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Federal Reserve Bank of Chicago

Can Structural Small Open Economy
Models Account for the Influence of
Foreign Disturbances?
Alejandro Justiniano and Bruce Preston

WP 2009-19

Can Structural Small Open Economy Models Account for the
In‡uence of Foreign Disturbances?
Alejandro Justinianoy

Bruce Prestonz

November 30, 2009

Abstract
This paper demonstrates that an estimated, structural, small open-economy model of
the Canadian economy cannot account for the substantial in‡uence of foreign-sourced disturbances identi…ed in numerous reduced-form studies. The benchmark model assumes
uncorrelated shocks across countries and implies that U.S. shocks account for less than
3 percent of the variability observed in several Canadian series, at all forecast horizons.
Accordingly, model-implied cross-correlation functions between Canada and U.S. are essentially zero. Both …ndings are at odds with the data. A speci…cation that assumes
correlated cross-country shocks partially resolves this discrepancy, but still falls well short
of matching reduced-form evidence.

First Version: 2005. We are grateful to Gunter Coenen, Charles Engel, Jordi Gali, Paulo Giordani, Thomas
Lubik, Adrian Pagan, Giorgio Primiceri and two anonymous referees for discussions and detailed comments.
We also thank seminar participants at the Federal Reserve Bank of Atlanta, Federal Reserve Bank of Chicago,
Board of Governors of the Federal Reserve, Federal Reserve Bank of Cleveland Conference on “DSGE and
Factor Models”, Duke University conference on “Identi…cation and estimation of structural models”, the joint
ECB, Lowy Institute and CAMA conference on “Globalization and Regionalism”, Reserve Bank of Australia,
The Riksbank conference on “Structural Analysis of Business Cycles in the Open Economy” and University
of Washington. Preston thanks the PER Seed Grant at Columbia University for …nancial support. The usual
caveat applies. The views expressed in this paper are those of the authors’ and should not be interpreted as
re‡ecting the views of the Federal Reserve Bank of Chicago or any other person associated with the Federal
Reserve system.
y
Federal Reserve Bank of Chicago, Research Department, 230 South La Salle St., Chicago, IL 60604. E-mail:
ajustiniano@frbchi.org
z
Department of Economics, Columbia University, 420 West 118th St, New York NY 10027 and CAMA,
Australian National University. E-mail: bp2121@columbia.edu.

1

1

Introduction

This paper investigates whether an estimated microfounded semi-small open-economy model
can reproduce the observed comovements in international business cycles. Focusing on Canada
as the semi-small open economy, the starting point for the analysis is the large body of
empirical work that identi…es a signi…cant in‡uence of U.S. shocks on Canadian economic
‡uctuations.
There has been ample theoretical work seeking to replicate the observed comovements in
economic activity across countries. Until recently, the empirical validation of these models
largely relied on calibrations aimed at matching selected moments in the data — see the contributions of Backus et al. (1992, 1995), Stockman and Tesar (1995) and Baxter (1995) for
a review. The New Open Economy Macroeconomics (NOEM) has since produced signi…cant
theoretical advancements in international macroeconomic modeling. Given the empirical success of closed-economy models built on similar foundations, it is not surprising that there is
a growing literature estimating NOEM models. These include amongst others: Ambler et
al. (2003), Bergin (2003, 2004), Del Negro (2003), Ghironi (2000), Justiniano and Preston
(2008b), Lubik and Schorfheide (2003, 2005), Lubik and Teo (2005) and Rabanal and Tuesta
(2005).
To our knowledge, the ability of these NOEM models to explain the observed comovement
in economic ‡uctuations has not been previously systematically analyzed in this empirical
literature. This paper …lls this gap by evaluating a workhorse semi-small NOEM model in
this particular dimension. The focal point is the model’s ability to replicate the fraction of
the variance in Canadian macroeconomic series attributed to U.S. shocks. We also contrast
the cross-country correlation functions in the model and data, particularly for output.
The analysis is pursued using generalizations of the small open-economy framework proposed by Gali and Monacelli (2005).1 Following Monacelli (2005), we allow for deviations from
the law of one price. In addition, we consider incomplete asset markets, a large set of disturbances, and incorporate other real and nominal rigidities (e.g., wage stickiness, indexation
and habits) which have been found crucial in …tting closed-economy models as documented
by Christiano et al. (2005) and Smets and Wouters (2007).
The model is estimated using Bayesian methods with data for Canada and the United
1

The model is technically a semi-small open economy model, where domestic goods producers have some
market power, but we shall nonetheless refer to it as a small open economy. Note also that our analysis appeals
to an earlier interpretation in Gali and Monacelli (2005) of a small-large country pair, rather than as an analysis
of a continuum of small open economies.

1

States. Our baseline speci…cation assumes that shocks across these two countries are independent. This contrasts with much of the international real business cycle literature which often
assumes correlated cross-country technology shocks, but is consistent with all of the empirical
NOEM studies cited above.2 Under independent shocks, the channels of transmission embedded in the model (e.g. risk sharing and expenditure switching e¤ects) must account for the
cross-country comovement in aggregate ‡uctuations.
The main contribution of this paper is to document that the baseline speci…cation fails to
account for the in‡uence of foreign shocks. A structural variance decomposition reveals that
all U.S. shocks combined cannot explain more than 3 percent of the variability in Canadian
output, interest rates or in‡ation. Furthermore, model-implied cross-correlation functions
between these two countries are estimated to be essentially zero. Both …ndings are in stark
contrast with reduced-form empirical evidence in the same data. These results are shown to
be robust across alternative speci…cations, priors and detrending methods.
Model parameters chosen based on previous calibrated studies can deliver both large shares
of domestic variance being attributed to U.S. shocks and substantial cross-country correlation
in some series. Therefore, our …ndings indicate that the inability to reproduce some international correlations — known as the quantity anomaly in the case of output (see Baxter and
Crucini (1995))— is exacerbated in estimated models. The results also suggest caution in
extrapolating to the international dimension the empirical success of related closed-economy
models.
A second contribution of this paper is to document that the international comovement
problem can only be partially resolved by introducing disturbances that are correlated across
countries. To do this, each Canadian structural shock is written as the sum of two orthogonal
components: a disturbance common to the same type of shock in the U.S. block, and a
country-speci…c disturbance. This decomposition can be viewed as a rough approximation to
reduced-form dynamic factor models that have been used for business cycle analysis.3
When all U.S. shocks are common to the domestic block the DSGE model gets closer to
matching the reduced-form variance decomposition. However, there are at least three reasons
for not viewing this speci…cation as a panacea for the model’s inability to replicate the observed
in‡uence of foreign disturbances. First, at medium to long horizons, the fraction of output
2

For example, Gali and Monacelli (2005) consider the role of technology spillovers in their calibration study.
But likelihood-based empirical studies have typically excluded this possibility.
3
In a closed economy setting, Boivin and Giannoni (2006) establish a formal link between DSGE and dynamic
factor models.

2

variation explained by U.S. disturbances is still below the reduced-form evidence. Second,
this speci…cation engenders an extreme version of the exchange rate disconnect puzzle — see
Devereux and Engel (2002). Third, some of the induced correlations are di¢ cult to rationalize
on structural grounds.
A third contribution of our analysis is to elucidate reasons for the model’s failure in this
crucial dimension. The inability to match the comovement in the data is signaled by crosscorrelation amongst supposedly orthogonal innovations identi…ed in our baseline model. These
estimates point to a complex pattern of covariation, beyond pairing the same type of disturbance across countries. This explains the limited success of the common shocks models. More
promising guidance for future research is given by the observation that while U.S. shocks
can a priori match some bivariate cross-country correlations, they also have strong counter
factual predictions, particularly involving the real exchange rate and the terms of trade, as
well as domestic in‡ation. This tension helps understand, at least in part, why the estimated
model shuts down international linkages and indicates ample scope to improve the transmission
mechanism of foreign disturbances in this class of model.
This paper broadly relates to the international business cycle literature and recent empirical work with NOEM models. More closely related is Adolfson et al. (2007) who presents a
state-of-the-art model, more richly speci…ed than the one considered here. While their model
performs very well in several dimensions, an earlier version, Adolfson et al. (2005), reported
variance decompositions revealing little transmission of foreign-sourced disturbances from the
European Union to Sweden — a property that is not remarked upon. Similar observations
apply to an extension of this framework by Christiano et al. (2009) and also de Walque
et al. (2005) in a two-country model for the U.S. and the Euro Area. We also build on
Schmitt-Grohe (1998) who evaluates whether a calibrated small open-economy real business
cycle model can replicate impulse responses to a single foreign output shock, extracted from
a bivariate U.S.-Canada vector autoregression.4 Our results suggest that in estimation the
failure to capture international linkages may be worse than when the model is calibrated.
4

Schmitt-Grohe (1998) concludes that …nancial and trade linkages are not capable of reproducing the strong
response of Canadian hours, output and investment to innovations in U.S. GNP. She suggests that these
di¢ culties might be alleviated by the introduction of sticky prices. Our analysis reveals that the inability to
capture the in‡uence of foreign shocks persists in an estimated model even when various nominal rigidities are
considered.

3

2

Evidence on International Linkages

A central empirical regularity that international business cycle models seek to explain is the
observed cross-country comovement amongst economic variables. This section documents a
number of statistics suggesting comovement is a salient feature of U.S. and Canadian business
cycles, understanding that earlier literature testi…es to the generality of these insights in other
economies. This close link is not surprising considering the U.S. accounts for 75 percent of
Canada’s average trade share.5

2.1

Data

We use data for twelve series that in section 4 constitute the observable states in the estimated
DSGE model. These are: real per-capita output, in‡ation, nominal interest rates, real wages
and hours in both the U.S. and Canada, as well as the bilateral terms of trade and the real
exchange rate. Details of the data are in appendix A. Consistent with the model presented
later, output and real wages are expressed in log-deviations from a common linear trend. The
real exchange rate and the terms of trade are given in log-di¤erences. Section 6 evidences the
robustness of our results to alternative detrending of these series. In‡ation and interest rates
are expressed as percentages and, like hours, are not transformed, except that all series are
demeaned. The sample runs from 1982q1 to 2007q1, although the …rst 8 quarters are used to
initialize the Kalman …lter.

2.2

Reduced-Form Evidence

The solid black lines in …gure 1 give the sample cross-correlations between Canadian and
lagged U.S. series, at lags zero through four. The remaining lines correspond to the estimated
DSGE model and are discussed in section 4. For presentation purposes only we exclude these
statistics for the terms of trade and the real exchange rate but discuss them later on.
For many series these cross-correlations are large at various lags and rarely equal to zero.
For example, the contemporaneous correlations between Canadian and U.S. output, in‡ation,
nominal interest rates and wages are: 0.69, 0.45, 0.83 and 0.72, respectively. This is consistent
with earlier studies on international comovement, such as Backus et al. (1992), Stockman and
Tesar (1995) and Ambler at al. (2004).
5

In our sample, 1/2 the share of U.S. imports in total Canadian imports plus 1/2 the share of total Canadian
exports oriented to the U.S. equals 75.1 percent.

4

We rely on two statistical models to compute the variance share of these Canadian series
that is attributable to U.S. shocks. The …rst model is a VAR subject to the exclusion restriction
of no feedback from Canada to the U.S. that is embedded in the DSGE model. It is formally a
seemingly unrelated regression (SUR). Variance decompositions are obtained with a Cholesky
decomposition of the SUR innovations with no attempt to identify any particular shock. We
only wish to infer the variance shares explained by disturbances also a¤ecting the U.S. block.6
The SUR is estimated with the e¢ cient block-recursive Gibbs algorithm proposed by Zha
(1999). Details are in appendix B.
Table 1 reports variance shares attributable to all foreign shocks in a SUR with 4 lags
at 1, 4, and 8 quarter horizons, and the stationary, or long-horizon, variance. We report
medians and 90 percent posterior probability bands. In the short, medium and long run, U.S.
disturbances account for a substantial fraction of variation in Canadian series. For example,
at a 4 quarter horizon, shares vary from 25 percent for hours to 44 percent for output. At long
horizons, contributions vary from 65 percent for in‡ation to 76 percent for output. The latter
is almost identical to the 74 percent share for U.S. shocks in the smaller, but overidenti…ed,
structural SUR model of Cushman and Zha (1997).
The SUR analysis is limited by sample considerations to a dozen series. An alternative
is to estimate a dynamic moving average factor model, which can encompass richer sources
of shocks and channels of transmission by accommodating a larger number of series. Hence,
we also mention variance decomposition estimates from such a model, estimated for the U.S.
and Canada on a similar sample. The reader is referred to an earlier version of this paper,
Justiniano and Preston (2006), which builds on Justiniano (2007), for further details.
To explain a panel of 32 series (16 for each country) formal model comparisons dictate
including four factors, two of which are common to both countries (foreign factors), with the
remaining two exclusive to the Canadian economy (domestic). The factors and idiosyncratic,
series-speci…c, components follow independent autoregressive processes of order three. Measures of …t also suggest the presence of moving average dynamics in the loadings, indicating
that spillover e¤ects may be important for some variables.
Justiniano and Preston (2006) show that the median share of the long-horizon variance
of Canadian output, in‡ation, interest rates, the terms of trade and the real exchange rate
explained by the two foreign factors is 0:71, 0:15, 0:31, 0:22 and 0:11. While di¤erences in
sample and data preclude direct comparisons with the SUR results, this distinct methodology
6

The results obtained with this identi…cation procedure are invariant to re-ordering of the series.

5

clearly indicates an important role for U.S. shocks in explaining Canadian business cycles,
particularly for output. Similar …ndings are reported by Kose et al. (2003, 2008), Lumsdaine
and Prasad (2003) and Bowden and Martin (1995) with related methodologies.
Taken together, these various statistics suggest strong comovement between Canadian and
U.S. business cycles. The remainder of the paper explores whether a structural model can
similarly capture these international linkages.

3

The Model

Building on Gali and Monacelli (2005), Monacelli (2005) and Justiniano and Preston (2008b),
the following section details a small open-economy model, allowing for habit formation, indexation of prices, labor market imperfections and incomplete markets. These papers extend
the microfoundations described by Clarida et al. (1999) and Woodford (2003) for analyzing
monetary policy in a closed-economy setting to an open-economy context.

3.1

Households

Each household maximizes
E0

1
X

t

t=0

where Nt is the labor input; Ht
household and 0 < h < 1;

1; '

~"g;t

"

(Ct

hCt

Ht )1
1 1=

1

~"l;t Nt1+'
1+'

1=

#

is an external habit taken as exogenous by the

> 0 are the inverse elasticities of intertemporal substitution

and labor supply; and ~"g;t and ~"l;t denote preference and labor supply shocks respectively. Ct
is a composite consumption index
h
Ct = (1

1

1

) (CH;t )

+

1

1

(CF;t )

i

1

where CH;t and CF;t are Dixit-Stiglitz aggregates of the available domestic and foreign produced goods given by

CH;t

2 1
Z
4
=
CH;t (i)
0

where

1

3

di5

1

and

CF;t

2 1
Z
4
=
CF;t (i)
0

1

3

di5

1

> 0 gives the elasticity of substitution between domestic and foreign goods;

> 1 is

the elasticity of substitution between types of di¤erentiated domestic or foreign goods; and
the relative weight of these goods in the overall consumption bundle.
6

Assuming the only available assets are one-period domestic and foreign bonds, optimization
occurs subject to the ‡ow budget constraint
Pt Ct + Dt + St Bt = Dt

1 Rt 1

+ St Bt

1 Rt 1 t (At )

+

H;t

+

F;t

+ Wt N t + Tt

(1)

for all t > 0, where Dt and Bt denote holdings of one-period domestic and foreign bonds with
gross interest rates Rt and Rt . St is the nominal exchange rate. The price indices Pt , PH;t and
Pt correspond to the domestic CPI, domestic goods prices and foreign prices and are de…ned
below. Households receive wages Wt for labor supplied and

H;t

and

F;t

denote pro…ts from

equity holdings in domestic and retails …rms. Tt denotes taxes and transfers.
Following Benigno (2001), Kollmann (2002) and Schmitt-Grohe and Uribe (2003), the
function

t(

) is interpretable as a debt elastic interest rate premium given by
t

= exp

h

i

At + ~ t

where

At

St 1 Bt 1
CF Pt 1

is the real quantity of outstanding foreign debt expressed in terms of domestic currency as a
fraction of steady state consumption of the imported good and ~ a risk premium shock. This
t

ensures stationarity of the foreign debt level in a log-linear approximation to the model.
Implicitly underwriting this expression for the budget constraint is the assumption that
all households in the domestic economy receive an equal fraction of both domestic and retail
…rm pro…ts and that labor income risk is pooled across agents. Absent this assumption, which
imposes complete markets within the domestic economy, the analysis would require modeling
the distribution of wealth across agents. This assumption also ensures that households face
identical decision problems and choose identical state-contingent plans for consumption.
The household’s optimization problem requires allocation of expenditures across all types
of domestic and foreign goods both intratemporally and intertemporally. This yields the
following set of optimality conditions. The demand for each category of consumption good is
CH;t (i) = (PH;t (i) =PH;t )

CH;t and CF;t (i) = (PF;t (i) =PF;t )

CF;t

for all i with associated aggregate price indexes for the domestic and foreign consumption
bundles given by PH;t and PF;t : The optimal allocation of expenditure across domestic and
foreign goods implies the demand functions
CH;t = (1

) (PH;t =Pt )

Ct

and

7

CF;t = (PF;t =Pt )

Ct

(2)

h
where Pt = (1

1
1
) PH;t
+ PF;t

i

1
1

is the consumer price index. Allocation of expendi-

tures on the aggregate consumption bundle satis…es
t

= ~"g;t (Ct

Ht )

1=

(3)

and portfolio allocation is determined by the optimality conditions

for Lagrange multiplier

t

t S t Pt

=

E t Rt

t+1 t+1 St+1 Pt+1

(4)

t Pt

=

Et [Rt

t+1 Pt+1 ]

(5)

attached to the constraint (1) The latter when combined with (3)

gives the Euler equation.
The household problem in the foreign economy is similarly described with the exceptions
now noted. Because the foreign economy is approximately closed (the in‡uence of the domestic
economy is negligible), the available consumption bundle comprises the continuum of foreign
produced goods CF;t (j) for j 2 [0; 1] : Foreign households need only decide how to allocate
expenditures across these goods in any time period t and also over time. Foreign debt in the
foreign economy is in zero net supply, using the property that the domestic economy engages
in negligible …nancial asset trade. There is no access to domestic debt markets for foreign
agents. Conditions (3) and (5) continue to hold with all variables taking superscript “*”.

3.2

Optimal Labor Supply

Following Erceg et al. (2000) and Woodford (2003), assume a single economy-wide labor
market and that producers of the domestic good hire the same bundle of labor inputs at
common wage rates. Firm j produces good j with technology Yt (j) = ~"a;t f (Nt (j)) where
~"a;t is a neutral technology shock and f ( ) satis…es the usual Inada conditions.

The labor

input used in the production of each good j and associated aggregate wage index are given
by the CES aggregators
Nt (j)

R1

Nt (k)

w 1
w

w
w 1

dk

and

Wt =

0

for

w

R1

1

1

Wt (k)

1
w

w

dk

0

> 1. Firm j’s demand for each type of labor k is determined by maximizing the former

index for a given level of wage payment. This gives the demand function
Nt (k) = Nt (j)

8

Wt (k)
Wt

w

:

(6)

Households supply their labor under monopolistic competition. They face a Calvo-style
wage-setting problem, having the opportunity to re-optimize their wage with probability 1
each period, where 0 <

w

< 1. As in Christiano et al. (2005) and Woodford (2003),

w

households not re-optimizing adjust their wage according to the indexation rule
log Wt (k) = log Wt
where 0
and

t

1 (k)

+

w t 1

1 measures the degree of indexation to the previous-period’s in‡ation rate

w

= log (Pt =Pt

1 ).

Since all households having the opportunity to reset their wage face

the same decision problem, they set a common wage, Wt .
The household’s wage-setting problem in period t is to maximize
"
#
1
P
~"l;t NT (k)1+'
PT 1 w
T t
Et
( w )
NT (k)
T Wt (k)
Pt 1
1+'
T =t
by choice of Wt (k) subject to the labor demand function (6). The …rst-order condition for
this problem is
Et

1
P

(

w

)T

t

T

T =t

PT
Pt

w

1

NT (k) + Wt (k)

1

@NT (k)
@Wt (k)

~"l;t NT'

@NT (k)
= 0:
@Wt (k)

(7)

Households in the foreign block face an identical problem, with appropriate substitution of
foreign variables and technology and preference parameters.

3.3

Domestic Producers

There is a continuum of monopolistically competitive domestic …rms producing di¤erentiated
goods. Calvo-style price setting is assumed, allowing for indexation to past domestic goodsprice in‡ation. In any period t, a fraction 1
0<

H

H

< 1 of goods prices are adjusted according to the indexation rule
log PH;t (i) = log PH;t

where 0
and

of …rms set prices optimally, while a fraction

H;t

H

1 (i)

+

H H;t 1 ;

(8)

1 measures the degree of indexation to the previous-period’s in‡ation rate

= log(PH;t =PH;t

1 ).

Since all …rms having the opportunity to reset their price in
0

period t face the same decision problem, they set a common price PH;t . Firms setting prices
in period t face a demand curve
yH;T (i) =

PH;t (i)
PH;T

PH;T
PH;t
9

1
1

H

CH;T + CH;T

(9)

for all t and take aggregate prices and consumption bundles as parametric.
The …rm’s price-setting problem in period t is to maximize the expected present discounted
value of pro…ts
Et

1
X

T t
H Qt;T

PH;t (i)

T =t

PH;T
PH;t

H

1

yH;T (i)

WT f

1

1

yH;T (i)
~"a;t

subject to the demand curve (9), where Qt;T is interpreted as a stochastic discount factor
evaluated at aggregate income. This implies the …rst-order condition
Et

1
X

T t
H Qt;T yH;T

(i) PH;t (i)

T =t

PH;T
PH;t

H

1

1

1

PH;T M CT = 0

(10)

where M Ct is the marginal cost function of …rm i.
Foreign …rms face an analogous problem. Thus the optimality condition takes an identical
form, with all variables taking the superscript “*” and the subscript H being changed to F .
Preferences and shocks are allowed to di¤er and the small open-economy assumption implies
that Pt is equivalent to PF;t .

3.4

Retail Firms

Retail …rms in the small open economy import foreign di¤erentiated goods for which the law
of one price holds at the docks. In determining the domestic currency price of imported goods
they are monopolistically competitive. Pricing power leads to a violation of the law of one
price in the short run.
Like domestic …rms, retail …rms face a Calvo-style price-setting problem allowing for indexation to past in‡ation. A fraction 1
0<

F

F

of …rms set prices optimally, while a fraction

< 1 of goods prices are adjusted according to an indexation rule analogous to (8) with

indexation parameter 0 <

F

< 1. Firms setting prices in period t face a demand curve

CF;T (i) =

PF;t (i)
PF;T

PF;T
PF;t

F

1

CF;T

(11)

1

for all t and take aggregate prices and consumption bundles as parametric. The …rm’s pricesetting problem in period t is to maximize the expected present discounted value of pro…ts
Et

1
X

T t
F Qt;T CF;T

(i) PF;t (i)

T =t

PF;T
PF;t

1

F

ST PF;T (i)

1

subject to the demand curve, (11), and implies the …rst-order condition
Et

1
X

T =t

T t
F Qt;T

PF;t (i)

PF;T
PF;t

1
1

10

F

1

e~T PH;T (i) = 0:

In the foreign economy there is no analogous optimal pricing problem. Because imports form
a negligible part of the foreign consumption bundle, variations in the import price have a
negligible e¤ect on the evolution of the foreign price index, Pt ; and need not be analyzed.

3.5

International Risk Sharing and Prices

Optimality conditions for domestic and foreign bond holdings imply the uncovered interest
rate parity condition
Et

t+1 Pt+1 [Rt

Rt (St+1 =St )

t+1 ]

= 0;

(12)

placing a restriction on the relative movements of domestic and foreign interest rates, and
changes in the nominal exchange rate.
The terms of trade is de…ned as PF;t =PH;t . The real exchange rate is given by St Pt =Pt :
Since Pt = PF;t , when the law of one price fails to hold ~ F;t St Pt =PF;t 6= 1, which de…nes
what Monacelli (2005) calls the law of one price gap. The models of Gali and Monacelli (2005)
and Monacelli (2005) are respectively characterized by whether or not ~ F;t = 1.

3.6

Monetary and Fiscal Policy

Monetary policy is conducted according to a Taylor-type rule
Rt
=
R

Rt 1
R

i

"

Pt
Pt 1

Yt
Y

y

Yt
)
(
Yt 1

St
y(
)
St 1

S

#(1

i)

~"m;t

where R and Y are steady state values of nominal interest rates and output and ~"m;t is
an exogenous disturbance. Policy responds to contemporaneous values of in‡ation, output,
output growth and the growth rate in the nominal exchange rate. Evidence for rules that
respond to exchange rates in various small open economies is found in Lubik and Schorfheide
(2005b) and Justiniano and Preston (2008b). Fiscal policy is speci…ed as a zero debt policy.

3.7

Exogenous Disturbances

All shocks have unit means. In log deviations from steady the following assumptions are made.
In the foreign block, the technology, preference and labor disutility shocks are …rst-order
autoregressive processes. The monetary policy innovation and cost-push shock in the pricing
of foreign goods are i.i.d. In the domestic block, technology, preference, labor disutility shocks
and the cost-push shock in imported goods pricing are …rst-order autoregressive processes, as is
the risk premium shock. The monetary policy shock and the cost-push shock to domestic price

11

setters are i.i.d. Justiniano and Preston (2006) discusses identi…cation issues which motivate
these speci…cations.

3.8

General Equilibrium

Equilibrium requires that all markets clear. Goods market clearing requires
YH;t = CH;t + CH;t and Yt = Ct

(13)

in the domestic and foreign economies respectively. The model is closed assuming foreign
demand for the domestically produced good is speci…ed as
CH;t =
where

PH;t
Pt

Yt

> 0. This demand function is standard in small open economy models (see Kollmann

(2002) and McCallum and Nelson (2000)) and nests the speci…cation in Monacelli (2005)
by allowing

to be di¤erent from , the domestic elasticity of substitution across goods in

the domestic economy, to give additional ‡exibility in the transmission mechanism of foreign
disturbances to the domestic economy. Our results are una¤ected by the parametrization of
this demand function.7 The dynamics of Yt and other foreign variables remain speci…ed by
the structural relations developed above. Domestic debt is in zero net supply so that Dt = 0
for all t.8
The analysis considers a symmetric equilibrium in which all domestic producers setting
prices in period t set a common price PH;t . Similarly, all domestic retailers and foreign …rms
each choose a common price PF;t and Pt . Analogous conditions hold for wage setters in the
domestic and foreign economies. Finally, we assume households have identical initial wealth,
so that each faces the same period budget constraint and make identical consumption and
portfolio decisions.

4

Estimation Methodology and Data

4.1

Estimation and Priors

Model parameters are estimated using Bayesian methods now used extensively in the empirical
macroeconomics literature — see Schorfheide (2000) for a seminal reference and Justiniano
7

Constraining to equal results in identical insights from the estimation.
A similar condition holds for the foreign economy once it is noted that domestic holdings of foreign debt,
Bt , is negligible relative to the size of the foreign economy.
8

12

and Preston (2006) for further details in the context of the model estimated here. We work
with a log-linear approximation of the model in a neighborhood of a non-stochastic steady
state. The observables used in estimation were described in section 2.
The …rst column of table 2 presents the priors for the coe¢ cients, indicating the density,
mean and standard deviation. They are motivated by earlier work reported in Justiniano and
Preston (2008b), are fairly uncontroversial, and accord with other studies adopting Bayesian
inference. Several parameters, not well identi…ed, are calibrated. The discount factor is …xed
at 0.99. The elasticities of demand across varieties of goods and labor inputs in both the
domestic and foreign block are set equal to 8, as in Woodford (2003). Following Benigno
(2001), the parameter governing the interest rate elasticity of debt is …xed at 0.01.9
Priors that are particularly germane to the transmission of foreign shocks deserve further
comment. The densities for the degree of openness, , and the the elasticity of substitution
between home and foreign goods, , are chosen to generate a tight distribution for the steady
state share of imports to GDP, centered at 0.27 as in the data.10 For

we specify a beta

density with mean 0.29, matching the average trade share in our sample, and a tight standard
deviation of 0.1. For

we choose a normal with mean 0.9 and also small dispersion of 0.1. Our

results are even stronger with looser priors on ; which produce implausibly low estimates.11
For the exogenous shocks, priors are guided both by closed-economy estimates of similar
disturbances for the U.S. and consistency of the implied degree of volatility and persistence
with the corresponding observables in each country. Our baseline speci…cation also includes
a “tilt” towards foreign block disturbances, which are assumed twice as volatile and more
persistent than their domestic counterparts.

4.2

Estimates and Model Fit

Table 2 reports parameter estimates for the baseline model.12 The robustness of our results to
alternative priors and speci…cations is addressed later. Parameter estimates for the baseline
model are reasonable. The degree of price stickiness in home produced goods, both in the
domestic and foreign blocks of the model, is high. However, estimates for the foreign economy
agree with Levin et al. (2005). Note that cost-push shocks to the domestic and foreign Phillips’
9

In the working paper version we evidenced the robustness of our results to alternative calibrations with the
elasticities of demand equal to 4 or when setting the interest elasticity of interest rate debt to 1e-4.
10
We are grateful to one of the referees for this suggestion.
11
None of our results are a¤ected when calibrating at 0.29.
12
We initialize multiple chains using random starting values after launching 50 optimization runs to ensure
they all converge to the same mode. Convergence of the MCMC chains is diagnosed looking at trace plots and
the potential scale reduction factors for variances and 90% posterior bands.

13

curve are white noise and we do not rely on shocks to the in‡ation target in order to impart
in‡ationary inertia. The Calvo adjustment parameters for wages in the domestic and foreign
economies are similar to those reported in Del Negro et al. (2007) on a longer sample for the
U.S. Imported goods prices are re-optimized most frequently, every 2 quarters.
The degree of habit persistence is close to 0.6 in both countries, tightly estimated and
in line with values in Boldrin et al. (2001). The intertemporal elasticity of substitution
and elasticity of labor supply accord with earlier macroeconomic studies of this kind. The
estimated coe¢ cients of the Taylor rule align with conventional wisdom. Technology and
preference shocks are highly persistent in both countries. This is also true of risk premium
and imported goods cost-push shocks in Canada. The median estimate for the elasticity of
substitution across home and foreign goods is 0.86, below the value of 1.5 used in calibrations
by Chari et al. (2002) and Schmitt-Grohe (1998), but consistent with estimates in Gust et al.
(2008). Finally, the posterior density for the degree of openness lies well in the left tail of our
very tight prior.
In Justiniano and Preston (2006) we show that the model matches the volatility and
persistence of the data within blocks.13 The rest of the paper is devoted to the model’s
performance across blocks.

5

Accounting for the In‡uence of Foreign Shocks

This section documents the central result of the paper: the baseline model with independent
shocks is unable to account for international comovement. Two pieces of evidence are adduced.
First, variance decompositions reveal that U.S. disturbances explain a negligible fraction of
variation in the domestic economy. Second, model-implied cross-country correlations are very
close to zero. Both …ndings are clearly at odds with the reduced-form evidence discussed in
section 2.

5.1

Variance Decompositions in the DSGE model

Using the draws from the posterior density of model parameters, table 3 reports the posterior
variance shares in the domestic series — including the real exchange rate and terms of trade
— that is attributable to all …ve foreign disturbances, at several forecast horizons.14 We report
13

This is also evident from the unreported cross-correlation functions within each block.
According to the prior variance decomposition — see table 3 in Justiniano and Preston (2008a) — U.S.
shocks combined account for roughly 40% of Canadian output and hours ‡uctuations, half of the variability in
in‡ation, nominal interest, terms of trade and real exchange rate, and, about 30% of the variance in real wages,
14

14

medians and 90 percent posterior probability bands. Simulated moments which also account
for small-sample uncertainty are discussed in the on-line appendix yield similar conclusions.
Regardless of forecast horizon, virtually none of the observed variation in domestic series
is attributable to foreign disturbances. For output, interest rates, in‡ation, hours and wages,
their maximum contribution at a horizon of 1 quarter is 3 percent. At longer horizons U.S.
shocks explain at most 1 percent. Furthermore, the 95 percentiles for the variance shares of
these series never exceeds 4 percent.15 For the real exchange rate and terms of trade, these
statistics reveal a slightly larger contribution of foreign shocks, but still, below 7 percent.
Compared with the reduced-form evidence in table 1, it is clear that this speci…cation of the
model cannot account for the in‡uence of foreign shocks.

5.2

Cross-Country Correlations in the DSGE Model

Section 2 discussed the empirical cross-correlations between Canadian and U.S. series shown in
…gure 1 (solid). Here we revisit that …gure focusing on the moments implied by the estimated
model. These population statistics are computed using the posterior distribution of the DSGE
parameters and the model’s state-space solution. We report median (dotted) and [5,95] percent
posterior probability bands (dashed).
The median model-implied population cross-correlations are virtually zero at all horizons.
The DSGE model cannot replicate the common ‡uctuations of domestic series with U.S.
variables. Virtually all data cross-correlations lie outside the posterior probability bands of
the corresponding model moments. This mismatch between model and data is also evident
for the real exchange rate and the terms of trade (not shown for space considerations).16
Section 8 demonstrates that the lack of meaningful e¤ects from foreign shocks in the
domestic series is not an inherent feature of the DSGE model. Moreover, the inability to
explain the in‡uence of foreign disturbances is not unique to the estimated model of this
paper. Adolfson et al. (2005) estimate a richer model which …ts the data very well in several
across di¤erent horizons.
15
A simulation-based decomposition of the stationary variance (using the same posterior draws) constructed
by feeding arti…cial sequences of domestic and foreign shocks one block at a time is presented in table 1A of
the on-line appendix. There it is shown that the median shares are essentially identical to the those reported
here, for all series, while the upper-ends of the posterior probability bands are roughly 0.02 points higher.
16
Figures 1A and 6A in the on-line appendix present simulated cross-correlations which account for smallsample uncertainty. While the median estimates are virtually identical, the posterior probability bands are
only very slightly wider, so long as care is taken to decompose the correlations into a “true” component
and “spurious” component that arises in small samples, but vanishes in population. Failure to account for
this “spurious” small-sample correlation produces posterior probability bands that may seem too wide and
inconsistent with all other evidence on the model’s inability to generate comovement. We are very grateful to
one of the referees for pointing out this apparent inconsistency in an earlier version of the paper.

15

dimensions but also reveals, for Sweden, negligible variance shares for shocks originating in
the rest of the world. While the authors do not comment on this issue, their estimated
model includes features such as a stochastic trend, investment, variable capital utilization
and a working capital channel, whose absence here could have been suspected as culprit for
our results. This is also true of Christiano et. al. (2009) which advances that analysis by
including …nancial frictions and unemployment. Similarly, de Walque et al. (2005) fail to
identify signi…cant cross-country linkages in an estimated two-country model for the U.S. and
the Euro area, suggesting that the small open-economy assumption is not responsible for our
…ndings either.

6

Robustness

The benchmark speci…cation makes a range of assumptions, both on model structure and its
match with data. Table 4 presents the estimated contribution of foreign disturbances to the
variability of Canadian series for a number of alternative speci…cations. Further robustness
checks are conducted in Justiniano and Preston (2006). To present a worst-case scenario
against our …ndings, the numbers reported are for the horizon at which the share for output
is greatest. A comparison with the …rst column, which replicates our baseline speci…cation,
makes clear that our central result remains intact.
Column 2 presents the decomposition when the prior standard deviations of all shocks are
uniform between 1e-4 and 10, while the prior for the persistence parameters is a fairly ‡at Beta
density with mean 0.5 and dispersion 0.25. Compared with the benchmark results there is
clearly little di¤erence in the variance decompositions with this more agnostic prior. Column 3
estimates the model using maximum likelihood.17 Comovement again fails. The most notable
di¤erence in parameter estimates resides in the openness coe¢ cient which is found to be 0:01
— essentially shutting down open economy linkages. These two exercises suggest our priors
are not responsible for the absence of comovement.
The next two columns evaluate the sensitivity of our conclusions to the choice of observables
used to confront the model with data. Column 4 reports shares when output and wages are
in …rst di¤erences rather than in level deviations from a common trend. The results are
unchanged. Column 5 includes the observed terms of trade and the real exchange rate in
levels rather than di¤erences. This matters little for the contribution of U.S. shocks in Canada,
17

Due to weak identi…cation the inverse Frisch elasticities are calibrated to 5 — the upper bound of admissible
values to which all MLE modes converged — without a¤ecting the results.

16

except for a somewhat larger share for the terms of trade and real exchange rate. Column
6 speci…es cost-push shocks in imports as i.i.d. as opposed to persistent disturbances. Once
again, the variance shares are small, dropping to zero for the terms of trade.
Coordinated policy responses could perhaps explain part of the comovement in Canadian
and U.S. business cycles. In the baseline speci…cation monetary policies are assumed to be
independently determined. However, interest rate decisions in Canada might be in‡uenced by
changes in U.S. interest rates beyond what can be accounted for with an explicit response to the
exchange rate. Given the estimated degree of price stickiness, including a direct link between
U.S. and Canadian monetary policy decisions may better capture international comovement.
In this spirit, a log-linearized alternative speci…cation for Canadian monetary policy is
it =

i it 1

+ (1

i)

i

it

1

+

t

+

y yt

+

y

yt + "m;t

where there is now an explicit dependence on lagged realizations of U.S. interest rates. All
remaining modeling equations are unchanged.18 With a posterior mode estimate for

i

of

0.04, it is not surprising that the variance decompositions are largely unchanged (column
6). Identical conclusions obtain even when policy responds to contemporaneous U.S. interest
rates.
Finally, we consider a speci…cation that …rst independently estimates the foreign block of
the model.19 We then impose very tight priors (with dispersion 0.01) around the posterior
estimates of the foreign block, and choose the prior persistence and volatilities of domestic
innovations to match closely the moments observed in Canadian data. While in clear violation
of specifying prior beliefs before looking at the data, this model is quite informative on which
foreign disturbances are responsible for comovement a priori, a feature later exploited in section
8. The last column in table 4 evidences that this speci…cation cannot account for the in‡uence
of foreign shocks either.

7

Common Shocks

The benchmark model assumes that all shocks in the U.S. and Canada are independent. However, the empirical evidence presented in section 2 is consistent with both spillovers from
U.S. speci…c disturbances and the existence of common shocks a¤ecting both countries. This
18

The prior for i is normal with mean 0.3 and dispersion 0.2, allowing it to take negative values.
Priors are as in the baseline speci…cation, although for robustness we impose uniform priors [1e-4,10] on
the innovation standard deviations and a Beta density with mean 0.5 and dispersion 0.25.
19

17

section presents alternative model speci…cations that accommodate the latter. Such speci…cations are unusual in the new open-economy macroeconomics literature. Notable exceptions
are Adolfson et al. (2007) and de Walque et al. (2005) which include a common stochastic
trend in neutral technology.

7.1

Speci…cation

Common shocks are introduced by expressing the Canadian disturbances in the model as the
sum of two orthogonal shocks. The …rst one is shared with the same type of disturbance in
the U.S. block and referred to as the common shock. The second component a¤ects only the
domestic block and is labelled a country-speci…c shock. There is still no spillover from the
Canadian to the U.S. economy given the small open-economy assumption.
As an illustration, when modeling a common shock in neutral technology this disturbance
in Canada is written as at = at + adt where the common shock, at , and country-speci…c shock,
adt , evolve as independent AR(1) processes. The common shock is the corresponding structural disturbance in the U.S. block. Its share of variability in Canadian neutral technology,
V ar(a )=V ar(a), and implied correlation, corr(a; a ), can be readily computed.
In this way, common components are introduced between Canadian disturbances to preferences, labor disutility, home-goods in‡ation and monetary policy, and their respective counterparts in the U.S. This can be viewed as a DSGE structural approximation to the decomposition
into common and idiosyncratic components using reduced-form dynamic factor models, as in
Kose et al. (2003, 2008). An advantage of this speci…cation relative to the direct estimation
of the correlations, corr(a; a ), is that it allows for a clean decomposition of the variance of
all series attributed to each component.
Given the emphasis on technology shocks in the international RBC literature, a natural
starting point for adding common shocks would be to introduce a common unit root in neutral
technology. A di¢ culty with this approach is strong evidence against a common stochastic
trend in U.S. and Canadian output, at least in our sample. Tests for cointegration between
log output per-capita in both countries do not reject the null hypothesis of no cointegration,
regardless of the speci…cation of lags and deterministic components.20 Similarly, the null of
20

We use both the trace and maximum eigenvalue tests, allowing for 1-6 lags while also varying the presence/absence of an intercept in the VAR or the cointegrating relationship, gauging relative …t using both the
BIC and AIC. For each lag length, both information criteria prefer a speci…cation with an intercept in the VAR
and cointegrating equation (as expected) in which case the null of no cointegration cannot be rejected with
either test (for all lags considered). The p-values for the null of no cointegration are never below 0.2 and close
to 0.5 if the preferred lag lengths are used.

18

a unit root in the di¤erence in levels of these two series cannot be rejected, while the null of
stationarity is rejected.21 These results accord well with a persistent gap in labor productivity
across these two countries; a topic that has been the subject of substantial research and policy
discussion in Canada — see Eldridge and Sherwood (2001) and references therein.22

7.2

Posterior variance shares with common shocks

For each U.S. shock and Canadian counterpart we re-estimate the model when common components are initially introduced one at a time. This permits identifying which common disturbances can help match the comovement in the data. A speci…cation with a common component
in all shocks is also presented. Priors are as in the baseline model with one exception. For
both common and country-speci…c shocks we specify the same density: a B(0:6; 2) for the
autoregressive coe¢ cients, and an IG for their standard deviations equal to that of the corresponding U.S. shock in table 1. Common and country-speci…c disturbances are on equal
footing.23 Results would be very similar using the prior from the baseline speci…cation.24
Panel A in table 5 reports posterior variance shares for speci…cations with a single common
shock. We report the horizon with the largest share for output. Comparing these results with
the baseline variance decomposition — reproduced in column 1 — yields several interesting
…ndings.
Introducing a common component in neutral technology alone does little to alter the
contribution of U.S. shocks, except for hours (column 2). Spillovers in neutral technology
here play a small role in reproducing comovement. The intuition for this …nding is that
in our model U.S. neutral technology shocks induce a negative comovement between output
and hours within the foreign block, as documented in closed-economy models by Gali (1999),
Ireland (2004) and Gali and Rabanal (2004). There is a tension between having technology
shocks as a source of international comovement and …tting the large hours-output comovement
21

The null of a unit root is not rejected at the 10 percent signi…cance level when using the test of Elliot et
al. (1996) or any of the test statistics proposed by Ng and Perron (2001), both with automatic lag selection.
The null of stationarity under the KPSS tests is rejected at the 5 percent level.
22
Labor productivity is an observed state in our model since we are using data on output and hours for each
country. The …ltered series matches labor productivity from Statistics Canada (Table 383-0012).
23
The implied prior distribution of the correlation coe¢ cient between the aggregate Canadian disturbance
and its common component, is quite dispersed with a mean and median of roughly 0.7, standard deviation of
0.23 and 5-95% bands covering 0.08 to 0.99. This is also the prior correlation with the country-speci…c part of
the shock, e.g. corr(a; ad ). By construction the sum of these two squared correlations equals 1.
24
In this case with the tilt towards the foreign block, the mean and median prior variance shares of the U.S.
shocks would have jumped to 90% or above. Also, for each composite disturbance the median prior correlation
with its common component would have been tightly centered around 0.95. Nonetheless, the variance shares
are only 1 to 3 percentage points higher with this alternative, extreme prior.

19

observed in U.S data.
A common shock to the disutility of labor only (column 3) has a negligible e¤ect on the
variance decomposition of output, in‡ation and interest rates, but helps improve the foreign
share in wages. Cost-push shocks (column 4) only bump up the foreign contribution to in‡ation
variability. Meanwhile, with a common shock only in the monetary policy rules (column 5),
the fraction of the variance in Canadian interest rate and output attributable to foreign shocks
climbs to 23 and 10 percent. The largest increase in the share of output variability explained
by U.S. disturbances occurs with a common component in preference shocks (column 5), but
even in this case only 11 percent of output ‡uctuations are accounted for by all foreign shocks.
Panel B reports shares at various horizons in a speci…cation with common components in
all U.S. shocks and their respective Canadian counterparts. The fraction of variation explained
by all foreign disturbances is now larger than in the baseline, particularly for output, hours
and interest rates. These results show that the comovement observed in the data can be partly
reproduced by correlating domestic disturbances with all of their U.S. counterparts.
The last row in each panel of the table reports the marginal data density, computed using the modi…ed harmonic mean. Most speci…cations achieve a lower …t than the baseline
(-1003.3), even when all common shocks are added simultaneously (-1010.6). The …t is almost indistinguishable from the baseline when either monetary policy or cost-push shocks
are correlated across countries. While caution is warranted when comparing these marginals
due to di¤erences in priors, this suggests that neither of the common shocks speci…cations
substantially improves the model’s …t, relative to the baseline without common shocks.
There are at least three further reasons why these speci…cations with common shocks
should not be viewed as panacea for the model’s failure in accounting for the in‡uence of
foreign shocks. First and foremost, while shares in panel B align well with those from the
SUR at a 1 quarter horizon, for longer horizons the SUR posterior bands do not encompass
the smaller DSGE estimates — compare table 2. Second, some of the common components
are hard to rationalize on structural grounds. Recall that neither a speci…cation of the Canadian policy rule including a direct response to the exchange rate nor to U.S. interest rates
could explain comovement, unless shocks are correlated. This suggests that cross-equation
restrictions prevent the model from structurally explaining the cross-correlation in these two
series. Third, panel B demonstrates an extreme manifestation of the exchange rate disconnect
analyzed by Devereux and Engel (2002). Fluctuations in the real exchange rate and the terms
of trade are completely disconnected from the U.S. block and for the most part from the real
20

domestic variables as well.25 In summary, even with common shocks there is ample scope to
improve the model’s ability to capture the contribution of foreign shocks.

8

On the Source of Model Failure

The results so far have documented an important model failure with little said about its
determinants. This section provides several insights on model and data features which limit
comovement. We …rst show that the unaccounted correlation seen in the data translates into
correlated innovations — in violation of the maintained assumption of orthogonality. This
information, together with insights into which U.S. disturbances are a priori responsible for
comovement, guide a set of exercises attempting to understand which shocks, transmission
mechanisms and data series pose di¢ culties for the model.

8.1

Where Does the Correlation Go?

The adopted likelihood-based procedure provides estimates of structural parameters and unobserved shocks that perfectly match the data. The large cross-country correlations in the
observables which are not explained by the model get re‡ected in correlated innovations, a
clear indication of model misspeci…cation. This correlation is not picked up in the various
exercises conducted in this paper as, with the exception of the common shocks models of
the previous section, the disturbances are assumed to be orthogonal. This is the standard
assumption in empirical DSGE models.
Table 6 reports the cross-correlation between the supposedly orthogonal two-sided U.S. and
Canadian innovations to the exogenous shocks, in the baseline speci…cation. Seven of those
correlations are statistically di¤erent from zero (in bold). Interestingly, in …ve of these seven
cases, the correlation occurs across disturbances of di¤erent type (e.g. U.S. preference and
Canadian technology shocks). This helps explain why the common shock models estimated
in the previous section — which allow for correlation only amongst disturbances of the same
type — could not fully reconcile model and data. A more complex set of interactions across
disturbances is revealed.
We next turn to a prior and posterior comparison that provides evidence on why these
correlations cannot be captured by the transmission mechanisms embedded in the model.
25

Risk-premium and import cost-push shocks account for roughly 90 and 85 percent of the variance of the
real exchange rate and the terms of trade, respectively, at all horizons, while explaining only about 5 percent
of the variability in domestic output, real wages and hours.

21

8.2

The Transmission Role of Disturbances and Data

Identifying the mechanisms limiting comovement is a challenging task. It requires assessing
numerous cross-equation restrictions, the prior and posterior properties of a model with 47
estimated parameters and the statistical covariance properties of 12 observable time series. A
clean narrative would ideally attribute model failure to one cross-equation restriction or one
particular time series. Unfortunately matters are not so simple in a model of this dimension.
Having said that, we conduct additional exercises suggesting a few culprits which serve to
guide future research on this topic.
The prior-posterior comparisons here are based on the model discussed in section 6 which
pre-estimates and then “calibrates” the U.S. block of the economy. This is done for the following reasons. First, in contrast to the benchmark prior, this “prior” is highly informative
as to which shocks are most relevant for dynamics in the foreign block and therefore comovement. In particular, U.S. preference shocks explain the bulk of U.S. output ‡uctuations and
a substantial portion of interest rate variability, especially at longer horizons. U.S. monetary
policy shocks are also important for U.S. interest rates, while cost-push shocks drive U.S.
in‡ation. This highlights the same set of foreign disturbances suggested by the relative …t of
the common shocks speci…cations in table 5 and the analysis of section 8.1.26
Second, by …xing properties of the U.S. block, attention is focused on di¤erences between
the prior and posterior implications for the domestic block and its interaction with the foreign
block, narrowing the scope of inquiry. Third, a priori the average variance share explained
by all U.S. shocks is roughly 0.4 for all Canadian series — without recourse to correlated
innovations — with prior bands covering the interval 0.1 to 0.7. Clearly, the prior suggests
substantial comovement while, as documented in table 4, the posterior decomposition implies
a negligible role for U.S. shocks in the domestic economy.
To understand why the posterior severs cross-country linkages, we analyze the international transmission of U.S. monetary policy, preference and cost-push shocks. Taking these
disturbances jointly and in isolation, we ask what are their prior implications for modelimplied cross-correlations and how do these square with the data. This uncovers a number of
counter factual prior implications which help explain why the posterior shuts down the role of
U.S. shocks. We provide a brief summary of our …ndings, with additional details and graphs
discussed in the on-line appendix.
26

This variance decomposition for the foreign block is not surprisingly very similar to the posterior in the
baseline speci…cation.

22

A priori output comovement can be captured by U.S. preference shocks. However, they
induce a strong negative correlation between U.S. output and both Canadian in‡ation
and interest rates. In the data these correlations are positive, particularly in the case
of the latter two series. Furthermore, U.S. preference shocks imply Canadian output is
negatively correlated with both Canadian in‡ation and nominal interest rates, as well
as the terms of trade. Again this is strongly counter factual.
Similarly, U.S. cost-push shocks a priori capture the comovement between U.S. in‡ation
with Canadian in‡ation and nominal interest rates. However, these disturbances imply
large positive correlations between U.S. and Canadian in‡ation with each of the terms
of trade and real exchange rate. These correlations are somewhat negative in the data.
Monetary policy shocks in the U.S. generate comovement with Canadian interest rates
and in‡ation. But their key counter factual prediction is a positive correlation between
Canadian in‡ation and both the terms of trade and real exchange rate. Since large U.S.
monetary policy shocks are required to match the substantial comovement between U.S.
and Canadian nominal interest rates this exacerbates the inability to match the terms
of trade and real exchange rate.
Taken together these observations permit several insights. First, while foreign preference,
cost-push and monetary policy shocks are important determinants of U.S. ‡uctuations, and in
principle Canadian ‡uctuations, they have signi…cant counter factual predictions for various
series vis-a-vis Canadian in‡ation, the terms of trade and real exchange rate, as well as amongst
these three. Posterior inference reveals that once confronted with the data the ability of these
shocks to generate comovement is severely limited.
Second, and related, is that the shifting importance of shocks across the prior and posterior
implications of the model are consistent with exchange rate disconnect being a factor in the
model’s failure. Furthermore, posterior estimates from a model in which both series are
unobservable states improves the comovement properties to some degree — around 10 percent
of variation in Canadian series is attributed to U.S. originating disturbances, without resorting
to correlated shocks. Treating any other observable Canadian series (such as in‡ation) in the
benchmark estimation as unobservable does not have similar implications.
The exchange rate disconnect hypothesis is provided further support given the importance
of imported goods cost-push shocks and risk premium shocks as a source of variation for these
two series, without a meaningful role for the remaining observables, domestic or foreign. This
23

issue is discussed in greater detail in an earlier version of this paper — see Justiniano and
Preston (2006).
To conclude we o¤er the following remarks on the model’s inability to explain the in‡uence
of foreign shocks. First, some correlation in exogenous disturbances appears warranted, despite
the assumption of orthogonality being common practice in the DSGE literature.27 Second,
allowing for correlation across countries only amongst disturbances of the same type will
not fully resolve the comovement problem. Third, prior-posterior comparisons point to deeper
mechanisms, operative through particular cross-equation restrictions and evidenced by counter
factual implications for the terms of trade and the real exchange rate, particularly in regards to
their link with domestic in‡ation. As to which cross-equation restrictions and model features
need to be re-considered to solve this disconnect is beyond the current exercise but clearly an
exciting area of research.

9

Conclusion

This paper shows that an empirical new open-economy model fails to account for one important dimension of Canadian data: the in‡uence of U.S. disturbances. We initially assume
uncorrelated shocks across countries, as it is done in almost all the empirical literature with
this class of models. Variance decompositions reveal that the fraction of variation in Canadian
series attributed to all shocks originating in the U.S. economy is negligible at all forecast horizons. Accordingly, the cross-country correlation functions implied by the model are close to
zero. These …ndings contrast sharply with earlier work documenting strong linkages between
these two countries and reduced-form evidence presented here.
Alternative speci…cations with common shocks can only partially resolve this problem. A
model in which all U.S. shocks have a common component with the corresponding Canadian
disturbance begins to reconcile the in‡uence of foreign shocks in the model and the data.
However, the variance shares explained by all U.S. disturbances still fall short of those observed
in the data at medium and long horizons. While the empirical evidence is consistent with
both common shocks and spillovers, there remains the question of what economic e¤ects do
these common shocks capture in the model. In particular, whether they correspond to purely
exogenous disturbances or are instead simply capturing model misspeci…cation. Finally, any
gains with common shocks come at the expense of fully detaching ‡uctuations in the exchange
rate and the terms of trade from the foreign block.
27

An interesting recent contribution in the closed economy setting in this regard is Curdia and Reis (2009).

24

Analyzing the prior implications for the transmission of U.S. shocks indicates a role for
exchange rate disconnect in the model’s failure. In particular, we uncover a number of prior
counter factual correlations between U.S. and Canadian series (particularly in‡ation) with the
real exchange rate and the terms of trade.
Overall our …ndings suggest that additional work on the international transmission mechanisms of various shocks could improve the empirical performance of these models in this
crucial dimension. An interesting exercise in this vein would be to alter the supply side of
the model to account for cross-country linkages at multiple stages of production as in Huang
and Liu (2007) and Burstein et al. (2008). Alternatively, expanding on international …nancial
linkages and the role of asset prices might help explain the importance of U.S. disturbances
abroad, as made evident by the current …nancial crisis.

10

Appendix A: Data

All series are downloaded from Haver Analytics. For the U.S., real per-capita GDP measures
output, in‡ation corresponds to the log-di¤erence in the GDP de‡ator, and the e¤ective federal
funds rate taken for interest rates. Nominal compensation per hour in the non-farm business
sector divided by the GDP de‡ator measures wages. Total hours in the non-farm business
sector is divided by population.
For Canada, real per-capita GDP is constructed with data from Statistics Canada (StatCan). The quarterly log di¤erence in the consumer price index excluding food and energy
(StatCan) measures overall in‡ation. The o¢ cial discount rate published by the Bank of
Canada corresponds to interest rates. Hours worked in the total economy (StatCan table
383-0012) is divided by population. From the same table we obtain total compensation and
convert it into real terms. In accordance with the model, the GDP de‡ator proxies for the
price of home produced goods, while CPI in‡ation represents the aggregate price index.
For consistency, the log di¤erence in the bilateral real exchange rate is constructed as the
sum the log growth rates in the U.S. GDP de‡ator and the nominal exchange rate (Canadian
dollars per U.S. dollars) minus Canadian aggregate in‡ation, as measured above. An earlier
version of the paper used the bilateral real exchange rate constructed by the IMF with identical
…ndings.
Finally, for the terms of trade we take the ratio of the de‡ator for imports to exports
(Statcan) matching in our model, log (PF;t =PH;t ). According to Canada’s national accounts
data, this measure of the terms of trade would correspond more closely to log PF;t St =PH;t ,
25

but this would not be consistent with the real exchange rate using aggregate U.S. in‡ation.
As there is no perfect match between model variables we adopted the former measure for
estimation. Inference with the latter interpretation does not a¤ect our results.

11

Appendix B: SUR model

To match the reduced-form representation of the DSGE model we impose on a VAR the same
zero restrictions of no feedback from Canada to the U.S. The resulting SUR model is estimated
on the same sample of twelve series used for inference with the DSGE model.
Inference is substantially more involved than with a standard VAR, as the explanatory
variables are not the same across all series. However, the estimation is feasible with the e¢ cient
block-recursive Gibbs algorithm proposed by Zha (1999), who documents the distortions to
inference from not imposing the exclusion restrictions in a SUR between Canada and the U.S.
We simply outline the model and refer the readers to Zha (1999) for details. Partitioning
the vector of observables yt into U.S. and Canadian variables, ytU S and ytCN , respectively, the
two blocks of the SUR are given by
AU S;U S (0)
ACN;U S (0)

0
ApU S;U S (L)
p
ACN;U S (L) ACN;CN (0) ApCN;U S (L)

ytU S
ytCN

=

US
t
CN
t

for matrices of conformable size, where Ai;j (0) corresponds to the impact matrix and Api;j (L)
denotes a matrix of lag-polynomials, of order p, in the positive powers of L: The structural
errors [

0U S ; 0CN ]0
t
t

are orthogonal with unit variance.

Our goal is not to identify each of the structural disturbances but simply to compute
the variance shares of the Canadian series attributed to the sum of all U.S. disturbances,
US.
t

To this end, we impose a lower triangular structure in the impact matrices AU S;U S (0)

and ACN;CN (0). This is equivalent to a Cholesky decomposition of the reduced-form SUR
covariance matrix. Results on the sum of all block-speci…c disturbances are invariant to
ordering.
We report results with p = 4 in light of recent work by Fernandez-Villaverde et al. (2007)
and Del Negro et al. (2007) who have brought attention to the issue of lag truncation in VARs
as approximations to DSGE models. To deal with the large number of parameters relative
to sample length, we use priors that shrink coe¢ cients at distant lags. More speci…cally,
we specify the priors Aij (1)

N (0:9; 0:2) for i = j and N (0; 0:4) for i 6= j:28 There’s no

distinction between own and others’ lags for k > 1 and assume a normal prior centered at
zero with a dispersion equal to 0.2 for k = 2, 0:15 for k = 3; and 0:1 for k = 4: The lower
28

For the exchange rate and terms of trade the mean is 0:3, since these are expressed in log-di¤erences.

26

triangular elements of the contemporaneous matrices are Aij (0)

N (0; 10): Results are largely

insensitive to looser priors, and, when feasible (p is 1 or 2), pretty much identical to sampling a
single block SUR with an uninformative Inverse-Wishart prior on the reduced-form covariance
matrix.
The Gibbs sampler is initialized at random starting values from the prior (or a classical
SUR with 2 lags) and we run 3 chains, discarding, for each, the …rst 40,000 draws, and retaining
1 in 10 of the remaining 50000. For each draw we compute the fraction of the variability in
ytCN ; explained by the sum of all …ve U.S. shocks, at di¤erent horizons.

References
Adolfson, M., S. Laseen, J. Linde, and M. Villani (2005): “Bayesian Estimation of an
Open Economy DSGE Model with Incomplete Pass-Through,” Working Paper Series 179,
Sveriges Riksbank.
(2007): “Bayesian Estimation of an Open Economy DSGE Model with Incomplete
Pass-Through,” Journal of International Economics, 72(2), 481–511.
Ambler, S., E. Cardia, and C. Zimmerman (2004): “International Business Cycles: What
are the Facts?,” Journal of Monetary Economics, (51), 257–276.
Backus, D. K., and P. J. Kehoe (1992): “International Evidence on the Historical Properties of Business Cycles,” American Economic Review, 82, 864–888.
Backus, D. K., P. J. Kehoe, and F. E. Kydland (1992): “International Real Business
Cycles,” Journal of Political Economy, 100, 745–773.
(1995): “Internation Business Cycles: Theory and Evidence,”in Frontiers of Business
Cycle Research, ed. by T. F. Cooley, pp. 331–356.
Baxter, M. (1995): “International Trade and Business Cycles,” in Handbook of Internation
Economics, ed. by G. Grossman, and K. Rogo¤. North Holland.
Baxter, M., and M. Crucini (1995): “Business Cycles and the Asset Structure of Foreign
Trade,” International Economic Review, 36, 821–854.
Benigno, P. (2001): “Price Stability with Imperfect Financial Integration,” unpublished,
New York University.
Bergin, P. (2003): “Putting the ‘New Open Economy Macroeconomics’to a Test,” Journal
of International Economics, 60(1), 3–34.
(2004): “How well can the New Open Economy Macroeconomics Explain the Exchange Rate and the Current Account,” unpublished, University of California Davis.
Boivin, J., and M. Giannoni (2006): “DSGE Models in a Data-Rich Environment,”NBER
Working Paper no. 12772.
27

Boldrin, M., L. J. Christiano, and J. D. M. Fisher (2001): “Habit Persistence, Asset
Returns, and the Business Cycle,” American Economic Review, 91(1), 149–166.
Bowden, R., and V. Martin (1995): “International Business Cycles and Financial Integration,” The Review of Economics and Statistics, 77, 305–320.
Burstein, A., C. Kurz, and L. Tesar (2008): “Trade, Production Sharing, and the International Transmission of Business Cycles,” unpublished, UCLA.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and
the Dynamic E¤ects of a Shock to Monetary Policy,”Journal of Political Economy, 113, 1.
Christiano, L. J., M. Trabandt, and K. Walentin (2009): “Introducing Financial Frictions and Unemployment into a Small Open Economy Model,” unpublished, Northwestern
University.
Curdia, V., and R. Reis (2009): “Correlated Disturbances and U.S. Business Cycles,”
unpublished, Columbia University.
Cushman, D. O., and T. Zha (1997): “Identifyiung monetary policy in a small open economy
under ‡exible exchange rates,” Journal of Monetary Economics, 39, 433–448.
de Walque, G., F. Smets, and R. Wouters (2005): “An Open Economy DSGE Model
Linking the Euro Area and the US Economy,” unpublished, National Bank of Belguim.
Del Negro, M. (2003): “Fear of Floating? A Structural Estimation of Monetary Policy in
Mexico,” unpublished, Federal Reserve Bank of Atlanta.
Devereux, M. B., and C. Engel (2002): “Exchange rate pass-through, exchange rate
volatility, and exchange rate disconnect,” Journal of Monetary Economics, 49, 913–940.
Eldridge, L. P., and M. K. Sherwood (2001): “A Perspective on U.S.-Canada Manufacturing Productivity Gap,” Monthly Labor Review, pp. 31–48.
Elliot, G., J. Stock, and T. Rotehnberg (1996): “E¢ cient Tests for An Autoregressive
Unit Root,” Econometrica, (64), 813–836.
Erceg, C. J., D. W. Henderson, and A. T. Levin (2000): “Optimal Monetary Policy
with Staggered Wage and Price Contracts,” Journal of Monetary Economics, 46(281-313).
Fernandez-Villaverde, J., J. F. Rubio-Ramirez, M. Watson, and T. Sargent
(2006): “A, B, C’s and (D)’s For Understanding VARS,” American Economic Review,
97(3), 1021.
Gali, J. (1999): “Technology, Employment and the Business Cycle: Do Technology Shocks
Explain the Business Cycle,” American Economic Review, 249, 249–271.
Gali, J., and T. Monacelli (2005): “Monetary Policy and Exchange Rate Volatility in a
Small Open Economy,” Review of Economic Studies, 72.
Gali, J., and P. Rabanal (2004): “Technology Shocks and Aggregate Fluctuations: How
Well Does the RBC Model Fit Postwar U.S. Data?,” NBER Macroeconomics Annual.
28

Ghironi, F. (2000): “Towards and New Open Economy Macroeconometrics,”Boston College
Economics Department Working Paper No. 469.
Gust, C., S. Leduc, and N. Sheets (2008): “The Adjustment of Global External Balances:
Does Partial Exchange Rate Pass-Through to Trade Prices Matter?,”unpublished, Federal
Reserve Board of Governors.
Huang, K., and Z. Liu (2007): “Business Cycles with Staggered Prices and International
Trade in Intermediate Goods,” Journal of Monetary Economics, 54, 1271–1289.
Ireland, P. (2004): “Technology Shocks in the New Keynesian Model,” The Review of
Economics and Statistics, 86(4), 923–936.
Justiniano, A. (2007): “Factoring In Canadian Cycles,” in Northern Star - Canada’s Path
to Economic Prosperity, ed. by T. Bayoumi. International Monetary Fund.
Justiniano, A., and B. Preston (2006): “Can Structural Small Open Economy Models
Account for the In‡uence of Foreign Disturbances?,” CAMA Working Paper Series no. 12.
(2008a): “Can Structural Small Open Economy Models Account for the In‡uence of
Foreign Disturbances?,” NBER Working Paper 14547.
(2008b): “Monetary Policy and Uncertainty in an Empirical Small Open Economy
Model,” forthcoming, Journal of Applied Econometrics.
Kollmann, R. (2002): “Monetary Policy Rules in the Open Economy: E¤ects on Welfare
and Business Cylces,” Journal of Monetary Economics, 49, 989–1015.
Kose, M. A., C. Otrok, and C. H. Whiteman (2003): “International Business Cycles:
World, Region and Country-Speci…c Factors,” American Economic Review, 93, 1216–1239.
(2008): “Understanding the Evolution of World Business Cycles,” Journal of International Economics, 75(1), 110–130.
Levin, A., A. Onatski, J. C. Williams, and N. Williams (2005): “Monetary Policy
under uncertainty in Micro-Founded Macroeconometrics Models,” .
Lubik, T. A., and F. Schorfheide (2005a): “A Bayesian Look at New Open Economy
Macroeconomics,” in NBER Macroeconomics Annual, ed. by M. Gertler. NBER.
(2005b): “Do Central Banks Respond to Exchange Rate Movements? A Structural
Investigation,” Journal of Monetary Economics, 54(4), 1069–1087.
Lubik, T. A., and W. L. Teo (2005): “Do World Shocks Drive Domestic Business Cycles?
Some Evidenec from Structural Estimation,” unpublished, Johns Hopkins University.
Lumsdaine, R., and E. Prasad (2003): “Identifying the Common Component if International Fluctuations: A New Approach,” The Economic Journal, 113, 101–127.
McCallum, B. T., and E. Nelson (2000): “Monetary Policy for an Open Economy: An
Alternative Framework with Optimizing Agents and Sticky Prices,”Oxford Review of Economic Policy, (16), 74–91.
29

Monacelli, T. (2005): “Monetary Policy in a Low Pass-through Environment,” Journal of
Money, Credit and Banking, 37, 1047–1066.
Ng, S., and P. Perron (2001): “Lag Selection and the Construction of Unit Root Tests
with Good Size and Power,” Econometrica, 69(6), 1519–1554.
Rabanal, P., and V. Tuesta (2005): “Euro-Dollar Real Exchange Rate Dynamics in an
Estimated Two-country Model: What is Important and What is Not,” unpublished, International Monetary Fund and Banco Central de Reserva del Peru.
Schmitt-Grohe, S. (1998): “The International Transmission of Economic Fluctuations: Effects of US Business Cycles on the Canadian Economy,”Journal of International Economics,
44, 257–287.
Schmitt-Grohe, S., and M. Uribe (2003): “Closing Small Open Economy Models,”Journal of International Economics, 61, 163–195.
Schorfheide, F. (2000): “Loss Function-Based Evaluation of DSGE Models,” Journal of
Applied Econometrics, 15, 645–670.
Smets, F., and R. Wouters (2007): “Shocks and Frictions in US Business Cycles: a
Bayesian DSGE Approach,” American Economic Review volume = 97, number = 3, pages
= 586-606,.
Stockman, A. C., and L. L. Tesar (1995): “Tastes and Technology in a Two-country
Model of the Business Cycle: Explaining International Comovements,”American Economic
Review, 85(1), 168–185.
Woodford, M. (2003): Interest and Prices: Foundations of a Theory of Monetary Policy.
Princeton University Press.
Zha, T. (1999): “Block Recursion and Structural Vector Autoregression,”Journal of Econometrics, 90, 291–316.

30

Table 1: SUR Posterior Variance Shares1 of Canadian Series
Attributed to All U.S. Shocks
Median variance shares and [5,95] posterior bands for all U.S. shocks 2

Series

1 quarter horizon

4 quarter horizon

Output

0.22

[ 0.07 , 0.41 ]

0.44

[ 0.19 , 0.68 ]

Inflation

0.20

[ 0.06 , 0.39 ]

0.37

[ 0.14 , 0.63 ]

Interest Rate

0.14

[ 0.03 , 0.31 ]

0.37

[ 0.14 , 0.63 ]

Real Wages

0.13

[ 0.03 , 0.28 ]

0.34

[ 0.12 , 0.59 ]

Hours

0.07

[ 0.02 , 0.16 ]

0.25

[ 0.08 , 0.48 ]

Real Exchange Rate

0.07

[ 0.01 , 0.17 ]

0.17

[ 0.06 , 0.35 ]

Terms of Trade

0.12

[ 0.03 , 0.26 ]

0.22

[ 0.08 , 0.40 ]

Series

8 quarter horizon

Stationary Variance 3

Output

0.52

[ 0.25 , 0.76 ]

0.76

[ 0.44 , 0.98 ]

Inflation

0.42

[ 0.20 , 0.69 ]

0.65

[ 0.33 , 0.95 ]

Interest Rate

0.47

[ 0.21 , 0.73 ]

0.71

[ 0.40 , 0.97 ]

Real Wages

0.49

[ 0.22 , 0.74 ]

0.79

[ 0.49 , 0.98 ]

Hours

0.42

[ 0.16 , 0.69 ]

0.75

[ 0.43 , 0.98 ]

Real Exchange Rate

0.26

[ 0.10 , 0.49 ]

0.62

[ 0.29 , 0.95 ]

Terms of Trade

0.29

[ 0.13 , 0.49 ]

0.57

[ 0.27 , 0.92 ]

Notes:
1 Variance shares cover [0,1] interval. Hence 0.01 corresponds to 1 percent.
2 Median of the sum of all five U.S. shocks computed for each draw of the SUR parameters
obtained with a Gibbs simulator. Details of the SUR are given in Appendix B. Mean shares are
very similar and if anything slighlty higher in some cases.
3 Stationary refers to the long-horizon variance.

Table 2: Prior densities and posterior estimates for baseline model (domestic block)
Prior
Coefficient Description

Prior Density 1

Posterior
Mean

Std

Median

Std

[

2

5

,

95 ]

φ

Inverse Frisch

N

1.00 0.30

1.27

0.27

[ 0.84 , 1.72 ]

σ

Intertemporal ES

N

1.00 0.40

1.43

0.30

[ 0.98 , 1.95 ]

αH

Calvo domestic prices

B

0.60 0.10

0.86

0.04

[ 0.78 , 0.92 ]

αF

Calvo import prices

B

0.50 0.20

0.42

0.06

[ 0.33 , 0.52 ]

αW

Calvo wages

B

0.60 0.10

0.88

0.04

[ 0.79 , 0.93 ]

γH

Indexation domestic prices

B

0.50 0.20

0.42

0.12

[ 0.25 , 0.63 ]

γW

Indexation wages

B

0.50 0.20

0.22

0.11

[ 0.07 , 0.44 ]

h

Habit

B

0.50 0.10

0.64

0.06

[ 0.53 , 0.73 ]

τ

Openess

B

0.29 0.02

0.24

0.02

[ 0.21 , 0.27 ]

η

Elasticity H-F goods

N

0.90 0.10

0.86

0.09

[ 0.70 , 1.01 ]

θπ

Taylor rule, inflation

N

1.80 0.30

2.00

0.26

[ 1.57 , 2.42 ]

θy

Taylor rule, output

G

0.25 0.13

0.21

0.08

[ 0.09 , 0.34 ]

θ dy

Taylor rule, output growth

N

0.30 0.20

0.70

0.18

[ 0.42 , 1.00 ]

θ de

Taylor rule, nominal exchange rate

G

0.30 0.20

0.31

0.10

[ 0.17 , 0.50 ]

θi

Taylor rule, smoothing

B

0.60 0.20

0.88

0.02

[ 0.84 , 0.91 ]

ρa

Technology

B

0.60 0.20

0.94

0.02

[ 0.91 , 0.96 ]

ρg

Preferences

B

0.60 0.20

0.92

0.02

[ 0.88 , 0.95 ]

ρL

Labor disutility

B

0.60 0.20

0.51

0.12

[ 0.30 , 0.70 ]

Cost-push imports

B

0.60 0.20

0.92

0.03

[ 0.87 , 0.96 ]

ρ rp

Risk premium

B

0.60 0.20

0.98

0.01

[ 0.96 , 0.99 ]

σa

sd technology

I

0.50 1.00

0.52

0.04

[ 0.46 , 0.59 ]

σi

sd monetary policy

I

0.15 1.00

0.21

0.02

[ 0.18 , 0.25 ]

σg

sd preferences

I

1.00 1.00

4.32

0.96

[ 3.05 , 6.10 ]

sd cost-push domestic

I

0.15 1.00

0.70

0.07

[ 0.61 , 0.83 ]

sd labor disutility

I

2.00 1.00

3.51

1.79

[ 1.68 , 7.37 ]

sd cost-push imports

I

1.00 1.00

2.12

0.60

[ 1.37 , 3.32 ]

sd risk premium

I

1.00 1.00

0.31

0.03

[ 0.26 , 0.38 ]

ρ cp,F

σ cp,H
σL
σ cp,F
σ rp

(continued in the next page with the foreign block)

Table 2: Prior densities and posterior estimates for baseline model (foreign block)
Posterior

Prior
Coefficient Description

Prior Density 1 Mean Std

Median

Std

[

2

5

, 95 ]

φ*

Inverse Frisch

N

1.00 0.30

1.19

0.27

[ 0.77 , 1.65 ]

σ*

Intertemporal ES

N

1.00 0.40

0.99

0.27

[ 0.62 , 1.48 ]

α H*

Calvo prices

B

0.60 0.10

0.91

0.02

[ 0.86 , 0.94 ]

α W*

Calvo wages

B

0.60 0.10

0.87

0.03

[ 0.81 , 0.91 ]

γ H*

Indexation prices

B

0.50 0.20

0.58

0.12

[ 0.40 , 0.79 ]

γ W*

Indexation wages

B

0.50 0.20

0.29

0.16

[ 0.09 , 0.60 ]

h*

Habit

B

0.50 0.10

0.56

0.07

[ 0.45 , 0.68 ]

λ*

Elasticity foreign demand

N

1.50 0.50

0.54

0.11

[ 0.38 , 0.74 ]

θ π*

Taylor rule, inflation

N

1.80 0.30

1.76

0.26

[ 1.35 , 2.19 ]

θ y*

Taylor rule, output

G

0.25 0.13

0.19

0.06

[ 0.09 , 0.28 ]

θ dy*

Taylor rule, output growth

N

0.30 0.20

0.77

0.15

[ 0.54 , 1.02 ]

θ i*

Taylor rule, smoothing

B

0.60 0.20

0.85

0.02

[ 0.81 , 0.88 ]

ρ a*

Technology

B

0.80 0.15

0.93

0.02

[ 0.90 , 0.97 ]

ρ g*

Preferences

B

0.80 0.15

0.90

0.03

[ 0.85 , 0.94 ]

ρ L*

Labor disutility

B

0.80 0.15

0.37

0.08

[ 0.23 , 0.51 ]

σ a*

sd technology

I

1.00 2.00

0.47

0.04

[ 0.42 , 0.53 ]

σ i*

sd monetary policy

I

0.25 2.00

0.13

0.01

[ 0.11 , 0.15 ]

σ g*

sd preferences

I

2.00 2.00

2.55

0.44

[ 1.92 , 3.35 ]

σ g*

sd cost-push

I

0.25 2.00

0.22

0.02

[ 0.19 , 0.26 ]

σL*

sd labor disutility

I

4.00 2.00

3.41

0.89

[ 2.33 , 5.22 ]

Relative to the text, the standard deviations of the innovations are scaled by 100 for the estimation, which is reflected in the prior and posterior
estimates.
1
2

N stands for Normal, B Beta, G Gamma and I Inverted-Gamma1 distribution

Median and posterior percentiles from 4 chains of 100,000 draws generated using a Random walk Metropolis algorithm, where we discard the
initial 50,000 and retain one in every 5 subsequent draws. For convergence we monitor trace plots as well as the potential scale reduction factors both
for the variances and 90% posterior probability bands.

Table 3: Posterior Variance Shares1 of Canadian Series
Attributed to All U.S. Shocks in Baseline DSGE
Median variance shares and [5,95] posterior bands for all U.S. shocks2
1 quarter horizon

4 quarter horizon

Output

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.01 , 0.02 ]

Inflation

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.01 , 0.02 ]

Interest Rate

0.03

[ 0.02 , 0.04 ]

0.02

[ 0.01 , 0.03 ]

Hours

0.00

[ 0.00 , 0.01 ]

0.00

[ 0.00 , 0.01 ]

Real Wages

0.01

[ 0.01 , 0.01 ]

0.01

[ 0.01 , 0.01 ]

Real Exchange Rate

0.03

[ 0.02 , 0.03 ]

0.03

[ 0.02 , 0.04 ]

Terms of Trade

0.04

[ 0.02 , 0.06 ]

0.04

[ 0.03 , 0.06 ]

Series

Series

8 quarter horizon

3

Stationary Variance

Output

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.01 , 0.02 ]

Inflation

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.01 , 0.02 ]

Interest Rate

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.01 , 0.02 ]

Hours

0.00

[ 0.00 , 0.01 ]

0.01

[ 0.00 , 0.02 ]

Real Wages

0.01

[ 0.01 , 0.02 ]

0.01

[ 0.00 , 0.02 ]

Real Exchange Rate

0.03

[ 0.02 , 0.04 ]

0.03

[ 0.02 , 0.04 ]

Terms of Trade

0.05

[ 0.03 , 0.07 ]

0.05

[ 0.03 , 0.07 ]

Notes:
1 Variance shares cover [0,1] interval. Hence 0.01 corresponds to 1 percent.
2 Median of the sum of the shares for all five U.S. shocks computed with the posterior
simulators of model parameters. We report means since domestic and foreign shares add up to
one for each draw, but clearly given the tight posterior bands the medians are almost identical.
3 Stationary refers to the long-horizon variance.

Table 4: Variance Shares1 of Canadian Series Attributed to All U.S. Shocks in Alternative Specifications

2

Looser prior
on
volatilities
and
persistence3

Maximum
likelihood4

Output and
wages in
first
differences

RER
and
TOT in
levels

Import costpush shocks
i.i.d

Response
to foreign
interest
rate in
policy
rule5

U.S. block
estimated
first6

Specification

Baseline

Series \ Horizon

Horizon 1

Horizon 1

Stationary

Horizon 12

Horizon 12

Horizon 1

Stationary

Horizon 12

Output

0.01

0.02

0.01

0.01

0.01

0.01

0.01

0.00

Inflation

0.01

0.01

0.00

0.01

0.02

0.00

0.02

0.01

Interest Rate

0.03

0.03

0.01

0.01

0.01

0.01

0.01

0.01

Real Wages

0.00

0.01

0.00

0.01

0.01

0.00

0.03

0.00

Hours

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.00

Real Exchange Rate

0.03

0.03

0.02

0.03

0.05

0.03

0.03

0.04

Terms of Trade

0.04

0.05

0.03

0.04

0.14

0.00

0.06

0.06

Notes:
1 Variance shares cover [0,1] interval. Hence 0.01 corresponds to 1 percent. These are computed at the mode of each specification. We select the horizon
with the highest share for output. All shocks are independent from one another.
2 Reproduced from table 3.
3 Prior for all domestic and foreign standard deviations is Uniform [1e-4,10] while for all persistence parameters, Beta with mean 0.5 and standard deviation
0.25.
4 Maximum likelihood. Inverse Frisch elasticities are calibrated to 5, since consistently hit this upper bound which generated convergence problems for the
optimization routines
5 Policy rule in Canada includes a direct response to lagged U.S. interest rates.
6 U.S. block is estimated first, using the same prior as in table 2, but with uniform distributions for volatilities and persistence parameters. For the foreign
block a very tight "prior" is then specified around these posterior estimates (standard deviation 0.01) in order to estimate the domestic block, while selecting
the "prior" for the volatilities of the domestic shocks in order to match the standard deviations in Canadian data. The "prior" for all remaining parameters in
the domestic block are as in table 2.

1

Table 5: Variance Shares of Canadian Series Attributed to All U.S. Shocks in
Specifications with Common Shocks
Panel A. One Common Shock Only
Baseline
without
common
2
shocks
Series \ Horizon

Output
Inflation
Interest Rate
Real Wages
Hours
Real Exchange Rate
Terms of Trade
Marginal Data Density 4

3

Technology

Labor
Disutility

Cost-Push

Monetary
Policy

Preference

1 Period

1 Period

Stationary

1 Period

1 Period

1 Period

0.01
0.01
0.03
0.00
0.01
0.03
0.04

0.02
0.01
0.03
0.00
0.21
0.02
0.04

0.02
0.06
0.04
0.13
0.01
0.04
0.08

0.02
0.11
0.05
0.04
0.01
0.02
0.03

0.10
0.00
0.23
0.00
0.06
0.01
0.01

0.11
0.02
0.04
0.01
0.08
0.04
0.06

-1003.3

-1033.5

-1037.8

-1002.6

-1005.8

-1037.2

Panel B. All Common Shocks Simultaneously5
Series \ Horizon5

Output
Inflation
Interest Rate
Real Wages
Hours
Real Exchange Rate
Terms of Trade
Marginal Data Density 4

1 Period

4 Periods

8 Periods

Stationary

0.23
0.11
0.26
0.13
0.30
0.00
0.00

0.20
0.13
0.22
0.16
0.26
0.00
0.01

0.18
0.13
0.18
0.17
0.24
0.00
0.01

0.16
0.13
0.12
0.16
0.23
0.00
0.01

-1010.6

Notes:

1 Variance shares cover [0,1] interval. Hence 0.01 corresponds to 1 percent. Disturbances in Canada are given by the sum
of two orthogonal components: a country-specific shock and a disturbance in common with the corresponding U.S.
shock. These shares now include the variability attributed to the common component(s) of the corresponding Canadian
composite disturbance.
2 Reproduced from table 3.
3 Each specification has a common component in that disturbance only. These are computed at the mode. We report the
horizon with the highest share for output.
4 Computed using the Modied Harmonic Mean
5 All 5 shocks from Panel A now have a common component with the corresponding U.S. disturbances. These variance
shares are computed at the mode. We report the same horizons as in tables 1 and 3.

Table 6: Cross Correlation between U.S. and Canadian innovations in
1
baseline DSGE

U.S.
Technology

U.S.
Monetary
Policy

U.S.
Preference

U.S. CostPush

U.S. Labor
Disutility

Technology

0.16

-0.12

0.30

0.06

0.11

Monetary Policy

-0.12

0.47

0.12

-0.07

0.06

Preference

-0.08

0.08

0.10

0.21

0.10

Cost Push Home Goods

-0.05

-0.01

0.06

0.39

-0.07

Labor Disutility

0.20

-0.06

0.21

0.01

0.11

Cost Push Foreign Goods

0.13

-0.04

0.08

-0.09

0.01

Risk Premium

0.12

-0.03

0.04

-0.29

-0.03

Innovations

Notes:

1 Cross-correlation of the smoothed innovations at the mode of the baseline model.
Those in bold exceed in absolute value 1.96 times the inverse of the square root of the

Figure 1: Data and DSGE population cross-correlations Canada-U.S.
y CNt , y USt-k

y CNt , dp USt-k

y CNt , nom USt-k

0.4

0.6

y CNt , w USt-k
0.1

0.3
0.4

0.3

0.4

0.2

0.2
0.2

0.1

0

0

0.1

dp CNt , nom USt-k

dp CNt , w USt-k

0.4

0.4

0.2

0.1

0.1

0.1

0

0

0

nom CNt , y USt-k

nom CNt , dp USt-k

nom CNt , nom USt-k

0.6

nom CNt , w USt-k

0.6

0

0.05
0

0.4

-0.05

0.4

0.2

0.2

nom CNt , hours USt-k

0.6

0.8
0.4

0.4

0.02
0
-0.02
-0.04
-0.06
-0.08

0.3

0.2

0.2

dp CNt , hours USt-k

0.4

0.3

0.3

0

0

0

dp CNt , dp USt-k

0.2

0.05

0.2

dp CNt , y USt-k
0.4

y CNt , hours USt-k

0

w CNt , y USt-k

0.2

0.2

0

0

w CNt , dp USt-k

-0.1
-0.15

w CNt , nom USt-k

w CNt , w USt-k

w CNt , hours USt-k

0.8

0.4
0.3
0.2

0.3

0.6

0.2

0.4

0.1

0.1

0.4

0.2

0.2

0

0

0

0

hours CNt , y USt-k

hours CNt , dp USt-k

0.2
0.1
0
0

1

2

3

4

0

0.6

-0.2
-0.4

hours CNt , nom USt-k

0.2

0.1

0.15

0

0.1

-0.1

0.05

-0.2

0

-0.3

hours CNt , w USt-k

hours CNt , hours USt-k

0

0.2

-0.1

0.1
0

-0.2
0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

0

Legend: Data (solid dark), DSGE median (dotted grey) and [5,95] posterior probability bands (dashed blue)
y (output), dp (inflation), nom (nominal interest rate), w (real wage) and hours.
X-axis: k lags of U.S. variables, 0 through 4 (in quarters)

1

2

3

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