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!