Quantifying and decomposing the uncertainty in appraisal value of travel time savings

Institute for Transport StudiesFACULTY OF ENVIRONMENT

Quantifying and decomposing the uncertainty in

appraisal value of travel time savings

Phill Wheat, Senior Research Fellow

and Richard Batley

06/06/2014

Highlights

• Work to quantify uncertainty in appraisal Values of Travel

Time Savings (VTTS) (non-work)

• Important as Travel Time Savings are often major benefits in

transport projects

– Uncertainty in VTTS implies uncertainty in CBAs which could impact

on rankings of projects – at least under sensitivity scenarios

• Statistical exercise, initially to motivate a new VTTS study in

Great Britain

• However in doing the analysis, some wider policy

implications for the best use of scarce research funds have

emerged:

– Do moderate sized VTTS studies often as this minimises uncertainty

in appraisal VTTS

Background – Appraisal VTTS

• Current non-work values in Britain (and general approach

taken in other countries e.g. Switzerland and Netherlands)

are estimated as follows:

– In 1994, Stated Preference data used to form a model for VTTS

Separate models were estimated for Commuting and “Other” leisure

travel.

Base VTTS = [/c].

CInc

C

C

Inc

Inc

00

.. ,

Background – Appraisal VTTS

– An overall distance-weighted average was obtained by weighting the

combinations according to the distribution (for all mechanised modes)

in the NTS 1995-2000 data defined in income and distance bands.

– The base VTTS was then up rated by applying the income elasticity

from a separate meta analysis model – GDP elasticity of 0.8

V =

Incy Dd

dyd

Incy Dd

dydyd

DN

DNV

.

..

8.0

1994

GDP

GDPVVTTSAppraisal t

t

Thus Appraisal VTTS are much more than just the base VTTS – multiple

sources of uncertainty

Research approach

• Construct a confidence interval around the VTTS

estimates

– Interval estimation

– Gives a lower and upper bound estimate for the Appraisal

VTTS for a given statistical confidence level (typically

95%)

• Two stage process utilising both asymptotic

simulation (Krinsky and Robb, 1986) and the delta

method

– Quantifies uncertainty arising from the base VTTS and from the use

of an estimated GDP uprating factor

Results – Commuting All Modes

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080

Valu

e o

f T

ravel T

ime S

avin

g (

pence p

er

min

ute

)

Year

Central VOTT estimate (p/min) Lower 95% CI Bound (p/min) Upper 95% CI Bound (p/min)

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080

Valu

e o

f T

ravel T

ime S

avin

g (

pence p

er

min

ute

)

Year

Central VOTT estimate (p/min) Lower 95% CI Bound (p/min) Upper 95% CI Bound (p/min)

Results – Commuting All Modes

Base VoTT (1994)

has relatively little

uncertainty

associated with it

Given the functional form,

uncertainty becomes

much larger once GDP

moves away from the

base level

NOTE: the larger intervals for later years does not reflect uncertainty in GDP

forecasts, merely the effect of uncertainty in the GDP elasticity estimate

Improving the model

• Two questions:

– What would be the implication for uncertainty in Appraisal VTTS of a

new (base) VTTS study if that study was of a similar accuracy of the

previous study?

– What if such a study resulted in much greater precision (3 times more

precise base VTTS)

• Trade-off:

– More costly one-off study yielding greater accuracy

– Or Greater frequency of smaller scale studies

• Which of the above to go for in terms of spending finite research

funds?

Resampling in 2015

39%

narrower

in 2075

Resampling in 2015 – Improved

Precision

Only 3.4%

narrower

in 2075

Don’t ignore the GDP elasticity in

research…

0.00

10.00

20.00

30.00

40.00

50.00

60.00

1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080

Valu

e o

f T

ravel T

ime (

pence p

er

min

ute

)

Year

Central VoTT Updated Income Elasticity Lower CI Updated Upper CI Updated

Central VOTT Existing Income Elasticity Lower CI Existing Upper CI Existing

20%

narrower

in 2075

Updated GDP elasticity of 0.9 (from 0.8) (Abrantes and Wardman, 2011) (SE

reduced circa 33%)

Summary

• Scheme time saving benefits often arise five or even ten

years after a project begins

• Thus the necessary extrapolation of the base year VTTS to

Appraisal values adds a large degree of uncertainty (over

and above the uncertainty in the original VTTS modelling)

• Resampling is important, but not to get more precise

estimates, more to minimise the extent of extrapolation to

form Appraisal VTTS

– However estimates of base VTTS need to be unbiased

• The uncertainty in the uprating process is important – here

the GDP elasticity

Policy Recommendations

• When faced with a constrained set of research funds:

– Do moderate size resampling exercises frequently

• As opposed to very large size resampling exercises less

frequently

– Continue to review and update the uprating parameters

• Improvements to the precision of these can yield large reductions

in uncertainty of Appraisal VTTS