the ten
year government bond yield does. Nevertheless, it is worthwhile to test the robustness
of the results to this alteration. Figure 3.5 demonstrates that the overall qualitative
nature of the results is not changed when the Baa-Aaa variable is used as the measure
of EFP. The responses of the real variables are also quantitatively similar to the
benchmark ones. Nevertheless, the response of interest rates is significantly weaker.
The reason for this could be due to the Aaa yield not being an adequate measure of
the risk free rate as the ten year government yield.
71
Third, one may be concerned that the shock being identified in this paper is
not a credit supply shock but rather a credit demand shock. So as to rule out this
conjecture, I applied my identification procedure in a VAR that replaced the leverage
ratio variable with a measure of debt gauged by total credit market instruments of
nonfarm nonfinancial corporate business, deflated by the GDP deflator. I added the
debt variable so as to be able to determine whether my identified shock constitutes a
credit supply shock or a credit demand shock, as a credit supply shocks should lower
the level of debt along with raising EFP. Figure 3.6 shows the results from the latter
exercise. It is apparent that the quantity of debt declines following the shock, a finding
which confirms that the identified shock cannot constitute a credit demand shcok but
rather a credit supply shock that raises the price of credit and lowers its quantity.
Moreover, it is also clear that the main result of the paper that EFP shocks have the
potential of generating business cycles is maintained as the latter continue to generate
business cycle comovement, reduce inflation, and raise interest rates.
Lastly, one might be worried that the identifying restriction that the identified
shock have no effect on TFP is too restrictive given the recent line of research that
argues that adverse credit supply shocks increase TFP via the destruction of the least
productive jobs (i.e. Petrosky-Nadeau (2011)). Thus, an identification procedure
where the latter identification restriction is relaxed was also employed. The results
from this identification procedure are nearly identical to the benchmark results.
Moreover, even though the response of TFP turn moderately positive after three
quarters, this effect is statistically insignificant. These results indicate that the
inference made based on the benchmark results is valid.
Overall, the results of this section indicate that the central result that EFP
shocks have the potential of driving business cycles is robust to various alterations of
the benchmark model, including changes in the specification of the empirical model
as well as changes in the maximization problem underlying identification.
72
4 A DSGE model with a Financial Accelerator
This section presents a DSGE model augmented with the financial accelerator ˋa la
BGG (1999) in which credit supply shocks generate impulse responses consistent
with the observed empirical responses obtained in section 3. I also provide simulation
evidence that the identification procedure performs well on data generated from this
model in terms of identifying credit supply shocks and their dynamic effects.
4.1 Model
I consider the by now classic Smets and Wouters (2007) model augmented with three
elements: the financial accelerator mechanism via the BGG (1999) framework,
specification of the cost of utilization in terms of increased depreciation of capital, as
originally proposed by Greenwood et.al (1988) in a neoclassical setting8, and finally
the model also includes credit supply shocks and net worth shocks.9 I will now
present the model.
Each household [0,1]j∈ maximizes the utility function
1 1
0
0
1( ) exp(
1
1
c lct t t
t b lt
t c
C hC L
E
σ σσσ
β εσ
− +∞
=
− − +
−
∑ (7)
Where E0 denotes the expectation conditional on the information available at time
zero, 0 < β < 1, lσ > 1, χ > 0, Cσ > 0, b
tε is the preference shock, and h is the habit
formation parameter.
The budget constraint and the capital accumulation equation are given as
1 1( ) ( ) k
t t t t t t t tt t t
t t t t t t
B B W j L j R Z K DivC I T
R P P P P P
− −+ + − ≤ + + + (8)
[ ]1 1(1 ( )) 1 ( / )i
t t t t t t tK Z K S I I Iδ ε− −= − + − (9)
8 Traditionally, the cost of utilization is specified in terms of forgone consumption following
Christiano et al. (2005), who studied the effects of monetary policy shocks. I follow Khan and
Tsoukalas (2009) who use the capital depreciation specification and show that it has a superior fit with
the data relative to the Christiano et.al (2005) specification. This specification is also used in Jaimovich
and Rebelo (2009). Aside from this specification difference, the model here is identical in structure to
Gilchrist, Ortiz and Zakrajsek (2009). 9 TFP and IST news shocks are also included in the model so as to account for the potential importance
of these shocks.
73
respectively, where tI is investment, is
tε is investment specific technology, tB are
nominal government bonds, tR is the gross nominal interest rate, tP is the price level,
tT is lump-sum taxes, Wt(j) is the nominal wage, k
tR is the rental rate on capital, tZ is
the utilization rate of capital, ( )tZδ is an increasing and convex function of the
utilization rate as in GHH (1988), and tDiv the dividends distributed to the
households from labor unions. The left hand side of (9) represents real expenditures at
time t net of taxes on consumption, investment, and bonds. The right hand side of (9)
indicates real receipts from wage income, earnings from supplying capital services net
of cost, and dividends. In (3), 1( / )t tS I I − is a convex investment adjustment cost
function. In the steady state it is assumed that S=S'=0, and S''>0. The aggregate
resource constraint is
t t t tC I G Y+ + = (10)
The first-order condition for optimal utilization of capital is given by the
following equation:
'( )k
tt t
t
RQ Z
Pδ= (11)
Where tQ is the price of physical capital in period t. The BGG framework focuses on
an entrepreneurial sector that borrows funds to purchase physical capital in period t at
price tQ , which it then operates in period t+1 and resells it at the end of period t+1 at
price 1tQ + . Therefore, the demand for capital by entrepreneurs is determined by
maximizing entrepreneurs' profit in period t+1 given that their cost of external
financing is 1
k
t tE R + . The BGG framework assumes a costly-state verification problem
between entrepreneurs and risk neutral financial intermediaries where the latter need
to pay monitoring costs in order to observe entrepreneurs' realized income in case of
default. BGG show the optimal debt contract in this framework implies the following
equation:
1 1
1
k
t t tt
t t
R Q KE s
R N
+ +
+
=
(12)
74
Where s is an increasing function in the leverage ratio and tN is the net worth of the
entrepreneur. Lastly, BGG assume that entrepreneurs are long lived but discount the
future more heavily than households, thus implying that entrepreneurial net worth
depends on past net worth and on the return on capital relative to the expected return,
as described in log-linear form equation (T.16).
All of the equilibrium conditions of the model log-linearized about the
balanced growth path, along with the definition of the variables, are presented in table
3.3. Labels, definitions and benchmark values of the parameters are in Table 4. The
means by which these values were derived are described in the next subsection.
Equation (T.1) is the aggregate resource constraint; Eq. (T.2) is the Euler
equation for consumption; Eq. (T.3) is the Euler equation for investment derived from
solving the optimal quantity of investment supplied on the part of capital producers;
Eq.(T.4) describes the dynamics of Tobin’s q as derived from solving the optimal
quantity of capital demanded by entrepreneurs; Eq.(T.5) is the aggregate production
function; Capital services used in production by entrepreneurs are a function of capital
installed in the previous period and capital utilization, as described by eq. (T.6); Eq.
(T.7) expresses the optimal capital utilization rate as a function of the value of capital
and the marginal product of capital, as derived from log linearization of the first order
condition of entrepreneurial profit with respect to capital utilization rate; Eq. (T.8) is
the capital accumulation equation; The price mark up is defined by Eq. (T.9);
Inflation dynamics are described by the New-Keynesian Phillips curve in Eq. (T.10);
Combining the production function (T.5) with the log linearized first order condition
of entrepreneurs' profit with respect to labor implies that the capital-labor ratio is
inversely related to the marginal product of capital and positively related to the wage
rate, as described by eq. (T.11); The wage markup is given by Eq. (T.12); The wage
inflation dynamics are described by Eq. (T.13); Eq. (T.14) describes the monetary
policy rule;10 Eq. (T.15) represents the credit supply equation where the external
10 This rule was used by a number of recent papers (for example, Barsky and Sims (2008), Coibion and
Gorodnichenko (2007), Fernandez-Villaverde and Rubio-Ramirez (2007), Erceg, Guerriei, and Gust
(2006), and Ireland (2004), and it postulates that the central bank sets nominal interest rates according
75
finance premium, 1
k
t t tE r r+ − , is a function of entrepreneurs leverage ratio and the
credit supply shock;11
Lastly, Eq. (T.16) depicts the evolution of net worth of
entrepreneurs.
4.2 Estimation
Following Kurmann and Otrok (2010), the parameters are partitioned into two groups.
The first group includes parameters that are calibrated in accordance with the DSGE
literature while the second group of parameters is estimated by minimizing a weighted
distance between the model-implied IRFs to a credit supply shock and the empirical
counterparts from the VAR. This estimation method was used by Christiano et.al
(2005) in the context of monetary policy shocks and more recently by Kurmann and
Otrok (2010) in the context of TFP news shocks. In particular, denote by Ψ
a vector
of empirical IRFs to a credit supply shock attained from a VAR. Likewise, denote by
( )Ψ Φ the same vector of IRFs implied by the model, where Φ contains all the
structural parameters of the model. The estimator for the second group of
2Φ ⊆ Φ parameters is:
2
12 2 2arg min ( ( )) ' ( ( ))−
ΦΦ = Ψ −Ψ Φ Ω Ψ −Ψ Φ
Where Ω is a diagonal matrix with the sample variances of 2Φ along the diagonal
and the first 40 elements of each impulse response function are included. This
estimation approach is used to study whether a theoretical model that incorporates the
financial accelerator mechanism and credit supply shocks is capable of generating
IRFs that resemble the empirical counterparts which were interpreted as credit supply
shocks based on their dynamic effects on variables such as EFP, leverage, inflation,
interest rates and macroeconomic aggregates such as output, investment,
consumption, and hours.
to a partial adjustment mechanism where the interest rate in any period is equal to a convex
combination of the lagged interest rate and the central bank’s target rate, where the target rate is
adjusted in response to deviations of output growth and inflation from constant targets. For simplicity, I
assume the targets are equal to the steady state values of output growth and inflation. 11
This shock can be interpreted as an exogenous change in the variance of idiosyncratic shocks that
affect entrepreneurs' profitability. Hence, it is essentially a shock which originates in the credit market
as it reflects changes in the perception about borrowers' creditworthiness on the part of the financial
intermediaries.
76
Table 3.4 presents the values for the calibrated parameters followed by the values of
the estimated parameters. The benchmark value of the discount factor is set in
accordance with Jaimovich and Rebelo (2009). The leverage ratio value corresponds
to the average leverage ratio in the U.S. nonfinancial corporate sector over our sample
period, as demonstrated in GOZ, the value of the survival rate of entrepreneurs
follows BGG, and the value for the standard deviation of the net worth shock follows
CMR. The values for the news persistence parameters follow Barsky and Sims (2009)
while the standard deviation of the news shocks is set in accordance with Khan and
Tsoukalas (2010). All remaining calibrated parameters' values by and large follow the
estimates of Smets and Wouters (2007).12
Overall, the point estimates of the estimated parameters do not deviate to a
large extent from the ones obtained in the DSGE literature. The estimate of the
inverse intertemporal elasticity is 0.98, compared to a mean estimate of 0.95 in GOZ.
Moreover, the wage and price rigidity parameter constrained estimates are 0.75 and
0.5 compared to 0.74 and 0.77, respectively, in GOZ.13
The monetary policy rule
smoothing and inflation parameters estimates are consistent with the empirical
estimates of Coibion and Gorodnichenko (2007), Fernandez-Villaverde and Rubio-
Ramirez (2007), Erceg, Guerriei, and Gust (2006), and Ireland (2004), while the
output growth parameter is very low. The elasticity of the external finance premium
with respect to the leverage ratio (0.027) is in between the GOZ estimate and the
Christensen and Dib (2008) estimate. Lastly, the capital utilization elasticity
parameter estimate is higher than the one estimated in Khan and Tsoukalas (2011) and
assumed in Jaimovich and Rebelo (2009) while the inverse of the labor supply
elasticity parameter is 2.3, consistent with the Smets and Wouters (2007) estimate of
2.4.
12
The empirical results in Ben Zeev (2010) indicate that the unanticipated IST shock is very persistent.
Therefore, I calibrate its persistence parameter to be equal to the 95th
percentile of the posterior
distribution of the AR(1) parameter for the IST process as estimated in Smets and Wouters (2007). 13
When necessary, I constrained the parameter values to avoid getting estimates which seemed to high
or low relative to the DSGE literatue. For instance, the wage and price rigidity parameters'
unconstrained estimates were too high at nearly one.
77
4.3 Results
Figure 3.6 depicts the model IRFs to credit supply shocks along with the empirical
IRFs from the VAR and their bootstrapped 90% confidence intervals. Overall, the
model does fairly well in generating responses that are similar both qualitatively and
quantitatively to the empirical counterparts. Nevertheless, the model's major failure,
in quantitative terms, is in replicating the strong empirical response of interest rates
while its major failure in qualitative terms is replicating the hump shaped response of
hours. These two failures seem to manifest a shortcoming of the model and a need for
a richer model that is capable of generating a stronger decline in interest rates and a
hump shaped response of hours and consumption. Nonetheless, in accordance with
the empirical responses, the credit supply shock generates both a decline in interest
rates and hours.
There are two additional discrepancies related to the qualitative nature of the
response of leverage and consumption. The model delivers an immediate jump in
leverage in contrast to a hump shaped increase following the empirical EFP shock.
Nevertheless, the model successfully delivers a decrease in leverage following the
initial increase. Furthermore, consumption starts to exhibit a hump shaped response
only a year after the shock, whereas the empirical response is hump shaped from the
initial period. Nonetheless, this response is negative in accordance with its empirical
counterpart.
The model does a good job of generating the hump shaped response of output
and investment as well as the negative deflationary effect. The credit supply shock
behaves like a pure demand shock in that it reduces both economic activity and
inflation. Moreover, it causes a decline the risk free rate while increasing the external
finance premium. One can use the response of leverage to differentiate between credit
supply shocks and net worth shocks. Aforementioned, similarly to the empirical shock
identified in the previous section, the adverse credit supply shock initially increases
leverage after which it starts decreasing leverage. This contrasts with adverse net
worth shocks (not shown) which generate a persistent increase in leverage. These
78
results were also reported by GOZ and are supportive of the interpretation of the
identified shock from the previous section as a credit supply shock.
4.4 Simulation Evidence
I simulate 2000 sets of data with 229 observations each, drawing all ten exogenous
shocks from normal distributions. So as to make the simulated data as close as
possible to actual data, the simulated series are transformed by adding back in trend
growth where applicable.14
For each simulation, I estimate a two-lag VAR with a
constant that includes the levels of TFP, IST, EFP, leverage, output, investment,
consumption, hours, nominal interest rate and inflation, which coincides with the
benchmark empirical VAR in Section 3. The truncation horizon is set at H = 20. In
other words, I identify the credit supply shock as that shock orthogonal to current TFP
and IST which maximally explains EFP over a horizon of five years. I follow the
identification procedure outlined in section 2 and collect the estimated impulse
responses and identified time series of credit supply shocks for each simulation.
Figure 3.7 depicts both theoretical and estimated impulse responses averaged
over the simulations to a credit supply shock. The theoretical responses are
represented by the solid lines and the average estimated responses over the
simulations are depicted by the dashed lines, with the dotted lines depicting the 5th
and 95th percentiles of the distribution of estimated impulse responses. It is apparent
that the estimated empirical impulse responses are roughly unbiased on impact and for
a number of quarters thereafter. While the estimated impulse responses are
moderately downward biased at longer horizons, the estimated dynamics are fairly
close to the true dynamics at all horizons.
The average and median correlation between the identified credit supply shock
and the true credit supply shock across simulations is 0.93, with the 5th and 95th
percentile correlations 0.89 and 0.96, respectively. The results improve even further
as the size of the simulated samples becomes arbitrarily large. While small biases still
14
Following Fernandez-Villaverde (2009), quarterly trend growth rates of 0.28% and 0.34% are added
to TFP and IST, respectively, and in accordance with the balanced growth path 0.63% is added to
output, investment and consumption.
79
persist in large samples, the estimated impulse responses to credit supply shocks are
extremely close to the true responses at all horizons and the correlation between the
identified and true shocks exceeds 0.95.
The suitability of the identification strategy appears quite robust to alternative
calibrations of the model as well as to differences in the truncation horizon parameter
H and number of lags in the VAR. Nevertheless, in terms of the calibration of the
model, the method does perform better when there is more variation in EFP directly
attributable to the credit supply shock. The benchmark parameter values imply that
credit supply shocks drive a considerable part of EFP fluctuations, though the share
declines with the time horizon from 99% at the two year horizon to 88% and 78% at
the five year and ten year horizons, respectively. This is mainly due to an increasing
share attributed to unanticipated TFP shocks.
I also confirmed the superiority of the identification method with respect to the
original Uhlig (2003) procedure by relaxing the two identifying restrictions imposing
on the identified shock to have no effect on both and TFP and IST. The accuracy of
identification, as measured by the length of the IRF's confidence interval, is
considerably better for the benchmark identification method. For instance, the 90%
confidence interval at business cycle frequencies for the output IRF's under Uhlig's
original procedure is 73% and 94% wider than the benchmark case at the first and
second quarter horizons, respectively, after which it is more than twice as wide.
Overall, the main conclusion of this sub-section is that as long as credit supply
shocks drive a considerable share of EFP in relation to the other demand shocks in the
model, the proposed identification method will do a good job of identifying credit
supply shocks and their effects on macroeconomic variables. Furthermore, adding the
exogeneity restrictions of TFP and IST with respect to the identified shock results in a
significantly more accurate identification.
80
5 Conclusion
This paper extends Uhlig's (2003) method for the identification of a shock that has no
effect on both neutral and investment specific technology and explains the most of
EFP variation over a horizon of ten years. This shock is found to generate business
cycle comovement while increasing EFP and reducing inflation and interest rates.
Even though it does not explain a significant amount of the business cycle variation of
output, the historical decomposition results indicate that it has played a non negligible
role in six of the last nine U.S recessions.
The empirical IRF's lead me to interpret the identified shock as a credit supply
shock. In particular, it is shown that credit supply shocks from a New Keynesian
DSGE model with a financial accelerator can generate theoretical IRF's which are
consistent with the observed empirical IRF's. Furthermore, monte carlo simulation
results indicate that the identification method used in this paper is capable of
identifying credit supply shocks and their effects on macroeconomic variables from
model generated data.
Hence, the results of the paper can be used to infer that credit supply shocks
have the potential of generating business cycles. The results also confirm the view
that these shocks played an especially important role in the most recent recession.
Even though these shocks may not constitute a substantial source of business cycles
on average, particular periods in which large credit supply shocks hit the economy are
likely to transform into serious recessions.
81
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84
Table 3.1
Correlation Estimates
Unconditional Conditional
Output 1 1
Consumption 0.56 0.97
Investment 0.87 0.92
Hours 0.74 0.94
Notes: Panel A in table 3 reports estimates of both unconditional and conditional correlations
between the growth rate of output and the growth rates of consumption, investment and hours.
Panel B reports estimates of both unconditional and conditional correlations between the
growth rate of leverage and the first difference of the external finance premium. The
unconditional correlations are computed directly from the data whereas the conditional
correlations estimates are based upon the benchmark VAR model assuming EFP shocks are
the only shocks present in the economy.
85
Table 3.2
Historical contribution of EFP shocks to Output per Capita loss
in U.S Recessions
Recession Percentage Change in
Output per Capita (deviation
from trend growth)
Contribution of EFP Shocks
1957:3-1958:2 -5.7 -0.8
1960:2-1961:1 -3 -0.2
1969:4-1970:4 -4.4 -0.6
1973:4-1975:1 -8.2 0.1
1980:1-1980:3 -4 -0.1
1981:3-1982:4 -6.7 -1
1990:3-1991:1 -2.8 0.1
2001:1-2001:4 -1.7 -0.3
2007:4-2009:2 -8.3 -4.7
Notes: Table 4 reports estimates of the contribution of credit supply shocks to each of the
recessions in my sample period. The first column presents the percentage change from peak to
trough of output per capita, relative to trend growth, in every recession. The second column
reports the contribution of EFP shocks, based on the benchmark VAR model, to the
corresponding output loss. I assume a 2% output per capita annual trend growth, which is
consistent with the average growth rate of output per capita over the sample.
86
Table 3.3
The Variables and Equations of the Model
(a) The variables of the model; (b) the equations of the model
a)
L a b e l D e f i n i t i o n
O u t p u t
I n v e s t m e n t
C o n s u m p t i o n
H o u r s
I n s t a l l e d c a p i t a l
C a p i t a l s e r v i c e s
N e t W o r t h
I n f l a t i o n r a t e
T o b i n 's q
R e a l c a p i t a l r e n t a l r a t e
N o m i n a l r a t e
U t i l i z a t i o n r a t e
P r i c e m a r k - u p
W
t
t
t
t
t
s
t
t
t
t
k
t
t
t
p
t
w
t
y
i
c
l
k
k
n
q
r
r
z
u
u
π
a g e m a r k - u p
b)
t y t y t 1y = (1-i -g - )c + i i + g g
y y y t y tn n nε ++ (T.1)
* *(1 )(1 )
1 * t t t+1 t-1 t t+1 t t t 11 1 (1 ) (1 )
c = E c - c - E (l - l ) - (r - E )
hW Lh h
c C
th h h hc c
σλ λ
σ σλ λ λ λ
π
− − + + + + +
(T.2)
1
t t-1 t t+1 t1 2
1 1i = i + E i + (q + )
1c
c
is
t
σσ β ε
β ϕ−
−
γ + γ γ
(T.3)
*t t+1 t t+1 t t+1
* *
r (1 )E r = + E mpk + E q
r (1 ) r (1 )
kk
t k kq
δδ δ
−−
+ − + − (T.4)
t ty = ( k + (1- )l + )s a
p t tφ α α ε (T.5)
t-1 tk = k + zs
t (T.6)
z ( )t t tmpk qψ= − (T.7)
'
*t t-1 t
(1- ) (1- ) (1- )k = k + 1- i + 1- i
t t
Zz
δ δ δ δε
ν ν ν ν −
(T.8)
t t(k -l ) + p s a
t t tu wα ε= − (T.9)
1 1
t t-1 t t+11 1 1
(1- )(1 ) = + E -
1 1 (1 )(1 ( 1) )
c c
c c c
p p p p p
t
p p p p p p
u
σ σ
σ σ σ
ι β ι β ξ ξπ π π
β ι β ι β ι φ ε ξ
− −
− − −
γ γ −
+ γ + γ + γ + − (T.10)
t t tmpk (k -l ) + ws
t = − (T.11)
87
t 1
1u = w ( )
1
w
t l t t tl c hch
σ
λ
−
− + − −
(T.12)
1
t t-1 t t+1 t t+1 t t-11 1 1 1
1
1
1 1 1 = + 1 (E +E )
1 1 1 1
(1- )(1 ) ((1 ) )(( 1) 1)
c
c c c c
c
c
w
w ww wt t
w w w
w w w
u
σ
σ σ σ σ
σ
σ
β ιπ π π
β β β β
β ξ ξε
β ξ φ ε
−
− − − −
−
−
+ γ− − + + γ + γ + γ + γ
γ −− +
+ γ − +
(T.13)
1 (1 )( ) r
t r t r t y t tr p r p yππ ε−= + − Θ +Θ ∆ + (T.14)
t t+1 1 1E r ( )k risk
t t t t tr q k nχ ε+ +− = + − + (T.15)
1 1 11 ( )k nw
t t t t t t t
K Kn n r s r
N Nϑ π ε+ − −
= + − − + − +
(T.16)
1 1
a a a a
t a t t tgε ρ ε η− −= + + (T.17)
1
a a a
t t tg g eκ −= + (T.18)
1
b b b
t b t tε ρ ε η−= + (T.19)
1
g g g
t g t tε ρ ε η−= + (T.20)
1 1
w w w w
t w t t w tε ρ ε η κ η− −= + − (T.21)
1 1
is is is is
t i t t tgε ρ ε η− −= + + (T.22)
1
is is is
t t tg g eκ −= + (T.23)
1
cs cs cs
t risk t tε ρ ε η−= + (T.24)
Notes: This table presents the equations of the DSGE model of section 4.1. The ten
disturbances are: TFP unanticipated shocka
tε ; TFP news shocka
tg ; monetary policy
shockr
tε ;preference shockb
tε ; government spending shockg
tε ; Wage mark-up shockw
tε ;IST
unanticipated shock is
tε ; IST news shock is
tg ; Credit supply shockcs
tε ; Net worth shock nw
tε .
In particular, 1
a
tg − and 1
is
tg − are stochastic drift terms that follow AR(1) processes (T.16) and
(T.21), respectively. Following Sims (2009) and Barsky and Sims (2008, 2009), the
corresponding i.i.d shocks a
te and is
te .in (T.16) and (T.21) are defined as TFP and IST news
shocks as they portend future changes in TFP and IST, respectively.
88
Table 3.4
Description of the Parameters of the Model and Benchmark
Values
L a b e l D e f i n i t i o n B e n c h m a r k V a l u e
E n t r e p r a n u r i a l s u r v i v a l r a t e 0 . 9 7 3
G o o d s m a r k e t c u r v a t u r e 1 0
L a b o r m a r k e t c u r v a t u r e 1 0
S t e a d y s t a t e l a b o r m a r k e t m a r k - u p 1 . 2 5
D e t e r m i n i s t i c o u t p u t g r
C a l i b r a t e d P a r a m e t e r s
p
w
w
ϑεεφγ
*
o w t h 0 . 0 0 6 3
D e t e r m i n i s t i c c a p i t a l g r o w t h 0 . 0 0 9 2
D i s c o u n t f a c t o r 0 . 9 8 5
L S t e a d y s t a t e h o u r s 0 . 5 3
/ S t e a d y S t a t e L e v e r a g e R a t i o 1 . 7
T F P p e r s i s t e n c e 0 . 9 5
P r e f e r e n c e s h o c k p e r s i s t e n c e 0 . 2 2
G o v e r n m e n t s p e n d i n g
a
b
g
K N
νβ
ρρρ p e r s i s t e n c e 0 . 9 5
W a g e m a r k - u p p e r s i s t e n c e 0 . 9 0
W a g e m a r k - u p M A 0 . 9 0
I S T p e r s i s t e n c e 0 . 9 0
N e w s s h o c k p e r s i s t e n c e 0 . 7 5
T F P s h o c k s t . d e v . 0 . 0 0 4 5
T F P n e w s s h o c k s t . d e v . 0 . 0 0 0 9
P r e f e r e n c e s h o c k s t . d e v .
w
w
i
a
a
e
b
ρκρκσσσ 0 . 0 0 2 3
G o v e r n m n t s p e n d i n g s h o c k s t . d e v . 0 . 0 0 0 1 6
M o n e t a r y p o l i c y s h o c k s t . d e v . 0 . 0 0 2 3
I S T C s h o c k s t . d e v . 0 . 0 0 4 5
I S T C n e w s s h o c k s t . d e v . 0 . 0 0 1 9
N e t W o r t h s h o c k s t . d e v 0 . 0 0 4
E s t i m a t e d P a r a m e t
g
r
i s
i s
e
n
σσσσσ
L a b e l D e f i n i t i o n B e n c h m a r k V a l u e
I n v e r s e i n t e r t e m p o r a l e l a s t i c i t y 0 . 9 8
I n v e r s e l a b o r e l a s t i c i t y 2 . 3 1
C a p i t a l s h a r e 0 . 2 1
C a l v o w a g e s 0 . 7 5
C a l v o p r i c e s 0 . 5
W a g e i n d e x a t i o n 0 . 4 9
P r i c e i n d e x a t i o n 0 . 2 7
F i x
e r s
c
l
w
p
w
p
p
σσαξξιιφ e d c o s t s h a r e 1 . 3 2
M o n e t a r y P o l i c y r u l e i n f l a t i o n 2 .0 0
M o n e t a r y P o l i c y r u l e s m o o t h i n g 0 . 6
M o n e t a r y P o l i c y r u l e o u t p u t g r o w t h 0 . 0 1
I n v e s t m e n t a d j u s t m e n t c o s t 4
H a b i t F o r m a t i o n 0 . 9 5
1 / C a p i t a l u t i l i z a t i o n
r
y
p
h b
π
ϕ
ψ
Θ
Θ
e l a s t i c i t y 0 . 3 8
E F P e l a s t i c i t y 0 . 0 2 7
R i s k s h o c k p e r s i s t e n e 0 . 8 0
R i s k s h o c k s t . d e v 0 . 0 0 2 7
r i s k
r i s k
χρσ
Notes: This table presents a description of the parameters of the DSGE model of section 2.2
as well as their benchmark values.
89
Figure 3.1
Empirical Impulse Responses to EFP Shocks
Dashed lines represent 5th and 95th percentile Hall (1992) confidence bands generated from a
residual based bootstrap procedure repeated 2000 times.
0 10 20 30 40-0.1
0
0.1
0.2
0.3
0.4EFP
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1
-0.5
0
0.5
1Leverage
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2Output
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.4
-0.2
0
0.2
0.4Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-2
-1
0
1
2Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1
-0.5
0
0.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-60
-40
-20
0
20Interest Rate
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.3
-0.2
-0.1
0
0.1Inflation
Horizon
Pe
rce
nta
ge
Po
ints
90
Figure 3.2
Share of Forecast Error Variance Attributable to Identified
Shocks (EFP shock, Unanticipated IST and TFP shocks)
The above bar diagrams show the share of forecast error variance of each variable attributable
to the identified EFP shock, unanticipated IST and unanticipated TFP shocks. As the
identification pursued in the paper is a partial one, the sum of relative contributions of all
three shocks do not necessarily add up to one as there are potentially additional unidentified
shocks also accounting for part of the forecast error variance.
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
EFP
EFP Shock
Unanticipated IST
Unanticipated TFP
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Leverage
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Output
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Consumption
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Investment
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Hours
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Interest Rate
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cas
t E
rro
r
Inflation
91
Figure 3.3
Identified EFP Shock Time Series and U.S Recessions
Smoothed EFP Shock Series
This figure plots the time series of identified EFP shocks from the benchmark VAR. U.S
recession are represented by the shaded areas. So as to render the figure more readable, the
plotted data is smoothed using a one year moving average. Specifically, it is calculated
as 3 2 1( ) / 4s
t t t t tε ε ε ε ε− − −= + + + . The series begins in 1955:2 and ends in 2010:2. I lose
four observations at the beginning of the sample due to the lag length and three additional
observations at the beginning and end of the sample due to the moving average.
92
Figure 3.4
Impulse Responses to EFP shocks: Smaller Sample
The above are responses to an EFP shock from the benchmark VAR using a sub-sample
starting in 1984:Q1. Dashed lines represent 1th and 99th percentile Hall (1992) confidence
bands generated from a residual based bootstrap procedure repeated 2000 times.
0 10 20 30 40-0.2
0
0.2
0.4
0.6EFP
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-2
-1
0
1
2Leverage
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1
-0.5
0
0.5
1Output
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1
-0.5
0
0.5Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-4
-2
0
2
4
6Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1.5
-1
-0.5
0
0.5
1Hours
HorizonP
erc
en
tag
e P
oin
ts
0 10 20 30 40-100
-80
-60
-40
-20
0
20Interest Rate
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.2
-0.1
0
0.1
0.2Inflation
Horizon
Pe
rce
nta
ge
Po
ints
93
Figure 3.5
Impulse Responses to EFP shocks: Alternative Measure of EFP
The above are responses to an EFP shock from the benchmark VAR using Baa–Aaa spread as
the measure of EFP. Dashed lines represent 5th and 95th percentile Hall (1992) confidence
bands generated from a residual based bootstrap procedure repeated 2000 times.
0 10 20 30 40-0.1
0
0.1
0.2
0.3EFP
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.4
-0.2
0
0.2
0.4
0.6Leverage
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2Output
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.4
-0.2
0
0.2
0.4Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-2
-1.5
-1
-0.5
0
0.5
1Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-1
-0.5
0
0.5Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-40
-20
0
20
40Interest Rate
Horizon
Pe
rce
nta
ge
Po
ints
0 10 20 30 40-0.3
-0.2
-0.1
0
0.1
0.2Inflation
Horizon
Pe
rce
nta
ge
Po
ints
94
Figure 3.6
Impulse Responses to EFP shocks: Including Credit Quantity
The above are responses to an EFP shock from the benchmark VAR replacing the leverage
ratio variable with a measure of debt gauged by total credit market instruments of
nonfarm nonfinancial corporate business, deflated by the GDP deflator. Dashed lines
represent 5th and 95th percentile Hall (1992) confidence bands generated from a residual
based bootstrap procedure repeated 2000 times.
0 5 10 15 20-0.1
0
0.1
0.2
0.3
0.4EFP
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-1.5
-1
-0.5
0
0.5Debt
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0Output
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-0.4
-0.3
-0.2
-0.1
0
0.1Consumption
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-2
-1.5
-1
-0.5
0
0.5
1Investment
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0Hours
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-50
-40
-30
-20
-10
0
10Interest Rate
Horizon
Pe
rce
nta
ge
Po
ints
0 5 10 15 20-0.3
-0.2
-0.1
0
0.1Inflation
Horizon
Pe
rce
nta
ge
Po
ints
95
Figure 3.7
Impulse Responses to Credit Supply Shock for DSGE Model
The dashed lines show the theoretical impulse response to credit supply shocks from the
model of sub-section 4.1. The solid lines depict the empirical impulse response from the
VAR, with the shaded area representing the 90% bootstrapped VAR confidence interval.
96
Figure 3.8
Model and Monte Carlo Estimated Impulse Responses to Credit
Supply Shocks
The solid lines show the theoretical impulse response to a credit supply shock from the model
of sub-section 2.2. The dashed lines depict the average estimated impulse responses over
2000 Monte Carlo simulations, with the dotted lines representing the 5th and 95th percentiles
of the distribution of estimated impulse responses.
0 10 20 30 40-0.1
0
0.1
0.2
0.3EFP
Horizon
Pe
rce
nta
ge
Po
int
De
via
tio
n
Model
Estimated
0 10 20 30 40-1
-0.5
0
0.5
1Leverage
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 10 20 30 40-0.3
-0.2
-0.1
0
0.1Output
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 10 20 30 40-0.15
-0.1
-0.05
0
0.05
0.1Consumption
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 10 20 30 40-1.5
-1
-0.5
0
0.5
1Investment
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 10 20 30 40-0.3
-0.2
-0.1
0
0.1Hours
Horizon
Pe
rce
nta
ge
De
via
tio
n
0 10 20 30 40-0.15
-0.1
-0.05
0
0.05
0.1Interest Rate
Horizon
Pe
rce
nta
ge
Po
int
De
via
tio
n
0 10 20 30 40-0.1
-0.05
0
0.05
0.1Inflation
Horizon
Pe
rce
nta
ge
Po
int
De
via
tio
n
97
Chapter IV
The Role of Domestic and Foreign News and
Animal Spirits Shocks in a Small Open
Economy
1. Introduction
In this paper, I formulate a theoretical small open economy New Keynesian model
that incorporates domestic and foreign news shocks and animal spirits (noise) shocks
and allows an examination of the implications of these shocks for a small open
economy. To my knowledge, the effects of both news and animal spirits shocks have
not been studied in an open-economy setting. Hence, my contribution lies in
proposing such a setting in which the effect of both foreign and domestic news and
animal spirits shocks can be studied. The reason such an extended setting is
interesting is twofold. First, it is appealing to examine whether the effects of domestic
news and animal spirits shocks are different for a small open economy model relative
to a closed economy model. The findings indicate that the effects are similar to the
closed economy model as positive domestic news are expansionary and deflationary
while positive domestic animal spirits are expansionary and inflationary playing the
role of aggregate demand shocks.1 Second, it is interesting to study how the effects of
foreign news and animal spirits shocks differ from their domestic counterparts. The
findings indicate a difference with respect to the response of inflation which is
attributable to exchange rate behavior. In particular, it is found that positive foreign
news are expansionary and induce inflation on impact (due to currency depreciation)
followed by deflation at longer time horizons which is imported by the deflation in the
foreign economy, while positive foreign animal spirits are expansionary and lead to
1 Positive news and animal spirits shocks, as will be explained in detail in the next section, pertain to
the expectation that future productivity will be higher in the future, with news shock constituting
changes in expectations about future productivity that are correct, on average, whereas animal spirits
represent erroneous optimism about future productivity.
98
deflation on impact (due to currency appreciation) and inflation afterwards as the
demand side effects of the shocks become more dominant than the exchange rate
effect.
Recently there has been a growing interest in examining the role of news
shocks as a driving force of business cycles. The literature includes, among others,
Beaudry and Portier (2004, 2006, 2007), Christiano, Motto, and Rostagno (2006) and
Jaimovich and Rebelo (2009). As is well known, in the standard neoclassical real
business cycle model, changes in expectations induced by the arrival of new
information to the economy (or news shocks) move consumption and labor in
opposite directions due to the wealth effect. For instance, if an increase in the
expected level of future productivity raises the present discounted value of income,
the consumer increases both consumption and leisure today, and hence reduces labor
supply. It follows that output and investment decline as well.
In order for news shocks to generate business cycles (i.e, comovement
between consumption, investment, labor, and output), the papers listed above modify
preferences and/or technology from the standard model. For instance, Beaudry and
Portier (2004, 2007) introduce a certain type of complementarity between production
technologies in a two-sector model; Christiano, Motto, and Rostagno (2006) introduce
habit persistence in consumers’ preference and a specific form of the adjustment costs
in investment; Jaimovich and Rebelo (2009) assumes preferences without income
effect on labor supply, the same adjustment cost as in Christiano, Motto and Rostagno
(2006), and variable capital utilization.
The role of news and noise shocks in a closed economy setting has been
studied by Barsky and Sims (2009), who incorporate both news shocks and noise
shocks in a new Keynesian economy model and show that news shocks are
deflationary and have a long lasting effect on economic activity whereas noise shocks
are inflationary and have a transitory effect on economic activity. In their model,
agents receive noisy signals about the future level of productivity. They interpret a
pure noise innovation as an animal spirits shock, as it is associated with erroneous
99
consumer optimism or pessimism. This paper closely follows their modeling strategy
and extends it to a small open economy setting. It should be noted that the response of
the domestic variables to the domestic news and animal spirits shocks in the small
open economy of this paper is qualitatively similar to the ones found in Barsky and
Sims' (2009) closed economy model. That the shocks continue to be expansionary in a
mall poen economy setting is to be expected as both news and animal spirits shocks
cause real exchange rate depreciation in my model, hence generating an additional
channel through which output can increase following these shocks.
Two recent papers, Blanchard, Huillier and Lorenzoni (2009) and Lorezoni
(2008), have focused on noise shocks related to signals about current productivity
rather than future productivity and showed that noise shocks are a potentially
important driver of business cycles. My paper differs from theirs in that its modeling
strategy follows the one used by Barsky and Sims (2009) which follows the modeling
assumptions of the news shocks literature and offers a more natural setting for the
analysis of both news and noise shocks2.
The role of news shocks in an open economy setting has also been studied
recently. Beaudry, Dupaigne and Portier (2008), henceforth BDP, demonstrate that
the data supports the existence of news-driven international business cycles.
Furthermore, BDP propose a quantitative assessment of the international propagation
of news shock in a two-country extension of Beaudry and Portier (2004) closed
economy model in which they show that the model responses to a local technological
news shocks display an aggregate boom at home, and that this boom is also
transmitted to the foreign country. BDP also show that a more standard quantitative
international real business cycle (IRBC) model such as Backus, Kehoe, and Kydland
(1994) fails reproducing the latter conditional response to technological news shocks.
Moreover, Jaimovich and Rebelo (2008) propose a small open-economy model that
generates business cycles with respect to news about future domestic TFP and
2 As discussed above, the news literature has defined news shocks with respect to the level of future
productivity. Therefore, I choose to follow this modeling assumption as it allows me to model news
shocks, as defined in the news literature, in addition to noise shocks.
100
investment-specific technical change. The key elements of their model are a weak
short run wealth effect on the labor supply and adjustment costs to labor and
investment. Nevertheless, their paper focuses on the effect of domestic news shocks
and not international news shocks.
In sections 2 and 3, I develop a small open economy New Keynesian general
equilibrium model, a la Gali and Monacelli (2005), with six structural disturbances;
three domestic shocks and three foreign shocks3. The four fundamental shocks are
domestic and foreign technology shocks and news shocks. The technology shock is an
immediate and permanent innovation to the level of technology, while the news shock
is a permanent but not immediate innovation to the level of technology as it portends
a future change in technology orthogonal to the present. Following Barsky and Sims
(2009), I only allow domestic and foreign households to observe a noise-ridden signal
of domestic and foreign news, respectively, and interpret a pure noise innovation as
an animal spirits shock, as it is associated with erroneous consumer optimism or
pessimism. Hence, the two latter domestic and foreign animal spirits shocks together
with the four fundamental shocks comprise the structural shocks of the model. In
section 4, I discuss the implications of each of the six structural shocks of the model
for the domestic endogenous variables of the model. Moreover, I show in sub section
4.4 that the qualitative nature of the results is quite robust to deviations from the
benchmark values of the calibrated parameters.
The remainder of the paper is organized as follows. In the next section I lay
out the details of my model. Section 3 derives the equilibrium in log-linearized form.
Section 4 presents the main results of the paper and provides a sensitivity analysis of
the results. The final section concludes.
3 The foreign economy is modeled as a closed New Keynesian economy model which is exogenous to
the domestic economy.
101
2. A Small Open Economy Model
2.1 Households
A representative agent in the model chooses sequences of consumption and leisure to
maximize
1 1
0
0 1 1
t t t
t
C NE
σ η
βσ η
− +∞
=
− − +
∑ (1)
where tN denotes hours of labor and tC is a composite consumption index defined by
1 1 1 1 1
tC (1 ) ( ) ( )
aa a a
h fa a a at tC Cλ λ
− − − ≡ − +
(2)
where h
tC is an index of consumption of domestic goods and f
tC is an index of
consumption of foreign goods given by the CES functions:
1 11 11 1
0 0
( ) ( )h h f f
t t t tC C j dj and C C j dj
χ χχ χχ χχ χ− −− −
= = ∫ ∫ (3)
where [0,1]j∈ denotes the good variety (See Gali and Monacelli (2005)).4
Parameter [0,1]λ∈ in (2) measures the degree of openness of the economy as it
represents the steady state share of foreign goods consumption out of total
consumption, parameter 0a ≥ in (2) measures the substitutability between domestic
and foreign goods, from the viewpoint of domestic consumers, and parameter 0χ > in
(3) denotes the elasticity of substitution between varieties of goods within domestic
and foreign goods.5
The demand function for each domestic and foreign good j can be derived by
minimizing the cost of purchasing a given amount of h
tC and f
tC , respectively:
( ) ( )
( ) ( )h f
h h f ft tt t t th f
t t
P j P jC j C and C j C
P P
χ χ− −
= =
(4)
4 Domestic firms produce a continuum of differentiated goods, represented by the unit interval. 5 The elasticity of substitution between varieties of goods is assumed to be the same within domestic
and imported goods.
102
Where the aggregate price indexes are defined as
1 11 11 1
1 1
0 0
( ) ( )h h f f
t t t tP P j dj and P P j djχ χ
χ χ− −
− − ≡ ≡ ∫ ∫ (5)
The maximization of (1) is subject to a sequence of budget constraints of the form
, 1 1 h h f f
t t t t t t t t t t tP C P C E Q D D W N+ ++ + ≤ + (6)
for t = 0, 1, 2, . . ., where h
tP and f
tP are the price indexes of domestic consumption
goods and imported foreign consumption goods, respectively (expressed in domestic
currency, i.e. the currency of the importing country whose economy is being
modeled). 1tD + is the nominal pay-off in period t +1 of the portfolio held at the end of
period t, tW is the nominal wage, and , 1t tQ + is the stochastic discount factor for one-
period ahead nominal pay-offs relevant to the domestic household. I assume that
households have access to a complete set of contingent claims, traded internationally.
Prior to solving (1) subject to (6), the household optimally allocates any given
expenditure on a consumption basket between domestic and foreign goods. In
particular, the household chooses h
tC and f
tC so as to minimize h h f f
t t t tP C P C+ subject
to (2), yielding the following relative demand function:
1
ah h
t t
f f
t t
C P
C P
λλ
− − =
(7)
I now define an overall consumer price index (CPI), tP , as
1
1 1 1(1 )( ) ( )h a f a at t tP P Pλ λ− − − ≡ − + (8)
Accordingly, total consumption expenditures by domestic households are given by
h h f f
t t t t t tP C P C PC+ = . Thus, the period budget constraint can be rewritten as
, 1 1 t t t t t t t t tP C E Q D D W N+ ++ ≤ + (9)
Now, I turn to solving (1) subject to the constraint (6), yielding the following two first
order conditions:
tt t
t
WC N
P
σ η = (10)
103
1, 1
1
t tt t
tt
C PQ
PC
σβ
σ+
++
− = −
(11)
where (10) is a standard intratemporal optimality condition and (11) is an
intertemporal Euler condition applied for a certain state of nature in period t+1
conditional on a given state of nature in period t. Taking conditional expectations on
both sides of (11) and rearranging terms a conventional stochastic Euler equation is
obtained:
1
1
1t tt t
tt
C PR E
PC
σβ
σ+
+
− = − (12)
Where , 11 / t t t tR E Q += is the gross return on a riskless one-period discount bond
paying off one unit of domestic currency in t + 1 (with , 1 t t tE Q + being its price). For
future reference it is useful to note that (10) and (12) can be respectively written in
loglinearized form around a zero steady state inflation rate as:
t t t tw p c nσ η− = + (13)
1 1
1 ( )t t t t t tc E c i E π
σ+ += − − (14)
where lower case letters denote the deviation in percentage terms of the respective
variables from their steady states.
2.1.1. The real exchange rate and the terms of trade.
Before proceeding with my analysis of the equilibrium I introduce several
assumptions and definitions that enable a derivation of a relation between the real
exchange rate and the terms of trade. First, I assume that the law of one price holds.
This implies that
f
t t tP P∗= Χ (15)
where tP∗ is the foreign currency price of foreign produced goods and tΧ is the
nominal exchange rate (price of foreign currency in terms of domestic currency). For
simplicity, I assume that all foreign goods sell for the price f
tP . This specification
104
assumes complete exchange rate pass-through. It will be useful to define the terms of
trade, the price of foreign goods in terms of domestic goods as
f
tt h
t
PS
P≡ (16)
Log-linearization of the CPI formula (8) around a symmetric steady state along with
employing the definition of the terms of trade yields:
(1 ) h f h
t t t t tp p p p sλ λ λ= − + = + (17)
where, once more, lowercase letters denote percentage deviation around the steady
state of the corresponding uppercase letter.
Next, a relationship between the terms of trade and the real exchange rate is derived.
First, the real exchange rate is defined as
t tt
t
PV
P
∗Χ= (18)
It then follows that
(1 )f
t t t t t t tv x p p p p sλ∗= + − = − = − (19)
where both (13) and (14) were utilized in the above derivation.
2.1.2. The Foreign Economy and International risk sharing.
To keep the analysis simple, it is assumed that the foreign country is large relative to
the home country. This is taken to mean that it is unnecessary to distinguish between
consumer price inflation and domestic inflation in the foreign country, and that
domestic output and consumption are equal (See Walsh, 2003).6 Goods produced in
the home country are sold to domestic residents and to foreigners. Let *h
tC be the
foreign country’s consumption of the domestically produced good. Similar to
domestic households, foreign households optimally allocate any given expenditure on
a consumption basket between domestic and foreign goods yielding the following
relative demand function of foreign households:
6 The home economy is assumed to be small relative to the foreign economy, which can be thought of
as the rest of the world economy. Namely, the home economy goods' share in the foreign economy's
consumption is negligible, thereby allowing me to assume that foreign consumption is equal to foreign
output.
105
1 h
t t
fhtt
Y P
PC
γλ
λ
−∗
∗
− =
(20)
where tY∗ represents foreign output and 0γ ≥ measures the substitutability between
domestic and foreign goods, from the viewpoint of foreign consumers. For simplicity,
it is assumed that foreign households derive utility only from consumption as the
amount of hours worked in the foreign economy is assumed to be constant, implying
that all fluctuations in foreign output are caused by technological changes.7
Under the assumption of complete securities markets, a first order condition
analogous to (11) must also hold for the representative household in the foreign
economy:
1, 1
1 1
t t tt t
t tt
PCQ
PC
σβ
σ
∗∗+
+∗∗+ +
− Χ =
− Χ (21)
Combining (11) and (21), together with the real exchange rate definition and the
equality between foreign consumption and foreign output, it follows that
1
t t tC Y V σϑ ∗= (22)
for all t, and whereϑ is a constant which will generally depend on initial conditions
regarding relative net asset positions (See Gali and Monacelli, 2005). Henceforth, and
without loss of generality, symmetric initial conditions are assumed (i.e. zero net
foreign asset holdings), in which case 1ϑ = . Log linearization of (22) around the
steady state, together with (16), generates the following equation linking domestic
consumption, foreign output and the terms of trade:8
1
t t tc y sλ
σ∗ − = +
(23)
2.1.3. Uncovered interest parity
Taking conditional expectations on both sides of (21) and rearranging terms a
standard intertemporal Euler condition for the foreign economy is obtained:
7 The specific modeling of foreign technology and the corresponding information structure will be
discussed in detail in section 2.2.1. 8 A similar relationship holds in many international RBC models. See, e.g. Backus and Smith (1993).
106
1
1
1t tt
t
tt
Y PR E
PY
σβ
σ
∗ ∗
∗ +∗∗+
− = −
(24)
Where 1, 11 / t
t t tt
t
R E Q∗ ++
Χ=
Χ . The previous equation can be combined (12) to
obtain a version of the uncovered interest parity condition:
1, 1
, 1
tt t t
tt
t t tt
E QR
R E Q
++
∗+
Χ
Χ = (25)
Log-linearizing around the steady state, yields the familiar expression
1t t t ti i E x∗+= + ∆ (26)
It is important to point out that condition (26) is not an additional independent
equilibrium condition that will determine the dynamics of the exchange rate in the
solution of the model (See Gali and Monacelli (2005)). In particular, in the solution of
the model the dynamics of the exchange rate are already determined by the other
equations of the model involving the exchange rate. Specifically, condition (26) can
be obtained by combining Euler condition (14) and the risk sharing condition (23).
Therefore, the fact that (26) holds only provides the dynamics of exchange rate
expectations.
2.2 Firms
2.2.1. Technology and News Shocks
There is a continuum of identical monopolistically-competitive firms which have the
following production function:9
( ) ( )t t tY j AN j= (27)
where ( )tY j is a differentiated good, tA is total productivity and ln( )t tz A= follows the
unit root process
t 1 t-1z zt tg ε+−= + (28)
9 As is common in the literature dealing with open economy new Keynesian models, I abstract from the
inclusion of capital in the model. Nevertheless, it is interesting and challenging for future research to
examine the ability of news and noise shocks to generate business cycle comovement when
endogenous capital accumulation is included.
107
Here tε is the contemporaneous technology shock and 1tg − is a stochastic drift term
which obeys the stationary AR(1) process 1t g t tg g eρ −= + , Where te is an i.i.d news
shock which is imperfectly observed by agents in period t, as will be further explained
below in sub-section 2.2.2 . I call te a news shock because it portends of future
changes in Technology. It is simply a smooth version of the news shocks studied by
Beaudry and Portier (2004) and Jaimovich and Rebelo (2009)10
.
Assuming a symmetric equilibrium for all j firms, log linearization of the aggregate
version of (27) around the steady state yields
t t ty z n= + (29)
An analogous equation to (29) for the foreign economy is
t t ty z n∗ ∗ ∗= + (30)
Where tz∗ represents foreign technology shocks, which follow the unit root process
1 t-1t
z zt tg ε∗ ∗ ∗ ∗+−= + (31)
Here, tε∗ is the contemporaneous i.i.d technology shock and 1tg
∗− is a stochastic drift
term which obeys the stationary AR(1) process * 1t g t tg p g e∗ ∗ ∗−= + , where te
∗ is an i.i.d
foreign news shock. Moreover, I follow the literature on IRBC (International Real
Business cycles) models and assume that technology shocks of the two economies are
contemporaneously correlated (See for example Backus et al. (1992), Baxter and Farr
(2005) and Wen (2006))11
. In our framework, assuming that technology shocks are
correlated naturally leads to the postulation that domestic and foreign news shocks are
also correlated as news shocks are simply anticipated future technology shocks. As I
discuss in sub-section 4.1, the correlation coefficients between domestic and foreign
technology and news shocks are set to 0.258.12
10
For simplicity, I assume here that the news shock occurs one period in advance. In general, it can
occur j periods in advance. Nevertheless, the assumption that the effect of the news shock on the drift
term is persistent implies that news arriving in the economy in the current period don't solely anticipate
a change in next period's technology, but also portend a gradual change in further future periods'
technology. 11 This assumption is based on empirical studies such as Backus et al. (1992), Reynolds (1993), and
Baxter and Crucini (1995) which estimated the correlation to be 0.258. 12
The assumption about the correlation between domestic and foreign technology and news shocks,
which aims to reflect technological spillover between the two economies, is not necessary for
generating expansionary foreign news and noise shocks in the model. In particular, for reasonable
108
I should note here that due to the assumed nominal rigidities in the model,
there is an avenue here for output to expand upon the arrival of good news about the
future and therefore the model is not subject to the “bust” feature of neoclassical
models in which output declines after agents receive advance signals about future
technology.
2.2.2. Perceptions and Animal Spirits
While households observe the level of technology tz at each point in time, it is
assumed that they never explicitly observe shocks to technology tε and observe only
a noisy signal of the true news shock te . The signal they receive is equal to:
t t tv e u= + (32)
where tu constitutes and i.i.d noise shock in signal tv and is uncorrelated with both
the technology shock tε and news shock te . Following Barsky and Sims (2009), I will
interpret the noise innovation tu as an animal spirits shock. A positive tu means that
households erroneously believe that the future will be better. Given this belief, they
will desire to consume more immediately. Because firms do not share this belief,
there is no shock on the supply side of the model. In this way, this animal spirits
shock is a pure demand shock.
The set up described above is essentially a signal extraction problem in which
households imperfectly observe the stochastic drift term tg and need to estimate it. It
is posited that they update their perceptions according to a simple linear filter (See
Barsky and Sims (2009)):
1 1 1 1 2(1 ) ( )p p
t g t g t t tg g z z vρ ρ− −= −Ω + Ω − +Ω (33)
gρ is the autoregressive parameter of the drift term process, and the coefficients 1Ω
and 2Ω are functions of the variances of the shocks in the economy. In particular,
2 2
1 22 2 2 2
u e
u e u
andε
σ σσ σ σ σ
Ω = Ω =+ +
(34)
calibrations, both news and noise shocks are capable of generating economic fluctuations domestically
in the absence of the latter correlation, whereby foreign news behave essentially as pure demand
shocks as they no longer affect domestic productivity in the absence of technological spillover.
Nevertheless, I assume positive correlation in the benchmark model as to allow for technological
spillover.
109
It is useful to consider a couple of extreme cases as well as intermediate cases
so as to better understand the assumed linear filter. If 2 0uσ = (i.e. there is no noise in
the signal pertaining to the true news shock) then 2 1Ω = , 1 0Ω = , and the perceived
drift term is equal to the truth at all times. If 2 0εσ = (i.e. there are no shocks to the
current level of technology), then 1 1Ω = . Namely, agents will be uncertain about the
current level of the true news shock due to the noise in the signal, but the realization
of next period's technology will reveal perfectly to them today’s actual news shock,
hence rendering no endogenous persistence of a false signal for more than one period.
With respect to intermediate cases, as the variance of the noise term in the signal
grows, 2Ω becomes smaller and 1Ω gets bigger – people will place little weight on a
very noisy signal but will place a lot of weight on the realization of actual technology
growth relative to their previous period’s perception in updating their current belief.
As 2
εσ gets bigger, 1Ω becomes smaller, implying that household perceptions about
the technology drift term will be more persistent. Intuitively, a very high variance of
technology shocks means that a realization of technology growth different from what
was expected is less likely to mean that the original perception of the drift term was
wrong, and more likely that there was simply an offsetting technology shock.
An analogous analysis to the one depicted above applies also to foreign
households. In particular, I assume that foreign households also observe level of
technology tz∗ at each point in time but that they never explicitly observe shocks to
technology t
ε ∗ and observe only a noisy signal of the drift term tg∗ . The signal they
receive is equal to:
t t tv e u∗ ∗ ∗= + (35)
where tu∗ constitutes i.i.d noise shock in signal tv
∗ and is uncorrelated with both the
technology shock tε∗and drift term tg
∗ as well as domestic news and noise shocks. I
will interpret the noise innovation tu∗ as a foreign animal spirits shock along the lines
of the analysis above for domestic households. A positive tu∗ means that foreign
households erroneously believe that the future will be better. Given this belief, they
will desire to consume more immediately inducing a foreign demand shock.
110
Moreover, the assumption that domestic and foreign news shocks are correlated
implies that domestic and foreign signals are correlated. Therefore, foreign noise
which affects the foreign signal will also have an effect on the domestic signal and
thus domestic perceptions13
.
Lastly, foreign households face an analogous signal extraction problem to the
one faced by domestic households. It is assumed that their perceptions of the drift
term tg∗behave precisely as the perceptions of domestic households with respect to tg :
1 11 1 2
(1 ) ( )p p
t t t t tg gg g z z vρ ρ∗ ∗∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗
− −= −Ω + Ω − +Ω (36)
where all coefficients are defined analogously to the analysis of the domestic case.
2.2.3. Price–Setting
Following Calvo (1983) I assume that each individual firm j resets its price with
probability 1 θ− each period, independently of the time elapsed since its last price
adjustment. Thus, each period a measure 1 θ− of (randomly selected) firms reset
their prices, while a fraction θ keep their prices unchanged. Let ( )h
tP j denote the
price set by a firm adjusting its price in period t. Under the Calvo price-setting
structure, ( ) ( )hhtt kP j P j+ = with probability kθ for k = 0, 1, 2…. . Since all firms
resetting prices in any given period will choose the same price, I henceforth drop the j
subscript.
When setting a new price in period t firm j seeks to maximize the current
value of its dividend stream, conditional on that price being effective:
,
0
( )max ( )
h
th
h t t t k t t khPt kt
P jkE Q C j MCP
θ∞
+ +=
− ∑
(37)
subject to the sequence of demand constraints given by (4), where / h
t t t tMC W AP=
is the firm's real marginal cost. Using the demand curve for domestic good j in (4) to
eliminate ( )h
tC j , this objective function can be written as
13
This mechanism is not significantly important for the results of the model as foreign animal spirits are
still expansionary also in its absence.
111
1
,0
( ) ( )max
h h
t th
h t t t k t k t kh hPt kt k t k
P j P jkE Q C MCP P
χ χ
θ
− −∞
+ + += + +
− ∑
(38)
While individual firms produce differentiated products, they all have the same
production technology and face demand curves with constant and equal demand
elasticities. In other words, they are essentially identical, except that they may have
set their current price at different dates in the past. However, all firms adjusting in
period t face the same problem, so all adjusting firms will set the same price.
Therefore, the j subscript is henceforth dropped. The first order condition for the
optimal choice of h
tP is:
,0
1(1 )
h h
t th
t t t k t k t kh h hk
t k t kt
P PkE Q C MCP PP
χ
θ θ θ
−∞
+ + += + +
− + ∑
(39)
Using the fact that ,
k t k tt t k
t t k
C PQ
C P
σ
β−
++
+
=
, I can rewrite the previous condition as
( )
( )
1
0
11
0
1
hk k h t k
t t k t k hhk
tt
hh
t k k h t kt t k t k h
kt
PE C MC
PP
P PE C MC
P
χσ
χσ
θ βχ
χθ β
∞ −+
+ +=
−∞ −
++ +
=
∑
= − ∑
(40)
Equation (40) shows how adjusting firms set their price, conditional on the current
aggregate price level of domestically produced goods h
tP . This aggregate price index
is an average of the price charged by the fraction 1 θ− of firms setting their price in
period t and the average of the remaining fraction θ of all firms setting their price in
earlier periods. However, because the adjusting firms were selected randomly from
among all firms, the average price of the nonadjusters is just the average price of all
firms that prevailed in period 1t − . Thus, from (39), the average price in period t
satisfies
( ) ( ) ( )11 1
1(1 )hh htt tP P P
χχ χθ θ
−− −
−= − + (41)
112
Equations (40) and (41) can be loglinearized around a zero inflation steady-state to
obtain an expression for aggregate domestic inflation (see Walsh (2003)) of the form
1h h
t t t tE mcπ β π ω+= + (42)
Where (1 )(1 ) /ω θ βθ θ= − − is an increasing function of the fraction of firms able to
adjust each period and tmc is real marginal cost, expressed as a percentage deviation
around its steady-state value. Equation (42) is often referred to as the new Keynesian
Phillips curve and it implies that current inflation depends on expected inflation and
current real marginal cost.14
3. Equillibrium
In the first subsection, I derive an equation describing the demand side of the
economy. In the second subsection, I derive an equation describing the supply side of
the economy.
3.1. The Demand Side: Aggregate demand and output
determination
Goods market clearing in the small open economy requires that total domestically
produced output equals its consumption by domestic households and foreign
households:15
h h
t t tY C C∗
= + (43)
Notice that consumption of domestic output by foreign consumers, h
tC∗
, is simply the
amount of exports of the domestic economy. In the steady state, assuming a
symmetric equilibrium where ss ssh f
t tP P= , it can be deduced from (7) and (2) that the
steady state shares of domestic produced goods and imported goods out of total
consumption are respectively 1 λ− and λ . Furthermore, since that in the steady state
the trade balance must equal zero thereby implying that total consumption equals total
output, log linearization of (43) around the steady state yields the following:
(1 ) h h
t t ty c cλ λ∗
= − + (44)
14 Equation (41) can be solved forward to show that current inflation depends upon present discounted
value of current and future real marginal costs (See Walsh (2003)). 15
I assume here that the goods are not durable and cannot be stored.
113
Next, by log linearizing around the steady state equations (2) and (7), respectively, I
obtain
(1 ) h f
t t tc c cλ λ= − + (45)
f h
t t tc c as= − (46)
where ts denotes the percentage deviation around the steady state of the terms of
trade. Combining (45) and (46), I attain
h
t t tc c asλ= − (47)
Moreover, log linearization around the steady state of equation (20) gives
h
t t tc y sγ∗ ∗= + (48)
Now, using equations (23), (44), (47) and (48) I can obtain
t t ty c sλκσ
= + (49)
where (1 )( 1)aκ σγ λ σ≡ + − − . Notice that 1aσ γ= = = implies 1κ = .
Combining (49) with (23) gives
1
t t t
a
y y sσ
∗= + (50)
Where / (1 )aσ σ λ λκ= − + . Lastly, combining (17), (49) and (50) with Euler
equation (14) a final equation describing the demand side of the economy is obtained:
1 11
1 ( ) ( 1)( )h
t t t t t t t tt
a
y E y i E E y yπ λ κσ
∗ ∗+ ++
= − − + − − (51)
3.2. The Trade Balance
Let 1 t
t t th
t
Pnx Y C
PY
= −
denote net exports in terms of domestic output, expressed as
a fraction of steady state outputY . Moreover, a first order approximation of the above
relation yields t t t tnx y c sλ= − − which combined with (49) implies
( 1)t tnx sκ
λσ
= − (52)
Notice that in the special case 1a γ σ= = = we have 0tnx = for all t . For my
baseline parameter calibrated values, there's a positive relationship between the terms
of trade and net exports. Thus, any shock that improves the terms of trade will raise
114
net exports. For example, domestic technology shocks which decrease domestic
inflation and therefore improve the terms of trade will cause an increase in net
exports.
3.3. The supply side: marginal cost and inflation dynamics
In the small open economy, the dynamics of domestic goods' inflation in terms of real
marginal cost are described by equation (42). The determination of the real marginal
cost as a function of domestic output in the small open economy differs somewhat
from that in the closed economy, due to the existence of a wedge between output and
consumption, and between domestic and consumer prices. Thus, we have
( ) ( )
(1 )
h
t t t t
h
t t t t t
t t t t
t t tt
mc w p z
w p p p z
c n s z
y y s z
σ η λ
σ η η∗
= − − =
− + − − =
+ + − =
+ + − +
(53)
where the last equality makes use of (13), (23) and (29). Thus, we see that marginal
cost is increasing in the terms of trade and world output. Both variables end up
influencing the real wage, through the wealth effect on labour supply resulting from
their impact on domestic consumption. In addition, changes in the terms of trade have
a direct effect on the product wage, for any given real wage. The influence of
technology (through its direct effect on labour productivity) and of domestic output
(through its effect on employment and, hence, the real wage—for given output) is
analogous to that observed in the closed economy.
Finally, using (50) to substitute for ts , I can rewrite the previous expression for
the real marginal cost in terms of domestic output and productivity, as well as world
output:
( ) ( ) (1 )t a t a t tmc y y zσ σ σ η η∗= − + + − + (54)
Notice that in the special cases 0λ = and/or 1aσ = = , which imply aσ σ= , the
domestic real marginal cost is completely insulated from movements in foreign
output.
115
3.4. Closing the Model: Domestic monetary policy rule and
Foreign Economy Equilibrium
Following the literature on new Keynesian models, I specify a domestic nominal
interest rate rule implemented by the central bank. Following a number of recent
papers (for example, Barsky and Sims (2008), Coibion and Gorodnichenko (2007),
Fernandez-Villaverde and Rubio-Ramirez (2007), and Ireland (2004)), it is postulated
that the central bank sets nominal interest rates according to a partial adjustment
mechanism where the interest rate in any period is equal to a convex combination of
the lagged interest rate and the central bank’s target rate, where the target rate is
adjusted in response to deviations of output growth and inflation from constant
targets:
1 (1 )( ( *) ( *))t t t y ti pi p y yπ π π−= + − Θ − + Θ ∆ − ∆ (55)
Note that policy rule (55) can coexist with the uncovered interest rate parity rule (26)
because of the endogeneity of the exchange rate. In particular, any shocks that affect
the domestic interest rate and generate domestic-foreign interest rate differentials also
affect the expectations regarding exchange rate future depreciation rate so that
condition (26) is satisfied. For instance, a shock that renders a positive differential
implies that agents expect the exchange rate to depreciate as the expected future
depreciation makes it worthwhile to hold foreign bonds that earn a lower interest rate
than domestic bonds.
As previously discussed in sub section 2.1.2, the foreign economy is treated as
a closed economy as it is essentially the rest of the world economy. I model the
foreign economy as the standard New Keynesian model (see Woodford (2003) or Gali
(2008) for complete derivation), implying the following two final equilibrium
equations:
1 1
1 ( t t t t t ty E y i E π
σ∗ ∗ ∗ ∗
+ += − − (56)
1t t t tE mcπ β π ω∗ ∗ ∗+= + (57)
116
where (1 )(1 ) /ω θ βθ θ= − − is an increasing function of the fraction of firms able to
adjust prices each period, measured by 1 θ− , and ( ) (1 )t t tmc y zσ η η∗ ∗ ∗= + − + is real
marginal cost, expressed as a percentage deviation around its steady-state value. For
simplicity, I assume that the foreign preference parameters are equal to the domestic
ones. Equation (55) is simply the Euler equation for a closed economy. Equation (57)
is often referred to as the new Keynesian Phillips curve and it implies that current
inflation depends on expected inflation and current real marginal cost. I close the
foreign economy model with a nominal interest rate rule identical to the domestic one
in (55).
4. Numerical Results
4.1. Calibration
In this section I present some quantitative results based on a calibrated version of my
model economy. Let me first state the main assumptions underlying my baseline
calibration, which is taken as a benchmark. Following Gali and Monacelli (2005), I
set σ=1, assume β=0.99 (with the interpretation of the unit of time as one quarter, this
implies a riskless annual return of about 4% in the steady state), set a=1 (substitution
elasticity between domestic and imported goods) and set parameter δ equal to 0.75, a
value consistent with an average period of one year between price adjustments.
Following Barsky and Sims (2009), I set the labor supply elasticity to equal 1,
assume a value of 0.85 for AR parameter of the stochastic drift term and set
0.75, 4.5, 2.5yp π= Θ = Θ = in the monetary policy rule. Moreover, the standard
deviations of technology shocks and news shocks are chosen so that each leads to an
ultimate increase in technology of one percent and the standard deviation of the noise
shock is chosen so that it is the same as the news shock (i.e. both shocks raise the
signal by an amount prognostic of an ultimate increase in the level of technology of
one percent).16
This implies a value of 0.5 for 2Ω and 0.022 for 1Ω .
16
Barsky and Sims (2009) also perform structural estimation of a closed economy new Keynesian
model augmented with a structural specification for consumer confidence and attain estimates of the
117
I set the correlation coefficient between domestic and foreign technology and
news shocks to 0.258, in line with standard calibration in the IRBC literature (See
Backus et al. (1992), Reynolds (1993), Baxter and Crucini (1995), Baxter and Farr
(2005) and Wen (2006)). Lastly, I set a baseline value for λ (or degree of openness) of
0.4. The latter corresponds roughly to the import/GDP ratio in a prototype small open
economy (See Gali and Monacelli (2005)).
4.2. Impulse Responses to the Structural Shocks
Figure 4.1 shows the responses of output, consumption, hours of work, technology,
CPI inflation, domestic inflation, nominal exchange rate, real exchange rate and
exports to domestic and foreign technology shocks17
. The sizes of the shocks are
chosen so that each leads to an ultimate increase in technology of one percent. For all
variables the figures show the percentage response relative to the initial non-
stochastic steady state, aside from the inflation variables for which the response
shown is percentage point deviation from the zero inflation steady state. By
construction, both shocks lead to an immediate jump in technology that is expected to
remain forever at the new higher level, where the foreign shock has a smaller effect in
accordance with the calibrated correlation coefficient of 0.258 between the two
shocks. As is common in new Keynesian models, the domestic technology shock
leads to a decline in hours of work whereas the effect of the foreign shock is
essentially inexistent. The effect of both shocks on output is nearly identical to their
effect on technology as the response of hours is moderate relative to the response of
technology.
noise and news standard deviation parameters that are very similar to the calibrated standard deviations
used in this paper. 17
Although it is not shown here, I should note that the response of the foreign endogenous variables to
the foreign structural shocks is consistent with the findings in Barsky and Sims (2009); technology and
information shocks are deflationary and associated with persistent movements in measures of real
activity, while the animal spirits shocks are inflationary and associated with transitory increases in
domestic spending.
118
Moreover, the domestic technology shock is deflationary in terms of both CPI
and domestic inflation while the foreign shock is deflationary in terms of CPI
inflation but inflationary in terms of domestic inflation. The reason for the latter result
lies in that the domestic technology shocks induces a supply side effect which is
stronger than the wealth driven demand side effect thus leading to domestic deflation,
whereas the foreign shocks induces a weaker supply side effect thus leading to
domestic inflation. CPI inflation is comprised of domestic inflation and imported
inflation which in turn depends on foreign inflation and the rate of change in the
foreign exchange rate. The foreign technology shock induces foreign deflation (not
shown in the figure) and currency appreciation that offset domestic inflation thereby
generating the resultant CPI deflation. While the domestic shock leads to currency
depreciation, the latter effect is weaker than the increase in domestic deflation which
dominates and generates overall CPI deflation as well. Lastly, it is apparent that the
foreign shock has a bigger effect on consumption than the foreign shock during the
first year following the shock and thereafter the domestic shock dominates. The
reason for this result can be explained by the risk sharing condition (23); foreign
technology shocks increase foreign consumption hence causing an increase in
domestic consumption as well. Nevertheless, the foreign shock also induces real
currency appreciation which eventually enables the effect of the domestic shock,
which causes real currency depreciation, to dominate at longer time horizons. The
latter behavior of the real exchange rate also explains the stronger effect of the
domestic shocks on exports.
Figure 4.2 shows the responses of output, consumption, hours of work,
technology, CPI inflation, domestic inflation, nominal exchange rate, real exchange
rate and exports to domestic and foreign news shocks. The sizes of the shocks are
chosen so that each leads to an ultimate increase in domestic and foreign technology
of one percent, respectively. In response to both shocks, output jumps on impact and
is expected to rise towards its new steady state value. Quite naturally, the effect of
domestic news is stronger given the imperfect correlation between domestic and
119
foreign technology shocks. Both shocks raise employment on impact but the behavior
of employment thereafter is different following the two shocks. After the impact
effect, employment remains above its steady state for several periods before
converging to it following the foreign shock whereas it becomes negative relative to
its steady state following the domestic shock. This consequence is simply a
manifestation of the effect of the realized anticipated technology shocks portended by
the domestic news shock.
Moreover, the domestic news shock is deflationary in terms of both CPI and
domestic inflation while the foreign shock is inflationary on impact and thereafter
deflationary in terms of CPI inflation but inflationary in terms of domestic inflation.
Domestic news portend future supply shocks which reduce real marginal cost hence
causing deflation today as inflation is equal to the present value of future real
marginal costs. Notice that even though that domestic news generate currency
depreciation this is not strong enough to offset the decline in domestic inflation. In
contrast, foreign news reflect more of a wealth driven demand side effect than a
supply side effect hence causing domestic inflation. Nevertheless, foreign news also
induce foreign deflation (not shown in the figure) which cause CPI deflation but only
after causing CPI inflation on impact as the effect of currency depreciation dominates
initially. Lastly, both news shocks have an almost identical effect on consumption
despite the positive effect of foreign news on foreign consumption. This is due to real
currency depreciation/appreciation caused by domestic/foreign news which offset the
latter effect and also explain the bigger effect of domestic news on exports.
Figure 4.3 shows the responses of output, consumption, hours of work,
technology, CPI inflation, domestic inflation, nominal exchange rate, real exchange
rate and exports to domestic and foreign animal spirits shocks. The sizes of the shocks
are chosen so that they are the same as the corresponding news shocks (i.e. both
shocks raise the signal by an amount prognostic of an ultimate increase in the level of
domestic and foreign technology of one percent, respectively). By construction, the
shocks never have any effect on the actual level of technology. Both animal spirits
120
shocks are differentiated from the news or technology shocks in that they are
associated with a transitory response of output. Furthermore, both shocks raise
employment and domestic inflation and resemble pure demand shocks. Nevertheless,
while domestic animal spirits raise CPI inflation as well foreign animal spirits induce
mild deflation on impact due to currency appreciation, after which CPI inflation turns
positive. The initial response of consumption is higher following foreign animal
spirits owing to the increase in foreign consumption but afterwards the effect of
domestic animal spirits is moderately higher due to the real currency
depreciation/appreciation domestic/foreign animal spirits induce which also explains
the bigger effect of domestic animal spirits on exports.
4.3. Variance Decomposition
Figure 4.4 illustrates the forecast error variance decomposition of output,
consumption, CPI inflation and the nominal exchange rate in terms of the six
structural shocks. It is apparent that unanticipated technology shocks play a bigger
role in economic fluctuations than anticipated shocks. At a horizon of 3 years, for
example, technology shocks account for 65% of output fluctuations compared to 26%
accounted for by domestic news. Foreign technology shocks matter mainly in the very
short run accounting for 32% and of output fluctuations on impact. With respect to
consumption, foreign technology shocks play an especially important role accounting
for 72% of consumption fluctuations on impact while foreign news shocks gain in
significance over longer time horizons explaining 20% of consumption fluctuations at
the 8 year time horizon. The observation that foreign shocks matter more for
consumption than output can be explained by the assumption of complete markets
yielding the risk sharing condition which strongly ties domestic consumption with
foreign consumption.
Fluctuations in CPI inflation are mostly explained by domestic technology and
news shocks accounting for 30% and 60% of inflation variation at the 3 year horizon,
respectively. The latter result is also obtained for the forecast error variance
decomposition of domestic inflation (not shown here). This outcome illustrates that
121
supply shocks are an important factor in the determination of inflation as the latter
equals the present value of future real marginal costs. Lastly, exchange rate
fluctuations are mainly explained by domestic and foreign animal spirits which
account for 30% and 23% on impact and maintain these weights at longer horizons as
well. This is an interesting result as it implies that animal spirits affect the foreign
exchange rate more that pure news or unanticipated technology shocks. Furthermore,
domestic news attain the biggest weight on impact accounting for 23% of exchange
rate contemporaneous variation, whereas at longer time horizons the influence of
domestic news steadily declines.
4.4. Robustness
The qualitative nature of the results is quite robust to deviations from the benchmark
values of the calibrated parameters. Nevertheless, some of the results are sensitive to
the choice of monetary policy rule. In the benchmark model I assume a nominal
interest rate rule in the form of equation (55). However, it is worthwhile to examine
how the results differ when more standard monetary policy rules are considered. In
particular, in the present section I analyze the macroeconomic implications of two
alternative monetary policy regimes for the small open economy. Two of the simple
rules considered are stylized Taylor-type rules examined in Gali and Monacceli
(2005). The first has the domestic interest rate respond systematically to domestic
inflation, whereas the second assumes that CPI inflation is the variable the domestic
central bank reacts to18
. The main result is that rule (55) is needed in order to generate
news shocks that are deflationary, an outcome which was also discussed in Barsky
and Sims (2008).
Formally, the domestic inflation-based Taylor rule (DITR, for short) is
specified as follows:
h
t ti ψπ= (58)
The CPI inflation-based Taylor rule (CITR, for short) is assumed to take the form
18
It is assumed that the foreign monetary authority also responds only to inflation under the two
regimes.
122
t ti ψπ= (59)
I follow the original Taylor estimate and set 1.5ψ = to reflect an aggressive monetary
policy rule which raises the interest rate by more than the increase in inflation so that
the real interest rate increases as well.
Figures 4.5 and 4.6 display the impulse responses of output, consumption,
hours of work, technology, CPI inflation, domestic inflation, nominal exchange rate,
real exchange rate and exports to domestic and foreign technology shocks of one
percent, respectively, under the benchmark monetary policy rule (55) and the CITR
and DITR as depicted in equations (58) and (59), respectively. It is apparent that
under CITR and DITR the negative effect of improved domestic technology on hours
is much weaker and in fact is even slightly positive under CITR. Therefore, the short
run increase in output is much higher under the latter regimes compared to the
benchmark case. Similarly, consumption and exports also exhibit bigger increases.
Likewise, foreign technology also generates a bigger increase in output and
consumption, especially under CITR where the effect on hours is significantly
positive.
An additional dissimilarity arises with respect to CPI inflation, domestic
inflation and the nominal and real exchange rates. Under CITR and DITR, domestic
technology shocks are inflationary rather than deflationary as in the benchmark model
while also generating much stronger nominal and real currency depreciation. On the
other hand, foreign technology shocks generate higher domestic inflation but are more
deflationary in terms of CPI inflation due to stronger currency appreciation.
Figures 4.7 and 4.8 display the impulse responses of output, consumption,
hours of work, technology, CPI inflation, domestic inflation, nominal exchange rate,
real exchange rate and exports to domestic and foreign news shocks, respectively,
under the benchmark monetary policy rule (55) and the CITR and DITR as depicted
in equations (58) and (59), respectively. The sizes of the shocks are chosen so that
each leads to an ultimate increase in domestic and foreign technology of one percent,
respectively. It is evident that domestic news is more expansionary in terms of output,
123
consumption and hours under the two alternative regimes. Moreover, domestic news
generate both domestic inflation and CPI inflation under CITR and DITR as opposed
to deflation in under the benchmark regime. The latter results can be explained by the
lack of response to output growth by the monetary authority under CITR and DITR
which allows for more expansionary monetary policy in response to favorable news
hence causing inflation and a bigger increase in output. Moreover, domestic news also
cause stronger real currency depreciation which supports a bigger increase in exports.
With respect to foreign news, it is evident that the impulse responses are very similar
under DITR and the benchmark regime. Nevertheless, foreign news are more
expansionary under CITR causing a bigger increase in output, consumption, hours
while also being more inflationary. This can be explained by the fact that foreign
news generate domestic inflation compared to CPI deflation under the benchmark
regime and DITR. This means that a monetary authority that responds to CPI inflation
as opposed to domestic inflation would be more expansionary in response to foreign
news shocks thereby leading to a bigger increase in economic activity.
Figures 4.9 and 4.10 display the impulse responses of output, consumption,
hours of work, technology, CPI inflation, domestic inflation, nominal exchange rate,
real exchange rate and exports to domestic and foreign animal spirits shocks,
respectively, under the benchmark monetary policy rule (55) and the CITR and DITR
as depicted in equations (58) and (59), respectively. The sizes of the shocks are
chosen so that they are the same as the corresponding news shocks (i.e. both shocks
raise the signal by an amount prognostic of an ultimate increase in the level of
domestic and foreign technology of one percent, respectively). Not surprisingly,
domestic animal spirits are more expansionary and inflationary under the two
alternative regimes as monetary policy is more expansionary in response to positive
animal spirits shocks since it does not react to output growth. Moreover, CITR and
DITR allow for a bigger currency depreciation which in turn generates a bigger
increase in exports. The impulse responses to foreign animal spirits are quite similar,
124
although it is apparent that foreign animal spirits cause stronger currency appreciation
under the two alternative regimes.
5. Conclusion
This paper studies the potential role of domestic and foreign news and animal spirits
shocks in the business cycle of a small open economy using a small open economy
new Keynesian model a la Gali and Monacelli (2005). I follow the approach of
Barsky and Sims (2009) and assume that domestic and foreign households observe a
noise-ridden signal of domestic and foreign news, respectively, and interpret a pure
noise innovation as an animal spirits shock, as it is associated with erroneous
consumer optimism or pessimism. Impulse response results indicate that foreign news
are expansionary and induce inflation on impact followed by deflation at longer time
horizons, while foreign news are expansionary and deflationary. Domestic animal
spirits are expansionary and inflationary playing the role of aggregate demand shocks
whereas foreign animal spirits are expansionary and lead to deflation on impact (due
to currency appreciation) and inflation afterwards.
In terms of the modeling framework, a potential avenue for future research
would be to introduce endogenous animal spirits whereby the optimism and
pessimism of agents partly depend on the variables of the model. For instance, it
seems reasonable to extend the model so that animal spirits depend on the business
cycle itself as expansionary (contractionary) periods could potentially lead to higher
optimism (pessimism). While this paper's results are theoretical, it seems important
and interesting to empirically investigate the role of foreign and domestic news and
animal spirits shocks in the business cycle of small and open economies. A challenge
that arises in such an empirical framework is being able to properly identify the
shocks and impulse responses. My ongoing research builds on the results of this paper
and further addresses the business cycle implications of news and noise shocks.
125
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Figure 4.1
Impulse Responses to Technology Shocks
Dashed and Solid lines represent responses to foreign and domestic technology shocks,
respectively. The figure shows the percentage response relative to the initial non-stochastic
steady state for all variables aside from CPI and domestic inflation for which the response
shown is the percentage point deviation from the steady state zero inflation.
0 5 10 15 200.2
0.4
0.6
0.8
1Output
0 5 10 15 200.2
0.3
0.4
0.5
0.6
0.7Consumption
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2Hours
0 5 10 15 200.2
0.4
0.6
0.8
1Technology
0 5 10 15 20-0.2
-0.15
-0.1
-0.05
0
0.05CPI Inflation
0 5 10 15 20-0.4
-0.3
-0.2
-0.1
0
0.1Domestic Inflation
0 5 10 15 20-0.1
-0.05
0
0.05
0.1Nominal Exchange Rate
0 5 10 15 20-1
-0.5
0
0.5
1Real Exchange Rate
0 5 10 15 200.2
0.4
0.6
0.8
1Exports
128
Figure 4.2
Impulse Responses to News Shocks
Dashed and Solid lines represent responses to foreign and domestic news shocks,
respectively. The figure shows the percentage response relative to the initial non-stochastic
steady state for all variables aside from CPI and domestic inflation for which the response
shown is the percentage point deviation from the steady state zero inflation.
0 5 10 15 200
0.2
0.4
0.6
0.8
1Output
0 5 10 15 200
0.2
0.4
0.6
0.8Consumption
0 5 10 15 20-0.06
-0.04
-0.02
0
0.02
0.04Hours
0 5 10 15 200
0.2
0.4
0.6
0.8
1Technology
0 5 10 15 20-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02CPI Inflation
0 5 10 15 20-0.15
-0.1
-0.05
0
0.05Domestic Inflation
0 5 10 15 20-0.08
-0.06
-0.04
-0.02
0
0.02
0.04Nominal Exchange Rate
0 5 10 15 20-1
-0.5
0
0.5
1Real Exchange Rate
0 5 10 15 200
0.2
0.4
0.6
0.8
1Exports
129
Figure 4.3
Impulse Responses to Animal Spirits Shocks
Dashed and Solid lines represent responses to foreign and domestic noise shocks,
respectively. The figure shows the percentage response relative to the initial non-stochastic
steady state for all variables aside from inflation for which the response shown is the
percentage point deviation from the steady state zero inflation.
0 5 10 15 20-0.01
0
0.01
0.02
0.03
0.04
0.05Output
0 5 10 15 200
0.01
0.02
0.03
0.04Consumption
0 5 10 15 20-0.01
0
0.01
0.02
0.03
0.04
0.05Hours
0 5 10 15 200
0.1
0.2
0.3
0.4Technology
0 5 10 15 20-0.01
0
0.01
0.02
0.03
0.04
0.05CPI Inflation
0 5 10 15 20-0.01
0
0.01
0.02
0.03Domestic Inflation
0 5 10 15 20-0.1
-0.05
0
0.05
0.1
0.15Nominal Exchange Rate
0 5 10 15 20-0.03
-0.02
-0.01
0
0.01
0.02
0.03Real Exchange Rate
0 5 10 15 20-0.01
0
0.01
0.02
0.03
0.04
0.05Exports
130
Figure 4.4
Forecast Error Variance Decomposition
The figure shows the shares of the forecast error variances of output, consumption, CPI
inflation, and nominal exchange rate attributable to the six structural shocks of the model.
5 10 15 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cast
Err
or
Output
Domestic News
Foreign News
Domestic Technology
Foreign Technology
Domestic Noise
Foreign Noise
5 10 15 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cast
Err
or
Consumption
Domestic News
Foreign News
Domestic Technology
Foreign Technology
Domestic Noise
Foreign Noise
5 10 15 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cast
Err
or
CPI Inflation
Domestic News
Foreign News
Domestic Technology
Foreign Technology
Domestic Noise
Foreign Noise
5 10 15 200
0.2
0.4
0.6
0.8
1
Time
Pro
po
rtio
n o
f F
ore
cast
Err
or
Nominal Exchange Rate
Domestic News
Foreign News
Domestic Technology
Foreign Technology
Domestic Noise
Foreign Noise
131
Figure 4.5
Impulse Responses to Domestic Technology Shocks under
Alternative Policy Rules
Solid, dashed and dotted lines represent impulse responses to domestic technology shocks
under monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 200.2
0.4
0.6
0.8
1
1.2Output
Benchmark
DITR
CITR
0 5 10 15 200
0.2
0.4
0.6
0.8Consumption
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2Hours
0 5 10 15 200
0.2
0.4
0.6
0.8
1
Technology
0 5 10 15 20-0.2
0
0.2
0.4
0.6CPI Inflation
0 5 10 15 20-0.3
-0.2
-0.1
0
0.1Domestic Inflation
0 5 10 15 200
0.5
1
1.5Nominal Exchange Rate
0 5 10 15 200
0.2
0.4
0.6
0.8Real Exchange Rate
0 5 10 15 200.2
0.4
0.6
0.8
1
1.2Exports
132
Figure 4.6
Impulse Responses to Foreign Technology Shocks under
Alternative Policy Rules
Solid, dashed and dotted lines represent impulse responses to foreign technology shocks
under monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 200.2
0.3
0.4
0.5
0.6
0.7Output
0 5 10 15 200.2
0.4
0.6
0.8
1Consumption
0 5 10 15 20-0.1
0
0.1
0.2
0.3
0.4Hours
0 5 10 15 200
0.2
0.4
0.6
0.8
1Technology
0 5 10 15 20-0.3
-0.2
-0.1
0
0.1CPI Inflation
0 5 10 15 20-0.05
0
0.05
0.1
0.15Domestic Inflation
0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0Nominal Exchange Rate
0 5 10 15 20-0.5
-0.4
-0.3
-0.2
-0.1Real Exchange Rate
0 5 10 15 200.2
0.3
0.4
0.5
0.6
0.7Exports
Benchmark
DITR
CITR
133
Figure 4.7
Impulse Responses to Domestic News Shocks under Alternative
Policy Rules
Solid, dashed and dotted lines represent impulse responses to domestic news shocks under
monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 200
0.2
0.4
0.6
0.8
1Output
Benchmark
DITR
CITR
0 5 10 15 200
0.2
0.4
0.6
0.8Consumption
0 5 10 15 20-0.1
-0.05
0
0.05
0.1Hours
0 5 10 15 200
0.2
0.4
0.6
0.8
1Technology
0 5 10 15 20-0.1
-0.05
0
0.05
0.1
0.15CPI Inflation
0 5 10 15 20-0.1
-0.05
0
0.05
0.1
0.15Domestic Inflation
0 5 10 15 20-0.5
0
0.5
1
1.5
2Nominal Exchange Rate
0 5 10 15 200
0.2
0.4
0.6
0.8Real Exchange Rate
0 5 10 15 200
0.2
0.4
0.6
0.8
1Exports
134
Figure 4.8
Impulse Responses to Foreign News Shocks under Alternative
Policy Rules
Solid, dashed and dotted lines represent impulse responses to foreign news shocks under
monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 200
0.1
0.2
0.3
0.4Output
0 5 10 15 200
0.2
0.4
0.6
0.8Consumption
0 5 10 15 200
0.02
0.04
0.06
0.08Hours
0 5 10 15 200
0.05
0.1
0.15
0.2
0.25Technology
0 5 10 15 20-0.05
0
0.05
0.1
0.15CPI Inflation
0 5 10 15 200
0.02
0.04
0.06
0.08
0.1
0.12Domestic Inflation
0 5 10 15 20-1.5
-1
-0.5
0
0.5Nominal Exchange Rate
0 5 10 15 20-0.5
-0.4
-0.3
-0.2
-0.1
0Real Exchange Rate
0 5 10 15 200
0.1
0.2
0.3
0.4Exports
Benchmark
DITR
CITR
135
Figure 4.9
Impulse Responses to Domestic Animal Spirits under
Alternative Policy Rules
Solid, dashed and dotted lines represent impulse responses to domestic noise shocks under
monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 200
0.02
0.04
0.06
0.08
0.1Output
0 5 10 15 200
0.01
0.02
0.03
0.04
0.05
0.06Consumption
0 5 10 15 200
0.02
0.04
0.06
0.08
0.1Hours
0 5 10 15 20-0.1
-0.05
0
0.05
0.1Technology
0 5 10 15 200
0.05
0.1
0.15
0.2CPI Inflation
0 5 10 15 200
0.02
0.04
0.06
0.08
0.1Domestic Inflation
0 5 10 15 200
0.2
0.4
0.6
0.8Nominal Exchange Rate
0 5 10 15 200
0.01
0.02
0.03
0.04
0.05
0.06Real Exchange Rate
0 5 10 15 200
0.02
0.04
0.06
0.08
0.1Exports
Benchmark
DITR
CITR
136
Figure 4.10
Impulse Responses to Foreign Animal Spirits under Alternative
Policy Rules
Solid, dashed and dotted lines represent impulse responses to foreign noise shocks under
monetary policy rules (55), (58) and (59) respectively. The figure shows the percentage
response relative to the initial non-stochastic steady state for all variables aside from inflation
for which the response shown is the percentage point deviation from the steady state zero
inflation.
0 5 10 15 20-0.02
0
0.02
0.04
0.06Output
0 5 10 15 200
0.02
0.04
0.06
0.08Consumption
0 5 10 15 20-0.02
0
0.02
0.04
0.06Hours
0 5 10 15 20-0.1
-0.05
0
0.05
0.1Technology
0 5 10 15 20-0.03
-0.02
-0.01
0
0.01
0.02CPI Inflation
0 5 10 15 20-5
0
5
10
15x 10
-3Domestic Inflation
0 5 10 15 20-0.5
-0.4
-0.3
-0.2
-0.1
0Nominal Exchange Rate
0 5 10 15 20-0.05
-0.04
-0.03
-0.02
-0.01
0Real Exchange Rate
0 5 10 15 20-0.02
0
0.02
0.04
0.06Exports
Benchmark
DITR
CITR
137
Chapter V
Conclusion
The literature that has studied business cycles and their driving forces is a vast one.
This dissertation belongs to this literature in that it has taken a close look at potential
business cycle driving shocks. While chapter II and III provide empirical evidence
that IST news shocks and credit supply shocks have the potential of generating
business cycles, chapter IV offers a theoretical open economy framework in which the
effects of news shocks and noise shocks can be studied. All three chapters deal with
potential sources of the business cycles in which a great deal of interest has been
shown recently by the business cycle literature.
The results found in chapter II are the strongest in the sense that they put
forward a shock that generates business cycles in a dominant manner. From an
empirical standpoint, I think it would be worthwhile for future research to focus on
extending the study of these shocks to other economies, both large and small. On the
theoretical front, it would be interesting for future research to continue to explore
additional frameworks in which these shocks are business cycle drivers. The findings
in chapter III are important in that they are able to provide evidence of a demand
shock that is capable of generating business cycles and in fact has done so in terms of
contributing to six of the last nine U.S recessions, being the most dominant in the
recent recession. Combining the findings of chapters II and III, we have two shocks
that drive the business cycle and account well for post war business cycles.
Chapter IV is related to the news and noise shocks literature and thus is
naturally linked to chapter II which also belongs to the news shocks literature. It
seems interesting for future research to try to empirically gauge the role of noise
shocks in a framework of the kind that was used in chapter IV. In particular, it seems
especially challenging to do so without imposing any structure on the data but rather
using a model free approach such as the one employed in chapters II and III. This is
mainly difficult because there aren't enough identifying restrictions from the
theoretical model that an econometrician can rely upon in order to identify these
shocks.
