international interdependence of national growth rates: a structural trends anakysis

JOURNALOF Monetary ECONOMICS ELSEVIER Journal of Monetary Economics 40 (1997) 73-96

International interdependence of national growth rates: A structural trends analysis

Betty C. Daniel*

Department of Economics, The University at Albany, Albany, NY 12222, USA

Received October 1994; final version received April 1997

Abstract

This paper identifies two structural trends responsible for growth in per capita industrial production in the US, the UK and Japan. First, using Johansen's multivariate cointegration approach, the number of common trends in the three industrial production series and the real price of oil is estimated to be two. Next, long-run restrictions are used to separate structural errors with temporary effects from those with permanent effects. Finally, it is assumed that the oil price is affected by only a single structural trend. This identifies a trend, which has a structural interpretation as a natural resource constraint, and another trend with positive drift, interpreted as productivity.

Keywords: Structural trends; Cointegration; Oil prices JEL classification: El3; C32

I. Introduction

The study of growth and its relationship to business cycles has become a re- cent priority in macroeconomics. Theoretical contributions include the burgeoning

* Tel.: 518-442-4747; fax: 518-442-4736; e-mail: [email protected].

The author would like to thank an anonymous referee, Ron Bewley, Trevor Breusch, John Campbell, Valentina Corradi, Frank Diebold, Lance Fisher, Hal Fried, Terry Kinal, Kajal Lahiri and Adrian Pagan for valuable comments on earlier drafts. Thanks also go to seminar participants at The Australian National University, The University of New England, The University of New South Wales, The University of Western Australia, The University of Pennsylvania, and the Australian Econometric Society Meetings. The author also gratefully acknowledges financial support from the University of New South Wales, where a substantial portion of this research was conducted, and from National Science Foundation Grant #GER94-50140.

0304-3932/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PH S0304-3932(97)00034-2

74 B. C Daniel~Journal of Monetary Economics 40 (1997) 73 96

literature on endogenous growth, implying a potentially greater role for macroeconomic policy than simply stabilization. Empirical contributions have focused on the non-stationary behavior of output, and sought to link the long-run determinants of output with the determinants of business cycles. This literature (Blanchard and Quah, 1989; King et al., 1991; Gali, 1992) tends to find that 45-90% of the variation in US GNP at business cycle frequencies is due to shocks with permanent effects. Following neoclassical theory, these shocks are usually labeled supply or productivity shocks.

To date, there has been no attempt to provide any further identification of these long-run shocks. However, if negative productivity shocks are a primary cause of recession, then understanding them is important. Further, taken literally, negative productivity shocks do not make sense, since it is hard to imagine how a country's productive sector could collectively lose knowledge. When questioned about what negative productivity shocks could be, the answer is frequently something like oil price shocks.

This paper takes that response seriously by examining the effect of oil prices on growth. The importance of changes in oil prices in the determination of business cycles is well-established. Hamilton (1983, 1994) shows that over the post-World War II period, all but one of the US recessions were preceded by a large oil price increase. Gisser and Goodwin (1986) document the importance of oil prices to US business cycles after the formation of OPEC. Burbidge and Harrison (1984) establish the importance of oil price shocks in the timing of business cycles across countries. Given that most variation in output at business cycle frequencies is caused by shocks with permanent effects, it stands to reason that one of these shocks could be represented by oil prices.

This paper analyzes the role of oil prices in the growth of industrial production for the US, the UK and Japan. Industrial production is chosen as the output measure since oil prices should have their closest link to the industrial sector. The countries were selected to represent industrial countries with varying dependencies on imported oil. The US is a net importer, but produces some of its own; Japan is totally dependent on imported oil; and the UK's status changed from net importer to net exporter following the formation of OPEC. To adjust for differences in population growth, per capita measures are used.

Johansen's multivariate cointegration technique is used to determine the number of common trends in the set of variables given by the three countries' per capita levels of industrial production and the real price of oil. We find two common trends. This is consistent with the findings of other researchers, who fail to find bivariate cointegration and who find multiple common trends in models containing larger numbers of industrial countries (Cogley, 1990; Bernard and Durlauf, 1991; Neusser, 1991). Following the work by Blanchard and Quah (1989), King et al. (1991) and Gali (1992), we use long-run restrictions to separate the shocks with permanent effects from those with transitory effects. This permits a decomposition of each series into a permanent and transitory component, yielding a

B.C. DanielIJournal of Monetary Economics 40 (1997) 73 96 75

multivariate version of Beveridge and Nelson's (1981) univariate decomposition. With the additional restriction that only one stochastic trend has a long-run effect on oil prices, the two permanent shocks are further decomposed into an oil shock and another shock. Following other researchers, the non-oil permanent shock is labeled a productivity shock.

The picture that emerges is one of growth being determined by trends in productivity and natural resources, identified using oil prices. The productivity trend has a relatively strong positive drift, and the natural resource trend has a negligible drift, a strong levels shift with the formation of OPEC, and several smaller levels shifts thereafter. Differing growth rates across countries are due to differing weights on the two trends. The two trends are important in the determination of business cycles, since over 75% of the variation in industrial production at business cycle frequencies is due to permanent shocks.

The remainder of this paper is organized as follows. Section 2 sketches a simple growth model and relates it to the empirical representation of common trends. Section 3 contains tests for the number of common trends in the four variable system. Section 4 describes the procedure used to identify the common trends as an oil shock and a productivity shock, and computes the variance decomposition. This reveals their relative importance in the determination of each variable at alternative horizons. Section 5 contains conclusions.

2. A simple growth model

The purpose of this section is to illustrate the link between a simple growth model and a common trends analysis of the determinants of growth. Consider a simple constant-returns-to-scale Cobb-Douglas production function for a particular country, given by

YI = AlKt~' L~t 2,

where

A t = B ~ R I -~'-~2,

Kt is the capital stock, Lt is the supply of labor, Rt is an index of raw materials, B I' is an index of technology and ill, r2 and 1 - fll - r 2 represent the share of capital, labor, and raw materials, respectively. Per capita values are denoted by small letters, hence, the per capita output is given by

yt = a tk f ~ ,

where

a,

76 B. C Daniel l Journal of Monetary Economics 40 (1997) 73-96

Let the at index be decomposed into a stationary component, st, and n non- stationary 1(1) components with possibly different coefficients such that

n 2 at = st H ai~"

i=1

Assuming the capital-labor ratio stationary, 1 the trend rate of growth of per capita output for a particular country is given by the linear combination of the non-stationary trends according to

d In Yt _ ~ ~. d lnait

dt i=1 TM dt "

Consider a world comprised of many countries, which share the same functional forms for production, with possibly different values for inputs and parameters. Let ai be defined such that the rate of growth of per capita output in all countries is determined by the same a i with possibly differing (perhaps zero) coefficients (,~i)-

In principle, the a index could be broken into an infinite number of components. However, if the 2i on each of the ai components are identical across countries, up to a multiplicative constant, then it will not be possible to identify these components as distinct. The same linear combination would affect growth in all countries. This implies that distinct common trends are identified only when the associated 2i differ relatively across countries.

Let ai be ordered such that values with 2is identical up to a scale factor are adjacent. Let vj be the logarithm of the j th linear combination of the ais in which the 2i are identical across countries up to a scale factor, such that

qJ

/)j = E )~i In air, i=qj_j+l

where qj is the ordered position of the last ai which enters the j th trend. A test for the number of distinct common trends in a group of outputs is a test for the number of vjs comprising the a index.

Consider an example motivated by the foregoing production function. Assume that Bt and rt have identical non-stationary components across countries, and to simplify, assume that these components are the indices themselves. For this case, there would be two common trends given by

ql

Vlt = ln Bt = Y~ 2i ln ait, i=1

v2t = In rt = ~ •i In ait. i=ql+l

1 This assumption simplifies the presentation and is of no consequence. Any non-stationary component of the capital-labor ratio would be part of the a index.

B.C. Daniel l Journal o f Monetary Economics 40 (1997) 73-96 77

The logarithm of the permanent component o f per capita output for each country would be given by

In Yh~ = "~hUlt + ( 1 - - f l lh -- fl2h )l)2t,

where h indexes the country. In practice, the vjt are referred to as ' common trends', and the multiplicative constants are called ' loadings' . Note that even if countries share the same trends, their trend rates of growth can differ when the loadings differ. Additionally, if the non-stationary components o f Bt and rt were not identical across countries, then there would be more than two common trends determining the permanent component of output.

3. Tests for the number of common trends

This section presents tests for the number o f common trends in the data set given by real per capita industrial production for the US, the UK, and Japan, and the real price of oil. Data are quarterly from 1960:1 until 1992:2. Industrial production is from the OECD, and population data are quarterly interpolations o f annual data provided in the UN Monthly Bulletin. 2 The nominal price o f oil is given by the Iraqi price through 1988:1 and by the UAE price thereafter. 3 It was made real by deflating by the US producer price index, also from the OECD.

Recently, attention has focused on the effects o f using seasonally adjusted data in testing for unit roots. For the univariate case, Ghysels and Perron (1993) have shown that the use o f seasonally adjusted data tends to bias upwards the estimated sum of coefficients in the moving average representation, when a unit root is absent, leading to the inference of a unit root too often. Therefore, it is plausible that using seasonally-adjusted data could lead to misleading inferences about the number o f unit roots in a set o f variables. However, use of seasonally unadjusted data is not appropriate if the data contain seasonal unit roots. Hylleberg et al. (1990) argue that the presence of a seasonal unit root as well as a unit root at zero frequency could lead to misleading inferences on cointegration, and suggest a test for seasonal unit roots. Using this test, it is not possible to reject the null of a seasonal unit root at frequency 1/4 in the seasonally-unadjusted industrial production data for the US and the UK. However, due to low power of the test,

2 The industrial production figures have base year 1985. The per capita measures were constructed by creating a population index with base year 1985 and dividing industrial production by the population index. The resulting series is multiplied by 100 so that 1985 per capita industrial production equals 100.

3 For the nominal oil price, we chose a price which appeared representative of all oil price series and which was available consistently for the longest period. This was the Iraqi price. Since this price ends in 1989:1, we spliced it with the UAE price, which had very similar behavior. In 1988, these prices were virtually identical, so we chose this period to switch price series. The prices are index numbers with 1985 as the base year. Oil price series are from the IMF.

78 B. C. Daniel~Journal of Monetary Economics 40 (1997) 73-96

frequent rejection o f seasonal integration in most series tested, and lack o f a plausible economic mechanism generating the seasonal unit root, arguments by Beaulieu and Miron (1993), Osborn (1993), and Diebold (1993) imply that a pragmatic strategy would be to proceed with the seasonally unadjusted data on the assumption that seasonal unit roots were absent. We, therefore, conduct the full analysis twice, with seasonally adjusted data, and with seasonally unadjusted data. As the results using the two data sets are incredibly similar, only the results with the seasonally-unadjusted data are presented here. 4

Johansen 's (1988, 1991) maximum likelihood approach is used to estimate the number o f common trends in the set o f data given by per capita industrial production and the real price o f oil. Prior to implementing Johansen's test procedure, it is necessary to choose a model. The specification chosen here allows a trend in the data. This hypothesis is later tested and accepted. Seasonal dummies are incorporated to allow for deterministic seasonality. In addition, a dummy, ini- tially taking the value o f 0 and a value o f 1 two periods after the 1973 oil price increase until the end o f the sample, is used to al low for the growth slowdown so widely noted in the industrial countries, s Sims ' (1980) l ikelihood ratio tests for lag length are used to choose a specification with seven lags. 6 The major results are robust to alternative lag lengths, but the addition o f too many lags leads to loss o f power and failure to find any cointegration. The model estimated is therefore given by

Xt = u + ODt + / / 1 ) ( t - I + "'" + FlkXt-k + gt, (l)

where Xt is a p × 1 vector o f variables, •t is a vector o f white noise disturbances, u is a vector o f constants, D is a vector containing seasonal dummies and the slowdown dummy, k is the maximum lag, and the Hi are p × p matrices. The vector error correction model is given by subtracting Xt_l from both sides and rearranging terms to yield

AXt = u + aDt + FIAXt-1 + " " + F k - l A X t - k + l - / / X , - k + gt, (2)

4 Results with seasonally adjusted data are available from the author on request.

5 Its absence yields cointegrating vectors which have an upward trend, suggesting a finding of too much cointegration. Also, when the dummy is omitted, Sims' lag selection criteria chooses a model with very long lags.

6 Beginning with a model with nine lags, we successively omit the most distant lag and test the restriction that the coefficients on that lag are zero. The Schwarz criterion, penalizes lags strongly and leads to a choice of a one lag model. However, Gonzalo (1994) finds that using too few lags leads to misleading inferences, and Banerjee et al. (1993) note that since the purpose of the lags is to 'whiten the error', the Schwarz criterion is not likely to prove optimal. A one lag model with seasonally unadjusted data does not seem reasonable and does not 'whiten the error'.

B.C. DaniellJournal of Monetary Economics 40 (1997) 73-96 79

Table 1 Cointegration: US, UK, Japan, oil price

p-r Lambda Lambda max Trace

1 0.003 0.379 0.379 2 0.061 7.677 8.056 3 0.222 30.835 38.891 4 0.346 52.307 91.198

Table 2 Critical values

p-r Lambda max (0.90) Trace (0.90) Lambda max (0.95) Trace (0.95)

1 2.69 2.69 3.76 3.76 2 12.07 13.33 14.07 15.41 3 18.60 26.79 20.97 29.68 4 24.73 43.95 27.07 47.21

where

i k ~ = ~2 Hs - I ; H = I - ~ Hj.

j=l j=l

Under the hypothesis of cointegration, H is a matrix of reduced rank (r < p) which can be factored into two p x r matrices such that H = ~3'.

Results of the tests for the number of common trends in industrial production for the three countries and the real price of oil are given in Table 1. The number of cointegrating vectors is given by r, so that the number of common trends is given by p - r. Critical values, taken from Osterwald-Lenum (1992, Table 1) assuming the presence of a trend, are given in Table 2. There is strong evidence of two common trends in the set of four variables. Both the trace and lambda max statistics for the null of at most three common trends (p - r = 3) are well above their 0.95 critical values. Therefore, the null of three common trends is

rejected in favor of two. However, using Monte Carlo techniques, Cheung and Lai (1993), have found

that Johansen's approach finds too much cointegration, that is, too few common trends. They suggest a small sample correction factor, 7 which effectively reduces the size of the estimated test statistics based on the number of right-hand side variables relative to the sample size. The correction factor for this model is 0.748.

7 Cheung and Lai suggest adjusting the value of the test statistics by a factor of 0.9DF/T + 0.1, where DF is given by the number of observations (T) minus the number of right-hand side variables. They find that Sims" adjustment factor of DF/T is too large.

80 B.C. Daniell Journal of Monetary Economics 40 (1997) 73-96

Table 3 Diagnostic statistics: US, UK, Japan, Oil price

Statistic US UK Japan Oil price

BP Q(23) 19.489 21.078 16.794 26.383 ARCH(7) 6.832 13.067 3.965 6.332 Skewness -0.126 -0.392 --0.264 1.393 Ex. kurt. -0.015 0.647 -0.232 9.110 JB norm 0.328 5.292 1.707 465.149

Critical values Z2(2) Z2(7) Z2(23)

0.90 4.61 12.02 32.01 0.95 5.99 14.07 35.17

To make this adjustment, multiply the test statistics by the correction factor. The adjusted lambda max statistic (23.065) remains well above the 0.95 critical value while the adjusted trace statistic (29.090) barely misses significance at the 0.95 level. 8 This confirms the presence of two common trends and two cointegrating vectors. 9

To verify that the critical values assuming the presence of a trend are appropriate, it is necessary to test for the presence of trends in the data. Johansen (1991) shows that this can be formulated as a likelihood ratio statistic. In this case, the ~2 statistic has two degrees of freedom and takes a value of 20.201, strongly rejecting the restriction. The critical values, based on the presence of a trend in the data, are appropriate.

The only evidence creating serious doubt about these results is that produced by one of the diagnostic tests on the residuals of the error correction equations. These results are contained in Table 3. The Box-Pierce Q statistic shows no evidence of serial correlation in the residuals, 1° and there is no evidence of autoregressive conditional heteroskedasticity. The Jarque-Bera test statistic for normality of the residuals for the industrial production equations is within acceptable limits, but for the oil price equation, this statistic is huge. As evidenced by the measure of excess kurtosis, there are too many large values for the residuals to be consistent with the hypothesis of normality.

8 Given the jump in the estimated value of the third eigenvalue, the lambda max statistic is probably more reliable.

9 The inference of two common trends is robust to the alternative lag lengths of 5 and 6 using the lambda max statistic.

10 The statistic presented here sums 30 autocorrelations. Degrees of freedom are given by the number of autocorrelations summed minus the lag length.

B. C Daniel/Journal o f Monetary Economics 40 (1997) 73-96 81

Table 4 Cointegration: US, UK, Japan; and oil price weakly exogenous


1 0.032 4.001 4.001 2 0.211 29.184 33.185 3 0.337 50.494 83.678

Since oil price behavior deviates so spectacularly from the assumptions necessary to test for the number of common trends, it is necessary to examine the robustness of the inference of two common trends in the set of four variables. If the price of oil were weakly exogenous with respect to the parameters • and t , then it would be possible to estimate them consistently by conditioning directly on the oil price itself without modeling its determinants. Johansen (199 l b) shows that weak exogeneity of the nth variable for the cointegrating parameters requires that the nth row of the at matrix contain zeros. The value of the likelihood ratio test for this restriction is estimated as 3.47. This statistic is distributed asymp- totically as Z2(2), implying significance at only at the 0.18 level. We conclude that the price of oil is weakly exogenous for the purpose of estimating the cointegrating parameters, and reexamine the determination of the number of common trends assuming weak exogeneity.

The results of the tests for the number of common trends in the set of four variables, imposing weak exogeneity of the price of oil, are given in Table 4. The evidence strongly supports the hypothesis of two common trends. To see this, first consider the number of common trends in the three variable system, conditioned on the oil price. The lambda max and trace statistics for the null of at most two common trends are well above their 0.95 critical values, even after application of the size adjustment factor (0.751). The three variable conditional system therefore seems to have a single common trend.

If the coefficient on the oil price in the cointegrating vector is non-zero, then given that the oil price is I(1), there are two common trends in the four variable system. H Therefore, this model is used to test whether all the variables, including the price of oil, belong in the cointegrating vectors, that is, to test whether the fls multiplying a particular variable are zero. The likelihood ratio statistics are distributed Z 2 with two degrees of freedom. For the US, the UK, Japan, and the oil price, the statistics are 25.51, 37.94, 32.24, 29.40, respectively. Since the critical value of X2(2) is 9.21 at the 0.99 level, these statistics are highly significant, implying that all four variables belong to the cointegrating equations.

11 A Dickey-Fuller test fails to reject the null that the oil price contains a unit root.

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Table 5 Diagnostic statistics: US, UK, Japan; oil price weakly exogenous

Statistic US UK Japan

BP Q(23) 18.520 21.900 16.182 ARCH(7) 5.905 13.025 4.471 Skewness -0 .137 -0 .407 -0 .106 Ex. kurt. -0 .020 0.800 -0 .387 JB norm 0.387 6.677 1.001

Table 6 Cointegration: US, UK, Japan


1 0.023 2.88 2.88 2 0.124 16.325 19.240 3 0.237 33.216 52.457

Therefore, it is not possible to drop one variable and retain the two cointegrating vectors. The four variable system has two common trends. 12

Diagnostic statistics for this equation are presented in Table 5. The Q statistic shows no evidence of serial correlation, and there is no evidence of autoregressive conditional heteroskedasticity. There is a slight problem with the normality assumption for the UK equation. The rejection of the normality assumption appears to be due to excess kurtosis. There are a few large residuals. This type of problem often arises, and Monte Carlo experiments suggest that it is not too serious (Gonzalo, 1994).

As a final check on the evidence that the four variables contain two common trends, given the presence of a variable whose innovations are not normally distributed, the price of oil is dropped from the model, and the model is re- estimated with the three countries' industrial production levels. These results are given in Table 6. Once the size adjustment factor (0.810) is applied, the results are ambiguous. The trace statistic rejects the null of at most two common trends at the 0.95 level, but the lambda max statistic rejects this null at only the 0.90 level.

The results therefore imply that the three industrial production series contain either one or two trends. Either result is consistent with the inference that the four variable system contains two common trends. However, the potential inference

12 This result is highly robust to alternative lag lengths. We have tried 4, 5, 6 and 8, all with the same result. When the number of lags is increased beyond 8, however, loss of power seems to result in difficulty finding cointegration.

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Table 7 Diagnostic statistics: US, UK, Japan

Statistic US UK Japan

BP Q(23) 14.125 25.593 21.159 ARCH(7) 7.063 11.805 10.888 Skewness -0.727 -0.387 -0.369 Ex. kurt. 1.526 1.160 0.392 JB norm 22.766 9.959 3.581

that there is a single common trend in the three variable system contradicts the result above in the conditional system, that it is not possible to drop a variable and retain two cointegrating vectors.

Diagnostic statistics for the three variable model are contained in Table 7. They reveal more problems with the specification than for the conditional model. Normali ty is more strongly rejected for the UK and is strongly rejected for the US as well.

Therefore, the model omitting oil prices does not appear to fit the data as well as the models containing oil prices. However, this model does include the possibil i ty of two common trends in the four variable system, consistent with the results in the models including oil prices. 13

In summary, per capita industrial production for the US, the UK, and Japan, and the real price of oil seem to contain two non-stationary components and two cointegrating vectors. The two non-stationary components determine the long-run behavior of the four series. The fact that the four series share only two non- stationary trends implies that non-stationary shocks to industrial production are global, not idiosyncratic in nature. The purpose of the next section is to determine the contribution o f oil prices to the non-stationary trends.

4. Specification of a structural common trends model

In this section, long-run restrictions are used to separate permanent and temporary structural disturbances, following Blanchard and Quah (1989); King et al. (1991) and Gali (1992). 14 The model chosen for the decomposi ton imposes the estimates of c~ and /~ obtained in Johansen's analysis under the assumption of

13 The structural identification is done under the assumption of two common trends. If there is only a single non-stationary trend in the vector of industrial production series, and the series are incorrectly modeled as having two non-stationary trends, then either all the coefficients on the irrelevant trend would be zero, or the coefficients on the two trends would be identical.

14 Recently, Faust and Leeper (1995) have criticized this strategy. Comments on this are contained at the end of the section.

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weak exogeneity o f oil prices. Therefore, the industrial production equations are the vector error correction equations. The oil price equation is specified as an autoregressive model in first differences with all the variables entering as ex- planatory variables.15

To identify the structural trends using long-run restrictions, it is necessary to obtain the common trends representation o f the reduced form model. Using the Granger Representation Theorem, the difference model, given by Eq. (2), can be inverted and summed to yield the common trends representation:

t

Xt = Xo + C(1 ) ~ (ei + u + 6Di) + St, (3) i=1

where X0 is a vector o f initial permanent values, and St is stationary. C(1) is a p × p matrix o f long-run effects, and is calculated according to

c( 1 ) : /~ . (~2 ~'/~± ) - ~ i ,

where the subscript (_L) denotes a matrix orthogonal to the original matrix and is given by

k - 1

~, = i p - Z r, + krt. i= l

This suggests a partition o f the vector Xt into a permanent component given by Xt - S t , and a stationary component, given by St, yielding a multivariate version o f the Bever idge-Nelson decomposition. Since the stochastic portion o f the permanent component is a constant multiple o f the innovations in the error corrections model, it is a random walk. ~6 Note that the role o f the constant term and the dummies is to determine the trend rate o f change o f the variables. Inclusion o f deterministic seasonals allows the mean rate o f change o f each series to differ by quarter.

The next step is specification o f the relationship between the structural and reduced form models. The reduced form model is given by Eq. (1). Let the

15 The weak exogeneity model is chosen over the unrestricted model since the departures of oil price behavior from normality could affect the estimates of the cointegrating coefficients. Another alternative would be to derive the permanent component of each series without modeling oil prices and treating oil prices themselves as one trend. However, without a model for oil prices, it is not possible to consider the contribution of oil prices to variance. As a check on the behavior of the trends, however, we did construct the permanent components for the conditional model and found that they behave similarily.

16 In the univariate Beveridgc--Nelson decomposition, permanent and transitory components are perfectly correlated. However, in a multivariate version with p variables, there are p linearly indepen- dent combinations of the p innovations in the reduced form model. With p- r permanent components, and r > 0 transitory components, the permanent and transitory components are orthogonal.

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structural model be given by pre-multiplying the reduced form model by a p × p matrix H yielding

H X t = H u + HfDt + Hll lXt_t + "'" + HllkXt_k + vt, (4)

where

l)t = Her,

such that the vt are orthogonal structural errors with covariance matrix given by the identity matrix. The covariance matrix of the reduced form errors, ~t, is given by (2. Identification of the p2 elements in H identifies the structural model. For this purpose, it is necessary to identify only mp of the coefficients in H, where m is the number of common trends. In identifying these parameters, we follow King et al. (1991) (KPSW).

First, note that the reduced form model, given by Eq. (1), can be differenced and inverted to obtain the moving average representation of the model. The stochastic part of the moving average model can be represented by

AJ(~ = C(L )~,

where C(L) is a polynomial in the lag operator L such that C(L)= 1 + CIL + C2 L2 + . . . .

Similarly, the structural model can be differenced and inverted and the stochastic part can be written as

AXt = G( L )vt,

where G(L) is a polynomial in the lag operator L such that G o = H -1, and Gi = CiH- 1.

The two moving average representations, together with the definition of vt, imply that

C ( L ) = G ( L ) H and C(1)=G(1)H,

0~3 where C(1 ) is a p × p matrix given by 1 + ~ i = 1 Ci and G( 1 ) is a p x p matrix given by ~ i ~ o Gi.

These representations can be used to identify the needed mp parameters in H. 17 Since r ( p - m) structural disturbances have no long-run effects, the matrix G(1 ) can be restricted to impose this. This is equivalent to requiring that the last r (2 in this case) columns of G(1) contain only zeros. Partitioning G(1) into a p × m matrix of parameters, and a p x r matrix of zeros, yields

G( 1 ) -- [K IO].

17 A good description of the technical details of the solution procedure is contained in Fisher et al. (1995).

86 B. C Daniel~Journal of Monetary Economics 40 (1997) 73-96

This partition reveals that long-run restrictions can only be used to identify the first m rows of the H matrix, denoted Hm, that is, the needed mp parameters. Identification of K is sufficient to solve for these Note that the coefficients in the matrix Hm form a in the reduced form model used to construct the coefficients in the matrix K contain the loadings equation for each variable.

parameters, using C(1 ) -- KHm. linear combination of the errors structural common trends. The for each structural trend in the

To identify the mp parameters in the matrix K, use the fact from the Granger Representation Theorem that f l 'C(1)=0 . KPSW suggest choosing K such that fltK = 0. Since fl is p x r, and K is p x m, this provides rm restrictions on K, leaving m 2 free parameters. Next, the covariance matrix can be used to provide an additional m(m + 1 )/2 equations since C(1 )(2C(1 ) ' = KK t, and C(1 ) has rank m. This leaves m(m - 1 )/2 free parameters in K. When m > 1, the remaining restrictions are less straightforward.

KPSW suggest that these be determined by assuming K to be lower triangular, that is by assuming that the first variable is affected by only one structural shock, the second by only two, etc. This is simply an application of Sims' identification technique for VAR's, implying the same advantages and disadvantages.

Since the current model has two non-stationary components, one long-run zero restriction is sufficient to identify the long-run structural components. The restriction imposed is that oil prices are affected by only one of the two permanent shocks in the long run. This ordering seems relatively obvious since one would not want to assume that oil prices had no effect on output. Therefore, the first long-run structural shock is allowed to affect the oil price and the levels of industrial production, whereas the second structural shock is allowed to affect only the levels of industrial production. This identification scheme is equivalent to lump- ing anything which has a long-run effect on the price of oil into the oil price category. These could be shocks due to changes in market structure, as with the oil price changes created by OPEC, or technological change that causes a long- run oil price change. This implies that the second shock represents productivity which is orthogonal to any productivity which affects oil prices. The third and fourth structural shocks have only transitory effects, and no attempt is made to further identify them.

The Hm matrix gives the weights on the errors and deterministic components from each error correction equation used to form the structural shocks. Solving for and using these weights, the two permanent structural components are given by

vlt = 8.637zorn + 0.433rust + O.O18ruKt + 0.407z jr,

v2t = 1.451Voet + 41.420rust + 1.748VUKt + 38.977"cjt,

where "rht = E l = l(~hi + t~hDhi q- Uh) where h indexes one of the four VAR equations. Thus, the first structural shock is weighted relatively toward the residuals

B. C Daniel~Journal of Monetary Economics 40 (1997) 73 96 87

125-

100-

75-

50

25

-25

e ~

I t n s

e

s S

t o~

s ~

'1 ' " I ' " 1 ' " 1 ' " 1 ' " 1 " '1 ' " I ' " 1 " '1' " 1 " '1"~ I' "1 ' "1 " ' I' ' q " ' 1 ' " 1 ' " 1 " '1" '1~' '1" '1 ' " 1 ' " I ' " 1 ' " I ' " 1 " ' l ' " l

62 64 66 68 70 72 74 76 78 80 82 84 86 88 90

, OIL PRICE TREND . . . . . PRODUCTIVITY TREND]

Fig. 1. Two structural trends.

and deterministic components in the oil price VAR while the second is weighted relatively toward those components in the industrial production error correction equations.

To understand the nature of these two trends and their contribution to trend behavior of industrial production, it is useful to turn to graphs. Note, however, that inclusion of the seasonal dummies in the summed residuals and deterministic terms, given by the zs, allows the mean rate of change of each trend to differ by quarter. Since the primary interest is not in seasonals, we present graphs in which the deterministic seasonals have been eliminated. The seasonally adjusted zs are given by:

l

"Cht = ~ (13hi -]- Uh "+" ~h q'- t~h4D4i), (5) i-1

where ~ = ~3q = 1 ~q/4, the first three elements of the dummy vector are the seasonals, and Dai is the growth slowdown dummy. Additionally, when comparing trends with the actual series, we plot seasonally adjusted series (OECD data) to avoid confusion between trend smoothing and seasonal smoothing. 18

Fig. 1 plots the two seasonally-adjusted structural trends. One trend behaves very much like the price of oil. This is not surprising, given that it was identified

18 The seasonal fluctuations in the UK series are particularly dramatic due to the effect of the August vacation.

88 11. C. Daniel l Journal of Monetary Economics 40 (1997) 73-96

as anything which had a long-run effect on the price of oil. This trend has a negligible drift, a strong levels shift around the time of the formation of OPEC, and several smaller levels shifts thereafter. The second structural trend has a strong positive drift over the first part of the period and a weaker positive drift over the second part of the period. Given that this shock rises over time, and given the tendency to attribute long-run gains in industrial production to productivity, this shock will be referred to as a productivity shock. The weaker drift after 1973 reflects the productivity slowdown so widely noted in the industrial economies.

The K matrix gives the loadings for each structural trend in the determination of each variable. Using these estimates, the permanent component of each variable can be expressed as

Oil price =X01 + 0.125/)1,

U S ----X02 - 0 .008/) 1 + 0.006v2,

UK =X03 - 0.013vl + 0.004v/,

Japan =Xo4 - 0.012vl + 0.017v2,

where Xoj represents the estimated value of the initial permanent value for the j th variable. It is estimated by forecasting 123 periods ahead beginning in 1961:4 and subtracting the deterministic portion of the forecast.

Fig. 2 plots the oil price against its permanent component. The permanent component tracks the actual series closely, implying that oil prices have a very small transitory component. 19

The equations, expressing trend output as a linear combination of the two structural trends, have interesting implications for the relative growth performance of countries. Since vl is relatively flat with several levels shifts, and v2 rises over time, growth can be viewed as a consequence of productivity gains in the presence of changes in natural resource constraints, as measured by changes in the real price of oil. Note that Japan's superior growth performance is explained by the relatively larger loading on productivity. Therefore, although all countries experience the same productivity trend, Japan is more successful in using it to increase industrial production. However, since v2 contains stochastic components as well as drift, Japan also experiences a higher variance, due to productivity disturbances, than other countries. It is also interesting to note that oil prices seem to have effects across countries which are much more similar than the effects of productivity. This is in spite of the fact that the countries in the analysis vary tremendously in their dependence on imported oil. It is consistent with the

19 The actual oil price series is not seasonally adjusted. IMF does not provide seasonally adjusted data on oil prices, and there is not a strong seasonal component to complicate comparison o f the data with the estimated trend.

B.C. Daniel/Journal of Monetary Economics 40 (1997) 73-96 89

5.0

4,5

4.0

3,5-

3.0-

2.5- 1

62 64 66 68 70 72 74 76 78 80 8~ 84 86 88 90

_ _ O I L PRICE ..... PERMANENT COMPONENT I

Fig. 2. Oil price and permanent component.

interpretation o f the price o f oil as representative of a general natural resource constraint.

To determine the contribution of oil prices to trend growth in industrial production, it is useful to plot each industrial production series against its permanent component and against the permanent component which would have been obtained with vl = 0, that is, the permanent component due only to productivity. Figs. 3-5 contain these graphs. Compare each actual series with its estimated permanent component. In general, the estimated series appear to track well, with the permanent component being a smoothed version o f the actual. However, prior to the first oil shock, the permanent components o f the oil price and of US and Japanese industrial production seem to miss the actual by a constant. For UK industrial production, the permanent component misses by a positive constant prior to the first oil shock and by a negative component thereafter. Over the sub- periods, broken by the 1973 oil shock, the slope appears to track well. The graphs suggest that the permanent components o f the US and UK series experienced smaller shifts, and the permanent components o f the Japanese and oil price series experienced larger shifts with the 1973 oil shock, than those estimated by the model. This implies that the two structural trends representation is too restrictive for this one very large levels shock. 2° However, the two structural

20 For the model to fit this one shock, it would seem necessary to allow C(1) to take on a different value to multiply the large oil shock. Note that a dummy does not help because it gets added to the error in determining the permanent component (Eq. (3)).

90 B. C Daniel~Journal of Monetary Economics 40 (1997) 73-96

4.8

4.7

4.6

4.5

4.4

4.3

4.£

4.1

4.0

f J ~ I j

f l , ; -

62 64 66 68 70 7~ 74 76 78 80 82 84 86 88 90

I IP . . . . . PERMANENT COMPONENT _--PRODUCTIVITY COMPONENT I

Fig. 3. US industrial production.

trends model does track the movement of each series over time well, with this single exception.

To determine the contribution of oil prices to trend growth, compare the estimated permanent components with the values which the permanent components would have taken on in the absence of oil price changes. These conditional trends are labeled productivity components. Particularly notable is the large levels drop in each permanent component, relative to its productivity component, with the 1973 oil shock. 21 The figures also suggest that the growth slowdown would have been more pronounced had oil prices not fallen in the 1980s. Therefore, oil prices have been important determinants of the permanent component of industrial production. It is also possible to use this analysis to study oil prices and business cycles.

As a first impression of the contribution of oil prices to business cycles, Fig. 6 plots the stochastic components of the two trends together with vertical lines indicating NBER reference cycles for the US. In reading this graph, note that recessions are typically of shorter duration than expansions, and that the first vertical line denotes a peak. Consider the contribution of oil prices to business cycles. Note that all recessions except the November 1970 recession were preceded by an oil price increase (Hamilton, 1983, 1994). Additionally,

21 Eventhough the magnitudes of these drops appear overestimated for the US and the UK, the graphs do suggest a sizeable drop. Additionally, for Japan, the drop appears underestimated.

B.C. Daniel~Journal of Monetary Economics 40 (1997) 73-96 91

4.8

4.7

4.6

4.5

4.4

4.3

4.2

~ " J ,,t " / / / / ~,/ . / i , • , " s ~ s

j.,/- / V < ] " '1' ' l l l l g l ' ' l I ' ' I p ' ' I " '1' " 1 ' ' '1 " 1 1 " ' I IIl~ TM I rT i1,, , l , , , i I ,,1 i i i ] l r l l ' ' ' l ' ' r [i ' ' l ' ' ' 1 ' ' ' 1 ' " U ' ' I ' '11 ~''1 I11 I'1'1 62 64 66 68 70 72 74 76 78 80 8~ 84 86 88 90

UK IP . . . . . PERMANENT COMPONENT - _ - P R O D U C T I V I T Y COMPONENT]

Fig. 4. UK industrial production.

5.0 .....

4.5

4.0

3.5

3 . 0

f k / / ' J

V " U " U " U " l - I I I I l ~ l l l I III I TM I ' r l [ ' r '1' ' '1 'H [ " ' 1 ' " I ' ' ' p " [ ' ' ' 1 ' ' ' U' ' 1 ' " I TM I I l l ~ lIT I " '1 [ l l l l l ' l ] " l lIE I ' r ' [

62 64 66 68 70 72 74 76 78 80 82 84 86 88 90

_ _ J A P A N IP . . . . . PERMANENT COMPONENT ___PRODUCTIVITY COMPONENT]

Fig. 5. Japanese industrial production.

92 B.C. Daniel~Journal of Monetary Economics 40 (1997) 73-96

125

1 0 0

75

50

2 5

0

- 2 5 -

s"

62 64 66 68 70 72 74 76 78 80 82 84 86 88 90

_ _ O I L PRICE TREND . . . . . PRODUCTIVITY TREND]

Fig. 6. Structural trends and NBER reference cycles.

the long expansions in the 1960s and the 1980s were accompanied by falling oil prices. However, there are also periods in which expansion occurs in spite of rising oil prices and periods in which oil price increases do not immediately precede recessions. Clearly, oil prices cannot take sole responsibility for business cycles, although they appear to have a role.

Consider the effect of the trend labeled productivity. Note that this trend seems to have peaks and troughs near the peaks and troughs for the NBER reference cycles. However, there are other peaks and troughs in the productivity trend of similar magnitudes, which are not associated with NBER reference cycles. Also, Fig. 1 and Fig. 6 show that the productivity trend, including deterministic components, continues to exhibit declines even though the effect of oil price shocks has been eliminated. 22

To get a more quantitative impression of the contribution of oil prices to business cycles, it is useful to compute a variance decomposition. These results are reported in Tables 8 and 9. Note, first, the importance of oil in explaining the forecast error variance at all horizons. This variable, so noted as a cause of recessions, is responsible for 32-85% of the five-year variance of industrial production, depending on the country. Between 5% and 36% of the forecast error variance at one-year horizons and between 17% and 76% of the forecast error variance at medium-term horizons is due to oil price shocks. This is confirmation of the

22 This could be due to the commingling of nominal shocks with productivity shocks, as discussed below, or to additional unspecified supply shocks.

B.C. Daniel~Journal of Monetary Economics 40 (1997) 73 96 93

Table 8 Variance decomposition: oil price

Horizon 4 quarters 8 quarters 16 quarters 60 quarters

Oil price 99.55 99.53 99.62 99.89 US 6.64 29.71 44.97 53.04 UK 36.45 67.17 76.43 85.28 Japan 5.40 17.02 22.82 32.23

Table 9 Variance decomposition: productivity

Horizon 4 quarters 8 quarters 16 quarters 60 quarters

Oil price 0.34 0.28 0.24 0.07 US 67.03 53.36 42.52 40.43 UK 31.71 20.55 14.47 11.04 Japan 79.27 74.52 71.62 66.23

emerging stylized fact that shocks responsible for the long-run determination o f output are also very important in its short-run determination.

Note, additionally, the difference across countries in the relative importance of oil in explaining the forecast error variance at all horizons. Oil is most important in the UK, next in the US, and least important in Japan. This difference can be explained by comparing the loadings for each structural trend across countries. The coefficients on the oil trend are much more similar than the coefficients on the productivity trend. Therefore, oil seems to account for relatively less of the forecast error for Japan, not because oil is less important, but because the productivity trend is so much more important. That is, less of the forecast error variance for Japan is attributed to oil, not because the forecast error variance attributed to oil is smaller, but because the total forecast error variance is larger due to the larger coefficient on the productivity shock. The natural resource shock seems to affect countries in roughly equal magnitudes, while the productivity shock has more diverse effects.

Note, finally, the relative lack of importance o f transitory shocks even over short horizons. 23 Only 15-32% of the forecast error variance o f industrial production at an annual frequency is due to transitory shocks. This confirms work by other researchers, establishing the importance o f shocks with permanent effects on business cycle behavior.

Faust and Leeper (1995) have cautioned against using long-run restrictions to identify disturbances. They note that, in the absence o f strong assumptions,

23 Residual variance at each horizon is due to transitory shocks.

94 B. C. Daniel~Journal o f Monetary Economics 40 (1997) 73-96

estimates of C(1), upon which long-run identifying restrictions are based, have confidence intervals of infinity, reflecting the near observational equivalence of trend stationary and difference stationary models. Additionally, unless structural disturbances satisfy strong dynamic restrictions, it is possible to commingle the structural disturbances in the attempt to identify them. These caveats have implications for the interpretation of the results in this paper, particularly for the identification of the disturbance which we label productivity. Since the model excludes many variables which have only transitory effects and might Granger cause industrial production, the model probably commingles the effects of productivity and other disturbances with transitory effects. That is, if we were to add nominal variables to the model, as KPSW did, then we would probably find a di- minished role for productivity disturbances in the variance decompositions. 24 It is also possible that the addition of nominal variables would reduce the incidence of downtums in the 'productivity' trend. However, given that it is so hard to find any variables which Granger cause oil prices (Hamilton, 1994), it is un- likely that these omissions affect the relative importance attributed to oil prices. These considerations caution against placing too much emphasis on the results of the variance decompositions for productivity, but they suggest that the variance decompositions for oil prices are probably robust to alternative specification.

5. Conclusion

This paper finds that growth in per capita industrial production for the US, the UK and Japan has been determined by two non-stationary components (trends). In addition, a structural identification of these trends is proposed. This is done by including oil prices in the set of variables analyzed. Using long-run restrictions, it is possible to separate the errors in the four-variable system into two temporary and two permanent errors. The permanent errors can be further identified by assuming that a single stochastic trend affects oil prices in the long-run. This results in the identification of the two permanent trends as a weighted average of the summed residuals and deterministic components in the vector error corrections model. The weights are such that one stochastic trend appears to be the permanent component of the oil price, whereas the other could be identified reasonably as productivity.

This brings together the research on the importance of non-stationary shocks in the long-run determination of output (Blanchard and Quah, 1989; King et al., 1991; Gali, 1992), and research on the importance of oil price changes in generating recession (Hamilton, 1983; Gisser and Goodwin, 1986; Burbidge and

24 This conjecture is supported by the pattern of productivity variance. The proportion of variance, attributed to the productivity shock as the horizon lengthens, decreases. This pattern would be expected for a shock which includes components with transitory effects.

B.C. Daniel~Journal of Monetary Economics 40 (1997) 73 96 95

Harrison, 1984). The oil price trend has had a substantial impact on trend growth over the period. The permanent components of industrial production experienced a strong levels shift due to the 1973 oil shock, and the productivity slowdown would have been more pronounced had oil prices not fallen in the 1980s. Addi- tionally, the trend identified with oil prices explains a substantial portion of the short-run variation in industrial production. Therefore, the variable so noted as a cause of business cycles is also important in the determination of trend growth in industrial production.

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international interdependence of national growth rates: a structural trends anakysis

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