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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
• 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
Context
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?
27 models take rebound Approach A
27 models take rebound Approach B
24 static models
24 dynamic models
6 co-integrating models
54 final 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
Coefficients Standard Stability Parsimony Functional Form
Measure
A
Measure
B Measure
A
Measure
B
Measure
C
Measure
A
Measure
B
Measure A
Measure B
Meas
ure C
Measure A
Measure
B
2 points
2 points
2 points
1 point
1 point
2 points
2 points
1 point
1 point
1 point
2 points
2 points
Coefficients Standard Stability Goodness of fit
Measure A
Measure B Measu
re A
Measure A
Measure
A
2 points
2 points
1 point
2 points
1 point
Static and dynamic models
Co-integrating models
Results – rebound (long run)
n = 28
= complex robustness
= simple robustness
Systematic - SATURATING
Results – oil price dummy
Systematic – LINEAR
n = 22
= complex robustness
= simple robustness
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!