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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