## 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.

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## Notes

This statement can easily be verified by observing that a change in energy consumption in an industry can be decomposed into changes in energy intensity and output. Defining energy consumption in production as

*E*=*E Y*×*Y*, where*E*is the energy consumption,*Y*is the output, and*E*/*Y*is the energy intensity, we can write the rate of change in energy consumption as the sum of the rates of changes in energy intensity and output: Δ*E*/*E*= Δ (*E*/*Y*)*E*/*Y*+ Δ*Y*/*Y*. For the rate of change in energy consumption to be negative, therefore, either both energy intensity and output should decline or the rate of the decline in one of them must offset the rate of increase in the other. In the context of a growing economy, that is, when Δ*Y*/*Y*is positive, the only mechanism to reduce energy consumption is by achieving a reduction in energy intensity at a faster rate than the rise in output.NAICS stands for North American Industry Classification System.

KLEMS stands for capital, labor, energy, materials, and services.

The responsiveness of investments in efficient energy-using capital has been widely documented in the context of studies on purchase and utilization decisions of certain energy-using equipment and appliances (e.g., Hausman 1979; Dubin and McFadden 1984; Boyd and Karlson 1993; Bento et al. 2006). But notably, there are also a number of research reporting existence of energy-efficiency gap, the difference between the actual level of investment in energy efficiency, and the higher level that could be achieved (Sorrell et al. 2004; Jaffe and Stavins 1994; Jaffe et al. 2004), suggesting existence of untapped energy efficiency improvement potentials.

Services (S) will not be included in this model because we observe in the data set that there is nearly perfect correlation between labor and service price indexes. It is also highly correlated to other input prices (see Table 2).

Cobb-Douglas cost specification is a restricted specification in the sense that it does not accommodate complementary relationships among the inputs. The empirical estimates are, however, not necessarily going to conform to this restriction. We can, therefore, utilize the specification to motivate the empirical relationships.

See Appendix for the technical details.

Stata’s xtpmg command employs the algorithm which begins with initial estimates of the long-run coefficient vector

*θ*_{ i }^{′}. The short-run coefficients and the group-specific speed of adjustment terms are then estimated with iterations continuing until convergence are achieved.The test statistics and their critical values are presented, respectively, in Tables 1 and 2 in Pedroni (1999).

NAICS stands for North American Industry Classification System.

Services consist of the following nine types: communications; finance and insurance; real estate rental; hotel services; repair services; business services, including equipment rental, engineering, and technical services and advertising; vehicle repair; medical and educational services; and purchases from government enterprises.

Phillips-Perron test is robust to structural breaks in the data, a desired feature given that the data used in this study cover periods of structural breaks, notably the significant increase in energy price in early 1970s.

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## Appendix

### Appendix

### Panel unit root

The test regression is of the form

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 2*N* degrees of freedom, *μ* → *χ*
^{2}(2*N*), 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.

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Gamtessa, S.F. The effects of energy price on energy intensity: evidence from Canadian manufacturing sector.
*Energy Efficiency* **10**, 183–197 (2017). https://doi.org/10.1007/s12053-016-9448-5

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DOI: https://doi.org/10.1007/s12053-016-9448-5