Download On The International Transmission Of Productivity Shocks

9th Global Conference on Business & Economics
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On The International Transmission Of Productivity Shocks
Daniela Buscaglia†
ABSTRACT
This paper represents a contribution to the study of the international transmission of business cycle shocks. A
domestic positive productivity shock hitting countries vis-à-vis the rest of the world is identified in a VAR
model following the methodology of sign restriction. By this informal identification criterion, restrictions are
imposed on selected variables and based on robust predictions by standard theory, namely the least
controversial implications of the shock. The sign of the variables of interest is left agnostically open. The
results show that positive productivity shocks do not necessary seems to have depreciating effects on relative
prices: it generates an appreciation of both the real exchange rate and the terms of trade in a big and closed
economy (US) and a depreciation of the two relative prices in a small and open economy (UK). These findings
are in line with a growing new literature on international business cycle transmission stressing incomplete
consumption risk sharing across countries. Overall, these results suggest that international risk sharing finds no
empirical support.
JEL classification: C11, F23, F41
Keywords: International transmission, Real exchange rates, Technology shocks, Terms of trade, VAR
I would like to thank Giancarlo Corsetti, Carluccio Bianchi, Luca Dedola, Gianni Amisano, Fabio Fornari,
Guido Ascari, Helmut Lutkepohl, Massimiliano Pisani, Tommaso Monacelli for helpful discussions.
†University of Pavia, via S.Felice 5, 27100 Pavia (Italy) and ISTAT, Department of National Accounts and
Economic Analysis, via A.Depretis 74b, 00184 Roma (Italy).
Email: [email protected] Phone: (+39)0646733172
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INTRODUCTION
Understanding international spillovers of macroeconomic shocks is one of the most controversal issues in the
open economy literature. International relative price movements and changes in the trade balance are key points
to focalise in understanding this matter. In particular, in the analysis of the international transmission of country
specific disturbances is basic to understand whether international relative prices provide insurance against
shocks, thus reducing consumption risk.
What are the international effects of a supply shock hitting the economy is still an open issue and different
assumptions about size of a country, degree of openness, trade elasticity, degree and persistence of shocks yield
conflicting theoretical responses. Standard International Real Business Cycle (IRBC) literature (e.g. Stockman
and Tesar (1995)) claims that a positive technology disturbance generates a self-correcting mechanism: an
increase in domestic output, domestic consumption and domestic investment and a decrease in export prices. It
follows that the terms of trade worsen and the real exchange rate depreciates, so a trade balance improve due to
increase in exports. This mechanism represents an unambiguously positive international spillover, because
prices abroad are decreasing so that foreigners can buy at cheaper prices, the initial gap between wealth at home
and abroad is reduced, and the consumpition risk decreases. Therefore, such a class of models suggests that
technology disturbances can be identified via the restriction that in response to positive shocks real variables
increase and prices decrease, either simultaneously or with lags. This kind of models is constructed under the
assumption of complete risk sharing. Nevertheless, it is well recognised in academic and policy circles that
empirical evidence suggests lack of international consumption risk sharing. In particular, already in 1993,
Backus and Smithi demonstrated that the assertion that domestic households should consume more when their
consumption basket is relatively cheap is at odds with data, providing a powerful demonstration of lack or
international consumption risk sharing.
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An attractive proposal to reconcile standard international business cycle models with the empirical evidence of
lack of risk sharing comes from a recent line of research: Corsetti, Dedola and Leduc (Corsetti et al. (2006),
Corsetti et al. (2008)) suggest that under some key hypotheses the traditional transmission mechanism is
reversed and a positive technology shock can lead to a terms of trade improvement and real exchange rate
appreciation and a countercyclical movement of the trade balanceii. This result is due to a domestic absorption
change that is more than proportional than the initial increase in domestic wealth following the shock. In this
case the shock magnifies the consumption risk and generates a negative international spillover of the
technology shock. This result is particularly relevant because it has strong implications for the international
adjustment mechanism. In the current world economy the US are running large trade deficits while
experiencing a high productivity growth: the idea is that, under these new results, we cannot expect this large
trade deficit to improve. Key points in this result are strong wealth and demand effects in a framework of
incomplete market, where the increase in productivity of tradable sectors and output expansion may cause the
terms of trade and the real exchange rate to appreciate.
Several authors as Obstfeld and Rogoff (2005) and Rebucci and Hunt (2005) studying the late 1990s experience
have already analysed the link between productivity-driven US expansion, the US real exchange rate
appreciation and the US trade balance worsening. Bailey et al. (2001) demonstrated that a productivity growth
in the tradable goods sector can lead to a real exchange rate appreciation of the dollar due to the HarrodBalassa-Samuelsoniii. The result of Corsetti and others is somewhat interesting since it not only link the effect
on the real exchange rate of an asymmetric disturbance in the tradable sector to the Harrod-Balassa-Samuelson
effect, but also consider further basic mechanisms at work.
The existing limited empirical work on the international transmission mechanisms motivated this paper, drafted
in order to investigate the issues just introduced. My results provide an empirical contribution to this literature,
through the application of a new method of analysis in a VAR framework.
Sign restriction is a new agnostic identification procedure adopted in order to impose only minimum
requirements to data. In a recent paper, Uhlig (2005) vigorously stressed the “circularity problem” affecting the
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macroeconomic literature. Results obtained from empirical analyses look reasonable if they match conventional
wisdom, otherwise they are called “puzzles”. Following Uhlig’s argument, economic theory is crucially
important for identifying macroeconomics shocks and the study of the effects of a shock is often already
restricted by a priory implicit or explicit theorising: the circularity problem comes from the fact that it is usually
hard to distinguish between assumptions and conclusions. The sign restriction procedure for the identification
of a shock represents an informal identification criterion and a way to make the a priori theorising explicit: the
effects of a shock are identified by directly imposing sign restrictions on the impulse responses. This approach,
recently adopted by the applied economics literature (see also Faust (1998), Canova and De Nicolò (2002),
Dedola and Neri (2007), Peersman (2009)), allows to show assumptions, usually tacitly adopted in the
economic literature, and let them be subject to debate. Restrictions imposed on the impulse responses of some
variables at a few periods following the shock come from the stylized facts of the literature. The sign of the
variables of interest is left agnostically open, letting data to decideiv.
In this paper I follow this approach applying the procedure of sign restriction, mainly employed to identify a
monetary policy shock, to identify a positive technology shock on labour productivity in manufacturing. The
manufacturing sector is my proxy for the tradable sector because it accounts for a large share of international
trade. The choice to study a shock hitting a specific sector instead of a disturbance to a whole economy is
motivated by the fact that in the former case the analysis is easier and the identification cleaner. In particular,
my interest is on the effects of a productivity shock on the real exchange rate and on the trade balance: I
consider an asimmetric shock hitting countries vis-`a-vis the rest of the world and I use as sign restrictions only
robust predictions by standard theory, letting the real exchange rate and net exports free to move after the
shock. I work with two countries: a big and closed country, the United States, and a small and open one, the
United Kingdom. I obtain a clear result for variables that are left unconstrained by my identifying assumptions.
The structure of the paper is as follows: the next section illustrates some recent developments of the literature
about the international spillovers of productivity shocks; in section three is presented the methodology adopted;
in section four is illustrated the model used to identify technology shocks; section five shows the results
obtained; section six concludes.
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THE INTERNATIONAL TRANSMISSION OF BUSINESS CYCLE SHOCKS: SOME RECENT
DEVELOPMENTS IN THE LITERATURE
Seminal contributions to the International Real Business Cycle literature have been developed assuming either
complete markets or a high degree of risk sharing. In this framework, a positive idiosyncratic supply shock that
raises a country’s supply of tradables necessarily worsens the country’s terms of trade and the real exchange
rate. The fall in the international price of the domestic good benefits foreign consumers via favorable import
price movements. So that, movements in relative prices may contain the consumption risk of output fluctuations
by reducing their impact on relative wealth.
In the framework of modern International Real Business Cycle literature, Corsetti et al. (2006) and Corsetti et
al. (2008) in a two-country, two-good endowment economy study the international transmission mechanism
under different asset markets structures, different assumptions about trade elasticities and a different degree of
shock persistence. The basic idea is that we need to understand more deeply the international relative price
movements following a productivity shock because this kind of disturbance affects the exchange rate in ways
that are not considered in standard macro models. They find new interesting results: under complete markets
the traditional result of a real exchange rate depreciation applies, but under incomplete markets the positive
technology shock can improve the terms of trade and appreciate the real exchange rate (RER) however defined
i.e. as a consumer price index based RER or as a producer price index based RER. Standard theory is consistent
with the idea that a positive tradable goods supply shock may appreciate the CPI based RER, because of an
increase in the relative price of domestic non-tradable via the Harrod-Balassa-Samuelson effectv, but the
appreciation found on the real exchange rate measures based on producer price indexes and on export prices is
new and remarkable.
In the rest of this section, I’ll summarize the results of this new literature.
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Complete Risk-Sharing
With complete markets domestic households trade a complete set of state contingent Arrow-Debreu securities
and they can insure their consumption against idiosyncratic supply shocks. A positive supply shock at home
unambiguously worsens the domestic terms of tradevi. The efficient risk sharing condition in the international
economy states that
U k*'
 RERk
U k'
(1)
where on the LHS is the ratio of marginal utilities of consumption between foreigners and domestic households;
on the RHS,  represents the risk sharing wedge, which depends on the initial conditions of the problem, while
RERk is the real exchange rate in the state of nature k. With efficient risk sharing, domestic consumption
should be higher in those states of the world in which the price of domestic consumption is relatively cheaper
because domestic residents should receive contingent income transfers to take advantage of the favorable goods
prices. Hence, in response to a domestic supply shock, consumption grows more at home than abroadvii.
Under this condition, the ratio between the marginal utilities of home and foreign consumption is proportional
to the relative price of consumption across all states of nature k, and thus it is proportional to the real exchange
rate. It is easy to see that domestic consumption rises relatively to foreign consumption only if the real
exchange rate is depreciating: under complete risk sharing, the terms of trade effect always prevails on the
Harrod-Balassa-Samuelson effect, so that a positive supply shock generates a real exchange rate depreciation.
In other words, after a positive productivity shock, the worsening of the terms of trade must prevail on the
Harrod- Balassa-Samuelson effect, because the RER has to depreciate in order to satisfy the efficient risk
sharing condition.
In general, the correlation between the real exchange rate and the terms of trade depends on the degree of home
bias; in particular the correlation is positive in the presence of a home bias, zero if the PPP holds and negative
in the absence of a home bias.
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Incomplete Risk-Sharing
In incomplete markets, trade is limited to some assets. Supply shocks drive a wedge between domestic and
foreign wealth, leading to a much richer array of results relatively to the case of efficient risk insurance. In
particular, an increase in the relative consumption does not require the real exchange rate to depreciate, because
of wealth effects. Crucially, these effects depend upon two key variables: the trade elasticities, in particular the
elasticity of substitution between home and foreign goods  (the higher  , the more homogeneous goods are),
and aH , the share of domestically produced goods in home consumption expenditure ( aH  1/ 2 captures a
home bias in consumption, i.e. preference for local goods).
A change in the terms of trade modifies the relative prices faced by home households as consumers and the
value of home output relatively to foreign output. A deterioration in the terms of trade generate two effects on
the domestic demand for home goods: an increase, thanks to substitution effects (since foreign goods are
substituted by domestic ones) and a decrease due to income effects (because the value of home output decreases
in relative terms). If  is higher than one, the substitution effect is stronger than the income effect in absolute
value; if  is smaller than one, the negative income effect will more than offset the substitution effect. The
foreign demand for home tradables will always be increasing in the terms of trade and, independently of  , the
substitution effect and the income effect abroad are both positive. Summing the domestic and foreign effects of
a decrease in the domestic terms of trade (TOT), it follows that as long as the negative income effect in the
home country is not too strong, the world demand for home goods will be increasing in the terms of trade: the
bigger the deterioration, the larger world demand. Conversely, when  is sufficiently below one and the home
bias in consumption is sufficiently high, word demand is falling in the terms of trade: the higher the
appreciation, the larger world demand.
The general equilibrium implications of Corsetti et al. (2008) can be summarized determining three cases, as
follows:
• the validity of the conventional view of international transmission: a positive innovation in home output
worsens the terms of trade and depreciates the real exchange rate as long as
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
1
2 aH
(2)
In this case, the international transmission is positive: a positive home output shock benefits foreign consumers
via lower import prices; international movements have the same sign as under complete markets, so that
relative consumption and the real exchange rateviii are positively correlated.
• With home bias, a positive innovation in domestic output may actually appreciate the terms of trade and the
real exchange rate when the following condition is satisfied:

1 
0    1 

 2aH 
(3)
In this case, in the short run after the shock, home output rises but the increase of home demand is more than
proportional, in anticipation of future output gains, so that the excess demand pushes prices up: the world
demand for home goods is upward sloping, for a positive supply shock to home output to be matched by an
increase in world demand, the domestic terms of trade need to appreciate: we have then negative international
transmission because a positive output innovation actually harms foreign consumers, as the price of home
goods rises. Relative consumption and the real exchange rate are now negatively correlated.
• In the third case where

1
1 
 2 aH

1
 
2 aH

(4)
transmission is excessively positive, in the sense that a positive innovation to home output worsen the terms of
trade and depreciates the real exchange rate and the fall in the domestic terms of trade is so large that foreign
consumers benefit from a home supply shock more than domestic consumers. Foreign consumption rises
relatively to domestic consumption as the domestic real exchange rate depreciates. The correlation between
relative consumption and the real exchange rate is again negative.
Allowing for trade in noncontingent bonds in incomplete markets, it can be demonstrated that the same results
apply: for a sufficiently low elasticity, the transmission is negative, for a higher elasticity the transmission
becomes excessively positive and after a determined value of the elasticity the transmission becomes only
positive. This is due to the fact that, even if now agents are allowed to trade in a noncontingent international
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bond, in a stochastic environment the bond is traded only after the elimination of uncertainty and does not
provide households with ex-ante insurance against country-specific income shocks. Hence, unexpected shocks
can have large wealth effects and the real exchange rate and relative consumption can comove negatively.
The same transmission mechanisms found for financial autarky extend also to an economy where people can
trade in a noncontingent bond, and can be interestingly discussed referring to the persistence of the shock. If the
disturb is persistent, agents have no incentive to smooth consumption and the response of the terms of trade is
the same as under financial autarky.
With a large difference between short and long run output and with  high enough, the short run component of
the terms of trade, negative, will prevail on the long run component, positive. The dynamic response of the
terms of trade is a short run appreciation and a long run depreciation. The latter will be less than proportional
compared to the change in endowment, so that, in the long run the value of home output rises relatively to
world output. This generates, in the short run, a domestic output boom due to positive wealth effects. Because
of the home bias, the domestic consumption boom creates an excess demand for home goods, because
consumption-smoothing agents raise demand above output anticipating future output and income gains; an
impact appreciation of the terms of trade and a current account deficit will follow. In the short run a negative
correlation between relative consumption and the real exchange rate will ensue. Over time, as the dynamics of
home output endowment fill the gap with demand, the terms of trade appreciation will switch to a depreciation.
THE
METHODOLOGY:
IDENTIFICATION
OF
PRODUCTIVITY
SHOCKS
VIA
SIGN
RESTRICTION
Impulse response analysis in the framework of VAR models has been pioneered by C. Sims (Sims (1980) and
Sims (1981)) as an alternative to classical macroeconomic analyses and rapid progress has been made in last
decades. My empirical implementation follows strictly Uhlig (2005).
A Vector Autoregression Model is given by
Yt  B1Yt 1  B 2Yt 2  ...  Bl Yt l  ut
t  1, 2,..., T
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where Yt is an  mx1 vector of data at date t  1, 2,..., T , Bi  are coefficient matrices of size  mxm  and ut is
the one-step ahead prediction error with variance-covariance matrix  assumed to be non singular. In order to
examine the impulse responses to a fundamental innovations, we need to decompose the one-step ahead
prediction error ut as a linear combination of orthogonalized structural shocks. Suppose there are a total of m
mutually independent fundamental innovations normalized to be of variance 1, so that E vv '  I m were  is
the vector of innovation of size  mx1 . We need to find a matrix A such that ut  Avt . The jth column of A
then represents the immediate impact on all variables of the jth fundamental innovation, one standard error in
size. Identification amounts to providing enough restrictions as to solve uniquely for the following
decomposition of the estimated covariance matrix of the reduced form VAR residuals  (up to an orthonormal
transformation):
  E u u   AE v v  A  AA
'
t t
'
t t
'
'
(6)
Hence, there are m(m  1) / 2 degrees of freedom in specifying A , so that further restrictions are needed to
achieve identification. Usually, these restrictions come from imposing a recursive ordering (Sims (1986)) or
structural restrictions on A or A1 (Bernanke (1986), Blanchard and Watson (1987)).
The procedure proposed by Uhlig is different from the previous ones and the aims is to be minimalistic. We can
be interested in the response to only a shock, in our case a productivity one, so that there is no reason to identify
also the other  m  1 fundamental innovations. A first example in this direction has been the work of Bernanke
and Mihov (1998) and that of Christiano et al. (1999) who concentrate the identification exercise on only a
limited set of variables which interact with the shock. Similarly, Uhlig (2005) proposed to concentrate only on
finding the innovation corresponding to a single shock: this amounts to identifying an impulse vector, that is a
single column a  R m of the matrix A in the last equation.
A productivity shock impulse vector is defined as an impulse vector a , so that the impulse responses to a of
manufacturing output and labour productivity are not negative and the impulse response of PPI over services
CPI is not positiveix, at all horizons k  0,..., K .
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Α  B, , K  is the set of all productivity shock impulse vectors
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obtained from inequality constraints, this set will typically either contain many elements or be empty; therefore
one typically cannot obtain exact identification at this point.
As is well known, it is possible to use the OLS estimate of the VAR, B  B and    , fix K or try out a few
choices for K and look at the entire range of impulse responses, as a Α  B, , K  is varied, provided it is not
empty. The set
Α
therefore results in an interval for the impulse responses which we wish to calculate. This
can be accomplished by generating many impulse vectors, calculating their implied impulse response functions
and checking whether or not the sign restrictions are satisfied. The Cholesky-responses are calculated once and
then the response for some given impulse vector is obtained by calculating a weighted sum of the responses.
Generating these impulse vectors randomly is the easiest way: draw a from a standard normal in
1
of entries which violate sign restrictions, multiply by A
m
, flip signs
to calculate the corresponding m-dimensional vector


of unit length  and divide by its length to obtain a candidate draw for a . Check whether a Α B, , K by
checking the sign restrictions of the impulse responses for all relevant horizons k = 0, ...,K, so that generate a
large number of candidate draws for a .
The pure sign restriction approach is based on a Bayesian method x and it is a clean method, because it literally
only imposes the weak prior beliefs. A-priory a non-zero probability is attributed only to structural impulse
vectors which, for a given reduced-form estimate of the VAR, yield impulse response whose sign are consistent
with the assumed restrictions. All impulse vectors satisfying the impulse response sign restrictions are
considered equally likely. It is simultaneously an estimation of the reduced-form VAR alongside the impulse
vectors: VAR parameter draws, which do not permit any impulse vector to satisfy the imposed sign restrictions,
receive zero prior weights, and VAR parameter draws which easily permit satisfaction of the sign restrictions
receive more weight. Let
unitary radius in
Pm x S m .
m
Pm
be the space of positive definite  mxm  matrices and let
. Numerically, the parameters
 B, , K 
Sm
be the unit sphere of
are drawn jointly from a prior on
lxmxm
x
The prior is proportional to a Normal-Wishart in  B,   , i.e. is proportional to a Normal-Wishart
density multiplied by an indicator variable on A      Α  B, , K  , where A    is the lower triangular
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Cholesky factor of  . The posterior is given by the usual Normal-Wishart posterior for  B,   , given the
assumed prior for  B,   , times the indicator function on A      Α  B, , K  . To draw from this posterior, it
is taken a joint draw from both the posterior for the unrestricted NW posterior for the VAR parameters  B,  
as well as a uniform distribution over the unit sphere  in
Sm .
After constructing the impulse vector a ,
calculating the impulse responses at horizons k  0,..., K for the variables j and representing the restricted
variables, if all these impulse responses satisfy the sign restrictions, I keep the draw, otherwise I discard it.
Finally, I repeat sufficiently times.
Crucially, the sign restriction procedure allows to impose assumptions that seem to be the least controversial
implications of a particular shock and that seem to be the distinguishing features of that particular innovation
compared to other shocks prominently proposed in the literature. Obviously, identification in any econometric
exercise rests on assumptions and this method of identification has its limits, for example by sign restriction
shocks with similar effects cannot be ruled out and combinations of other shocks could potentially look like the
shock under analysis, but the assumptions used in sign restriction are particularly reasonable: they most directly
reflect how economists informally evaluate empirical results. Finally, different priors are likely to generate
different results, but the sensitivity of the results to the choice of the prior may not be too large, as demonstrated
by Faust (1998).
THE MODEL: SPECIFICATIONS AND RESTRICTIONS
A traditional reduced form VAR model
Yt  B  L  Yt 1  ut
(7)
is estimated in several specifications, following the methodology adopted by Dedola and Neri (2007)xi. The
vector Yt is of dimension (6x1) and includes variables of interest, B  L  is a lag polynomial of order p xii. All
variables are in logs and seasonally adjusted, the frequency is quarterly and data span from 1970q1 to
2006q2xiii. Each specification is tested for two countries and measured in terms of cross-country differentialsxiv:
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xv
the US or the UK vis-à-vis an aggregate of the remaining G7 countries called ROW . I estimate three different
specifications, where I use different variables, most of them specified in relative terms:
• (the log of) labour productivity in domestic manufacturing as a deviation from (the log of) labour productivity
in ROW manufacturing;
• the ratio between domestic manufacturing output and domestic total GDP;
• the ratio between domestic and ROW manufacturing output;
• (the log of) domestic consumption volume as a deviation from (the log of) ROW consumption volume;
• the ratio between domestic net exports and domestic GDP;
• a consumer-price-index-based real exchange rate (CPI based RER);
• a producer-price-index-based real exchange rate (PPI based RER);
• the terms of trade (TOT);
• the ratio between the producer price index and the services consumer price index (PPI/CPIs).
I run three different specifications, where I imposed sign restrictions on the impulse responses of key variables
for several periods after the shock. Firstly, in order to identify a positive productivity shock I impose a positive
sign to domestic labour productivity in the manufacturing sector as a deviation from the same variable for the
rest of the world and a positive sign to domestic manufacturing output as a deviation from the same variable of
the rest of the world. These two restrictions are imposed in order to isolate shocks with country j-specific
effects. A positive sign to the manufacturing output as a deviation from domestic total output is imposed in
order to isolate shocks with manufacturing-specific effects. Finally, a negative sign to the ratio between the
producer price index and the consumer services price index is imposed as evidence in support of the HarrodBalassa-Samuelson hypothesis: the consumer services price index includes a much larger share of nontraded
goods and in response to sector specific productivity gains nontraded good prices appreciate relatively to
tradables, so that the ratio between PPI and services CPI has to fall. The fifth variable used in each specification
is a different measure of the relative international price: in specification one I use the consumer-price-indexbased real exchange rate; in specification two I employ the producer-price-index-based real exchange rate; in
specification three I use the terms of tradexvi. The last variable is always the ratio between net exports and GDP.
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The number of steps constrained is k = 20 quarters. The set of restrictions on the sign of the impulse responses
imposed in the VAR analysis is summarized in the Table 1. The results of these specifications are shown in
Figures 1, 2 and 3 for the United States and in Figures 4, 5 and 6 for the United Kingdom, and discussed in the
next sections.
RESULTS
Figure 1 shows the results obtained for the US vis-à-vis the ROW according to the pure sign restriction
approach-specification 1. The median (the black line) and the 16th and 84th percentiles (the blue lines) are
reported. A positive productivity shock determines for the US a sizable increase in labour productivity (0.9%
reached between 10 to 20 quarters), in relative manufacturing output (1.1% reached between 4 to 6 quarters)
and in domestic manufacturing output over GDP (0.6% after 3 quarters). The shock is also very persistent: the
16th percentile of the responses of these variables is positive even after 8 years. The shock also causes a fall in
the ratio between PPI and services CPI, in accordance with the Harrod-Balassa-Samuelson results. The negative
peak is around -0.6% between 3 to 4 quartersxvii. The result for the variables left unconstrained is clear: the
shock determines a pronounced and persistent deterioration in the NX/GDP ratio, growing over time, in line
with the intertemporal approach to the CA literature, and a strong CPI-based RER appreciation. This effect is
quite persistent as well: the median response is hump-shaped and reaches a peak in the initial quarters after the
shock. The response of the CPI-based RER reaches zero by about the 40th-quarter horizon. The results for the
US obtained from the second specification are shown in Figure 2 and are very similar to the former ones. The
fall in the ratio of PPI over services CPI is of about -0.5% reached around 12 quarters after the shock. The
pattern shown by the NX/GDP ratio is very similar to the previous specification, and the PPI based RER
appreciation is very persistent, with a peak of about 0.4%. The third specification also generates similar results
too. Figure 3 shows that the terms of trade appreciate of about 0.6% after 3 quarters and that the effect is very
persistent.
Let us turn now to the UK results. The estimated impulse responses to a positive productivity shock in the UK
obtained under the sign restrictions corresponding to specification 1 are presented in Figures 4. Relative
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productivity reaches a peak of 1% after 3 quarters, relative manufacturing production reaches a peak of 0.95%
after 7 quarters, the ratio between manufacturing output and GDP increases very persistently, PPI over services
CPI reaches a negative peak of -0.85% after 2 quarters. Hence, the restricted variables show very persistent
patterns. With reference to unrestricted variables, the NX/GDP ratio deteriorates of about 0.4% in the initial
quarters after the shock, together with a persistent depreciation of the CPI-based RER of about 1.5%.
Specifications 2 and 3 yield very similar results: in particular, in the former case, the PPI based RER
depreciates persistently of about 0.7%, while in specification 3 the TOT depreciate of about 0.5%-0.9% after 2
quarters and change sign after 27 quarters.
Let us now consider the main differences between the US and the UK results. First, the deterioration of the
NX/GDP ratio is always greater in the UK case. The range of negative peaks for the US in the 3 specifications
studied is between -0.25% and -0.15%; for the UK the range is between - 0.75% and -0.4%. Second, the
response of the RERs is of the opposite sign (appreciation for the US and depreciation for the UK) and of about
0.5% for the US, 1% or more for the UK . With reference to the TOT, the response peak is around 0.6% for the
US, and around 1% for the UK and it is very persistent only for the US.
Let us now relate these results to the relevant economic theory. Summarizing: In the US, the positive
productivity shock produces strong wealth effects that generate a rise in absorption higher than domestic supply
and a crowding out of external demand. This generates international price movements that hinder risk sharing:
following a productivity increase, the home TOT and the RER appreciate harming foreign consumption. This is
the case identified by Corsetti et al. (2008) as case number two, where international consumption spillovers are
negative.
The UK evidence corresponds instead the last case studied by Corsetti et al. (2008), that of an excessively
positive transmission: after the positive disturbance, the RER and the TOT depreciate; domestic demand
increases but not enough to crowd out foreign demand. In particular, foreign consumption will increase more
than domestic consumption, because of the strong deterioration of the TOT.
Indeed, testing in a VAR model with seven variables also the impulse response for the ratio between domestic
and foreign consumption (C/C*), I find that the impulse response for this ratio exhibits a persistent increase for
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the US and a decrease for the UK as shown in Table 1. This is a clear evidence of the negative correlation
between relative consumption (C/C*) and the RERxviii, as assumed in the negative transmission mechanism and
in the excessively positive transmission case. In order to perform another check, I also worked with
consumption in levels, and as supposed, both the US and UK consumption impulse responses are found to be
positive. This evidence is clearly against the idea of immiserizing growthxix (Bhagwati (1958)): even if the
home terms of trade fall, it will never be the case that their adverse movements causes immiserizing growth
because domestic consumption will never fall in absolute level in response to a positive supply shock. In order
to perform a sensitivity analysis, I also varied the restriction horizon, adding or subtracting 8 quarters relatively
to the baseline specification. All the results reported above remain broadly unchanged when I re-estimate the
VAR model imposing restrictions over an horizon of 28 quarters. Results become marginally less persistent
when I impose restrictions over an horizon of 12 quarters.
CONCLUSIONS
In this paper, I provide empirical evidence of the main features of the international transmission of a
productivity shock in the manufacturing sector for two countries: the US, as an example of a big and close
economy, and the UK, as an example of small and open one, where each country is considered vis-à-vis an
aggregate of industrial countries. I apply the procedure of sign restrictions to identify the shock in several
specifications of a VAR model, using only robust predictions of standard theory and letting the real exchange
rate and net exports free to move after the shock. The shock is quite persistent in both cases, and I obtain a clear
result for the variables that are left unconstrained. Crucially, the macroeconomic dynamics in response to
productivity shocks are dominated by movements in domestic absorption and wealth effects.
In the US case, the shock boosts consumption, causing an overall deterioration of the US trade balance, in full
accordance with the intertemporal approach to the current account. The response of US absorption relatively to
its foreign partners is quite strong, so that relative consumption rises too. All measures of international relative
prices (CPI-based RER, PPI-based RER and TOT) appreciate. Over time, the US relative prices tend to
depreciate. This case provides empirical evidence of a negative international transmission: international price
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movements hinder risk sharing because the RER appreciation harms foreign consumption. Hence, in the US
case, the VAR model supports the conclusion of a negative international transmission of the shock.
In the UK case, the wealth effect on domestic absorption is again strong, but in this case imports are a large
component of domestic demand. The deterioration of the trade balance now is greater than the US case because
the country now is much more open. The effect on domestic demand is not large enough to overcome the effect
on supply; hence, all measures of international relative prices (CPI-based RER, PPI-based RER and TOT) have
to depreciate. Indeed, checking for the behaviour of relative consumption, in the UK case the impulse response
is negative, stressing the fact that foreign consumption increases more than domestic one. Nevertheless, this is
not a case of immiserizing growth, as clarified by the fact that, testing for the domestic consumption level, its
impulse response is positive, as for the US. Rather, this is a clear evidence of an excessive positive transmission
of the shock: the depreciation of the TOT in the UK is so high that foreigners benefits from the productivity
shock more than domestic consumers.
Overall, these results suggest that international risk sharing finds no empirical support and that the idea of
testing international transmission mechanisms differentiated for different degrees of openness and size of
countries certainly is a promising avenue of future research.
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APPENDIX: TABLES, FIGURES AND DATA DESCRIPTION
Tables
Table 1: Sign restrictions on VAR variables
Specification 1
a
y
j
M
j
y
M
j
 arw   0
Specification 2
a
M
 yrw
0
y
 yj   0
y
j
M
j
M
j
 arw   0
Specification 3
a
M
 yrw
0
y
 yj   0
y
j
M
j
M
j
 arw   0
M
 yrw
0
 yj   0
 PPI / CPIs   0
 PPI / CPIs   0
 PPI / CPIs   0
CPIbasedRER free
PPIbasedRER free
TOT free
 NX / GDP 
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free
 NX / GDP 
18
free
 NX / GDP 
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Figures
Figure 1: Specification 1 US
Impulse responses of the US to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the CPIbased RER shows a strong appreciation, while the
response of the NX/GDP ratio shows a pronounced deterioration. Both responses are very
persistent.
Figure 2: Specification 2 US
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Impulse responses of the US to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the PPIbased RER shows an appreciation, while the
response of the NX/GDP ratio is a pronounced deterioration. Both responses are very persistent.
Figure 3: Specification 3 US
Impulse responses of the US to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the TOT is a strong appreciation, the response of the
NX/GDP ratio is a pronounced deterioration. Both responses are very persistent.
Figure4: Specification 1 UK
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Impulse responses of the UK to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the CPI based RER is a strong depreciation and is very
persistent; the response of the NX/GDP ratio is a deterioration.
Figure 5: Specification 2 UK
Impulse responses of the UK to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the PPI based RER is a depreciation, the response of the
NX/ GDP ratio is a pronounced deterioration and changes sign after about 33 quarters.
Figure 6: Specification 3 UK
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Impulse responses of the UK to a positive productivity shock using the pure sign restriction
approach, with K=20. The response of the TOT is a strong depreciation. The TOT impulse
responses change sign after about 26 quarters. The response of the NX/ GDP is a pronounced and
persistent deterioration.
Figure 7: Relative consumption
Impulse responses of relative consumption for US vis-à-vis the rest of the world and for UK visà-vis the rest of the world to a positive productivity shock using the pure sign restriction
approach, with K=20.
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Data description
The countries included in the sample are: Canada (CA), France (FR), Germany (GE), Italy (IT), Japan (JP),
United Kingdom (UK), United States (US). I use quarterly data spanning from 1970q1 to 2006q2. Main data
source are: IMF-IFS, OECD, BIS, WDI.
ROW variables are constructed as GDP (PPP constant-base year 2000) weighted variables,
i.e. H rw 
G 7 1
H
i 1
i
* qi with the weight qi 
GDPi
G 7 1
 GDP
i 1
.
i
.The subscript j represents the US or the UK. The variables are defined as follows:
LABOUR PRODUCTIVITY
a
j

 G 71

 arw   log  productivity j   log   productivityi * qi 
 i 1


where labour productivityj is equal to the ratio between the index of production in total manufacturing SA
(2000y) and the product between employees in manufacturing SA and weekly hours worked in manufacturing.
The US data are retrieved from the OECD database; the JP data are retrieved from the OECD database (weekly
hours worked in manufacturing are computed dividing monthly data by four); the UK data are retrieved from
the BIS database; the CA data are retrieved from the OECD database (production in total manufacturing has
been seasonally adjusted with the Tramo Seats procedure); the GE data are retrieved from the OECD database;
the FR data are retrieved from the OECD database and from the ILO database; the IT data are retrieved from
the BIS database.
MANUFACTURING OUTPUT
G 7 1


M
M
y

y

log
manufacturing

log(
 manufacturingi * qi ) 
 j rw   

j
i 1


Manufacturing is the index of production in total manufacturing, seasonal adjusted.
Indexes are retrieved from the OECD database.
MANUFACTURING OUTPUT as a share of GDP
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y
M
j
ISBN : 978-0-9742114-2-7

 y j  log  manufacturing j   log(GDPj ) 
GDP volumes are retrieved from the OECD database.
NET EXPORTS over GDP ratio
 NX / GDPj    NetExports j / GDPj 
Data are retrieved from the OECD database.
HARROD-BALASSA-SAMUELSON INDICATOR
 PPI
j
/ CPIs j   producer price index over services consumer price index
Data are retrieved from the OECD database and from the Bureau of Labour Statistics database.
RELATIVE INTERNATIONAL PRICES INDICES
PPI_based RERj defined as
PPI based RERj =
PPI j
G 7 1
 PPI q
i 1
i i
CPI_based RERj defined as
CPI j
CPI based RERj = G 7 1
 CPIi qi
i 1
TOTj defined as
ExpDefl j
ExportDeflator based RERj = G 7 1
 ExpDefli qi
i 1
Export deflators are retrieved from the OECD database.
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i
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See Backus and Smith (1993).
ii
Some autors (Mendoza (1991), Glick and Rogoff (1995), Backus et al. (1995)), have given a proof of the existence of a
countercyclical trade balance. In particular, Backus and al. demonstrated that in an economy with investment, a positive productivity
shock in the domestic country can generate a persistent trade deficit due to the fact that the shock leads to a large capital inflow
triggered by the expectation of high returns. According to the Intertemporal Approach to the current account, a permanent shock to
technology leads to a large deficit because investments rise and saving fall owing to the fact that output in future periods is higher
than in the current period, so that consumption smoothing leads to a level of consumption higher than current income (see Dornbusch
(1983), Bergin and Sheffrin (2000), Nason and Rogers (2006), Engel and Rogers (2006)).
iii
See Harrod (1933), Balassa (1964) and Samuelson (1964).
This represents another way to look at Sim’s main criticism (Sims (1980), Sims (1981)) about macroeconometric models. Under his
view, macroeconometric models are often not based on sound economic theories or available theories are not capable of providing a
completely specified model. In a VAR approach, fairly loose models are set up which do not impose rigid a priori restrictions on the
data generation process and statistical tools must be applied to determine possible constraints and to interpret these models.
iv
v
Usually, after a positive technology shock, two main effects on prices arise:
- due to the increase in the supply of home-produced goods on world markets, the price of exports decreases, and worsening in
the terms of trade defined as the ratio between export prices and import prices follows;
- - due to spillovers across sectors, the Harrod-Balassa Samuelson effect guarantees that countries with higher productivity in
tradables compared with nontradables have a higher price level, so that the ratio between domestic and foreign prices
increases.
Defining the real exchange rate as
R
 P*
P
, where

is the nominal exchange rate between the domestic and foreign currency,
P*
is the price of foreign consumption and P is the price of domestic consumption. The impact on the RER of a positive shock to
technology in the manufacturing sector depends on the net effect of the two forces listed above: we have a real depreciation of the
domestic currency if the change in the terms of trade prevails; conversely, if the Harrod-Balassa Samuelson effect prevails, we have
an appreciation of the domestic currency (see also Lewis (2007)).
vi
The sign of the response of the terms of trade is a crucial indicator of the degree of risk sharing.
vii
In particular, the consumption growth difference tends to fall with the elasticity of substitution between goods.
viii
The assumption is that the RER is defined, as previously highlighted, as foreign over domestic prices, otherwise the correlation
with relative consumption would be defined negative.
ix
See the next section for details.
x
See Sims and Uhlig (1991).
xi
The estimation of a Var in levels takes into account of any possible stochastic or deterministic trend and also possible cointegration
relationships. See Sims, Stock, Watson (1990) results. See also Hamilton (1994), chapter 20, for further details.
xii
The optimal lag length is four and was selected according to the Akaike Information Criteria.
xiii
See the Data Appendix for details.
xiv
See Clarida and Gali (1994).
xv
ROW is constructed as (G7-country j), so that for the US the ROW is defined as the sum of Japan, UK, Canada, Germany, France
and Italy each weighted by GDP shares at PPP values, with 2000 as base year; for the UK, the ROW amounts to the weighted sum of
the US, Japan, Canada, Germany, France and Italy.
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xvi
Proxied by the export deflator of country j over the weighted sum of export deflators of G7-j countries. See the data appendix for
details.
xvii
The shape of this impulse response function is peculiar, because the convergence to zero is obtained only in the very long run, due
to an oscillatory trajectory. Same observations apply to many of PPI/CPIs irf obtained.
xviii
In my empirical work, the RER is defined as the ratio between domestic and foreign prices, so that the correlation found is
positive because of my definition of the RER. See the data appendix for details.
Immiserizing growth is a long-term phenomenon that occurs when the gain in a country’s social welfare arising from economic
growth is more than offset by the loss in welfare associated with an adverse shift in the terms of trade. In a case explored many years
ago by Jagdish Bhagwati, immiserizing growth occurs in a developing nation that has started economic growth but faces unfavourable
international demand conditions as it increases its traditional exports. In another case recently explored by Samuelson, immiserizing
growth occurs for the growing industrialized country when its trade partner follows a policy of import substituting growth and, as a
result, shifts the terms of trade against the exporting country.
xix
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