2007 Oxford Business & Economics Conference
ISBN : 978-0-9742114-7-3
Testing for Non-linearity in Balancing Item of Balance of Payments Accounts: The
Case of 20 Industrial Countries
Tuck Cheong Tang*
Monash University Malaysia
Abstract
This study is aimed to explore the non-linearity in balancing item of balance of payments
accounts. A sample of 20 industrial countries is used. A battery of nonlinearity tests illustrates
non-linearity in balancing item over 13 of 20 industrial countries. An immediate implication is
that a special attention should be taken into account when studying the balancing item of balance
of payments accounts due to its non-linearity in nature.
JEL Classification: C22; F32
Keywords: Balancing item; Balance of payments accounts; Industrial Country; Non-linearity
School of Business, Monash University Malaysia, 2 Jalan Kolej, Bandar Sunway,
Petaling Jaya, Selangor Darul Ehsan 46150, Malaysia
E-mail address: tang.tuck.cheong@buseco.monash.edu.my
*
I would like to thank Kian-Ping Lim for raising the motivation of testing the nonlinearity in
balancing item of balance of payments accounts, and the sharing of knowledge of Nonlinear
Toolkit as well. All remaining errors remain the responsibility of the author.
June 24-26, 2007
Oxford University, UK
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2007 Oxford Business & Economics Conference
ISBN : 978-0-9742114-7-3
Testing for Non-linearity in Balancing Item of Balance of Payments Accounts: The
Case of 20 Industrial Countries
1. Introduction
Broadly speaking, as cited in both empirical and theoretical literature the assumption of
linearity is fundamentally rooted in modeling economic and financial time series. In this
context, many researchers and policymakers have designed the fiscal and monetary
policy via various linear modeling frameworks. With the recent development of nonlinearity literature both in empirical test and theoretical understanding, the assumption of
linearity in financial time series and macroeconomic series as well are no longer valid given a fact that many theoretical macroeconomic models are highly non-linear (Ashely
and Patterson 2000: 1). Clearly, as reinforced by Potter (1999), “Successful nonlinear
time series modeling would improve forecasts an produce a richer notion of business
cycle dynamics than linear time series models allow. For this to happen two conditions
are necessary. First, economic time series must contain nonlinearities. Second, we need
reliable statistical methods to summarize and understand these nonlinearities suitable for
time series of the typical macroeconomic length”.
Over the last decade, the insight that financial time series are characterized by non-linear
behaviour has been gaining a widespread consideration. Hinich and Patterson (1985)
have found empirical evidence of non-linearity in daily stock returns. Other study on
stock market is from Panagiotidis (2005). Liew, Chong, and Lim (2003) have examined
the linearity of real exchange rates for 11 Asian economies, and most of the cases
nonlinearity is favoured. Other similar study is Lim, Hinich, and Liew (2003). In recent,
several studies have been carried out in order to test whether macroeconomic time series
are non-linear. For example, Ashley and Patterson (2000) have investigated the nonlinearity of the US real GNP, and the study finds persuasive evidence that the generating
mechanism for this series is non-linear. On the other hand, using a battery of nonlinearity tests, Panagiotidis and Pelloni (2003) have documented that non-linearity is
found in the German labour markets but this is not the case in the UK where in most
cases the assumption of linearity is accepted.
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ISBN : 978-0-9742114-7-3
This study contributes to the literature by exploring the non-linearity character in
balancing item of balance of payments accounts via a battery of non-linearity tests. The
sample covers a range of industrial countries. Broadly speaking, the balancing item is
obtained simply by calculating the difference between total recorded credit transactions
and total recorded debit transactions per time period (Brooks and Fausten 1998: 31). The
net balance of errors (transactions are recorded incorrectly) and omissions (transactions
are not recorded at all) constitute the balancing item (Fausten and Brooks 1996: 1303).
Basically, double entry bookkeeping principle tells us that balance of payments accounts
are constrained by the ‘adding up’ problem - total debit is not equal to total credit. As a
result, a value so-called errors and omissions, is then added in order to validate this
principle. From recent literature search, study in regard to the balancing item of balance
of payments accounts becomes a significant area in international economics both from
the perceptive of researchers and policymakers because of its implications. That is the
size of balancing item indicates the reliability of balance of payments statistics. Moreover,
a positive value of the balancing item does suggest a systematic over-reporting of debit
transactions, or under-reporting of credit transactions and vice versa.
In 1971, Duffy and Renton (1971) published their work on an analysis of the UK’s
balancing item. With a vacuum exists in betweens, twenty six year later, Fausten and
Brooks (1996), Tombazos (2003), and Fausten and Pickett (2004) have provided insight
on studying the balancing item in Australia’s balance of payments accounts using various
methodology. In addition, Tang (2005, 2006a, and 2006b) has empirically examined the
economic factors that potentially contribute to the balancing item in Japan’s balance of
payments accounts. In sum, the studies find that Japan’s balancing item is essentially due
to timing errors. Interestingly, all the above-cited studies have been carried out under a
strong assumption that the balancing item is linear, and it is best to be estimated under
linear specification. However, if this assumption is not the case, the results of those
studies may be interpreted with caution. Motivated by these events, detecting non-linear
in balancing item is desired, and avoids the possibility of specification error. Eventually,
the presence of non-linearity in balancing item should be taken into account by
policymakers and researcher as well.
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Second section discusses the data and methods used in this study. The next section
reports and discusses the results of non-linearity tests. The study has been concluded in
Section 4.
2. Data and Methods
Data
The quarterly ‘errors and omission’ series used for this study are obtained from
International Financial Statistics, International Monetary Fund. The 20 industrial
countries have been selected due to data availability for a sufficient sample span. The
countries are New Zealand (1980.1-2005.1), the US (1973.2-2005.2), the UK (1970.12005.2), Norway (1975.1-2005.2), Portugal (1975.1-2005.3), Iceland (1976.1-2005.1),
Sweden (1975.1-2005.1), Greece (1976.1-2004.4), Finland (1975.1-2005.2), Ireland
(1981.1-2005.2), Canada (1975.1-2005.3), Australia (1959.2-2005.2), Denmark (1981.12004.4), Japan (1977.1-2005.1), Netherlands (1976.1-2005.2), Germany (1971.1-2005.3),
Austria (1970.1-2005.2), Italy (1970.1-2005.2), France (1975.1-2005.2), and Spain
(1975.1-2005.3). These data are plotted in Appendix 1. They appear to be reasonably
stationary over the sample period. The summary statistics are also illustrated in Table 1;
interestingly, the distribution of balancing item is found to be normally distributed only
for the case of Japan.
Insert Table 1 here
Methods
A battery of statistical test for non-linearity can be used in order to indicate whether or
not the generating mechanism of a time series is or is not linear. These tests are selected
for two reasons. First, most of the existing nonlinearity tests have differing power against
different classes of nonlinear processes and none dominates all others, as shown in
various Monte Carlo simulations (see, for example, Ashley et al., 1986; Ashley and
Patterson, 1989; Lee et al., 1993; Brock et al., 1991, 1996; Barnett et al., 1997; Patterson
and Ashley, 2000). Second, the estimations can be carried out using the Nonlinear
Toolkit provided by Patterson and Ashley (2000), and it has been used in the literature by
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Panagiotidis (2002, 2005), Panagiotidis and Pelloni (2003) and Ashley and Patterson
(2006).1 It is important to note that the main objective is not to determine the precise
nature of the nonlinearity but to determine whether or not nonlinearity exists in the full
sample of the returns series under study.
They are McLeod-Li test (McLeod and Li, 1983), Bicovariance test (Hinich, and
Patterson, 1995), Tsay test (Tsay, 1986), Engle LM test (Engle, 1982), and BDS test
(Brock, Dechert, and Scheinkman, 1996). All the tests work under the null hypothesis
that the series under consideration is an i.i.d. (independently and identically distributed)
process. Given that the null is i.i.d., and not linearity, the linear dependence has to be
filtered out from the data, so that any rejection of the null of i.i.d. is due to nonlinear
dependence. Those linear dependence is removed by fitting an AR(p) model. In brief, the
procedure is follow. First, the study determines the pre-whitening model, AR(p). The
values of p from 0 to 10 are considered and the one with the minimum SC is chosen. The
“best” AR model for each series over the 20 industrial countries is not reported here but
available from author upon request. Given the sample size is ranged between 96 and 195,
which is available, the tests have been estimated using the bootstrap. For the bootstrap
results, 1000 new samples are independently drawn from the empirical distribution of the
pre-whitend data. Each new sample is used to calculate a value for the test statistic under
the null hypothesis of serial independence. The obtained fraction of the 1000 test
statistics, which exceeds the sample value of the test statistic from the original data, is
then reported as the significance level at which the null hypothesis can be rejected.
(Panagiotidis, 2002, p.5). This study does not detail the methodology behind the tests
because it is well-documented in literature such as Ashley and Patterson (2000), and
Panagiotidis (2002) as well. The non-linearity tests are computed via Nonlinear Toolkit
(version 4.52) (http://ashleymac.econ.vt.edu/).
The
toolkit
can
be
downloaded
from
Richard
Ashley’s
webpage
at
http://ashleymac.econ.vt.edu/ashleyhome.html, while instructions and interpretations of all the tests are
given in chapter 3 of Patterson and Ashley (2000).
1
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3. Results
For a meaningful interpretation, only the results of the ‘bootstrapped’ significance levels
are reported as in Appendix 2. This is straightforward; rejection of linearity can be drawn
based on the decision rule that p-value of less than 0.10 is obtained. Almost all
bootstrapped p-values are zero of McLead-Li test, Bicovariance test, Engle test, and Tsay
test for the case of Austria, Canada, France, Iceland, Ireland, Germany, New Zealand,
Portugal, the UK, and the US, which the null hypothesis of linearity can be rejected,
suggesting that some kind of hidden structure, non-linearity exists in balancing item.
There is no evidence of nonlinearity is no evidence of nonlinearity for the case of
Australia, and Japan under Tsay test. However, this is not the case under McLead-Li test,
Bicovariance test, and Engle test (lag of 8 and 10 for Japan). On the other hand, the null
hypothesis of linearity is accepted by the results of Bicovariance test and Tsay test for
Greece, but McLead-Li and Engle test do not. For the case of Spain, Italy, and Sweden,
in contrast, linearity is supported by the results of McLeod-Li test and Engle test, but
Bicovariance test and Tsay test provide an opposite finding indicating some kind of
hidden structure – non-linearity. All four non-linearity tests provide empirical evidence
of linearity in the balancing item series at which the bootstrapped p-values are greater
than 0.10 for the case of Finland, Netherlands, and Norway. Also, there is evidence of
linearity in balancing item for Denmark, at least at 0.05 level. This inconsistency of nonlinearity tests is in line with Ashley and Patterson (2000) that, excluding the BDS test, the
other tests are quite inconsistent in their power across the various alternatives considered
(see, Ashley and Patterson, 2000, p.30).
As documented in Ashley and Patterson (2000), the BDS test has relatively high power
against all the alternatives, making it a reasonable choice as a “nonlinearity screening
tests” for routine use. The results of BDS test, in significance level (p-value) are also
reported in Appendix 2 (the second table). As indicated by the results of BDS test, the
null hypothesis that the elements of balancing item are i.i.d. can be rejected in most cases
(all dimensions and EPS) in the case of Austria, Australia, Denmark, France, Greece,
Iceland, Germany, New Zealand, Portugal, the UK, and the US. For Finland,
Netherlands, Norway, Spain and Sweden, most of the p-values are greater than 0.10
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indicating acceptance of the null hypothesis of linearity. However, mixture findings are
found across the dimensions and EPS in regard to non-linearity of balancing item in
balance of payments accounts of Canada, Ireland, Italy, and Japan. Generally speaking,
this discrepancy may be contributed to different power of non-linearity tests as described
in Ashley and Patterson, 2000).
Overall, based on the results discussed in this section; linearity is found to be reasonably
existed for the case of Denmark, Finland, Italy, Netherlands, Norway, Spain, and Sweden.
To summarize, a battery of nonlinearity tests illustrates non-linearity in the balancing
item over 13 of 20 industrial countries.
4. Concluding Remarks
This study is aimed to explore the possible hidden structure, in particular non-linearity
contained in the balancing item series of balance of payments accounts. This is applied to
20 selected industrial countries because of its sample span available. In this study, most
of the balancing item in industrial countries’ balance of payments accounts would
contradict the assumption of linearity. The overall results of the five nonlinearity tests
illustrate non-linearity in the balancing item over 13 of 20 industrial countries. In other
words, only Denmark, Finland, Italy, Netherlands, Norway, Spain, and Sweden would
corroborate the assumption of linearity. An immediate implication of this finding is that
the studies assume linearity of balancing item such as Duffy and Renton (1971) for the
UK, Fausten and Brooks (1996), Tombazos (2003), and Fausten and Pickett (2004) for
Australia, and Tang (2005, 2006a and 2006b) for Japan require further investigation
before it can be generalized.
No study is free from limitations. First, this study does not try to find what kind of nonlinear model is appropriate, and to implement a non-linear model in the series such as
ARCH, GARCH, TAR, two state Markov, Quadratic models, and Cubic models. Second,
this is worthwhile to identify the source of non-linearity in balancing item of balance of
payments accounts. It may help to reduce the possible ‘errors and omissions’ in recording
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both debit and credit side of external accounts – trade account and current account.
However, further study is required in order to implement the above-stated drawbacks.
References
Ashley, R.A., D.M. Patterson, and M.J. Hinich (1986). A Diagnostic Test for Nonlinear
Serial Dependence in Time Series Fitting Errors. Journal of Time Series Analysis
7 (3): 165-178.
Ashley, R.A. and D.M. Patterson (1989). Linear Versus Nonlinear Macroeconomies: A
Statistical Test. International Economic Review 30 (3): 685-704.
Ashley, R. A., and D. M. Patterson (2000). Nonlinear Model Specification/Diagnostics:
Insights from a Battery of Nonlinearity Tests. Economics Department Working Paper
E99-05: 1-38, Virginia Tech, at
http://ashleymac.econ.vt.edu/working_papers/E9905.pdf
Ashley, R.A. and D.M. Patterson (2006). Evaluating the Effectiveness of State-Switching
Time Series Models for U.S. Real Output. Journal of Business and Economic
Statistics, forthcoming.
Barnett, W.A., A.R. Gallant, M.J. Hinich, J. Jungeilges, D. Kaplan, and Jensen, M.J.
(1997). A Single-Blind Controlled Competition among Tests for Nonlinearity and
Chaos. Journal of Econometrics 82 (1): 157-192.
Brock, W.A., W.D. Dechert, J.A. Scheinkman, and B. LeBaron, (1996) A Test for
Independence based on the Correlation Dimension. Econometric Reviews 15 (3):197235.
Brock, W.A., W. Dechert, and J. Scheinkman, (1996). A Test for Independence Based on
the Correlation Dimension. Econometric Reviews 15 (3): 197-235.
Brock, W.A., D.A. Hsieh, and B. LeBaron (1991). Nonlinear dynamics, chaos, and
instability: statistical theory and economic evidence. Cambridge: MIT Press.
Brooks, R, D., and D. K. Fausten (1998). Macroeconomics in the Open Economy,
Addison Wesley Longman Australia Pty Limited, South Melbourne, Australia.
Duffy, M., and A., Renton (1971). An Analysis of the UK Balancing Item. International
Economic Review 12 (3): 448-464.
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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Fausten, D.K., and R. D. Brooks (1996). The Balancing Item in Australia’s Balance of
Payments Accounts: An Impressionistic View. Applied Economics 28 (10): 13031311.
Fausten, D. K., and, B. Pickett (2004). Errors & Omissions in the Reporting of
Australia’s Cross-Border Transactions. Australian Economic Papers 43 (1): 101-115.
Hinich, M., and D. M. Patterson (1995). Detecting Epochs of Transient Dependence in
White Noise. Unpublished manuscript, University of Texas at Austin.
Hinich, M., and D. M. Patterson (1985). Evidence of Nonlinearity in Daily Stock Returns.
Journal of Business and Economic Statistics 3 (1): 69-77.
Lee, T.H., H. White, and C.W.J. Granger (1993). Testing for Neglected Nonlinearity in
Time Series Models: A Comparison of Neural Network Methods and Alternative
Tests. Journal of Econometrics, 56 (3): 269-290.
Liew, V.K.S., T.T.L. Chong, and K.P. Lim (2003). The Inadequacy of Linear
Autoregressive Model for Real Exchange Rates: Empirical Evidence from Asian
Economies. Applied Economics 35 (12): 1387-1392.
Lim, K.P., M. Hinich, and V.K.S. Liew (2003). Episodic Non-Linearity and NonStationarity in ASEAN Exchange Rates Returns Series. Labuan Bulletin of
International Business & Finance 1 (2): 79-93.
McLeod, A. I., and W. K. Li (1983). Diagnostic Checking ARMA Time Series Models
using Squared-Residual Autocorrelations. Journal of Time Series Analysis 4 (4): 269273.
Patterson, D.M. and Ashley, R.A. (2000) A Nonlinear Time Series Workshop: A Toolkit
for Detecting and Identifying Nonlinear Serial Dependence. Boston: Kluwer
Academic Publishers.
Panagiotidis, T., and G. Pelloni (2003). Testing for Non-Linearity in Labour Markets:
The Case of Germany and the UK. Journal of Policy Modeling 25 (3): 275-286.
Panagiotidis, T. (2002). Testing the Assumption of Linearity. Economics Bulletin 3 (29):
1-9.
Panagiotidis, T. (2005). Market Capitalization and Efficiency. Does It Matter? Evidence
from the Athens Stock Exchange. Applied Financial Economics 15 (10): 707-713.
Potter, S.M. (1999). Nonlinear Time Series Modeling: An Introduction. Journal of
Economic Surveys 13 (5): 505-528.
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Tombazos, C. G. (2003). New light on the ‘impressionistic view’ of the balancing item in
Australia’s balance of payments accounts. Applied Economics 35 (12): 1369-1378.
Tang, T. C. (2005). Does Exchange Rate Volatility Matter for the Balancing Item of
Balance of Payments Accounts in Japan? An Empirical Note. RISEC, International
Review of Economics and Business 52 (4): 581-590.
Tang, T. C. (2006a). The Influences of Economic Openness on Japan’s Balancing Item:
An Empirical Note. Applied Economics Letters 13 (1): 7-10.
Tang, T. C. (2006b). Japan’s Balancing Item: Do Timing Errors Matter? Applied
Economics Letters 13 (2): 81-87.
Tsay, R. S.(1986). Nonlinearity Tests for Time Series. Biometrika 73 (2): 461-466.
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Appendix 1. Plot of Balancing Item of Balance of Payments Accounts for 20 Industrial Countries
US (in US billion)
Canada (in US million)
80
Australia (in US million)
8000
6000
40
Japan (in US billion)
800
2000
10
0
2000
0
-40
1000
-400
-2000
0
-1000
-10
-1200
-6000
-120
-8000
60
65
70
75
80
85
90
95
00
05
65
Denmark (in US million)
70
75
80
85
90
95
00
05
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
-1000
-1000
-2000
-2000
-3000
-3000
70
75
80
85
90
95
60
65
00
05
80
85
90
95
00
05
-3000
60
65
France (in US million)
70
75
80
85
90
95
00
05
0
90
95
00
05
90
95
00
05
0
0
-400
00
05
00
05
00
05
-800
-20
-20
85
85
400
10
-1200
-30
80
80
800
-10
-10
75
75
30
10
70
70
Greece (in US million)
20
65
65
1200
40
60
60
Germany (in US billion)
50
-40
60
65
Ireland (in US million)
0
75
20
Iceland (in US million)
400
70
30
-4000
65
-20
Finland (in US million)
5000
60
-2000
-1600
60
6000
0
-800
-4000
-80
3000
400
4000
0
Austria (in US million)
20
70
75
80
85
90
95
00
05
-1600
60
Italy (in US million)
65
70
75
80
85
90
95
00
05
60
65
Netherlands (in US million)
6000
8000
12000
4000
4000
8000
2000
0
4000
70
75
80
85
90
95
Norway (in US million)
2000
1000
0
-1000
-400
0
-4000
0
-2000
-8000
-4000
-4000
-12000
-8000
-2000
-800
-3000
-4000
-1200
-1600
-6000
60
65
70
75
80
85
90
95
00
05
-16000
60
65
Portugal (in US million)
70
75
80
85
90
95
00
05
65
Spain (in US million)
3000
2000
-5000
-12000
60
70
75
80
85
90
95
00
05
-6000
60
65
70
Sweden (in US million)
2000
8000
1000
4000
75
80
85
90
95
00
05
UK (in US billion)
0
-1000
-4000
65
70
75
80
85
90
95
New Zealand (in US million)
30
3000
20
2000
10
1000
0
60
1000
0
0
0
-10
-1000
-1000
-20
-2000
-2000
-8000
-3000
-12000
-2000
-30
-3000
60
65
70
75
80
85
90
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95
00
05
60
65
70
75
80
85
90
95
00
05
-40
60
65
70
75
80
85
11
90
95
00
05
-3000
60
65
70
75
80
85
90
95
00
05
60
65
70
75
80
85
90
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Appendix 2. Summary of non-linearity tests on balancing item –bootstrapped p-values
Country:
Test:
McLeod-Li test
Using up to lag 4
Using up to lag 8
Using up to lag 12
Using up to lag 20
Using up to lag 24
Bicovariance test
Using up to lag [.]
Engle test
Using up to lag 1
Using up to lag 2
Using up to lag 3
Using up to lag 4
Using up to lag 8
Using up to lag 10
Tsay test
Continues…
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Austria
Australia
Canada
Denmark
Finland
France
Greece
Iceland
Ireland
Italy
0.000
0.002
0.013
0.006
0.015
0.000
0.000
0.000
0.000
0.000
0.007
0.004
0.013
0.016
0.013
0.580
0.735
0.662
0.883
0.786
0.795
0.384
0.246
0.374
0.242
0.009
0.018
0.002
0.007
0.015
0.001
0.001
0.000
0.003
0.011
0.028
0.058
0.103
0.082
0.095
0.028
0.069
0.211
0.182
0.275
0.448
0.840
0.836
0.941
0.950
0.042 [7]
0.001 [8]
0.025 [8]
0.179 [6]
0.274 [6]
0.004 [6]
0.123 [6]
0.007 [6]
0.000
[6]
0.003
[7]
0.000
0.000
0.001
0.002
0.020
0.032
0.093
0.002
0.000
0.000
0.001
0.001
0.003
0.332
0.506
0.013
0.029
0.026
0.032
0.046
0.032
0.792
0.369
0.559
0.696
0.694
0.828
0.077
0.847
0.662
0.843
0.927
0.683
0.719
0.592
0.006
0.009
0.014
0.011
0.040
0.015
0.048
0.000
0.001
0.001
0.001
0.001
0.000
0.190
0.672
0.020
0.033
0.046
0.079
0.115
0.000
0.309
0.075
0.159
0.028
0.071
0.152
0.030
0.706
0.675
0.523
0.521
0.894
0.959
0.002
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Country:
Test:
McLeod-Li test
Using up to lag 4
Using up to lag 8
Using up to lag 12
Using up to lag 20
Using up to lag 24
Bicovariance test
Using up to lag [.]
Engle test
Using up to lag 1
Using up to lag 2
Using up to lag 3
Using up to lag 4
Using up to lag 8
Using up to lag 10
Tsay test
Continues…
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ISBN : 978-0-9742114-7-3
Germany
Japan
Netherlands
Norway
New
Zealand
Portugal
Spain
Sweden
the UK
the US
0.000
0.000
0.000
0.000
0.000
0.332
0.000
0.001
0.000
0.001
0.933
0.922
0.656
0.690
0.637
0.849
0.570
0.647
0.304
0.256
0.005
0.010
0.022
0.121
0.209
0.014
0.068
0.208
0.505
0.535
0.360
0.798
0.908
0.751
0.734
0.613
0.465
0.661
0.794
0.887
0.000
0.001
0.001
0.005
0.005
0.000
0.000
0.000
0.000
0.000
0.000 [7]
0.063 [6]
0.538 [7]
0.984 [6]
0.004 [6]
0.049 [6]
0.086 [6]
0.007 [6]
0.003 [7]
0.013 [7]
0.005
0.007
0.010
0.011
0.030
0.036
0.000
0.585
0.850
0.481
0.622
0.003
0.010
0.753
0.883
0.980
0.999
0.975
0.968
0.676
0.527
0.280
0.535
0.709
0.861
0.650
0.766
0.941
0.060
0.011
0.030
0.046
0.074
0.056
0.093
0.004
0.016
0.031
0.054
0.140
0.246
0.014
0.221
0.230
0.179
0.280
0.670
0.769
0.015
0.871
0.607
0.799
0.747
0.708
0.733
0.034
0.016
0.000
0.000
0.001
0.005
0.008
0.000
0.104
0.058
0.001
0.001
0.004
0.006
0.035
13
2007 Oxford Business & Economics Conference
BDS test
Dimension
2
3
4
Dimension
2
3
4
Dimension
2
3
4
Dimension
2
3
4
Dimension
2
3
4
Dimension
2
3
4
Dimension
2
3
4
June 24-26, 2007
Oxford University, UK
Austria
EPS=0.5
0.000
0.000
0.000
Denmark
EPS=0.5
0.067
0.005
0.003
Greece
EPS=0.5
0.001
0.000
0.000
Italy
EPS=0.5
0.010
0.002
0.001
Netherlands
EPS=0.5
0.147
0.004
0.010
Portugal
EPS=0.5
0.441
0.040
0.012
the UK
EPS=0.5
0.000
0.000
0.000
ISBN : 978-0-9742114-7-3
EPS= 1.0
0.000
0.000
0.000
EPS= 2.0
0.005
0.001
0.001
EPS= 1.0
0.158
0.032
0.008
EPS= 2.0
0.421
0.119
0.086
EPS= 1.0
0.002
0.000
0.000
EPS= 2.0
0.000
0.000
0.000
EPS= 1.0
0.194
0.054
0.010
EPS= 2.0
0.670
0.575
0.264
EPS= 1.0
0.519
0.174
0.127
EPS= 2.0
0.397
0.332
0.319
EPS= 1.0
0.114
0.005
0.001
EPS= 2.0
0.021
0.060
0.083
EPS= 1.0
0.000
0.000
0.000
EPS= 2.0
0.058
0.021
0.008
Australia
EPS=0.5
0.000
0.000
0.000
Finland
EPS=0.5
0.158
0.013
0.001
Iceland
EPS=0.5
0.002
0.000
0.000
Germany
EPS=0.5
0.000
0.000
0.000
Norway
EPS=0.5
0.230
0.089
0.048
Spain
EPS=0.5
0.968
0.616
0.056
the US
EPS=0.5
0.000
0.000
0.000
EPS= 1.0
0.000
0.000
0.000
EPS= 2.0
0.004
0.000
0.000
EPS= 1.0
0.408
0.102
0.033
EPS= 2.0
0.235
0.250
0.283
EPS= 1.0
0.003
0.000
0.000
EPS= 2.0
0.212
0.041
0.024
EPS= 1.0
0.000
0.000
0.000
EPS= 2.0
0.001
0.000
0.000
EPS= 1.0
0.590
0.378
0.203
EPS= 2.0
0.791
0.634
0.580
EPS= 1.0
0.942
0.762
0.606
EPS= 2.0
0.329
0.202
0.107
EPS= 1.0
0.000
0.000
0.000
EPS= 2.0
0.076
0.016
0.000
14
Canada
EPS=0.5
0.904
0.137
0.040
France
EPS=0.5
0.000
0.000
0.000
Ireland
EPS=0.5
0.290
0.123
0.094
Japan
EPS=0.5
0.000
0.000
0.000
New Zealand
EPS=0.5
0.017
0.006
0.013
Sweden
EPS=0.5
0.306
0.028
0.016
EPS =1.0
0.659
0.075
0.023
EPS = 2.0
0.642
0.271
0.207
EPS =1.0
0.000
0.000
0.000
EPS = 2.0
0.031
0.031
0.039
EPS =1.0
0.284
0.105
0.034
EPS = 2.0
0.038
0.018
0.024
EPS =1.0
0.017
0.006
0.000
EPS = 2.0
0.268
0.289
0.264
EPS =1.0
0.003
0.000
0.000
EPS = 2.0
0.033
0.003
0.004
EPS =1.0
0.683
0.373
0.199
EPS = 2.0
0.128
0.120
0.161
2007 Oxford Business & Economics Conference
ISBN : 978-0-9742114-7-3
Table 1: Summary statistics on balancing item for 20 industrial countries (millions of U.S.
dollars)
the US
2873.3
3500
63660
-80530
21569.9
-0.3
5.6
37.9
0.0
373530
130
France
Mean
0.3
Median
0.2
Maximum
20.5
Minimum
-19.6
Std. Dev.
4.7
Skewness
0.1
Kurtosis
9.1
Jarque-Bera
188.4
Probability
0.0
Sum
36.4
Observations
122
Norway
Mean
-620.5
Median
-306.0
Maximum
1633.0
Minimum
-5634.0
Std. Dev.
1203.8
Skewness
-1.7
Kurtosis
7.2
Jarque-Bera
138.4
Probability
0.0
Sum
-70740
Observations
114
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Observations
June 24-26, 2007
Oxford University, UK
Canada
-218.0
-56.0
6932.0
-6658.0
2173.7
0.0
5.2
40.6
0.0
-42508.0
195
Germany
896.5
280
40180
-39230
9005.7
0.3
9.4
236.0
0.0
124620
139
Portugal
10.9
33.0
2425.0
-2009.0
656.5
-0.1
5.7
36.5
0.0
1343.0
123
Australia
7.6
31.5
758.0
-1212.0
331.1
-0.7
4.4
32.1
0.0
1393.0
184
Greece
-33.2
-33.0
1130.0
-1472.0
366.3
-0.4
5.7
36.3
0.0
-3717.0
112
Spain
-314.2
-316.0
1729.0
-2698.0
749.9
-0.2
4.5
12.1
0.0
-38642.0
123
15
Japan
-119.8
0.0
16230
-18880
6156.5
0.0
3.9
3.8
0.15
-13540
113
Iceland
-24.9
-7.0
262.0
-1413.0
150.1
-7.0
64.6
19457.7
0.0
-2918.0
117
Sweden
-353.6
-185.0
6542.0
-7894.0
2186.1
-0.1
5.2
25.2
0.0
-42789
121
Austria
83.7
52.5
2682.0
-2055.0
687.7
0.5
6.3
68.0
0.0
11882.0
142
Ireland
-27.2
23.5
5283.0
-4468.0
1400.3
0.1
6.9
62.4
0.0
-2664.0
98
the UK
1078.4
320
24930
-29670
7051.9
0.1
7.2
105.5
0.0
153130
142
Denmark
Finland
10.6
-22.4
-84.0
-11.5
5174.0
4429.0
-2826.0
-3385.0
1085.3
1062.4
1.0
0.7
7.7
8.0
102.4
138.0
0.0
0.0
1021.0
-2728.0
96
122
Italy
Netherlands
-976.8
-463.2
-303.5
-23.0
5850.0
10814.0
-15473.0
-10281.0
2953.9
2774.1
-1.8
-0.1
7.9
6.4
217.6
73.9
0.0
0.0
-138706.0
-71334.0
142
154
New Zealand
-10.3
0.0
2258.0
-2372.0
734.8
-0.4
4.6
13.3
0.0
-1039.0
101