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- 1. 8th IIASA-TITECH Technical Meeting 17th-18th September 2006 Investigating the causal relationships between the efficient use of energy and output growth in Japan Benjamin Warr and Robert Ayres IIASA
- 2. Objectives What are the causality relationships between energy (exergy), useful work and output growth ? Is there evidence of a virtuous cycle of positive feedbacks? Is it possible to restrict exergy (work) consumption without affecting output growth: so-called ‘neutrality hypothesis’ Is there a stable long-run relation between factors of production and GDP ?
- 3. Integration Stationary stochastic processes generate data series that are invariant with respect to time (mean, variance and covariances), they are I(0). Integrated or unit root processes (e.g. a random walk) are non-stationary. If first differences are stationary they are I(1) ‘spurious regression’. Consider yt=α + βxt-1+εt If xt and yt are both random walks and β=0, this equation is spurious, BUT it is common to find β≠0. OLS estimate does not converge to any well- defined population parameter, hence not useful for inference (Granger and Newbold, 1974).
- 4. Cointegration Intuition: if variables are I(1), but trend similarly, they may share a common stochastic trend – they are linked by some long-run relationship. Taking first-differences ‘filters’ the long-run relation, so is not a solution for fitting and hypothesis testing. Cointegration is the statistical expression of equilibrium relationships and analysis methods permit use of non-differenced non- stationary data for regression analysis.
- 5. 2 6 index (1900=1) 0 4 Output and factors of production: Japan 1900 1920 1940 1960 1980 2000 year ln(GDP) ln(capital) ln(labour) ln(useful work) ln(exergy)
- 6. Tests for order of integration (Phillips-Perron) Variable Levels First Differences ln(y) - 1.86 - 8.56*** ln(k) - 1.30 - 4.27*** ln(l) - 1.91 - 8.16*** ln(b) - 1.89 - 3.82*** ln(u) - 1.02 - 4.42*** *** rejection of unit-root hypothesis at 99% significance level.
- 7. Vector Error Correction Models p −1 ∆y t = α ( βy t −1 + µ ) + ∑ Γi ∆y t −1 + v + ε t i =1 β = coefficients of cointegrating equation – long run or error correction (EC) relation α = adjustment coefficients µ = constant in cointegration space v = linear trend in the levels of the data ε = n.i.i.d. error term
- 8. Granger causality (GC) (an example) 1. SHORT-RUN or “weak” G-C: Show that lagged values of ∆Energy (given we know past values of ∆GDP) provide statistically significant information on future values of ∆GDP. Test exclusion of Γ coefficients. LONG-RUN or “strong” G-C: The α coefficients represent how fast deviations from the long-run equilibrium are eliminated following changes in each variable. Joint test of Γ and α coefficients indicates which variables weight this adjustment to establish equilibrium.
- 9. Short-run Causality Japan *** GDP Exergy Work *** *** Capital * Labour
- 10. Long-run Causality Japan *** GDP Work Exergy *** *** *** * * * * * *** * Capital *** Labour
- 11. Summary of results Evidence of short-run and long-run bi- directional causality from useful work to GDP growth. Inclusion of useful work into VECM reveals causality structure. However, has the VECM identified a long-run ‘equilibrium’ between factor inputs and output ?
- 12. Possible structural change in multivariate relation Output and factors of production: Japan (with identified dates of structural change) 6 1925 1944 1958 1973 ln(GDP) ln(capital) 5 ln(labour) ln(work) 4 3 2 1 0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 year
- 13. Dynamic disequilibrium ln(GDP) and cointegrating vectors for models 1a and 1b : Japan (with identified years of structural change) 1.4 4.5 1.2 model 1a 4 model 1b 1 3.5 ln(GDP) deviation from equilibrium 3 0.8 2.5 ln(GDP) 0.6 2 0.4 1.5 0.2 1 0 0.5 -0.2 0 -0.4 -0.5 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 year
- 14. Conclusions Strong bidirectional causality between useful work and GDP growth. Evidence of dynamic multivariate relations between factor inputs and output, but NO LONG-TERM EQUILIBRIUM. ‘Decoupling’ caused by – Level of investment in capital – Shifts in the composition of energy inputs and useful work demand – Improvements in efficiency of energy (exergy) use.

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