Warr 8th Iiasa Titech Technical Meeting

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Investigating the causal relationships between the efficient use of energy and output growth in Japan

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Warr 8th Iiasa Titech Technical Meeting

  1. 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. 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. 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. 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. 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. 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. 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. 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. 9. Short-run Causality Japan *** GDP Exergy Work *** *** Capital * Labour
  10. 10. Long-run Causality Japan *** GDP Work Exergy *** *** *** * * * * * *** * Capital *** Labour
  11. 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. 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. 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. 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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