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Responding to the Monetary Superpower
Investigating the Behavioral Spillovers of U.S. Monetary Policy
Colin Gray
Under the Supervision of Dr. John Taylor
Stanford University, Department of Economics
Gray 2 Abstract
Between 2002 and 2006, the United States Federal Reserve set interest rates significantly
below the rates suggested by well-known monetary policy rules. There is a growing body
of research suggesting that this helped fuel an excess of liquidity in the U.S. that
contributed to the 2008 worldwide financial crash. What is less well known is that a
number of other central banks also lowered interest rates during this period. An important
question, then, is what role the Federal Reserve played in influencing other central banks
to alter their own monetary policies, which could have magnified the Fed’s actions in
creating global liquidity. This paper addresses the issue by showing how spillovers in
central bank behavior occur in theoretical rational expectations models. It then establishes
empirically how U.S. monetary policy actions affect the actions of other major central
banks, particularly in terms of interest rates and currency interventions. The data suggest
that the U.S. lowering its policy rate, in general or in reference to a specific monetary
policy rule, influences other central banks to lower their own policy rates and intervene in
currency markets, even when controlling for worldwide macroeconomic trends. Finally,
this paper shows that spillovers from U.S. actions are partially responsible for the
worldwide lowering of interest rates and the increase in currency reserves in the early
2000’s that may have contributed to the subsequent worldwide liquidity boom.1
1 The author would like to thank Professors John Taylor, Manuel Amador, Geoffrey Rothwell, Pete Klenow, and Ronald McKinnon of the Stanford Economics Department, as well as Mitchel Scott, for helpful guidance and feedback. Gray 3 Table of Contents
I.
II.
III.
IV.
Introduction
A.
Motivation
B.
Existing Literature
Theoretical Model
A.
Model Description
B.
Model Calibration
C.
Solution Algorithm
D.
Results: Symmetric Version
E.
Results: Asymmetric Version
Empirical Evidence from Pooled Regression
A.
Data
B.
Policy Rates
C.
Robustness Checks: Policy Rates
D.
Currency Reserves
Empirical Evidence: Case Study of the Eurozone
A.
Alternative Explanations for ECB Behavior
B.
Testing the Hypothesis
V.
Policy Implications
VI.
References
VII.
Appendix
A.
Model Details
B.
Data Details
C.
Case Study Model Fit to Countries Outside the Eurozone
Gray 4 I.
Introduction
Motivation
Beginning in the early 2000’s, the United States Federal Reserve (Fed) deviated
significantly from a popular monetary policy rule known as the Taylor rule2. The chart
below shows the U.S. federal funds rate alongside the rate suggested by the Taylor rule3.
Figure 1A
Over the same period, many other central banks also lowered their policy rates below the
Taylor rule. The actions of the European Central Bank (ECB) provide an especially clear
example. The chart below shows the Main Refinancing Operations (MRO) rate, the
2 The Taylor rule, first published by Taylor (1993) in his paper “Discretion versus policy rules in practice” is the most popular monetary policy rule in existence. Specified as i = 1 + 0.5y + 1.5π, where i is the nominal interest rate set by the central bank, y is the percent deviation in output from trend level, and π is average inflation over the previous four quarters, the Taylor rule is the simplest and most ubiquitous rule in the monetary economics literature. It is therefore the most appropriate benchmark to use in studying central bank behavior relative to well-­‐established monetary policy rules. 3 Unless noted otherwise, the data used is from Datastream. Gray 5 closest equivalent to the federal funds rate for the ECB4, and the policy rate
recommended by the Taylor rule.
Figure 1B
The ECB is not unique in this regard. Indeed, the correlation between the U.S. deviation
from the Taylor rule and the deviation from the Taylor rule in several other countries is
quite strong5.
The purpose of this paper is to explain this phenomenon by studying measurable
reactions of central banks around the world to changes in U.S. monetary policy,
particularly in terms of these countries’ policy rates and currency interventions. I find that
a large part of the monetary policy innovations in other countries can be explained by
monetary policy innovations in the U.S. Comparative statics are consistent with the
hypothesis that the actions of the Federal Reserve in the early 2000’s towards increasing
liquidity were magnified by the behavioral responses of other central banks, in terms of
both interest rates and an increase in foreign reserves that could be reinvested in
developed economies6.
4 While not exactly identical to the Fed Funds rate, the MRO rate is the figure published as the ECBs baseline monetary policy rate. It is the interest rate at which most ECB open market operations occur. 5 Charts of these correlations (line and scatter plots) are provided in Appendix B: Data Details. 6 Throughout the paper, I use the term “monetary policy transmission” to refer to how the actions of one
central bank affects the actions of another central bank. This is distinct from “international monetary policy
transmission”, which generally refers to how the actions of one central bank affect the economies of other
Gray 6 The following section summarizes the literature surrounding behavioral monetary
policy transmission across countries. Chapter II shows how behavioral transmission
occurs in a standard macroeconomic rational expectations model. Chapter III discusses
the empirical evidence for behavioral transmission in pooled data. Chapter IV gives
further evidence of behavioral transmission by means of a case study, which compares
existing explanations for the ECBs deviation from the Taylor rule with the behavioral
transmission hypothesis. Chapter V concludes with a discussion of the policy
implications of behavioral monetary policy transmission.
Existing Literature
The paper most relevant to the topic of behavioral monetary policy transmission is
Beckworth & Crowe (2011). With a variety of qualitative and quantitative arguments7,
the authors argue that the actions of foreign central banks magnified the effects of the
Federal Reserve’s liquidity creation in the mid-2000’s, resulting in the “Great Liquidity
Boom”. This happened both through the channel of policy rates, as “the Bank of Japan
and the European Central Bank had to follow to some extent the stance of U.S. monetary
policy lest their currencies become over-valued”, and through currency interventions, as
“U.S. monetary policy got recycled back to the advanced economies via the dollarpegged economies’ acquisition of foreign exchange reserves” which were reinvested in
developed markets. The high demand for safe dollar-denominated assets due to this
demand for reserves fueled the creation of complex structured investment products,
which researchers often link to the financial crisis of 2008. The authors conclude that
“the Federal Reserve…was effectively a monetary superpower that created a global
liquidity boom” (3) and call this hypothesis the “monetary superpower hypothesis”.
countries. It is also distinct from “domestic monetary policy transmission”, which generally refers to the
mechanisms by which the actions of a central bank affect the domestic economy. The reader should take
care to ensure that these distinctions are clear. This paper is primarily focused on behavioral monetary
policy transmission.
7 Their quantitative methods include tracking key macroeconomic variables over time, Granger causality testing U.S. monetary policy against monetary policy of other countries, and plotting U.S. monetary policy variables against observed economic imbalances. Gray 7 To fully understand the transmission of monetary policy behavior, it is useful to
understand the literature surrounding international monetary policy that precedes
Beckworth & Crowe (2011) and this paper. One important related topic is how U.S.
monetary policy affects other countries’ economies. Among the most widely cited
empirical findings on this topic is that of Kim (2000), who runs a vector auto regression
(VAR) and finds that “U.S. monetary expansion has a positive spillover effect on nonU.S., G-6 output” that “seems to happen through the world capital market” (342). Most of
the literature building off of Kim (2000) deals with the Federal Reserve’s influence on its
closest international analog, the ECB. Belke & Gros (2005) use data on the Bundesbank
and the ECB to argue that “there is empirically little support for the proposition that there
has for a long time been a systematic asymmetric leader-follower relationship between
the ECB and the Fed” (921). Yet, they also point out that, since the creation of the Euro
in 1999, innovations in the federal funds rate have Granger caused innovations in the
ECB MRO rate and not the other way around, suggesting an influence from the Federal
Reserve to the ECB that is not reciprocated. The authors posit a number of alternative
explanations for this result, including a lag in the business cycle of the Eurozone and the
option value of waiting8. I do not address these issues in this paper, since my questions
and findings are primarily contemporaneous. Ehrmann & Fratzcher (2005) and Monticini
et al (2011) analyze the responses of international markets’ and ECB interest rates,
respectively, to Federal Reserve announcements, and argue that Federal Reserve
announcements affect both markets. Indeed, as Beckworth & Crowe (2011) note, “there
is strong evidence that Fed policy influences the monetary environment in the Eurozone
[and elsewhere], with no evidence of any influence in the opposite direction” (13).
Another relevant branch of literature considers the effects of atypical monetary
policy on specific markets and on the economy as a whole. With regard to the period of
2002-2006, some researchers argue that the federal funds rate was “too low for too long”.
Taylor (2007, 2010) argues that the deviation from the Taylor rule played a significant
role in fueling asset bubbles, particularly in the housing market. Kohn (2007) makes a
8 The “option value of waiting” is the value of waiting before reacting to relevant news, given macroeconomic uncertainty and risk aversion. Belke & Gros (2005) propose that the ECB may have a higher option value of waiting than does the Fed, and therefore responds independently to the same innovations as the Fed, but a bit slower. This would result in the 1-­‐2 quarter Granger causality that the authors observe, with no underlying causality. Gray 8 similar argument9. Ahrend et al (2008) provide evidence for a strong link between
departures from the Taylor rule and changes in indicators of housing market buoyancy,
including home loan volumes, house prices, housing investment, and construction
investment, although the magnitude of this effect remains controversial. A detailed
summary of the existing literature for and against this link is found in Kuttner (2011).
This literature suggests that the short-run reactions by foreign central banks that this
paper will show may have harmful medium-run effects on foreign economic stability.
While existing literature suggests a connection between U.S. monetary policy,
foreign macroeconomic variables, and domestic markets, Beckworth & Crowe (2011)
take the first step in addressing the behavioral side of U.S. monetary policy spillovers.
My findings corroborate their conclusion and generalize their findings to a wider array of
countries using quantitative methods, including rational expectations modeling, pooled
regression analysis, and case study simulations. With each method, I find more evidence
that foreign central banks are influenced by U.S. monetary policy in terms of the interest
rates they set and the currency reserves they accumulate. This is consistent with the
hypothesis that the efforts of the Fed to create liquidity in the early 2000’s generated
unexpected liquidity in foreign markets, and created a feedback effect through the
reinvestment of foreign reserves into safe assets that suppressed long-term interest rates
and fueled a global liquidity boom.
9 Kohn (2007) is quoted on page 1 of Jarocinski & Smets (2008). Gray 9 II.
Theoretical Model
Before pursuing more complex mathematical modeling, the reader may wish to gain
more solid intuition about why behavioral monetary policy transmission may take place.
That is: when a country sets an abnormally low policy rate10, what qualitative responses
do we expect to see from another country?
Suppose there exist two countries that international investors see as roughly
comparable in that they provide a similar array of returns, safety, liquidity, and other
important characteristics with regards to possible investments. Give one the label
“domestic” and the other the label “foreign”. Consider an abnormal drop in the monetary
policy rate of the domestic country. Agents in the foreign country expect to see
investments move from the domestic country, now with a low interest rate, into their own
country, and an accompanying appreciation of the foreign currency that may have
harmful economic effects on the foreign country. To counter the negative effects of a
sudden shift in investment, the foreign central bank can take a combination of the
following three actions:
[1] Lower the domestic monetary policy rate.
[2] Build up stocks of the “domestic” countries’ currency to induce relative depreciation
of their own currency, in the process expanding foreign currency reserve holdings.
[3] Institute capital controls.
Because the period I study (1980Q1-2008Q2) is known to be a period of few to no capital
controls among developed countries, I do not consider option [3]. With regards to [1] and
[2], testable hypotheses exist. All else fixed, I expect the foreign country to lower
monetary policy rates and/ or build up foreign currency reserves when the domestic
country lowers its monetary policy rate below a “standard” value for economic
conditions, such as the Taylor rule.
10 A precise definition of “abnormal” is omitted on purpose. This paper deals with abnormally low policy rates as a negative deviation from the Taylor rule, or simply a reduction in the policy rate from a previous level. Definitions of “abnormal” involving more subtle expectations of policy rates are not addressed here, but do not change our qualitative hypothesis. Gray 10 To add rigor to this hypothesis, I build a rational-expectations model using the
skeleton provided by a Mundell-Fleming model, such as that in Walsh (2010). While my
model does not include multiple sectors of the economy, as an Obstfeld-Rogoff (1994)
model would, it is simple, stable, and quite robust. I first describe my model, then explain
the calibration I have chosen and the solution method I use. I report the results for two
very similar models: one in which the domestic and foreign country are entirely
symmetric, and another in which the domestic country is “large” and the foreign country
is “small”.
Model Description
The model I use is summarized in Table 1. It contains ten equations, ten endogenous
variables, and three exogenous “shocks”. All variables represent log deviations from
trend values. The variables p and pf represent log deviations in the price level for the
domestic and foreign country, respectively, indicating unusually high inflation for
positive values and disinflation for negative values relative to trend. The variables y and
yf represent the output gap for the domestic and foreign country, respectively. The
variables i and if represent nominal interest rates, while r and rf represent real interest
rates, both in deviations from trend values. Finally, s represents the log deviation of the
nominal exchange rate, measured as domestic currency per unit of foreign currency; an
increase in s, then, represents a relative depreciation of domestic currency and
appreciation of foreign currency. The variable q is the same as s, but represents the real
exchange rate rather than the nominal exchange rate. The exogenous “shocks” are e and
ef, representing exogenous movements in policy rates for the domestic and foreign
country, respectively, and u, which represents a shock to the nominal exchange rate and
can be affected by currency intervention on the part of either country.
Equations [1] and [2] are aggregate supply (AS) curves for the domestic and
foreign economy, respectively, and describe a short-term positive relationship between
prices and output. Equations [3] and [4] are investment-savings (IS) curves for the
domestic and foreign economies, respectively, which relate output and the real interest
Gray 11 Table 1 Symmetric 10 Equation Rational Expectations Model AS Curves [1] 𝑝! = 𝑎! 𝑦! + 𝑎! 𝑞! + 𝑎! 𝑝!!! [2] 𝑝𝑓! = 𝑎! 𝑦𝑓! − 𝑎! 𝑞! + 𝑎! 𝑝𝑓!!! IS Curves [3] 𝑦! = 𝑏! 𝑞! − 𝑏! 𝑟! + 𝑏! (𝑦𝑓! ) [4] 𝑦𝑓! = −𝑏! 𝑞! − 𝑏! (𝑟𝑓! ) + 𝑏! 𝑦! Taylor Rules [5] 𝑖! = 𝑐! 𝑝! − 𝑝!!! + 𝑐! 𝑦! + 𝑒 [6] 𝑖𝑓! = 𝑑! (𝑝𝑓! − 𝑝𝑓!!! ) + 𝑑! (𝑦𝑓! ) + 𝑒𝑓 Uncovered Interest Parity [7] 𝑠! = 𝑖𝑓! − 𝑖! + 𝐸! 𝑠!!! + 𝑢 Real Exchange Rate with Capital Mobility [8] 𝑞! = 𝑠! + 𝑝𝑓! − 𝑝! Fischer Equations [9] [10] 𝑟! = 𝑖! − 𝐸! 𝑝!!! − 𝑝! 𝑟𝑓! = 𝑖𝑓! − 𝐸! (𝑝𝑓!!! − 𝑝𝑓! ) Subscripts indicate discrete times… …p & pf indicate domestic & foreign prices, y & yf indicate domestic & foreign output, i & if indicate domestic & foreign nominal interest rates, !"#$%&'(
s & q indicate the nominal & real exchange rates ( !"#$%&' ), r & rf indicate domestic & foreign real interest rates… … and a1 = 0.645, a2 = 0.03, a3 = 0.85, b1 = 0.1, b2 = 1.2, b3 = 0.1, c1 = d1 = 1.5, c2 = d2 = 0.5 Gray 12 rate when total output and total spending are in equilibrium. These four curves have been
adjusted to an open-economy setting. Equations [5] and [6] are Taylor rules for the
domestic and foreign country, respectively. Equation [7] is the uncovered interest parity
identity, which states that there exist no arbitrage opportunities between the domestic and
foreign markets. Equation [8] gives the identity for the real exchange rate, again barring
any arbitrage opportunity. Finally, equations [9] and [10] are the Fischer equations,
which define the real interest rates of both countries.
Initially, I consider a model where countries are entirely symmetric. To create
asymmetry, I will retain all equations and modify a few choice coefficients, which will
require very few modifications. A detailed summary of the symmetric model is below.
Model Calibration
In selecting coefficient values for the model above, I use results from the literature as
well as empirical data analysis.
The value of a1 comes from Gamber (1996). The value of a2 comes from Kamin
& Klau (1997), who study the effects of the real exchange rate on output and find slightly
varying estimates when controlling for different variables in log difference regressions of
the exchange rate on output. I use the estimated coefficient with controls, resulting in
a2 = 0.03 after reorganizing the equations into the form of equations [1] and [2]. The
coefficient a3 is a dampening term that allows for stability in our model. This dampening
term is justified by the inclusion of Et-1(pt – pt-1) in the more common form of the model,
which creates an expectations-augmented Phillips curve. Conditional on economic agents
expecting a gradual return to long run trends proportional to the prevailing deviation, this
extra term can be proxied by the inclusion of a dampening coefficient a3 on pt-1 such that
0 < a3 < 1. The specific value of a3 comes from regressions in the form of equation [1]
using data on the U.S., the U.K., and Canada from the St. Louis Federal Reserve
Economic Database (FRED).
Gray 13 The coefficients b1, b2, and b3 come from the two-country model in Taylor11
(1999). Equations (4A) ad (4B) in Taylor’s model are exactly equivalent to the equations
[3] and [4] in my model with [8] substituted in. Using Taylor’s coefficients, a1 = f = 0.1,
a2 = d = 1.2, and a3 = g = 0.1.
Finally, I set ci = di for all i, since both countries in my model use the standard
Taylor rule. Because variables are in deviations from long run trends, c1=d1=0 is the most
reasonable value, since there should be no systematic deviations from trend values. The
remaining coefficients c2=d2 and c3=d3 are from the standard Taylor rule, which is
already in log form. The remaining equations in the model are identities, which do not
require estimation of coefficients.
Solution Algorithm
To solve the model, I employ the rational expectations solution methods available in
eViews 7. Since the model involves expectations of both past and future variables
determining current variables’ values, I cannot solve the model for each time period in
sequence. Instead, the solution algorithm I use12 solves the system of equations for each
time period in sequence, holding the values of variables fixed for all other time periods.
After iterating through each time period in this manner, the algorithm repeats the process
again from the first time period, now using the future values estimated in the previous
loop. This looping continues until the changes in all variables from one loop to the next
are smaller than a given value13. Intuitively, the algorithm takes a guess for variables
across time periods, iterates to solve the model in each successive time period using these
future values, and performs this iterative solution method in a loop until all variables at
all time periods fit the model to with a very small error. This allows me to solve the given
rational expectations model quickly and accurately, and to track each variable’s response
to an exogenous shock over a long time horizon.
11 The model is on page 24 12 The algorithm is a Gauss-­‐Seidel iterative algorithm similar to the Fair-­‐Taylor method. I use it in conjunction with the Broyden solver, and use deterministic expectations. 13 In my model, this value is 1*108. Gray 14 Results: Symmetric Version
I now show how an exogenous shock to the domestic nominal interest rate has temporary
disruptive effects on exchange rates, output, and the price level of the foreign country. I
focus on the nominal and real exchange rates, output, and the price level, although more
complete model responses are available in Appendix A: Model Details.
I simulate an exogenous shock to the domestic nominal interest rate that pushes it
away from the rate recommended by the Taylor rule. I model this as a shock of -4% to e
for 8 consecutive quarters. The domestic deviation from the Taylor rule results in sharp
currency appreciation for the foreign country’s currency that recedes only gradually, as
well as very moderate losses in output and moderate disinflation.
Reaction of Foreign Economy to Shock e
Figure 2A
Gray 15 Faced with these deleterious shocks, the central bank has an interest in acting
towards stabilizing nominal and real exchange rates, output, and the price level. In my
model, the two tools at its disposal are a deviation away from its own Taylor rule,
modeled as an exogenous shock to ef, and currency intervention, modeled as an
exogenous shock to u. Depending on the model parameters and the preferences of the
foreign central bank, any combination of the two may be used to stabilize each of the four
endogenous variables s, q, yf, and pf to varying degrees. Rather than assume particular
preferences for the central bank in question, I model the variables of interest for three
example responses by the foreign government: no response, a shock of -0.5% to ef for the
duration of the domestic interest rate shock, and a shock of -2% to u for the duration of
the domestic interest rate shock.
Reactions of Foreign Economy to Different Central Bank Actions
Figure 2B
Gray 16 While different magnitudes and combinations of shocks will stabilize different variables,
reactions in interest rates or currency interventions can clearly work to stabilize the
adverse effects of the domestic interest rate shock on the foreign economy.
Results: Asymmetric Version
In the interest of completeness, I modify the initial model to create asymmetry between
the domestic country, which is now “large” in the sense that it follows a closed-economy
model, and the foreign economy, which is now “small” in the sense that it follows an
open-economy model. Practically speaking, this modification results in modified
equations
𝑝! = 𝑎! 𝑦! + 𝑎! 𝑝!!!
[1]
[3]
𝑦! = −𝑏! 𝑟!
while the other equations and coefficients remain as in the symmetric model. This
modification insulates the domestic economy from innovations in the foreign economy.
The differences between the symmetric and asymmetric model given the initial domestic
interest rate shock are given below. Solid lines indicate the symmetric model, while
dotted lines indicate the asymmetric model. It is clear that results from this model are
almost identical to the results from the symmetric model, although the effects of the
shock to e on the foreign economy are slightly more extreme.
Gray 17 Symmetric vs. Asymmetric Models Figure 2C
As one would expect, the foreign central bank can mitigate the instability caused by the
domestic nominal interest rate shock using a mix of policy rate reduction and currency
intervention. The effects of the example responses used before (in the symmetric model)
are almost identical in the asymmetric model, so I omit a graph here to avoid redundancy.
It is important to note that the parameters I choose in the model affect the strength of the
reaction of the foreign economy to the domestic Taylor rule deviation. Namely, higher
values of bi (indicating higher sensitivity of the foreign economy to the domestic
economy) may have significant effects on the policy choices of the central bank. I forego
further discussion from the body of the paper and leave it for Appendix A: Model Details.
Gray 18 The construction of a rigorous rational expectations model formally justifies my
hypothesis. Namely, one expects a foreign central bank to respond to especially low
domestic policy rates with a mix of policy rate reductions and currency interventions.
This would theoretically magnify the effect of liquidity generation by the central bank of
a large country, such as the U.S., through the actions of other relatively less powerful
central banks. I now give evidence that these responses exist in empirical data, and are
more extreme than my model suggests.
Gray 19 III. Empirical Evidence from Pooled Regressions
This section presents empirical evidence for a behavioral spillover effect of U.S.
monetary policy over the past 30 years. After describing the data, I use panel regression
analysis to show that, controlling for worldwide macroeconomic trends and key
macroeconomic variables, monetary policy movements in the U.S. appear to affect
interest rates and foreign currency reserves abroad.
Data
I use panel data from 12 countries with well-developed central banks and the U.S., going
as far back as 1980Q1 and through 2008Q2. While the selection of central banks is
primarily based on data availability and personal judgment, the results are quite robust to
country selection. Selection bias in terms of countries used or data availability for those
countries should not be a problem, if one assumes that data availability correlates closely
with having a well-developed central bank14. The table below summarizes the countries
used in the primary dataset.
14 In other words, I claim that the point at which data became available for these countries is the point at which their central banks became sufficiently developed to be considered roughly comparable to the central banks of other developed countries. Gray 20 Countries Used in the Empirical Dataset
1
2
3
4
5
6
7
8
9
10
11
12
Country
Australia
Canada
South Korea
United Kingdom
Norway
New Zealand
Denmark
Israel
Brazil
Eurozone
China
Indonesia
Data
Since…15
1980
1980
1980
1980
1983
1987
1991
1995
1996
1999
2001
2001
Figure 3A
Monthly and weekly data are interpolated into quarterly averages, such that all values in
the final dataset are quarterly. Trend values are all calculated using a standard HodrickPrescott filter with λ = 1600. Further details regarding data and methodology are
summarized in Appendix B: Data Details.
Policy Rates
The first empirical question is whether a change in the U.S. policy rate affects the policy
rates of other countries, particularly in reference to a monetary policy rule such as the
Taylor rule. Simple plots and correlations give evidence of some positive relationship
between the Taylor rule deviations of the Federal Reserve and those of other countries16.
Univariate regressions of country policy rates on U.S. Taylor rule deviations reveal
15 “Data Since…” refers to basic data needed to compare policy rates and Taylor rule deviations. For some control variables used in my regressions, some countries do not have data until more recently than is indicated on this chart. Since our general findings are robust to specific controls or time periods used, this is not a substantial concern. 16 Line plots and scatter plots for the 12 countries in the sample are given in Appendix B: Data Details. Gray 21 statistical significance (at the 5% level) of the U.S. Taylor rule deviation in affecting
country policy rates for 9 of 12 countries in our sample, according to t and F statistics17.
To address this question more rigorously, I run two sets of pooled panel
regressions. The first set addresses the question of whether a change in the policy rate of
the Federal Reserve affects the policy rates of other countries. The second addresses the
question of whether a deviation from the Taylor rule by the Federal Reserve causes
similar deviations in other countries. The two questions are slightly distinct, but both
address the ways in which the Federal Reserve exports monetary policy behavior, thereby
magnifying the effects of its actions. A natural next step is to parse out whether policy
rate levels or deviations from policy rules are most important in transmitting monetary
policy behavior. Unfortunately, significant collinearity between U.S. policy rates and
U.S. deviations from the Taylor rule confounds any attempt to answer this question
confidently, as regressions including both terms yield insignificant results due to this
correlation18. I keep the two questions separate for this reason, and treat them both
individually.
Before describing and reporting both regressions, the reader should keep two facts
in mind. First, I make no argument as to the cause of empirical behavioral monetary
policy transmission. Countries may mimic U.S. monetary policy innovations for
economic considerations as suggested by the model in Chapter II, or may just see the
Federal Reserve as a role model. Second, the regressions below are accurate if one
assumes that U.S. monetary policy affects other countries’ monetary policy and not vice
17 As an aside, the U.S. Taylor rule deviation also appears helpful in describing monetary policy rules that
central banks have historically practiced. The addition of the U.S. deviation from the Taylor rule to the
empirical policy rates of a given country generally adds 10-25% explanatory power (judging by the
adjusted R2) and is statistically significant in the positive direction at the 5% level. In contrast, the addition
of an exchange rate term to these countries’ Taylor rules adds little to no explanatory power and is either
not statistically significant at the 5% level, or is less significant than the U.S. Taylor rule deviation for
every country in the sample. One simple explanation of why the U.S. deviation may be more useful than
the exchange rate for describing historical monetary policy is that central banks purposely prevent currency
appreciation by acting as soon as the U.S. deviation is realized, rather than waiting for exchange rates to
adjust before acting. This suggests that the large body of literature building exchange rates into monetary
policy rules may be improved upon by instead focusing on U.S. actions or the actions of other monetary
superpowers in describing historical monetary policy rules.
18 The high correlation between the U.S. policy rate and the U.S. deviation from the Taylor rule is interesting in its own right. The correlation is significant and positive (70.68%), suggesting that the Federal Reserve historically overreacts to economic developments. Gray 22 versa. While the literature suggests that this is the case (at least for the most part), the
reader should always be wary of endogeneity, which in this case would make my results
larger and more significant than the true effect. I address this issue in robustness checks,
and establish that my results hold even when correcting for possible endogeneity.
The first regression model considers the effects of policy rate changes in the U.S.
on policy rates abroad. The model is as follows:
𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 + 𝐵! ∗ 𝑝𝑜𝑙𝑖𝑐𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
+ 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟. Here, the “policy control variable” is the average policy rate of every country in the
sample other than the U.S. and the country of interest, and thus controls for wider
macroeconomic trends that do not represent shifts in the U.S. policy rate. Due to
significant autocorrelation of residuals in standard models, I use the Generalized Least
Squares (GLS) regression model, which is the Best Linear Unbiased Estimator (BLUE)
in the presence of autocorrelation and heteroscedasticity. The results are shown below in
four different specifications.
Gray 23 Dependent Variable: Country Policy Rate U.S. Policy Policy Control GDP Gap 1 0.3978** 0.2844** -­‐0.0412 {0.0865} {0.0761} {0.0484} 2 0.3816** 0.3621** -­‐0.0564 {0.0779} {0.0672} {0.0460} 3 0.5360** 0.2160** -­‐0.0799 {0.0804} {0.0764} {0.0486} 4 0.6253** -­‐-­‐-­‐ -­‐0.0370 {0.0620} -­‐-­‐-­‐ {0.0488} Inflation 0.2657** {0.0510} 0.2632** {0.0477} -­‐-­‐-­‐ -­‐-­‐-­‐ 0.2287** {0.0506} Reserves Constant -­‐7.09e-­‐06** 3.1717** {9.05e-­‐07} {0.5080} -­‐-­‐-­‐ 1.9346** -­‐-­‐-­‐ {0.4280} -­‐6.68e-­‐06** 3.9917** {9.25e-­‐07} {0.4979} -­‐7.54e-­‐06** 4.5416** {9.06e-­‐07} {0.3550} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 + 𝐵! ∗ 𝑝𝑜𝑙𝑖𝑐𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
+ 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟. The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. The policy control term is the average policy rate for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. Reserves denotes the dollar denominated volume of foreign reserves. Results suggest that U.S. policy rates affect foreign policy rates strongly, even when control for macroeconomic variables and worldwide policy trends. Figure 3B It appears that, controlling for standard macroeconomic variables and worldwide trends,
each percentage point movement in the U.S. policy rate causes about a 0.40 percentage
point contemporaneous movement in a developed country’s policy rate. This result is
very strong and statistically significant at any standard significance level. Furthermore, a
U.S. policy rate innovation affects a given country more than an innovation in the
average policy rate in all other developed countries.
As expected, when the policy control term is excluded I find a stronger effect of
the U.S. policy rate in the positive direction. The sign on inflation suggests that central
banks raise rates when inflation rises, as expected. The negative sign on reserves suggests
that countries react to macroeconomic developments using policy rates and currency
interventions simultaneously, as a fall in policy rates is associated with a rise in reserves,
as expected. Finally, the constant indicates a baseline equilibrium policy rate. Excluding
certain time periods or countries from the sample changes these results very little.
Gray 24 The second regression model is similar, but uses deviations from Taylor rules
rather than policy rate levels. The model is
𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝐵! + 𝐵! ∗ 𝑈𝑆 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 +𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟 Again, I use a GLS model to correct for serial autocorrelation in the residuals. The
“deviation control” term is the average of the Taylor rule deviation for all countries in the
sample other than the U.S. and the country of interest. The results of four different
specifications are shown below.
Dependent Variable: Country Deviation from the Taylor Rule U.S. Deviation Deviation Control GDP Gap Inflation 1 0.6725** 0.1070 -­‐0.1990** -­‐1.0005** {0.09765} {0.0690} {0.0515} {0.0525} 2 0.7443** 0.2008** -­‐0.2240** -­‐0.9824** {0.0881} {0.0609} {0.0490} {0.0481} 3 0.3896** 0.4553** -­‐0.0052 -­‐-­‐-­‐ {0.1191} {0.0821} {0.0623} -­‐-­‐-­‐ 4 0.7526** -­‐-­‐-­‐ -­‐0.2052** -­‐1.0221** {0.0830} -­‐-­‐-­‐ {0.0514} {0.0507} Reserves Constant -­‐8.17e-­‐06** 5.5142** {9.65e-­‐07} {0.2890} -­‐-­‐-­‐ 4.570** -­‐-­‐-­‐ {0.2560} -­‐9.16e-­‐06** 1.7056** {1.19e-­‐06} {0.2577} -­‐8.34e-­‐06** 5.7245** {9.61e-­‐07} {0.2557} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
+ 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟. The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. The policy control term is the average deviation from the Taylor rule for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. Reserves denotes the dollar denominated volume of foreign reserves. Results suggest that a U.S. deviation from the Taylor rule strongly affects foreign deviations from the Taylor rule, even when control for macroeconomic variables and worldwide policy trends. Figure 3C While parameter estimates vary, it appears that a one percentage point deviation from the
Taylor rule for the U.S. causes another country to deviate from its Taylor rule by about
Gray 25 0.7 percentage points in the same direction. The general results are robust to modifying
the time period or countries used in the sample, and hold in fixed effects of Prais-Winsten
models as well.
Robustness Checks: Policy Rates
While the results above are quite robust to different specifications and time periods, I do
not correct for the possibility that other countries’ monetary policy affects U.S. monetary
policy. If true, this would make the results from the regression above more extreme than
the reality. In order to address this concern, I include a lagged U.S. policy term in both
regressions and report the results. The significance of the lagged term as well as the
contemporaneous U.S. policy term indicates that, even controlling for contemporaneous
U.S. monetary policy actions (which may be affected by foreign interest rates), U.S.
monetary policy has a strong effect on monetary policy in other countries. In some
respects, one could consider the coefficient on the lagged term to be a lower bound on the
effect of U.S. monetary policy on foreign monetary policy.
With regard to policy rate levels, the inclusion of a lagged U.S. policy rate term
shows that recent U.S. monetary policy strongly affects foreign monetary policy,
controlling for current policy rates and worldwide policy trends. Furthermore, including
the lagged U.S. policy term reduces the magnitude and statistical significance of the
policy control term, suggesting that U.S. monetary policy plays a role in affecting
worldwide policy trends with a lag as well as contemporaneously.
Gray 26 Dependent Variable: Country Policy Rate U.S. GDP Lag(4) Policy Control Policy Gap Inflation 0.2032* 0.3517** 0.1664* -­‐0.0084 0.2561** {0.1009} {0.0963} {0.0821} {0.0487} {0.0506} Reserves -­‐6.96e-­‐
06** {8.97e-­‐07} Constant 3.3139** {0.5047} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 + 𝐵! ∗ 𝑈. 𝑆. 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 4𝑡ℎ 𝑙𝑎𝑔
+𝐵! ∗ 𝑝𝑜𝑙𝑖𝑐𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 + 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝
+𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟 .
The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. The policy control term is the average policy rate for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. Reserves denotes the dollar denominated volume of foreign reserves. Results suggest that U.S. policy rates affect foreign policy rates strongly, even when control for macroeconomic variables and worldwide policy trends. Figure 3D
In the same way, a recent U.S. deviation from the Taylor rule strongly affects
foreign deviations from the Taylor rule, even when controlling for the current U.S.
deviation. Again, including lagged U.S. deviations eliminates the significance of the
deviation control term, suggesting that the U.S. strongly influences average world interest
rates with a lag.
Dependent Variable: Country Deviation from the Taylor Rule Deviation U.S. Deviation Lag(4) GDP Gap Inflation Reserves Constant Control 0.4064** 0.3503** 0.0716 -­‐0.2015** -­‐1.0114** -­‐7.94e-­‐06** 5.4963** {0.1380} {0.1445} {0.07554} {0.0517} {0.0534} {9.67e-­‐07} {0.2885} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝐵! + 𝐵! ∗ 𝑈𝑆 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑈. 𝑆. 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (4𝑡ℎ 𝑙𝑎𝑔) + 𝐵! ∗ 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 + 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 +𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑒𝑟𝑟𝑜𝑟. The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. The policy control term is the average deviation from the Taylor rule for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. Reserves denotes the dollar denominated volume of foreign reserves. Results suggest that a U.S. deviation from the Taylor rule strongly affects foreign deviations from the Taylor rule, even when control for macroeconomic variables and worldwide policy trends. Figure 3E
Gray 27 These regressions make it evident that developed countries tend to mimic U.S.
monetary policy behavior in terms of policy rates and deviations from policy rules. Next,
I address how foreign central banks react to U.S. monetary policy in terms of currency
reserves.
Currency Reserves
In addition to affecting foreign interest rates, theory suggests that U.S. policy innovations
may cause foreign governments to intervene in currency markets. If the U.S. sets rates
abnormally low, one would expect a foreign government to intervene in currency markets
to prevent an appreciation of their currency against the dollar. It would do so by
accumulating large quantities of reserves, which can be sold for dollars and thus increase
the quantity of that country’s currency in global markets relative to the U.S. dollar. The
theoretical model developed in Chapter II corroborates this hypothesis. I use the change
in the volume of each country’s foreign currency holdings as a proxy for the process of
currency intervention. At first glance, it is certainly true that global attitudes towards
foreign reserves took a shift from the early 2000’s onwards. As shown below, fitting a
trend line to median reserves of our sample countries before and after the year 2000
results in very different slopes (the coefficient changes from about 350 to about 825,
depending on the countries included)
Gray 28 Shift in Median Rate of Reserves Accumulation
Figure 3F
This increased rate of foreign exchange accumulation may be due to a number of factors.
The most obvious reason – added caution by Asian economies after the financial crises of
the late 1990’s – does not provide a full explanation, since the finding above still holds
when we exclude Asian economies. There is evidence that at least part of this shift is due
to the U.S. deviation from the Taylor rule. Indeed, the negative correlation I predict
between U.S. deviation from the Taylor rule and reserve holdings of foreign governments
is evident in the data19. Univariate regressions show significant coefficients for about half
the countries in the sample.
Again, one can perform a more rigorous analysis by controlling for other factors
that may explain this accumulation of reserves. I use GLS regression due to the presence
of serial autocorrelation in the residuals. Again, I employ two separate models: one with
policy rate levels as explanatory variables, and another with deviations from the Taylor
rule as explanatory variables. While changes in U.S. policy rate levels may or may not
spur currency intervention, as many of these changes will be expected or considered
appropriate by economic agents and therefore may cause little stir in currency markets,
one would certainly expect U.S. deviations from the Taylor rule to spur currency
19 Country by country scatter plots are provided in Appendix B: Data Details. Gray 29 intervention, since it indicates monetary policy movement that may be considered
unexpected and/ or inappropriate.
The model using policy rate levels is as follows:
𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝐵! + 𝐵! ∗ 𝑈𝑆 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 + 𝐵! ∗ 𝑝𝑜𝑙𝑖𝑐𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 +𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝑒𝑟𝑟𝑜𝑟. Results for four specifications are below.20
Dependent Variable: Country Reserves Volume U.S. Policy Policy Control GDP Gap 1 -­‐981 -­‐11771** 376 {2973} {2592} {976} 2 -­‐4331 -­‐11539** 946 {3507} {2933} {1438} 3 -­‐10758** -­‐-­‐-­‐ 461 {2075} -­‐-­‐-­‐ {988} 4 -­‐13918** -­‐-­‐-­‐ 1104 {2547} -­‐-­‐-­‐ {1452} Inflation 1475 {1518} 5962** {2031} 2692 {1512} 7367** {2020} FX Rate -­‐-­‐-­‐ -­‐-­‐-­‐ -­‐12** {3.77} -­‐-­‐-­‐ -­‐-­‐-­‐ -­‐12** {3.81} Constant 163957** {16575} 169128** (18423} 109757** {11646} 117063** {12947} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑟𝑒𝑠𝑒𝑟𝑣𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 + 𝐵! ∗ 𝑝𝑜𝑙𝑖𝑐𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
+ 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 + 𝑒𝑟𝑟𝑜𝑟. The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. Reserves denotes the dollar denominated volume of foreign reserves. The policy control term is the average policy rate for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. The FX Rate is the nominal exchange rate (foreign currency per U$). Excluding the exchange rate term models a country with a floating exchange rate, while including the exchange rate term models a country with a fixed exchange rate. Results indicate that U.S. policy rate levels do not significantly affect other countries’ currency reserve volumes independent of worldwide policy trends. Figure 3G 20 The concerns of reverse causality in these regressions are not as evident here as in the last section, since
it is unlikely that the Federal Reserve considers smaller countries’ reserves to be a high priority in
determining U.S. monetary policy. For this reason, I omit a “Robustness Checks” section from my
consideration of currency interventions and mention basic robustness checks in the body of this section. Gray 30 Again, the “policy control” term is the average policy rate for the 11 countries that are
not the U.S. nor the country of interest, and thus acts as a control for worldwide monetary
policy trends. Note that the inclusion of the nominal foreign exchange rate allows us to
model the empirical responses of a country fixing its exchange rate to the U.S. dollar. As
expected, the response of reserves to U.S. monetary policy innovations is more extreme
under a fixed exchange rate regime. While contemporaneous U.S. policy rates appear to
affect currency reserves in the expected direction, when controlling for world
macroeconomic trends I cannot reject the null hypothesis of no effect. These results are
robust to the use of different controls, lags, sample periods, and most country
specifications. The policy control term is no longer significant when using an OLS fixed
effects model21. It appears that changes in U.S. policy rate levels do not spur currency
intervention by foreign governments, although worldwide policy trends likely affect
reserve levels.
A similar model can be applied to the effects of a U.S. deviation from the Taylor
rule on currency reserve volumes by foreign governments. The model is then
𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝐵! + 𝐵! ∗ 𝑈𝑆 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 + 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝑒𝑟𝑟𝑜𝑟. The results of this GLS regression are below.
21 The fixed effects OLS is unbiased but is not BLUE in the presence of serial autocorrelation. Thus, while providing useful a robustness check, disagreement by an OLS regression does not strongly rebuff our conclusion using a GLS model. Gray 31 Dependent Variable: Country Reserves Volume U.S. Deviation Deviation Control GDP Gap 1 -­‐11463** -­‐8653** 54 {3108} {2117} {970} 2 -­‐12182** -­‐8859** 551 {3548} {2493} {1432} 3 -­‐18036** -­‐-­‐-­‐ 316 {2686} -­‐-­‐-­‐ {978} 4 -­‐19251** -­‐-­‐-­‐ 934 {2962} -­‐-­‐-­‐ {1440} Inflation -­‐476 {1425} -­‐9.05* {3.67} 470 {1419} 3882* {1832} FX Rate -­‐-­‐-­‐ -­‐-­‐-­‐ -­‐9.05* {3.67} -­‐-­‐-­‐ -­‐-­‐-­‐ -­‐10.51** {3.67} Constant 78576** {8555} 74913** {9535} 64212** {7878} 60111** {8649} * denotes significance at the 5% level, ** denotes significance at the 1% level. Using the sample period 1980Q1-­‐2008Q2, I run the regression 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑟𝑒𝑠𝑒𝑟𝑣𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝐵! + 𝐵! ∗ 𝑈. 𝑆. 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑇𝑅 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
+ 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐵! ∗ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 + 𝑒𝑟𝑟𝑜𝑟. The regression is Generalized Least Squares (GLS) to correct for serial autocorrelation. Reserves denotes the dollar denominated volume of foreign reserves. The deviation control term is the average deviation from the Taylor rule for the 11 countries that are not the U.S. nor the country of interest. The GDP gap is the log deviation of real GDP from trend GDP, calculated using a standard Hodrick-­‐Prescott filter (λ=1600). Inflation is the annual change in the GDP deflator. The FX Rate is the nominal exchange rate (foreign currency per U$). Excluding the exchange rate term models a country with a floating exchange rate, while including the exchange rate term models a country with a fixed exchange rate. Results indicate that U.S. deviations from the Taylor rule significantly affect other countries’ foreign exchange reserves, even when controlling for worldwide policy trends. Figure 3H Framing the study in terms of Taylor rule deviations results in significance for the U.S.
deviation term. It appears that, on average, foreign governments accumulate an added
$11.5 billion worth of reserves for every percentage point deviation of the U.S. below its
Taylor rule. Modifying controls, including lags, or modifying countries from the sample
changes these results little. Results are similar but lose significance when using an OLS
fixed effects model. Modifying the sample period to omit the 2000’s eliminates the
significance of the U.S. deviation term, perhaps due to the low variation of this variable
through the 1980’s. As expected, U.S. deviations from the Taylor rule appear to spur
significant currency interventions by foreign governments.
Thus, while U.S. policy levels appear to matter little in spurring currency
intervention when controlling for worldwide policy rate trends, a U.S. deviation from the
Gray 32 Taylor rule does appear to make a substantial difference in currency interventions by
foreign governments.
The hypotheses developed in Chapters I and II indeed appear to hold empirically.
It appears that U.S. monetary policy innovations have had significant effects on policy
rates and currency interventions abroad.
Gray 33 IV. Empirical Evidence: Case Study of the Eurozone
Recall from Chapter I that the original motivation for this study was the deviation from
the Taylor rule by the ECB at the same time as a similar U.S. deviation. Another
appropriate empirical test for the existence of behavioral monetary policy spillovers
would be to compare alternative explanations of the ECB’s deviation with an explanation
based on behavioral monetary policy transmission. If the theory of behavioral monetary
policy transmission is as consistent with the data as other explanations, this is evidence
for the hypothesis developed in Chapter II.
I explain and test three alternative theories of why the ECB deviated from the
Taylor rule in the early 2000’s. I then show that my hypothesis of U.S. behavioral
monetary policy transmission explains the ECB’s deviation as well as or better than these
other theories.
Alternative Explanations for ECB Behavior
I propose three hypotheses for the deviation of the ECB from its Taylor rule in the early
2000’s.
(1) Modified Taylor Rule Coefficients
The first natural criticism of fitting a standard Taylor rule to ECB monetary policy is that
the ECB may have different preferences between inflation and the GDP gap, represented
by different coefficients on the Taylor rule
𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = 𝐵! + 𝐵! ∗ 𝐺𝐷𝑃 𝑔𝑎𝑝 + 𝐵! ∗ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 . Gray 34 Yet, an OLS regression of the form above results in a negative sign on the parameter B2,
suggesting a monetary policy that is destabilizing22. That is, a negative coefficient on
inflation suggests that lower inflation leads to a higher policy rate, which further dampens
inflation and leads to an even higher policy rate. The finding remains when we add nonlinearities to account for an added fear of inflation when inflation is low or high, or when
we include variables capturing a preference towards the economies of certain countries23.
Since the ECB is well known for prioritizing price stability in its official mandate,
simulations of policy rules with lower coefficients on the GDP gap may capture the idea
that the ECB simply cares less about the GDP gap than the Taylor rule suggests. These
simulations, pictured below, still reveal large deviations in the actual policy rate from
these modified Taylor rules (with coefficients B1 on the GDP gap of 0, 0.1, 0.25, and 0.5
and the standard value B2 = 1.5).
Taylor Rules with Alternate Values for B1
Figure 4A
In sum, a non-standard Taylor rule on aggregate Eurozone data cannot explain the ECBs
deviation from the Taylor rule during this period
22 Mutual causation (and resulting endogeneity) is of little concern in this regression, since in general changes in policy rates act on GDP and inflation with a lag of more than a quarter. 23 For example, including Germany’s GDP gap and inflation as distinct from the rest of the Eurozone does not change our results. Gray 35 (2) Pure Inflation Targeting
Another hypothesis that fits with the institutional history of the ECB is that the
sole goal of the ECB is to stay below the published 2% inflation target. In ECB policy
memos, the 2% inflation target is generally expressed as the main reason for monetary
policy decisions. The 2003 ECB Annual Memo states that rates were kept low in the
early 2000’s out of inflationary fears, due to “considerable uncertainty related to the high
degree of geopolitical tension in the Middle East and associated turbulence in oil prices
and financial markets” (21). While inflation rose above the 2% target when rates were
lowered below the Taylor rule, it did stay relatively close to this target. Two measures of
inflation, the Harmonized Index of Consumer Prices (HICP) and the GDP Deflator, are
shown below during the period in question.
Inflation Rates in the EMU During the Deviation from the Taylor Rule
Figure 4B
The main counterargument to this hypothesis is that the empirical reactions of the ECB to
inflation innovations are not consistent with stabilizing monetary policy. Univariate
regressions of the ECB policy rate to inflation in the previous few quarters reveals a
negative coefficient on inflation, suggesting that higher inflation leads to a lower policy
rate in the following quarters. This is a destabilizing policy that does not fit the story of
Gray 36 pure inflation targeting by a sophisticated central bank. Inflation targeting does not seem
to provide a complete explanation of the ECBs deviation from monetary policy rules.
(3) Differential Weighting of Core and Peripheral Countries
Perhaps the most powerful explanation for the ECB’s monetary policy that does not
include direct considerations of the U.S. is the hypothesis that the ECB gives more
weight to “core” countries in setting monetary policy than it gives to “peripheral”
countries. Following country divisions proposed by Nechio (2011), the “core” countries
are Austria, Belgium Finland, France, Italy, and Germany, while the “peripheral”
countries are Portugal, Ireland, Greece, and Spain24. Nechio (2011) gives the following
chart, which can be closely replicated in my own data, and proposes that the ECB was
following a Taylor rule for the “core” countries during this period.
“Core” and “Periphery” Taylor Rules
Figure 4C
Source: Nechio (2008)
24 Some readers will recognize the “peripheral” countries as the PIGS or GIPS often mentioned in macroeconomics literature. OECD data show significant differences in the inflation and GDP gaps of these countries relative to more “core” countries, which are relatively similar amongst themselves. The division proposed by Nechio (2011) thus seems reasonable. Gray 37 A regression of the MRO rate against Taylor rules for the “core” and “periphery”
suggests the data generating process
1 𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = −0.82 + 0.70 ∗ 𝑐𝑜𝑟𝑒 𝑇𝑎𝑦𝑙𝑜𝑟 𝑟𝑢𝑙𝑒 + 0.16 ∗ 𝑝𝑒𝑟𝑖𝑝ℎ𝑒𝑟𝑦 𝑇𝑎𝑦𝑙𝑜𝑟 𝑟𝑢𝑙𝑒
and provides a strong fit, with an R2 of almost 90%.
The (similar) hypothesis that the ECB prioritized the target 2% inflation rate for
the “core” countries is also consistent with the data, and univariate regression of the
MRO (policy) rate against lagged values of inflation reveal positive coefficients,
suggesting that the ECB is acting rationally to stabilize inflation in the “core” countries.
Figure 4D This is certainly a potential explanation of the ECBs actions, and has a good deal
of explanatory power. Still, the data do not show an irrefutable fit except in examples
contrived to fit the data (such as regression [1]). I now show that, at least in the case of
the ECB, the hypothesis that behavioral spillovers from the U.S. influenced ECB
monetary policy provides almost as much explanatory power as the hypothesis above,
and uses weaker assumptions.
Gray 38 Testing the Hypothesis
In the empirical study of policy rates from Chapter III, I show that U.S. deviations from
the Taylor rule have a strong influence on deviations from the Taylor rule for foreign
central banks. Using lagged variables, I establish that a 1% deviation in the Taylor rule
by the U.S. results in a deviation of at least 0.4% on average across the twelve countries
in my sample. After many robustness checks, the maximum empirical effect appears to
be around 0.75%. Selecting a moderate value of 0.5% for this effect and simulating the
ECB’s policy rate provides an imperfect, but considerably improved fit to the empirical
policy rate of the ECB. Below is a graph of the actual policy rate pursued by the ECB, the
Taylor rule, and the simulation in which the ECB follows the modified Taylor rule
𝑝𝑜𝑙𝑖𝑐𝑦 𝑟𝑎𝑡𝑒 = 1 + 1.5𝜋 + 0.5𝑦 + 0.5𝐷 + 𝑒
where π refers to average inflation over the previous four quarters, y refers to the current
output gap as measured by a standard (λ = 1600) Hodrick-Prescott filter, and D refers to
the current U.S. deviation from the Taylor rule.
Simulation of ECB Deviation from the Taylor Rule Figure 4E Gray 39 It seems that most of the ECBs deviation from the Taylor rule can be explained by monetary policy spillovers of the U.S. Federal Reserve. Admittedly, this particular rule applied to any country in my sample does not unanimously provide a strong fit, as shown in Appendix C: Model Fitting to Countries Outside the EMU. One may argue that the hypothesis provided by Nechio (2011) provides a better fit to the data. I do not refute this, but do point out that the argument posed by Nechio requires assumptions regarding the division of groups within the EMU and preferential weighting of those groups by the ECB, with which the reader may or may not agree. The hypothesis provided here requires only the assumption that the ECB acts similarly to other developed central banks, so long as the reader believes the results of the paper thus far. Both hypotheses are broadly consistent with the data, and it is likely that both provide partial explanations. While one cannot conclude from this that behavioral monetary policy spillovers from the U.S. is or is not the reason for these particular actions, it is a simple and powerful explanation that is broadly consistent with the data. Gray 40 V.
Policy Implications
This paper provides substantial evidence that U.S. monetary policy influences monetary policy in other countries. After proposing a qualitative hypothesis in the context of existing literature, I show how behavioral spillovers of U.S. monetary policy are evident in a standard rational expectation model. I then show empirically that U.S. monetary policy has influenced monetary policy abroad to a large degree, and that deviations from the Taylor rule by the Federal Reserve have influenced currency intervention by foreign governments in a manner that may create large excesses of liquidity. Finally, I show that the ECBs behavior in the early 2000’s is broadly consistent with a reaction to U.S. monetary policy, although it is not the only hypothesis consistent with the data. I do not address whether foreign central banks mimic U.S. policy rate movements due to economic concerns or because they view the Federal Reserve as a role model. In either scenario, these findings have significant policy implications. The most important policy implication of my findings is that the behaviors of other central banks magnify the effect of the Federal Reserve’s actions in generating liquidity. My findings indicate that when the Federal Reserve set interest rates lower than monetary policy rules suggested in the mid-­‐2000s, other countries set interest rates lower than they otherwise would have and accumulated large quantities of reserves to prevent currency appreciation. Countries’ accumulation of liquid reserves such as U.S. Treasuries drove up the demand for safe U.S. assets, further suppressing interest rates and disproportionately affecting long-­‐term interest rates, and spurred the development of increasingly complex securities throughout the U.S. financial system. A growing body of research links low interest rates and financial securitization to incipient housing bubbles, both in the U.S. and abroad. The combination of these two phenomena (securitization and the housing bubble) is usually cited as a primary cause of the 2008 global financial meltdown. Both appear to be connected to the U.S. deviation from the Taylor rule in the early 2000’s through the mechanism of behavioral monetary policy transmission. Gray 41 As well as providing an explanation for the build-­‐up of currency reserves, low long-­‐term interest rates, and trend of financial securitization in the 2000’s, this hypothesis has clear implications for the future of Federal Reserve policy. If international behaviors continue to magnify the effect of Federal Reserve actions, the Fed would do best at maintaining domestic and worldwide macroeconomic stability by taking behavioral monetary policy spillovers into account when enacting policy. While there exist legitimate disagreements25 about how closely the Federal Reserve should follow standard monetary policy rules, it is clear that a large, sustained deviation from monetary policy rules can have disastrous effects, especially when the reactionary behavior of other central banks is not properly anticipated. 25 An illustrative contrast can be found by comparing the work of Taylor (2010) and Bernanke et al (2011). Gray 42 VI. References
2003 ECB Annual Memorandum. Frankfurt, Germany. 2003.
Ahrend, Ridiger; Cournede, Boris; Price, Robert (2008) “Monetary Policy, Market
Excesses, and Financial Turmoil”. Working Paper, OECD.
Beckworth, David; Crowe, Christopher (2011) “The Great Liquidity Boom and the
Monetary Superpower Hypotheses”. Working Paper, Texas State University &
International Monetary Fund.
Bernanke, Ben S.; Bertaut, Carol; DeMarco, Laurie Pounder; Kamin, Steven (2011)
“International Capital Flows and the Returns to Safe Assets in the United States,
2003-2007.
Belke, Ansgar; Gros, Daniel (2005) “Asymmetries in Transatlantic Monetary
Policymaking: Does the ECB Follow the Fed?” Journal of Common Market
Studies. Vol. 43, No. 5, pp. 921-946
Drukker, David M. (2003) “Testing for serial correlation in linear panel-data models” The
Stata Journal. Issue 3, Number 2, pp. 168-177
Ehrmann, Michael; Fratzcher, Marcel (2005) “Equal Size, Equal Role? Interest Rate
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Demand Curves for the Post-War U.S. Economy” Southern Economic Journal.
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Grilli, V., Roubini, N., 1995. “Liquidity and exchange rates: puzzling evidence from the
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Jarocinski, Marek; Smets, Frank R. (2008) “House Prices and the Stance of Monetary
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Kamin, Steven B.; Klau, Marc (1997) “Some Multi-Country Evidence on the Effects of
Real Exchange Rates on Output” Bank for International Settlements. Basle,
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Kennedy, Peter. “A Guide to Econometrics: 6th Edition” Blackwell Publishing, Malden,
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Gray 43 Kim, Soyoung (2000) “International transmission of U.S. monetary policy shocks:
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Gray 44 VII. Appendices Appendix A: Model Details For the more curious reader, I report more detailed model output. First I report the response of all endogenous variables to my original domestic interest rate shock (-­‐4% shock to e for 8 consecutive quarters). 1. -­‐4% Shock to e for 8 Consecutive Quarters, Symmetric Model Figure 7A Gray 45 Next, I consider the responses of all variables to the three example responses of the foreign central bank in the symmetric model. 2. Example Responses by Foreign Central Bank, Symmetric Model Figure 7B Gray 46 Third, I consider the different responses of all variables to the initial shock to e in the symmetric and asymmetric models. 3. Different Responses to the Shock to e in Symmetric and Asymmetric Models Figure 7C Gray 47 As mentioned in the body of the text, the sensitivity of the IS curve makes a substantial difference in the magnitude of the foreign response to the initial shock to e. This is particularly evident in the asymmetric model, where I change the sensitivity of the IS curve by changing the coefficient values in equation [4]. I focus here on output and the price level, which has especially variable responses at different IS curve sensitivities. 4. Foreign Economy Reaction to e Shock at Various Sensitivities
Figure 7D
Finally, I note that a response that may be adequate for a lower IS curve sensitivity may not be adequate given a higher IS curve sensitivity. Changing the IS curve coefficients from b1 = b3 = 0.1 to b1 = b3 = 0.3 reveals that responses that are adequate for the first case are no longer adequate for the second when the initial shock to e occurs and is transmitted to the foreign economy via the IS curve. Gray 48 5. Inadequacy of the Initial Interest Rate Response Given Higher IS Curve Sensitivity, Asymmetric Model Given coefficients of 0.3, the original -­‐0.4% nominal interest rate shock (dotted blue line) is inadequate. A more extreme response, this time of -­‐0.8%, is necessary to stabilize our variables. Figure 7E One can see that asymmetry matters little, but the sensitivity of the foreign country to the domestic country via the IS curve matters a good deal in the strength of the foreign economy’s reaction to a domestic nominal interest rate shock. In order to mitigate the instability caused by a domestic interest rate shock, one can expect a foreign central bank to lower its own interest rate and/ or intervene in currency markets towards currency depreciation. Gray 49 Appendix B: Data Details Here I report more details about the data set of Section III and the methodology used to construct it. The chart in the “Data” section of the text gives dates after which I have full data on each country. The data I use are taken from Datastream. I use all available data on the following series going as far back as 1980: baseline policy interest rate, nominal GDP, the GDP deflator, quarterly exchange rates with the U.S. dollar, and volumes of foreign reserves for each country. The baseline policy interest rate is a generic term for each country’s analog to the Federal funds rate. The table below illustrates which series I use for each country to populate this series. Country Australia Brazil Canada China Denmark Eurozone Indonesia Israel New Zealand Norway South Korea U.S. United Kingdom Policy Rate Used Cash Rate Target SELIC Target Rate Overnight Money Market Financing Rate Interbank Overnight Offered Rate Denmark Policy Middle Rate Main Refinancing Operations (MRO) Rate BI Rate "Headline" Interest Rate Cash Rate Target Norway Overnight Lending Middle Rate Bank of Korea Base Rate Federal Funds Rate Frequency Monthly Monthly Monthly Daily Daily Monthly Monthly Monthly Monthly Daily Monthly Quarterly Bank of England Base Rate Monthly Figure 7F Nominal GDP is in local currency and is usually reported quarterly, although it is only used to calculate the GDP gap via a Hodrick-­‐Prescott filter, and so units of measurement may be ignored. The GDP deflator is generally reported quarterly, Gray 50 although in the case of China it is reported annually. I use linear interpolation between annual values in this isolated case, which results in a negligible degree of measurement error for this series. Quarterly exchange rates are all local currency per U.S. dollar. Reserves denotes total international reserve assets, measured in U.S. dollars or converted to U.S. dollars using nominal exchange rates. Where data is available only in terms of local currency, I divide by the exchange rate to put the data in terms of U.S. dollars. In order to make all data comparable, I run the data through simple Excel VBA programs to take quarterly averages whenever data is not already quarterly26. I use these data to construct the series’ used in Section III, which are reported below along with basic summary statistics across the entire panel data set. For all variables, a Shapiro-­‐Wilk test rejects normality at any standard significance level. Series Obs. Mean Median Std. Dev. Country Statistics… Policy Rate 909 8.55 7.03 5.73 Taylor Rule 955 7.38 5.87 5.4 TR Deviation 809 1.11 1.00 5.65 GDP Gap 991 -­‐0.02 -­‐0.03 5.22 Inflation 1006 4.13 3.21 3.78 Exchange Rate 966 396.32 2.22 1612.823 Reserves 968 58414 19434 149077 U.S. Statistics… Policy Rate 114 6.23 5.50 3.53 TR Deviation 110 0.52 0.85 1.98 Other… Policy Control 1368 9.51 8.59 3.28 TR Dev. Control 1320 1.73 1.95 3.01 Figure 7G I use this panel dataset to test my hypotheses in Section II. 26 For monthly data, I simply take quarterly averages. For daily data, I calculate the average value over each month, and then take quarterly averages of the resulting monthly values. Gray 51 As mentioned in the body of the text, these data show a very basic correlation between deviations from Taylor rules across countries. Below is a line plot charting distance from the Taylor rule for each country over time. The dotted vertical lines indicate periods in which the U.S. set rates lower than its Taylor rule for an extended period of time. While one does not see many effects of the first such deviation (in the early 1990’s), one can see that during the deviation of the early 2000’s most developed countries either deviated from their Taylor rule in the negative direction, or lowered any existing gap very quickly27. Deviations from the Taylor Rule for 12 Large Economies
27 South Korea is a notable exception. Gray 52 Figure 7H
Gray 53 Scatter plots of U.S. deviation from the Taylor rule (vertical axis) against each country’s deviation form the Taylor rule (horizontal axis) illustrate that, while there exists a reasonable amount of noise for most countries, there is certainly a significant positive correlation in most cases. As mentioned in the body of the text, univariate regressions of the U.S. deviation on each country’s deviation shows statistical significance in the positive direction for 9 of the 12 countries in my sample. Deviations from the Taylor Rule of the U.S. Versus Other Large Countries
Gray 54 Figure 7I
Gray 55 I now display scatter plots of the U.S. deviation from the Taylor rule (vertical axis) against the volume of foreign reserves held by each foreign central bank. As mentioned in the body of the text, univariate regressions display statistical significance for about half of the countries in my sample. Foreign Currency Reserves versus U.S. Deviations from the Taylor Rule
Gray 56 Figure 7J
Gray 57 Appendix C: Case Study Model Fit to Countries Outside the Eurozone I show in Section IV that a very simple simulation, in which the ECB follows a Taylor rule including the U.S. Taylor rule deviation with a coefficient of 0.5, fits the empirical data on the ECB quite closely. One does not expect the same simulation to fit the data from every country, since each country reacts differently to U.S. monetary policy innovations. Yet, since the simulation is presented in Section IV, the reader may wish to see the same simulation performed on other countries’ data. For a few countries, the simulation was a closer fit to the policy rule than the standard Taylor rule. Figure 7K For a few others, the simulation provides a different fit that is closer than the Taylor rule in some time periods and worse in others. Gray 58 Figure 7L For most countries, though, this particular simulation illuminates little about the underlying causes of the Taylor rule deviation. Gray 59 Figure 7M This may make the reader wary of the model in Section VI, since the model that fits well for the EMU fits quite poorly for numerous countries in our sample. Yet, the result of this particular simulation does not counter the main results of the paper. Regardless of which specific simulations are consistent with the behavior of which central banks, we have established a strong connection between the behavior of the Federal Reserve and that of central banks around the world. While other models Gray 60 incorporating the findings in this paper may be consistent with the behavior of other central banks, I leave those simulations for further research.