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Volume 29, Issue 2

Measuring the external risk in the United Kingdom

EstelaSáenz

University of Zaragoza

MaríaDoloresGadea

University of Zaragoza MarcelaSabaté

University of Zaragoza

Abstract

This paper aims to describe the evolution of the external risk in the United Kingdom between 1961 and 2008. We first

present a theoretical description of the risk indicator. Then, we calculate this measure for the British economy in the

period of study. In general, the results reveal a very small increase of external risk. Finally, the relationship between

the two dimensions of external risk: trade openness and external volatility is analysed.

The authors acknowledge the financial support from a CICYT Project (SEJ2005-00215) and the SEIM Research Group (SEC 269-124).

Citation:EstelaSáenzandMaríaDoloresGadeaandMarcelaSabaté,(2009)''MeasuringtheexternalriskintheUnitedKingdom'',

Economics Bulletin, Vol. 29 no.2 pp. 1182-1189.

Submitted:Apr062009. Published: May 28, 2009.

1

1. INTRODUCTION

Among the authors who found a positive relation between international economic

integration and public sector size, we can mention Rodrik (1996, 1998), who devised a

hypothesis that nowadays is known as the hypothesis of compensation. The idea behind

it is that more open economies are exposed to a greater risk as a result of the possible

turbulences in the international markets which can affect their domestic economy. As

the public sector is "the safe" sector of the economy, both in terms of employment and

income, it can exert an isolation function over the external risk that affects the other

sectors, increasing its participation in the economy as a whole. So, to calculate the

degree of the external risk that an economy is exposed to, it is necessary to use

measures that reflect the volatility of income derived from the external shocks.

The paper is organised as follows. In the second section, we describe the

calculation of the indicator of external risk and show its evolution in the British

economy. In the third section, we carry out an analysis of the relation between trade

openness and external volatility. This has never been done previously for the case of the

United Kingdom. Finally, we sum up the main conclusions of this work.

2. THE INDICATOR OF EXTENAL RISK

The measure used by Rodrik (1996, 1998), and that was subsequently used in all

the works of cross-country and panel data about this topic, was the interaction term of

trade openness and volatility of terms of trade. This volatility is the standard deviation

of the terms of trade growth rate. That is to say, it is necessary to distinguish between

exposure to external risk and openness. Two countries can have similar levels of

exposure to trade and have quite different levels of exposure to external risk -if the

volatility of their terms of trade is different-. Openness refers to the exposure to

international economy and external risk refers to the instability of the terms and

conditions under which an economy trades with foreign economies1. The important

thing is the interaction between the two variables.

As we are working in a time series context, we need a measure of external risk

that varies over time. So, to calculate the volatility of the terms of trade, in line with

Islam (2004), we use the GARCH (Generalized Autoregressive Conditional

Heteroskedasticity) model2. In this technique, frequently employed to calculate

volatilities, above all for financial time series, the variance is not constant. The

prediction of the volatility of some variables is very important not only for financial

planners but also for the agents who participate in international trade, because the

variability of some variables such as exchange rates or terms of trade may involve huge

profits or losses.

The simplest and most frequently used GARCH model is the GARCH (1, 1)3:

212

2110

2

−− ++= ttt u

σααασ

The conditional variance in period t depends on the squared error term and the

conditional variance in the previous period. This model calculates the conditional

variance of the terms of trade growth rate. Therefore, the volatility of the terms of trade

1 Kim (2007). Examples of open economies with little risk are those of Southeast Asia.

2 This model was developed by Bollerslev (1986), as an extension of the ARCH model proposed by Engle

(1982).

3 It is equivalent to an ARCH(2) model.

2

will be the square root of this variance (VOLTT). Finally, multiplying this series by

trade openness, we obtain a measure of external risk.

2.1 The volatility of the terms of trade in the British economy

In Figure 1, we show the evolution of the terms of trade in the United Kingdom

between 1960 and 20084.

Figure 1. Terms of trade and terms of trade less oil

0

20

40

60

80

100

120

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

TT TTLO

Source: Own elaboration. Terms of trade are from the AMECO Database (National Accounts), European

Commission, Economic and Financial Affairs. Terms of trade less oil data are from the UK office for

National Statistics.

In general, we can say that there has been an improvement in the British terms of

trade. On the one hand, the British economy is more or less self sufficient in oil and,

because of this, terms of trade have not been significantly affected by shocks in oil

prices -as can be seen in Figure 1-. On the other hand, the United Kingdom has tended

to import those goods that have undergone the largest price decrease. In Figure 2, we

can see the volatility of the terms of trade, derived from the aforementioned GARCH (1,

1) model. This figure also reflects the stability of the terms of trade series, since its

volatility is both very low and stable. The only significant increase is clearly linked to

the international economic crisis of the seventies.

Figure 2. Volatility of terms of trade

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Source: Own elaboration from data in Figure 1.

4 We have chosen this period because of the availability of data for terms of trade.

3

Figures 3 and 4 show the evolution of the external risk (the interaction term), with

openness measured in current terms and real terms, respectively5. As can be

appreciated, the external risk has undergone a slight increase in the period of study.

Figure 3. External risk: 1/2*XMGDP*VOLTT

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Source: Own elaboration. Data of exports, imports and GDP in current terms are from the AMECO

Database (National Accounts), European Commission, Economic and Financial Affairs.

Figure 4. External risk: 1/2*XMGDPREAL*VOLTT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Source: Own elaboration. Data of exports, imports and GDP in real terms are from the AMECO Database

(National Accounts), European Commission, Economic and Financial Affairs.

Kim (2007) classifies geographical regions according to their levels of openness

(total trade as a percentage of GDP) and external volatility -averaged for the second half

of the nineties- into four groups6.

5 The measure of the external risk, 1/2*OPENNESS*VOLTT, is derived from the following argument.

Let x, m and y stand for volumes of exports, imports, and GDP, respectively. Let π be the natural

logarithm of the price of exports relative to imports (the terms of trade). Let the log of the terms of trade

follow a random walk, possibly with drift. The unanticipated component of the income effects of a terms

of trade change can then be expressed (as a % of GDP) as 1/2 [(x+m)/y] [dπ-α], where α is the trend

growth rate in the terms of trade. The standard deviation of this is 1/2 [(x+m)/y] x st. dev. (dπ). Hence, the

interaction ofthe measure of openness [(x+m)/y] with the standard deviation of the first (log) differences

in the terms of trade gives us (twice) the appropriate measure of external risk. Rodrik (1998), pp. 1014.

6 Kim (2007) carried out and panel data analysis of the relationship between openness, external risk and

economic volatility, thorough a sample of 175 countries in the period 1950-2002.

4

(1) More-open/lower-volatility economies. Examples of regions that fall into this

category are East Asia, which countries are the most trade-open and at the same time

have low levels of external volatility and Western Europe, with the lowest level of terms

of trade volatility (0.0284).

(2) More-open/higher-volatility economies. Example countries in this group

include Central Asia.

(3) Less-open/higher-volatility economies. Latin America and Sub-Saharan

Africa are in this category.

(4) Less-open/lower-volatility economies. North America countries have the least

trade-open economies (53.78%) and also very low levels of terms of trade volatility

(0.035).

According to this classification, the United Kingdom is included in the fourth

group. On the one hand it has very low levels of terms of trade volatility (0.0314 and

0.0281 for the period 1961-2008 and 1995-2000, respectively). One the other hand it is

not a very open economy, even taking into account the coefficient of openness in real

terms7. Thus, we can say that the British economy is not very exposed to the risk

emanating from turbulence in world markets.

3. THE RELATION BETWEEN TRADE OPENNESS AND THE VOLATILITY

OF THE TERMS OF TRADE

In the previous sections, we have carried out a theoretical and graphical

description of the indicator of external risk. In this section we use UK data from 1961-

2008 to test more formally for an effect of trade openness on external volatility8. We

should mention the papers of Lutz and Singer (1994) and Easterly and Kraay (2000),

where these authors did not find evidence that a higher level of openness increases the

risk of shocks in the terms of trade. The explanation of this result was that the

diversification derived from the increase of openness involves new, non-traditional

exports.

We start with a simple analysis of the coefficients of correlation of openness and

the volatility of the terms of trade.

Table 1. Correlations

XMGDP/VOLTT

0.31

XMGDPREAL/VOLTT

-0.21

Source: Author’s calculations.

7 The average of trade of goods (as a % of GDP) for 1995-2000 is 41.93% (current terms) and 38.11%

(real terms). Kim’s classification is based on Penn World Tables, namely on total trade of good and

services (as a % of GDP) in current terms. Our conclusions are the same taking into account the trade of

services, because the averaged trade of good and services for the aforementioned period is 56.08%, very

near to that of North America.

8 According to the argument of Rodrik (1998) and Kim (2007), a higher degree of openness does not

necessarily involve greater volatility of the terms of trade.

5

As we can see in Table 1, the process of trade openness in the British economy

did not raise the volatility of the terms of trade. Both indicators of openness show a very

small coefficient of correlation with external volatility. Moreover, in the case of total

trade in real terms this coefficient is negative.

We complete our analysis with the cointegration test of Johansen to assess

whether there is a long-term relation between the two variables. We carry out a test of

unit roots to find out the integration order of the series. We apply the tests of Dickey

Fuller (1979, 1981) (ADF), Phillips-Perron (1988) (PP), Dickey Fuller GLS of Elliott,

Rothenberg and Stock (1996) (DF-GLS), the optimum point of Elliot, Rothenberg and

Stock (1996) (ERS) and Ng and Perron (2001) (NG-P). Alternatively, we use the test of

Kwiatkowski, Phillips, Schmidt and Shin (1992) (KPSS), where the null hypothesis is

stationarity. Looking at Tables 2 and 3, we can say that VOLTT is I(0) and the

measures of openness are I(1). Taking into account that our interest variables have

different order of integration, it can be expected that the cointegration analysis does not

reveal a long-term relation between them. Because of this, the estimators derived from

an OLS equation will be inefficient. To solve this problem, as we have said, we use the

multivariant technique of Johansen, based on the VAR model. The main advantage

compared to uniequational methods is that it does not suppose that there is just one

direction in the relation studied, as it is a system of equations in which all variables are

endogenously fixed.

Table 2. Test of unit roota

Test of

stationaritya

Variable

(in levels) ADF PP DF-GLS ERS NG-P KPSS

XMGDP -2.44 -2.44 -2.42 9.91 -2.15 0.17**

XMGDPREAL -2.47 -2.41 -2.16 14.29 -1.90 0.21**

VOLTT -3.51** -2.49 -3.39*** 1.10** -3.34*** 0.18

a) The series in levels include trend and intercept. ** Significant at 5%.

The critical value of the ADF and PP tests are in Mackinnon (1996), DF-GLS and ERS in Elliott,

Rothenberg and Stock (1996), KPSS in Kwiatkowski, Phillips, Schmidt and Shin (1992) and NG-P in Ng

and Perron (2001). The information criterion used to assess the optimum lag is the SIC. The choice of the

residual spectrum of zero frequency is based on the estimation proposed by the author of each test. The

method of bandwidth is from Newey-West (1994). These tests check the null hypothesis of the existence

of unit roots, with the exception of the KPSS test, where the null hypothesis is the existence of

stationarity.

Table 3. Test of unit roota

Test of

stationaritya

Variable

(in first

differences)

ADF

PP

DF-GLS

ERS

NG-P

KPSS

XMGDP -7.28

*** -7.42

*** -7.33

*** 1.46

*** -3.35

*** 0.10

XMGDPREAL -6.19

*** -7.67

*** -7.03

*** 0,29

*** -3.39

*** 0.19

VOLTT -6.84

***

a) Without trend and intercept in ADF and PP tests, except XMGDPREAL, which has an intercept.

***, ** and * Significant at 1%, 5% and 10%, respectively.

6

We have specified a model of two endogenous variables (openness and volatility

of the terms of trade). The optimum length of the VAR in accordance with the LR and

SC criteria, which allows the residuals fulfil the requirements of normality,

homoscedasticity and absence of correlation is two lags for XMGDP and one lag for

XMDPREAL. The next step involves choosing one of the five cases proposed by

Johansen (1995) in order to make some suppositions about the underlying trend in the

data. According to the unit root test, we consider two possibilities. The first is that they

have no trend (model 2) and the second is that they have a stochastic trend (model 3).

The LR, SC and AIC criteria select model 2 for XMGDP and model 3 for

XMGDPREAL.

The results of the test of Johansen about the relation between trade openness and

the volatility of the terms of trade are shown in Table 4. In the case of total trade in real

terms (XMGDPREAL), both trace and eigenvalue tests accept the null hypothesis of no

cointegration because the result is lower than the critical value. However, for the total

trade in current terms (XMGDP), there is cointegration.

Table 4. Cointegration test of Johansen:

Trade openness and volatility of the terms of trade, 1961-2008

Cointegration based on max eigenvalues:

Endogenous

Variable Null

Hypothesis Alternative

Hypothesis Statistic Critical Value

5% Probability

XMGDP r=0

r≤1 r≥1

r=2 17.40

5.92 15.89

9.16 0.03

0.20

XMGDPREAL r=0

r

≥16.95 14.26 0.50

Cointegration based on trace of stochastic matrix:

Endogenous

Variable Null

Hypothesis Alternative

Hypothesis Statistic Critical Value

5% Probability

XMGDP r=0

r≤1 r≥1

r=2 23.32

5.92 20.26

9.16 0.02

0.20

XMGDPREAL r=0

r

≥16.95 15.49 0.58

The relation between the cointegrated variables adjusts, according to the first

vector of the cointegration test, to the following terms:

VOLTT = -0.002 + 0.0008XMGDP

(1.64)

with t-ratio in brackets.

As can be seen, there is a positive, although very small, effect of trade openness

on the volatility of the terms of trade.

5. CONCLUSIONS

In this paper, we have presented a theoretical description of a measure that

reflects external risk, that is to say, the risk derived from the turbulences in the

international markets. Then, we have calculated this indicator for the British economy in

1961-2008. In general, we can say that external risk hardly increased in the United

7

Kingdom during this period. Finally, the econometric analysis of the relation between

trade openness and the external volatility shows that these variables are different

concepts. That is to say, there is no causal effect of openness on volatility in the UK.

6. BIBLIOGRAPHY

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Journal of Econometrics, 31, 307-327.

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time series with a unit root”, Journal of The American Statistical Association, 74

(366), 427-431.

Dickey, D.A. and W.A. Fuller (1981): “Likelihood ratio statistics for autoregressive

time series with a unit root”, Econometrica, 49 (4), 1057-1072.

Elliott, G., Rothenberg, T.J. and J.H. Stock (1996): “Efficient tests for an autoregressive

unit root”, Econometrica, 64, 813-836.

Easterly, W. and A. Kraay (2000): “Small States, Small Problems”, Mimeo,

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Engle, R.F. (1982): “Autoregressive conditional heteroskedasticity with estimates of the

variance of united kingdom inflation”, Econometrica, 50 (4), 987-1007.

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Johansen, S. (1995): Likelihood-based inference in cointegrated vector autoregressive

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compensation hypothesis”, International Organization, 61, 181-216.

Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Y. Shin (1992): “Testing the null

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Econometrics, 54, 159-178.

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terms of trade: an empirical investigation”, World Development, 22 (11), 1697-

1709.

Mackinnon, J.G. (1996): “Numerical distribution functions for unit root and

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Ng, S. and P. Perron (2001): “Lag length selection and the construction of unit root tests

with good size and power”, Econometrica, 69 (6), 1519-1554.

Rodrik, D. (1996): “Why do more open economies have bigger governments?”, NBER

working paper number 5537.

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of Political Economy, 106 (5), 997-1032.