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Institute for International Integration Studies
IIIS Discussion Paper
No.309 / November 2009
IIIS Discussion Paper No. 309
Vertical Specialization and Nonstationarities in International
Trade Series
Sabaté Marcela, Dolores Gadea and Noelia Camara
University of Zaragoza
IIIS Discussion Paper No. 309
Vertical Specialization and Nonstationarities in
International Trade Series
Sabaté Marcela, Dolores Gadea and Noelia Camara
University of Zaragoza
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1
Vertical Specialization and Nonstationarities in
International Trade Series
Sabaté Marcela, Dolores Gadea and Noelia Camara
University of Zaragoza
Abstract
In this paper, we analyze the statistical properties of a large sample of trade
openness series in the Second Era of Globalization (from 1948 to the recent crisis) and
find a clear stationary pattern for developing countries versus a unit root pattern for
developed countries. Most interestingly, we show how the progress of vertical
specialization can rationalize this presence of unit roots in the ratio of export to GDP.
We use scattered data of vertical specialization (defined as the imported input content of
exports) for ten OECD countries to construct yearly export series free from the upwards
bias introduced by vertically specialised trade in the official values. We find that when
the statistical analysis is applied to the unbiased series of openness, they become trend
stationary for nearly all the countries, corroborating the responsibility of vertical
specialization in the presence of unit roots.
Key Words: Vertical Specialization; Unit Roots; Multi-accounting bias, Degree of
Development
JEL: C22, F15
2
I. Introduction
In the last decade, there has been a large increase in the academic literature on
the change in the nature of international trade. Unlike the horizontal specialization
(specialization in goods) that dominated the First Era of Globalization (1870-1913), the
Second Era of Globalization (from 1948 until the present crisis) has been characterized
by vertical specialization (specialization in stages of the production process).
Feenstra (1998) has referred to this change as the disintegration of production in
the global economy1. During the Second Globalization, and especially since the 1970’s,
the trade share of GDP has risen worldwide and, apart from the standard factors
(income convergence, tariffs and transport-cost reductions), Feenstra (1998) mentions
the need to consider the international disintegration of the production processes to
explain this very considerable growth. According to this author, the disintegration of
production means that inputs cross borders several times during the productive process,
which introduces an upward bias into the openness ratio, because the numerator is gross
value (in the export statistics) while the denominator is value-added (GDP). This
upward bias has also been the main explanation given by Baier and Bergstrand (2001)
in a much-cited article where, after carrying out a gravity equation analysis, they find
that income convergence and reductions in tariffs and transport costs only explain 40
per cent of the world trade growth in 1958-19882. Due to this vertically specialized
1 Other terms to refer to the fragmentation phenomenon have been “slicing up the value chain” [Krugman,
1996], “delocalization” [Leamer, 1996], “outsourcing” [Feenstra and Hanson, 1996], “international
production sharing” [Feenstra, 1998 and Yeats, 2001], “offshoring” [Arndt and Kierzkowski, 2001],
“multi-stage production” [Dixit and Grossman, 1982], “vertical specialization” [Hummels et al, 1998],
“kaleidoscope comparative advantage” [Bhagwati and Dehejia, 1994], “intra-product specialization”
[Arndt, 1997], “intra-dediate trade” [Antweiler and Trefler, 1997], “vertical production networks”
[Hanson et al. 2005], “production relocation” and “international segmentation of production” [Jones and
Kierzkowski, 2001].
2 Moreover, the bias is used to explain, as in Chen et al. (2005), that the goods export share rises while
that of services declines, even though the manufacturing share of GDP declines and that of services
increases in developed countries. The fact that a value-added criterion is applied to services, instead of a
3
trade, according to the last World Trade Report [World Trade Organization, 2009], the
slump of the world openness in the present recession is greater than that registered in
past slow-downs.
The goal of this paper is to show how the progress of vertical specialization,
together with the above mentioned multiple-accounting bias, has been the cause of the
presence of unit roots in international trade series (exports to GDP) until the outbreak of
the current crisis. So far, very little attention has been paid to the study of the statistical
properties of these series. While the volume of literature for the study of the integration
order of some macroeconomic series is enormous3, there are only two works whose goal
is the study of trade (import, export and openness) series. One of them is Ben-David and
Papell’s (1997) article, where the authors analyze, for a large number of countries,
whether the behaviour of the international trade shares of GDP changed gradually or not
in the second half of the past century. The second article is that of Serrano et al. (2008),
where the authors study the statistical properties of the Spanish openness series in the
very long run (1870-2000).
However, neither of these works deals with vertical specialization and its
potential effects on the international trade series, on which we focus our analysis. More
specifically, we try to explain the puzzle of finding unit roots for most of the series of
openness in the second half of the twentieth century [Ben-David and Papell, 1997], by
relating this non-stationarity to the increase of the disintegration of production in the
global economy. We call it a puzzle because the presence of unit roots is not consistent
gross value, explains the relatively slower advance of their export share compared with that of
manufacturing trade.
3 In a seminal article, Nelson and Plosser (1982) studied the integration order of fourteen macroeconomic
series, among them, real, nominal and per capita real GNP, unemployment, prices and interest rates. The
same series have been studied in many other works [for instance, Perron, 1989; Zivot and Andrews, 1992;
Lumsdaine and Papell, 1997; Lee and Strazicich, 2003]. Among the works analysing the properties of
GDP and GNP, we can highlight Perron (1989), Stock and Watson (1988), Kormendi and Meguire
(1990), Ben-David and Papell (1995, 1998), McCoskey and Kao (1998), Phillips and Moon (2000),
Kapetanios (2002) and Carrión-i-Silvestre et al. (2005).
4
with the analysis of bounded variables which, in theory, the ratio of exports over GDP
is. Our hypothesis is that, if unit roots are not simply masking the existence of structural
breaks, they might be reflecting the upward bias introduced by the vertical
specialization into the openness series, as a consequence of which the export shares of
GDP do not necessarily have to be bounded between 0 and 1.
To support this hypothesis, we start by carrying out an analysis of the statistical
properties of the series of exports over GDP for 54 countries in 1948-2005. When
applying time series analysis, in accordance with the results of Ben-David and Papell
(1997), we find an overwhelming presence of unit roots in the ratios. However, if we
consider the possibility of breaks, while most of the Less Developed Countries’ (LDC)
series become stationary, non-stationarity continues to affect more than half of the
Developed Countries’ (DC) series. Most interestingly, when applying a panel analysis
with structural changes, a clear pattern of unit roots for DC versus stationarity for LDC
emerges. The whole sample shows evidence of stationarity, but when dividing the panel
according to the degree of development, we find that the rejection of non stationarity
only remains for the LDC group. Thus, the finding is fully consistent with the theory of
the disintegration of production, which assigns a major role to the decline of trade costs
in the process and predicts difficulties for these LDC to join the international network.
Poorer infrastructure and institutional frameworks hinder the entrance of LDC into the
network, so their series are not necessarily affected by the multi-accounting bias that
vertical specialization introduces into the openness ratios. Meanwhile, the non-
stationarity in the openness series of DC might be related to the advance of vertical
specialization and its consubstantial multi-accounting bias.
The next step is to relate the presence of unit roots and vertical specialization in
the DC for which we have available data. We have scattered data of vertical
5
specialization (as the percentage of imports embodied in domestic exports) for about
five different years between 1968 and 1998 in ten OECD countries. We use this
information, provided by Hummels et al. (2001) and Chen et al. (2005), to obtain a new
measure of openness free from the bias introduced by the vertical specialization for each
available year. Then, by interpolating data into this new measure, we generate ten yearly
series, which we assume are representative of the evolution of the export value actually
added in each country between 1948 and 2005. Finally, we apply unit root tests to the
unbiased openness series and find that, as expected, the results change substantially
from those obtained with the original series. Once the multiple-accounting effect of the
vertical specialization is taken into account, the export share of output becomes
stationary for nine out of the ten countries, in contrast to the results obtained for the
original openness series, where only three countries out of the ten exhibited a stationary
trend.
In sum, this paper contributes to illustrating the different statistical properties of
openness series in the Second Era of Globalization, depending on the degree of
development of the countries. We find a clear pattern of stationarity for LDC versus a
pattern of unit roots for DC. Most importantly, the paper relates the predominance of
unit roots in DC to the advance of vertical specialization in recent decades. As a result,
by considering the upward bias introduced by vertical specialization into the official
gross-valued export series, the paper rationalizes the econometric puzzle of typifying
external openness as unit root series when openness, as a ratio, is supposed to be a
bounded variable.
The rest of the paper is organised as follows. Section II summarises some
stylised facts related to the international disintegration of production. Section III
analyses the statistical properties of the series of openness in the Second Era of
6
Globalization (1948-2005) for a sample of 54 countries, by applying time series and
panel data analysis. Section IV presents the unbiased openness series we construct for
ten OECD countries. It also contrasts the different properties of the original series and
the modified ratios of openness, having removed the multi-accounting induced by
vertical specialization. Finally, Section V concludes.
II. The advance of vertical specialization
In recent years, a consensus has been reached about the new nature of
international trade. Current productive processes have come a long way from the
horizontal specialization of the First Era of Globalization [O’Rourke and Findlay,
2003]. In the last four decades, a new international trade has arisen as a consequence of
the vast fragmentation in the productive processes4. The new international trade in the
Second Era of Globalization not only involves the exchange of entire products, but also
an increasing trade in intermediate inputs, so companies compete in final products as
well as in unfinished products. While the First Globalization allowed the spatial
separation of factories and consumers, the Second Globalization has divided up the
factories themselves [Baldwin, 2006].
On the theory side, the failure of traditional international trade models, and even
monopolistic competition models, to explain this very new trade behaviour has
generated a flourishing literature about the new circumstances in production and trade.
The first theoretical works started by introducing intermediate goods in Heckscher-
Ohlin type models, as in Brata and Casas (1973) and Dixit and Grossman (1982). In a
second round, following the much-cited work of Jones and Kierzkowski (1990), a
4 The term “fragmentation” was proposed by the international trade theorists Jones and Kierzkowski
(1990).
7
rapidly growing literature proposed different mathematic models that, also in a
Heckscher-Ohlin setting, explain the advance of the international fragmentation and its
consequences in terms of prices, wages and production [Venables,1999; Deardorff
2001a, b, 2005; and Yi, 2003, among others]5. More recently, Grossman and Rossi-
Hansberg (2006a, b; 2008) have moved away from the traditional international goods
trade approach and modelled what they call task trade, that is to say, the specialization
of a country not in goods but in stages of production. Finally, Baldwin and Robert-
Nicoud (2007) propose a model to explain the consequences of trading in tasks, which
is also applied in a monopolistic competition setting.
In any case, whatever the approach, the decision to outsource abroad always
requires the cost savings of disintegrating different stages of production to be higher
than the costs associated with the spatial fragmentation. The advance of vertical
specialization would not have been feasible without a sustained reduction in the special
fragmentation-related costs, also generally referred to as trade costs. There is direct
evidence, in the second half of the twentieth century, of a worldwide downward trend in
tariff barriers6. With respect to non-trade barriers, the elimination of Voluntary Exports
Restrictions (VERs), the disappearance of the Multi-Fibre Agreement (MFA) and the
phasing-out of agricultural quotas in developed countries confirm the idea that the
downward trend also applies to them. As regards transport costs, a number of works
[Hummels, 1999, 2001, 2007] have documented a noticeable reduction in the transport
times of long-haul air freights (since WWII) and of maritime shipping (mostly due to
the use of containers in the seventies7). Moreover, the time spent in administrative and
5 See Baldwin and Robert-Nicoud (2007) for a recent review of models of international
disintegration/fragmentation
6 See Anderson and van Wincoop (2004) for a comprehensive discussion on the measurement problems
and trends in tariff, non-tariff and other trade barriers, including transport costs.
7 Hummels (2001) estimates that the combined time reductions in air and maritime transport was
equivalent to a fall in the tariff on manufactures from 32 to 9 % in 1950-1998.
8
certification procedures has also undergone an important decrease which, added to the
time saved in the transportation process, has led to a significant reduction in the need
for storage and the associated costs. Finally, there is no need to emphasize how
technological progress has eased communication across countries in recent decades and,
by dropping its cost to almost zero, has spectacularly reduced the efforts necessary to
find suppliers abroad. The overall decline in these costs is behind the phenomenon of
international fragmentation, whose advance in recent decades can be traced with the
help of different measures.
The literature suggests different data sources to quantify the phenomenon of
international fragmentation, among them, international trade statistics on parts and
components and Input-Output tables8. A first rough measure of the advance of the
process can be proxied by the performance of trade on parts and components. In the
nineties, this kind of trade grew much faster than the total world trade, even faster than
the intra-industry trade [Jones, Kierzkowsky and Lurong, 2005], and despite the slow-
down of recent years, data document a more dynamic performance of trade in
intermediate inputs than trade in final goods during 1988-2006 [World Trade
Organization, 2008]9.
The same advance of international fragmentation can be inferred from two more
accurate measures of external orientation based on Input-Output information. The first
measure concentrates on the foreign content of domestic production by using the index
share of direct imported inputs in production or in total inputs. It was developed by
Feenstra and Hanson (1996) and has been widely used to assess the consequences of
fragmentation on wages and employment, as in Egger and Egger (2003), Bardhan and
8 See Bauman and di Mauro (2007) for a wide review about different methods and data, and Amador and
Cabral (2008) for a review of the three main different data sources and methods used by the empirical
trade literature to quantify the fragmentation phenomenon.
9 Yeats (2001), although restricted to the machinery sector, goes back further and provides evidence of
the advance of trade on parts and components in the OECD countries from 1978 to 1995.
9
Kroll (2003), Wei (2004), Hijzen (2005) and Geishercker et al. (2008)10. This measure
has also been used to assess the degree of external orientation by Campa and Goldberg
(1997) who, focusing on U.S., U.K., Canada and Japan, observe an increase in imported
inputs into production for all countries except Japan. One more example is Feenstra
(1998), who presents results for the whole manufacturing sector and several
disaggregated industries across a wider range of developed countries. This measure also
provides evidence that international fragmentation has progressed recently, as the world
percentage of imported intermediate inputs over total inputs has increased from 18.8 to
22 between 1995 and 2000 [World Trade Organization, 2008].
The second type of Input-Output measure focuses on the foreign content of
exports. Whereas the first measure only captures the direct import content of exports
(imported intermediate inputs), the second measure reflects the direct and indirect
import content of exports. This second measure is proposed by Hummels et al. (1998)
and Hummels et al. (2001), who labelled it vertical specialization (VS)11. In comparison
with the first Input-Output measure, Hummels et al.’s (2001) vertical specialization
measure is narrower, because it only considers the imported inputs embodied in the
exported output. Nevertheless, it is the best measure to approach the change in the
nature of international trade that we are interested in.
This measure of VS is defined as the importation of intermediate goods used by
a country to make goods or goods in process, which are in turn, exported to another
country. So, three conditions have to hold for VS to occur. Firstly, the good has to be
produced in at least two sequential stages. Secondly, two or more countries have to add
value during the productive process and, finally, the country that uses the imported
10 See Horgos (2007) for a detailed analysis of this index.
11 Originally, the term vertical specialization was used by Balassa (1967) to refer to the process according
to which, to take advantage of market size and scale economies, manufacturing parts, components, and
accessories were produced in separate establishments.
10
inputs must export some of the resulting output. Therefore, vertical specialization offers
a complete perspective of the changed nature of international trade since it captures, on
the import side, the essence of international outsourcing (the decision of firms to
substitute domestic value added through the import of intermediate goods) and, on the
export side, the trading of either intermediate or final goods.
Analytically, the Vertically Specialized trade is defined for sector i as:
X
outputgross
IIM
VSi*
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
where IIM denotes the value of Imported Intermediate Inputs in sector i, and X
represents the merchandise exports.
Thus, the VS trade for country k is the sum of i
VS across all sectors:
∑∑ ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
==
ii k
ki
ki
i
kk X
outputgross
IIM
VSVS *
and the measure given by Hummels et al. (2001) is the VS trade share of X:
∑
∑
=
iki
iki
k
kX
VS
X
VS .
They estimate VS for ten developed countries and four developing countries
between 1970 and 1990 and find that it accounts for more than 20% of exports and
explains 30% of the growth in the overall export/GDP. The World Trade Organization’s
(2008) calculations for a sample of 28 countries confirm that VS (ranging from 14 to
60%) has continued to advance and accounts for an important share of export growth in
the period 1995-2000. The following sections look for the effects of this international
fragmentation process on the statistical properties of the external openness series.
11
III. Stochastic properties of the international trade series
We work with a set of 54 economies from 1948 to 2005, which includes two
sub-samples, one of 32 Less Developed Countries (LDC) and the other of 22 Developed
Countries (DC), according to the World Bank criteria. Yearly data on exports, GDPs
and exchange rates come from the International Financial Statistics of the International
Monetary Found (2007). We work with nominal terms of GDP and exports, the latter
being converted into national currency by using the annual average of the official or
market exchange rates, depending on the country.
a. Exploiting time variation
We start the analysis of the integration order of the openness series by applying
the Augmented Dickey and Fuller (1979, 1981) (ADF) and the Ng and Perron (2001)
(NP) unit root tests, and the stationarity test of Kwiatkowski et al. (1992) (KPSS)12. The
results show that, according to the unit root tests, almost all the series have a unit root,
whereas the opposite is found when applying the KPSS test. The contradiction between
the unit root and stationarity tests might be a symptom of the presence of structural
changes in the series, which in turn, would fit in with the break found by Ben-David and
Papell (1997) in their international trade series, according to Vogelsang’s (1997) test.
Thus, taking into account the outcomes obtained by Ben-David and Papell
(1997), we consider the possibility that, in the second half of the twentieth century, the
market integration prompted by trade liberalization and a decrease in transport costs,
12 To select the correct order of the autoregressive process in the ADF and NP tests, we use the Modified
Akaike Information Criterion. We use the MZGLS statistic (AR spectral – GLS detrending) of the unit
root test developed by NP. The KPSS test has been modified by using the spectral estimation window
proposed by Sul et al. (2003), since Carrión-i-Silvestre and Sansó (2005) demonstrated that, if it is used
to estimate the long-run variance, the KPSS test shows a smaller size distortion and a satisfactory power.
Tables are available on request
12
caused breaks in the X/GDP ratios. We test for the presence of breaks in the series by
using the new method proposed by Perron and Yabu (2008)13, as a pre-test to obtain
certain information on the existence or not of structural changes in the series. This test,
that considers the three traditional models (A,B and C) proposed in Perron (1989)14, is
able to detect the presence of one structural break in the trend function without any prior
knowledge as to whether the noise component is stationary or contains an
autoregressive unit root. When this test is applied to our data, we find that there is at
least one significant structural break in most of the series. The results, in Table 1, show
a strong rejection of the null of a stable trend function in favour of a trend function with
a shift in forty countries out of fifty four. Six of the fourteen countries without a
structural change are LDC and eight DC. Thus, in relative terms, there is more evidence
of stability in the trend function for developed countries.
Following to Perron (1989), the next step is to test again for a unit root, but with
a test that allows for the presence of structural changes. We use the test developed by
Lee and Strazicich (LS) (2004) that considers the presence of one structural break in the
series under both the null hypothesis of a unit root and the alternative hypothesis of
stationarity. These authors showed the negative consequences of considering structural
breaks only under the alternative hypothesis in unit root tests15 and, trying to avoid these
problems, developed a new LM type test that determines the break points
endogenously16. So, with the LS test, the rejection of the null hypothesis unambiguously
implies that the series are trend stationary.
13 This test improves the finite sample properties by using the bias corrected version of the OLS estimate
of α proposed by Roy and Fuller (2001). It is also more powerful than Vogelsang’ s (1997) test largely
used in the empirical literature.
14 That is, model A (the “crash” model), that permits a change in the levels of the series; model B, that
permits a change in the rate of growth; and model C, that allows both changes.
15 As occurs in Zivot and Andrews (1992), Perron (1997), Lumsdaine and Papell (1997) and Vogelsang
and Perron (1998), among others.
16 Lee and Strazicich (2003) show that, if we do not consider breaks under the null in tests with
endogenous breaks, the test statistics may diverge and lead to a rejection of the null when the DGP is
13
TABLE 1.—Analysis of Structural Change. Perron and Yabu (2008)
Developing Countries Exp-W
FS
1
Developed Countries Exp-W
FS
1
1
Algeria
12.47489
b
1
Australia
91.90455
b
2
Barbados
1.02926 2
Austria
3.55738
b
3
Colombia
2.19358 3
Canada
1.1568
4
Congo, Rep.
4.09633
b
4
Denmark
2.11751
b
5
Costa Rica
19.81272
b
5
Finland
0.88589
6
Cyprus
7.06194
b
6
France
1.14495
7
Dominican, Rep.
1.44693 7
Germany
6.766
b
8
Egypt
5.48717
b
8
Greece
4.5408
b
9
El Salvador
13.39325
b
9
Iceland
11.88411
b
10
Fiji
0.87336 10
Ireland
8.50329
b
11
Guatemala
4.01152
b
11
Italy
1.15126
12
Guyana
5.95367
b
12
Japan
3.65051
b
13
Haiti
2.45393
b
13
Korea, Rep.
8.32728
b
14
Honduras
4.72385
b
14
Netherlands
17.22745
b
15
India
2.3889 15
New Zeeland
8.51407
b
16
Jamaica
17.11131
b
16
Norway
2.59666
17
Mali
8.93994
b
17
Portugal
20.22143
b
18
Malta
4.8154
b
18
Spain
2.46568
b
19
Mauritius
2.57125
b
19
Sweden
1.01961
20
Mexico
26.50599
b
20
Switzerland
1.50549
21
Morocco
3.67226
b
21
United Kingdom
1.66018
c
22
Nigeria
13.41796
b
22
United States
0.86151
23
Pakistan
8.92512
b
24
Panama
6.21344
b
25
Paraguay
15.57105
b
26
Philippines
100.5456
b
27
South Africa
1.62728
c
28
Sri Lanka
17.31538
b
29
Sudan
16.7434
b
30
Thailand
5.9129
b
31
Trinidad y Tobago
18.55183
b
32
Venezuela
1.14358
1
Critical values are provided in Perron and Yabu (2008)
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively
Models A, B and C [Perron 1989] represent changes in levels, trend and both
levels and trend together, respectively
Source: own elaboration.
integrated with structural breaks, as in the Lumsdaine and Papell (1997) test. In addition, these
approaches, derived by assuming no structural breaks under the null, might present problems in empirical
applications because the rejection of the null does not necessarily imply the rejection of a unit root per se,
but may imply the rejection of a unit root without breaks. Similarly, the alternative hypothesis does not
necessarily imply trend stationarity with breaks, but may indicate a unit root with breaks. For a complete
description of the test, see Lee and Strazicich (2003 and 2004).
14
LS (2004) propose two of the three above mentioned structural break models
considered in Perron (1989), A and C, to simulate the Data Generating Process (DGP)17,
based on the unobserved components model:
,' 1tttt XZy
ε
β
δ
++= −
where t
Zincludes exogenous variables, the unit root null hypothesis is described by
1=
β
and ),0(~ 2
σε
iidN
t. For Model A, which allows for one break in the intercept,
[]
′
=tt DtZ ,,1 , where 1=
t
D for ,1
+
≥B
Tt and 0 otherwise. B
T is the break year and
()
., 21
δ
δ
δ
=
′ For Model C, that allows for a change in the intercept and in the trend
slope,
[]
′
=ttt DTDtZ ,,,1 , where Bt TtDT
−
=
for 1
+
≥B
Tt and 0 otherwise18. To
correct the auto-correlated errors, we have included augmented terms following the
general-to-specific procedure described in Perron (1989) and suggested in Ng and
Perron (1995) to determine the optimal number of lags (p)19. Once the test statistic has
been obtained, the location of the break ( B
T) is determined by calculating the unit root
test t-test statistic in all the possible break points and then, selecting the one for which
the test statistic is minimized20. Finally, to choose between models A and C, we use the
information criteria of Akaike (AIC) and Swartz (SBIC).
Following these econometric advances, we show that, once one break is taken
into account, 26 out of the 40 countries with structural change, become trend stationary.
More interestingly, we find a clear difference between LDC and DC. While more than
seventy percent of countries in the first group (19 out of 26) become trend stationary,
17 They omit Model B, without any risk of losing generality, as it is commonly held that most economic
time series can be adequately described by models A or C.
18 See LS for a detailed explanation about how to construct the break LM unit root test.
19 We begin with a maximum number of lagged first-differenced terms p= 4, obtained from the formula
3T. This technique has been shown to perform well as compared to other data-dependent procedures to
select the number of augmented terms in unit root tests [Ng and Perron, 1995].
20 We select a trimming of 10%.
15
only fifty per cent (7 out of 14) do so stationary in the second21. However, before
drawing any conclusions on this finding, we consider the warning of Perron (1989)
about the loss of power of tests when ignoring a break and continue the analysis looking
for a second one. So, we apply the LS (2003) test, which, in the same line as LS (2004)
for one break, allows for the presence of two breaks under the null and the alternative
hypotheses. Analogously, model A allows two changes in levels ttt DDtZ 21 ,,,1[=]´,
jt
D being a dummy variable equal to 1 if 2,1,1
,
=
+
≥jTt j
B and 0 otherwise, where j
B
T
is a break year. Model C allows two changes, in both levels and trend, so that
ttttt DTDTDDtZ 2121 ,,,,,1[=]´, where jt
DT = j
B
Tt
−
if 2,1,1 =
+
≥jTt j
B and 0
otherwise.
Thus, the null and alternative hypotheses in model A are:
,: 11221100 ttttt yBdBdyH
υ
μ
+
+
++= −
,: 2221111 tttt DdDdtyH
υ
γ
μ
+
++
+
=
where t1
υ
and t2
υ
are stationary error terms, and 1
=
jt
B if 2,1,1 =+
=
jTt Bj and 0
otherwise22. Analogous argument can be applied to model C for both hypotheses:
ttttttt yDdDdBdBdyH 112413221100 :
υ
μ
+
+
+
+
++= −
tttttt DTDTDdDdtyH 221221111 :
υ
γ
μ
+
+
+
++
+
=
Proceeding as in LS (2004), the endogenous two-break LM unit root test shows
that the outcomes barely change if they are compared with those resulting from the
consideration of one break. Only the openness series of one LDC becomes stationary
when considering two breaks. The results of this analysis are presented in Tables 2 and
21 If we include Barbados, Colombia and Sweden, without breaks according Perron and Yabu (2008), in
the test of LS (2004) they also have a stationary trend.
22 The H0 includes the dummy variable Bjt so it is necessary to ensure that the asymptotic distribution of
the test statistic is invariant to the size of breaks (d) under the null [Perron, 1989].
16
3, together with those obtained by applying unit root tests without breaks MZGLS [Ng
and Perron, 2001] and the unit root test with one structural break
τ
LM [LS, 2004]. We
find an overwhelming presence of unit roots in the LDC (30 countries out of 32) but
most of them disappear when we consider breaks in the unit root test (only 10 countries
continue to show unit roots). The results for the DC again show a predominance of unit
roots (20 out of 22) when we do not take structural breaks into account, but when we
allow for breaks, although the presence of unit roots diminishes (13 countries maintain
the unit roots), it does not do so to such an extent as in the LDC. In sum, we observe
that the overwhelming presence of unit roots in the DC seems not to be a consequence
of structural breaks; 60% of the openness series maintain their non-stationarity after the
break analysis. Conversely, in the LDC, only 30% of the series show unit roots when
we allow for structural changes.
b. Exploiting time and cross-country variations
In the analysis of the sample of 54 countries (1948-2005), we use the stationarity
test with structural changes developed by Carrion-i-Silvestre et al. (2005). This test
allows for multiple structural breaks that can differ in time, intensity and location across
individuals23. We test the null hypothesis of panel stationarity with multiple structural
breaks against the alternative of first order integrated, since some authors have proposed
using the two types of tests (unit root and stationarity tests) to carry out a sort of
confirmatory analysis24.
23 The seminal contributions to the analysis of unit roots in a panel framework are from Quah (1994),
Phillips and Moon (1999) and Levin et al. (2002). However, while several tests have been proposed, less
attention has been paid to the presence of temporal structural changes in panel data analysis. Exceptions
are the well-known papers of Carrion-i-Silvestre et al. (2002), Im et al. (2005) and Carrion-i-Silvestre et
al. (2005), among others.
24 See Maddala and Kim (1998) for a summary.
17
TABLE 2.—X/GDP. Analysis of Unit Root: Less Developed Countries
Country Stat.
1
Model
2
Break year
1
Algeria -3.403
c
A1985
2
Barbados -2.5919
--
3
Colombia -2.1842
--
4
Congo, Rep. -4.743
C 1974-1990
5
Costa Rica -4.1783
b
A1955
6
Cyprus -4.5396
b
C1978
7
Dominican, Rep. -2.8673
c
--
8
Egypt -5.0408
b
C1991
9
El Salvador -5.9613
b
C 1978-1988
10
Fiji -2.1491
--
11
Guatemala -4.7868
b
C1968
12
Guyana -4.6861
C 1979-1991
13
Haiti -4.6222
C 1975-1994
14
Honduras -4.8332
C 1976-1989
15
India -0.7015
--
16
Jamaica -4.9211
b
C1995
17
Mali -5.3554
C 1965-1985
18
Malta -4.7592
b
C1971
19
Mauritius -4.6574
b
C1985
20
Mexico -4.4133
c
C1975
21
Morocco -4.223
b
A1993
22
Nigeria -3.4804
c
A1986
23
Pakistan -4.5365
b
C1975
24
Panama -4.523
C 1974-1985
25
Paraguay -4.8296
b
C1977
26
Philippines -9.9627
a
C1996
27
South Africa -4.7183
b
C1976
28
Sri Lanka -4.4595
c
C1975
29
Sudan -4.853
b
C1986
30
Thailand -4.431
C 1965-1995
31
Trinidad y Tobago -4.4708
c
C1980
32
Venezuela -3.5290
a
--
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively.
We apply the general-to-specific procedure, described in Ng and Perron (1995), to select
the number of lags with a kmax equal to
1
Represents either t-statistics of MZGLS [Ng and Perron, 2001], LMτ [LS, 2004] or LMτ [LS, 2003]
depending on whether exist 0, 1 or 2 structural breaks respectively in the series.
2
Model A: break in levels. Model C: break in both levels and trend. [Perron 1989]
Source: own elaboration.
The test proposed by Carrion-i-Silvestre et al. (2005) is based on the KPSS
panel data version developed by Hadri (2000) and generalizes existing proposals in the
18
field. The null hypothesis implies stationarity so there has to be strong evidence against
trend stationarity to conclude in favour of the non-stationarity of the panel. The test is
TABLE 3.—X/GDP. Analysis of Unit Root: Developed Countries
Country Stat.
1
Model
2
Break year
1
Australia -5.3551
a
C1960
2
Austria -5.0199
C 1959-1997
3
Canada -1.9371
--
4
Denmark -4.9987
C 1955-1968
5
Finland -2.3346
b
--
6
France -2.2339
--
7
Germany -4.6289
b
C1989
8
Greece -5.0984
C 1958-1984
9
Iceland -5.534
a
C1958
10
Ireland -4.289
c
C1992
11
Italy -2.0223
--
12
Japan -3.8189
C1985
13
Korea, Rep. -4.9441
C 1971-1989
14
Netherlands -4.9328
C 1978-1990
15
New Zeeland -5.516
a
C1975
16
Norway -3.0313
b
--
17
Portugal -6.0608
a
C1981
18
Spain -4.4514
C 1963-1994
19
Sweden -2.1979
--
20
Switzerland -1.8438
--
21
United Kingdom -3.4532
c
A1973
22
United States -2.2039
--
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively.
We apply the general-to-specific procedure, described in Ng and Perron (1995), to select
the number of lags with a kmax equal to
1
Represents either t-statistics of MZGLS [Ng and Perron, 2001], LMτ [LS, 2004] or LMτ [LS, 2003]
depending on whether exist 0, 1 or 2 structural breaks respectively in the series.
2
Model A: break in levels. Model C: break in both levels and trend. [Perron 1989]
Source: own elaboration.
normally distributed and shows a good finite sample performance, as well as allowing
the inclusion of individual fixed effects and/or a specific individual time trend.
More specifically, the null hypothesis is equivalent to
considering Ni
iv ,...,1,0
2
,=∀=
σ
, where 2
,iv
σ
is the variance of the error that includes the
individual effects in the data generating process (DGP):
tiititi ty ,,,
ε
β
α
+
+=
19
Under the null, the model becomes:
,
,
11
*
,,,,,,, ti
m
k
m
ktkikiitkikiiti
ii
DTtDUy
εγβθα
∑∑
==
++++=
with the dummy variable being 1
,,
=
tki
DU for ikb
Tt ,
> and 0 elsewhere, and ikb
T,
denoting the kth date of the break for the ith individual, 1,,...,1 ≥
=
ii mmk . The dummy
is ikbtki TtDT ,,, −=
∗ for ikb
Tt ,
> and 0 elsewhere, 1,,...,1 ≥
=
ii mmk . The model includes
individual effects, individual effects with structural breaks25, temporal effects ( 0≠
i
β
)
and temporal effects with structural breaks26 if 0
,
≠
ki
γ
.
Two kinds of models are considered in the analysis. First, we consider Model
1)0( ,== kii
γ
β
[Perron and Vogelsang, 1992], without either time effects or structural
breaks in the time trend. Model 2 )0( ,
≠
≠
kii
γ
β
is the model C developed in Perron
(1989) and allows a time trend and structural changes affecting either the trend or the
level27.
The procedure begins by detecting the structural changes of the individuals in
the panel. Given a maximum number of break points (mmax), we estimate the position
for each mi ≤ mmax, i = 1,…, N, and then test the significance of the breaks to obtain the
optimum number and location for each series. To select the break date, we follow Bai
and Perron (1998) in their criterion for locating the breaks using to the argument that
minimizes the sequence of individual SSR
(
)
:,..., ,1,
imb
i
bi
TT
(
)
imb
i
bi
TT ,1, ˆ
,...,
ˆ),...,(minarg ,1,
,..., ,1,
imb
i
b
TT i
ii
mb
i
bTTSSR=,
where the trimming applied locates the break point in the interval
[
]
TT 95.0,05.0 . To
select the optimum number of breaks, we use the information criterion of LWZ
25 Shifts in the mean caused by the structural breaks.
26 Shifts in the individual time trend.
27 The use of model C (Perron, 1989) lets us obtain homogeneous outcomes if we compare it with those
of the time series analysis.
20
proposed in Bai and Perron (1998). We obtain a vector for each individual with the
optimum number of breaks and, if we find an individual without breaks, we use the test
without structural breaks. As we are working with trending variables, we assume a trend
in the deterministic component28. The long-run variance estimate is obtained as
described in Sul et al. (2003), with the specification of an
(
)
pAR process for the
prewithening and using both the Bartlett and the Quadratic spectral window with
automatic bandwidth selection [Andrews, 1991, Andrews and Monahan, 1992, Sul et
al., 2003]. The order of the autoregressive process in the prewithening stage is fixed by
using the BIC information criterion with a 4
max =p lags.
In practice, we set a maximum of two breaks to obtain comparable outcomes to
those of the time series analysis. Then, we select the optimum number of breaks for
each country with the LWZ information criterion29. The results, in Table 4, report the
impossibility of rejecting the null hypothesis of stationarity in the whole panel at a
significance level of 10%. In other words, the analysis shows evidence in favour of
stationarity for the whole sample of X/GDP series. However, when repeating the
analysis with the panel divided into two sub-panels, one for LDC and the other for DC,
the results change substantially, in line with the outcomes in the previous time series
analysis. We find strong evidence against stationarity in the panel for DC and evidence
in favour of stationarity in the panel for LDC.
When exploiting jointly the time structure and the cross-sectional dimension of
the data and, consequently, enhancing the power of tests, we obtain additional support
for the idea that changes in international trade have not been affecting LDC and DC
28 Carrion-i-Silvestre (2005).
29 We work with a balanced panel from 1954 to 2004 for reasons of simplicity. We eliminate Algeria,
Congo, Germany, Haiti, Malawi, Netherlands, Paraguay and Sudan from the panel due to the lack of data
to construct the balanced panel.
21
Panel A: Whole panel
Bartlet
Estadístico (p-value)
Exports/GDP 1.837 (0.033)
Panel B: Sub-panels for LDC and DC
Bartlet
Estadístico (p-value)
LDC 0.108 (0.457)
DC 6.168 (0.000)
Source: Own elaboration.
TABLE 4.—X/GDP. Stationary panel data test
The maximum numbre of break points allowed is two.
The long-run varia nce is es timeted as suming homogeneity.
equally during the Second Era of Globalization. Our hypothesis is that the
predominance of unit roots in the openness series of DC reflects their active role in the
advance of international fragmentation, while the stationarity of the series of LDC
mirrors their exclusion from the international production network. The reason is that,
although international trade costs have plummeted, some important country-specific
barriers (quality of port, airport and communication infrastructures, administrative
requirements for imports and exports,…) remain comparatively high in LDC, thus
hindering their connection to the international network [World Trade Organization,
2008].
IV. Marrying unit roots to vertical specialization
The analysis of the statistical properties of a number of series of export over
GDP shows that the majority of those corresponding to DC are non stationary. This
means that they can be modelled as the sum of a stochastic trend, the shifts registered
each period and a non-permanent (transitory) term. In other words, any stochastic shock
has a permanent effect on the process and there is no reversion to a deterministic trend
22
path. Ben-David and Papell (1997) had already accepted a difference stationary
representation of the international trade series for a broad sample of countries in the
second half of the twentieth century. What stands out in the literature is the absence of
controversy over the integration order of the series that we are examining (export over
GDP), unlike many macroeconomic variables.
If we take this variable as a fraction, we are assuming that is bounded in the [0,
1] interval. However, when working with bounded variables, the presence of unit roots
is econometrically excluded because it implies that the long-run variance increases
indefinitely over time. In other words, we are facing the puzzle of typifying external
openness for developed countries as a unit root series when openness, as a fraction, is
supposed to be a bounded variable. In order to solve this puzzle, we propose to consider
the upward bias introduced by vertical specialization in the export series. Since the
numerator of the variable export over GDP is gross value and the denominator is value-
added, there are no reasons to think that the so-called openness ratio has to be bounded
between 0 and 1. Thus, vertical specialization emerges as a potential explanation for the
presence of unit roots, which is precisely the hypothesis that we test for the ten
developed countries of the OECD in what follows.
As we said before, Hummels et al. (2001) provide scattered information about
the percentage of imports embodied in the domestic exports of ten developed countries
between 1970 and 1990. This analysis was updated by Chen et al. (2005) so that, in
total, including the estimations of Minondo and Rubert (2002) for Spain, we have
information for the countries and years specified in Table 530.
30 There are VS trade estimations for other countries: Cardaso et al. (2007) estimate the measure for nine
European countries, Breda et al. (2007) for Italy and six other European countries, Dean et al. (2007) for
China and Cheng and Chang (2006) for Taiwan and South Korea and WTO (2008) for 28 countries. We
do not use this information because it is only provided for one year or two at the most.
23
As seen in the previous section, when applying a time-series analysis, we find
that the series of exports over GDP show a unit root for most of these ten countries. The
key question is to what extent this non-stationarity is merely reflecting the advance in
vertical specialization of recent decades. To explore this possibility, we start by
constructing new series of openness after removing the multi-accounting bias. From the
information available for the countries and years specified in Table 5 and the openness
ratios constructed with the data provided by the International Financial Statistics (IMF),
we have created a new measure X*/GDP, representative of the real value added
exported (X*) by a particular country over its GDP.
This variable X*/GDP for a country k is defined as follows:
k
kk
k
kGDP
VSX
GDP
X−
=
*
where X is the value taken from the IMF statistics and VS is the value of imports
embodied in the domestic export value. Thus, this variable, which represents only the
value embodied and exported by the country itself, is free from the foreign added valued
incorporated by the multi-accounting associated with vertically specialized trade. We
have then interpolated to create yearly series from 1968, when many authors establish
the beginning of the vertical specialization phenomenon, to 2005. We have used cubic
spline polynomials, which are the approximating functions of choice when a smooth
function is to be approximated locally and are preferable to the method of truncated
Taylor series. The general idea of any interpolation method is to compute the values of
f(x) in the interval [a,b] knowing f(a) and f(b) 31.
31 The truncated Taylor series provides a satisfactory approximation for the series at each point x if its
path is sufficiently smooth and the interpolation point is sufficiently close to a or b. But if a function is to
be approximated on a larger interval, the degree, of the approximating polynomial may have to be chosen
unacceptably large. The alternative is to subdivide the interval [a,b] of approximation into sufficiently
small intervals [
ζ
j
,...ζ
j+1
]
, with a=
ζ
1<…<
ζ
j+1=b, so that, on each of them, a polynomial Pj of relatively
low degree can provide a good approximation to the time series. This can even be done in such a way that
the polynomial pieces blend smoothly, so that the resulting patched or composite function s(x) that equals
24
TABLE 5.— VS AS A SHARE OF MERCHANDISE EXPORTS: AVAILABLE DATA
Australia Canada Denmark France Germany Japan Netherlands Spain UK US
1968 1971 1972 1972 1978 1970 1972 1970 1968 1972
1974 1976 1977 1977 1986 1975 1977 1990 1978 1977
1986 1981 1980 1980 1988 1980 1981 1994 1983 1982
1989 1986 1985 1985 1990 1985 1986 1990 1985
1995 1990 1990 1990 1995 1990 1995 1998 1990
1997 1995 1995 1996 1997
1996 1997
1997 1998
Source: Chen el al. (2005) and Minondo and Rubet (2002) for Spain.
The new series are compared to the original ones in Figure 1, and they clearly
show the advance of the new kind of trade after the late 1960s. Most importantly, the
findings when analysing the statistical properties of the new series change radically. The
results are in Table 6 and show how, when we take the vertically specialized trade into
account, working with the variable X*/GDP, the unit root test MZGLSατ identifies three
countries (France, Japan and the UK) as having a stationary trend. Also, the Perron and
Yabu (2008) test confirms, as before, that there is at least one structural break in most of
the series (see Table 7).
Table 8 shows the results of the LS (2004) test. We find that all the series except
the U.S. have a stationary trend when excluding the effect of the multi-accounting bias
introduced by VS and simultaneously considering the possible presence of one break
Pj(x) for x∈[
ζ
j
,...ζϕ+1]
, and all j, has several continuous derivatives. Any such smooth piecewise
polynomial function is called a spline.
25
TABLE 6.— X*/GDP. UNIT ROOT TEST OF NG AND PERRON (2001)
Country MZGLS
Australia -0.571
Canada -1.647
Denmark -1.080
France -2.715
c
Germany 0.099
Japan -1.656
c
Netherlands -0.964
Spain -2.097
United Kingdom -1.908
c
United States -2.187
Critical values are provided in Ng and Perron (2001)
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively
Spectral estimation method: AR spectral – GLS detrending
We use the Modified Akaike criterion to select the lag length the tests
with a kmax equal to
Source: own elaboration.
3T
TABLE 7.— X*/GDP. PERRON AND YABU (2008): Exp-W
FS1
X*/GDP
Country Model A Model B Model C
Australia 15.2639
a
81.2075
a
90.6548
a
Canada 5.5349
a
0.3496 5.1141
a
Denmark 11.1370
a
0.4699 29.7873
a
France 0.8435 0.0614 0.7941
Germany 4.8582
a
0.7757 16.1011
a
Japan 2.3201
b
0.2777 2.3776
Netherlands 12.7608
a
0.1362 12.9237
a
Spain 3.4188
a
0.2059 1.6977
United Kingdom 1.6599
c
0.1853 2.6651
United States 0.9623 0.0985 0.8594
1
Critical values are provided in Perron and Yabu (2008)
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively
Models A, B and C [Perron 1989] represent changes in levels, trend and both
levels and trend together, respectively
Source: own elaboration.
in the ratio of openness. Nine series become broken trend stationary in contrast with the
three countries that we found (Australia, Germany and the U. K.) when we worked with
the official series of exports. When we consider the possibility of two breaks, the results
are very similar: eight stationary series out of the ten, as shown in Table 9. In this case,
Canada does not become stationary.
26
FIGURE 1.--EXPORTS OVER GDP, 1948-2005
Note: Solid lines represent the official statistics of exports over GDP and dashed lines represent the new measure
(
)
GDPX *: export, net of imported inputs, over GDP. Source: own elaboration.
0
0.05
0.1
0.15
0.2
0.25
0.3
1949
1955
1961
1967
1973
1979
1985
1991
1997
2003
AUS AUS*
0
0.1
0.2
0.3
0.4
0.5
1948
1954
1960
1966
1972
1978
1984
1990
1996
2002
CA N CA N*
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1950
1956
1962
1968
1974
1980
1986
1992
1998
2004
DEN DEN*
0
0.05
0.1
0.15
0.2
0.25
1950
1956
1962
1968
1974
1980
1986
1992
1998
2004
FRA FRA*
0
0.1
0.2
0.3
0.4
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
GER GER*
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
JA P JAP*
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1956
1961
1966
1971
1976
1981
1986
1991
1996
2001
NETH NETH
0
0.05
0.1
0.15
0.2
0.25
1954
1959
1964
1969
1974
1979
1984
1989
1994
1999
2004
SPA SPA *
0
0.05
0.1
0.15
0.2
0.25
1948
1954
1960
1966
1972
1978
1984
1990
1996
2002
UK UK*
0
0.02
0.04
0.06
0.08
0.1
1948
1954
1960
1966
1972
1978
1984
1990
1996
2002
US US*
27
To sum up, the last two tables clearly illustrate how vertical specialization
affects the stochastic properties of the international trade series, in that stationary trends
characterize exports over GDP series once we have removed the bias associated with
vertical specialization and once the deterministic components of the Data Generating
Processes are considered correctly.
TABLE 8.— X*/GDP. MINIMUM LM UNIT ROOT TEST (ONE BREAK)
Country Model
1
Break time t-statistic AIC
2
Australia C 1960 -5.2422
b
-8.820
Canada C 1995 -4.3588
a
-9.431
Denmark C 1972 -4.2594
a
-9.048
France C 1998 -5.5912
c
-10.042
Germany C 1990 -5.0459
c
-9.576
Japan C 1990 -4.9661
b
-10.163
Netherlands A 1971 -4.1205
b
-7.999
Spain A 1962 -3.2038
a
-10.037
United Kingdom A 1973 -3.8512
b
-9.815
United States A 1973 -2.871 -11.044
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively. Critical
values in Lee and Strazicich (2004)
We apply the general-to-specific procedure, described in Ng and Perron (1995), to select
the number of lags with a kmax equal to
1
Model A: break in levels. Model C: break in both levels and trend. [Perron 1989]
2
Information criterion of Akaike
Source: own elaboration.
3T
TABLE 9.— X*/GDP. MINIMUM LM UNIT ROOT TEST (TWO BREAKS
)
Country Model
1
Break time t-statistic AIC
2
Australia C 1961, 1967 -7.274
a
-9.603
Canada C 1964, 1992 -4.88 -9.507
Denmark C 1959, 1975 -5.957
b
-9.527
France C 1970, 1996 -6.984
a
-10.327
Germany C 1989, 1998 -6.556
a
-9.679
Japan C 1979, 1990 -5.884
b
-10.421
Netherlands A 1971, 1975 -4.090
b
-8.008
Spain A 1960, 1962 -3.721
c
-10.127
United Kingdom A 1966, 1973 -3.948
b
-9.990
United States A 1973, 1998 -2.990 -11.059
a, b and c denote a statistic significant at the 1%, 5% and 10% level respectively. Critical
values in Lee and Strazicich (2003)
We apply the general-to-specific procedure, described in Ng and Perron (1995), to select
the number of lags with a kmax equal to
1 Model A: break in levels. Model C: break in both levels and trend. [Perron 1989]
2
Information criterion of Akaike
Source: own elaboration.
3T
28
V. Conclusion
The goal of this paper has been to show how the progress of vertical
specialization can explain the puzzle of finding unit roots in the series of openness of
developed countries in the second half of the twentieth century. Our hypothesis is that
the unit roots are reflecting the upward bias introduced by the vertical specialization
into the numerator of the openness series, as a consequence of which, the export shares
of GDP are not necessarily bounded between 0 and 1. To test this hypothesis, we have
started by analysing a large sample of countries and found a clear pattern of stationarity
for the openness series of LDC in contrast to the pattern of unit roots of DC. The next
step was to test whether vertically specialised trade was responsible for this unit root
pattern in DC. We used the scattered data of vertical specialization for ten OECD
countries to construct new yearly export series of domestic added value exported.
Corroborating our hypothesis, we have found that, when the statistical analysis is
applied to the unbiased series of openness, the majority of countries (nine out of ten)
became stationary, in contrast to the results obtained for the original openness series,
where only three out of the ten exhibited a stationary trend.
This paper, consequently, both illustrates the influence of vertical specialization
on the stochastic properties of the international trade series and rationalizes the
econometric puzzle of typifying external openness (when vertical specialization is not
taken into account) as series with a unit root.
29
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Institute for International Integration Studies
The Sutherland Centre, Trinity College Dublin, Dublin 2, Ireland
