Transcript systematic relationships between model robustness and coefficient

Exploring the direct rebound effect:
systematic relationships between model
robustness and coefficient estimates
Lee Stapleton, Steve Sorrell, Tim Schwanen
I was last at the 2007 incarnation of
this conference in Chennai…
Contents
• Headline Summary
• Context
• Methods
• Results
• Implications
Headline Summary
• Rebound estimates vary from 10.6% to 26.8%
(average = 18.1%)
• The estimates are higher when the models are
more robust in a statistical sense
• The estimated effects of other variables (e.g.
income and oil price shocks) also depend on
model robustness
• The correlations between coefficient size and
robustness may have implications for modelling
beyond our study
Context
• Technical improvements lower
transport costs and thereby
encourage increased transport
activity and energy use
• Passengers travel further and more
often in larger, faster, more
powerful and emptier cars
• But establishing causality is difficult
when (i) data are limited and
uncertain (ii) data exhibit limited
change over time (near horizontal
lines in geometric terms); (iii)
appropriate regression methods
are complicated to implement
Methods – data I
Methods – data II
Methods – modelling rebound
• Approach one: how does improved technical
efficiency (declining vehicle fuel intensity and
declining fuel prices) increase how far people
travel (vehicle kilometres travelled - VKM)?
• Approach two: how does improved technical
efficiency (declining fuel costs) increase how far
people travel (vehicle kilometres travelled VKM)?
Methods – model types
• Static regression models: quantify the change
in car travel over time attributable to different
variables
(rebound
variables,
income,
urbanisation and congestion and oil price
shocks)
• Dynamic regression models: acknowledge that
car travel in any particular year is partly
dependent on car travel in previous years
• Co-integrating regression models: in effect,
these are similar to static regression models
but (may be) optimal for ‘trending’ variables
Methods – how many models?
54 final models
27 models take
rebound Approach A
24 static models
24 dynamic models
27 models take
rebound Approach B
6 co-integrating
models
Methods – diagnostics
(static and dynamic models)
• Coefficients: do they behave? [2 tests]
• Residuals: do they behave? [3 tests]
• Stability: are predictions stable? [2 tests]
• Parsimony: is their a sound balance between good
predictions and model complexity? [3 tests]
• Functional form: is the model structure
appropriate? [2 tests]
48 MODELS x 12 DIAGNOSTIC TESTS = 576 TESTS ON STATIC AND DYNAMIC MODELS
Methods – diagnostics
(co-integrating models)
• Coefficients: do they behave? [2 tests]
• Residuals: do they behave? [1 test]
• Stability: are predictions stable? [1 test]
• Goodness of fit: how well does the model match
the data? [1 test]
6 MODELS x 5 DIAGNOSTIC TESTS = 30 TESTS ON CO-INTEGRATING MODELS
Methods - robustness
Methods – robustness composites I
Robustness (health / strength)
Methods – robustness composites II
2
points
1
point
1
point
C
2
points
A
Goodness
of fit
Measure
Stability
A
2
points
2
points
Measure
B
Measure
2
points
A
A
Co-integrating models
Standard
1
point
Measure
Static and dynamic models
Measure
Coefficients
B
2
points
Measure
1
point
A
1
point
Measure
Measure
2
points
Functional Form
Measure
Measure
B
A
Measure
B
A
Measure
C
Parsimony
Measure
B
Stability
Measure
2
points
A
B
Measure
2
points
Standard
Measure
A
Measure
Coefficients
1
point
2
points
1
point
Results – rebound (long run)
n = 28
= complex
robustness
= simple
robustness
Systematic - SATURATING
Results – oil price dummy
n = 22
= complex
robustness
= simple
robustness
Systematic – LINEAR
Results - other
Implications - rebound
•
The size of the long run direct rebound effect for
personal automotive travel in Great Britain
suggested by our results (range = 10.6% - 26.8%;
mean = 18.1%) accords well with previous studies
which have attempted to measure this particular
rebound effect in other country contexts.
•
However, the aggregate rebound effect (including
direct, indirect and economy wide components) is
more important yet extremely difficult to quantify
unacceptable levels of uncertainty.
Implications -methods
• Calls into question the extent to which we
understand different phenomena where that
understanding is predicated upon the
application of explicit methodologies (as,
possibly, opposed to theoretical and tacit
understandings of phenomena)
• Is this a first step towards the construction of
true coefficients / outcomes / results?
Thanks!