The effects of energy price on energy intensity: evidence from Canadian manufacturing sector

Abstract

This study provides estimates for the long-run elasticity of energy intensity with respect to energy price in Canadian manufacturing industries. The time-series properties of the data are investigated using panel unit root, and the long-run relationships are ascertained based on panel co-integration tests. Estimation of long-run elasticities is then conducted using panel error correction and panel fully modified ordinary least square (PFMOLS) methods. The estimated long-run elasticity is in the tune of −0.4 for the overall manufacturing sector, but there is significant variation across the industries.

Appendix

Panel unit root

The test regression is of the form

$$ \varDelta {y}_{i,t}=\gamma^{\prime }{z}_i+{\rho}_i{y}_{i,t-1}+{\sum}_{j=1}^J{\lambda}_{ij}\varDelta {y}_{i,t-j}+{e}_{i,t} $$

where the lag length is selected by Bayesian information criterion; z _i is a vector of deterministic factors, namely, the individual effects and the time trends, whereas γ′ is a vector of corresponding coefficients. The null hypothesis of unit roots across all panels is tested against the alternative that allows some of the individual series to have unit roots. That is, the null hypothesis is H ₀:ρ _i  = 0 for all i and the alternative is H ₁: ρ _i  < 1, i = 1,…,N ₁; ρ _i  = 0, i = N ₁ + 1,…,N. That is, the alternative says that the series is non-stationary at least in some of the panels. The Fisher-type test statistic is computed under the null hypothesis from the p values of the unit-root test for each cross section. That is, denoting μ _i as the p value of a unit-root test for cross section i; then, we compute μ = − 2 ∑ ^N _i = 1  ln(μ _i ) _, where μ _i is asymptotically chi-squared distributed with 2N degrees of freedom, μ → χ ²(2N), under the null hypothesis H ₀. The Fisher-PP unit-root test in heterogeneous panels uses a non-parametric method of controlling for serial correlation and potential heteroscedasticity in the data series. It considers a non-augmented Dickey-Fuller (DF) test regression and modifies the t-statistic of the ρ _i coefficient so that serial correlation and heteroscedasticity do not affect the asymptotic distribution of the test statistic. The Fisher-PP test is based on the statistic ${\tilde{t}}_{\rho i}\kern0.33em =\sqrt{\frac{{\widehat{\gamma}}_{0i}}{\lambda_i}}{t}_{\rho i}\kern0.33em -\kern0.33em \left(\widehat{\lambda}i\kern0.33em -\kern0.33em {\widehat{\gamma}}_{0i}\right)\ T\kern0.33em \times \kern0.33em \frac{\frac{se\left(\widehat{\rho}i\right)}{s_i}}{\widehat{\lambda}{i}^{\frac{1}{2}}}$, where t _ρi is the usual t-statistic of the coefficient of the lagged dependent variable in the DF test regression; T is the time-series dimension; $se\left(\widehat{\rho}i\right)$ is the standard error the coefficient; $\widehat{\rho}i,\kern0.58em {s}_i$ is the standard error of the test regression; and γ̂ _0i is a consistent estimate of the error covariance in the test regression, computed as ${\widehat{\gamma}}_{0i}\kern0.33em =\kern0.33em \left(T\kern0.33em -\kern0.33em k\right){s}_i^2/T,$  where k is the number of regressors in the test regression that depends on whether a model with or without trend is considered. Specifically, k = 3 if both intercept and time trend are included. The $\widehat{\lambda}i$ term is an estimate of the residual spectrum at frequency zero using, for example, a kernel-based sum of covariance. The truncation-lag parameter for the order of serial correlation can be specified by the Newey-West bandwidth using Bartlett kernel. The critical values for this test are the same as for the Fisher-ADF test.