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