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Intertemporal relationships between industrialized economies
European Economic Review 28 (1985) 363-376. North-Holland
INTERTEMPORAL RELATIONSHIPS BETWEEN INDUSTRIALIZED ECONOMIES William L. HUTH* Northeast Louisiana Unioersity, Monroe, LA 71209, USA Received October 1984, final version received April 1985 This paper describes a multivariate time series analysis of the intertemporal relations between industrial production in seven different western economies. A major thrust of the study was an attempt to provide a time series validation of the results from the Project LINK global econometric model. The analysis was also used as a further examination of empirical support for the existence of an international business cycle.
1. Introduction
The pl~ititudinous remark, 'when the United States economy sniffles the remainder of the western world sneezes (or worse)', is well known to economists and laypersons alike and is primarily due to the U.S.'s perceived dominant international stance with respect to its trading partners. The fact that interconnections between economies exist is obvious. Bergsten has stated the 'interdependence is now a cold reality' and modern international texts include treatments (albeit somewhat limited) of the interdependence phenomenon, see, for example, Dornbusch (1980) and Ethier (1983). The linkage between economies has received explicit treatment in the literature, mainly under the auspices of Project LINK and other attempts at world model building. See Hickman (1983) for a survey of the more recent work. Project LINK, which includes 25 different national econometric models and contains some 6,000 variables, achieves linkage, for the most part, through current account trade flows. Thus, the international transmission mechanism for economic perturbations resides in changing import demand and export prices of the perturbed economy. The linkage is made operational by the development of a trade share matrix whose elements are determined by the proportion of a particular nation pair's exports to a single nation's total imports. The international interdependence between nations is then deduced by simulating the linked national econometric models given policy *The author would like to thank an anonymous referee of this journal for pertinent comments. 0014-2921/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)
364
W.L. Huth, lntertemporal relationships between industrialized economies
scenarios for a particular country and estimating lag structures and multipliers, see Klein et al. (1979) and Filatov et al. (1983). Criticism of the LINK system has been directed at the dearth of validation oriented studies of the simulation results and the lack of explicit specifications about the nature and direction of the interrelationships between the national economies. In addition, the system fails to develop alternate transmission mechanisms, especially those involving the dynamics of capital account items. This last point is particularly pertinent in the light of some of the recent work concerning the international flow of capital and the resulting ramifications on the insulatory effect of flexible exchange rates. International interdependence has also been examined by Barren and d'A1 Cantara (1976) and Swoboda (1983). Barten and d'A1 Cantara develop a linked econometric model involving the European Economic Community (EEC) and, based on experiments with the linked model, conclude '... considerable interdependency between the various national economies'. In discussing the purpose of their model they invoke the 'reverse' scientific method where data relationships are used to search fdr more fundamental economic relations. The authors state that the purpose of their model is to '...provide empirical basis for theoretical hypotheses in order to make meaningful projections'. The Swoboda paper looks at the interdependency effect due to alternative exchange rate regimes by examining the variability of simple correlations between variables computed for different subsamples of data. The subperiod delineation was based upon the switch from the Bretton Woods fixed rate system to the current flexible rate system. Swoboda concludes '... there does appear to be "real" interdependence under flexible, as well as under fixed, exchange rates'. In addition it was noted that the degree of association between the variables was, apparently, enhanced as a result of the regime switch. This result provides additional support for the hypothesis that insulation under flexible rates has a low 'R' factor. That is, the a priori theoretical deduction that flexible exchange rates lead to a reduction in the perturbation transmission and incremental improvements in the degree of policy autonomy lacks empirical support, perhaps due to alterations in the transmission channel. Based on his correlation analysis, a principal component study of inflation rates and output growth for several nations, the apparent increment in interdependence, and an unpublished study by Huber and Saidi (1982), Swoboda gleans support for the hypothesis that a world business cycle with superimposed national cycles exists. He states (p. 98) '... the close interdependence in business cycles that was witnessed jn the 1970s may well find its origin in a world business cycle in a closely integrated international economy rather than in the transmission of disturbances from one country, or group of countries, to the rest of the world.'
W.L. Huth, lntertemporal relationships between industrialized economies
365
This last statement is given some support by the Project LINK simulation results in Filatov et al. (1983) where significant international stability was observed even given simultaneous shocks, The previous work cited has certainly moved the concept of international interdependence from the umbra of heresy into, at least, the penumbra of circumstance. The purpose of this study is to continue that movement (hopefully in the correct direction) by examining the nature and direction of international linkages in a time series framework. In particular, empirical answers are sought to several questions. First, does the U.S. economy serve as an indicator of change in other western economies, that is, is the direction of influence from the U.S. to other industrialized nations? Second, do some countries mitigate or exacerbate the cyclical fluctuations of other countries, in other words, are economic expansions or slowdowns 'catching'? This last question comes to grips with the hypothesis of an international business cycle as mentioned above. Another objective of this work is an attempt at providing a time series validation of the econometric simulation results from Project LINK. To that end, the results of the time series analysis are compared with those of a recent Project LINK report. An outline of the time series methodology is discussed in the next section and the following section describes the country set, corresponding data, and the empirical results of the time series analysis. The concluding section summarizes the results obtained herein.
2. Time series methodology The method used to assess the relations between the economies considered below is an accumulation of efforts by Box and Jenkins (1970), Sims (1972), Haugh (1976), Haugh and Box (1977), Granger and Newbold (1977a, b), Pierce and Haugh (1977), Granger (1980), and Geweke (1982). Two time series, Yt and X , t = 1..... T, both realizations from a stochastic process and represented by integrated autoregressive moving average models of the form c~y(B)(1 -- B) d Yt = Oy(B)a,,
(1)
q~x(B)(1 - B)nXt = Ox(B)bt,
(2)
and
where ~b(B) and O(B) are parameter polynomials in the backshift operator B of order p and q, respectively. The term ( 1 - B ) a indicates that d differences of each process realization are required to produce time invariant (stationarity in both the mean and variance) series. The at and bt are i.i.d. N(0, tr2), white noise, residuals. Given identification (specification of p, d, and q), estimation,
366
W.L. Huth, lntertemporal relationships between industrialized economies
and a residual diagnostic check of eqs. (1) and (2); that is, the estimation of the true whitening filters, the residual series at and bt will contain the interrelationships between the original series. The prewhitening process described above results in joint covariance stationary innovations of the basic data. The series are innovations in that the within variable relationships have been removed through the prewhitening process while preserving the fundamental variable relations, see Pierce and Haugh (1977). Rather than throwing the baby out with the bathwater, the filter simply removes the bathwater. The interinnovation relationship can be examined by computing the correlation between the innovations at various time lags. These crosscorrelations are given by
rob(k)=
cov(a, b,+k)
SaS~
,
k = 0, _+1, __+2.... ,
(3)
where raa(k) represents an estimate of the bidirectional correlation between the two innovation series, at and bt, at lag k. The numerator in eq. (3) is the covariance between the two series and the denominator is the product of the innovation standard deviations. It has been shown, Haugh (1976), that the asymptotic distribution of the rob(k), under the assumption of serial independence, is chi-square. Thus, the presence of a temporal relation can be determined by examining the statistic J
SI=T ~
rob(k)2
(4)
k= - j
in relation to a critical chi-square value with 2j + 1 degrees of freedom with the variance of the tab(k) given by 1/T. Unfortunately, the test just described can only show support or lack thereof for the existence of a temporal relation, not its direction. It is possible, however, to subjectively assess the direction of the temporal relation between innovations by using the information contained in the cross-correlation behavior. Given 'one-sided' crosscorrelations, r(0)=0, r(k)#0 for some k > 0 and r(k)=0 for k < 0 (or the reverse), support for a succession relation is present. In both situations, the fact that r(0)=0 implies that the temporal relation is 'pure' in that no contemporaneous relation is present. Given that r(0)#0 then the possibility of a contemporaneous relation, perhaps combined with other relations, is suggested. An additional difficulty with the statistical test is its low power and bias toward accepting the independence hypothesis, Pierce (1977), Sims (1977), and Pierce and Haugh (1977). This independence bias explains Pierce's conclusion of widespread independence between theoretically connected economic variables. Given a bias towards an independence detection,
W.L. Huth, lntertemporal relationships between industrialized economies
367
some protection is provided against a type I statistical error in that the type II error is more likely. Thus, when the Haugh test results in the rejection of the independence hypothesis, credence is established for the dependence relation. On a more firm statistical footing, corroborating evidence for a directional relation can be found by using the estimated cross-correlations to identify and fit either a dynamic regression model, Haugh and Box (1977), or a bivariate transfer function model, Granger (1980). With either method, the end result is the detection of the presence or absence of a directional relation on the basis of the incremental predictive performance due to the bivariate model as compared with a univariate prediction. Given an enhancement in predictive precision as measured by the reduction in mean square error or other summary statistics, the directional relation can be inferred. It should be noted that Geweke (1982) has demonstrated that linear dependence between time series can be decomposed into bidirectional (first series to second and vice versa) and instantaneous linear feedback.
3. Empirical presentation Eight western, industrial economies are considered: the United States, OECD Europe, the United Kingdom, Canada, the Federal Republic of Germany, France, Italy, and Japan. In each case, the countries' index of industrial production is used as the representative measure of economic activity. This choice was based on data availability (historical data is available on the BEA BCD data tape) and the fact that the U.S. index has been classified as a coincider with NBER reference cycles. It is assumed, without empirical support, that the indices for the other countries also coincide with that countries' business cycle. Although unsubstantiated, the assumption seems reasonable. Each index of industrial production measures change in real value added as a result of industrial activity (manufacturing, mining, etc.). Consistent data were available for each economy over the twelve-year span from January 1970 to December 1981. As a result, a total of 144 observations ( T = 144) comprised the process realizations from which the analysis below was carried out. Initially, each of the eight industrial production series was appropriately differenced and autocorrelations and partial autocorrelations were computed to facilitate the order identification of the polynomials in B, p, and q, in eqs. (2) and (3). Each identified filter was then estimated, using a non-linear least squares algorithm, and diagnostically checked for an appropriate residual distribution. The estimation results for each of the eight filters are shown in table 1 and were used to generate, through an ex post simulation, the innovation series, a~,, and bi, t, i = 1,..., 8 and t = 1..... 144. Given the eight innovation series there were 28 possible cross-correlations
368
W.L. Huth, Intertemporal relationships between industrialized economies
Table 1 Filter estimation results. ARIMA u.s. Europe U.K. Canada F.R.G. France Italy Japan
(p,d,q)
MSE
1, 1,0 1, 1, 0 1, 1, 0 1,1,1 0, 1, 1 1, 1, 0 0, 1, 1 1,2,1
1.033 3.027 5.400 3.221 5.278 7.590 3.000 7.650
~
IZl
0.712 11.76 -0.178 2.16 0.180 2.19 -0.753 2.30 ----0.336 4.25 ---0.333 3.62
0 ---0.666 -0.271 -0.390 -0.764
Izl ---1.80 3.34 -4.96 12.10
between the paired time series. The O E C D Europe industrial production measure includes some of the indexes for other nations considered above. Specifically, O E C D Europe includes the indexes for the U.K., the F.R.G., France, and Italy as well as other European nations. Because of the obvious contemporaneous relation problem, the correlations between O E C D Europe and each of the included series were excluded from the study, leaving 24 cross-correlations for inspection. The rab(k) were computed using eq. (3) for k = 0 , + l , + 2 . . . . . +_10. The resulting cross-correlations for specific country pairs are presented and discussed next. In the tables shown in this section, the correlations are initially compared with confidence bounds computed using l I T as the variance of the estimated coefficient. Approximate 95 percent test bounds are _ 0.17 for the innovation series considered here. Cross-correlations within the bounds are not statistically different from zero whereas those outside the limits are statistically significant. The cross-correlation behavior is then used to infer the temporal interinnovation relations, given, of course, the caveats noted above. Table 2 contains the cross-correlation between the U.S. production measure and each of the seven remaining countries. U p o n inspection, it appears that the overall relation between the U.S. and each of the seven other economies is negligible, as evidenced by the computed H a u g h test statistic, S, shown in table 3. The critical chi-square value with 21 degrees of freedom and a 0.05 level of significance is 32.7. As can be observed, the independence hypothesis is accepted for all relations, except the connection between the U.S. and the Canadian economies, where S=38.9. Individual inspection of these cross-correlations shows a contemporaneous temporal relation combined with a succession relation from the U.S. to C a n a d a after a two-period (month) delay, T h a t is, the correlation r ( + 3)=0.19 indicates that a full two-period delay occurs between the impulse and the response in the third period. Additionally, the relation between the U.S. and J a p a n is significant at the 0.10 level. This relation is a purely successive one in that
Table 2 Cross-correlations. United States with k
0
1
2
3
4
5
6
7
8
9
10
Europe + -
0.19
-0.08 -0.07
0.13 0.12
0,01 -0,01
0.20 -0.09
0.08 0.01
0.12 -0.10
0.04 -0.06
0.00 -0.05
0,02 0,00
-0.02 -0.01
0.12
-0.02 --0.01
0.00 -0.02
-0,03 0.17
0.11 -0.17
0.11 0.00
0.12 -0.11
0.07 -0.08
0.11 -0.11
0.03 0.13
-0.03 0.06
0.11 -0.03
0.12 0.10
0.19 -0.01
-0.03 0.05
0.01 0.00
0.14 -0.05
0.03 -0.09
0.02 0.05
0.12 -0.16
0.01 0.00
0.14 -0.11
0.14 0.01
0.06 0.11
0.08 -0.08
0.07 -0.07
0.16 0.05
0.06 -0.09
" 0.06 -0.08
0.00 0.12
-0.04 -0.10
0.16
0.09 0.05
0.08 0.12
0.01 0.00
0.06 -0.07
0.04 -0.10
0.08 -0.10
0.12 0.09
0.03 -0.11
0.07 -0.10
0.04 -0.02
0.04
0.01 0.05
0.09 -0.04
0.05 -0.06
0.21 0.05
-0.02 -0.03
0.00 -0.12
-0.03 -0.06
0.05 -0.08
-0.01 0.03
-0.03 0.11
0.17 0.09
0.20 -0.11
0.09 -0.09
-0.02 0.06
-0.06 -0.07
-0.12 0.10
-0.10 0.13
-0.04 0.05
U.K. +
Canada + -
0.35
F.R.G. +
0.17
-
France + -
Italy +
Japan +
0.05
0.00 -0.08 0.16 -0.01
Table 3 Haugh test statistics,a Dependent (0.01 level)
S
'Dependent' (0.25 to 0.10)
S
1. 2. 3. 4. 5. 6. 7. 8. 9.
38.9 39.1 53.9 57.3 59.7 48.3 82.8 79.9 41.3
1. U.S. 2. U.S. 3. U.K.
26.0 27.7 27.4
U,S. F.R.G. F.R.G. F.R.G. F.R.G. Japan Japan Japan Europe
Canada Canada France Italy Japan France Italy Europe Canada
Dependent (0.10 to 0.01) 1.
U.S.
2. 3. 4.
F.R.G. Canada France
Japan U.K. France Italy
S 30.1 31.5 32.8 32.0
U.K. F.R.G. Canada
Independent (0.25 or less)
S
1. 2. 3. 4. 5. 6, 7. 8.
24.0 21.3 15.1 20.2 13.5 19.4 20.8 20.2
U.S. U.S. U.S. U.K. U.K. U.K. Canada Canada
Europe France Italy France Italy Japan Italy Japan
W.L. Huth, Intertemporal relationships between industrialized economies
370
the contemporaneous correlation between the two innovations is statistically insignificant Jr(0)=0], the relation direction appears to be from the U.S. to Japan with a full three-period delay. Thus, given a current impulse in U.S. industrial production there is a Japanese production response four periods later. The other intercountry relations do contain some statistically significant correlations, however, in aggregate there is an apparent independence relation. Given the test's independence bias, the relationship between the U.S. and both the U.K. and the F.R.G. are marginally insignificant (S values of 26.0 and 27.7, respectively). The directional implications associated with the U.S./U.K. relation are interesting. It appears that a purely successive relation from the U.K. to the U.S. exists. The relation between the U.S. and the F.R.G. is, at best, contemporaneous and then only marginally so, The cross-correlation for the West German innovation series and the U.K., Canadian, French, Italian, and Japanese production innovations are shown in table 4. The Haugh test statistics for the correlations are again displayed in table 3. It is obvious that the German economy has strong connections with a number of other economies. The independence hypothesis is rejected at the 0.01 level for the relationship between Germany and Canada, France, Italy, and Japan, and at the 0.05 level for the German/U.K. relation. The F.R.G. and Canada exhibit a pure succession relation from Germany to Table 4 Cross-correlations. Federal Republic of k
•
Germanywith
0
1
2
3
4
5
0.23
0.11 0.00
0.03 0.06
0.11 0.09
0.04 0.02
0.07 -0.03
0.07 0.27
0.16 0.08
0.06 0.22
0.05 --0.04
0.23
0.16 --0.06
0.13 0.17
0.22 0.25
0.21
-0.09 0.09
0.26 -0.07
-0.16 0.08
0.15 -0.02
6
7
8
9
I0
-0.16 0.18
0.03 0.11
0.07 0.16
0.00 -0.12
0.00 -0.07
0.10 0.11
0.14 --0.13
0.11 0.00
0.01 0.00
-0.15 0.08
-0.02 --0.08
0.02 0.01
0.11 --0.12
-0.03 0.17
0.01 0.13
0.17 --0.08
0.07 --0.03
-0.12 --0.07
-0.04 0.19
0.11 0.17
0.22 0.01
-0.19 --0.06
0.15 -0.05
0.11 -0.04
0.10 -0.19
--0.09 0.11
-0.02 0.11
-0.16 0.11
0.04 0.12
-0.20 0.03
-0.10 0.10
0.11 0.16
-0.03 0.16
-0.20 -0.02
U.K,
+ -
Canada + --
0.03
France + --
Italy + -
Japan + -
0.36
Vv'.L. Huth, lntertemporal relationships between industrialized economies
371
Canada after a one-period delay. In the other cases, there are both synchronicity (feedback) and contemporaneous temporal relations. The connection between F.R.G. and Japan is particularly interesting in that the successive part of the combined contemporaneous succession relation indicates an inverse relation between the two economies. An increment in German industrial production is positively correlated with the current level of Japanese production and negatively related to Japanese production after a five-period delay, perhaps due to a substitution relation between the commodity components of the industrial production indexes. This last point is certainly worth further study. Table 5 contains the interconnections between the U.K. and Canada, France, Italy and Japan, and between Canada and France, Italy, and Japan. The correlation behavior between Japan and Italy, France, and Europe, between France and Italy, and between Europe and Canada is displayed in table 6. For the most part, the independence hypothesis is accepted, as can 5
Table Cross-correlations.
k
0
1
2
3
4
5
6
7
8
9
10
U.K. with Canada + -
0.07
0.08 -0.10
-0.03 0.12
0.20 0.12
-0.07 0.03
0.14 0.21
-0.01 0.05
-0.09 -0.02
0.02 0.14
-0.05 0.01
0.04 0.03
0.12 0.08
0.11 0.13
0.04 0.14
0.02 0.02
-0.05 0.06
-0.07 0.05
0.09 -0.05
0.00 -0.08
-0.03 0.09
-0.01 -0.02
-0.05 0.09
0.03 0.09
0.12 0.00
-0.07 -0.11
0.13 0.01
0.02 0.08
0.02 -0.02
0.04 -0.03
0.02 -0.01
0.13 0.01
-0.02 0.13
0.03 0.04
-0.16 0.07
-0.10 0.01
0.11 0.07
-0.06 0.15
-0.07 0.01
0.03 0.20
0.12 0.05
0.14 0.09
0.08 0.01
0.11 -0.03
0.07 0.10
0.07 0.04
0.03 -0.07
0.00 0.03
0.00 0.02
0.00 0.07
0.18 0.01
-0.10 0.07
0.09 0.02
0.12 -- 0.01
0.13 --0.05
-0.04 - 0.09
-0.02 --0.09
-0.10 O.12
-0.03 0.00
0.06 0.00
-0.18 0.14
-0.06 - 0.03
0.09 0.08
-0.07 0.08
-0.07 0.04
-0.08 0.04
U.K. with France +
0.07
-
0.17 0.01
U.K. with Italy +
0.11
-
0.01 0.06
U.K. with Japan + -
0.05
-0.08 0.01
Canada with France + -
0.29
0.09 -0.03
Canada with Italy + --
0.13
0.12 0.07
Canada with Japan + -
0.02
0.09 0.08
W.L. Huth, Intertemporal relationships between industrialized economies
372
Table 6 Cross-correlations. k
0
1
2
3
-0.18 0.20
0.21 -0.02
0.06 0.16
4
5
6
7
8
9
10
0.14 0.06
-0.22 0.25
-0.19 -0.21
-0.05 0.03
-0.08 0.07
-0.12 0.21
-0.13 0.00
0.00 0.14
-0.10 0.16
-0.14 0.25
0.00 0.18
-0.06 0.03
-0.15 0.23
-0.07 0.11
-0.12 0.01
-0.05 0.12
0.14 0.06
-0.14 0.08
-0.15 0.28
-0.22 -0.12
-0.01 0.11
-0.07 0.21
-0.06 0.21
-0.24 -0.01
0.24 0.03
0.16 0.08
0.04 0.03
-0.06 0.03
-0.01 0.I0
0.20 -0.03
0.02 -0.02
-0.01 0.03
-0.11 -0.05
0.17 0.07
0.16 0.11
-0.01 0.15
0.15 0.08
-0.03 0.13
-0.08 0.11
0.06 0.18
-0.01 -0.14
-0.05 -0.01
Italy with Japan + -
0.36
-0.I1 -0.07
France with Japan + -
0.11
-0.07 -0.07
Europe with Japan +
0.38
-
-0.14 0.00
France with Italy +
0.07
-
-0.06 0.22
Europe with Canada + -
0.24
0.12 0.03
be observed from the estimated test statistics presented in table 3. Notable exceptions are the relationships between Japan and France, Italy, and OECD Europe and those between France and Italy and Canada and Europe. There are pure succession connections between Canada and Italy and Japan and France with the direction from the former to the latter in each case. The remaining dependence relations involve, for the most part, combined feedback and contemporaneous interconnections.
4. Comparison of the time series results with Project LINK Estimated international income elasticity multipliers from a seven-year simulation (1979-1985) of the linked national econometric models are given in Filatov et al. (1983). The mean multiplier value for the seven-year simulation of the countries considered herein were computed from their table and are shown here in table 7. In each case, the elasticity multiplier represents the mean percentage change in real income for the column country that was induced from a unit percent shock in the row country. The real demand shock was a sustained exogenous increase of government expenditures in the row country over the horizon of the simulation experiment. The main diagonal of the table shows each country's own multiplier
I¥.L. Huth, lntertemporal relationships between industrialized economies
373
Table 7 International elasticity multipliers for real income.
U.S. U.K. Canada F.R.G. France Italy Japan
U.S.
U.K.
Canada
F.R.G.
France
Italy
Japan
2.54 0.05 0.04 0.12 0.04 0.05 0.02
0.15 1.10 0.01 0.15 0.05 0.06 0.03
0.77 0.08 1.41 0.11 0.04 0.05 0.03
0.41 0.19 0.03 2.12 0.19 0.23 0.06
0.09 0.05 0.01 0.15 1.08 0.07 0.02
0.31 0.14 0.02 0.45 0.14 1.95 0.04
0.27 0.06 0.01 0.15 0.05 0.06 1.22
while the upper and lower triangles can be used to examine the directional nature of the multiplier effect. The first row and column of the table show, respectively, the effect of a U.S. shock on the rest of the countries and shocks from the other countries on the United States. As an example, the mean impact of a one percent increment in U.S. government spending on Canadian real income is 0.77 percent while the reverse (a one percent change in Canadian government expenditures) scenario results in a 0.04 percent change in U.S. real income. Clearly, U.S. policy impacts Canadian income to a greater extent than Canadian policy impacts U.S. income. This observation from Project L I N K agrees with the time series results presented above. There was a dependence relation between U.S. and Canadian industrial activity as evidenced by the Haugh statistic. The cross-correlations shown in table 3 indicate a strong correlation between current levels of industrial production in the two countries and also show a succession relation from the U.S. to Canada after a two-period delay. The directional implication from the innovation correlation is, in most cases, consistent with the relative magnitudes of the elasticity multipliers. The mean real income elasticity multipliers between the German and Italian economies are also relatively large: 0.45 for the impact of a German shock on Italy and 0.23 for the reverse. Again, support for this relation is found in the results presented above. The independence hypothesis is rejected at the 0.01 level for the time series relation between the industrial production innovations for the two countries. In addition, the innovation correlation behavior indicates a strong contemporaneous relation coupled with feedback effects. In general, Filatov et al. (1983) noted that '...the F.R.G. is an important trading partner of most countries in the group, With especially close ties with its European neighbors'. This quality of the German economy is certainly indicated in the time series analysis above. Among the nine country pairs with test statistics indicating a dependence relation significant at the 0.01 level, four are country pairs in which the F.R.G. is included.
374
W.L. Huth, Intertemporal relationships between industrialized economies
In general, with a few exceptions, the analysis presented above provides time series corroboration for the econometric results of the Project LINK simulations. Some exceptions include the large elasticity multiplier effect of a U.S. shock on F.R.G. income when the independence hypothesis is accepted at the 0.10 level and the rampant independence between U.S. production and that of the remaining nations when the first row in table 7 indicates large multiplier effects for a U.S. shock. It should be noted that the multipliers in table 7 are weighted by the ratio of incomes in the impulse and response countries. Thus the U.S. multipliers are disproportionately large when compared to the time series cross-correlations that represent the unweighted multiplier. Given the income ratio weighting of the LINK multipliers, the U.S. independence findings are not so surprising. Another exception involves the relationships between Japan and the other nations. In the time series analysis, Japan was influential in relation to France, Italy, Europe, and, to an extent, the United States. From table 7, however, the mean elasticity multipliers for Japan were, for the most part, low. A complete study of the time series interconnection between the other countries in the LINK project, as well as consideration of measures other than the indexes of industrial production, is beyond the scope of this study but definitely worthy to be entertained.
5. Summary and conclusions This paper has examined the temporal interrelationships between economic activity in seven industrialized nations. In each ease, a country's level of economic activity was represented by the level of its industrial production. The major findings of the analysis are presented in this section. From the empirical results, it appeared that there were significant relationships between the Federal Republic of Germany and several European nations and Japan. In most eases, an industrial activity change in Germany was positively related to similar activities in the countries for which a dependence relation was uncovered. Additionally, changes in F.R.G. production are negatively related and tend to lead (a succession relation) corresponding measures for the Japanese economy. The time series results here were also consistent with both the Project LINK and Swoboda conclusion of general stability in the international environment. Thus, additional support for the existence of an international business cycle may be provided here in that a considerable degree of independence was found to exist among the productivity indexes of the various economies and few transmission channels from one country to another (succession relations) were uncovered. In conjunction with the last point, it should be mentioned that the specific country set used above was somewhat limited and .narrow in that a major sector of the international
W.L. Huth, lntertemporal relationships between industrialized economies
375
environment was not considered. Specifically, production measures for the oil producing segment of the international economy were excluded from the analysis. Further analysis of international interdependence along time series lines should incorporate O P E C production measures. This addition would, perhaps, allow for endogenous perturbations in the oil consuming economies discussed above and explain Swoboda's business cycle interdependence finding. In addition, another caveat regarding the foregoing discussion is in order due to the fact that the time series methodology does not consider the uneven diffusion of impulses among trading partners as noted by Hickman and Schleicher (1978). Finally, the study has provided some corroborating results with respect to the Project L I N K simulation results in Filatov et al. (1983). The analogue representations were compatible with regard to the influence of the Federal Republic of Germany and divergent in the cases of the U.S. and Japan. An explanation of the different findings regarding the U.S. was mentioned above and involved the consideration of alternative perturbation transmission channels, mainly U.S. financial influence. The minimal impact of Japan in the L I N K multiplier development was explained, in Filatov et al., by the failure to include trade flows between Japan and the Asian sector. Another explanation, as evidenced from the above analysis, may be that the L I N K model fails to consider alternative disturbance transmission ehannels. In addition, the simulation results were for changes in government spending which may not significantly alter Japanese economic activity given the organizational structure and size of Japanese industry.
References Barten, A. and G. d'Al Cantara, 1976, The linkage of models of the EEC countries, in: H. Glejser, ed., Quantitative studies in international economics(North-Holland, Amsterdam). Box, G. and G. Jenkins, 1970,Time series analysis (Holden-Day, San Francisco, CA). Dornbusch, R., 1980, Open economy macroeconomics(Basic Books, New York). Ethier, W., 1983, Modern international economics(Norton, New York). Feige, E. and J. Johannes, 1981, Testing the casual relationships between the domestic credit and reserve components of a country's monetary base, Journal of Macroeconomics3, 75-102. Filatov, V., B. Hickman and L. Klein, 1983, Long-term simulations with the project LINK system, 1978-1985, in: B. Hickman, ed., Global international econometric models (NorthHolland, Amsterdam). Geweke, J., 1982, Measurement of linear dependence and feedback between multiple time series, Journal of the American Statistical Association 77, 304-313. Granger, C., 1980, Testing for causality, Journal of Economic Dynamics and Control 2, 329-352. Granger, C. and P. Newbold, 1977a, Identification of two-way causal systems, in: M. Intriligator, ed., Frontiers of quantitative economics,Vol. IIIA (North-Holland, Amsterdam). Granger, C. and P. Newbold, 1977b, Forecasting economic time series (Academic Press, New York). Haugh, L., 1976, Checking the independence of two covariance-stationary time series: A univariate residual cross-correlation approach, Journal of the American Statistical Association 71, 378-385.
E.E.R.-- D
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Haugh, L. and G. Box, 1977, Identification of dynamic regression models connecting two time series, Journal of the American Statistical Association 72, 121-130. Hickman, B., ed., 1983, Global international economic models (North-Holland, Amsterdam). Hickman, B. and S. Schleicher, 1978, The interdependence of national economies and the synchronization of economic fluctuations: Evidence from the LINK project, Weltwirtschaftliches Archly 114, 642-708. Klein, L., V. Su and P. Beaumont, 1979, Coordination of international fiscal policies and exchange rate revaluations, in: J. Sawyer, ed., Modeling the international transmission mechanism (North-Holland, Amsterdam). Mixon, L., L. Pratt and M. Wallace, 1979, Cross-national money to income causality, Journal of Money, Credit and Banking 11, 419-426. Pierce, D., 1977, Relationships - - and the lack t h e r e o f - between economic time series, with special reference to money and interest rates, Journal of the American Statistical Association 72, 11-22. Pierce, D. and L. Haugh, 1977, Causality in temporal systems, characterization and a survey, Journal of Econometrics 5, 265-293. Sawyer, J., 1979, Modeling the international transmission mechanism (North-Holland, Amsterdam). Sims, C., 1972, Money, income, and causality, American Economic Review 62, 540-552. Sims, C., 1977, Comment, Journal of the American Statistical Association 72, 23-24. Swoboda, A., 1983, Exchange rate regimes and European-U.S. policy interdependence, IMF Staff Papers 30, 75-102. Waelbroeck, J., 1973, The methodology of linkage, in: R. Ball, ed., The international linkage of, national economic models (North-Holland, Amsterdam).
INTERTEMPORAL RELATIONSHIPS BETWEEN INDUSTRIALIZED ECONOMIES William L. HUTH* Northeast Louisiana Unioersity, Monroe, LA 71209, USA Received October 1984, final version received April 1985 This paper describes a multivariate time series analysis of the intertemporal relations between industrial production in seven different western economies. A major thrust of the study was an attempt to provide a time series validation of the results from the Project LINK global econometric model. The analysis was also used as a further examination of empirical support for the existence of an international business cycle.
1. Introduction
The pl~ititudinous remark, 'when the United States economy sniffles the remainder of the western world sneezes (or worse)', is well known to economists and laypersons alike and is primarily due to the U.S.'s perceived dominant international stance with respect to its trading partners. The fact that interconnections between economies exist is obvious. Bergsten has stated the 'interdependence is now a cold reality' and modern international texts include treatments (albeit somewhat limited) of the interdependence phenomenon, see, for example, Dornbusch (1980) and Ethier (1983). The linkage between economies has received explicit treatment in the literature, mainly under the auspices of Project LINK and other attempts at world model building. See Hickman (1983) for a survey of the more recent work. Project LINK, which includes 25 different national econometric models and contains some 6,000 variables, achieves linkage, for the most part, through current account trade flows. Thus, the international transmission mechanism for economic perturbations resides in changing import demand and export prices of the perturbed economy. The linkage is made operational by the development of a trade share matrix whose elements are determined by the proportion of a particular nation pair's exports to a single nation's total imports. The international interdependence between nations is then deduced by simulating the linked national econometric models given policy *The author would like to thank an anonymous referee of this journal for pertinent comments. 0014-2921/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)
364
W.L. Huth, lntertemporal relationships between industrialized economies
scenarios for a particular country and estimating lag structures and multipliers, see Klein et al. (1979) and Filatov et al. (1983). Criticism of the LINK system has been directed at the dearth of validation oriented studies of the simulation results and the lack of explicit specifications about the nature and direction of the interrelationships between the national economies. In addition, the system fails to develop alternate transmission mechanisms, especially those involving the dynamics of capital account items. This last point is particularly pertinent in the light of some of the recent work concerning the international flow of capital and the resulting ramifications on the insulatory effect of flexible exchange rates. International interdependence has also been examined by Barren and d'A1 Cantara (1976) and Swoboda (1983). Barten and d'A1 Cantara develop a linked econometric model involving the European Economic Community (EEC) and, based on experiments with the linked model, conclude '... considerable interdependency between the various national economies'. In discussing the purpose of their model they invoke the 'reverse' scientific method where data relationships are used to search fdr more fundamental economic relations. The authors state that the purpose of their model is to '...provide empirical basis for theoretical hypotheses in order to make meaningful projections'. The Swoboda paper looks at the interdependency effect due to alternative exchange rate regimes by examining the variability of simple correlations between variables computed for different subsamples of data. The subperiod delineation was based upon the switch from the Bretton Woods fixed rate system to the current flexible rate system. Swoboda concludes '... there does appear to be "real" interdependence under flexible, as well as under fixed, exchange rates'. In addition it was noted that the degree of association between the variables was, apparently, enhanced as a result of the regime switch. This result provides additional support for the hypothesis that insulation under flexible rates has a low 'R' factor. That is, the a priori theoretical deduction that flexible exchange rates lead to a reduction in the perturbation transmission and incremental improvements in the degree of policy autonomy lacks empirical support, perhaps due to alterations in the transmission channel. Based on his correlation analysis, a principal component study of inflation rates and output growth for several nations, the apparent increment in interdependence, and an unpublished study by Huber and Saidi (1982), Swoboda gleans support for the hypothesis that a world business cycle with superimposed national cycles exists. He states (p. 98) '... the close interdependence in business cycles that was witnessed jn the 1970s may well find its origin in a world business cycle in a closely integrated international economy rather than in the transmission of disturbances from one country, or group of countries, to the rest of the world.'
W.L. Huth, lntertemporal relationships between industrialized economies
365
This last statement is given some support by the Project LINK simulation results in Filatov et al. (1983) where significant international stability was observed even given simultaneous shocks, The previous work cited has certainly moved the concept of international interdependence from the umbra of heresy into, at least, the penumbra of circumstance. The purpose of this study is to continue that movement (hopefully in the correct direction) by examining the nature and direction of international linkages in a time series framework. In particular, empirical answers are sought to several questions. First, does the U.S. economy serve as an indicator of change in other western economies, that is, is the direction of influence from the U.S. to other industrialized nations? Second, do some countries mitigate or exacerbate the cyclical fluctuations of other countries, in other words, are economic expansions or slowdowns 'catching'? This last question comes to grips with the hypothesis of an international business cycle as mentioned above. Another objective of this work is an attempt at providing a time series validation of the econometric simulation results from Project LINK. To that end, the results of the time series analysis are compared with those of a recent Project LINK report. An outline of the time series methodology is discussed in the next section and the following section describes the country set, corresponding data, and the empirical results of the time series analysis. The concluding section summarizes the results obtained herein.
2. Time series methodology The method used to assess the relations between the economies considered below is an accumulation of efforts by Box and Jenkins (1970), Sims (1972), Haugh (1976), Haugh and Box (1977), Granger and Newbold (1977a, b), Pierce and Haugh (1977), Granger (1980), and Geweke (1982). Two time series, Yt and X , t = 1..... T, both realizations from a stochastic process and represented by integrated autoregressive moving average models of the form c~y(B)(1 -- B) d Yt = Oy(B)a,,
(1)
q~x(B)(1 - B)nXt = Ox(B)bt,
(2)
and
where ~b(B) and O(B) are parameter polynomials in the backshift operator B of order p and q, respectively. The term ( 1 - B ) a indicates that d differences of each process realization are required to produce time invariant (stationarity in both the mean and variance) series. The at and bt are i.i.d. N(0, tr2), white noise, residuals. Given identification (specification of p, d, and q), estimation,
366
W.L. Huth, lntertemporal relationships between industrialized economies
and a residual diagnostic check of eqs. (1) and (2); that is, the estimation of the true whitening filters, the residual series at and bt will contain the interrelationships between the original series. The prewhitening process described above results in joint covariance stationary innovations of the basic data. The series are innovations in that the within variable relationships have been removed through the prewhitening process while preserving the fundamental variable relations, see Pierce and Haugh (1977). Rather than throwing the baby out with the bathwater, the filter simply removes the bathwater. The interinnovation relationship can be examined by computing the correlation between the innovations at various time lags. These crosscorrelations are given by
rob(k)=
cov(a, b,+k)
SaS~
,
k = 0, _+1, __+2.... ,
(3)
where raa(k) represents an estimate of the bidirectional correlation between the two innovation series, at and bt, at lag k. The numerator in eq. (3) is the covariance between the two series and the denominator is the product of the innovation standard deviations. It has been shown, Haugh (1976), that the asymptotic distribution of the rob(k), under the assumption of serial independence, is chi-square. Thus, the presence of a temporal relation can be determined by examining the statistic J
SI=T ~
rob(k)2
(4)
k= - j
in relation to a critical chi-square value with 2j + 1 degrees of freedom with the variance of the tab(k) given by 1/T. Unfortunately, the test just described can only show support or lack thereof for the existence of a temporal relation, not its direction. It is possible, however, to subjectively assess the direction of the temporal relation between innovations by using the information contained in the cross-correlation behavior. Given 'one-sided' crosscorrelations, r(0)=0, r(k)#0 for some k > 0 and r(k)=0 for k < 0 (or the reverse), support for a succession relation is present. In both situations, the fact that r(0)=0 implies that the temporal relation is 'pure' in that no contemporaneous relation is present. Given that r(0)#0 then the possibility of a contemporaneous relation, perhaps combined with other relations, is suggested. An additional difficulty with the statistical test is its low power and bias toward accepting the independence hypothesis, Pierce (1977), Sims (1977), and Pierce and Haugh (1977). This independence bias explains Pierce's conclusion of widespread independence between theoretically connected economic variables. Given a bias towards an independence detection,
W.L. Huth, lntertemporal relationships between industrialized economies
367
some protection is provided against a type I statistical error in that the type II error is more likely. Thus, when the Haugh test results in the rejection of the independence hypothesis, credence is established for the dependence relation. On a more firm statistical footing, corroborating evidence for a directional relation can be found by using the estimated cross-correlations to identify and fit either a dynamic regression model, Haugh and Box (1977), or a bivariate transfer function model, Granger (1980). With either method, the end result is the detection of the presence or absence of a directional relation on the basis of the incremental predictive performance due to the bivariate model as compared with a univariate prediction. Given an enhancement in predictive precision as measured by the reduction in mean square error or other summary statistics, the directional relation can be inferred. It should be noted that Geweke (1982) has demonstrated that linear dependence between time series can be decomposed into bidirectional (first series to second and vice versa) and instantaneous linear feedback.
3. Empirical presentation Eight western, industrial economies are considered: the United States, OECD Europe, the United Kingdom, Canada, the Federal Republic of Germany, France, Italy, and Japan. In each case, the countries' index of industrial production is used as the representative measure of economic activity. This choice was based on data availability (historical data is available on the BEA BCD data tape) and the fact that the U.S. index has been classified as a coincider with NBER reference cycles. It is assumed, without empirical support, that the indices for the other countries also coincide with that countries' business cycle. Although unsubstantiated, the assumption seems reasonable. Each index of industrial production measures change in real value added as a result of industrial activity (manufacturing, mining, etc.). Consistent data were available for each economy over the twelve-year span from January 1970 to December 1981. As a result, a total of 144 observations ( T = 144) comprised the process realizations from which the analysis below was carried out. Initially, each of the eight industrial production series was appropriately differenced and autocorrelations and partial autocorrelations were computed to facilitate the order identification of the polynomials in B, p, and q, in eqs. (2) and (3). Each identified filter was then estimated, using a non-linear least squares algorithm, and diagnostically checked for an appropriate residual distribution. The estimation results for each of the eight filters are shown in table 1 and were used to generate, through an ex post simulation, the innovation series, a~,, and bi, t, i = 1,..., 8 and t = 1..... 144. Given the eight innovation series there were 28 possible cross-correlations
368
W.L. Huth, Intertemporal relationships between industrialized economies
Table 1 Filter estimation results. ARIMA u.s. Europe U.K. Canada F.R.G. France Italy Japan
(p,d,q)
MSE
1, 1,0 1, 1, 0 1, 1, 0 1,1,1 0, 1, 1 1, 1, 0 0, 1, 1 1,2,1
1.033 3.027 5.400 3.221 5.278 7.590 3.000 7.650
~
IZl
0.712 11.76 -0.178 2.16 0.180 2.19 -0.753 2.30 ----0.336 4.25 ---0.333 3.62
0 ---0.666 -0.271 -0.390 -0.764
Izl ---1.80 3.34 -4.96 12.10
between the paired time series. The O E C D Europe industrial production measure includes some of the indexes for other nations considered above. Specifically, O E C D Europe includes the indexes for the U.K., the F.R.G., France, and Italy as well as other European nations. Because of the obvious contemporaneous relation problem, the correlations between O E C D Europe and each of the included series were excluded from the study, leaving 24 cross-correlations for inspection. The rab(k) were computed using eq. (3) for k = 0 , + l , + 2 . . . . . +_10. The resulting cross-correlations for specific country pairs are presented and discussed next. In the tables shown in this section, the correlations are initially compared with confidence bounds computed using l I T as the variance of the estimated coefficient. Approximate 95 percent test bounds are _ 0.17 for the innovation series considered here. Cross-correlations within the bounds are not statistically different from zero whereas those outside the limits are statistically significant. The cross-correlation behavior is then used to infer the temporal interinnovation relations, given, of course, the caveats noted above. Table 2 contains the cross-correlation between the U.S. production measure and each of the seven remaining countries. U p o n inspection, it appears that the overall relation between the U.S. and each of the seven other economies is negligible, as evidenced by the computed H a u g h test statistic, S, shown in table 3. The critical chi-square value with 21 degrees of freedom and a 0.05 level of significance is 32.7. As can be observed, the independence hypothesis is accepted for all relations, except the connection between the U.S. and the Canadian economies, where S=38.9. Individual inspection of these cross-correlations shows a contemporaneous temporal relation combined with a succession relation from the U.S. to C a n a d a after a two-period (month) delay, T h a t is, the correlation r ( + 3)=0.19 indicates that a full two-period delay occurs between the impulse and the response in the third period. Additionally, the relation between the U.S. and J a p a n is significant at the 0.10 level. This relation is a purely successive one in that
Table 2 Cross-correlations. United States with k
0
1
2
3
4
5
6
7
8
9
10
Europe + -
0.19
-0.08 -0.07
0.13 0.12
0,01 -0,01
0.20 -0.09
0.08 0.01
0.12 -0.10
0.04 -0.06
0.00 -0.05
0,02 0,00
-0.02 -0.01
0.12
-0.02 --0.01
0.00 -0.02
-0,03 0.17
0.11 -0.17
0.11 0.00
0.12 -0.11
0.07 -0.08
0.11 -0.11
0.03 0.13
-0.03 0.06
0.11 -0.03
0.12 0.10
0.19 -0.01
-0.03 0.05
0.01 0.00
0.14 -0.05
0.03 -0.09
0.02 0.05
0.12 -0.16
0.01 0.00
0.14 -0.11
0.14 0.01
0.06 0.11
0.08 -0.08
0.07 -0.07
0.16 0.05
0.06 -0.09
" 0.06 -0.08
0.00 0.12
-0.04 -0.10
0.16
0.09 0.05
0.08 0.12
0.01 0.00
0.06 -0.07
0.04 -0.10
0.08 -0.10
0.12 0.09
0.03 -0.11
0.07 -0.10
0.04 -0.02
0.04
0.01 0.05
0.09 -0.04
0.05 -0.06
0.21 0.05
-0.02 -0.03
0.00 -0.12
-0.03 -0.06
0.05 -0.08
-0.01 0.03
-0.03 0.11
0.17 0.09
0.20 -0.11
0.09 -0.09
-0.02 0.06
-0.06 -0.07
-0.12 0.10
-0.10 0.13
-0.04 0.05
U.K. +
Canada + -
0.35
F.R.G. +
0.17
-
France + -
Italy +
Japan +
0.05
0.00 -0.08 0.16 -0.01
Table 3 Haugh test statistics,a Dependent (0.01 level)
S
'Dependent' (0.25 to 0.10)
S
1. 2. 3. 4. 5. 6. 7. 8. 9.
38.9 39.1 53.9 57.3 59.7 48.3 82.8 79.9 41.3
1. U.S. 2. U.S. 3. U.K.
26.0 27.7 27.4
U,S. F.R.G. F.R.G. F.R.G. F.R.G. Japan Japan Japan Europe
Canada Canada France Italy Japan France Italy Europe Canada
Dependent (0.10 to 0.01) 1.
U.S.
2. 3. 4.
F.R.G. Canada France
Japan U.K. France Italy
S 30.1 31.5 32.8 32.0
U.K. F.R.G. Canada
Independent (0.25 or less)
S
1. 2. 3. 4. 5. 6, 7. 8.
24.0 21.3 15.1 20.2 13.5 19.4 20.8 20.2
U.S. U.S. U.S. U.K. U.K. U.K. Canada Canada
Europe France Italy France Italy Japan Italy Japan
W.L. Huth, Intertemporal relationships between industrialized economies
370
the contemporaneous correlation between the two innovations is statistically insignificant Jr(0)=0], the relation direction appears to be from the U.S. to Japan with a full three-period delay. Thus, given a current impulse in U.S. industrial production there is a Japanese production response four periods later. The other intercountry relations do contain some statistically significant correlations, however, in aggregate there is an apparent independence relation. Given the test's independence bias, the relationship between the U.S. and both the U.K. and the F.R.G. are marginally insignificant (S values of 26.0 and 27.7, respectively). The directional implications associated with the U.S./U.K. relation are interesting. It appears that a purely successive relation from the U.K. to the U.S. exists. The relation between the U.S. and the F.R.G. is, at best, contemporaneous and then only marginally so, The cross-correlation for the West German innovation series and the U.K., Canadian, French, Italian, and Japanese production innovations are shown in table 4. The Haugh test statistics for the correlations are again displayed in table 3. It is obvious that the German economy has strong connections with a number of other economies. The independence hypothesis is rejected at the 0.01 level for the relationship between Germany and Canada, France, Italy, and Japan, and at the 0.05 level for the German/U.K. relation. The F.R.G. and Canada exhibit a pure succession relation from Germany to Table 4 Cross-correlations. Federal Republic of k
•
Germanywith
0
1
2
3
4
5
0.23
0.11 0.00
0.03 0.06
0.11 0.09
0.04 0.02
0.07 -0.03
0.07 0.27
0.16 0.08
0.06 0.22
0.05 --0.04
0.23
0.16 --0.06
0.13 0.17
0.22 0.25
0.21
-0.09 0.09
0.26 -0.07
-0.16 0.08
0.15 -0.02
6
7
8
9
I0
-0.16 0.18
0.03 0.11
0.07 0.16
0.00 -0.12
0.00 -0.07
0.10 0.11
0.14 --0.13
0.11 0.00
0.01 0.00
-0.15 0.08
-0.02 --0.08
0.02 0.01
0.11 --0.12
-0.03 0.17
0.01 0.13
0.17 --0.08
0.07 --0.03
-0.12 --0.07
-0.04 0.19
0.11 0.17
0.22 0.01
-0.19 --0.06
0.15 -0.05
0.11 -0.04
0.10 -0.19
--0.09 0.11
-0.02 0.11
-0.16 0.11
0.04 0.12
-0.20 0.03
-0.10 0.10
0.11 0.16
-0.03 0.16
-0.20 -0.02
U.K,
+ -
Canada + --
0.03
France + --
Italy + -
Japan + -
0.36
Vv'.L. Huth, lntertemporal relationships between industrialized economies
371
Canada after a one-period delay. In the other cases, there are both synchronicity (feedback) and contemporaneous temporal relations. The connection between F.R.G. and Japan is particularly interesting in that the successive part of the combined contemporaneous succession relation indicates an inverse relation between the two economies. An increment in German industrial production is positively correlated with the current level of Japanese production and negatively related to Japanese production after a five-period delay, perhaps due to a substitution relation between the commodity components of the industrial production indexes. This last point is certainly worth further study. Table 5 contains the interconnections between the U.K. and Canada, France, Italy and Japan, and between Canada and France, Italy, and Japan. The correlation behavior between Japan and Italy, France, and Europe, between France and Italy, and between Europe and Canada is displayed in table 6. For the most part, the independence hypothesis is accepted, as can 5
Table Cross-correlations.
k
0
1
2
3
4
5
6
7
8
9
10
U.K. with Canada + -
0.07
0.08 -0.10
-0.03 0.12
0.20 0.12
-0.07 0.03
0.14 0.21
-0.01 0.05
-0.09 -0.02
0.02 0.14
-0.05 0.01
0.04 0.03
0.12 0.08
0.11 0.13
0.04 0.14
0.02 0.02
-0.05 0.06
-0.07 0.05
0.09 -0.05
0.00 -0.08
-0.03 0.09
-0.01 -0.02
-0.05 0.09
0.03 0.09
0.12 0.00
-0.07 -0.11
0.13 0.01
0.02 0.08
0.02 -0.02
0.04 -0.03
0.02 -0.01
0.13 0.01
-0.02 0.13
0.03 0.04
-0.16 0.07
-0.10 0.01
0.11 0.07
-0.06 0.15
-0.07 0.01
0.03 0.20
0.12 0.05
0.14 0.09
0.08 0.01
0.11 -0.03
0.07 0.10
0.07 0.04
0.03 -0.07
0.00 0.03
0.00 0.02
0.00 0.07
0.18 0.01
-0.10 0.07
0.09 0.02
0.12 -- 0.01
0.13 --0.05
-0.04 - 0.09
-0.02 --0.09
-0.10 O.12
-0.03 0.00
0.06 0.00
-0.18 0.14
-0.06 - 0.03
0.09 0.08
-0.07 0.08
-0.07 0.04
-0.08 0.04
U.K. with France +
0.07
-
0.17 0.01
U.K. with Italy +
0.11
-
0.01 0.06
U.K. with Japan + -
0.05
-0.08 0.01
Canada with France + -
0.29
0.09 -0.03
Canada with Italy + --
0.13
0.12 0.07
Canada with Japan + -
0.02
0.09 0.08
W.L. Huth, Intertemporal relationships between industrialized economies
372
Table 6 Cross-correlations. k
0
1
2
3
-0.18 0.20
0.21 -0.02
0.06 0.16
4
5
6
7
8
9
10
0.14 0.06
-0.22 0.25
-0.19 -0.21
-0.05 0.03
-0.08 0.07
-0.12 0.21
-0.13 0.00
0.00 0.14
-0.10 0.16
-0.14 0.25
0.00 0.18
-0.06 0.03
-0.15 0.23
-0.07 0.11
-0.12 0.01
-0.05 0.12
0.14 0.06
-0.14 0.08
-0.15 0.28
-0.22 -0.12
-0.01 0.11
-0.07 0.21
-0.06 0.21
-0.24 -0.01
0.24 0.03
0.16 0.08
0.04 0.03
-0.06 0.03
-0.01 0.I0
0.20 -0.03
0.02 -0.02
-0.01 0.03
-0.11 -0.05
0.17 0.07
0.16 0.11
-0.01 0.15
0.15 0.08
-0.03 0.13
-0.08 0.11
0.06 0.18
-0.01 -0.14
-0.05 -0.01
Italy with Japan + -
0.36
-0.I1 -0.07
France with Japan + -
0.11
-0.07 -0.07
Europe with Japan +
0.38
-
-0.14 0.00
France with Italy +
0.07
-
-0.06 0.22
Europe with Canada + -
0.24
0.12 0.03
be observed from the estimated test statistics presented in table 3. Notable exceptions are the relationships between Japan and France, Italy, and OECD Europe and those between France and Italy and Canada and Europe. There are pure succession connections between Canada and Italy and Japan and France with the direction from the former to the latter in each case. The remaining dependence relations involve, for the most part, combined feedback and contemporaneous interconnections.
4. Comparison of the time series results with Project LINK Estimated international income elasticity multipliers from a seven-year simulation (1979-1985) of the linked national econometric models are given in Filatov et al. (1983). The mean multiplier value for the seven-year simulation of the countries considered herein were computed from their table and are shown here in table 7. In each case, the elasticity multiplier represents the mean percentage change in real income for the column country that was induced from a unit percent shock in the row country. The real demand shock was a sustained exogenous increase of government expenditures in the row country over the horizon of the simulation experiment. The main diagonal of the table shows each country's own multiplier
I¥.L. Huth, lntertemporal relationships between industrialized economies
373
Table 7 International elasticity multipliers for real income.
U.S. U.K. Canada F.R.G. France Italy Japan
U.S.
U.K.
Canada
F.R.G.
France
Italy
Japan
2.54 0.05 0.04 0.12 0.04 0.05 0.02
0.15 1.10 0.01 0.15 0.05 0.06 0.03
0.77 0.08 1.41 0.11 0.04 0.05 0.03
0.41 0.19 0.03 2.12 0.19 0.23 0.06
0.09 0.05 0.01 0.15 1.08 0.07 0.02
0.31 0.14 0.02 0.45 0.14 1.95 0.04
0.27 0.06 0.01 0.15 0.05 0.06 1.22
while the upper and lower triangles can be used to examine the directional nature of the multiplier effect. The first row and column of the table show, respectively, the effect of a U.S. shock on the rest of the countries and shocks from the other countries on the United States. As an example, the mean impact of a one percent increment in U.S. government spending on Canadian real income is 0.77 percent while the reverse (a one percent change in Canadian government expenditures) scenario results in a 0.04 percent change in U.S. real income. Clearly, U.S. policy impacts Canadian income to a greater extent than Canadian policy impacts U.S. income. This observation from Project L I N K agrees with the time series results presented above. There was a dependence relation between U.S. and Canadian industrial activity as evidenced by the Haugh statistic. The cross-correlations shown in table 3 indicate a strong correlation between current levels of industrial production in the two countries and also show a succession relation from the U.S. to Canada after a two-period delay. The directional implication from the innovation correlation is, in most cases, consistent with the relative magnitudes of the elasticity multipliers. The mean real income elasticity multipliers between the German and Italian economies are also relatively large: 0.45 for the impact of a German shock on Italy and 0.23 for the reverse. Again, support for this relation is found in the results presented above. The independence hypothesis is rejected at the 0.01 level for the time series relation between the industrial production innovations for the two countries. In addition, the innovation correlation behavior indicates a strong contemporaneous relation coupled with feedback effects. In general, Filatov et al. (1983) noted that '...the F.R.G. is an important trading partner of most countries in the group, With especially close ties with its European neighbors'. This quality of the German economy is certainly indicated in the time series analysis above. Among the nine country pairs with test statistics indicating a dependence relation significant at the 0.01 level, four are country pairs in which the F.R.G. is included.
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W.L. Huth, Intertemporal relationships between industrialized economies
In general, with a few exceptions, the analysis presented above provides time series corroboration for the econometric results of the Project LINK simulations. Some exceptions include the large elasticity multiplier effect of a U.S. shock on F.R.G. income when the independence hypothesis is accepted at the 0.10 level and the rampant independence between U.S. production and that of the remaining nations when the first row in table 7 indicates large multiplier effects for a U.S. shock. It should be noted that the multipliers in table 7 are weighted by the ratio of incomes in the impulse and response countries. Thus the U.S. multipliers are disproportionately large when compared to the time series cross-correlations that represent the unweighted multiplier. Given the income ratio weighting of the LINK multipliers, the U.S. independence findings are not so surprising. Another exception involves the relationships between Japan and the other nations. In the time series analysis, Japan was influential in relation to France, Italy, Europe, and, to an extent, the United States. From table 7, however, the mean elasticity multipliers for Japan were, for the most part, low. A complete study of the time series interconnection between the other countries in the LINK project, as well as consideration of measures other than the indexes of industrial production, is beyond the scope of this study but definitely worthy to be entertained.
5. Summary and conclusions This paper has examined the temporal interrelationships between economic activity in seven industrialized nations. In each ease, a country's level of economic activity was represented by the level of its industrial production. The major findings of the analysis are presented in this section. From the empirical results, it appeared that there were significant relationships between the Federal Republic of Germany and several European nations and Japan. In most eases, an industrial activity change in Germany was positively related to similar activities in the countries for which a dependence relation was uncovered. Additionally, changes in F.R.G. production are negatively related and tend to lead (a succession relation) corresponding measures for the Japanese economy. The time series results here were also consistent with both the Project LINK and Swoboda conclusion of general stability in the international environment. Thus, additional support for the existence of an international business cycle may be provided here in that a considerable degree of independence was found to exist among the productivity indexes of the various economies and few transmission channels from one country to another (succession relations) were uncovered. In conjunction with the last point, it should be mentioned that the specific country set used above was somewhat limited and .narrow in that a major sector of the international
W.L. Huth, lntertemporal relationships between industrialized economies
375
environment was not considered. Specifically, production measures for the oil producing segment of the international economy were excluded from the analysis. Further analysis of international interdependence along time series lines should incorporate O P E C production measures. This addition would, perhaps, allow for endogenous perturbations in the oil consuming economies discussed above and explain Swoboda's business cycle interdependence finding. In addition, another caveat regarding the foregoing discussion is in order due to the fact that the time series methodology does not consider the uneven diffusion of impulses among trading partners as noted by Hickman and Schleicher (1978). Finally, the study has provided some corroborating results with respect to the Project L I N K simulation results in Filatov et al. (1983). The analogue representations were compatible with regard to the influence of the Federal Republic of Germany and divergent in the cases of the U.S. and Japan. An explanation of the different findings regarding the U.S. was mentioned above and involved the consideration of alternative perturbation transmission channels, mainly U.S. financial influence. The minimal impact of Japan in the L I N K multiplier development was explained, in Filatov et al., by the failure to include trade flows between Japan and the Asian sector. Another explanation, as evidenced from the above analysis, may be that the L I N K model fails to consider alternative disturbance transmission ehannels. In addition, the simulation results were for changes in government spending which may not significantly alter Japanese economic activity given the organizational structure and size of Japanese industry.
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