Resources and Energy 14 (1992) 259-266. North-Holland

Cointegration tests of energy consumption, income, and employment

Eden S.H. Yu

Louisiana State University, Baton Rouge, LA 70803, USA Chinese University of Hong Kong, N.T., Hong Kong

Jang C. Jin

Kyungnam University, Masan, Kyungnam, South Korea

A recently developed methodology of the cointegration test is employed to determine whether energy consumption has a long-run equilibrium relationship with the level of income or employment. It is found that the long-run equilibrium relationship fails to exist in either case. The finding implies a long-run neutrality of energy consumption, which is consistent with the short-run neutrality found in the literature. The results are further confirmed by splitting the sample into two sub-periods.

1. Introduction

The causal relationships between energy consumption and real income or total employment have been studied for over a decade. Kraft and Kraft (1978), for example, provided evidence that unidirectional Granger-causality runs from GNP to energy consumption. An interesting implication of the finding is that energy conservation would be a feasible policy without creating damaging effects on national income. In addition, Akarca and Long (1979) found that total employment is negatively Granger-caused by energy consumption. This suggests that total employment will rise if the energy conservation policy is implemented.

In contrast to the favorable findings for energy conservation policies, a number of studies support the neutrality hypothesis that energy conservation plays no role in affecting economic activity. For the relationship with real income, Akarca and Long (1980), Yu and Hwang (1984), Yu and Choi (1985), and Erol and Yu (1987a) found no causal relationships between real GNP and energy consumption. For the relationship with employment, Erol and Yu (1987b), Yu, Chow and Choi (1987/1988), and Erol and Yu (1989) found that energy consumption is neutral with respect to total employment. These findings are consistent with the short-run neutrality of energy con- sumption with respect to real income or employment.

01654572/92/$05.00 0 1992-Elsevier Science Publishers B.V. All rights reserved

260 E.S.H. Yu and J.C. Jin, Cointegration tests

Although the short-run independence has recently been supported, the findings will be more convincing if the two variables of interest do not display any reliable long-run relations. Recently, cointegration tests are employed to examine the long-run relations of the variables in several important economic issues [see, for example, Enders (1988), Atkins (1989), and Darrat (1990)]. Undoubtedly, the cointegration test provides insights into the long-run equilibrium relations on which the variables of interest tend to converge over time. Contrary to previous studies - which have concentrated on short-run relations - investigation of the long-run equili- brium relationship is the focus of this study. Using the cointegration test, this paper aims to investigate if energy consumption has, in the long run, a systematic co-movement with the level of either output or employment.

In addition, the impact of oil price shocks on the long-run relationship will be examined. As indicated by Hamilton (1983), oil-price shocks have influenced the U.S. economy significantly. Unfavorable impacts are primarily due to two waves of oil-price increases, one resulting from the OPEC price increases of 1973 and the other from the Iranian revolution of 1979. On the other hand, the low price of oil during the 1980s may have had a favorable impact on the U.S. economy. The positive and negative oil-price shocks that occurred during the 1970s and 198Os, respectively, may have disturbed the long-run relationships, if any, of the variables. Therefore, the two different oil-shock periods will be further examined to ascertain the potential sensiti- vity of the results.

The paper is organized as follows. Section 2 describes the motivation for using the cointegration test in determining the long-run equilibrium relation- ship of the variables. Choice of the data used for this study is also discussed. Section 3 provides the empirical results of the cointegration test. Our findings are consistent with the hypothesis of long-run neutrality of energy consumption. Section 4 presents a brief summary and conclusion.

2. Cointegration and data

2.1. The cointegration test

The concept of cointegration introduced by Granger (1981) and Engle and Granger (1987) is a useful statistical tool to test for long-run equilibrium relationships between non-stationary time series. If two series are individually non-stationary and a linear combination of the two series appears to be stationary, the two series are referred to as being cointegrated. To be specific, the amount by which actual observations temporarily deviate from a constant mean has a fixed distribution that does not change over time. That is, the two variables of interest may wander individually in a short period of time, but the linear combination has no tendency to vary over a long period of time.

E.S.H. Yu and J.C. Jin, Cointegration tests 261

The economic interpretation of such a relationship is that there is a systematic co-movement between the two variables in the long run. For example, energy consumption and income will have an equilibrium relation- ship if energy consumption has a tendency to move toward a fraction of income over time. In this case, temporary supply shocks (e.g., oil embargo) may often disturb a short-run relationship, but the two economic variables will move together in the long run if the two variables are cointegrated.

It should be noted that the cointegration test, unlike the Granger-causality test, does not discern the causal directions between the variables. This disadvantage, however, is far less serious if there are no relationships between energy consumption and income or employment. Given the diversity of plausible results, it is not obvious that a strong short-run relationship exists between the variables. Thus, concerns arise if energy consumption is, in the long run, associated with income or employment. It is for this reason that this paper employs the cointegration test and attempts to investigate the long-run rather than short-run relations of energy consumption. The presence of cointegration between energy consumption and income or employment will imply the existence of the long-run relationship of the two variables; and the absence of cointegration will be consistent with the neutrality hypothesis of energy consumption with respect to income or employment.

2.2. The data

Monthly U.S. data for the period 1974:1-1990:4 are used for the analysis. The data begins in 1974:l since the series for energy consumption is available from this period, and the sample period ends in 1990:4. All series are obtained from the Citibase and are seasonally unadjusted. The data used for the analysis are total energy consumption (EEC) in quadrillion Btu, and the industrial production index of manufacturing (IPMFG6), based on 1987= 100, as a proxy for real income. Real GNP is not used for the real income variable because its monthly series is unavailable and its quarterly series is seasonally adjusted. Also used is the series on total workers on non- agricultural payrolls (L6PNAG) to represent total non-farm employment.

The choice of the data is guided by the necessity of using seasonally unadjusted series in the analysis. As pointed out by Sims (1974) and Wallis (1974), seasonally adjusted data should not be used because they may create distortions in the information content of the raw data and render valid inferences somewhat difficult. Several varied procedures for removing seasonal compo- nents from the raw data may generate different series, depending on the methodology and time periods used. Therefore, use of seasonally unadjusted data is warranted to avoid the smoothing problems inherent in the process of seasonal adjustment.

262 E.S.H. Yu and J.C. Jin, Cointegration tests

3. Empirical results

The test for cointegration consists of two steps. First, a unit root test is conducted, prior to the cointegration test, to ascertain whether each indivi- dual series is integrated of order one (non-stationary). Second, if each series is characterized as non-stationary, the cointegration test will be used to determine whether a linear combination of two non-stationary series is stationary or not.

To conduct the augmented Dickey-Fuller unit root test as a first step, we specify the model used by Wasserfallen (1988). The model is appropriate for seasonally unadjusted series. Each variable is regressed on a constant, a time trend, a lagged dependent variable, and seasonal terms:

p-1

X,=al+M,TZME+ 1 6iDUMi,+rhOX,-l+~l(X,-p-X*-(p+l,) i=l

+P2(xt-1-xt-(p+1))+ t Yjwt-j+% j=l

where X, is the variable in levels under consideration, TIME is a determinis- tic linear time trend, and DUMay i= 1, 2,. . . , p- 1, are monthly seasonal dummies. The seasonal dummy variables are included in the model to capture deterministic seasonality. To allow for stochastic seasonality, we also include seasonal differences [the fifth and sixth terms at the right-hand side of eq. (l)]. The seasonal frequency, p, is set at 12, because monthly data are used [Hasza and Fuller (1982)].

In order to reduce any possible serial correlation of residuals, the model also posits w, =( 1 -L)( 1 - Lp)X, where L is the lag operator and p is again 12 months. The lag length, 4, is set at 13, so that residuals E, are white noise. The Ljung-Box Q statistic is used to test against high-order serial correlation of the residuals. The marginal significance levels of the Q-statistics range between 0.61 and 0.98, indicating that the serial correlation problem appears not serious. Choice of other lag lengths merely reduces the significance levels of the Q-statistics.

The null hypothesis in this regression is that the autoregressive process contains one unit root, i.e., H,: rho= 1. The null of one unit root is tested against the stationary alternative. Test statistics are calculated by subtracting one from the estimated coefficient and dividing this by the estimated standard error of the coefficient. Since the test statistics are not exactly distributed as conventional t-statistics, Fuller (1976) uses Monte Carlo experiments to tabulate the critical values of the test statistics. For the sample size (T= 170), the critical values are approximately -3.46 and -3.16 at 5% and 10% significance levels, respectively.

E.S.H. Yu and J.C. Jin, Cointegration tests 263

Table 1

Unit root test.=

Variable

Estimated coefficient of ‘rho’

1976:s1990:4 1976:s1981:3 1983:61990:4

EC 0.92( - 1.39) 1.09( 0.39) 0.71( - 1.20) IP 0.95( -2.20) 0.95( -0.42) 0.49( - 3.27) EMPL 0.971-2.61) 0.88( -2.24) 0.511-2.90)

“The variables used are energy consumption (EC), industrial production (IP), and total non-farm employment (EMPL). For each sample period, 26-month data were lost as pre- sample periods due to the characteristics of a lag-structured model. The numbers in parentheses beside the estimated coefficients are t-values under the null hypotheses H,: rho= 1. The critical values for the unit root test are approximately -3.46, -3.50, and -3.49 for the sample sizes of T= 170, 61, and 83, respectively, at the 5% significance level [Fuller (1976, table 8.5.2)].

The results for the entire sample period are presented in the first column of table. 1. All series are transformed to natural logs, and the model for each variable is estimated by least squares. For all variables, the null hypothesis of one unit root cannot be rejected even at the 10 percent significance level. This suggests that all individual series in log levels are non-stationary.

For the robustness of the results, the sample is split into two sub-periods, based on an oil-price spike in March 1981. Since then, the price of oil falls consistently. The most recent experience of oil price uprising is out of the ordinary, and for the purpose of this study, the sample period ends in April 1990. The sample period prior to April 1981 represents the increasing period of oil prices, whereas the sample period beginning from April 1981 represents the decreasing periods of oil prices. These two sub-periods are well character- ized by the two distinct oil-price movements.

The second and third columns in table 1 report the results of the unit root test for these two sub-periods. As expected, each variable behaves slightly differently. In particular, the test statistic for energy consumption series during the sample period prior to April 1981 appears to be positive. Although the positive sign is quite possible if the estimated coefficient, rho, is greater than one, the null hypothesis cannot be rejected because the unit root test is a one-tail test and the positive t-value still remains in the area of accepting the null hypothesis. The overall results indicate that all series appear to be non-stationary in log levels.

The cointegration test then evaluates whether the non-stationary series in levels is cointegrated with other non-stationary series. Utilizing the technique of Engle and Granger (1987), the cointegration test is performed by regressing the following two equations separately:

p-1

X,=~11+~(2 TIME+ C 6iDUMi,+U,Y,+U,, i=l

(2)

R.E. C

264 E.S.H. Yu and J.C. Jin, Cointegration tests

Table 2

Cointegration test.’

Cointegrating variables

Estimated coeffkient of ‘rho’

1976:3-1990:4 1976:3-1981:3 1983:6-1990:4

EC,lP 0.84( - 1.74) 0.72( - 1.31) 0.86( -0.83) EC, EMPL 0.85( - 1.89) 0.78( - 1.27) 0.69( - 1.48)

“See note to table 1. The smallest and largest critical values for the two-variable cointegration test are -3.17 and -3.29 at the 5% significance level [Engle and Yoo (1987, table 3)J.

where X, is energy consumption in log levels being tested for cointegration with another variable Y,. An intercept, a deterministic time trend, and deterministic seasonal dummies are also included in eq. (2), a so-called cointegrating regression. Then, the residuals u, from the cointegrating regression are used in eq. (3) for the augmented Dickey-Fuller test of the residuals. The unit root regression uses the same seasonal frequency (p= 12) and the same lag length (q= 13) as in the previous unit root test, and u, denotes a white-noise disturbance term.

The test for cointegration is a two-step procedure. First, the cointegrating regression uses real income or total employment as an independent variable Y,. As indicated by Engle and Granger (1987), least squares provide a consistent estimator of the coefficients, and thus the model is estimated by OLS. At the second stage, a unit root test is performed using the residuals of the cointegrating regression. The second step appears similar to the unit root test discussed above, but there are two notable differences: (a) the cointeg- ration test uses the residuals from the cointegrating regression to test for the presence of a unit root, and (b) the unit root regression excludes an intercept, a deterministic time trend, and seasonal dummies.

The null hypothesis of no cointegration (i.e., H,: rho= 1) is tested against the stationary alternative that the two variables are cointegrated. Test statistics are computed in a similar fashion to the ones for the unit root test. The critical values for the cointegration test are tabulated by Engle and Yoo (1987). For the sample size (T= 170), the critical values are approximately - 3.20 and -2.95 at 5% and 10% significance levels, respectively. Although Engle and Yoo did not include deterministic trends and seasonal dummy variables in their cointegrating regression, their table can be used as an approximate indication of the critical values.

Table 2 reports test statistics for two relations: (a) cointegration between

E.S.H. Yu and J.C. Jin, Cointegration tests 265

energy consumption and industrial production, and (b) cointegration between energy consumption and total non-farm employment. The first column in table 2 shows that for the entire sample period, the null hypothesis of no cointegration cannot be rejected even at the 10% significance level. The two sets of variables appear not to be cointegrated. This implies that energy consumption has no long-run equilibrium relationship with either the level of real output or total non-farm employment.

Our finding is convincing even when the sample is split into two sub- periods. The second and third columns in table 2 indicate that no test statistics are, in absolute values, greater than the critical values of the one- tail cointegration test, This suggests that a linear combination of the two variables is not stationary over time, and thereby no long-run equilibrium relationship exists between energy consumption and output or employment. The results reported here should not be surprising in view of the earlier findings of short-run neutrality by Erol and Yu (1989), among others. The long-run results of the implied neutrality of energy consumption is simply consistent with the short-run neutrality found in the literature.

4. Conclusion

A recently developed methodology of the cointegration test was employed to determined if energy consumption has a long-run equilibrium relationship with the level of real output or employment. In order to avoid the smoothing problems inherent in removing seasonal components from the raw data, seasonally unadjusted series were used for the test of cointegration.

We have found that the long-run equilibrium relationship fails to exist between energy consumption and the level of real output or employment. For the entire sample period, no cointegration was detected between the variables over time. The results were further confirmed when the sample was split into two sub-periods of increasing and decreasing oil prices. The findings of no cointegration over varied sample periods lead us to conclude that energy consumption is, in the long run, neutral with respect to real income or employment. The implied long-run neutrality of energy consump- tion is consistent with the previous findings of short-run neutrality in the literature. Thus, an energy conservation policy may not be instrumental in affecting economic activity.

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