NBER WORKING PAPER SERIES

WHAT ARE THE DRIVING FORCES OF INTERNATIONAL BUSINESS CYCLES?
Mario J. Crucini
M. Ayhan Kose
Christopher Otrok
Working Paper 14380
http://www.nber.org/papers/w14380

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
October 2008

We thank Vivian Yue for insightful comments. The views expressed in this paper are those of theauthors not the International Monetary Fund or the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2008 by Mario J. Crucini, M. Ayhan Kose, and Christopher Otrok. All rights reserved. Short sectionsof text, not to exceed two paragraphs, may be quoted without explicit permission provided that fullcredit, including © notice, is given to the source.

What Are the Driving Forces of International Business Cycles?
Mario J. Crucini, M. Ayhan Kose, and Christopher Otrok
NBER Working Paper No. 14380
October 2008
JEL No. E3,E32,F4,F41
ABSTRACT
We examine the driving forces of G-7 business cycles. We decompose national business cycles into
common and nation-specific components using a dynamic factor model. We also do this for driving
variables found in business cycle models: productivity; measures of fiscal and monetary policy; theterms of trade and oil prices. We find a large common factor in oil prices, productivity, and the termsof trade. Productivity is the main driving force, with other drivers isolated to particular nations or sub-periods.
Along these lines, we document shifts in the correlation of the G-7 component of each driver withthe overall G-7 cycle.

Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu
M. Ayhan Kose
Research Department
International Monetary Fundakose@imf.org

Christopher Otrok
Department of Economics
University of Virginia
PO Box 400182
Charlottesville, VA 22904-4182
cmo3h@Virginia.EDU

1. Introduction“What are the driving forces of international business cycles?” This has been
one of the central questions in the extensive literature on business cycles. The
question is a challenging one since there are many driving forces to consider,including total factor productivity shocks, …scal and monetary policy shocks, oilprice shocks, shocks to the terms of trade, shocks to preferences, news and manyothers. Moreover, these driving forces are in‡uenced by various domestic andexternal factors and understanding the relative importance of these factors isnecessary to get a good grasp of the channels through which the driving forcesa¤ect business cycles.
In order to answer this question, most previous work follows Backus, Kehoeand Kydland (1992) focusing on total factor productivity as the single driving
variable with the world divided into home and foreign locations. While the mostcommon driving variable is total factor productivity, monetary and …scal policy
shocks along with many others have been receiving more emphasis over time.
The reason quantitative equilibrium models have focused on small dimensional models in both the number of countries and number of driving variables
is tractability. There are two dimensions along which tractability is a concern.
The …rst is related to the ability of the researcher or the researcher’s audience
to sort out an expanding list of theoretical interactions as the dimension of themodel increases. To some extent this is alleviated by tracing out the time pro…lereaction of the macroeconomy to one shock in one location at a time. This is the
dynamic comparative statics counterpart to an impulse response function in timeseries econometrics.
The second constraint is data limitations. Even if the researcher decides tocalibrate preferences and technology using existing micro-studies, thereby economizing on the number of parameters to estimate using macroeconomic series,
the number of remaining parameters necessary to capture the dynamic covariancestructure of the shocks grows rapidly with the dimension of the model. This is aconsequence of the need –in dynamic rational expectations models –to forecast
the future evolution of exogenous variables and their interdependence.
The objective of this paper is to provide a detailed analysis of a number ofdriving forces of business cycles within and across G-7 countries over the period
1960-2005. We use the term driving force in the same manner as it is employedin dynamic rational expectations models of the international business cycle –variables assumed to be exogenous by the model builder. Our study contributes2

to the research program on international business cycles in three ways.
First, we mitigate the curse of dimensionality by employing dynamic factor
models. This allows us to characterize the stochastic processes for both endogenous variables and exogenous variables.
Second, our methodology helps us to di¤erentiate the domestic and external
factors in explaining these variables. We model the endogenous and exogenous
variables as the sum of three unobserved factors: a common G-7 factor, a nationspeci…c factor and an idiosyncratic factor. Aside from parsimony, this approachlends itself to the interpretation of shocks as arising from common or nationspeci…c sources; a distinction which is central for a number of international business cycle theories. For example, a class of intertemporal models of the current
account have the property that only idiosyncratic movements in exogenous variables lead to current account imbalances. Common factors are obvious candidates
for sources of international business cycle comovement, an enduring topic in theliterature.
Third, we have a comprehensive list of driving variables. In particular, our listof driving variables includes total factor productivity, government expenditures,the monetary base, short-term interest rates targeted by the central bank, therelative price of oil and the terms of trade. Apart from parsing the endogenousand exogenous variables into common, nation-speci…c and idiosyncratic variation,
we also estimate the fraction of variation of output, consumption and investment
attributed to each component of each shock. This enables us to study the joint
properties of ‡uctuations in output, consumption, and investment. Using multiple
macroeconomic aggregates, rather than just output, allows us to derive morerobust measures of common and nation-speci…c business cycles.
Our analysis is carried out using a dynamic factor model. Dynamic factor models have increasingly become a popular econometric tool for quantifying the degreeof comovement among macroeconomic time series.1 Kose, Otrok and Whiteman(2008) provide a brief survey of the literature employing these types of models
to study the extent of business cycles comovement. However, these models have
yet to be used to examine a large set of driving forces and their relationshipto macroeconomic variables. We characterize these relationships in terms of a1

While these models are often used to analyze the degree of business cycle comovement in theinternational business cycle literature, they have also been employed in other contexts such as
forecasting and monetary policy analysis. See Otrok and Whiteman (1998) for an application toa forecasting exercise, and Bernanke, Boivin and Eliasz (2005) for an application to the analysis
of monetary policy.

3

variance decomposition.
Our international business cycle variance decomposition is achieved using athree step procedure. First, we use national data on output, consumption andinvestment to estimate the common G-7, nation-speci…c and idiosyncratic components of each national business cycle. In step two, we use the same statisticalmodel to estimate the common G-7, nation-speci…c and idiosyncratic componentsof each driving variable.
In step three, we project measures of the components of the shocks on components of the endogenous variables. The objective of this exercise is to generate
a variance decomposition of the common and nation-speci…c components of G-7
business cycles into the common and nation-speci…c components of our driving
variables. This allows us to answer the key question we are interested in “whatare the driving forces of international business cycles?”We are also able to answer
narrower questions such as: “How much of the German business cycle is accounted
for by movements in G-7 productivity versus German productivity?”
In a related paper, Gregory and Head (1999) employ dynamic factor analysis
and Kalman …ltering methods to analyze the sources of ‡uctuations in productivity, investment and current account in the G-7 countries. They report that thecommon ‡uctuations have substantial impact on ‡uctuations in both productivity
and investment in these countries, but very little impact on the current account.
Empirical work using vector autoregressions to identify structural shocks and infer their contribution to output variance in an international context are few. An
important early contribution is Ahmed, Ickes, Wang and Yoo (1993). They allow
for home foreign and world supply shocks, a relative …scal shock, a relative preference shock and a relative money shock. Their data sample includes the U.S. andan aggregate of …ve major industrialized countries. They …nd that supply shocks
explain most of the variation in output.
In section 2, we explain how our empirical approach relates to existing dynamic
stochastic general equilibrium models of international business cycles. Section
3 provides information about the dataset we use. Section 4 describes the …rst
step of our variance decomposition of output, consumption and investment into
the common and nation-speci…c components. Section 5 explains the results ofvariance decompositions of driving forces. Section 6 analyzes the importance of
the G-7 and nation-speci…c driving variables in explaining ‡uctuations in output,
consumption and investment. Section 7 concludes.

4

2. The model
In this section, we …rst describe how a standard linear international business cycle
model relates to our empirical framework. This serves to highlight the curse ofdimensionality which limits the number of sources and number of driving variablesin this class of models. Next, we provide a brief description of the dynamic factor
model we employ.
2.1. Linear business cycle models
The common methodological approach in the business cycle literature is to specify
tastes, technology, constraints and asset market structure. Parametric functional
forms are speci…ed and either estimated or calibrated. Typically the models are
solved by linearizing the model around a steady-state level or balanced growthpath.
A convenient example given the focus of this paper is Baxter and Crucini(1995). Their stochastic dynamic general equilibrium model may be conveniently
summarized by two systems of linear equations. Linear here simply means a setof linear equations describing the equilibrium solution in either the levels of thevariables or their logarithms (which one depends on the method of linearization
employed).
The …rst system of equations describes the dynamic evolution of the vector ofstate variables:
St = M St 1 + et
(2.1)
While the system above is a …rst-order vector autoregression, it can be adapted toricher dynamics in either the predetermined or exogenous variables by augmenting
the length of the state vector. The state vector contains the irreducible collectionof predetermined and exogenous variables necessary for agents to decide on theircurrent period choices. In the Baxter and Crucini model they are: home andforeign capital stocks, kt and kt , one of the bond stocks, bt and domestic andforeign total factor productivity, At and At .2
The second system of equations are the decision rules, linking the vector of
endogenous choices, Zt , to the current state vector, St :
Zt =
2

St

The other bond stock is redundant because world market clearing requires that bt =

5

(2.2)
bt .

Each row in this system is the decision rule for an economic choice variable. For
example, if the …rst element in Zt is domestic consumption, the …rst row of thematrixcontains the coe¢ cients that describe the current period responses ofconsumption to each of the individual state variables. In the one sector twocountry bond economy with only productivity shocks, the state vector, St , hasonly …ve elements as noted earlier. Home consumption is a positive function of
all four (the coe¢ cients in the …rst row of are positive).
A key facet of the dynamic structure is the strict exogeneity of a subset of thevariables in the state vector. Expanding the …rst system of equations, makes thisobvious:
3 2
32
3 2
2
3
kt 1
0
kt
kk
kk
kb
kA
kA
76
7 6 0 7
6 kt 7 6 k k k k
k A
k A 7 6 kt 1 7
k b
7 6
6
6
7
7
6
7
6
7 6
6
7
St = 6 b t 7 = 6 b k
b k
b b
b A
b A 7 6 bt 1 7 + 6 0 7 : (2.3)
5 4 At 1 5 4 t 5
4 At 5 4 0
0
0
At
0
0
0
At 1
t
This may be written more compactly by collecting the predetermined choice variables (capital and bonds) into one vector and the exogenous variables (productivity shocks) into a second vector. The generic representation of the state andexogenous equations is now:
St =

Pt
Xt

=

PP

PE

0

Pt 1
Xt 1

+

0

:

(2.4)

t

Here it should be understood that the elements of the vector of predeterminedand exogenous variables depend upon the model structure, the number of shocks
and number of countries. What all models share, though, is the zero restrictionin the lower left sub-matrix of the coe¢ cient matrix, representing the exogeneity
restriction placed on the vector of variables, Xt . The block of coe¢ cients immediately to the right of the zero matrix is a matrix of coe¢ cients linking current
shocks to past shocks (it need not be …rst-order as assume here). The remainingcoe¢ cients of the system, denoted by the ’s, are complicated functions of all themodel’s deep structural parameters as well as those governing the dynamics of theshocks, and . The last feature worth noting is the innovation vector, containing
innovations to productivity at home and abroad, and zeros elsewhere. Since thepredetermined variables are assumed to be perfectly controlled by agents, there
are no random variations in them unrelated to the state vector itself.33

One could certainly think of reasons to deviate from this assumption: random natural events

6This business cycle model implies that the data generated from such a model
has a representation as a dynamic factor model. In the example here output,
consumption and investment are all driven by two common factors — home andforeign technology. In contrast, our factor model will have a common productivity shock, seven nation-speci…c shocks and idiosyncratic variation speci…c tothe series. The canonical linear business cycle model lacks these idiosyncraticcomponents. However, there are a number of ways to break this exact (and counterfactual) link between all variables in a business cycle model. For example,
Sargent (1989) shows how measurement error on the part of a statistical agency
would give rise to a model that meets the typical assumptions of a dynamic factor
model. In this case we would measure output, consumption and investment imperfectly, the estimated factor model on this data would then reveal three factors(interpreted as world, home and foreign technology factors) as well as idiosyncratic movements interpreted as measurement error. A second way is to introduce
sector speci…c technology shocks as in Long and Plosser (1983). Such a model will
also give rise to a dynamic factor structure as their work shows that such shocks
generate a common business cycle. A third way is to introduce additional shocks,
such as monetary and …scal shocks.4
We focus on the business cycle properties of output, consumption and investment of the G-7 countries. Output is not directly chosen; in the prototype
business cycle model it is a function of home and foreign total factor productivity
and the inputs of labor and capital. E¤ectively, then, the three choice variables
are consumption, labor e¤ort and investment for each of the G-7 countries, a totalof 21 choice variables. Studying a large set of shocks, as we do, has a clear cost
as the dimensionality and parameters to be estimated quickly becomes unwieldy.
Focusing on the exogenous driving variables in the business cycle model, Xt ,Xt = Xt 1 + t :

(2.5)

0
this vector is made up of I (the number of countries) subvectors, Xi;t
= [Ai;t ; mi;t
; gi;t ; pi;t ; qi;t ], ordered as national productivity, a target of monetary policy (ashort-term interest rate and a narrow monetary aggregate), a …scal policy variable (government spending, revenue and so forth), the relative price of oil and thethat destroy the capital stock, unanticipated in‡ation eroding the real value of bonds if they arenominally denominated, or simply measurement error.
4
Forni and Reichlin (1998) develop a classical estimator for dynamic factor models and apply
it to disaggregated sectoral output in the US. Their identifying assumptions allow them toidentify these factors as sector speci…c and aggregate technological shocks. Our complimentary
approach attempts to study the impact of a wider range of shocks.

7

terms of trade. Thus even if we reduce the number of variables to the absolute
minimum, the minimum being total factor productivity, a single measure of …scal
and monetary policy and the relative price of oil, will contain 784 parameters
to be estimated, the same is true for the variance-covariance matrix of the innovations. Even this is an understatement if the dynamics of the exogenous variables
extend beyond the …rst-order.
2.2. The dynamic factor model
To economize on the dimensionality of the system, we employ a dynamic factor
model. We study each driving variable separately and decompose the variationin each variable into common, nation-speci…c and variable speci…c factors. In
particular, we combine multiple measures of each driving variable and estimate
the following factor model in growth rates:
xij;t =

ij + Bij Ft + bij fi;t + "ij;t

.

(2.6)

Suppose xij;t is the growth rate of the jth empirical proxy for productivity
in country i. Then, Ft is a common productivity factor shared by the G-7,
fi;t is a nation-speci…c productivity factor and "ij;t is measurement error. Theinterpretation of measurement error here is that we have imperfect proxies fortrue total factor productivity. The error term is assumed to be uncorrelated
cross-sectionally at all leads and lags, and follows an autoregressive process oforder pi for each element in the vector. The factor fi;t follows an autoregressionof order qk . The B’s and b’s are factor loadings on the common and nation-speci…cfactors.
The estimation of the model is Bayesian and follows the procedure in Otrok
and Whiteman (1998). The priors on the model parameters are loose enough to
be uninformative except for the prior belief that the autoregressive polynomials
are stationary, which seems reasonable for data in growth rates. The estimation
procedure itself is based on the Gibbs sampler and is outlined in the Appendix.
There are at least three advantages to our approach. The …rst one is parsimony;
the number of parameters has been reduced from (I e)2 to (2 I J e) where I is thenumber of countries, J is the number of measures of the driving variable and e isthe number of driving variables. The decision rules go from having I e exogenous
in‡uences to having 2 e exogenous in‡uences. For example, if we consider thenumber of exogenous variables discussed above, the number of parameters to be
estimated would go down from 784 to 42. This is a major advantage in the8context of international business cycle research because the decision rules directly
capture the response of domestic consumption, say, to the common component ofthat driving variable (shock). This would otherwise be captured in consumption
response by some weighted average of the coe¢ cients on each nation’s driving
variable.
Second, having the common component and nation-speci…c component is very
useful in the context of international business cycle research. For example, Glickand Rogo¤ (1995) exploit the fact that a large class of models imply no current
account reaction to ‘common shocks,’which would imply a zero coe¢ cient on thecommon (world) factor for the current account equation. Models of risk sharing
imply that consumption should respond to common shocks, not nation-speci…cones, which is the opposite restriction on the coe¢ cients for the consumption
decision rule.
The third advantage is more descriptive, allowing us to compare the movementsof G-7 productivity with the G-7 component of output or the G-7 component of…scal policy. This leads one to immediately think about international businesscycle comovement in terms of common reactions to common shocks and, possibly,
asymmetric reactions to common shocks. Productivity movements naturally fall
into the former category and oil price shocks into the latter category if one chooses
to organize countries as net exporters and net importers as Backus and Crucini(2000) do.

3. The data
To analyze the driving forces of international business cycles, we construct a comprehensive database of the main macroeconomic and driving variables. We use
annual data covering the period 1960-2005. Our selection of annual frequency
stems from the fact that we include a broad set of measures for driving variables, some of which are not available at higher frequencies. Our macroeconomic
aggregate for output is real gross domestic product, consumption is real private
consumption expenditure and investment is real gross private capital formation.
These series are from the World Development Indicators (WDI) and World Economic Outlook (WEO) database. For the driving variables, we separate them into
policy and non-policy variables; all are treated as strictly exogenous.
We use multiple measures of driving variables, not simply because the factor
model methodology requires it, but because di¤erent measures of each driving
variable contain di¤erent information about the theoretical variable of interest.
9

An important by-product of the factor model is that the size of the idiosyncraticcomponent of a particular measure indicates the extent of independent variation
across competing measures of the same economic variable. This could be measurement error or conceptual di¤erences in the variable construction. Consequently,
empirical results that use the common factor may be more robust than those thatexamine only a speci…c measure, our analysis will help to distinguish these cases.
On the monetary policy side, we use short-term real interest rates and real
stocks of money, narrowly de…ned. The interest rates we employ are call rates
and other short-term interest rates, including the T-Bill rates and Discount Rates.
These are most closely in‡uenced by interest rates targeted directly by the central
banks, such as the Federal Funds rate in the United States. In our empirical work,
we use the ex post real interest rate, with in‡ation measured using the CPI. The
real monetary aggregates are represented by the sum of money and quasi money
series, also de‡ated by the CPI. Interest rates and monetary aggregates are fromthe International Financial Statistics (IFS) of the IMF and CPI series are fromWorld Economic Outlook (WEO) database.
On the …scal policy side, we include total expenditure, government consumption, and total revenue. This list is more extensive than is typically used in thebusiness cycle literature, allowing us to provide a broad …scal picture. The …scalseries are from the OECD and IFS sources, completed with the help of the WEO
database whenever the series are missing. The series are then de‡ated by the CPI.
The non-policy variables are productivity, the relative price of crude petroleum
and the terms of trade. Productivity is the central focus of the international realbusiness cycle literature. We use four di¤erent productivity measures. The …rst
two measures are based on the framework developed by Klenow and RodriguezClare (2005). These measures both use capital and labor input measures in thecomputation of total factor productivity. One of the measures also includes
human capital in the decomposition. To construct these productivity series, weemploy data from the Penn World Tables 6.2 (Heston, Summers and Aten, 2006).
The other two productivity measures use only labor data, not capital, which isconsistent with the approach used by Backus, Kehoe and Kydland (1992). The…rst uses gross domestic product and employment (number employed, not hours)
from the OECD. The second is from the Bureau of Labor Statistics and uses
manufacturing output and total hours in manufacturing.
We have four prices of crude petroleum in U.S. dollars: i) the world average
price, ii) the Dubai price, iii) the Brent price and iv) the West Texas price. The
latter three are the products produced in the markets referenced, the …rst is10

an expenditure weighted average of these prices. These U.S. dollar prices areconverted to domestic currency and then de‡ated by the domestic consumer priceindex. These series are taken from the IFS.
The terms of trade is the price of exports relative to imports. We have two
measures, one taken from the WEO and the other from the IFS. In the former,
the terms-of-trade is the terms-of-trade of goods and services computed using thetrade shares of all trading partners. In the latter, terms-of-trade refers to the ratioof unit value of exports to unit value of imports.

4. International business cycles
Following Gregory, Head and Raynauld (1997), we start by estimating a factor
model for the macroeconomic aggregates:
2
3
2
3
2
3
yi;t
Biy
biy
4 ci;t 5 = ij + 4 Bic 5 Ft + 4 bic 5 fi;t + "ij;t .
(4.1)
ii;t
Bii
bii
where the elements of the data vector are the growth rates of real gross domestic
product, real private consumption expenditure and real investment for country i,
respectively. The factor Ft is a common factor shared by all aggregates acrossall of the G-7 countries and this is what we will refer to as the G-7 factor. The
quantitative impact of the G-7 factor on an individual macroeconomic aggregate
is determined by the factor loading Bij . These factor loadings are di¤erent acrossmacroeconomic aggregates and across countries.5 Both the factors and the residual
entering the equation follow autoregressive processes. Innovations to both thefactors and the residuals are assumed to be contemporaneously uncorrelated.
An important starting point for our analysis is to compare the G-7 factor
with a well-known measure of the G-7 business cycle. The measure that we use
here is a country-size weighted average of the growth rates of the G-7 macroeconomic aggregates. Following the methodology employed by Crucini (1997), we use
Purchasing Power Parity valuations to arrive at the country weights. While theG-7 economies on average constitute about 50 percent of total world output, theUnited States alone accounts for roughly 46 percent of G-7 output and this number drops dramatically to about 15 percent for Japan, the next largest member.
The G-7 share of world output has declined in recent decades as emerging market economies, including China and India, have grown much faster than the G-7.
5

To save space, we do not report factor loadings, these are available from us upon request.

11However, the G-7 cycle is still –in a value-weighted sense –a good approximation
to the world business cycle.
Figure 1 compares the estimated G-7 factor to a G-7 aggregate growth ratecomputed as a country-weighted average of national output growth rates andand to U.S. output growth.6 The correlation between U.S. output and the G-7
aggregate is 0.81 and is readily evident in the …gure. While this may re‡ectcommon disturbances and genuine business cycle propagation across the U.S. andother G-7, it also re‡ects the large economic weight of the U.S. in the constructionof the G-7 aggregate. To a …rst approximation, the G-7 business cycle looks likea moderated version of the U.S. business cycle. The G-7 common real factor isthe smoothest of the three measures; its correlation with G-7 output growth is
0.84 compared to a mere 0.43 in the case of U.S. output. We conclude from thisthat the simple view that the U.S. business cycle drives the G-7 cycle is not areasonable description of international business cycles.
Casual inspection of Figure 1 also indicates that the G-7 factor captures the
major economic events of the past four decades: the relatively steady expansionof the 1960s; the rapid boom of the early 1970s; the sharp, but short recession of
the mid-1970s associated with the …rst oil price shock; the less abrupt and more
enduring recession of the early 1980s stemming from a variety of forces including
the tight monetary policies of major industrialized nations; the mild recession of
the early 1990s; the 2001 recession and the subsequent recovery and slowdown.7
How important is the G-7 factor in the evolution of national macroeconomic
aggregates? After all, if it is not quantitatively important, we should be lessconcerned about re…ning our measure of it. To address this question we computevariance decompositions using the factor model (see the Appendix). Table 1
reports our …ndings. Beginning with output, the usual business cycle reference
variable, the world and national components are of equal importance in accounting
for variation in the typical G-7 country. Based on this statistic, the world cycle
merits as much scrutiny as the nation-speci…c component. From the perspectiveof individual countries, though, the picture is quite di¤erent. The world factor
dominates the business cycles of France, Italy and Japan, on average accounting
6

The G-7 factor is estimated quite precisely evidenced by the tightness of 10 percent and 90
percent posterior quintile bands available from the authors upon request.
7
While not the focus of this paper, we also examine the behavior of nation -speci…c factors
in detail. The results suggest that the nation-speci…c factors capture most of the major peaks
and troughs of business cycles in each of the G-7 countries. The …gures of nation-speci…c factors
are available from us upon request.

12

for more than 70 percent of the variation. It is of less importance for the United
Kingdom and the United States, where it accounts for less than 15 percent of
output variation. There is no obvious correlation between the relative economic
size of a country and the importance of the G-7 factor.
Consumption tells a di¤erent story in a couple of respects. First, the G-7
factor on average accounts for a lower share of consumption variance than does thenation-speci…c factor. At …rst blush this seems consistent with the consumptionrisking sharing puzzle, national consumption variance is not shared even among
these highly integrated, …nancial developed nations. Note, however, that thenational component of consumption is not signi…cantly di¤erent from what we seein output. The di¤erence between income and consumption variance lies mostly inthe larger idiosyncratic term in the consumption decomposition. Thus it could bethat larger measurement errors in consumption than income measurement skew
international consumption correlations toward zero. While this certainly does
not solve the correlation or risk-sharing puzzle, it helps to mitigate the puzzle
somewhat.
Investment has a slightly more pronounced national component than output or
consumption. Averaging across the G-7 the nation-speci…c component accounts
for roughly 50 percent of the variation. Though this is not much higher than wastrue of output or consumption, the idiosyncratic component is almost as large
as the G-7 factor for the typical country. The international real business cycle
model predicts a large nation-speci…c component in investment ‡uctuations ascapital searches for its highest reward. The small G-7 component for investment
is consistent with this prediction.
To summarize, we have found sizable G-7, nation-speci…c and variable-speci…ccomponents in the main macroeconomic aggregates. The common and nationspeci…c components tend to be larger than the idiosyncratic component with the
exception of investment where it is on par with the G-7 component. Most of theheterogeneity we see is across countries, with France, Italy and Japan sharing alarge common component and the United Kingdom and the United States business cycles being mostly driven by national factors. Canada and Germany fall
between these extremes. The remainder of the paper is devoted to understanding
why there is a common cycle in the …rst place and how these similarities anddi¤erences arise across countries. To develop this understanding we begin withan analogous decomposition of our driving variables into G-7, nation-speci…c andvariable-speci…c components.

13

5. Properties of the driving variables
We begin this section brie‡y discussing each driving variable in isolation. We
ask similar questions regarding these driving variables as were addressed in our
analysis of macroeconomic aggregates in the previous section. We …rst analyze theevolution of each driving variable. We then focus on the relative importance of theG-7, nation-speci…c and variable-speci…c components in explaining the volatilityof the driving variables.
5.1. Productivity, oil prices and the terms of trade
We …rst examine the properties of driving variables that are not instruments ofpolicy: productivity, oil prices and terms of trade. Policymakers clearly scrutinize
these variables to re…ne their policy actions in light of the evolution of output
growth and in‡ation. Economic growth accompanied by labor productivity advance is viewed as less likely to alter in‡ation and in‡ation expectations thansituations when productivity growth stagnates. Oil price increases in the absenceof broad movements in in‡ation are appropriately viewed as relative price changes,
though unpleasant policy tradeo¤s may present themselves as a¢ rmed by the recent emergence of concern about stag‡ation voiced by o¢ cials at the U.S. Federal
Reserve. Productivity changes have been the dominant driver of quantitative
theory on business cycles in closed economy models, with oil prices and the termsof trade taking a more prominent role in small open economy models.
To compute our productivity series, we use a standard Solow residual decomposition for country i:ai;t = yi;tsi ni;t(1si )ki;twhere yi;t is the logarithm of output, si is the share of labor income in totalfactor income, and ni;t and ki;t are measures of labor and capital inputs. The
most commonly used version of this decomposition in the international businesscycle literature is the one employed by Backus, Kehoe and Kydland (1992), whichuses gross domestic product for the output measure and total employment as thelabor input measure. The capital stock is not included in their decomposition. A
considerable amount of research has taken place since and we draw upon more
recent data and methodologies.
As we brie‡y discussed in the data section, we use four di¤erent measures of
productivity. The construction of the …rst two measures follows the methodology in Klenow and Clare-Rodriguez (2005), using both capital and labor input
14

measures in the computation of total factor productivity. One of their capital
measures includes human capital. Consistent with the approach used by Backus,
Kehoe and Kydland (1992), our other pair of measures use only labor data on the
input side. The …rst of these two uses gross domestic product and employment(number employed, not hours) from the OECD. The second is from the Bureauof Labor Statistics and uses manufacturing output and total hours in manufacturing.8
The …rst panel of Table 2 reports the common, nation-speci…c and variablespeci…c components of productivity. We see that the nation-speci…c component
tends to dominate when we use the more elaborate decompositions including physical and human capital than those using basic labor input measures. The nationspeci…c component accounts for about two thirds of the variance in productivity
growth in these cases, the contribution of the G-7 and nation-speci…c components
fall when we move to the simpler measures, but only to the point of equality.
The appearance of large idiosyncratic components in the simpler measure is consistent with the omission of capital measures in the computation of the Solow
residual in these cases. The fact that the BLS measure has a full third of its variance accounted for by the idiosyncratic component may be due to the fact that
this measure includes only manufacturing while the other three span the entire
production side of the macroeconomy.
Taken at face value, the results indicate that while the G-7 countries are nottechnologically integrated in the literal sense of sharing a common productivity
level, there is a large common component. Figure 2 plots the G-7 business cycle
factor against the G-7 productivity factor, their correlation is 0.69. As we shallsee in the next section, productivity will be a key driving variable both at theG-7 and national level. The implication is that business cycle models focusing on
productivity shocks will need the nation-speci…c components of productivity to
8
Focusing on the manufacturing sector in each country, we used manufacturing output andemployment data from the BLS as our measures of output and labor input. Broadening ouranalysis to the entire economy, we used GDP measures and total civilian employment from theOECD. The correlation of the two productivity measures in growth rates averages 0.81, but there
are important di¤erences across them. First, manufacturing productivity is more volatile thanoverall productivity. The standard deviation of the growth rate manufacturing productivity is on
average roughly 2.5 times higher than the analogous measure using total output (1.97 compared
to 0.81). Second, the bilateral cross-country correlations of manufacturing productivity arehigher than those computed for GDP in most cases, but the di¤erences are not statisticallysigni…cant. This is consistent with a broader literature that documents larger international
productivity di¤erences in the service sector than the goods sector.

15

generate positive international output spillovers. Models with supply-side complementarities such as Ambler, Cardia and Zimmerman (2002) fall into this category.
Coordinated monetary and …scal policies that shift world demand are two othercandidates.
Turning to the relative price of oil in Table 3, we see that the G-7 component accounts for virtually all of the variation. Recall that this relative price iscomputed as the U.S. dollar price of, say, West Texas crude petroleum converted
to domestic currency at the spot exchange rate between the U.S. dollar and thehome currency and then de‡ated by the national CPI level. While it is well known
that the U.S. dollar prices of varieties of crude petroleum correlate strongly, it issurprising that this is also true of the relative price of oil in terms of the broader
consumer basket in each nation. As we shall we, oil is one of the few driving
variables that could be said to literally be a common shock to all G-7 nations.
The variance decomposition for the terms of trade is found in Table 4. As
noted by Backus and Crucini (2000), the terms of trade and the relative priceof oil tend to be highly correlated for the G-7 due to the higher variance of oil
prices relative to other goods and services entering into trade ‡ows. Moreover, oil
accounts for a non-trivial share of trade even in highly industrialized countries.
Figure 3 presents the G-7 common factor for oil and G-7 factor for the termsof trade along with the G-7 business cycle factor. The correlation of the termsof trade and the relative price of oil in terms of the common factors is evident in
the …gure, particularly at the points of the sharp oil price increases in 1974, 1979,
1999 and 2005 and the drop in 1986. The correlation between the two factors overthe entire sample is 0.76.
Backus and Crucini (2000) conclude that exogenous shifts in oil supply fromOPEC producers can account for only about 10% of output variance in a sample
of countries overlapping signi…cantly with those include here. Consistent with
their …ndings, the correlation between the G-7 business cycle factor and G-7 oilprice factor (G-7 terms of trade factor) is 0.03 (0.12) for the full sample. One
should keep in mind, however, that theory predicts an ambiguous sign: exogenous
oil supply shocks generate a negative correlation, while increases in oil demandby the G-7 generate a positive correlation. Since the oil price shocks are often
associated with periods of dramatic oil price changes, we tend to see oil prices,
the terms of trade and world output behaving consistently with the supply-shock
interpretation. In most periods, however, the correlation of the terms of trade,
oil and G-7 output is weak and ambiguous.
As one might expect, when the oil prices are less volatile the correlation of16

the terms of trade and oil prices falls considerably. This is evident when wecompare the variance decomposition of the terms of trade to that of the relative
price of oil. Table 4 shows that the G-7 terms of trade is not dominated by theworld component, though it remains considerable, at between 40 and 50 percent,depending on the terms of trade measure.
5.2. Monetary and …scal policy variables
Our goal is to capture periods of monetary and …scal expansion and contraction ineach country as well as the extent to which these policies are followed concurrently
across the G-7. What the dynamic factor model allows us to do is to extract thecommon dynamic component from the multiple observable measures of monetaryor …scal policy.
Formally, the model for …scal policy variables in country, i, can be written as:
3
2
3
2
2
3 2
3
" i;t
bi
Bi
i;t
4 ei;t 5 = 4 Bie 5 Ft + 4 bie 5 fi;t + 4 "ei;t 5
(5.1)
"gi;t
big
gi;t
Big

where
ei;t and gi;t are the growth rates of total revenue, total expenditurei;t ,and consumption by the national government of country i.
Thus we have three measures of …scal policy, each with a di¤erent amount of
information about the intentions of the …scal authority. Loosely speaking, if avariable contains a lot of information about …scal policy its factor loading, B orb, will be larger in absolute value, indicating that it reacts more to the changes in…scal policy. For example, it may be the case that a decision to change the thrustof …scal policy is largely carried out through changes in government revenues,
in this case the factor loading associated with revenues will be the highest (ourvariance decompositions give us more information on this). In the language of the
dynamic factor literature we are extracting a signal (here of …scal policy) fromthree measures of that signal.
The error terms ("’s) contain two components under this interpretation of thesignal extraction problem. One component is the noise component, which may beinterpreted as simply measurement error. The second component is the idiosyncratic movement in a particular variable that does not have an interpretation aschanges in broadly de…ned …scal policy but of targeted, sector speci…c changes, forexample, perhaps changes aimed to lessen income inequality (by lowering labortax rates and raising capital tax rates). We are unable to distinguish between thetwo interpretations of the error term.
17

For monetary policy we include a short-term real interest, ri;t , and a narrowmonetary aggregate, mi;t :
ri;t
mi;t

=

Bir
Bim

Ft +

bir
bim

fi;t +

"ir;t
"im;t

(5.2)

The short-term real interest rate is designed to capture changes in a variable targeted by the central bank. Of course, since we use market rates, much of thevariation will be due to supply and demand factors in each country and care must
be taken when we attempt to interpret movements in the context of monetary
policy discussions. The narrow monetary variable is included to incorporate thefact that central banks use monetary growth as an instrument as well. This may
take the form of medium term targeting of money growth with a particular in‡ation target in mind or some short term interaction of narrow monetary aggregates
and the setting of short-term interest rate targets.
Tables 5 and 6 contain the variance decompositions for the policy variables.
The most striking feature of these results is how di¤erent short-term interest rates
and monetary aggregates look through the lens of the factor model. Short term
real interest rates are dominated by a common G-7 component, with two-thirdsof the variance attributable to the common factor and almost none attributed to
the nation-speci…c component. Money growth, in contrast, is dominated by theidiosyncratic component though a sizable nation-speci…c variation is also found.
The large world component in short-term real interest rates has a number ofpossible interpretations. The most obvious interpretation is that …nancial markets
are highly integrated and capital mobility tends to drive the rate of return tocapital in the same direction internationally. This is good news for models thatfeature trade in bonds and physical capital mobility. A policy interpretationis also possible here, namely the desire to avoid either large short-term capital
movements or sharp exchange rate responses to uncoordinated movements in theinterest rate target across the G-7. Finally, the common factor could be picking up
the common factor in the business cycles of the G-7. Since business cycles tend to
be positively correlated across countries, it is natural to expect real interest rates
to share that correlation pattern too. The latter explanation is of particularinterest because the cyclicality of the real interest rate within individual countries
have been di¢ cult to establish. Therefore, to the extent we …nd one at the levelof G-7 countries, is encouraging.9
9Barro and Sal-i-Martin (1990) construct a world interest rate variable using a di¤erent
methodology and …nd it depends mostly on world factors.

18

That money growth lacks a large common component is not surprising given
the di¤erent in‡ationary histories of the countries in the cross-section. Somewhat
more surprising is the size of the idiosyncratic component. This could be due toshifts in money demand across near substitutes within a country and di¤erencesin the de…nitions of money across countries.
Figures 4 and 5 present the G-7 …scal and monetary factors, respectively,
alongside the G-7 business cycle factor. We see a dramatic swing in monetary
policy from stimulative in the 1970’s to contractionary in the late 1970s andparticularly the early 1980’s. This is consistent with the broad brush view thatmonetary growth and low nominal and real interest rates set the world economy
into a boom and in‡ationary spiral, followed by a concerted e¤ort by the U.S.
Federal Reserve and other central bankers to tame in‡ation. The very gradual
down-slope of the world monetary factor in the 1980’s and 1990’s is consistent
with the gradual disin‡ation and moderating real interest rate levels that were atleast partly a result of establishing central bank credibility on the in‡ation front.
The world …scal factor is sharply countercyclical in the …rst part of the sample,
most notable in the sharp recession of the early 1970’s. Later in the sample,
the correlation becomes ambiguous. The countercyclicality is likely due to thenormal evolution of tax revenue and non-discretionary spending over the cyclewith tax revenue falling and expenditure rising. The later period has some large
discretionary changes in tax rates, such as the Reagan and Thatcher tax cuts.
While tax cuts are unlikely to have a stimulative impact contemporaneously, they
may be responsible for a shift in the business cycle phase of …scal policy. We will
have more to say about this when we turn to rolling correlation analysis of theG-7 factors.

6. What drives international business cycles?
Up to now we have described the common and nation-speci…c components of national business cycles and the variables that business cycle theorists have proposed
as driving variables. What we would like to know is how much of a nation’s output
variation is generated by common and nation-speci…c sources of variation in eachof the driving variables.

196.1. Deconstructing the G-7 and national business cycle
The …rst step in undertaking this exercise, is to regress the common componentof the G-7 business cycle on the common G-7 components of each of the driving
factors:
FY;t = BM FM;t + BF FF;t + BO FO;t + BA FA;t + BT FT;t + "Y;t
By applying the variance operator to the both sides of this equation, we candecompose the variance of the estimated G-7 real business cycle into the partsdue to each of the driving variables plus an idiosyncratic component. In order toensure that the variance sums to one hundred, we …rst orthogonalize the factors
for each of the driving variables. Speci…cally, we orthogonalize the regressors by…rst regressing the second factor on the …rst factor, and retaining the residual
as the orthogonalized second factor. We proceed sequentially projecting factors
onto the orthogonalized factors until we have a set of 5 orthogonalized factors.
The order of orthogonalization we employ is the order the variables appear above:
monetary policy, …scal policy, oil prices, productivity and the terms of trade. Thisordering implies that we use the monetary factor as it is estimated by the factor
model and the orthogonal terms of trade factor is the part of the estimated factor
that is orthogonal to all other factors.
The result of this exercise suggests that productivity is the main driving variable for the common component of the business cycles among the G-7. In particular, this factor accounts for 47 percent of the ‡uctuations in the G-7 real factor
over the full sample period. The terms of trade factor accounts for less than 1.5
percent of the movements in the G-7 cycle, while oil, …scal and monetary factors
account for even less than one percent. A caveat to these results is that they
represent a decomposition of the unconditional variance over the whole period. It
is certainly plausible that some variables, such as oil, play an important role incertain sub-periods, as pointed out in section 5.1.
To complete our variance decomposition at the level of individual macroeconomic aggregates we need to also include the national speci…c components. To
accomplish this, we employ the procedure described above with one of the National Income and Product Accounts aggregates on the left hand side and either
the complete list of G-7 common factors (i.e., the common factor driving monetary policy, …scal policy, productivity, the terms of trade and oil across the G-7)
or complete list of the nation-speci…c driving variables on the right hand side.
It is important to note that while the factors are orthogonalized with respect toeach other in both the G-7 and nation-speci…c categories, these components need20

not have a zero covariance with each other. The nation-speci…c component of …scal policy may be correlated with the G-7 component of productivity, for example.
Thus, when we add up the contributions of the G-7 shocks and the nation-speci…cshocks, they need not add up to less than 100%. If these two factors are orthogonal, the result is a unique variance decomposition with only the idiosyncratic
factors left as a residual. In practice, the G-7 factors and nation-speci…c factor
have non-zero sample correlation so there are instances where some ambiguity
arises in assigning, say, the U.S. output ‡uctuations to the G-7 productivity factor versus the U.S. nation-speci…c monetary factor. The results suggest that thesum of the two variance decompositions is usually less than one hundred, andrarely much greater than one hundred. We interpret the results as being an upperbound on the variance contribution of the G-7 and nation-speci…c components.
We begin with the decomposition of output, reported in Table 7. Taken
together, the driving variables account for a substantial portion of the variationin output growth. The G-7 common factor on average explains a smaller share of
the variation than the nation-speci…c factors. Italy and Japan appear to be themost idiosyncratic with the national components of driving variables accounting
for more than 90 percent of the variation. Canada and the United States lie
at the other end of the distribution with a very signi…cant role for the common
components of the driving variables.
At …rst glance the results for France, Italy and Japan that the main driving
force of output in these countries is the nation-speci…c component seems at odds
with the results in section 4 that output ‡uctuations have a large G-7 component.
However, these results can be reconciled by …rst noticing that for these three
countries productivity has a small G-7 component but a large nation–speci…ccomponent. The latter component turns out to explain a large amount of output
variation. At the same time, our results above show that movements in the G7 productivity factor explain about 50 percent of the G-7 real factor. The G-7
component of movements in output in France, Italy and Japan are then due tothe 50 percent of the G-7 real cycle that remains unexplained.10
Turning to the individual driving variables, the columns are ordered by thefraction of output variance accounted for by the national component of the driving
variable. By this metric the most important driving variable, by far, is produc10

Recall also that the variance decomposition of the nation-speci…c and G7 components comefrom separate regressions and need not sum to one. It turns out that for France, Italy and Japanthe correlation between the country and G-7 factors is the largest, implying that the results forthese three countries must be somewhat less than the reported upper bounds.

21

tivity, followed by …scal factors and monetary factors. Oil prices and the terms oftrade play a very small role overall. For oil prices, it is the common component
that is slightly more important, which makes sense given the signi…cant role of
OPEC pricing decisions over the sample period we have.
To the extent that productivity movements re‡ect technological shifts, they
are not universally shared. The nation-speci…c component rivals the common G-7
component, each on average accounting for between 30 and 50 percent of output
growth. Variation in the contribution of the common factor in productivity inthe cross-section of countries is signi…cant, ranging from a low of 18 percent in
the United Kingdom to a high of 54 percent in Canada. Thus the importanceof the G-7 factors overall for Canada and the United States is a combination of
productivity shocks and the …scal factor.
Comparing monetary and …scal factors, the nation-speci…c component plays aslightly more important role in the case of monetary factors while the G-7 factor
tends to be more important in a few cases for …scal factors. We do not want tooverstate the di¤erences here because the absolute variances associated with them
are small and for most countries neither component plays a large role.
Table 7 reports the results for consumption growth. We see similar patterns
to what was found in our examination of output growth. In particular, taken
together, the G-7 and national components are both important and the productivity tends to dominate as a driving variable. Again, the nation-speci…c factors
are particularly strong in Italy and Japan while the G-7 factor is more relevantin Canada and the United States. The nation-speci…c monetary factors and theG-7 common …scal factor again account for a lower order of magnitude of businesscycles in consumption. While the role of oil is still marginal, the terms of tradeas a driving variable on average plays a slightly more important role in explaining
consumption than it does output. Given that consumption on average constitutes
two-thirds of aggregate output, the similarity of the output and consumption results is not altogether unexpected.
Table 7 also repeats the exercise for investment. Here a key di¤erence relative to earlier variables emerges, namely that nation-speci…c factor plays a much
more important role than the G-7 factor does when all of the driving variables are
considered together. In particular, the nation-speci…c productivity factor is much
more important than the G-7 productivity factor in explaining the investment
growth variation. This is consistent with the view that changes in the marginal
productivity of capital across countries is an important facet of investment dynamics in an integrated world economy. In the case of monetary and …scal policy
22variables, while the G-7 factor is more important than the nation-speci…c factors,
this results is mostly driven by a small set of countries. Neither oil price nor theterms of trade factor appears to matter in explaining investment ‡uctuations.
6.2. Toward a business cycle chronology
The seminal work by Friedman and Schwartz (1963) is most often associated withthe robust correlation between monetary events and the real business cycle. However, part of what distinguishes their work from modern business cycle research isthe attention to detail at the level of individual business cycles and even phases ofindividual business cycles. This allowed them to provide texture to the chronology, when monetary policy may have played a crucial role and when it was morepassive. Modern analysis typically reduces the business cycle to a set of moment
conditions, often without attention to possible shifts in the relationships among
endogenous and exogenous variables over time. A recent exception is the Great
Moderation literature which focuses on the falling business cycle volatility overthe most recent quarter century.
Here we draw inspiration from Friedman and Schwartz, but follow the modern
literature by characterizing the chronology of business cycles in terms of timeseries moments. We focus on the G-7 cycle. To accomplish this we computeten-year centered moving average correlations between the common G-7 businesscycle factor and the common G-7 components of each of the driving variables.
Figure 6 presents the results.
Since we are relating the common components to each other, a good starting
point is the correlation of the common real factor with aggregate G-7 output (notshown in Figure 6), which averages 0.76 over the period. Thus the common realfactor we extract from the G-7 NIPA aggregates is strongly correlated with theG-7 business cycle measured as a country-size weighted average of their output
series. The correlation is quite stable over time, rising from 0.71 to 0.80 as wemove from the …rst 10 year interval to the last (recall we lose 5 years of data at
each end point in the rolling correlation).
From here on we will use the term world business cycle to refer to the G-7
real factor. The correlation of the world business cycle and G-7 productivity is ahealthy 0.51, it falls only slightly from 0.56 to 0.46 as we move from about 1970
to 1995. Figure 6 shows the full time path of the rolling correlations. Note thatthe correlation of the other driving variables with the G-7 business cycle are both
lower and less stable over time.

23

The G-7 …scal factor, for example, is quite stable and negative over the …rst
part of the sample, it then jumps to about zero from the late 1980’s to the late1990’s, before falling back down toward the end of the sample. It is tempting tointerpret the earlier period as …scally passive in the sense of a tendency of tax
revenue to fall and expenditures to rise in the absence of legislative actions dueto the progressivity of the income tax, procyclicality of capital gains and pro…ttaxes and movements in non-discretionary spending, such as welfare payments
and unemployment assistance. The absence of a clear cyclical pattern to …scal
policy reported in many business cycle papers is consistent what we …nd toward
the end of the sample. The fact that the correlation is strikingly negative acrossthe world in the earlier period is important because it suggests a more importantrole for …scal policy in the past, which may have been overlooked in the existing
literature.
Monetary policy oscillates from a strongly positively correlated with the G-7
cycle to strongly negatively correlated. Broadly speaking, monetary policy appears to be accommodating in most periods except the early 1980’s, when central
bankers made concerted e¤orts to reduce in‡ationary trends, and in the mid1990’s which seems to match up with the increases in the discount rate during the
productivity and stock market boom.
The correlation of the oil price factor and the world business cycle moves from
-0.17 to 0.24 across the decades. While these averages are closer to zero thansome of the others, it is instructive to examine Figure 6 more carefully. We
see what appears to be a rising trend in the correlation with sharp reversals at
the dates of sharp increases in the relative price of oil. These patterns seembroadly consistent with a recent hypothesis concerning the relationship between
the business cycle and the relative price of oil. Some economists have argued thatthe relative importance of negative oil supply disruptions versus positive demand
shifts have changed signi…cantly over time. The conventional wisdom of sharp
exogenous increases due to supply disruption and OPEC pricing decisions seems
consistent with the negative correlation, a contractionary oil price increase. The
notion that sharply rising demand for energy by newly industrializing countries,
India and China prominent among them, would give rise to a positive correlation
to the extent the real growth spillovers to the G-7 are positive (which seems very
likely).
Examining the contribution of G-7 and nation-speci…c movements in the driving
variables over time and in particular business cycle episodes is an important areafor future research. The broad correlations outlined here are suggestive of some24

of the themes that could emerge from such an examination.

7. Conclusion
We have studied the time series properties of the key driving variables that often
appear in international business cycle models: productivity, monetary policy variables, …scal policy variables, oil prices and the terms of trade. In particular, we
employ dynamic factor models to estimate the common and nation-speci…c factors in each of these driving variables. We documented the role of a G-7 common
factor in each of these variables and found that the common factor is very dominant for oil prices, considerable for productivity, interest rates targeted by central
banks, and the terms of trade, but of minor importance for monetary aggregatesand …scal balance sheet items (such as total expenditure).
There has been much interest in the extent to which there is an international
business cycle in macroeconomic aggregates such as output, consumption andinvestment. We con…rm previous …ndings that such a cycle does indeed exist. We
then take the next step and …nd the source of the international business cycle tobe primarily driven by productivity, though we are only able to explain roughly
half of the variation in the G-7 cycle. A visual inspection of the international
cycle and the driving variables shows that in some episodes oil prices move withthe cycle, but this relationship has changed over time.
Turning to individual countries, our …ndings suggest that the common G-7
business cycle is important for the evolution of most macroeconomic aggregates
and the driving variables of business cycles, including policy variables. Despite
the signi…cance of the common G-7 component in many of these variables, mostappear to play a relatively minor role in explaining aggregate real business cycle‡uctuations, with the exception of productivity.
We believe that future work would bene…t from developing a chronology ofbusiness cycles along the lines of Friedman and Schwartz and Burns and Mitchell.
This could be done at the level of the world business cycle and nation-speci…cvariations from the common component. Such an exercise would likely bring
important nuances to individual business cycle episodes as well as policy responses
to di¤erent causal factors than it possible with the …rst pass we have attempted
here.

Statistical appendix
Bayesian estimation of dynamic factor models
25This appendix reviews the methodology used in estimating the dynamic factor
model. The model here is a multi-factor extension of the single dynamic unobserved factor model in Otrok and Whiteman (1998). Kose, Otrok, and Whiteman(2003) also employ a similar multi-factor model in an exercise studying International business cycles. Since they provide a detailed discussion of the multi-factor
model, this section is brief and closely follows the description in that paper.
Our interest in estimating the dynamic factor model is to characterize thejoint posterior of the model parameters and latent factors. Since analytic forms
for the joint posterior of the factors and parameters are unobtainable, we employ
numerical methods to simulate from the posterior. To do so we use a “dataaugmentation” algorithm to generate draws from the joint posterior of interest(see Tanner and Wong, 1987; Otrok and Whiteman, 1998). Data augmentation inthis context builds on the following key observation: if the factors were observable,
under a conjugate prior, the factor models we estimate would each constitute a
simple set of regressions with Gaussian autoregressive errors. Then, conditionalon the regression parameters and the data, one can determine the conditional
distribution of the factors. It is straightforward to generate random samples fromthis conditional distribution, and such samples can be employed as stand-ins forthe unobserved factors.
To be more speci…c, the dynamic factor models can be thought of as consistingof a speci…cation of a Gaussian probability density for the data fyt g conditionalon a set of parameters
and a set of latent variables fft g. Call this density function gy (Y j ; F ) where Y denotes the vector of data on the observable data, and F denotes the vector of dynamic factors. In addition, there isa speci…cation of a Gaussian probability density gf (F ) for F itself. Given aprior distribution for , ( ), the joint posterior distribution for the parameters and the latent variables is given by the product of the likelihood and prior,h( ; F jY ) = gy (Y j ; F )gf (F ) ( ). As is shown in Otrok and Whiteman (1998),
although the joint posterior h( ; F jY ) is extremely cumbersome, under a conjugate prior for the two conditional densities h( jF; Y ) and h(F j ; Y ) are quite
simple. Moreover, it is possible to use this fact and Markov-Chain Monte Carlo
methods (MCMC) to generate an arti…cial sample f j ; Fj g for j = 1; : : : ; J as
follows:
1. Starting from a value F0 in the support of the posterior distribution for F ,generate a random drawing 1 from the conditional density h( jF0 ; Y ).
2. Now generate a random drawing F1 from the conditional density h(F j 1 ; Y ).
3. This process is repeated, generating at each step drawings j ~h( jFj 1 ; Y )26

and Fj ~h(F j j 1 ; Y ).
Under regularity conditions satis…ed here (see Tanner and Wong, 1987), thesample so produced is a realization of a Markov chain whose invariant distribution
is the joint posterior h( ; F jY ). What makes this process feasible is the simplicityof the two conditional distributions. For example, h( jF; Y ) is easily constructedfrom the linear factor model when F is known. In particular, the linear factor
model is just a normal linear regression model for yi given the factors (albeit a
regression that has autocorrelated errors that requires the use of the procedure in
Chib and Greenberg, 1994, to simulate from the posterior). The other conditional
density, h(F j ; Y ) is a little more complicated because it is the solution to a
Gaussian signal extraction problem. Otrok and Whiteman (1998) derive this
distribution, which turns out to be a Normal distribution.
The prior on all the factor loading coe¢ cients is N (0; 10), which is quite di¤use.
For2the parameters3 of autoregressive polynomials, the prior is N (0; ), where
1 0
0=4 0 0:5 0 5 . Because the data are growth rates, this prior embodies
0 0 0:25
the notion that growth is not serially correlated though the prior is loose enoughto allow for signi…cant serial correlation; also, the probability that lags are zero
grows with the length of the lag.11 Experimentation with tighter and looser priors
for both the factor loadings and the autoregressive parameters did not produce
qualitatively important changes in the results reported below. The prior on theinnovation variances in the observable equations is Inverted Gamma (6; 0:001),
which is also quite di¤use.
Variance decompositions
To measure the relative contributions of the G-7, nation-, and variable-speci…cfactors to variations in aggregate variables in each country, we estimate the shareof the variance of each macroeconomic aggregate due to each factor. In particular,
we decompose the variance of each observable into the fraction that is due to eachof the two factors and the variable-speci…c component. With orthogonal factors
the variance of observable i can be written:
var(yi;t ) = (biG 7 )2 var(ftG 7 ) + (bnation)2 var(ftnation ) + var("i;t )i
11Otrok and Whiteman (1998) discuss the procedure for ensuring stationarity of the lag polynomial. The method involves drawing from a truncated Normal distribution in the MetropolisHastings step.

27

The fraction of volatility due to, say, the G-7 factor would be:
7 2(bG) var(ftG 7 )ivar(yi;t )These measures are calculated at each pass of the Markov chain; dispersion in
their posterior distributions re‡ects uncertainty regarding their magnitudes.

28

References[1] Ahmed, Shagil, Barry W. Ickes, Ping Wang and Byung Sam Yoo, 1993.
International business cycles. American Economic Review 83(3), 335:359.
[2] Ambler, Steve, Emanuela Cardia and Christian Zimmermann, 2002. International transmission of the business cycle in a multi-sector model. European
Economic Review 46(2), 273-300.
[3] Backus, David and Mario J. Crucini, 2000. Oil prices and the terms of trade.
Journal of International Economics 50(1), 185-212.
[4] Backus, David K., Patrick J. Kehoe and Finn E. Kydland, 1992. International
real business cycles. Journal of Political Economy 100, 745-75.
[5] Barro Robert and Xavier Sali-i-Martin, 1990. World real interest rates. National Bureau of Economic Research Working Paper No. 3317, April.
[6] Baxter, Marianne and Mario J. Crucini, 1995. Business cycles and the asset
structure of foreign trade. International Economic Review 36(4), 821-854.
[7] Bernanke, Ben S., Jean Boivin, and Piotr, Eliasz, 2005. Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR)
approach. Quarterly Journal of Economics 120 (1), 387-422.
[8] Crucini, Mario J., 1997. Country size and economic ‡uctuations. Review ofInternational Economics 5 (2), 204-220.
[9] Forni, Mario, and Lucrezia Reichlin, 1998. Let’s get real: a factor analytic
approach to business cycle dynamics. Review of Economic Studies 65, 453473.
[10] Friedman, Milton and Anna Jacobson Schwartz, 1963. A monetary historyof the United States, 1867-1960. Princeton: Princeton University Press.
[11] Glick, Reuven. and Kenneth Rogo¤, 1995. Global versus country-speci…c productivity shocks and the current account. Journal of Monetary Economics
35(1), 159-192.
[12] Gregory, Allan W., and Allen Head, 1999. Common and country-speci…c‡uctuations in productivity, investment, and the current account. Journal of
Monetary Economics 44(3), 423-451.
29

[13] Gregory, Allan W., Allen Head and Jean Raynauld, 1997. Measuring world
business cycles. International Economic Review 38, 667-702.
[14] Heston, Alan, Robert Summers and Bettina Aten, 2006. Penn World Table
Version 6.2, Center for International Comparisons of Production, Income andPrices at the University of Pennsylvania, September.
[15] Klenow, Peter J. and Andres Rodriuez-Clare, 2005. Externalities and growth.
Handbook of Economic Growth, Philippe Aghion and Steven Durlauf, editors. The Netherlands: Elsevier Science, 817-861.
[16] Kose, Ayhan, Christopher Otrok and Charles H. Whiteman, 2003. International business cycles: world, region, and country-speci…c factors. American
Economic Review 93(4), 1216-1239.
[17] Kose, Ayhan, Christopher Otrok and Charles H. Whiteman, “Understanding
the evolution of world business cycles,” Journal of International Economics,
Volume 75, Issue 1, May 2008, Pages 110-130.
[18] Long, John B, Jr and Charles I. Plosser, 1983. Real business cycles. Journalof Political Economy 91(1), 39-69.
[19] Otrok, Christopher and Charles H. Whiteman, 1998. Bayesian leading indicators: measuring and predicting economic conditions in Iowa. International
Economic Review 39(4), 997-1014.
[20] Sargent, Thomas J., 1989. Two models of measurements and the investment
accelerator. Journal of Political Economy 97(2), 251-287[21] Tanner, A.M., Wong, H.W. (1987), The calculation of posterior distributions
by data augmentation. Journal of the American Statistical Association 82(398), 84-88.

30

Figure 1. Three views of the world business cycle.

Figure 2. The G-7 business cycle factor and G-7 productivity.

31

Figure 3. The G-7 business cycle factor, G-7 terms of trade and G-7 relative oil price.

Figure 4. The G-7 business cycle factor and the common G-7 …scal factor.

32

Figure 5. The G-7 business cycle factor and the common G-7 monetary factor.

Figure 6. 10 year rolling correlations between the G-7 business cycle factor andthe common factors of each of the driving variables.

33

Table 1. Variance Decompositions for Macroeconomic Variables
Country

Factor33%

Output
50%

66%

33%

Consumption
50%
66%

33%

Investment
50%

66%

CanadaG-7Nation-SpecificVariable-Specific

33.50
49.51
10.19

35.91
52.32
11.67

38.43
54.92
13.20

17.61
66.36
9.64

19.57
68.76
11.45

21.46
71.39
13.20

5.17
53.77
34.80

6.55
56.38
36.88

8.05
58.93
38.84

FranceG-7
Nation-SpecificVariable-Specific

77.21
10.51
5.28

79.98
13.37
6.59

82.68
16.30
7.90

51.11
16.16
18.17

56.15
22.30
20.83

61.09
29.65
23.00

51.24
12.89
26.44

54.32
16.68
28.74

57.57
20.81
30.69

Germany

G-7
Nation-SpecificVariable-Specific

45.73
38.66
6.72

48.97
42.31
8.34

52.26
45.95
10.02

30.71
38.58
22.77

33.37
41.88
24.91

35.67
45.32
27.09

19.11
51.96
20.67

21.64
55.50
22.84

24.35
59.12
24.90

Italy

G-7
Nation-SpecificVariable-Specific

70.15
10.48
10.28

73.98
13.83
12.00

77.53
17.00
13.70

60.28
13.14
15.64

64.91
17.73
17.29

69.36
22.43
18.94

28.20
28.90
30.75

31.45
35.09
33.92

34.66
40.40
37.35

Japan

G-7
Nation-SpecificVariable-Specific

54.83
36.52
1.85

57.96
39.64
2.24

61.16
42.77
2.71

48.26
32.62
10.96

52.04
36.27
11.62

55.64
39.81
12.33

51.60
37.42
4.27

54.82
40.26
4.84

57.74
43.59
5.39

UK

G-7
Nation-SpecificVariable-Specific

12.05
69.48
10.35

13.99
72.86
12.79

15.96
76.02
15.76

2.52
63.97
26.72

3.36
66.87
29.64

4.28
69.98
32.29

9.58
40.58
43.01

11.45
43.30
45.11

13.15
46.12
47.30

US

G-7
Nation-SpecificVariable-Specific

13.87
76.96
3.38

15.89
79.40
4.35

17.90
81.74
5.45

10.03
61.39
22.98

12.02
63.76
24.13

14.03
66.06
25.21

3.58
80.24
12.04

4.74
81.99
13.35

5.99
83.69
14.53

AVERAGE

G-7
Nation-SpecificVariable-Specific

46.67
44.82
8.28

34.49
45.37
19.98

26.42
47.03
26.53

MEDIAN

G-7
Nation-SpecificVariable-Specific

52.26
45.95
10.02

35.67
45.32
23.00

24.35
46.12
30.69

34

Table 2. Variance Decompositions for Productivity Measures
KRC1
KRC2
OECD

BLS

Country Factor

33%

50%

66%

33%

50%

66%

33%

50%

66%

33%

50%

66%

CanadaG-7Nation-SpecificVariable-Specific

34.05
43.57
0.74

47.23
51.69
0.88

55.32
65.02
1.04

33.22
44.22
0.80

46.55
52.27
0.95

54.61
65.55
1.12

61.48
10.06
14.20

69.33
14.84
15.48

74.31
24.16
16.56

62.77
2.08
21.07

70.57
4.69
23.51

76.49
11.86
25.97

FranceG-7
Nation-SpecificVariable-Specific

25.94
68.71
0.67

27.93
71.04
0.79

30.25
73.10
0.95

27.34
67.31
0.65

29.42
69.54
0.78

31.67
71.65
0.94

35.62
33.58
19.97

40.93
37.59
21.61

46.73
41.46
22.92

35.07
19.78
37.23

38.87
22.52
38.89

43.04
24.94
40.20

Germany

G-7
Nation-SpecificVariable-Specific

9.04
46.15
32.76

10.82
51.22
37.21

12.88
56.45
42.16

13.86
39.63
35.69

15.95
44.20
39.11

18.59
48.48
42.57

45.25
16.25
22.12

49.92
20.86
25.41

57.42
25.54
29.21

43.29
13.93
29.65

47.72
17.91
32.37

52.76
22.21
35.39

Italy

G-7
Nation-SpecificVariable-Specific

13.82
81.46
0.11

16.23
83.61
0.13

18.35
86.04
0.16

13.34
82.04
0.11

15.70
84.12
0.14

17.79
86.51
0.17

28.04
49.04
15.55

31.80
52.18
16.16

35.63
55.49
16.73

25.95
36.24
30.46

29.58
39.31
31.45

33.77
42.10
32.19

Japan

G-7
Nation-SpecificVariable-Specific

13.55
79.52
0.32

16.10
83.34
0.39

19.86
85.97
0.48

12.98
79.96
0.45

15.55
83.74
0.52

19.13
86.43
0.63

16.53
63.17
9.84

20.74
69.07
10.36

27.03
72.82
10.78

12.17
61.91
17.93

15.00
66.74
18.28

19.97
69.55
18.56

UK

G-7
Nation-SpecificVariable-Specific

27.36
63.08
1.06

31.70
66.84
1.25

35.46
71.22
1.48

22.04
68.77
0.99

26.31
72.39
1.20

29.91
76.62
1.44

21.02
44.07
29.78

23.36
46.40
30.30

25.72
48.83
30.80

29.07
19.88
45.34

31.45
21.89
46.48

33.65
24.19
47.53

US

G-7
Nation-SpecificVariable-Specific

34.00
43.54
5.30

43.26
50.34
6.08

49.83
59.61
6.91

44.60
34.11
3.46

55.11
40.95
4.02

61.65
51.07
4.64

38.25
34.15
12.68

47.25
39.73
13.45

52.53
48.24
14.22

25.12
20.30
39.03

33.16
26.45
40.02

39.40
34.63
41.04

AVERAGE G-7
Nation-SpecificVariable-Specific

27.61
65.44
6.68

29.23
63.89
6.67

40.48
40.10
18.97

38.05
28.50
33.00

MEDIAN

27.93
66.84
0.88

26.31
69.54
0.95

40.93
39.73
16.16

33.16
22.52
32.37

G-7
Nation-SpecificVariable-Specific35Table 3. Variance Decompositions for Measures of Oil Prices
Average
Dubai
Brent

West Texas

Country Factor

33%

50%

66%

33%

50%

66%

33%

50%

66%

33%

50%

66%

CanadaG-7Nation-SpecificVariable-Specific

88.23
6.83
0.03

89.31
10.67
0.04

93.14
11.75
0.05

89.65
4.68
1.13

90.53
8.30
1.15

94.22
9.20
1.17

86.75
5.89
3.37

87.91
8.72
3.40

90.70
9.86
3.43

85.80
8.45
0.03

86.98
12.98
0.05

91.49
14.15
0.06

FranceG-7
Nation-SpecificVariable-Specific

88.98
5.40
0.02

89.76
10.23
0.03

94.59
10.98
0.04

89.25
4.39
1.02

90.06
8.89
1.03

94.60
9.69
1.05

86.97
5.04
3.13

87.72
9.14
3.15

91.81
9.87
3.17

86.53
7.13
0.02

87.37
12.61
0.04

92.86
13.44
0.05

Germany

G-7
Nation-SpecificVariable-Specific

89.20
5.29
0.02

89.99
10.00
0.03

94.71
10.78
0.05

90.06
3.81
0.96

90.85
8.13
0.99

95.23
8.91
1.02

86.94
5.18
3.15

87.68
9.14
3.17

91.63
9.89
3.19

86.68
7.03
0.02

87.56
12.42
0.04

92.94
13.28
0.05

Italy

G-7
Nation-SpecificVariable-Specific

89.34
5.31
0.02

89.99
9.99
0.03

94.67
10.64
0.05

89.71
4.16
1.10

90.36
8.51
1.12

94.73
9.13
1.15

87.22
4.91
3.29

87.97
8.73
3.31

91.77
9.46
3.33

86.88
7.04
0.02

87.60
12.37
0.04

92.94
13.09
0.05

Japan

G-7
Nation-SpecificVariable-Specific

85.09
9.42
0.03

86.25
13.72
0.04

90.53
14.86
0.05

87.32
6.73
0.90

88.40
10.69
0.93

92.41
11.77
0.95

81.94
10.73
2.98

83.08
13.87
3.02

86.33
15.03
3.06

82.70
11.05
0.03

83.95
16.00
0.05

88.88
17.24
0.07

UK

G-7
Nation-SpecificVariable-Specific

88.63
5.56
0.02

89.45
10.54
0.04

94.42
11.34
0.05

89.41
3.98
1.16

90.23
8.55
1.19

94.88
9.37
1.21

87.19
4.45
3.38

87.99
8.62
3.41

92.14
9.39
3.43

86.05
7.36
0.03

86.94
13.04
0.04

92.61
13.92
0.05

US

G-7
Nation-SpecificVariable-Specific

86.97
7.38
0.03

88.10
11.88
0.04

92.59
13.01
0.05

88.45
5.20
1.12

89.43
9.44
1.15

93.70
10.39
1.17

85.25
6.36
3.35

86.44
10.19
3.38

90.28
11.37
3.40

84.35
9.20
0.03

85.58
14.40
0.04

90.76
15.61
0.06

AVERAGE G-7
Nation-SpecificVariable-Specific

88.98
11.00
0.04

89.98
8.93
1.08

86.97
9.77
3.26

86.57
13.40
0.04

MEDIAN

89.45
10.54
0.04

90.23
8.55
1.12

87.72
9.14
3.31

86.98
12.98
0.04

G-7
Nation-SpecificVariable-Specific36Table 4. Variance Decompositions for Measures of Terms of Trade
Country

Factor

33%

TOT1
50%

66%

33%

TOT2
50%

66%

CanadaG-7Nation-SpecificVariable-Specific

30.28
32.90
24.59

32.28
37.62
29.71

34.32
43.02
34.37

6.70
47.08
31.39

7.63
53.98
38.17

8.70
60.65
45.25

FranceG-7
Nation-SpecificVariable-Specific

70.76
5.67
14.21

73.25
9.16
17.52

75.83
12.49
20.28

68.04
5.76
16.85

70.50
9.02
20.53

72.89
12.81
23.25

Germany

G-7
Nation-SpecificVariable-Specific

42.48
22.10
21.22

44.75
28.39
26.90

47.07
33.93
33.03

64.65
6.43
21.73

66.59
8.69
24.55

68.40
11.61
26.85

Italy

G-7
Nation-SpecificVariable-Specific

37.43
38.65
12.44

39.83
43.61
16.41

42.24
48.32
20.56

75.56
9.79
8.18

77.76
11.74
10.04

80.15
13.79
11.73

Japan

G-7
Nation-SpecificVariable-Specific

56.29
34.36
3.30

58.50
36.60
4.53

60.69
39.06
5.82

57.35
31.91
5.31

59.43
34.30
6.57

61.61
36.54
7.63

UK

G-7
Nation-SpecificVariable-Specific

8.62
48.78
29.55

10.02
54.05
35.57

11.52
60.24
41.08

14.97
46.00
26.39

16.44
51.46
31.70

18.09
57.06
37.07

US

G-7
Nation-SpecificVariable-Specific

36.81
47.58
8.62

38.94
50.50
10.74

40.89
53.26
12.81

49.38
37.52
6.64

51.35
39.99
8.43

53.30
42.46
10.36

AVERAGE

G-7
Nation-SpecificVariable-Specific

42.51
37.13
20.20

49.96
29.88
20.00

MEDIAN

G-7
Nation-SpecificVariable-Specific

39.83
37.62
17.52

59.43
34.30
20.53

37

Table 5. Variance Decompositions for Measures of Monetary Policies
Country

FactorShort-Term Real Interest Rates
33%
50%
66%

33%

Money Supply
50%
66%

CanadaG-7Nation-SpecificVariable-Specific

79.23
0.47
12.76

81.40
1.29
15.44

83.41
3.45
17.82

3.90
11.85
45.44

4.90
27.73
66.88

5.93
49.48
83.37

FranceG-7
Nation-SpecificVariable-Specific

65.49
2.03
19.60

68.16
5.36
23.87

70.94
10.48
27.53

1.05
3.10
76.24

1.61
8.80
89.05

2.21
22.06
94.77

Germany

G-7
Nation-SpecificVariable-Specific

32.38
2.77
49.46

34.47
6.49
56.48

36.69
14.73
60.96

1.12
10.50
45.04

1.63
27.60
70.73

2.19
52.88
87.50

Italy

G-7
Nation-SpecificVariable-Specific

64.84
10.58
15.24

67.23
13.66
18.38

69.46
17.35
21.39

0.38
34.74
42.67

0.78
44.73
54.31

1.32
56.38
64.27

Japan

G-7
Nation-SpecificVariable-Specific

44.19
9.56
33.82

46.41
14.03
38.90

48.58
19.41
43.41

13.93
21.96
43.80

15.53
31.02
53.33

17.17
40.59
62.20

UK

G-7
Nation-SpecificVariable-Specific

63.70
3.37
23.29

66.25
5.54
26.95

68.50
9.04
30.08

3.78
24.73
36.38

4.62
41.78
53.60

5.57
58.87
70.98

US

G-7
Nation-SpecificVariable-Specific

48.88
2.82
35.13

51.76
5.76
39.91

54.69
10.55
44.03

1.58
8.49
62.76

2.15
20.53
77.47

2.77
35.07
88.97

AVERAGE

G-7
Nation-SpecificVariable-Specific

59.38
7.45
31.42

4.46
28.89
66.48

MEDIAN

G-7
Nation-SpecificVariable-Specific

66.25
5.76
26.95

2.15
27.73
66.88

38

Table 6. Variance Decompositions for Measures of Fiscal Policies
Country

FactorGovernment Consumption
33%
50%
66%

Government Expenditure
33%
50%
66%

Government Revenue
33%
50%
66%

CanadaG-7Nation-SpecificVariable-Specific

12.28
10.62
62.57

14.94
15.32
68.58

17.97
20.36
73.83

0.31
41.46
39.36

0.74
50.43
48.32

1.40
59.41
57.00

11.57
21.46
46.82

14.77
28.00
55.52

18.23
35.74
63.17

FranceG-7
Nation-SpecificVariable-Specific

16.71
16.55
44.92

21.01
23.37
54.41

25.47
32.72
61.45

18.49
20.88
38.37

21.49
29.41
49.02

24.59
39.37
57.41

0.80
0.42
94.56

1.65
1.04
96.19

2.84
2.22
97.44

Germany

G-7
Nation-SpecificVariable-Specific

4.03
25.23
45.31

5.80
34.67
57.63

7.98
47.54
67.22

16.44
0.81
70.48

20.20
1.99
74.96

24.26
4.60
78.98

3.05
28.16
41.01

4.35
39.89
55.25

5.83
53.74
67.03

Italy

G-7
Nation-SpecificVariable-Specific

5.89
1.63
78.57

8.58
4.03
84.85

11.78
9.02
88.67

34.30
11.12
31.58

38.52
19.44
40.37

42.73
28.69
48.46

3.09
5.59
77.23

4.73
10.80
82.83

6.78
17.66
87.03

Japan

G-7
Nation-SpecificVariable-Specific

0.87
2.47
76.28

1.68
7.18
89.80

2.73
21.16
94.83

1.40
4.80
60.58

2.62
15.33
80.79

4.34
35.54
90.67

1.20
0.38
93.38

2.15
0.99
95.51

3.49
2.28
97.26

UK

G-7
Nation-SpecificVariable-Specific

27.89
13.60
41.39

32.88
19.84
46.20

38.09
26.18
50.57

22.88
31.35
25.94

27.25
39.53
32.43

32.18
47.28
38.42

0.15
12.32
76.02

0.35
17.13
82.27

0.73
23.27
86.95

US

G-7
Nation-SpecificVariable-Specific

0.41
54.72
32.30

0.95
60.36
37.89

1.90
65.97
43.31

3.76
51.59
29.01

6.23
57.53
34.53

9.21
63.14
40.20

38.93
1.74
44.71

44.23
3.48
50.73

49.55
5.90
56.69

AVERAGE

G-7
Nation-SpecificVariable-Specific

12.26
23.54
62.77

16.72
30.52
51.49

10.32
14.47
74.04

MEDIAN

G-7
Nation-SpecificVariable-Specific

8.58
19.84
57.63

20.20
29.41
48.32

4.35
10.80
82.27

39

Table 7. Variance Decompositions for Macroeconomic Variables
OutputCanadaFranceGermany
Italy
Japan
UK
US
AVERAGEMEDIAN

Productivity
G-7
National
53.84
10.42
40.13
78.84
35.69
15.87
20.15
86.20
25.74
80.29
18.11
43.70
38.43
24.45
33.16
48.54
35.69
43.70

Fiscal Policy
G-7
National
19.54
0.88
1.34
0.46
1.94
14.54
4.90
0.96
0.00
0.91
9.44
5.12
25.71
2.91
8.98
3.68
4.90
0.96

Monetary Policy
G-7
National
0.04
0.02
2.66
0.02
8.50
0.53
1.11
0.00
4.71
10.17
7.15
24.25
4.06
6.38
4.03
5.91
4.06
0.53

Oil Price
G-7
National
0.15
0.28
0.28
0.97
0.00
0.01
3.05
4.98
1.84
0.21
3.23
0.00
3.10
0.21
1.66
0.95
1.84
0.21

Terms of Trade
G-7
National
0.39
0.07
0.12
0.45
0.87
0.01
1.48
0.17
0.24
0.00
9.45
0.27
2.41
1.31
2.14
0.32
0.87
0.17

Total
G-7
National
73.95
11.66
44.53
80.73
47.00
30.95
30.69
92.32
32.52
91.58
47.38
73.34
73.71
35.25
49.97
59.40
47.00
73.34

Oil Price
G-7
National
0.05
0.20
2.56
0.48
1.04
0.30
0.07
0.55
1.26
0.04
1.85
0.32
8.84
0.21
2.24
0.30
1.26
0.30

Terms of Trade
G-7
National
2.30
1.62
3.51
2.30
1.54
5.83
0.29
0.01
1.23
0.34
13.61
1.40
8.77
0.30
4.46
1.69
2.30
1.40

Total
G-7
National
57.86
13.32
35.89
63.62
38.39
27.35
13.65
69.07
31.86
77.54
27.82
67.04
76.27
35.23
40.25
50.45
35.89
63.62

Oil Price
G-7
National
0.21
1.04
0.59
0.05
1.15
0.35
1.69
0.24
1.74
0.20
0.46
0.03
1.35
0.04
1.03
0.28
1.15
0.20

Terms of Trade
G-7
National
0.43
1.61
0.01
3.19
0.06
0.40
0.29
3.80
0.04
0.21
1.71
0.25
2.09
2.24
0.66
1.67
0.29
1.61

Total
G-7
National
28.24
34.16
27.30
77.54
32.69
31.82
5.34
58.77
30.36
91.89
22.60
42.47
62.65
39.45
29.88
53.73
28.24
42.47

Consumption

CanadaFranceGermany
Italy
Japan
UK
US
AVERAGEMEDIAN

Productivity
G-7
National
39.51
8.93
29.74
60.25
31.03
3.86
11.18
67.79
25.31
65.02
4.23
35.24
42.60
12.20
26.23
36.18
29.74
35.24

Fiscal Policy
G-7
National
12.67
1.06
0.05
0.00
1.06
14.75
0.67
0.66
0.00
2.70
0.67
0.68
11.26
3.90
3.77
3.39
0.67
1.06

Monetary Policy
G-7
National
3.33
1.52
0.02
0.58
3.72
2.60
1.44
0.06
4.07
9.44
7.47
29.40
4.79
18.63
3.55
8.89
3.72
2.60

Investment

CanadaFranceGermany
Italy
Japan
UK
US
AVERAGEMEDIAN

Productivity
G-7
National
7.90
29.29
17.40
71.63
17.34
12.40
0.50
54.05
18.63
75.75
7.54
27.60
24.29
31.68
13.37
43.20
17.34
31.68

Fiscal Policy
G-7
National
16.45
1.66
3.55
1.92
0.26
15.00
1.22
0.00
0.01
1.88
2.72
3.11
32.12
0.05
8.05
3.37
2.72
1.88

Monetary Policy
G-7
National
3.25
0.55
5.76
0.74
13.88
3.68
1.63
0.68
9.95
13.84
10.17
11.47
2.80
5.44
6.78
5.20
5.76
3.68

40