Real exchange rates and international co-movement : news-shocks and non-tradable goods with complete markets. No 1946 / August 2016
Date: 2016-10-04
Institutions: European Central Bank
Subjects: capital movement, economic cycle, exchange rate, macroeconomics

Kyriacos Lambrias 

Working Paper Series 

Real exchange rates and 
international co-movement:  
news-shocks and non-tradable 
goods with complete markets 

No 1946 / August 2016 

Note: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). 
The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
 
 
Abstract

We propose a fully (cid:29)exible, complete-market model of the international busi-
ness cycle that is consistent with two major empirical facts: positive cross-country
co-movement of economic aggregates and a negative correlation between the real ex-
change rate and relative consumption (the Backus-Smith puzzle). The novelty of our
paper is twofold. First, we allow for imperfect substitutability of capital which sig-
ni(cid:28)cantly reinforces Harrold-Balassa-Samuelson e(cid:27)ects, producing more empirically
relevant movements in real exchange rates. Second, we introduce changes in expecta-
tions (news-shocks) as an explanation to the Backus-Smith puzzle through movements
in relative hours across countries, while being consistent with expectations-driven eco-
nomic expansions.

Keywords: Backus-Smith Puzzle, Real-Exchange Rates, News-Driven Cycles
JEL Classi(cid:28)cation: F41, F44

ECB Working Paper 1946, August 20161Non-technical summary

International cyclical (cid:29)uctuations exhibit two distinctive features. First, macroeco-
nomic aggregates like output, consumption, investment and hours worked are posi-
tively correlated across countries. Second, the correlation between the real exchange
rate and relative consumption is low or negative. Inherent e(cid:30)ciency in a frictionless
model with complete markets as in Backus, Kehoe and Kydland (1992, 1994 hence-
forth BKK) is at odds with these facts. A productivity shock in the home country
implies higher imports of capital goods, thereby investment moves in opposite di-
rections across countries. Similarly, higher productivity increases wages and hours
worked at home but generates a wealth e(cid:27)ect in the rest of the world; increasing
leisure and decreasing hours. Further, under complete and perfect international (cid:28)-
nancial markets economic agents would sign contracts such that consumption is higher
where it is cheaper; implying a strong positive correlation between bilateral real ex-
change rates and relative consumption bundles. This is known in the literature as the
Backus-Smith puzzle (Backus and Smith 1993).

An immediate solution seems to be to move away from e(cid:30)ciency in (cid:28)nancial
markets. Nevertheless, market-incompleteness alone is not su(cid:30)cient to break the
tight link between consumption and real exchange rates (Chari, Kehoe and McGrattan
2002). This is largely because the optimal allocation under full international (cid:28)nancial
integration need not be very di(cid:27)erent from the allocation of an economy with a single,
unconditional bond (Heathcote and Perri 2002) or even (cid:28)nancial autarky (Cole and
Obstfeld 1991), provided that shocks are not permanent (Baxter and Crucini 1995).
On the other hand, shocks that change directly the marginal utility of consumption
(Stockman and Tesar 1995) or that generate strong wealth e(cid:27)ects (Corsetti et al 2008)
could imply a disproportionate increase in relative demand for the home good and
hence its relative price.

In this work, we suggest an alternative explanation to the Backus-Smith puzzle in
an economy with complete markets. The mechanism in our model operates through
two distinct but complementary channels. First, we allow for an imperfect substi-
tutability of capital across sectors of tradable and non-tradable goods production.
This generates a strong reaction in the price of the non-tradable good (Balassa-
Samuelson e(cid:27)ect); thereby breaking the tight link between relative consumption and
real exchange rates. Although achieving a strong decrease in the consumption-real
exchange rate correlation; the latter is still positive and high. Second, we allow for
sectoral productivity innovations to be perfectly anticipated one-period in advance;

ECB Working Paper 1946, August 20162what is called a news-shock. News-shocks have the allure of changing agents’ expec-
tations about future income without changing current fundamentals. The response
of hours to expected Total Factor Productivity (TFP) innovations becomes an im-
portant driver or real exchange (cid:29)uctuations and breaks the tight positive relation
between relative consumption and its relative price. The correlation between the
real exchange rate and relative consumption turns negative and the model’s (cid:28)t to
the data is signi(cid:28)cantly improved compared to the case of traditional, unexpected
disturbances.

Nevertheless, any model driven by expected disturbances should also be consistent
with an economic upturn following good news, and a recession following bad news.
As is well known, it is surprisingly di(cid:30)cult for standard business cycle models to
generate economic expansions following improved prospects about new technologies
(Beaudry and Portier 2007, Jaimovich and Rebelo 2009). The novelty of our work is
to lay down the theoretical underpinnings that allow the model to generate a world-
wide economic boom conditional on anticipated innovations to productivity, while
simultaneously generating empirically relevant movements in relative prices. Further,
the model produces positive unconditional correlations of output, consumption, hours
and investment across countries that are not far from their empirical counterparts.

ECB Working Paper 1946, August 201631

Introduction

International cyclical (cid:29)uctuations exhibit two distinctive features. First, macroeco-
nomic aggregates like output, consumption, investment and hours worked are posi-
tively correlated across countries. Second, the correlation between the real exchange
rate and relative consumption is low or negative. Standard macroeconomic theory
has di(cid:30)culty reconciling these facts. The frictionless, complete markets model of
Backus, Kehoe and Kydland (1992, 1994, henceforth BKK) suggests that following
a productivity shock resources move to the country that is the most productive, im-
plying a negative correlation of investment across countries. Moreover, wealth e(cid:27)ects
among the residents of the country whose productivity did not improve should in-
crease leisure, hence hours worked should also move in opposite directions. Further,
perfect risk sharing in the BKK world instructs that the international transmission of
productivity shocks is positive, working via a depreciation in the real exchange rate
at home and an improvement in the terms of trade abroad. E(cid:30)ciency and home-bias
imply an increase in relative consumption resulting in a strong positive correlation
which is missing in the data (Backus and Smith 1993). In the literature, this is re-
ferred to as the Backus-Smith puzzle1 or the consumption-real exchange rate anomaly
(Chari, Kehoe and McGrattan 2002).

The latter might suggest that markets are incomplete and that world residents
do not optimally share the risks of country-speci(cid:28)c shocks (Kollman 1995). Never-
theless, market-incompleteness alone is not su(cid:30)cient to break the tight link between
consumption and real exchange rates (Chari, Kehoe and McGrattan 2002). This is
largely because the optimal allocation under full international (cid:28)nancial integration
need not be very di(cid:27)erent from the allocation of an economy with a single, uncondi-
tional bond (Heathcote and Perri 2002) or even (cid:28)nancial autarky (Cole and Obstfeld
1991), provided that shocks are not permanent (Baxter and Crucini 1995). Cole and
Obstfeld (1991) call for an important role of the terms of trade in propagating the
bene(cid:28)ts of country-speci(cid:28)c shocks via price changes, and suggest that the degree of
substitutability of goods that are traded across countries can be important for the
extent of risk-sharing that this mechanism can provide. Another possible explana-
tion could be that cycles are driven by demand-type shocks, as in Stockman and
Tesar (1995), since these disturbances can simultaneously increase both prices and
quantities2.

1For the remaining of the paper we abbreviate the latter to B-S.
2Corsetti et al (2006) and Enders and M(cid:252)ller (2009) show empirically that the US real exchange
rate and terms of trade fall following a permanent increase in manufacturing and aggregate TFP.

ECB Working Paper 1946, August 20164We develop a two-country, complete-market model with non-tradables that is
able to reconcile these facts in a theoretical economy driven by sectoral productivity
shocks. The main contribution of our work is to propose an alternative explanation
to the Backus-Smith puzzle based on two main channels: strong Harrold-Balassa-
Samuelson (HBS) e(cid:27)ects and news-shocks. In a world with complete Arrow-Debreu
international markets, a negative correlation between the real exchange rate and rela-
tive consumption can arise only through a relatively strong appreciation of the home
non-tradable good. We achieve this by allowing for an imperfect substitutability of
capital services across tradable-goods and non-tradable-goods sectors - as in Mendoza
and Uribe (2000) and Arellano et al (2002). This ampli(cid:28)es HBS e(cid:27)ects contributing
to a substantially lower correlation between consumption and real exchange rates.
Nevertheless, this correlation is still positive unless shocks to TFP are anticipated.
News-shocks have the allure of changing agents’ expectations about future income
without changing current fundamentals. The response of hours to expected Total
Factor Productivity (TFP) innovations becomes an important driver or real exchange
(cid:29)uctuations and breaks the tight positive relation between relative consumption and
its relative price. The correlation between the real exchange rate and relative con-
sumption turns negative and the model’s (cid:28)t to the data is signi(cid:28)cantly improved
compared to the case of traditional, unexpected disturbances. Our result does not
depend on market ine(cid:30)ciency or very low levels of trade elasticity (see Corsetti et al
2008). Instead, it is the e(cid:30)cient allocation in an economy where preferences exhibit
low wealth e(cid:27)ects on labour supply, the price of non-tradables plays an important role
in real exchange rate movements - in accordance to the Harrod-Balassa-Samuelson
framework - and innovations to (sectoral) TFP are known one period in advance.
Nevertheless, any model driven by expected disturbances should also be consistent
with an economic upturn following good news, and a recession following bad news.
As is well known, it is surprisingly di(cid:30)cult for standard business cycle models to
generate economic expansions following improved prospects about new technologies
(Beaudry and Portier 2007, Jaimovich and Rebelo 2009). The novelty of our work is
to lay down the theoretical underpinnings that allow the model to generate a world-
wide economic boom conditional on anticipated innovations to productivity, while
simultaneously generating empirically relevant movements in relative prices. Further,
the model produces positive unconditional correlations of output, consumption, hours
and investment across countries that are not far from their empirical counterparts.

Therefore, models that rely on productivity to drive business cycles (RBC paradigm) also need to
be consistent with a low B-S correlation.

ECB Working Paper 1946, August 20165The model possesses several distinctive features that contribute to our results.
First, we assume preferences as in Jaimovich and Rebelo (2009, henceforth JR-
preferences), but parametrised to exhibit very low intertemporal substitution in labour
e(cid:27)ort, thus being very close to Greenwood, Hercowitz and Hu(cid:27)man (1988, henceforth
GHH). JR-preferences introduce strong non-separabilities between consumption and
leisure, thereby reducing the consumption-real exchange rate correlation. Moreover,
almost eliminating the wealth e(cid:27)ect in labour supply ensures a positive response of
hours in both countries given expected shocks to tradables’ TFP. Second, as dis-
cussed, we allow for an imperfect substitution of capital across sectors which triggers
sizable movements in the price of the non-tradable good. Indeed, the exchange rate
between the home and foreign non-tradable good appreciates in response to a technol-
ogy shock in the benchmark model whereas it depreciates in economies where capital
is homogeneous. The resulting unconditional B-S correlation in such economies is
positive and high - in line with the typical Backus-Smith model - and any changes
implied by news-shocks do not adequately decrease it. Third, we allow for variable
capacity utilisation which ensures an increase in the supply of labour and output in
response to improved expectations about the future state of productivity, following
the intuition in Jaimovich and Rebelo (2009). At the same time, variable capacity
utilisation ampli(cid:28)es the exogenous propagation mechanisms of the model (Jaimovich
and Rebelo 2009, Burnside and Eichenbaum 1996, Baxter and Farr 2005), further
intensifying the Balassa-Samuelson e(cid:27)ect and allowing for humped-shaped responses.
In the context of our theoretical economy, variable capacity utilisation is an essential
element to explain news-driven cycles and real exchange rate (cid:29)uctuations.

Our paper is found in the intersection of three di(cid:27)erent strands of the literature.
First is the literature that tries to reconcile empirical business cycle facts with ex-
pected innovations to TFP (Beaudry and Portier (2004, 2006, 2007, 2014), Jaimovich
and Rebelo (2008, 2009) and Schmitt-GrohØ and Uribe (2012)) and in particular to
contributions that look at news-driven international business cycles (Beaudry et al
2011). We add to this list an attempt to simultaneously account for movements in
quantities and relative prices, in a frictionless open-economy model. Opazo (2006)
and Nam and Wang (2010)[a] also investigate news-shocks as a potential source of the
consumption-real exchange rate correlation in models where markets are incomplete.
We show that a low B-S statistic can be the e(cid:30)cient allocation in an economy where
expected improvements in productivity trigger an economic expansion. Second, our
work lies in the class of multi-sector, international business cycle models trying to ex-
plain the Backus-Smith puzzle. Corsetti et al (2008) show that an incomplete-market

ECB Working Paper 1946, August 20166model where the trade elasticity is low is consistent with a low degree of international
risk sharing. Unlike Cole and Obstfeld (1991), their results suggest that movements
in the terms of trade aggravate the risk-sharing problem, instead of mitigating it, in
line with some empirical evidence (Corsetti et al 2006, Enders and M(cid:252)ller 2009). Be-
nigno and Thoenissen (2008) construct a model where movements in non-tradables’
prices are the main reason behind a negative B-S statistic in a world where a single
bond is traded. Stockman and Tesar (1995) suggest that accounting for taste-shocks
can be important to explain several facts of international cyclical (cid:29)uctuations. Ra(cid:27)o
(2010) proposes a mechanism via investment-speci(cid:28)c technology shocks to account
for the consumption-real exchange rate anomaly, as this type of disturbances cause
sizable shifts in domestic absorption and acts like a demand shock. As in our case,
this mechanism can also work in complete-market environments but can be inconsis-
tent with co-movements of investment across countries3. Karabarbounis (2010) shows
that accounting for a home-sector can potentially explain the observed limited degree
of international risk sharing. Lastly, our work is closely related to the open-economy
literature that analyses implications of imperfect capital substitutability (Mendoza
and Uribe 2000 and Arellano et al 2009) which, nonetheless, have not been extensively
investigated4. It’s importance for our results suggests that it merits further scrutiny.
The following section outlines the model. Our main results are given in sec-
tion three while section four inspects the mechanism that drives them, providing the
model’s underlying intuition. Section (cid:28)ve reports some sensitivity analyses to selected
parameter values and section six concludes.

2 The model

The model follows closely the workhorse international business cycle model of Backus,
Kehoe and Kydland (1992, 1994) extended with a non-tradables sector. Additional
features include JR preferences, imperfect substitutability of capital services and vari-
able capacity utilisation. There are two ex-ante symmetric countries, i = 1, 2. All
exchanges take place in a common currency. Markets are perfect and complete. Time
is discrete and in(cid:28)nite, t = 0, 1, 2, ....

3Moreover, it has been shown to be less relevant once the exogenous process is estimated in the

data (Mandelman et al 2011)

4The literature seems to favour more the imperfect substitution of labour, instead of capital,

across sectors; see for example ECB’s EAGLE model (Gomes et al (2010).

ECB Working Paper 1946, August 201672.1 Production

There is full-specialisation in production of intermediate goods; country one produces
intermediate good a and country two intermediate good b. Neither capital nor labour
are mobile across countries but intermediate goods can be freely exchanged around
the world. Output of intermediate goods is produced using a standard Cobb-Douglas
production function:

Yat = Z1T t(S1T t)αT (N1T t)1−αT
Ybt = Z2T t(S2T t)αT (N2T t)1−αT

(1)

where Sijt, Nijt, Zijt denote capital services (see below), labour and technology in
country i = 1, 2 and the tradables sector - j = T .

Final-good producers are competitive. They purchase domestic and foreign in-
termediate goods at prices qi
b, which are transformed into (cid:28)nal goods via a
constant-elasticity of substitution (CES) production function. Final goods are used
locally for consumption (CiT ) and investment (Ii):

a and qi

C1T t + I1t = {ωa

1t + (1 − ω)b

θ−1
θ

C2T t + I2t = {(1 − ω)a

θ−1
θ

2t + ωb

θ−1
θ

2t }

θ−1
θ

1t }

θ
θ−1

θ
θ−1

(2)

where ait and bit denote the use of good a and b in country i. We introduce home-
bias in each country by allowing ω > 0.5 and θ > 0 is the elasticity of substitution
between the two intermediate goods. For values of θ close to zero intermediate goods
are complements, θ = 1 corresponds to the Cobb-Douglas case and for θ → ∞ goods
are perfect substitutes. The world’s resource constraints for intermediate goods imply:

Yat = a1t + a2t

Ybt = b1t + b2t

(3)

Moreover, each country produces a (cid:28)nal non-tradable good using a Cobb-Douglas
production function. We assume that these goods are used only for consumption, as
in Corsetti et al (2008), Benigno and Thoenissen (2008) and Karabarbounis (2010).

C1N t = Z1N t(S1N t)αN (N1N t)1−αN
C2N t = Z2N t(S2N t)αN (N2N t)1−αN

(4)

where the subscript N stands for the non-tradables sector. Following the literature,

ECB Working Paper 1946, August 20168we maintain the assumption of homogeneous labour, and introduce sector-speci(cid:28)c
capital (Mendoza and Uribe 2000, Arellano et al 2009).
In particular, we assume
that the capital-services-transformation curve is a CES aggregator of sector speci(cid:28)c-
services:

uitKit = g(ST , SN ) = (S

ε−1
ε

iT t + S

ε−1
ε

iN t )

Nit = NiT t + NiN t

i = 1, 2

ε
ε−1

(5)

where uit the rate of capacity utilisation and Kit is aggregate capital in country i.
The parameter ε > 1 captures the elasticity of substitution of capital services across
sectors. Perfect homogeneous capital services correspond to the case where ε → ∞.
The production possibility frontier is concave, owing to di(cid:27)erences in factor intensities
across the two sectors as well as to the curvature of aggregate services as given by
g(.). We view this function as a simple way of capturing imperfect substitutability of
capital services across sectors, from the households’ point of view. That is households,
in lending their capital, have some preferences as to which sector their (cid:29)ows end to.
For example during the internet bubble, households may have had some exogenous
preference to invest in information technology. This would create a real friction in the
(cid:28)nancial markets with households requiring a di(cid:27)erent premium for lending capital
to di(cid:27)erent sectors. As in Arellano et al (2009) and Mendoza and Uribe (2000),
we remain agnostic about the exact functional form of the above in the real world,
we rather see it as a simple way to add a real friction into the model. As we shall
see, depending on the degree of substitutability, the price of non-tradables adjusts
accordingly with important implications for the real exchange rate in the spirit of the
Harrod-Balassa-Samuelson (HBS) framework. Finally, this approach has the practical
appeal of being relatively simple, and we can easily check the implications of our model
to di(cid:27)erent degrees of this elasticity, including homogeneous capital.

Aggregate consumption is a CES composite of tradable (CiT ) and non-tradable

goods (CiN ):

Cit = {ωT C

ρ−1
ρ

iT t + (1 − ωT )C

ρ−1
ρ

iN t }

ρ
ρ−1

i = 1, 2

(6)

where ωT captures the preference for the tradable good and ρ > 0 is the elasticity of
substitution between the two consumption goods.

ECB Working Paper 1946, August 201692.2 Capital Accumulation

Capital stocks evolve according to:

Kit+1 = (1 − δ(uit))Kit + Iit

1 − S(

(cid:18)

(cid:19)
)

Iit
Iit−1

(7)

The depreciation rate is an increasing and convex function of capital utilisation such
that δ(cid:48)(uit) > 0, δ(cid:48)(cid:48)(uit) ≥ 0. Function S(.) represents investment adjustment costs,
assumed to be zero at the steady-state, and is such that: S(1) = 0, S(cid:48)(1) = 0 and
S(cid:48)(cid:48)(1) > 0. When we abstract from adjustment costs in the (cid:29)ow of investment we set
S(.) = 0.

2.3 Households

Households are symmetric and their preferences are characterised by a utility function
as in Jaimovich and Rebelo (2009):

E0

∞
(cid:88)

t=0

where

βt (Cit − ψN ν

itXit)γ

γ

Xit = C φ

itX 1−φ

it−1

ı = 1, 2

(8)

(9)

and where Cit and Nit are consumption and hours worked in country i. We assume
that 0 < β < 1, ν > 1 and ψ > 0. The presence of Xit makes preferences non-time-
separable in consumption and hours worked. As explained in Jaimovich and Rebelo
(2009), these preferences nest as special cases two well-known classes of utility func-
tions. When φ = 1, we obtain preferences of the class discussed in King, Plosser, and
Rebelo (KPR, 1988). When φ = 0 we obtain the preferences proposed by Greenwood,
Hercowitz, and Hu(cid:27)man (GHH, 1988). The closest we are to GHH preferences, the
lower the wealth e(cid:27)ect on labour supply.

ECB Working Paper 1946, August 2016102.4 Prices and equilibrium

As the production function in (2) is homogeneous of degree one, we have in equilib-
rium:

C1T t + I1t = q1
P2T t(C2T t + I2t) = q2

ata1t + q1

btb1t
ata2t + q2

btb2t

(10)

at and qi

where qi
bt are the prices of the two intermediate goods in each country and
P2T t is the price of the country-two good; all expressed in units of the country-one
(cid:28)nal tradable good (the numeraire). Obviously, with free movement of intermediate
goods the law of one price holds: q1
at = q2
bt = qbt ∀ t. We
thus de(cid:28)ne the terms of trade as the marginal rate of transformation between the
two intermediate goods in country one evaluated at equilibrium quantities; which (in
equilibrium) equals their relative price5:

at = qat and q1

bt = q2

pt =

qbt
qat

=

dY1T t
db1t
dY1T t
da1t

=

(cid:16)1 − ω
ω

(cid:17)(cid:16)

a1t/b1t

(cid:17) 1

θ

Similarly, equilibrium in local markets requires that:

P1tC1t = C1T t + P1N tC1N t

P2tC2t = P2T tC2T t + P2N tC2N t

(11)

(12)

where Pit, PiN t are respectively the price of aggregate consumption and the price
of non-tradables in country i. The price of the non-tradable good is de(cid:28)ned as the
marginal rate of transformation of the CES aggregator of (cid:28)nal consumption (equation
(6)):

P1N t =

P2N t
P2T t

=

(cid:16) 1 − ωT
ωT
(cid:16) 1 − ωT
ωT

(cid:17)(cid:16)

C1T t/C1N t

(cid:17) 1

ρ

(cid:17)(cid:16)

C2T t/C2N t

(cid:17) 1

ρ

(13)

The real exchange rate is de(cid:28)ned as the relative price of aggregate consumption across
countries:

Qt =

P2t
P1t

(14)

5Notice that this is not the standard de(cid:28)nition of terms of trade, as it represents the relative
price of imports (the foreign good) in terms of exports (the local good). However, this is consistent
with the standard de(cid:28)nition of the real exchange rate in macroeconomic models.

ECB Working Paper 1946, August 2016112.5 Shocks

Finally, we close the model by specifying the technology process which constitutes
the exogenous variable in our system and the sole driving force of (cid:29)uctuations:









Z1T t
Z2T t
Z1N t
Z2N t

















=

0.9616 −0.0402 −0.2303
0.9616
−0.0402
0.0396 −0.0083
0.0396
−0.0083

0.1748
0.1748 −0.2303
0.0730
0.5595
0.5595
0.0730

















Z1T t−1
Z2T t−1
Z1N t−1
Z2N t−1











+















ε1T t−q
ε2T t−q
ε1N t−q
ε2N t−q

(15)

, q ≥ 0

with the following variance-covariance matrix:









V =

0.0059 0.0005 0.0015 0.0001
0.0005 0.0059 0.0001 0.0015
0.0015 0.0001 0.0018 0.0004
0.0001 0.0015 0.0004 0.0018









×

1
100

(16)

We estimate Solow residuals using the EU-KLEMS database for the period 1978-
20046. Country one is the US and country two is a (cid:16)Rest of the World aggregate(cid:17)
comprised by EU-15, Canada and Japan. Shocks are pure surprises when q = 0,
whereas assuming q > 0 allows the technology shock to be forecastable with certainty
in advance (news-shock). Note that under this speci(cid:28)cation, shocks are either ex-
pected or not, irrespective of the country or sector of origin. It is worth emphasising
that q > 0 does not change the exogenous sources of persistence and volatility of the
system since neither the matrix of autoregressive coe(cid:30)cients nor the volatility of the
shocks have changed7. The mere change is in the timing of the shock. In other words,
the two processes are observationally equivalent. That is, an econometrician trying
to estimate equation (15) cannot know whether shocks are expected or unexpected;
for as long as she uses only the data in vector Zt to estimate the shock.

2.6 Calibration, Steady-State and Solution Method

We calibrate all parameters of our model to annual data while following closely previ-
ous studies. We choose a rate of time preferences β equal to 0.9615 that corresponds
to an annual real interest rate of 4%. Following Jaimovich and Rebelo (2009), we

6See O(cid:48)Mahony, M. and Marcel, P. T. (2009).
7Any change would be endogenous, resulting from changes in the behaviour of rational agents in

light of new information.

ECB Working Paper 1946, August 201612set φ = 0.001, such that preferences are close to the GHH form, and ν = 1.4 corre-
sponding to an elasticity of labour supply equal to 2.5. Parameter ψ is adjusted so
that at the steady-state agents spend 33% of their time on market activities. The
elasticity of substitution of tradable intermediate goods seems to be one of the most
controversial parameters in the open-economy literature. This is not only due to
the uncertainty surrounding the empirical studies that attempt to estimate its value,
but mostly for its important implications about the transmission mechanism of TFP
shocks (see Cole and Obstfeld 1991, Corsetti et al 2008). According to Backus, Kehoe
and Kydland (1994) the most reliable empirical studies estimate it between one and
two, thus they calibrate it at 1.5, whereas Corsetti et al (2008) claim that the range
of variation is wider, from 0.1 to 2 (see Hooper et al 2000). On the other hand, the
trade industrialisation literature tends to assign higher values (see for example R. Jaef
2011). For our benchmark parametrisation we set trade elasticity to two, which is a
bit higher compared to BKK but well within the range of estimates mentioned above.
This value is also used by Benigno and Thoenissen (2008) and Karabarbounis (2010)
estimates it to 1.907. As part of our sensitivity analysis we test the performance of
our model to di(cid:27)erent values.

We assume that the two (cid:28)nal goods are complements in consumption (ρ = 0.74 <
1). This value is estimated by Mendoza (1991) and used by Corsetti et al (2008).
Stockman and Tesar (1995) set this parameter lower to 0.44 but their sample includes
developing countries as well. The degree of home-bias is calibrated assuming an
import share equal to 5% while the bias towards the tradable consumption good is
set assuming that its share in aggregate consumption is 47%, following Corsetti et
al (2008). As for the production function, we assume that the labour share is 61%
in tradables production and 56% in non-tradables production. We assume a level of
investment adjustment costs equal to 0.05. This value is lower than in other studies
where it is often chosen to match the relative variance of investment. In our model
investment is not too volatile so we set κ to the minimum value consistent with
expectations-driven cycles following a news-shock to the tradables sector in country
one under the benchmark parametrisation (see more below). We choose to focus on
the tradables sector since it is the main driver of aggregate (cid:29)uctuations.

We now move on to the choice of the elasticity of substitution of capital services,
for which to our knowledge there are no empirical estimates8. Given the uncertainty

8Mendoza and Uribe (2000) calibrate it to −0.11 for Mexican data because this value ensures
that the response of the non-tradables’ price to a (cid:16)devaluation-risk shock(cid:17) matches the empirical one
estimated in a Vector Autoregression (VAR). Arellano et al (2009) use this value for Ivory Coast,
simply following these authors. However, simply adopting this value would not be appropriate since

ECB Working Paper 1946, August 201613Table 1: Parametrisation

Preferences
β = 0.9615

1
ν−1
γ = −1
φ = 0.001
ψ

Elasticity of substitution

θ = 2
ρ = 0.74
ε = 1.67

Bias

ω = 0.772
ωT = 0.445

Technology
αT = 0.39

αN = 0.44

δ = 0.10

Investment
κ = 0.05

Utilisation

δ(cid:48)(cid:48)(¯u)
δ(cid:48)(¯u) ¯u = 0.15

Discount factor
Elasticity of labour supply at 2.5

Risk Aversion equal to two
Balance between KPR and GHH utility function
Steady-state labour supply: 33%

Annual interest rate of 4%
Jaimovich and Rebelo (2009)

Backus, Kehoe and Kydland (1994)
Jaimovich and Rebelo (2009)

Home and foreign intermediate good
Tradable and Non-tradable good
Capital Services

Benigno and Thoenissen (2008)
Mendoza (1991)
Estimated

Home bias
Bias in tradables consumption

Import share: 5%
Consumption share of tradables: 47%

Capital share in
tradables production
Capital share in
non-tradables production
Annual depreciation rate

Corsetti et al (2008)

Corsetti et al (2008)

Level of adjustment costs

Positive responses to expected shock

Elasticity of marginal depreciation

Jaimovich and Rebelo (2009)

ECB Working Paper 1946, August 201614and lack of empirical evidence surrounding the value of this parameter, we estimate it
as to minimise the distance between some theoretical moments - in economies driven
by surprise TFP shocks - and their empirical counterparts. The chosen moments are
the correlations of the real exchange rate with respect to relative output, terms of
trade, and the net exports to GDP ratio9. Strong HBS e(cid:27)ects are likely to drive the
(cid:28)rst two moments in opposite directions, so including them in the estimation ensures
a fair balance between the two. The last moment helps to resemble the co-movements
in relative prices and international trade (cid:29)ows as in the data. We perform the exercise
also using only the last two moments, i.e. the correlation of the real exchange rate
with the terms of trade and with the ratio of net exports over GDP. As mentioned,
investment adjustment costs are necessary in our model to ensure positive response
of hours, investment and output following an announced increase in tradables TFP.
We would like to choose the lowest value consistent with the latter. Therefore, we
proceed our exercise as follows: (cid:28)rst, we run our method of moments estimation for ε
in economies driven by unexpected shocks to TFP, using a relatively high value of the
investment adjustment cost parameter (0.055). Such a value ensures that the model
produces expectations-driven booms, once shocks are allowed to be anticipated, for
any degree of capital substitutability. This exercise gives an optimum value of ε equal
to 1.492 if we take into account all the three moments and 1.856 if we include only the
last two; on average 1.6710. At this value, the calibrated choice for the investment-
adjustment cost parameter is 0.05. Note that the minimum distance estimator of ε
when κ = 0.05 is still very close to 1.67, validating our choice.

Finally, we discuss issues concerning capacity utilisation. The depreciation func-

tion is assumed to be quadratic of the form:

δ(ut) = δ0 + δ1(uit − ui) +

δ2
2

(uit − ui)2

(17)

Setting δ0 = 0.1 we ensure that the depreciation rate is 10% per annum at the
steady-state. Moreover, we assume a constant steady-state utilisation rate (equal to
unity) and we calibrate the elasticity of marginal depreciation to δ(cid:48)(cid:48)(u)
u = 0.15,
following Jaimovich and Rebelo (2009). As these authors explain, a low elasticity

δ(cid:48)(u) u = δ2
δ1

we focus on developed economies.

9Speci(cid:28)cally, we estimate the sum of quadratic deviations of model-estimated (asymptotic) mo-
ments vis - (cid:224) - vis the data. We select the value of ε that minimises the quadratic loss function.
Moments are equally weighted, which ensures that the general method of moments estimator is
unbiased and consistent.

10Figure 13 in the Appendix plots these loss functions. They are both well de(cid:28)ned and a global

minimum is attained.

ECB Working Paper 1946, August 201615of δ(cid:48)(u) implies that utilisation is more responsive to shocks, resulting to a powerful
ampli(cid:28)cation mechanism.

Given the parameters, we solve the problem of the social planner who weights both
countries equally. We log-linearise the model around the symmetric, non-stochastic
steady-state and we solve it using standard numerical methods.

3 Results

3.1 Unconditional Correlations

In this section we describe our benchmark results, which are presented in Table 2.
Both empirical and model-generated data are HP-(cid:28)ltered with a smoothing parameter
equal to 10011. Theoretical moments are asymptotic.

First, we note that in this benchmark parametrization, the model is able to gener-
ate positive correlations of economic aggregates across countries for any type of shock.
For shocks that are pure surprises the model produces higher cross-country correla-
tions for consumption and hours than observed in the data and lower correlations of
output and investment. Cross-country correlations are slightly lower in news-driven
economies. Finally, the model produces a higher correlation in consumption than
output when we observe the contrary in the data.

The most novel results of the paper come from the statistics on relative prices
across countries. The correlation between bilateral relative consumption and the real
exchange rate is positive and relatively strong (0.51) in a world where shocks are
unexpected, but drops by almost sixty basis points and becomes negative (−0.10) in
news-driven cycles. Morover, the correlation between the real exchange rate and rel-
ative output which is positive when shocks are pure surprises becomes negative when
shocks are anticipated, as in the data. The correlation of the real exchange rate with
the terms of trade and net exports maintains the correct sign despite some changes
in magnitude. Importantly, these signi(cid:28)cant improvements observed when allowing
productivity shocks to be anticipated come at no cost in terms of international co-
movement. All international correlations remain largely unchanged and positive. At
the same time, a worldwide economic expansion pursues good news about the future
state of productivity (see below).

Other successful features include counter-cyclical net exports and strong pro-

11Our results are largely unchanged when we use a smoothing coe(cid:30)cient of 6.25 as advised in

Ravn and Uhlig (2002). These results are reported in Table 7.

ECB Working Paper 1946, August 201616Table 2: Baseline Model

St. Deviation relative to GDP

Consumption
Investment
Hours
Real Exchange Rate
Terms of Trade

Correlation between real GDP and

Real Net Exports

International co-movements

Output
Consumption
Hours
Investment

Correlation between RER and

Rel. Consumption
Rel. Output
Terms of Trade
Real NX over GDP

Unexpected News
Shocks

Shocks

Data

0.81
3.50
0.78
2.91
2.04

0.58
2.02
0.66
0.12
0.45

0.55
2.11
0.65
0.21
0.39

-0.56

-0.20

-0.38

0.35
0.25
0.12
0.21

-0.51
-0.46
0.72
0.35

0.21
0.32
0.26
0.13

0.51
0.45
0.72
0.56

0.16
0.28
0.23
0.08

-0.10
-0.22
0.34
0.83

Actual data are from UPENN World Tables, 1970-2011 at annual frequency. Both empiri-
cal and model-generated data are HP-(cid:28)ltered with a smoothing parameter equal to 100.
Theoretical moments are asymptotic.

cyclical movements in employment, investment and consumption within countries
(not shown). On the other hand, the model generates too little volatility, especially
for relative prices - a common problem of open-economy models (BKK, Heathcote
and Perri 2002). Nevertheless, the real exchange rate is almost twice as volatile in
the news-driven economy.

3.2

International Co-movements

The main insight of our model is that news-driven international cycles as discussed
in Beaudry, Dupaigne and Portier (2011) and Jaimovich and Rebelo (2009) can also
be consistent with a negative correlation between the real exchange rate and relative
consumption.

Consider an anticipated shock to the tradables TFP in country one.

Impulse
Investment adjustment costs provide an incentive
responses are given in (cid:28)gure 1.
for investment smoothing so that the response is positive on impact. An increase in
investment today lowers the value of installed capital since adjustment costs mean that
higher investment today lowers the cost of augmenting the capital stock in the future.
As capital is less valuable, it becomes e(cid:30)cient to increase its rate of utilisation. The

ECB Working Paper 1946, August 201617Figure 1: World expansion generated by an expected shock to the tradables sector TFP of
country one. Solid lines: country one. Dashed lines: country two. Percentage deviations
from steady-state, except for net exports.

latter increases the marginal productivity of labour hence, given almost zero wealth
e(cid:27)ects on labour supply, workers postpone leisure raising hours and output. In the
foreign country agents also anticipate a future increase in their income, coming from
positive cross-country productivity spillovers, since we assume that news is a common,
public announcement. Therefore, the response is similar to that of country one but
weaker.

Jaimovich and Rebelo (2009) show that preferences with low wealth e(cid:27)ects on
labour supply, investment adjustment costs and variable capacity utilisation are con-
sistent with a pro-cyclical response to news about a permanent change in TFP in
a single-sector, closed-economy model12. A major contribution of our work is to
extend their analysis to a two-country world consistent with news-driven economic
expansions both within and across countries. These elements serve as a powerful
source of international business cycle synchronization under expected shocks to the
(tradables) TFP. On the other hand, Beaudry and Portier (2007) show that cost-
complementarities can also deliver within country co-movements in a multi-sector

12In an earlier part of their work (Jaimovich and Rebelo 2008) they derive similar results in the

context of a small open-economy model.

024681000.511.5Consumption02468100123Output02468100246Investment024681000.511.52Hours02468100123Utilisation0246810−0.0500.050.10.15Net Exports over GDPECB Working Paper 1946, August 201618economy for as long as the elasticity of labour supply is not too low. Beaudry, Du-
paigne and Portier (2011) develop a multi-sector model of national and international
business cycles with complementarities between capital and labour in the produc-
tion of the consumption good, as well as sector-speci(cid:28)c factors of production. We
show that complementarities are not necessary once we allow for the elements of our
model.

To sum up, we have shown that our model is able to replicate two of the most
well-known empirical facts of international macroeconomics: positive international
co-movements of economic aggregates (both unconditionally and conditional to a
news-shock) and a negative correlation between relative consumption and the real
exchange rate. In what follows, we analyse in detail the mechanisms that drive our
results, especially with respect to the B-S correlation.

4

Inspecting the mechanism

4.1 The Balassa - Samuelson e(cid:27)ect

There is no consensus on the impact of sectoral productivity di(cid:27)erentials and the
relative price of non-tradables on real exchange rate movements. Kakkar (2003),
Bergstrand (1991), De Gregorio and Wolf (2004) and Corsetti et al (2006) document
empirical evidence in favour of Balassa-Samuelson e(cid:27)ects, whereas Betts and Kehoe
(2006) document an important role for the relative price of non-tradables to the US-
Canada and US-Mexico real rate (see also Mendoza and Uribe 2000). On the other
hand, Engel (1999), Engel and Rogers (1996) and Chari, Kehoe and McGrattan (2002)
(cid:28)nd that most of the real exchange rate variability is due to tradables and deviations
from the law of one price.

Consider a temporary, but persistent, TFP shock to the home tradable-good sector
alone13. The dynamics are governed by the well-known Harrold-Balassa-Samuelson
framework: the terms of trade depreciate - re(cid:29)ecting e(cid:30)ciency in international (cid:28)-
nancial markets - and the price of the non-tradable good increases re(cid:29)ecting sectoral
productivity di(cid:27)erentials and free labour mobility across sectors. The response of the
real exchange rate will depend on the relative strength of the two e(cid:27)ects: the terms
of trade e(cid:27)ect that pushes towards a depreciation and the Balassa-Samuelson e(cid:27)ect
that pushes towards an appreciation. Under our parametrization, the (cid:28)rst e(cid:27)ect wins

13We choose to analyse responses to shocks in the tradables sector TFP as these are the main
drivers of cycles. Responses to shocks to the non-tradables sector productivity are provided in the
appendix ((cid:28)gures 11 and 12).

ECB Working Paper 1946, August 201619Figure 2: The HBS e(cid:27)ect in the benchmark model. The response of relative prices (upper
panel), i.e. the real exchange rate (RER), the terms of trade (TT) and the relative price of
non-tradables (RER-NT), and relative consumption (lower panel) to one standard deviation
unexpected shock to the tradable-goods sector. Percentage deviations from the steady state.

and the real exchange rate depreciates on impact (see Figure 2). However, the real
exchange rate moves on a downward path for one period (appreciation) and then de-
preciates for several years before returning to its initial level. On the other hand, rel-
ative consumption increases on impact as home-bias drives home-consumption higher
and thereafter consumption-smoothing prevails to ensure a smooth, downward path.
The dynamics are a bit di(cid:27)erent when TFP improvements are perfectly antici-
pated one period in advance, where the correlation between the real exchange rate
and relative consumption is negative. Impulse Response Functions (IRFs) are given
in (cid:28)gure 3. When faced with unexpected technology improvements the terms of trade
depreciate to re(cid:29)ect the scarcity of the foreign good; they depreciate in response to
positive news about the future to re(cid:29)ect the fall in the relative demand of the home
good. The relative price of the home non-tradable good also falls, implying an overall
depreciation of the real exchange rate. The intuition is that following the announce-
ment, the home-country enjoys higher future wealth; a demand-side e(cid:27)ect that pushes
towards an appreciation. For the same reason, though, utilisation increases more in
the home-country, increasing relative supply and creating forces towards a deprecia-

0123456789−0.4−0.200.20.40.60.81Periods following the shock  RERRER − NTTT01234567890.70.80.911.1Periods following the shockECB Working Paper 1946, August 201620tion. Given the model’s features and the speci(cid:28)ed parametrization, the latter e(cid:27)ect
dominates and the real exchange rate depreciates on impact14. Thereafter, the real
exchange rate follows a downward path for one period when relative consumption
increases. This discrepancy in the response of the two variables during the interim-
period (i.e. between the announcement and the actual TFP change) drives their
correlation down. Abstracting from the impact response, the two variables move in
opposite direction for two periods instead of one as was the case for surprise shocks.
Had the news arrived two periods in advance, they would be moving so for three
periods and so on; which explains why the B-S statistic falls almost monotonically
with the length of the interim period15.

The dynamics of the real exchange rate can be more clearly understood from the
equations of the model. With complete markets, the real exchange rate equals the
ratio of the marginal utility of consumption, such that in the log-linearised model16:

ˆrert = ˆUc2t − ˆUc1t = A(ˆc1t − ˆc2t) − B(ˆn1t − ˆn2t)

=> corr( ˆrert, ˆc1t − ˆc2t) =

1
sd( ˆrert)

[A sd(ˆc1t − ˆc2t) − B corr(ˆn1t − ˆn2t, ˆc1t − ˆc2t) sd(ˆn1t − ˆn2t)]

(18)

where A and B are positive constants17 and sd(.) stands for standard deviation. Non-
seperability between consumption and leisure in the utility function breaks the tight
link between the real exchange rate and relative consumption. When the marginal
utility of consumption is not in(cid:29)uenced by the leisure choice (i.e. B = 0), the real
exchange rate moves in direct proportion to relative consumption. Quantitatively,
a strong positive correlation between relative consumption and relative hours con-
tributes to a lower correlation between the real exchange rate and relative consump-
tion. Indeed, the correlation between relative consumption and relative hours is pos-
itive and high in both versions of the model, a consequence of extremely low wealth
e(cid:27)ects on labour supply18. Allowing shocks to be perfectly anticipated one period in
advance has almost no e(cid:27)ect on the relative-consumption-relative-hours correlation;

14Di(cid:27)erently, the social planner chooses an equilibrium with lower prices but higher output for

the country that receives the good news and higher prices and lower output for the other.

15We analyse the performance of our model to lengthier interim periods later.
16This corresponds to the case of GHH preferences, i.e. for φ = 0. When φ (cid:54)= 0 the B-S correlation
is also in(cid:29)uenced by the corss-country di(cid:27)erence in Xt and the langrange multiplier on the constraint
in equation (9).

17A ≈ 4.96 and B ≈ 4.14.
18When φ = 1 the B-S correlation is 0.54 when shocks are surprises and 0.58 with news-shocks.
The correlation between relative consumption and relative hours is signi(cid:28)cantly lower, especially
when shocks are anticipated (0.37).

ECB Working Paper 1946, August 201621yet the B-S correlation is signi(cid:28)cantly lower. The channel through which this works is
via a bigger drop in the standard deviation of relative consumption vis-(cid:224)-vis relative
hours, such that the term in square-brackets becomes negative19. Low wealth e(cid:27)ects
on labour supply contribute signi(cid:28)cantly to the results on two dimensions: (cid:28)rst, they
allow for a strong positive co-movement between relative consumption and relative
hours irrespective of the timing of the shock. Second, following the news-shock hours
increase as part of the worldwide economic expansion and the B-S correlation turns
negative.

Our work suggests an alternative explanation to the consumption-real exchange
rate anomaly through two main channels: strong Balassa-Samuelson e(cid:27)ects and news-
shocks. Strong Balassa-Samuelson e(cid:27)ects are essential to give rise to a negative B-S
correlation in economies with complete asset markets. As the terms of trade depreci-
ate in response to productivity improvements to ensure a positive international trans-
mission of technological innovations, a low or negative correlation between the real
exchange rate and relative consumption can come about only through a relatively
strong appreciation of the relative price of the non-tradable good across countries
(see Corsetti, Dedola and Viani 2011). In our model, the Balassa-Samuelson e(cid:27)ect
is signi(cid:28)cantly ampli(cid:28)ed by the imperfect elasticity of substitution of capital services
across sectors, resulting in a strong appreciation of the relative price of non-tradables
(see (cid:28)gure 2). When the capital elasticity of substitution is less than in(cid:28)nite, and
indeed as low as 1.67, the response of the price of the non-tradable good is much
stronger re(cid:29)ecting the costly exchange of capital across sectors. Therefore, this im-
perfect substitutability of capital is an essential element for a correlation between the
real exchange rate and relative consumption that is low and quite far from unity - at
0.51 in economies where TFP innovations are not anticipated20. Note that in models
hinging on the price of non-tradables to explain the consumption-real exchange rate
anomaly, an almost unavoidable cost is a low correlation between the real exchange
rate and the terms of trade; which in the data is high and positive. Benigno and
Thoenissen (2008) also develop a model where the B-S result is achieved via Balassa-
Samuelson e(cid:27)ects but the correlation between the real exchange rate and the terms of
trade is negative in their benchmark case. In the context of our model the correlation
between the real exchange rate and the terms of trade remains positive under both

19However, as the standard deviation of the real exchange rate is almost twice as high in news-

driven economies, the absolute value of the B-S correlation is smaller.

20The B-S puzzle is much stronger when capital services are homogeneous and, in these economies,
the relative price of the non-tradable good depreciates in response to a shock in tradables’ TFP. We
analyse in detail the quantitative implications of sectoral capital substitution in the next sub-section.

ECB Working Paper 1946, August 201622Figure 3: The HBS e(cid:27)ect in the benchmark model. The response of relative prices (upper
panel), i.e. the real exchange rate (RER), the terms of trade (TT) and the relative price of
non-tradables (RER-NT), and relative consumption (lower panel) to one standard deviation
expected shock to the tradable-goods sector. Percentage deviations from the steady state.

theoretical economies with unexpected and expected TFP innovations. Notice also
that a low correlation between these two relative price measures is not ultimately
related to e(cid:30)ciency, as in the model of Benigno and Thoenissen (2008) markets are
incomplete21.

On the other hand, news-shocks contribute to our results by making (cid:29)uctuations
in relative hours an important determinant of movements in the real exchange rate, as
shown in equation (18). Corsetti et al (2008) show that a negative B-S correlation can
arise in economies where shocks are highly persistent, the trade elasticity of substitu-
tion is high (equal to 4) and markets are incomplete. Highly persistent shocks ensure
that the gap between the short-run and long-run response of output is su(cid:30)ciently
big; and by consumption-smoothing the increase in the demand of the home good is
high enough. Further, high elasticity of substitution is necessary in those cases to
ensure that the world economy absorbs the future larger supply of home tradables.

21Cole and Obstfeld (1991) and Heathcote and Perri (2002) show that the terms of trade depreciate
in response to a productivity shock even in conditions of (cid:28)nancial autarky in order to account for
the missing (cid:28)nancial markets.

0123456789−0.4−0.200.20.40.60.81Periods following the shock  RERRER − NTTT012345678900.20.40.60.811.21.4Periods following the shockECB Working Paper 1946, August 201623And (cid:28)nally, incomplete markets contribute to widening the gap between the wealth
e(cid:27)ects enjoyed by the consumers of each country; therefore implying a much higher
increase in the relative demand of the home good (see also Baxter and Cruccini 1995).
Our analysis complements Corsetti et al (2008) and Baxter and Cruccini (1995) by
analysing an economy where the shock-process is not only persistent22 but also inno-
vations are anticipated in advance, and the degree of substitution of tradable goods
is equal to two23. In that case, we show that a negative correlation between the real
exchange rate and relative consumption can also arise in Arrow-Debreu economies.

Our theoretical model has shown that the Backus-Smith puzzle is not necessarily
a question of imperfect risk sharing or of a low elasticity of substitution between
tradable goods.
Instead, a negative B-S correlation can be the e(cid:30)cient allocation
in an economy where wealth e(cid:27)ects on labour supply are very low, HBS e(cid:27)ects are
relatively strong, the elasticity of substitution of tradables is within the range of
empirical estimates and shocks are anticipated one period in advance. Corsetti et al
(2008) propose an alternative mechanism in incomplete markets: TFP improvements
endogenously generate wealth e(cid:27)ects that are so strong that result in a marked rise
in demand and drive up all prices24. Their argument is very intuitive and their model
matches international business cycle facts on many dimensions. Nevertheless, that
mechanism is a su(cid:30)cient explanation to the Backus-Smith puzzle for as long as the
trade elasticity is very low (0.425), quite lower relative to the values often used in the
literature (between 1-2); a point made also by Karabarbounis (2010). Corsetti, Dedola
and Vianni (2011) document empirically that the channel proposed in Corsetti et al
(2008) is important to explain the low degree of international risk sharing. Enders
and M(cid:252)ller (2009) support this view by showing that the international transmission
mechanism of permanent TFP shocks is consistent with a model where the elasticity
of substitution is low and international markets are incomplete.

Stockman and Tesar (1995) were among the (cid:28)rst to introduce non-tradables in an
otherwise standard model of the international business cycle. Despite some improve-
ments in explaining features of the data compared to models with only tradables (e.g.
BKK), they argue that a world-cycle driven by disturbances to both TFP and pref-
erences matches data much better. In a similar vein, we show that allowing for TFP

22Remember that the autoregressive parameter of tradables TFP shocks is 0.96 in our model.
23When the substitutability of the tradable goods across countries is low, the B-S correlation is
positive and high. We perform a sensitivity analysis to this parameter at a later part of the paper.
24Although their model features non-tradable goods, strong HBS e(cid:27)ects are not essential for their
results. Additionally, their model exhibits deviations from the law of one price for tradables due to
the presence of (non-tradable) distribution services in the production of tradable goods.

ECB Working Paper 1946, August 201624disturbances to be anticipated brings the model-results into greater conformity with
the data; especially with what concerns the relation between relative prices, quantities
and consumption bundles25. Our work shares some similarities with Stockman and
Tesar (1995): in both studies demand-side e(cid:27)ects come about from the exogenous pro-
cess of the model, and both type of disturbances - i.e. news-shocks and taste-shocks
- do not increase current e(cid:30)ciency. Nevertheless, taste-shocks cannot be very accu-
rately estimated in the data (Mandelman et al 2011), unlike TFP disturbances. At
the same time, our exogenous process is consistent with empirical evidence that TFP
innovations are to a large extent anticipated and can have important implications for
cyclical (cid:29)uctuations (Beaudry and Portier 2006).

Ra(cid:27)o (2010) proposes an alternative story to explain the consumption-real ex-
change rate anomaly, hinging on investment-speci(cid:28)c technology (IST) shocks (see
also Rabanal et al 2008). As he explains, such shocks cause big shifts in domestic
absorption, such that aggregate demand exceeds supply and the terms of trade have
to appreciate to clear the market. How appealing this mechanism can be, it implies
a low, if not negative, correlation of investment across countries. The non-tradables
sector in our model and the strength of the Balassa-Samuelson e(cid:27)ect decrease the
importance of this mechanism and can provide a low B-S correlation without huge
di(cid:27)erences in relative investment26. Ra(cid:27)o’s work has also been criticised by Mandel-
man et al (2011). They show that once IST shocks are estimated in the data they do
not appear to provide a su(cid:30)cient explanation to some well-known puzzles in interna-
tional economics. In our model we (cid:28)t exogenous sectoral-TFP shocks as estimated in
the data.

Finally, our work adds to the growing literature of expected innovations. Beaudry
and Portier (2004, 2007) and Jaimovich and Rebelo (2009) develop models that are
consistent with within-country news-driven cycles, whereas Beaudry, Dupaigne and
Portier (2011) extend the latter to international co-movements. We show that news-
shocks can also help us better understand movements in relative prices. To our
knowledge, Opazo (2006) was the (cid:28)rst to consider news-shocks as a possible expla-
nation of the B-S puzzle via demand-side e(cid:27)ects, but in his model investment and
employment in both countries fall in response to news and the unconditional cor-

25Corestti et al (2008) also analyse taste-shocks in their model to show that an economy with
Arrow-Debreu securities can also be compatible with a negative B-S correlation as these disturbances
weaken the tight link between relative consumption and relative marginal utility.

26Note that investment-speci(cid:28)c shocks and news-shocks to TFP share a common feature: they
do not a(cid:27)ect current aggregate e(cid:30)ciency, resembling taste-shocks. Yet, our model is successful in
generating a negative B-S correlation and a positive cross-country investment correlation.

ECB Working Paper 1946, August 201625relation of investment across countries is negative27. Moreover, the theoretical B-S
correlation is low but not negative. Our model improves on Opazo’s work by gen-
erating world expansions following improved technological prospects, a negative B-S
statistic and positive unconditional correlations. In a similar spirit, Nam and Wang
(2010)[a] observe that the US terms of trade and real exchange rate appreciate when
US labour productivity is high28. They show that this behavior can be replicated
in an incomplete markets model with monopolistic competition, sticky prices and
producer currency pricing driven by expected shocks to permanent productivity. Our
analysis complements theirs since we show that a negative B-S correlation need not be
necessarily connected to lack of risk sharing, imperfect competition, money or other
frictions in news-driven environments.

4.2

Imperfect Substitutability of Capital Services

The simple Balassa-Samuelson model has di(cid:30)culty replicating observed movements in
relative prices. If factors are homogeneous, movements in the price of non-tradables
depend on relative factor shares across sectors (αT − αN ) and changes to sectoral
capital-labour ratios. Empirically, however, there seems to be little evidence on the
massive sectoral shifts in capital-labour ratios required to produce large movements in
the price of non-tradable goods (Mendoza and Uribe 2000). Thereby, allowing capital
to be sector-speci(cid:28)c can be potentially promising as the prices would react to re(cid:29)ect
the degree of substitutability. This section analyses quantitatively this channel.

The consumption-real exchange rate anomaly arises in a world where capital ser-
vices are perfectly substitutable (function g(.) in equation (5) is linear). Statistics
for this economy are given Table 3. For a comparison with the benchmark case, we
reproduce graph 2 under economies with perfect substitutability of capital ((cid:28)gure 4).
The reaction of the terms of trade is not very di(cid:27)erent in the two economies. On
the other hand, the reaction of the relative price of non-tradables is much di(cid:27)erent,
appreciating strongly in the benchmark model but depreciating in economies with ho-
mogeneous capital (see (cid:28)gure 5). Therefore, the Balassa-Samuelson channel is strong

27Note also that Opazo (2006) assumes news to be an imperfect public signal.
28Enders and M(cid:252)ller (2009) show that technology shocks as identi(cid:28)ed in a SVAR with long-run
restrictions appreciate the US terms of trade. Corsetti et al (2006) obtain a similar response to per-
manent TFP shocks in manufacturing, their proxy for the tradables sector. Alquist and Chinn (2002)
show that a one percentage point increase in the US - Euro Area productivity di(cid:27)erential can imply
up to a (cid:28)ve percent appreciation in the dollar-euro real exchange rate, we get similar results using
SVAR and cointegration methods to identify permanent world technology shocks (Lambrias 2011).
Interestingly, Nam and Wang (2010)[b] show that news-shocks to technology are associated with a
US terms of trade appreciation whereas unexpected disturbances are associated with a depreciation.

ECB Working Paper 1946, August 201626Table 3: Homogeneous Capital Model

St. Deviation relative to GDP

Consumption
Investment
Hours
Real Exchange Rate
Terms of Trade

Correlation between real GDP and

Real Net Exports

International co-movements

Output
Consumption
Hours
Investment

Correlation between RER and

Rel. Consumption
Rel. Output
Terms of Trade
Real NX over GDP

Unexpected News
Shocks

Shocks

Data

0.81
3.50
0.78
2.91
2.04

0.64
1.89
0.69
0.26
0.45

0.61
1.97
0.69
0.25
0.39

-0.56

-0.10

-0.33

0.35
0.25
0.12
0.21

-0.51
-0.46
0.72
0.35

0.21
0.30
0.25
0.13

0.95
0.93
0.95
0.12

0.16
0.26
0.22
0.08

0.65
0.56
0.85
0.31

Actual data are from UPENN World Tables, 1970-2011 at annual frequency. Both empiri-
cal and model-generated data are HP-(cid:28)ltered with a smoothing parameter equal to 100.
Theoretical moments are asymptotic.

Figure 4: The HBS e(cid:27)ect in the model with homogeneous capital. The response of relative
prices (upper panel), i.e. the real exchange rate (RER), the terms of trade (TT) and the
relative price of non-tradables (RER-NT), and relative consumption (lower panel) to one
standard deviation unexpected shock to the tradable-goods sector. Percentage deviations
from the steady state.

01234567890.10.20.30.40.50.60.70.8Periods following the shock  RERRER − NTTT01234567890.70.80.911.11.2Periods following the shockECB Working Paper 1946, August 201627Figure 5: The response of the relative price of non-tradables (RER-NT) to one standard
deviation unexpected shock to the tradable-goods sector in the benchmark model (straight
line) and in the model with homogeneous capital (dashed line). Percentage deviations from
the steady state.

and signi(cid:28)cant in the benchmark model whereas it is hardly present in economies
where capital services are homogeneous across sectors as the price of non-tradables
moves in line with the terms of trade.

The reason why the response of the the price of non-tradable goods is di(cid:27)erent
across the two economies is because imperfect capital substitutability creates a bias
towards tradables, as it can be seen by the relative response of capital services across
sectors (ST 1t − SN 1t in (cid:28)gure 6, lower panel)29. The di(cid:27)erence in the capital allocated
across sectors is much higher in the benchmark economy compared to the perfect-
substitutability case. Similarly, the lower the substitutability of capital the higher this
di(cid:27)erence, as can be seen in the response of ST − SN for ε = 1.45 and the associated
response of PN ((cid:28)gure 6, upper panel). More intense use of capital in the tradables
sector boosts the marginal product of labour and consequently the wage; exactly in
line with the Balassa-Samuelson doctrine but only stronger. To demonstrate this
argument through the equations of the model, using the (cid:28)rst order conditions of
capital and labour across sectors and doing some algebra gives:

˜PN =

ZT
ZN

αT
αN
(cid:124)

(cid:16) ST
NT

(cid:17)αT −1(cid:16) SN
NN

(cid:123)(cid:122)
HBS ef f ect

(cid:17)−αN −1

(cid:125)

(cid:17)1/ε

(cid:16) ST
SN
(cid:125)
(cid:123)(cid:122)
(cid:124)
Ef f ect of g(.)

(19)

˜PN = PN /qa.

where ˜PN is the relative price of the non-tradable good to the intermediate good
a, i.e.
In the classic Balassa-Samuelson framework movements in
the non-tradables’ price occur due to di(cid:27)erences in factor intensities (αT − αN ) and
sectoral capital-labour shares. Allowing for ε < ∞ provides an additional source of
(cid:29)uctuations in PN and consequently the real exchange rate. From the prespective of
equation (18), when ε → ∞ the standard deviation of relative consumption is higher

29For what follows, the analysis is within country one.

0123456789−0.4−0.200.20.40.6  BenchmarkHomog. CapitalECB Working Paper 1946, August 201628Figure 6: Response of the price of non-tradables (PN , upper panel), and the capital services
di(cid:27)erential across sectors (ST − SN , lower panel) to an unexpected shock to tradables TFP,
for di(cid:27)erent values of ε. Percentage deviations from steady-state.

and hours lower. Thus, the B-S correlation is positive and high.

Finally, we evaluate the importance of imperfect capital substitutability to the
results by plotting the variation in the B-S correlation as a function of ε in (cid:28)gure 7.
The bulk of the e(cid:27)ect is felt for values of the elasticity of substitution between one
and two and the correlation between the real exchange rate and relative consumption
reaches 0.90 already for ε = 3.2. Empirical evidence is not su(cid:30)cient to justify any
particular parametrization of ε. However, what our exercise has shown is that if this
parameter is determined as a minimum distance estimator between some key theo-
retical and empirical moments of the real exchange rate, it can be consistent with a
negative B-S correlation as well. As explained, the contribution towards the quantita-
tive outcomes of the model comes through an ampli(cid:28)cation of the Balassa-Samuelson
e(cid:27)ect. However, the intuition by which expected shocks lower the consumption-real
exchange rate correlation still holds. Even with homogeneous capital, the B-S corre-
lation in news-driven economies is by 30 percentage points lower than when shocks
are surprises (Table 3), while being consistent with international co-movements and
news-driven expansions.

At this point it is also worth emphasising that a negative correlation in the bench-

01234567890.20.40.60.811.21.41.6Periods following the shockPN  Benchmark; ε = 1.67Homog. Capital; ε → ∞ε = 1.45012345678900.511.522.533.5Periods following the shockST − SN  Benchmark; ε = 1.67Homog. Capital; ε → ∞ε = 1.45ECB Working Paper 1946, August 201629Figure 7: The correlation between the real exchange rate and relative consumption for
di(cid:27)erent values of elastisticity of substitution of capital services - ε. The horizontal line
shows the corresponding empirical statistic.

mark economy is the e(cid:30)cient allocation. Given the friction in capital markets, the
social optimum is such that much more capital services are allocated to the tradables
sector and the B-S correlation is negative. Put di(cid:27)erently, consumption being higher
where it is more expensive is the price to pay for e(cid:30)ciency in a world where - among
other things - capital markets are characterised by the function above. On the other
hand, absent any frictions in the (cid:28)nancial markets, the social planner chooses a more
even distribution of capital which has much lower impact on the marginal product of
labour, the wage and (cid:28)nally the price of non-tradables30.

4.3 Variable Capacity Utilisation

Jaimovich and Rebelo (2008, 2009) show that variable capacity utilisation in a small
open-economy and a closed-economy set-up can induce economic expansions in re-
sponse to productivity news-shocks. On the other hand, Baxter and Farr (2005) show
how utilisation in a two-country, incomplete markets model can help to explain the co-
movement problem, while increasing the variability of economic aggregates (see also
Burnside and Eichenbaum 1996). We combine both of these (cid:28)ndings in our model
to show that variable utilisation is an important element for re-producing empirically
relevant movements in relative prices as well.

Table 4 presents the quantitative features of a model where utilisation of capital is
(cid:28)xed at the steady-state value, for economies driven by traditional and expected dis-
turbances. Although the B-S correlation is now lower than in the benchmark model
with unexpected innovations (0.06), it is still positive and actually slightly higher in

30This intuition shares some similarities with Kocherlakota and Pistaferi (2007) who show that the
B-S puzzle can be a result of imperfect functioning of (cid:28)nancial markets within, rather than across,
borders.

12345678−1−0.500.51ECB Working Paper 1946, August 201630Table 4: Fixed Capacity Model

St. Deviation relative to GDP

Consumption
Investment
Hours
Real Exchange Rate
Terms of Trade

Correlation between real GDP and

Real Net Exports

International co-movements

Output
Consumption
Hours
Investment

Correlation between RER and

Rel. Consumption
Rel. Output
Terms of Trade
Real NX over GDP

Unexpected News
Shocks

Shocks

Data

0.81
3.50
0.78
2.91
2.04

0.61
2.03
0.64
0.50
0.58

0.57
2.15
0.63
0.52
0.61

-0.56

-0.11

-0.08

0.35
0.25
0.12
0.21

-0.51
-0.46
0.72
0.35

0.09
0.38
0.15
-0.15

0.06
-0.24
0.17
0.80

0.06
0.23
0.11
-0.05

0.10
-0.20
0.22
0.81

Actual data are from UPENN World Tables, 1970-2011 at annual frequency. Both empiri-
cal and model-generated data are HP-(cid:28)ltered with a smoothing parameter equal to 100.
Theoretical moments are asymptotic.

news-driven economies. Whether shocks are pure surprises or anticipated does not
signi(cid:28)cantly change the properties of the model. Moreover, the (cid:28)xed-capacity model
does not exhibit positive international co-movements as the unconditional correlation
of investment is negative under both expected and unexpected disturbances. Further,
absent variable capacity utilisation the model fails to generate news-driven expansions
as investment falls in both countries on impact31, the response of employment is null
in both countries and output increases only in country one but remains stagnant in
country two. As expected, consumption increases in both countries due to perfect
international portfolio diversi(cid:28)cation. Finally, we observe a remarkable fall in the
variability of output (not shown), illustrating the ampli(cid:28)cation e(cid:27)ect of varying capi-
tal services (Jaimovich and Rebelo 2009, Burnside and Eichenbaum 1996, Baxter and
Farr 2005).

Figure 8 shows the response of the price of non-tradables in the benchmark econ-
omy, one where utilisation is (cid:28)xed (equivalently, costs of adjusting it are in(cid:28)nite:
δ2
→ ∞) and one where capital services are homogeneous ((cid:15) → ∞). As it can be
δ1
seen, both non-homogeneous capital and variable utilisation serve to reinforce the

31In the case of country two it remains negative for four periods.

ECB Working Paper 1946, August 201631Figure 8: IRFs of the price of non-tradables (PN ) in the benchmark economy (straight
line), under (cid:28)xed capacity (dashed line) and under homogeneous capital (line with circles)
to an unexpected shock to the tradables sector in country one. Percentage deviations from
steady-state.

Figure 9: The correlation between the real exchange rate and relative consumption ac-
cording to the length of the interim period. The horizontal line shows the corresponding
empirical statistic.

HBS e(cid:27)ect; but the former seems to be more important.

5 Sensitivity Analysis

5.1 Length of news

In this section, we check the sensitivity of our results to varying the length of the
arrival of news between zero and (cid:28)ve periods.

Figure 9 shows that the B-S correlation falls monotonically with the length of
the interim period. News-shocks also contribute to higher (relative) volatility in the
relative price of aggregate consumption and the relative price of non-tradables; but
to less volatile terms of trade (Table 5).

As we have shown in an earlier part of our work, the terms of trade depreciate
by less in response to a news-shock when this refers to a TFP improvement further

01234567890.20.40.60.811.2Periods following the shock  Benchmark;  ε = 1.67, δ2/δ1 = 0.15Fixed Capacity; ε = 1.67, δ2/δ1 → ∞Homog. Capital; ε → ∞, δ2/δ1 = 0.1512345−0.8−0.6−0.4−0.200.20.40.6ECB Working Paper 1946, August 201632Table 5: Standard-deviation relative to output: Cross-country prices under di(cid:27)erent
lengths of the interim period

News Real exchange Terms of Relative price

q=0
q=1
q=2
q=3
q=4
q=5

rate
0.12
0.21
0.30
0.35
0.37
0.38

Trade
0.45
0.39
0.33
0.29
0.27
0.26

of NT
0.23
0.40
0.55
0.63
0.66
0.66

in the future; and remain pretty stable until the change is materialised (Lambrias
2012)32. This behavior is consistent with both less volatile terms of trade and a lower
real exchange rate - relative consumption correlation. Regarding the volatility in the
price of non-tradables, this tends to be higher with expected shocks since these goods
cannot be transferred neither across countries nor through time.

5.2 Trade Elasticity

To match the B-S correlation, our model requires a relatively high degree of trade
elasticity, but still within the range of values estimated in empirical studies. Figure
10 reports the correlation of the real exchange rate with relative consumption for
di(cid:27)erent values of the trade elasticity of substitution. The correlation falls almost
monotonically and for values up to 3.38 it is always lower when shocks are antici-
pated. It changes sign at θ = 2.43 and θ = 1.81 for unexpected and expected shocks
respectively.

Corsetti, Dedola and Vianni (2011) show that for explanations of the B-S puzzle
hinging on the relative price of non-tradables, it must be that output (cid:29)uctuations are
mostly driven by tradables, trade elasticity is high, and the elasticity of substitution
between tradables and non-tradables is below one. Indeed, our model satis(cid:28)es these
conditions and their results follow even in a complete-market world33.

Corsetti et al (2008) show that a low elasticity of substitution can trigger strong
wealth e(cid:27)ects once the complete-market assumption is relaxed; leading to a negative

32The reason is because the strength of the impulse and the adjustment of relative demand across
countries is lower the longer it takes for technology to improve. At the same time, most of the de-
preciation necessary to clear the market occurs on impact, since no new information arrives between
the signal and the realisation. For a detail exposition of the latter mechanism in the context of the
BKK model see Lambrias (2012).

33Benigno and Thoenissen (2008) impose the same conditions in an incomplete markets model.

ECB Working Paper 1946, August 201633Figure 10: The correlation between the real exchange rate and relative consumption for
di(cid:27)erent values of the trade elasticity of substitution, given unexpected shocks (solid lines)
and shocks expected one period in advance (dashed lines). The horizontal line shows the
corresponding empirical statistic.

B-S correlation34. On the other hand, a BKK-type of model with complete markets
and only tradables is consistent with an appreciation in the terms of trade following
a TFP shock for as long as trade-elasticity is high35. Our theoretical economy with
strong HBS e(cid:27)ects - triggered by imperfectly substitutable capital services - and news-
shocks is consistent with a negative B-S correlation for a range of reliable values of
trade elasticity (1.8-2). Finally, even for values of trade elasticity below one, where
the model produces a strong and positive B-S correlation, allowing shocks to be
forecastable decreases its value signi(cid:28)cantly.

5.3 Level of adjustment costs to investment

The lower the adjustment costs to investment, the lower the correlation between
the real exchange rate and relative consumption. The intuition is discussed in Ra(cid:27)o
(2010): a lower value for this parameter is associated to a more responsive investment
leading to large shifts in domestic absorption and relative demand. Table 6 gives
theoretical moments of an economy where adjusting the (cid:29)ow of investment is costless
and shocks are surprises. The B-S correlation is negative and very strong.

This suggests that news-shocks may not be needed as an additional source for
a negative B-S correlation. In light of the above, we estimate the elasticity of sub-

34Low, and particularly below one, elasticity of substitution is associated with higher volatility
of prices across countries (Corsetti et al 2008, Ra(cid:27)o 2010, Heathcote and Perri 2002) and can be
instructive about the implications of models under di(cid:27)erent asset-market structures (Heathcote and
Perri 2002, Cole and Obstfeld 1991).

35We replicate the BKK model to show that this is the case for θ > 6.5. Consistently, Enders and
M(cid:252)ller (2009) show that the estimated value of trade elasticity in such a model is high, at 3.098. In
line with Corsetti et al (2008), their estimated value for the incomplete-market counterpart of this
model is 0.230.

012345678−1−0.500.51  q=0q=1ECB Working Paper 1946, August 201634Table 6: Model with zero investment-adjustment costs

St. Deviation relative to GDP

Consumption
Investment
Hours
Real Exchange Rate
Terms of Trade

Correlation between real GDP and

Real Net Exports

International co-movements

Output
Consumption
Hours
Investment

Correlation between RER and

Rel. Consumption
Rel. Output
Terms of Trade
Real NX over GDP

Unexpected
Shocks

Data

ε = 2.05

0.81
3.50
0.78
2.91
2.04

0.56
2.09
0.65
0.12
0.34

0.58
2.04
0.67
0.10
0.35

-0.56

-0.49

-0.48

0.35
0.25
0.12
0.21

-0.51
-0.46
0.72
0.35

0.12
0.27
0.20
0.02

-0.40
-0.46
0.10
0.88

0.12
0.26
0.20
0.02

0.23
0.17
0.64
0.49

Actual data are from UPENN World Tables, 1970-2011 at annual frequency. Both empiri-
cal and model-generated data are HP-(cid:28)ltered with a smoothing parameter equal to 100.
Theoretical moments are asymptotic.

stitution of capital services in a similar manner as before, assuming that adjusting
the (cid:29)ow of investment incurs zero costs. That gives a value of (cid:15) equal to 2.05. The
theoretical moments of an economy where shocks are pure surprises, (cid:15) = 2.05 and
κ = 0 are given in the last column of Table 6.

The most notable di(cid:27)erence is the B-S correlation which, in this case, is positive
and equal to 0.23 compared to −0.10 in the benchmark case with news-shocks. More-
over, the model fails to produce a negative correlation between the real exchange rate
and relative output. In terms of international co-movements the two models produce
similar results whereas the relative volatility of the real exchange rate is almost the
double in the benchmark model36. Overall, our model economy with mild investment
adjustment costs and expected innovations to TFP can be consistent with a negative
B-S correlation, compared to an economy with zero investment adjustment costs and
surprise shocks; while generating news-driven booms.

36Indeed, the benchmark model performs better in terms of quadratic deviations of theoretical

real exchange rate moments to empirical ones; as well as overall (i.e. all moments in the table).

ECB Working Paper 1946, August 2016356 Conclusion

We propose a fully (cid:29)exible, complete-market model of the international business cy-
cle that can be consistent with two major empirical facts: positive cross-country
co-movements of economic aggregates and a low correlation between relative con-
sumption and its relative price. We show that the latter is not necessarily connected
to market ine(cid:30)ciency and limited risk sharing, rather it can arise as the e(cid:30)cient
allocation in an economy where wealth e(cid:27)ects on labour supply are low, the price
of non-tradables plays an important role for real exchange rate determination and
innovations to technology are anticipated. We analyse how sector-speci(cid:28)c capital can
have dire consequences for movements in relative prices across countries in the context
of the Harrold-Balassa-Samuelson framework. Finally, the novelty of the paper is to
lay down the theoretical foundations, in line with Jaimovich and Rebelo (2009), that
are consistent with unconditional moments in prices and quantities, but also with
news-driven economic expansions.

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7 Appendix

ECB Working Paper 1946, August 201639Figure 11: The HBS e(cid:27)ect in the benchmark model. The response of relative prices (upper
panel), i.e. the real exchange rate (RER), the terms of trade (TT) and the relative price of
non-tradables (RER-NT), and relative consumption (lower panel) to one standard deviation
unexpected shock to the non-tradable-goods sector. Percentage deviations from the steady
state.

Figure 12: The HBS e(cid:27)ect in the benchmark model. The response of relative prices (upper
panel), i.e. the real exchange rate (RER), the terms of trade (TT) and the relative price of
non-tradables (RER-NT), and relative consumption (lower panel) to one standard deviation
expected shock to the non-tradable-goods sector. Percentage deviations from the steady
state.

0123456789−0.3−0.2−0.100.10.2Periods following the shock  RERRER − NTTT0123456789−0.4−0.3−0.2−0.100.10.20.3Periods following the shock0123456789−0.3−0.2−0.100.10.2Periods following the shock  RERRER − NTTT0123456789−0.4−0.3−0.2−0.100.10.20.3Periods following the shockECB Working Paper 1946, August 201640Figure 13: The upper panel shows values of the quadratic loss function in all three moments,
i.e. the correlation between the real exchange rate and relative output, terms of trade, and
net exports over GDP ratio. The lower panel shows values of this function when taking
into account only the last two moments. In both cases, moments are equally weighted and
estimations were carried out in economies where shocks are surprises. On the horizontal
axis are values of the elasticity of substitution in capital services ε.

Table 7: Baseline Model - HP Filter = 6.25

St. Deviation relative to GDP

Consumption
Investment
Hours
Real Exchange Rate
Terms of Trade

Correlation between real GDP and

Real Net Exports

International co-movements

Output
Consumption
Hours
Investment

Correlation between RER and

Rel. Consumption
Rel. Output
Terms of Trade
Real NX over GDP

Unexpected News
Shocks

Shocks

Data

0.77
3.67
0.78
2.00
1.71

0.59
2.00
0.67
0.16
0.50

0.54
2.14
0.65
0.28
0.42

-0.50

-0.06

-0.36

0.48
0.33
0.09
0.47

-0.20
-0.21
0.62
0.08

0.21
0.31
0.25
0.13

0.69
0.64
0.86
0.60

0.13
0.23
0.20
0.07

-0.05
-0.21
0.45
0.86

Actual data are from UPENN World Tables, 1970-2011 at annual frequency. Both empiri-
cal and model-generated data are HP-(cid:28)ltered with a smoothing parameter equal to 6.25.
Theoretical moments are asymptotic.

123456780123Elasticity of capital services123456780123Elasticity of capital servicesECB Working Paper 1946, August 201641Acknowledgements 
I thank Patrick Fève, Martial Dupaigne, Christian Hellwig, Franck Portier, Evi Pappa, Roberto Pancrazi, Gilles Saint-Paul, Ahmat Jidoud, 
Eric Mengus, Samuele Centorrino, Fabrice Collard, Paolo Guarda, Olivier Pierrard, Luca Dedola, Luca Marchiori, participants at the 
EABCN meeting on “Global Spillovers and Economic Cycles” at Banque de France in May 2013 and seminar participants in Frankfurt, 
Luxembourg and Toulouse for useful comments and discussions. All remaining errors and omissions are mine. The views expressed in 
this article are those of the author and do not necessarily reflect those of the European Central Bank or the Eurosystem. 

Kyriacos Lambrias 
European Central Bank; email: kyriacos.lambrias@ecb.europa.eu 

© European Central Bank, 2016 

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ISSN 
ISBN 
DOI 
EU catalogue No 

1725-2806 (online) 
978-92-899-2194-7 
10.2866/949206 
QB-AR-16-063-EN-N