Discussion Paper No. 87
Productivity Spillovers in the Global Market
Nazmus Sadat Khan
Jun Nagayasu

October, 2018

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANProductivity Spillovers in the Global Market
Nazmus Sadat Khan∗,

Jun Nagayasu‡

Abstract

This paper analyzes the effect of productivity shocks originating from other countries on economic growth in the home country. Traditionally, productivity shocks
have been considered as driving forces of economic growth in their home countries.
However, productivity improvements occur both at home and overseas. In liberalized global markets, economic growth is, in theory, also attributable to productivity
shocks from other countries. Using data from 18 countries, we show that numerous
countries benefit from productivity spillovers. Nevertheless, their impacts on theeconomy differ according to the origin of the economic shocks. On the one hand,
US shocks are rather pervasive and affect many economies and regions, regardlessof their development stage. On the other hand, shocks from other country groups
exert less influence over foreign economies.
Keywords: productivity, economic growth, international transmission, global vector autoregression
JEL classification: C32, O47∗

University of Muenster, Institute of International Economics, Universitatsstrabe 14-16, 48143 Munster, Germany, Email: Nazmus-Sadat.Khan@wiwi.uni-muenster.de, Tel: +49 251 83 2866 0, Fax: +49
251 83 2866 6.
‡
Corresponding author, Tohoku University, Graduate School of Economics and Management, Address:27-1 Kawauchi, Aoba-ku, Sendai, Miyagi 980-8576 JAPAN. Email: jun.nagayasu.d8@tohoku.ac.jp, Tel:
+81 22 795 6265, Fax: +81 22 795 6270.
This research was initiated when Khan was visiting Tohoku University. A financial support for travel
expenses was provided by the Japan Investment Advisers Association.

1

Introduction

Globalization has accelerated especially after World War II due to the initiatives of the
Bretton Woods institutions, such as the International Monetary Fund and the World
Bank. Economic liberalization has been considered to be particularly successful at regional
level. For example, the European Union (EU) and the Association of South-East Asian
Nations (ASEAN), among others, have removed virtually all trade barriers in order topromote intra-regional trade. Furthermore, the creation of single currency areas, likethe Eurozone, represents the ultimate form of regional liberalization. Such economic
liberalization is often related to the free movement of goods, services, capital, and laborand has been advanced on the basis of the standard economic theory, which predicts thatcountries will benefit from removing cross-border trade barriers.
However, advanced countries have recently shifted towards protectionism. The US
president, Donald Trump, expressed strong interest in protecting domestic industries, i.e.,
the ’America First’ policy, to correct prolonged and large US trade deficits. Conservative
movements have also occurred in Europe. Following its 2016 referendum, the UK has
decided to leave the EU to gain more independent control of its immigration policies. In
2017, Germany imposed a cap on immigration, particularly that from the Middle East.
In short, many people nowadays doubt the outcome of economic liberalization. Thereis a significant gap between the standard economic theory and actual economic policies
implemented by many advanced countries.
Against this background, our study attempts to investigate the role of spillover effects
of productivity shocks in the context of economic growth. More specifically, we analyze thefollowing spillover effects within the last three decades. First, we quantify the magnitudeof US spillover effects on the rest of the world because the US possesses many advanced
industries such as information technology. Second, in order to investigate the significanceof spillovers originating in the US, we compare them with productivity shocks originatingin other parts of the world. In short, we confirm that there are asymmetric effects inexternal spillovers and that US spillovers exert more influence over global markets.
This paper contributes to the literature in the following ways. First, at least in theory,
productivity improvements, along with capital and labor, are known to be an essential
factor for economic growth. However, despite efforts to remove cross-country barriers,2

productivity spillovers in the international context have rarely been studied, in particular
by using historic macroeconomic data (see the Literature survey section).1 We primarily
study the extent to which US productivity has affected its own economic growth andthat of other country groups. Whereas country-specific outcomes are important, we areinterested in a more general outcome that is relevant to formulating future international
economic policies in many countries.
Second, we use a Global Vector Auto-Regressive (GVAR) model (Pesaran et al. (2004))
in order to investigate the cross-country spillover effects of productivity shocks. The
empirical literature on productivity spillover remains limited largely due to technicalchallenges involving the handling of multi-country models with many variables. Two
broad approaches that have been used recently to handle this problem include GVAR
and the factor-augmented VAR (FAVAR) models. To the best of our knowledge, none ofthese methods have been used before in the context of productivity shocks. Comparedto the FAVAR, the GVAR approach can combine different macroeconomic variables ofa large number of countries in a much more efficient manner. GVAR models tackle the’curse of dimensionality’ problem by imposing restrictions directly on the parametersof the model. In particular, all foreign economies are typically approximated by one
representative economy, constructed as a (trade-) weighted average of foreign economies.
Here, individual country models are added by means of a consistent econometric approachto create a global model, where cointegration is allowed for variables within and acrosscountries. On the other hand, FAVAR models capture country-specific dynamics only
through idiosyncratic components (i.e., the residuals). Also, in GVAR models, data canbe used in levels and, therefore, long-run information in the data is retained.
Third, this paper contributes to the GVAR literature. Instead of generalized impulse
response functions (GIRFs) that are commonly used in the GVAR literature, structuralgeneralized impulse response functions (SGIRFs) are used for dynamic analysis, in order
to better identify the shocks. This goes beyond most previous studies to identify shocks
and at least partially overcomes one of the main criticisms regarding the identification
and use of GIRFs in GVAR models. Also, instead of commonly used fixed trade weights,
1

The inexplicit treatment of spillover effects in empirical studies is attributable to the standard statistical approach, such as panel data estimation methods, that often use common time dummies to capture
cross-sectional dependence across countries.

3

time-varying trade weights are used to construct foreign-specific variables of individual
country models. This is more realistic, as it controls for the changing relationship between
the participating countries for different parts of the business cycle (e.g., rapid growth in
the US economy throughout most of the 1990s, the dot-com bubble in 2001, and thefinancial crisis of 2008).
All subsequent parts of the paper are organized as follows: Section 2 reviews the literature on productivity spillover. Section 3 explains the GVAR model and Section 4 discusses
the data and some important statistical properties of the GVAR model. In Section 5, ourresults are presented and discussed. Finally, Section 6 presents our conclusions.

2

Literature Survey on economic growth and productivity spillovers

Economic growth has been recognized as an important research and policy topic. Therefore, many researchers have developed economic theories and attempted to discover what
factors contribute to economic growth using time-series and/or panel data. The classic
economic theory (Solow (1956)) points to labor and capital as essential ingredients for
economic growth. Therefore, as summarized in Eq. (1), the standard economic growthmodel can be expressed in terms of the Cobb-Douglas production function:

Yt = Ktα (At Lt )1−α(1)where Yt is aggregate production at time t (t = 1, ..., T ), Kt is capital, and Lt is labor.
A weight α represents the significance of capital in the production (α ∈ [0, 1]) and ahigher value of α shows that the country produces more capital-intensive goods. In theclassic economic growth theory, these production factors (K and L) are assumed to be
exogenous, whereby increases in these factors contribute to economic growth.
However, previous studies have found that capital and labor alone fail to explain thehistorical experiences of many countries.2 In this regard, more recent literature considers
productivity, human capital, education, and research and development (R&D) as addi2

See Jones (2016) for a comprehensive survey on empirical results.

4

tional factors contributing to economic growth.3 For example, Lucas (1988) discussed theimportance of education and diversification in skills. Similarly, Mankiw and David (1992)
confirmed human capital proxied by education as an important factor of economic growthusing a comprehensive set of countries. The importance of R&D is empirically confirmed
in India (Raut (1995)) and in a panel of countries (Coe and Helpman (1995); Coe andHoffmaister (1997)). These extensions are equivalent to the recognition of investment in
humans. Efforts to improve human capital are now widely included as part of economic
policies.
In terms of Eq. (1), A may capture these extra elements missing in the classic economic
theory and is known as the slow residual or as the total factor productivity (TFP). A canbe thought of as factors, such as innovation and R&D, to improve productivity. WhenA that is generated endogenously by R&D or human capital is included, the model can
explain sustainable economic growth. Therefore, economic growth has traditionally been
analyzed without considering the explicit role of cross-border spillovers, which is not
surprising when the market has only limited access to global markets.
Alternatively, education effects (S) and productivity can be treated separately (Halland Charles (1999), Frankel and Romer (1999)). Education is expected to improve labor
efficiency, closely following Mincers wage equation. (Mincer (1974)).

Yt = Ktα (eϑ(St ) At Lt )1−α

(2)

A theoretical link between international trade and economic growth has been developed over the last two decades. For example, Grossman and Helpman (1991) explained
the role of international trade in economic growth, and Ventura (1997) provided theoretical justification for quick economic growth experienced by export-oriented countries.
Previous studies looked at spillover effects of productivity improvements in a particularcountry, such as Spain (Barrios and Eric (2002)), China (Lin and Kwan (2016)), England (Girma (2005)), and India (Raut (1995)). Gorg and Strobl (2001) reviewed earlier
literature and found that spillover effects are more clearly observed in microdata analysis. Similarly, they observed large spillover effects in open and developing markets. By
identifying trade, financial, and indirect linkages, Arora and Athanasios (2005) showed
3

These factors may not be mutually exclusive.

5

that international trade as an engine of economic growth generally holds true for both advanced and developing countries. The indirect linkage is a channel through which businessand consumer confidence in advanced countries affects confidence in developing countries.
Keller (2002) documented that productivity at home is influenced by R&D originatingfrom both home and foreign countries. The 20% of home productivity improvements arefound to be caused by R&D in foreign countries. Keller and Yeaple (2013) pointed outthat knowledge transfer may occur through exchanging intermediaries, as well as directcommunication. They found evidence that direct communication becomes more difficult as the distance between companies increases. More broadly, productivity spillovers
contributed more to economic growth than did the international trade of goods (Weil(2009)).
We investigate spillover effects using macroeconomic data that have not been analyzed
as extensively as microdata, but are nonetheless useful in order to draw a general conclusion. Here, an economic growth equation is expressed in terms of per capita, which is
the most standard measure for aggregate economic activities when comparing economic
development across countries. This measure differs from another popular specification
based on GDP per labor. While GDP per labor may be more consistent with the conceptof productivity, we study GDP per capita because of its prevalence in economics and its
significant implications for economic policies. Furthermore, only a few countries under
our investigation release labor statistics. This an important factor in our decision, since
this study covers a wide range of countries. When multiple countries become researchtargets and population (N ) replaces labor, Eq. (1) can be re-stated for countries i as:
Yit
=
Nit



Kit
Nit

α

A1−α
it

(3)

Panel data allow us to utilize cross-sectional information resulting in statistically morereliable outcomes, in addition to being expected to offer a general conclusion relevant tomost investigated countries. In natural logarithmic form, we can derive the standard
growth equation that has been investigated by many researchers.
yit = αkit + (1 − α)ait

6(4)where yit = ln(Yit /Nit ), kit = ln(Kit /Nit ), and ait = lnAit . Similarly, Eq. (2) can be
expressed in terms of per capita as:
Yit
=
Nit



Kit
Nit

α

(Ait eϑ(Sit ) )1−α(5)oryit = αkit + (1 − α)ait + (1 − α)ϑ(Sit )(6)

Importantly, these questions are the classic specification for panel data analyses, whichassume cross-sectional independence and thus cannot capture spillover effects from overseas. In other words, they are designed for closed economies and do not contain foreign
variables that directly influence home economic growth. This assumption has become
increasingly unrealistic in the modern world. To mitigate it, we use the GVAR model
to extend these specifications to include spillover effects. This extension has been widely
recognized among researchers and is indeed in line with Lucas (1988), who introduced
human capital spillovers in order to explain different patterns in economic growth. Given
that people (or labor) and capital are less mobile than knowledge across countries, it ismore natural to consider the effect of cross-border technological transfers on per capita
income. In connection to this, Comin and Bart (2010), using data from 166 countries,
showed that the speed of technology diffusion has been accelerated in modern times. Over
25% of differences in per capita income can be explained by cross-country variation intechnological adoption.
Whenever economic growth at home can also be explained by productivity improvements in other countries (a∗it ), Eq. (6) will be stated in a more general form by including
varieties of external shocks originating from other variables. For example,
yit = αkit + (1 − α)ait + βa∗jt + (1 − α)ϑ(Sit )(7)

where i 6= j, and β > 0 when there are positive productivity spillovers from overseas.
However, β can be negative when productivity improvements in other countries lead to a
deterioration in external competitiveness of a home country. Furthermore, we extend thisspecification using the GVAR model and analyze the heterogeneous effects of productivity
shocks on economic growth, rather than the homogeneous effects that are assumed in Eq.
7

(7).

3

The GVAR model

The GVAR approach introduced by Pesaran et al. (2004) gives a relatively simple, yeteffective way to model present global economy, where each country, and different macroeconomic factors within countries, are related to each other. The methodology of GVAR
modelling consists of two different stages. First, a separate model known as the VARX
is estimated for each country separately, where the letter X indicates the presence of an
exogenous component in the VAR. If any of the variables have unit roots and are cointegrated, the model is estimated in their error-correcting form. In these individual VARX
(or the vector error correction model with exogenous variables, VECMX, in the presence of cointegration) models, each country has two different types of variables: domestic
and foreign. Domestic variables are endogenous in the model, while foreign variables are
exogenous and have their corresponding foreign variables. These foreign variables areconstructed using a weight matrix, so that the relative importance of different countries
is reflected properly in the analysis. They provide a connection between the evolution of
the domestic economy and that of the rest of the world. The foreign variables must be
weakly exogenous, an assumption that needs to be tested. In the second step, the individual VARX (or VECMX) models are combined together in a consistent manner withthe help of a link matrix to build a global model.
•Individual country model Let there be N + 1 countries in the model, indexed by
i = 0, 1, 2, ..., N , where country 0 is the reference country. Each country i then follows
the VARX (p, q) model, which can be defined as:

yi,t = ai,0 + ai,1 t +pXαi,j yi,t−j +

j=1

q
X

∗
βi,j yi,t−j+ ui,t(8)

j=1

for t = 1, 2, ..., T . Here, ki × 1 matrix yi,t represents the endogenous domestic variables∗
and ki∗ × 1 matrix yi,trepresents the corresponding (weakly) exogenous foreign variables.

k and k ∗ are the numbers of domestic and foreign variables respectively, ai,0 is a ki∗ × 1
vector of fixed intercepts and ai,1 is a ki∗ × 1 vector of coefficients on the deterministic
8

time trends. p and q are the lag lengths of domestic and foreign variables respectively.
They are selected according to the Schwartz Bayesian (SB) information criterion. Finally,ui,t ∼ iid(0, Σui ).
∗, is obtained from weighted averages
The vector of foreign country-specific variables, yi,tof each variable across all other countries in the sample. More specifically, for any i, j =0, 1, ..., N ,
∗
=
yi,t

N
X

wi,j,t yj,t ,

(9)

j=0

where wi,j,t is a weighting factor that captures the importance of a country j for a countryNPi, withwi,j,t = 1 and wi,i,t = 0. Most of the GVAR literature uses fixed trade weights
j=0

based on bilateral trade volumes. However, these may be subject to temporal changes and,as a result, a fixed weight might confuse the results. In order to account for the changes
that took place throughout the sample period, this paper uses time-varying weights toconstruct foreign variables in country-specific models. These are constructed as threeyear moving averages to smooth out short-run business cycle effects in the bilateral tradeflows. More compactly, setting pi = max(p, q), Eq. (8) can be written as:

Ai,0 zi,t = ai,0 + ai,1 t +pi
XAi,j zi,t−j + ui,t

(10)

j=1

where vector zi,t = (xi,t 0 , x∗i,t 0 )0 represents both domestic and foreign variables andcoefficient matrices are Ai,0 = (Ik,i , −βi,0 ) and Ai,j = (αi,j , βi,j ).
Because of the characteristics of the macroeconomic variables and to allow for the cointegrating relationship within and between countries, the country-specific VARX models
are estimated in the following error-correction form (VECMX):
pi −1
0

∗
∆yi,t = ci,0 − αi βi (zi,t−1 − a1,t (t − 1)) + βi,0 ∆yi,t+X

φi,j ∆zi,t−j + ui,t

(11)

j=1

Here, αi is a ki × ri matrix of rank ri and βi is a (ki + ki∗ ) × ri matrix of rank ri .
Country-specific VECMX models are estimated using reduced rank regressions conditional on weakly-exogenous foreign variables. This takes into account the possibility of
cointegration within domestic variables and across domestic and foreign variables. Thisway, estimates for ri , βi , and αi are obtained. Other parameters are estimated by OLS
9from this equation:∗∆yi,t = ci,0 + δECMi,t−1 + βi,0 ∆yi,t+ φi ∆zi,t−1 + ui,t(12)

where ECMi,t−1 are the error-correction terms referring to the ri cointegrating relations of the ith country model.
•Global model The next step is to combine individual country-specific parameter
estimates into a single global model. All country-specific variables are considered as a
N
P
0
0
0
0
single k × 1 global vector yt = (y0t
, y01
, ...., yNki , so that all the variablest ) where k =i=0

are endogenous in the system as a whole. For each country, the corresponding VARX
model is obtained from the VECMX model that was estimated. The link matrix Wi ,which is the (ki + ki∗ ) × k matrix collecting the trade weights wij , ∀i, j = 0, 1, 2, ..., N , isused to obtain the identity zi,t = Wi yt . From Eq. (10), it follows that:

Ai,0 Wi yt = ai,0 + ai,1 t +pi
XAi,j Wi yt−j + ui,t

(13)

j=1

for i = 0, 1, ..., N . Then, the N + 1 systems in Eq. (13) are combined to obtain the global
model in levels:
G0 yt = a0 + a1 t +p
X

Gi yt−i + ut

(14)

i=1

Here, G0 = (A00 W0 , A10 W1 , ..., AN 0 WN )0 is a known nonsingular k × k matrix that
depends on the trade weights and parameter estimates Gi = (A0i W0 , A1i W0 , ..., AN i WN )0
for i = 1, 2, .., p, a0 = (a00 , a10 , ..., aN 0 )0 , a1 = (a01 , a11 , ..., aN 1 )0 , ut = (u0t , u1t , ..., uN t )and p = max(pi ) across all i. Pre-multiplying Eq. (14) by G−1
0 , the GVAR (p) model isobtained as
yt = b0 + b1 t +p
XFi yt−i + εt

(15)

i=1
−1
−1
−1
where, b0 = G−1
0 a0 , b1 = G0 a1 , Fi = G0 Gi for i = 1, 2, ..., p and εt = G0 ut .

The dynamic properties of the GVAR model in Eq. (15) can then be examined using
Structural Generalized Impulse Response Functions (SGIRFs).

10

4

Data and relevant tests

Prior to the formal analysis, this section describes the data, the model specification, andthe results of the weak exogeneity test.

4.1

Data and model specification

We use quarterly data from 1991 to 2016 for advanced and developing countries. There
are 18 countries in the sample, divided into four groups. 1) The EU group consists ofseven countries including Belgium, France, Germany, Italy, Netherlands, Switzerland andthe UK.4 2) The non-OECD group consists of all the countries in the sample that are notpart of OECD. It includes Brazil, China, Hong Kong, India, Mexico, Russia, and Taiwan.
3) Countries in the sample that do not fall into the above two categories are includedin the ’Others’ group. These are Canada, Japan, and Korea. 4) The USA is consideredseparately, as we are primarily interested in investigating spillover effects from the US toother countries.
Regional variables for the groups ’EU’, ’Non-OECD’ and ’Others’ were constructedby aggregating country-specific variables over N countries.

yt =

N
X

ωi yi,ti=1where yt denotes a regional variable, yi,t is the value of that variable for country i, andωi represents the relative importance of a country i within the region. Following Deeset al. (2007), ωi is computed by dividing the PPP-GDP figure of each country by the total
sum across the N countries of the region, such that their weights add up to unity.
Spillover effects may be related to the level of trade with the rest of the world. Therefore, a country’s openness to other countries is calculated as (Import+Export)/GDP.
Table 1 shows the openness of each country vis-a-vis the USA. This table shows the ratio
being often greater than one. It follows that the majority of countries are indeed more
open than the US. Only two countries exhibit evidence of lesser openness than the US,
but even in these cases the ratios are close to the US level.
4

Though Switzerland is not part of the EU and the UK will soon exit from the EU, they are includedin this group for geographical proximity and historical links with the EU.

11

[Table 1]
The model will be estimated with data on real GDP growth, expenditure on R&D,
capital stock and the TFP. The TFP is used as a proxy for productivity. The source ofreal GDP and population data is Oxford Economics. Production data are expressed in
US dollars to make international comparisons later in our analysis. The TFP and capitalstock data are collected from Penn World Table Ver.9. R&D data are collected fromthe OECD and are only available for the countries in the sample that are part of theOECD. For non-OECD countries, we assume no significant R&D activities. Annual data
are converted to quarterly data, using a quadratic function of the Eviews.
[Fig. 1]The TFP of selected countries is shown in Fig. (1). Since this statistic indicates TFP
of a country relative to the US, it shows a marked difference in TFP among countries.
Germany exhibits steady improvements in TFP and convergence with that of the US.
Brazil and Japan fail to improve TFP after 1990 and show divergence from the US.
Chinese TFP shows rather different trajectories compared to other countries. It is highly
volatile and has shown steady increases since 2000, which is consistent with its rapid
economic growth. However, TFP of all four countries is less than one and thus is below
the level of the US, thereby confirming the significant size of the US TFP compared toall other countries.
[Fig. 2]
Fig. (2) shows the ratio of R&D to GDP for selected countries and regions. The OECDdata suggest that most countries spend about 1 to 3 percent of GDP on R&D. However,there is a variation in the trend of this variable among countries. While this ratio isstable over time for most countries and regions, China has increased R&D expenditure
remarkably in recent times. Nonetheless, this ratio remains relatively high in the US overthis century, while remaining low in Russia.
The correlation among key variables is summarized for each country group in Table
2. Generally, the variables are positively correlated with each other. Notably, the TFP
is positively correlated with GDP growth. On the other hand, contrary to expectations,capital has a negative relationship with other economic variables.
[Table 2]

12Next, we check the stationarity and cointegration of data. First, the stationarity ofdata is examined for all the country-specific domestic variables and their corresponding
foreign variables. In addition to the commonly used Augmented Dickey Fuller (ADF) test,
the Weighted-Symmetric Dickey Fuller (WS) test suggested by Park and Fuller (1995) isalso used for this purpose.5 The lag length was selected according to the SB criterion.
The unit root tests are conducted with variables in levels with an intercept and timetrend. The results for the level data for domestic variables are shown in Table 3. The
t-values are shown with the 5% critical values. As expected, there is a mix of stationary
and non-stationary data across country groups. However, the majority of data seem tofollow a non-stationary process, as we often fail to reject the null hypothesis of the unit
root process.
[Table 3]
The next step is to define the country-specific VARX models. The GVAR model has
the flexibility of handling different specifications for different countries (i.e., the numberof domestic and foreign variables that goes into each country-specific model). However,since the countries in the sample have trading relations and are expected to affect eachother, all the country models initially include all four variables as domestic and foreign
variables (constructed using the weight matrix mentioned in the previous section).6 Next,
the order of the country-specific VARX (pi , qi ) model is selected using the SB criterion.
While selecting the lag order, pi and qi were not allowed to go over 2, because of the small
sample size compared to the large number of parameters to be estimated. The selectedorder of the VARX model is shown in Table 4.
[Table 4]
For all country groups, the VARX (2,1) model is selected. Given that some of the variables are non-stationary, Johansen’s cointegration test is conducted in order to determine
the number of cointegrating relations for each country group. Here, the specifications
consider Case IV according to Pesaran et al. (2000), where a linear deterministic trend is
implicitly allowed for the cointegration space, but can be eliminated in the dynamic part
5

The WS test exploits the time reversibility of a stationary autoregressive process in order to increase
their power performance. Many authors like Leybourne et al. (2005) and Pantula et al. (1994) show
evidence of superior performance of the WS test as compared to the ADF test.
6
Several robustness checks were also conducted by leaving out some variables as foreign variables forcountries that are less integrated with other countries in terms of trade. However, the main findings ofthe paper are not affected.

13

of VEC models. The number of cointegration relations for each country group based on
the trace statistics is also shown in Table 4. All country groups seem to have either threeor four cointegrating relations. Next, individual country-specific VECMX models were
estimated, subject to the reduced rank restrictions. Corresponding error-correcting terms
were then derived. These ECMs were subsequently used to conduct the weak exogeneity
test.

4.2

Weak exogeneity test

As mentioned earlier, one of the main assumptions of the GVAR model is the weak∗
. In general, a variable in a VARX
exogeneity of the country-specific foreign variables yi,tmodel is considered weakly exogenous if it is not dependent on contemporaneous valuesof endogenous variables, but is likely to depend on the lagged values of these endogenous∗∗inis considered weakly exogenous if yi,t does not affect yi,tvariables. More formally, yi,t∗
the long-run, but yi,tis said to be ’long-run forcing’ for yi,t . As shown in Johansen (1992),

this assumption allows proper identification of the cointegration relations. In the formal
test, the joint significance of the estimated error-correction terms in auxiliary equations∗
is tested. Specifically, for each lth element offor the country-specific foreign variables yi,t∗yi,ta regression of the following form in conducted:∗∆yi,t,l= ai,l +

ri
X
j=1

∗

\ i,j,t−1 +δi,j,l ECM

pi
X

∗

φ0i,s,l ∆yi,t−s +

s=1

qi
X

∗
Ψi,s,l ∆eyi,t−s+ ηi,t,l

(16)

s=1

\ i,j,t−1 , for j = 1, 2, ..., ri are the estimated error-correction terms correwhere ECM
sponding to the ri cointegrating relations found for the i th country, and p∗i and qi∗ are theorders of the lagged changes for the domestic and foreign variables respectively. The test
for the weak exogeneity is an F -test of the joint hypothesis that δi,j,l = 0 for j = 1, 2, ..., riin the above equation. It is not necessary that lag orders of p∗i and qi∗ are the same forthe underlying country-specific model. They are selected using the SB criterion.
[Table 5]
The results are shown in Table 5. As can be seen, all the variables pass the weakexogeneity test, as the assumption of exogeneity cannot be rejected at the 5% level. This14

is a very desirable result, as it confirms the suitability of the GVAR model for this region.
Based on the eigenvalues, the model was also found to be stable.

5

Results

By means of the SGIRF analysis, this section investigates the effects of US TFP shocks
on the home economy (i.e., real GDP, R&D spending, and capital stock). Similarly, we
study the effects of TFP shocks of the major trading partners of the US (grouped into
the EU, non-OECD and other groups).

5.1

Structural generalized impulse response function (SGIRF)
analysis of US productivity shocks

The identification of shocks has been a major issue in GVAR models. In order to conduct
dynamic analysis, the vast majority of research papers using GVAR models rely on the
GIRF proposed by Koop et al. (1996) and further developed by Pesaran and Shin (1998).
The identification of shocks in a GVAR model is complicated due to the cross-country
interactions and high dimensionality of the model.
The identification in a traditional VAR analysis is usually achieved by using the orthogonalized impulse-response functions (OIRFs) that require a certain ordering of variables.
This approach is often not suitable for GVAR models, as it requires ordering not onlyof the variables, but also countries. As a result, when a large number of variables andcountries are included in the model, it becomes difficult to justify such ordering basedon economic theory and empirical findings. The advantage of GIRFs is that they are invariant to the ordering of countries and variables. This is very convenient for models like
GVAR that involve many countries and variables. However, it comes at a cost. Critics
often argue that in GIRFs, the error terms are not orthogonal and it allows correlation
among them. This, in turn, makes economic interpretation of shocks difficult.
We take this into account by using SGIRFs instead of GIRFs. The SGIRF allows
the most dominant economy in the model to be ordered first and also its variables tohave certain ordering. Since the main aim of this paper is to investigate spillover effects
of productivity shocks arising in the US, the largest economy in the model, the US and
15

its variables are ordered first. This means that the identifying scheme for the modelof the US is based on a lower-triangular Cholesky decomposition and has the following
ordering: [R&D, TFP, capital, GDP]’. Thus, for the US, R&D is ordered first, followed
by TFP because greater expenditure on R&D could increase TFP. This assumes thatR&D spending affects TFP contemporaneously, but not vice versa. TFP is then followedby capital and GDP. This ordering system assumes that GDP is the most endogenous
variable, which is a realistic assumption to make. Other countries and their variables are
kept unrestricted. More about the GIRF and SGIRF is discussed in the Appendix.
The main aim of this paper is to evaluate the effects of US productivity shocks on
the US itself as well as the spillover effects on other countries. This result is depicted
in Fig. (3). It shows the SGIRF for the US, the EU, non-OECD and the rest of thecountries (i.e., Others) to one standard deviation (SD) positive TFP shock to the US.
For each country, reactions of GDP, R&D, capital, and TFP are depicted for up to 40
quarters. The associated 90% bootstrap confidence bands, computed on the basis of 1000
replications, are also displayed by dotted lines.
[Fig. (3)]The results show that a TFP shock in the US not only has a positive effect on real
GDP of the US, but also has positive spillover effects on the real GDP of its main trading
partner countries. This effect is statistically significant for the US, the EU and non-OECD
country groups, but not highly significant for others. For all countries, the effect is muchsmaller on impact. It increases over time and stays significant for up to 16 quarters (i.e.,four years) for most country groups. This implies quick cross-country transmission of
innovation.
After a US TFP shock, R&D spending shows a statistically significant positive reaction in the US and some negative reaction in the EU and non-OECD countries (thoughsignificant only for the first few quarters). This result indicates that US productivity
shocks are positively associated with its own R&D spending, but it is not strongly correlated with other countries’ R&D spending. In fact, the initial reactions of the EU and thenon-OECD countries’ R&D are negatively associated with US productivity shocks.7 Similarly, the reaction of capital after a US TFP shock is mostly insignificant for all country
7

R&D shocks to the EU and non-OECD countries (results not showed here, but available on request)
actually also have no significant effect on the GDP of their own countries

16groups. The TFP instead shows some positive reaction to shocks in the US, but does notshow any significant results for other countries.

5.2

Productivity shocks in the EU, Non-OECD and Others

Fig. (4), (5) and (6) show the response of the same variables to one standard deviation(SD) positive shock in ’the EU,’ ’non-OECD,’ and ’Others’ country groups respectively.
The first row of each figure shows the response of GDP to a TFP shock. The EU’s
TFP shock does have some positive and significant effects on GDP of the EU and theother country groups. Compared to the US TFP shock, these reactions are smaller inmagnitude. EU’s TFP shock also increases US R&D and has a further positive effect on
its own TFP. Such reactions are, however, significant for a very short period of time. A
shock to the non-OECD group’s TFP has some positive significant effect on its own GDP,but spillover effects are not highly significant. A shock to the final group ’Others’ has no
significant effect on the GDP of any country groups either. In terms of the effect on othervariables, results are not very significant.
[Fig. (4), (5), (6)]Interestingly, a positive TFP shock is associated with increases in R&D spending
for the US and other country groups. This might be due to the size of the US R&D
and the fact that US multinational firms are much more global in terms of investing inother country groups. An increase in productivity in the rest of the world creates greater
incentives for them to expand their business by spending more on R&D. On the contrary,R&D spending in the EU decreases when there is a positive TFP shock in ’Non-OECD’
and ’Others’ country groups. These results might explain why the EU is still lagging
behind the US in terms of research and innovation and are in line with findings of Miller
and Atkinson (2014). While the US is able to make best use of productivity improvements
in other countries, the rest of the world fails to do so.

5.3

The asymmetric effect of productivity shocks

In order to compare the magnitude of US shocks with that of other country groups,
we calculate the ratio of impulse responses (Table 6). For country groups X and Y,
the ratio of (X→X)/(Y→Y) indicates the relative importance of shocks in the home17

economy. Therefore, (EU→EU)/(USA→USA) compares the impact of EU shocks on the
EU economy with that of US shocks on the US economy. If this ratio equals unity, itfollows that their impact on their own economy is identical. Similarly, (X→Y)/(Y→X)
gives us information about which direction of productivity shocks are relatively more
important between X and Y. When this ratio is higher than unity, it means that economic
shocks from X are greater than that from Y.
Table 6 shows the average of this ratio over 40 time horizons. Since this ratio isless than unity, we can interpret that the US shocks are more influential than shocks
from other country groups over its own economy as well as that of other country groups.
At times, we find a negative ratio, implying that productivity shocks have had negative
impacts on the economy in one of country group pairs. In short, there is asymmetry in
the effect of productivity improvements across country groups. Given that the US is not
the most open economy in the world, the relatively more significant effect of US shocks is
attributable to the amount of expenditure on productivity improvements and the presenceof multinational firms that utilize advanced technology. Thus, we confirm heterogeneous
responses of productivity shocks on the economy. Our results provide the reasons why
previous macroeconomic analyses often fail to detect the role of productivity spillovers ineconomic growth; that is, productivity spillovers are not long-lived and are insignificant
for some countries.
[Table 6]6

Concluding remarks

This paper empirically investigates the impact of productivity spillovers in global markets,
where productivity shocks affect not only home economies, but other countries too. Inorder to capture such spillover effects, we have used the GVAR to model global economies,
which allows us to estimate heterogeneous reactions to spillovers across country groups.
By doing so, we have arrived at noteworthy results.
Generally, we find that while productivity shocks are asymmetric in global markets,
productivity improvements have generally contributed to economic growth, leading us
to conclude that liberalizing international markets is beneficial to many (but not all)18

countries. Productivity shocks originating from the US are more influential over the restof the world than those from other countries. Our country group analyses suggest that
US shocks are positively correlated with economic growth of other countries and thus
global markets benefit from the spillover of productivity improvements. In contrast, sucha clear positive relationship can hardly be observed in the analysis of productivity shocks
originating from other country groups.
Because our analysis is based on macroeconomic data, we cannot provide a detailed
and insightful explanation regarding the asymmetric effect. However, our results are
consistent with the extent of the US innovation. The US spends more on innovation
than any other country. In this regard, the finding that global markets benefit from US
productivity shocks will be valuably supplemented by multi-country analyses using firmor industry-level data in future studies.

19Appendix
GIRF and SGIRF
The generalized impulse-response functions (GIRFs) was introduced by Koop et al. (1996)
and further developed by Pesaran and Shin (1998). Let us consider the model obtained
during the solution of the GVAR, expressed in terms of the country-specic errors given
by Eq. (14). The GIRFs are based on the definition:
GIRF (yt ; ui,l,t ; h) = E(yt+h |ui,l,t =√
σii,ll , It−1 ) − E(yt+h |It−1 )(17)where It−1 is the information set at time t − 1, σii,ll is the diagonal element of thevariance covariance matrix Σu corresponding to the lth equation in the ith country, andh is the horizon. GIRFs are invariant to the ordering of variables and they allow forcorrelation of the error terms (the error terms are not orthogonal).
The structural generalized impulse-response functions (SGIRFs) used in this paper
allows ordering of variables to one country. As the US is the largest and the most dominanteconomy in this model, it is ordered first and its variables are ordered in the way mentioned
in Section 4.1. The SGIRFs are invariant to the ordering of other countries and theirvariables. Let us consider the V ARX ∗ (p1 , q1 ) model for the US.

y1,t = a1,0 + a1,1 t +pX

α1,j y1,t−j +

j=1

q
X

∗
β1,j y1,t−j+ u1,t(18)

j=1

Let V1,t be structural shocks given by V1,t = P1 u1,t , where P1 is the k1 × k1 matrix
of coefcients to be identied. The identication conditions using the triangular approach ofSims (1980) require Σv,1 = Cov(v1,t ) to be diagonal and P1 to be lower triangular. Let Q100

be the upper Cholesky factor of Cov(u1,t ) = Σu,1 = Q1 Q1 so that Σv,1 = P1 Σu,1 P1 with
0

P1 = (Q1 )−1 Under this orthogonalization scheme Cov(vi,t ) = Ik0
Pre-multiplying the GVAR model in Eq. (14) by

20





P
0
0
0

 0




0
I
0
0
k
1

PG1 1 = 


..
.
 0 0
0 


0 0
0 Ikn
It follows thatPG1 1 G1 yt = PG1 1 G1 yt−1 + .... + PG1 1 Gp yt−p + vt
0
where vt = (v1t
, u01t , ....., u0N t ) and

(19)



V (v1t )Cov(v1t , u1t ) . . . Cov(v1t , uN t ) Cov(u1t , v1t )V (u1t ). . . Cov(u1t , uN t ) Σv = Cov(vt ) = 


..
..
..


.
.
.


Cov(uN t , v1t ) Cov(uN t , u1t ) . . .
V (uN t )withV (v1t ) = Σv,11 = P1 Σu,11 P11 and Cov(v1t , ujt ) = Cov(P1 u1t , ujt ) = P0 Σu1j
By using the definition of the generalized impulse responses with respect to structural

shocks given by
SGIRF (yt ; vl,t ; h) = E(yt+h |It−1 %0l vt =p%0l Σv %l ,) − E(yt+h |It−1 )(20)

it follows that for a structurally identified shock, vlt such as a US trade shock the
SGIRF is given by

SGIRF (yt ; vl,t ; h) =%j An (P G1 G1 )−1 Σv %l√, h = 0, 1, 2, ; j = 1, 2, ..., k%l Σ v %l

where %l = (0, 0, ..., 0, 1, 0, ..0)0 is a selection vector with unity as the lth element in
the case of a country-specific shock, Σv is the covariance matrix of structural shocks, and
PG0 1 G1 is defined by the identification scheme used to identify the shocks.

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23

Table 1: Country’s openness
Country group Country
Country’s openness relative to the USA
EU
Belgium
5.508
France2.047
Germany
2.188
Italy
1.923
Netherlands
4.945
Switzerland
3.960
UK
2.188
Non-OECD
Brazil
0.917
China
1.910
HK
13.551India
1.417
Mexico2.132
Russia2.306
Taiwan4.331
OthersCanada
2.712
Japan
0.986
Korea
2.929
Notes: The openness is calculated as (Export+Import)/GDP. The statistics show the ratio of
country’s openness vis-a-vis that of the USA.

24

Table 2: The correlation of variables within country groups
TFP
USA
TFP
R&D
GDP
Capital
EU
TFP
R&D
GDP
CapitalNon-OECD
TFP
R&D
GDP
CapitalOthersTFP
R&D
GDP
CapitalR&D

GDP

Capital

10.366
10.816 0.374
1-0.589 -0.692 -0.446

1

1
0.542
1
0.329 0.686
1-0.686 -0.925 -0.643

1

1
0.361
1
0.436 0.936
1-0.685 -0.822 -0.820

1

1
0.338
1
0.388 0.990
1-0.572 -0.896 -0.916

1

Notes: Full sample.

Table 3: Unit root tests for the domestic variables
Domestic variable Statistic
TFP
ADF
WS
R&D
ADF
WS
GDP
ADF
WS
CapitalWS
ADF

Critical value
-3.45
-3.24
-3.45
-3.24
-3.45
-3.24
-3.24
-2.89

EU
Non-OECD Others USA
-2.51
-1.80
-4.19 -1.88
-2.70
-1.01
-4.09 -2.20
-2.67
-1.63
-0.49 -5.12
-2.18
-1.15
-0.73 -4.88
-1.35
-2.29
-2.32 -1.50
-1.16
-1.87
-2.30 -1.27
-0.93
-2.03
-3.13 -1.54
1.06
0.20
0.22 -0.71

Notes: Unit root tests examine the null hypothesis of the unit root. The 5% critical values arereported.

25

Table 4: Order of the VARX model and the number of cointegrating relations
pi qi # Cointegrating relations
EU
2 1
3
Non-OECD 2 1
4Others
2 1
4
USA
2 1
3
Notes: The lag length is determined by the Schwartz Bayesian information criterion. The
number of cointegrating relationships is based on trace statistics of Johansen tests.

Table 5: Weak exogeneity test
Country
F -test Critical value TFP R&D GDP
EU
F(2,71)
3.12 1.27 2.48 2.29
Non-OECD F(5,68)
2.34 1.89 0.86 2.24
OthersF(3,70)2.73 0.08 1.27 1.73
USA
F(3,70)2.73 1.95 1.78 0.23
Notes: The 5% critical values are reported.

26

Capital
0.28
1.09
1.62
1.17

27

Average
Std Error
MediumMini
Max

Notes: The ratio of the magnitude of productivity shocks is reported.

(EU→EU)/ (EU→USA)/ (NonOECD→NonOECD)/ (NonOECD→USA)/ (Others→Others)/ (Others→USA)/(USA→USA) (USA→EU)(USA→USA)(USA→NonOECD)(USA→USA)(USA→Others)
0.244
0.060
-0.423-0.255-0.192-0.099
0.111
0.080
0.258
0.109
0.181
0.105
0.290
0.061
-0.385-0.302-0.231-0.248-1.172-0.834-5.168-1.276-2.335-0.944
1.594
1.324
2.384
1.866
1.717
1.571

Table 6: The impact of productivity shocks

Figure 1: Total factor productivity of selected countries

Notes: The data are from the Penn World Table Ver. 9. The US TFP is equal to one.

28

Figure 2: R&D (% of GDP)

Notes: Data source: http://stats.oecd.org/Index.aspx?DataSetCode=MSTI_PUB

29

Figure 3: Impulse response functions for an expansionary 1 SD shock to US TFP

1 S.D shock to USA TFP

GDP

USA

EU

Non-OECD

OTHERS

R&D

CapitalTFP

Notes: The figure reports structural generalized impulse response functions (SGIRFs) for the GDP, R&D, capital and TFP. The graphs show
bootstrap median estimates with the associated 90% bootstrap confidence bands computed on the basis of 1000 replications of the SGIRFs,
where the forecast horizon extends up to 40 quarters and is recorded along the horizontal axis.

30

Figure 4: Impulse response functions for an expansionary 1 SD shock to EU TFP

1 S.D shock to EU TFP
GDP

USA

EU

Non-OECD

CapitalR&D

TFP

Notes: see Fig.(3)31

OTHERS

Figure 5: Impulse response functions for an expansionary 1 SD shock to Non-OECD TFP

1 S.D shock to Non-OECD TFP

GDP

USA

EU

Non-OECD

R&D

CapitalTFP

Notes: see Fig.(3)32

OTHERS

Figure 6: Impulse response functions for an expansionary 1 SD shock to OTHERS TFP

1 S.D shock to ‘Others’ TFP

GDP

USA

EU

Non-OECD

R&D

CapitalTFP

Notes: see Fig.(3)33

OTHERS