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

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.