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Common trends and common cycles in international labor productivity
economics letters ELSEVIER
Economics Letters 48 (1995) 179-184
Common trends and common cycles in international labor productivity Giorgio Calcagnini Istituto de Scienze Economiche, Universitgt di Urbino, Urbino, 61029, Italy Received 23 February 1994; accepted 13 September 1994
Abstract
The objective of this paper is to present a trend-cycle decomposition of the industrial labor productivity series in six major industrialized countries, to study the relationship between trend and cycle innovations, and to highlight the role of monetary policy as a possible source of transitory and permanent variations in labor productivity.
JEL classification: E32; C32
1. Introduction
This paper aims to analyze and detect the existence of common features in international labor productivity at the industrial level. By common features we mean both common trends (i.e. comovements among non-stationary variables) and common cycles (i.e. comovements among stationary series). This area of research has received new incentive from the recent development of econometric techniques that allow us simultaneously to address issues of economic growth and business fluctuations. Traditionally, trends and cycles have been treated independently, since the latter were thought of as a time-series transitory, or non-permanent movement, component. Instead, more recent research stresses the importance of a trendcycle decomposition which assigns a role to cycles in triggering productivity growth-rate changes. Such reasoning contributes to resolving the debate among different theoretical models. Indeed, the Real Business Cycle (RBC) theory claims that permanent productivity (or technological) shocks are the dominant source of economic fluctuations, while alternative models underline the role of innovations associated with nominal variables to explain the cyclical variation in the real variables. This approach allows for a causal relationship between decisions of policy-makers to the cycle as well as to the trend. The multivariate procedure employed in this paper is that recently developed in the study of common components in time series (see Vahid and Engle, 1993; Engle and Issler, 1993; and 0165-1765/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0165-1765(94)00606-7
G. Calcagnini / Economics Letters 48 (1995) 179-184
180
Kozicki, 1993). The appealing feature of this procedure is that it generates a unique trend-cycle decomposition of the data, at least in the special case where the number of common trends and common cycles adds up to the number of variables in the data set. Moreover, we need not impose any conditions in order to be able to identify trend and cyclical components, as in the case of other decomposition procedures (see Blanchard and Quah, 1989; and King et al., 1991). Section 2 presents a brief description of the data employed and the results of cointegration and common feature tests. Conclusions and limitations are stated in Section 3.
2. Testing for the number of common trends and c o m m o n cycles
Series used in this paper are those of labor productivity, at the industrial level, of six of the most industrialized western countries (the United States, Japan, Germany, France, Italy and the United Kingdom). Labor productivity series were obtained as the ratio of the yearly industrial production index (1985 = 100) to the yearly industrial employment index (1985 = 100). Both sets of series were primarily obtained from the International Financial Statistics (IFS) data set of the International Monetary Fund (IMF). In some cases, series not available in the IFS data set were obtained from the O E C D data set or from national sources. The sample period is 1953-1991. We chose to work with the industrial productivity series because (a) it generally shows the highest degree of covariability with the overall economy productivity series (i.e. per capita GDP or GNP series); (b) it is more reliable for comparative purposes than per capita GDP series, given the difficulties existing in correctly defining and measuring the concept of productivity for the non-market service industry; and (c) it shows a closer relationship with the concept of technology shocks. We started our analysis running Dickey-Fuller's unit root tests (DF and A D F ) on each national productivity series. Both tests accept the null that series are I(1) at the 5% level. Since all series proved to be non-stationary, we tested for the existence of any cointegration relationships. Following Johansen (1988, 1991), we did find that series are cointegrated. In particular, the specification chosen for the VAR system is that which minimizes the Schwarz Bayesian Information Criterion (SIC); that is, with a number of lags equal to 2. Results from the cointegration procedure are shown in Table 1, from which we see that the data support the Table 1 Johansen cointegration tests Trace test
Max. eigenvalue test
Null hyp.
Statistic
95%
Null hyp.
Statistic
95 %
r r r r r r
41.34 22.06 18.16 11.34 9.50 0.19
39.37 33.46 27.07 20.97 14.07 3.76
r r r r r r
102.58 61.24 39.18 21.03 9.68 0.19
94.16 68.52 47.21 29.68 15.41 3.76
= < < < < <
0 = 1 =2 =3 =4 =5
= < < < < <
0 = 1 =2 =3 =4 =5
G. Calcagnini / Economics Letters 48 (1995) 179-184
181
existence of only one cointegrating relationship (or five c o m m o n trends) among the six variables. 1 Following Bernard and Durlauf (1993), this would imply that the industrial productivity of the six countries does not converge. This result should not be very surprising since it is consistent with national industries characterized by different sectoral structures and, therefore, by different technology shocks. Next, we moved on to test for the existence of c o m m o n cycles. The procedure developed by Vahid and Engle (1993) suggests looking for linear c o m b i n a t i o n s - i n our case, labor productivity growth r a t e s - that are uncorrelated with any linear combination of the R H S variables of the error correction model formed with a n u m b e r of error correction terms equal to the cointegration rank. This is equivalent to imposing a reduced rank condition on the coefficient matrix of lagged labor productivity growth rates and error correction terms. Vahid and Engle suggest performing this reduced rank condition test by canonical correlation analysis. More specifically, the cofeature rank, s, is the n u m b e r of statistically zero canonical correlations, where s ~< N - r (with N equal to the n u m b e r of series), and the n u m b e r of c o m m o n cycles is N - s. The squared canonical correlations and the value of the test statistic for the cofeature rank are reported in Table 2. At the 5% level of significance there are five cofeature vectors, or one c o m m o n cycle. First, we note that r + s = N. Therefore, the trend-cycle decomposition is unique, i.e. performing linear transformations in the cointegrating space, or cofeature space, in isolation will not change the estimated trends and cycle. Secondly, this decomposition gives rise to an interesting economic interpretation. Indeed, if on the one hand, the existence of several c o m m o n trends is likely to be the result of the structural and institutional differences in each country; on the other, the c o m m o n cycle outcome suggests that short-run labor productivity variability may depend upon the same kind of shocks everywhere. We think that innovations in the monetary policy in one (or two) of the six countries here considered (i.e. the United States and Germany) may be regarded as the main source of cycle innovations.2 Moreover, as long as trend and cycle innovations are correlated, innovations in monetary policies may have Table 2 Canonical correlation analysis Null hyp.
Squared correlation
X2 statistic
Degrees of freedom
p-value
s s s s s s
0.00 0.03 0.13 0.18 0.29 0.69
0.001 1.197 6.440 13.609 26.588 59.138
2 6 12 20 30 42
0.9995 0.9770 0.8923 0.8498 0.6448 0.0415
> > > > > >
0 1 2 3 4 5
i Although cointegration residuals from this specification passed the stationary and normality tests, the L j u n g Box Q statistics revealed significant residual correlation. Cointegration residual autocorrelation does not improve in the case of VARs of higher order. 2 As shown by Fiorito and Kollintzas (1993), government s p e n d i n g - a proxy for fiscal p o l i c y - b e h a v e s differently in each country. It is often uncorrelated with and lags the G N P / G D P cycle.
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G. Calcagnini / Economics Letters 48 (1995) 179-184
Table 3 Trend and cycle innovation analysis
France Germany Italy Japan UK US
Correlation coefficient
t-statistic
Trend (*) innovation
Cycle (* *) innovation
-0.81 - 0.74 -0.77 -0.58 -0.75 -0.64
-8.16 - 6.48 -7.09 -4.21 -6.66 -4.87
0.62 0.73 0.52 0.69 0.94 0.85
0.38 0.27 0.48 0.31 0.06 0.15
*% of the variance of labor productivity innovation attributed to trend innovation. **% of the variance of labor productivity innovation attributed to cycle innovation. an impact on long-run labor productivity as well. How strong this impact is depends on the relative weight of the two types of innovations. Table 3 shows the results of an analysis of trend and cycle innovations. 3 Columns 1 and 2 show the correlation coefficients between the two types of innovations and the associated t-statistic, respectively. Columns 3 and 4 report a principal c o m p o n e n t variance decomposition exercise. Figures are percentages of total variability due to trend and cycle innovations, respectively. We note that (a) trend and cycle innovations show a strong and significant negative correlation and (b) trend innovations are generally more important than cycle innovations, even though the latter have a relevant role in explaining total variance for Italy, France and Japan. If the negative correlation between the two types of shocks means that a 1% increase in the trend innovation will only lead to a 1% increase in the level of labor productivity in the long run (since the short-run dynamics push the productivity towards the other direction) we also notice that the strength of this mechanism is much lower in the United States than in the other countries. In other words, a technology shock gives the American industry a short-run advantage over its competitors. Moreover, the kind of interaction which emerged between the cycle and the trend may represent evidence in favor of the 'opportunity cost' approach to productivity growth (Saint-Paul, 1993). Indeed, this class of models, which insists on intertemporal substitution of productivity-improving activities along the business cycle, predicts that recessions are associated with a higher pace of productivity-improving activities. Finally, we studied the relationship between cycle innovations and different types of shocks traditionally considered as sources of variability in economic activity. In particular, we considered shocks to the monetary policy (real interest rates and real money growth) in the United States and in Germany, and to commodity prices. Results of this correlation analysis are shown in Table 4. Cycle innovations are significantly and negatively correlated to real interest rate innovations in Germany and, more strongly, to real money supply innovations both in the United States and in Germany. Correlations are not significant in the case of the US real interest rate and of commodity price innovations. 3 Trend innovations are calculated by first differencing the estimated labor productivity trend; cycle innovations are the residuals from a regression of the estimated labor productivity cycle on lagged detrended error correction terms.
G. Calcagnini / Economics Letters 48 (1995) 179-184
183
Table 4 Correlation analysis of innovations a
Interest rate innovations-US Interest rate innovations-Germany Money supply innovations-US Money supply innovations-Germany Commodity price innovations
Cycle innovations
t-statistic
-0.08 -0.37 -0.38 - 0.46 0.16
-0.42 -2.07 -2.14 -2.69 0.84
a Real interest rates are calculated as the difference between the yearly discount rates and the wholesale price index growth rates. Real money supply growth rates are calculated as the difference between the yearly Money plus Quasi-Money growth rate and the wholesale price index growth rates. Finally, we calculated the difference between the yearly commodity price index growth rates for the developing countries and wholesale price index growth rates. The source for all series is the IFS-IMF.
3. Conclusions In this paper, we applied a recent t r e n d - c y c l e decomposition technique to labor productivity series in six industrialized countries. A list of the main results includes (a) the t r e n d - c y c l e d e c o m p o s i t i o n is unique since the n u m b e r of c o m m o n trends plus the n u m b e r of c o m m o n features is equal to the n u m b e r of series (or countries) studied; (b) precisely, we d e t e c t e d five c o m m o n trends and one c o m m o n cycle; (c) trend and cycle innovations are significantly and negatively correlated; (d) trend innovations are generally m o r e important than cycle innovations; (e) cycle innovations are significantly and negatively correlated with m o n e t a r y policy innovations. T h e picture that emerges from our evidence shows that there is no convergence a m o n g the industrial sectors and allows for a causal relationship from economic policy decisions to the cycle and to productivity growth. E v e n if these conclusions seem quite robust, evidence should still be treated as tentative.
Acknowledgement Financial support from M U R S T (Ministero dell'Universit~ e della Ricerca Scientifica e Tecnologica) is gratefully acknowledged.
References Bernard, A.B. and S.N. Durlauf, 1993, Convergence in international output, Working Paper, Department of Economics, MIT, Cambridge, MA. Blanchard, O.J. and D. Quah, 1989, The dynamic effects of aggregate supply and demand disturbances, American Economic Review 79, 655-673.
184
G. Calcagnini / Economics Letters 48 (1995) 179-184
Engle, R.F. and J.I. Issler, 1993, Estimating sectoral cycles using cointegration and common features, Working Paper no. 4529, NBER, Cambridge, MA. Fiorito, R. and T. Kollintzas, 1993, Stylized facts of business cycles in the G7 from a real business cycles perspective, European Economic Review (forthcoming). Johansen, S., 1988, Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control No. 12. Johansen S., 1991, Estimating systems of trending variables, Lecture presented at the ESEM 1991, Cambridge UK, Unpublished manuscript, University of Copenhagen. King, R.G, C.I. Plosser, J.H. Stock and M.W. Watson, 1991, Stochastic trends and economic fluctuations, American Economic Review 81, 819-840. Kozicki S., 1993, Techniques for estimating dynamic comovement with an application to common international output fluctuations, Finance and Economics Discussion Series, no. 93-32, Federal Reserve Board, Washington, DC. Saint-Paul G., 1993, Productivity growth and the structure of the business cycle, European Economic Review 37, 861-890. Vahid, F. and R.F. Engle, 1993, Common trends and common cycles, Journal of Applied Econometrics 8, 341-360.
Economics Letters 48 (1995) 179-184
Common trends and common cycles in international labor productivity Giorgio Calcagnini Istituto de Scienze Economiche, Universitgt di Urbino, Urbino, 61029, Italy Received 23 February 1994; accepted 13 September 1994
Abstract
The objective of this paper is to present a trend-cycle decomposition of the industrial labor productivity series in six major industrialized countries, to study the relationship between trend and cycle innovations, and to highlight the role of monetary policy as a possible source of transitory and permanent variations in labor productivity.
JEL classification: E32; C32
1. Introduction
This paper aims to analyze and detect the existence of common features in international labor productivity at the industrial level. By common features we mean both common trends (i.e. comovements among non-stationary variables) and common cycles (i.e. comovements among stationary series). This area of research has received new incentive from the recent development of econometric techniques that allow us simultaneously to address issues of economic growth and business fluctuations. Traditionally, trends and cycles have been treated independently, since the latter were thought of as a time-series transitory, or non-permanent movement, component. Instead, more recent research stresses the importance of a trendcycle decomposition which assigns a role to cycles in triggering productivity growth-rate changes. Such reasoning contributes to resolving the debate among different theoretical models. Indeed, the Real Business Cycle (RBC) theory claims that permanent productivity (or technological) shocks are the dominant source of economic fluctuations, while alternative models underline the role of innovations associated with nominal variables to explain the cyclical variation in the real variables. This approach allows for a causal relationship between decisions of policy-makers to the cycle as well as to the trend. The multivariate procedure employed in this paper is that recently developed in the study of common components in time series (see Vahid and Engle, 1993; Engle and Issler, 1993; and 0165-1765/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0165-1765(94)00606-7
G. Calcagnini / Economics Letters 48 (1995) 179-184
180
Kozicki, 1993). The appealing feature of this procedure is that it generates a unique trend-cycle decomposition of the data, at least in the special case where the number of common trends and common cycles adds up to the number of variables in the data set. Moreover, we need not impose any conditions in order to be able to identify trend and cyclical components, as in the case of other decomposition procedures (see Blanchard and Quah, 1989; and King et al., 1991). Section 2 presents a brief description of the data employed and the results of cointegration and common feature tests. Conclusions and limitations are stated in Section 3.
2. Testing for the number of common trends and c o m m o n cycles
Series used in this paper are those of labor productivity, at the industrial level, of six of the most industrialized western countries (the United States, Japan, Germany, France, Italy and the United Kingdom). Labor productivity series were obtained as the ratio of the yearly industrial production index (1985 = 100) to the yearly industrial employment index (1985 = 100). Both sets of series were primarily obtained from the International Financial Statistics (IFS) data set of the International Monetary Fund (IMF). In some cases, series not available in the IFS data set were obtained from the O E C D data set or from national sources. The sample period is 1953-1991. We chose to work with the industrial productivity series because (a) it generally shows the highest degree of covariability with the overall economy productivity series (i.e. per capita GDP or GNP series); (b) it is more reliable for comparative purposes than per capita GDP series, given the difficulties existing in correctly defining and measuring the concept of productivity for the non-market service industry; and (c) it shows a closer relationship with the concept of technology shocks. We started our analysis running Dickey-Fuller's unit root tests (DF and A D F ) on each national productivity series. Both tests accept the null that series are I(1) at the 5% level. Since all series proved to be non-stationary, we tested for the existence of any cointegration relationships. Following Johansen (1988, 1991), we did find that series are cointegrated. In particular, the specification chosen for the VAR system is that which minimizes the Schwarz Bayesian Information Criterion (SIC); that is, with a number of lags equal to 2. Results from the cointegration procedure are shown in Table 1, from which we see that the data support the Table 1 Johansen cointegration tests Trace test
Max. eigenvalue test
Null hyp.
Statistic
95%
Null hyp.
Statistic
95 %
r r r r r r
41.34 22.06 18.16 11.34 9.50 0.19
39.37 33.46 27.07 20.97 14.07 3.76
r r r r r r
102.58 61.24 39.18 21.03 9.68 0.19
94.16 68.52 47.21 29.68 15.41 3.76
= < < < < <
0 = 1 =2 =3 =4 =5
= < < < < <
0 = 1 =2 =3 =4 =5
G. Calcagnini / Economics Letters 48 (1995) 179-184
181
existence of only one cointegrating relationship (or five c o m m o n trends) among the six variables. 1 Following Bernard and Durlauf (1993), this would imply that the industrial productivity of the six countries does not converge. This result should not be very surprising since it is consistent with national industries characterized by different sectoral structures and, therefore, by different technology shocks. Next, we moved on to test for the existence of c o m m o n cycles. The procedure developed by Vahid and Engle (1993) suggests looking for linear c o m b i n a t i o n s - i n our case, labor productivity growth r a t e s - that are uncorrelated with any linear combination of the R H S variables of the error correction model formed with a n u m b e r of error correction terms equal to the cointegration rank. This is equivalent to imposing a reduced rank condition on the coefficient matrix of lagged labor productivity growth rates and error correction terms. Vahid and Engle suggest performing this reduced rank condition test by canonical correlation analysis. More specifically, the cofeature rank, s, is the n u m b e r of statistically zero canonical correlations, where s ~< N - r (with N equal to the n u m b e r of series), and the n u m b e r of c o m m o n cycles is N - s. The squared canonical correlations and the value of the test statistic for the cofeature rank are reported in Table 2. At the 5% level of significance there are five cofeature vectors, or one c o m m o n cycle. First, we note that r + s = N. Therefore, the trend-cycle decomposition is unique, i.e. performing linear transformations in the cointegrating space, or cofeature space, in isolation will not change the estimated trends and cycle. Secondly, this decomposition gives rise to an interesting economic interpretation. Indeed, if on the one hand, the existence of several c o m m o n trends is likely to be the result of the structural and institutional differences in each country; on the other, the c o m m o n cycle outcome suggests that short-run labor productivity variability may depend upon the same kind of shocks everywhere. We think that innovations in the monetary policy in one (or two) of the six countries here considered (i.e. the United States and Germany) may be regarded as the main source of cycle innovations.2 Moreover, as long as trend and cycle innovations are correlated, innovations in monetary policies may have Table 2 Canonical correlation analysis Null hyp.
Squared correlation
X2 statistic
Degrees of freedom
p-value
s s s s s s
0.00 0.03 0.13 0.18 0.29 0.69
0.001 1.197 6.440 13.609 26.588 59.138
2 6 12 20 30 42
0.9995 0.9770 0.8923 0.8498 0.6448 0.0415
> > > > > >
0 1 2 3 4 5
i Although cointegration residuals from this specification passed the stationary and normality tests, the L j u n g Box Q statistics revealed significant residual correlation. Cointegration residual autocorrelation does not improve in the case of VARs of higher order. 2 As shown by Fiorito and Kollintzas (1993), government s p e n d i n g - a proxy for fiscal p o l i c y - b e h a v e s differently in each country. It is often uncorrelated with and lags the G N P / G D P cycle.
182
G. Calcagnini / Economics Letters 48 (1995) 179-184
Table 3 Trend and cycle innovation analysis
France Germany Italy Japan UK US
Correlation coefficient
t-statistic
Trend (*) innovation
Cycle (* *) innovation
-0.81 - 0.74 -0.77 -0.58 -0.75 -0.64
-8.16 - 6.48 -7.09 -4.21 -6.66 -4.87
0.62 0.73 0.52 0.69 0.94 0.85
0.38 0.27 0.48 0.31 0.06 0.15
*% of the variance of labor productivity innovation attributed to trend innovation. **% of the variance of labor productivity innovation attributed to cycle innovation. an impact on long-run labor productivity as well. How strong this impact is depends on the relative weight of the two types of innovations. Table 3 shows the results of an analysis of trend and cycle innovations. 3 Columns 1 and 2 show the correlation coefficients between the two types of innovations and the associated t-statistic, respectively. Columns 3 and 4 report a principal c o m p o n e n t variance decomposition exercise. Figures are percentages of total variability due to trend and cycle innovations, respectively. We note that (a) trend and cycle innovations show a strong and significant negative correlation and (b) trend innovations are generally more important than cycle innovations, even though the latter have a relevant role in explaining total variance for Italy, France and Japan. If the negative correlation between the two types of shocks means that a 1% increase in the trend innovation will only lead to a 1% increase in the level of labor productivity in the long run (since the short-run dynamics push the productivity towards the other direction) we also notice that the strength of this mechanism is much lower in the United States than in the other countries. In other words, a technology shock gives the American industry a short-run advantage over its competitors. Moreover, the kind of interaction which emerged between the cycle and the trend may represent evidence in favor of the 'opportunity cost' approach to productivity growth (Saint-Paul, 1993). Indeed, this class of models, which insists on intertemporal substitution of productivity-improving activities along the business cycle, predicts that recessions are associated with a higher pace of productivity-improving activities. Finally, we studied the relationship between cycle innovations and different types of shocks traditionally considered as sources of variability in economic activity. In particular, we considered shocks to the monetary policy (real interest rates and real money growth) in the United States and in Germany, and to commodity prices. Results of this correlation analysis are shown in Table 4. Cycle innovations are significantly and negatively correlated to real interest rate innovations in Germany and, more strongly, to real money supply innovations both in the United States and in Germany. Correlations are not significant in the case of the US real interest rate and of commodity price innovations. 3 Trend innovations are calculated by first differencing the estimated labor productivity trend; cycle innovations are the residuals from a regression of the estimated labor productivity cycle on lagged detrended error correction terms.
G. Calcagnini / Economics Letters 48 (1995) 179-184
183
Table 4 Correlation analysis of innovations a
Interest rate innovations-US Interest rate innovations-Germany Money supply innovations-US Money supply innovations-Germany Commodity price innovations
Cycle innovations
t-statistic
-0.08 -0.37 -0.38 - 0.46 0.16
-0.42 -2.07 -2.14 -2.69 0.84
a Real interest rates are calculated as the difference between the yearly discount rates and the wholesale price index growth rates. Real money supply growth rates are calculated as the difference between the yearly Money plus Quasi-Money growth rate and the wholesale price index growth rates. Finally, we calculated the difference between the yearly commodity price index growth rates for the developing countries and wholesale price index growth rates. The source for all series is the IFS-IMF.
3. Conclusions In this paper, we applied a recent t r e n d - c y c l e decomposition technique to labor productivity series in six industrialized countries. A list of the main results includes (a) the t r e n d - c y c l e d e c o m p o s i t i o n is unique since the n u m b e r of c o m m o n trends plus the n u m b e r of c o m m o n features is equal to the n u m b e r of series (or countries) studied; (b) precisely, we d e t e c t e d five c o m m o n trends and one c o m m o n cycle; (c) trend and cycle innovations are significantly and negatively correlated; (d) trend innovations are generally m o r e important than cycle innovations; (e) cycle innovations are significantly and negatively correlated with m o n e t a r y policy innovations. T h e picture that emerges from our evidence shows that there is no convergence a m o n g the industrial sectors and allows for a causal relationship from economic policy decisions to the cycle and to productivity growth. E v e n if these conclusions seem quite robust, evidence should still be treated as tentative.
Acknowledgement Financial support from M U R S T (Ministero dell'Universit~ e della Ricerca Scientifica e Tecnologica) is gratefully acknowledged.
References Bernard, A.B. and S.N. Durlauf, 1993, Convergence in international output, Working Paper, Department of Economics, MIT, Cambridge, MA. Blanchard, O.J. and D. Quah, 1989, The dynamic effects of aggregate supply and demand disturbances, American Economic Review 79, 655-673.
184
G. Calcagnini / Economics Letters 48 (1995) 179-184
Engle, R.F. and J.I. Issler, 1993, Estimating sectoral cycles using cointegration and common features, Working Paper no. 4529, NBER, Cambridge, MA. Fiorito, R. and T. Kollintzas, 1993, Stylized facts of business cycles in the G7 from a real business cycles perspective, European Economic Review (forthcoming). Johansen, S., 1988, Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control No. 12. Johansen S., 1991, Estimating systems of trending variables, Lecture presented at the ESEM 1991, Cambridge UK, Unpublished manuscript, University of Copenhagen. King, R.G, C.I. Plosser, J.H. Stock and M.W. Watson, 1991, Stochastic trends and economic fluctuations, American Economic Review 81, 819-840. Kozicki S., 1993, Techniques for estimating dynamic comovement with an application to common international output fluctuations, Finance and Economics Discussion Series, no. 93-32, Federal Reserve Board, Washington, DC. Saint-Paul G., 1993, Productivity growth and the structure of the business cycle, European Economic Review 37, 861-890. Vahid, F. and R.F. Engle, 1993, Common trends and common cycles, Journal of Applied Econometrics 8, 341-360.