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Nagel, K.; Kickhöfer, B.; Winter, M. (2015): Reverse-engineering of the rule-of-half in order to retrofit an
assessment procedure based on resource consumption. Zeitschrift für Verkehrswissenschaft. 89(2015), 3.
pp. 219–239.
Kai Nagel, Benjamin Kickhöfer, Martin Winter
Reverse-engineering of the rule-of-half in
order to retrofit an assessment procedure
based on resource consumption
Accepted manuscript (Postprint)
Journal article |
Reverse-engineering of the rule-of-half in order to retrofit
an assessment procedure based on resource consumption
VON KAI NAGEL, BENJAMIN KICKHÖFER, MARTIN WINTER, BERLIN
1Anschrift der Verfasser:
Prof. Dr. Kai Nagel
Dr.-Ing. Benjamin Kickhöfer
Dr. Martin Winter
Transport Systems Plan-
ning and Transport
Telematic Group
Technische Universität
Berlin
Salzufer 17-19
10587 Berlin
Transport Systems Planning
and Transport Telematic
Group
Technische Universität
Berlin
Salzufer 17-19
10587 Berlin
Workgroup for Infra-
structure Policy
Technische Universität
Berlin
Straße des 17. Juni 135
10623 Berlin
nagel@vsp.tu-berlin.de
kickhoef[email protected]-berlin.de
mw@wip.tu-berlin.de
1. Introduction
Policy measures are usually an attempt to improve the existing system while taking into
account current limiting conditions, and to assure a sustainable development in a changing
environment. In the transport sector, the necessary planning and decision process is sup-
ported by economic appraisal methods (e.g. Pearce and Nash, 1981; Short and Kopp, 2005),
an approach which is widely accepted due to the substantial investment costs of transport
infrastructure.
These appraisal methods vary substantially between countries mainly because of cultural,
historical, and economic differences (Grant-Muller et al., 2001). Several authors reviewed
and compared the appraisal methods from different countries (among others, e.g. Nakamu-
ra, 2000; Hayashi and Morisugi, 2000; Bristow and Nellthorp, 2000; Rothengatter, 2000).
In this context, Hayashi and Morisugi (2000) pointed out the importance of sharing the
methods that are applied in transport project appraisals with scientists and practitioners
from other countries. Olsson et al. (2012) take this recommendation one step further and
implement different countries’ appraisal methods for a specific rail project in Norway.
However, what they call the “German” method is in fact the result of the EU HEATCO
project, which resides in fact on a German server (Bickel et al., 2006), but has otherwise
little to do with the assessment procedure of the German Federal Ministry of Transport.
Daly et al. (2013) confirm that internationally available information on the German proce-
dure is scarce.
With the present paper, we aim at mitigating some of these issues by comparing the cost
benefit analysis (CBA) procedure of the German Federal Transport Infrastructure Plan
(‘Bundesverkehrswegeplan’ or BVWP) to an analysis based on basic consumer theory. The
BVWP is performed every 10 to 15 years by the German federal government, and forms the
decision basis for all major federal investments into long-distance (> ∼50km) surface
transport infrastructure.
2. The German Federal Transport Infrastructure Plan
Historically, the German BVWP assessment procedure is based on the concept of resource
consumption. This concept means that new transport infrastructure causes changes in the
consumption of time, money, safety, environment, etc. Monetized changes of those attrib-
utes are related to the construction and maintenance cost borne by the federal government,
and the resulting benefit-cost ratios provide indicators which help to prioritize investment
decisions (Rothengatter, 2000; BVU et al., 2003).
This assessment approach works well as long as all mode-specific demand remains fixed,
and the remaining question thus is to serve that demand as efficiently as possible. As soon
as demand is assumed to be elastic for the facility under consideration (e.g. when consider-
ing inter-modal interdependences or induced travel), this leads to inconsistencies between
the behavioral model and the evaluation method. The archetypical example is an accelera-
tion of a rail connection, while still remaining slower than the competing road connection.
Any logit model or similar would, in that situation, predict that some users switch from
road to rail. In terms of resource consumption, those travelers would afterwards consume
more time than before; in the absence of additional effects, for those travelers the project
would have a negative benefit according to the resource consumption approach. This is
intuitively not in line with basic consumer theory since in the choice model, there needs to
be a reason for these travelers to change mode. The conceptual shortcoming here is that the
trip by rail causes additional benefits which are not included in the (observed) variables
used for monetization. This shortcoming was, in the German context, pointed out by Helms
(2000), together with a recommendation to use the concept of consumer surplus/rule-of-half
in order to remove those inconsistencies.
There were, in fact, efforts by the Ministry of Transport to improve the assessment of mode
choice and latent demand (induced traffic):
The ministry commissioned a study (STASA et al., 2000, and references therein)
concerning the evaluation of so-called induced traffic (realized latent demand)
based on an advanced system-analytical traffic model (cf. the SILUS model in
NTUA and others, 2000). The parameterization approach developed in that study
was subsequently used in the BVWP 2003. This ignored a suggestion made by
Planco (1999, pp. 210) at the same time. It also ignored the recommendations
made by Helms (2000).
A reassessment of the BVWP 2003 projects, performed in 2010 as part of a regular
reassessment procedure (BMVBS, 2010), uses a version of the rule-of-half, but
only for travel time savings of rail passengers (BVU and ITP, 2010). A similar
procedure is used in the so-called Standardized Assessment (ITP and VWI, 2006),
used for the evaluation of urban public transit projects.
These modifications made the procedure more complex and in consequence more difficult
to handle. In some cases, they were applied to some parts of the procedure but not to others;
for example, the rule-of-half was used for travel times only but not for user prices (see Sec.
5), and it was used for rail passenger traffic but for nothing else.
Winkler (2011, 2012) once more pointed out the shortcomings and once more suggested a
switch to the consumer surplus/rule-of-half. According to this rule, new users of an im-
proved infrastructure gain on the average half of the benefits of existing users (e.g. UK
Department for Transport, 2011; Worldbank, 2005; Bickel et al., 2006, p. 17). The first new
user gains almost as much as the average existing user, while the last new user is almost
indifferent between both alternatives. Assuming linear demand functions, the average new
user gains half of the benefits of existing users. The rule-of-half greatly simplifies the esti-
mation of user benefits, as one only needs the initial and final quantities and the changes in
generalized costs, instead of all demand functions and cross-demand relations (Small and
Verhoef, 2007, p. 183). Even though the rule-of-half is an approximation, it has proved to
be a very powerful tool in project appraisal (Button, 2001, p. 73). Newer research suggests
the use of the logsum term directly derived from the logit model as evaluation measure (e.g.
de Jong et al., 2005; Winkler, 2011).
However, given the nature of the problem here, the issue is not to discuss the limitations of,
or the alternatives to the rule-of-half (for some proposals see e.g. Nellthorp and Hyman,
2001), but rather the question if, and how, the established German assessment procedure
can be made consistent with basic consumer theory. The present paper will propose an
easily applicable procedure to include the logic of the rule-of-half into the existing evalua-
tion approach. We show that the resulting calculation yields the same result as the rule-of-
half while maintaining the rest of the former evaluation method. Additionally, we also give
a behavioral interpretation of the newly introduced correction term that we call “implicit
utility”. Finally, we discuss how the Standardized Assessment for urban public transit pro-
jects (ITP and VWI, 2006) fits into the proposed procedure.
3. Going into the details
3.1 Comparing options a and b
We start by comparing options a and b. In transport, a might be car and b might be train. If
we plot generalized costs vertically, one obtains a diagram like Fig. 1. Here, ta and tb are the
travel times and pa and pb are the user prices (out-of-pocket costs) of options a and b, re-
spectively. The user price, p, can be decomposed into the resource cost, rc, and the produc-
er surplus, ps, where the resource cost is the variable part of the cost of providing the
transport service. In competitive markets, one would have p = rc and thus ps = 0. Since the
competitive market assumption may not hold, we do all our following calculations with the
assumption that the resource cost rc may be different from the user price p.
In the following, we assume that travel times, as well as all other contributions to the gen-
eralized travel costs, are given in monetary units.
3.2 Switching from a to b
Now let us assume that there is an improvement of the travel time of tb, from tb0 to tb1, and
as a result some demand shifts from option a to option b. The diagram would look as in
Fig. 2. We make the assumption that there is no change in generalized cost at the option a,
so the only reaction is a horizontal shift of the demand curve to the left. We also assume
that there are only switchers on option b, i.e. there was nobody on option b before. This is
just for illustration. Note that one needs, to make Fig. 2 possible, a mode choice model that
allows for users to select option a in the first place – i.e. a mode choice model where some
users select an option that does not have the least generalized cost. Logit mode choice mod-
els, for example, display this type of behavior.
3.3 Change in welfare
The standard welfare effects of this infrastructure measure are given by the three dark gray
areas of Fig. 3:
Gain in consumer surplus: ∆𝐶𝑆=1
2×(𝑡0
𝑏−𝑡1
𝑏)× |∆𝑥| – the usual rule-of-half,
with ∆𝑥=𝑥1
𝑏−𝑥0
𝑏=𝑥0
𝑎−𝑥1
𝑎.1
Gain in producer surplus on option b: ∆𝑃𝑆𝑏=𝑝𝑠𝑏× |∆𝑥|
Loss in producer surplus on option a: ∆𝑃𝑆𝑎=−𝑝𝑠𝑎× |∆𝑥|
For this to be valid, it is assumed that the rule-of-half is an applicable approximation, and
that there are no complications such as income effects (Jara-Díaz and Videla, 1989; Her-
riges and Kling, 1999) or income-dependent values-of-time.
3.4 Change in resource consumption
The German national assessment exercise typically computes the change in “resource con-
sumption” rather than the change in welfare. The changes in resource consumption of this
infrastructure measure are the four light gray areas of Fig. 4:
Reduction in time consumption ∆𝑇𝑎=−𝑡𝑎× |∆𝑥|
Reduction in resource costs ∆𝑅𝐶𝑎=−𝑟𝑐𝑎× |∆𝑥|.
Increase in time consumption ∆𝑇𝑏=𝑡1
𝑏× |∆𝑥|.
Increase in resource costs ∆𝑅𝐶𝑏=𝑟𝑐𝑏× |∆𝑥|.
3.5 Comparison
Fig. 5 shows the different areas together in one figure. It is difficult to draw immediate
visual conclusions since the economic benefit is
according to the welfare computation: the dark gray areas on the right minus the
dark gray area on the left
according to the resource consumption computation: the light gray areas on the left
minus the light gray areas on the right.
It is, however, immediately clear that the two computations will, in general, not lead to the
same result: One could, for example, assume a different ta while everything else remains
the same. In consequence, the related light gray area would change while all dark gray areas
remain the same. Hence, the result of the calculation according to resource consumption
would change while the result of the calculation according to welfare computation would
remain unchanged. Thus, in general they cannot yield the same result.
1 We use |∆𝑥| instead of ∆𝑥 throughout this paper to indicate that, for this paper, we always have a positive
number here.
Figure 1: Resource costs (rc), user prices (p), producer surplus (ps), and travel times
(t) of two options a and b.
Figure 2: Including demand curves, an improvement (reduction in travel time) for b,
and switching travelers.
Figure 3: The dark gray areas depict changes in welfare, i.e. the sum of consumer and
producer surplus. A “+” in the shape means that a larger shape increases the benefit;
a “−” in the shape means that a larger shape reduces the benefit.
Figure 4: The light gray areas depict changes in resource consumption. A “+” in the
shape means that a larger shape increases the benefit; a “−” in the shape means that a
larger shape reduces the benefit.
Figure 5: Visual comparison of the calculations according to welfare (dark gray) and
resource consumption (light gray). A “+” in the shape means that a larger shape in-
creases the benefit; a “−” in the shape means that a larger shape reduces the benefit.
Figure 6: Adding the “implicit utility” (gridded). A “+” in the shape means that a
larger shape increases the benefit; a “−” in the shape means that a larger shape re-
duces the benefit.
3.6 Implicit utility
When looking at Fig. 5, it seems that the dark gray and light gray areas complement each
other, with the exception of the area above the Db demand curve. This can be corrected by
including that area into the computation, see Fig. 6. We then have
(𝑟𝑐𝑎+𝑝𝑠𝑎+𝑡𝑎) × |∆𝑥|=(𝑟𝑐𝑏+𝑝𝑠𝑏+𝑡1
𝑏) × |∆𝑥| +𝐶𝑆+𝐺𝑟𝑖𝑑 ,
(1)
where CS is the consumer surplus according to the rule-of-half as defined earlier, and Grid
is the gridded area above Db. From this, we get
𝐶𝑆+(𝑝𝑠𝑏−𝑝𝑠𝑎) × |∆𝑥|=[(𝑟𝑐𝑎−𝑟𝑐𝑏)+(𝑡𝑎−𝑡1
𝑏)] × |∆𝑥| − 𝐺𝑟𝑖𝑑
or
∆𝑊𝑒𝑙𝑓𝑎𝑟𝑒=𝑅𝐶𝐶−𝐺𝑟𝑖𝑑 , (2)
where RCC means “resource consumption calculation”. That is, when the gridded area is
deducted from the result of the resource consumption calculation, the two computations are
equivalent.
An alternative way to express Eq. 1 – better to see directly from Fig. 6 – is
(𝑟𝑐𝑎+𝑝𝑠𝑎+𝑡𝑎) × |∆𝑥|=(𝑟𝑐𝑏+𝑝𝑠𝑏+𝑡𝑏
) × |∆𝑥| + 𝐺𝑟𝑖𝑑,
where 𝑡𝑏
=(𝑡0
𝑏+𝑡1
𝑏)/2is the average travel time before and after the change. This averag-
ing approach can indeed be extended to all variables, leading to
(𝑟𝑐𝑎
+𝑝𝑠𝑎
+𝑡𝑎
) × |∆𝑥|=(𝑟𝑐𝑏
+𝑝𝑠𝑏
+𝑡𝑏
) × |∆𝑥| + 𝐺𝑟𝑖𝑑
or
𝐺𝑟𝑖𝑑=[(𝑟𝑐𝑎
+𝑝𝑠𝑎
+𝑡𝑎
)−(𝑟𝑐𝑏
+𝑝𝑠𝑏
+𝑡𝑏
)] × |∆𝑥|
=[(𝑝𝑎
+𝑡𝑎
)−(𝑝𝑏
+𝑡𝑏
)] × |∆𝑥|. (3)
The final equality stems from the observation that 𝑝=𝑟𝑐+𝑝𝑠.
3.7 Behavioral interpretation of the gridded area: implicit utility
The behavioral interpretation of the gridded area is that there needs to be a reason why
users did not switch from a to b in the first place in spite of the fact that tb + pb is much
smaller than ta + pa. It is plausible to assume that this is caused by some difference in gen-
eralized cost or utility which is not included when considering only travel time and price.
More precisely, the leftmost height of the gridded area is what is missing to make the first
switching user indifferent between the options. Since, in basic consumer theory, that user is
assumed to be indifferent, that height needs to be due to one or more unobserved attributes.
The effect is rather similar to an alternative-specific constant in discrete choice models –
which absorbs all remaining differences in base utility between two options. One could
therefore also speculate that the gridded area should become smaller with the addition of
further explanatory attributes.
4. Adding the implicit utility to the resource consumption calculation
4.1 Approach
The above insights can be used to add a term to the established resource consumption cal-
culation in order to make it consistent with basic consumer theory. From Eqs. (2) and (3),
the correction term is
−𝐺𝑟𝑖𝑑=[−(𝑝𝑎
+𝑡𝑎
)+(𝑝𝑏
+𝑡𝑏
)] × |∆𝑥|=:∆𝑈𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 (4)
This is also what is recommended by Planco et al. (2015), except that in that recommenda-
tion it is assumed that option a is not affected by the measure, and thus the averaging is not
needed for option a, i.e. 𝑝0
𝑎=𝑝1
𝑎=𝑝𝑎
, and the same for 𝑡𝑎.
Note that the correction term, Eq. 4, is much easier to construct—but not necessarily easier
to justify—by recognizing that the first bracket denotes the loss of gross consumer surplus
by leaving the option a, and the second bracked denotes the gain of gross consumer surplus
by going to option b.
A resource consumption table would now look as Tab. 1. There, for completeness, the con-
version rate of travel time into monetary terms, βt, also called “Value of Time” or “Value of
Travel Time Savings”, and the number of switchers, |Δx|, have been included, and it is
assumed that the attributes of option a are not affected by the measure.
Adding these terms up and rearranging leads to a change in welfare of
∆𝑊𝑒𝑙𝑓𝑎𝑟𝑒=[𝛽𝑡×(𝑡𝑏
−𝑡1
𝑏)+(𝑝𝑏
−𝑟𝑐1
𝑏)−(𝑝𝑎−𝑟𝑐𝑎)]×|∆𝑥|
=[𝛽𝑡×(𝑡𝑏
−𝑡1
𝑏)+(𝑝𝑏
−𝑝1
𝑏)−(𝑝1
𝑏−𝑟𝑐1
𝑏)−(𝑝𝑎−𝑟𝑐𝑎)]×|∆𝑥| .
Table 1: resource consumption table
base case
policy case
resource
difference
gain in monetary terms
prod cost 𝑎
𝑟𝑐𝑎×𝑥0
𝑎
𝑟𝑐𝑎×𝑥1
𝑎
−𝑟𝑐𝑎×|∆𝑥|
+𝑟𝑐𝑎×|∆𝑥|
travel time 𝑎
𝑡𝑎×𝑥0
𝑎
𝑡𝑎×𝑥1
𝑎
−𝑡𝑎×|∆𝑥|
+𝛽𝑡𝑡𝑎×|∆𝑥|
prod cost 𝑏
0
𝑟𝑐1
𝑏×𝑥1
𝑏
+𝑟𝑐1
𝑏×|∆𝑥|
−𝑟𝑐1
𝑏×|∆𝑥|
travel time 𝑏
0
𝑡1
𝑏×𝑥1
𝑏
+𝑡1
𝑏×|∆𝑥|
−𝛽𝑡𝑡1
𝑏×|∆𝑥|
impl. utl. diff.
[−(𝑝𝑎+𝛽𝑡𝑡𝑎)
+(𝑝𝑏
+𝛽𝑡𝑡𝑏
)]
×|∆𝑥|
This is, however, exactly the calculation of the rule-of-half:
[𝛽𝑡×(𝑡𝑏
−𝑡1
𝑏)+(𝑝𝑏
−𝑝1
𝑏)] × |∆𝑥|=𝛽𝑡∗(𝑡0
𝑏−𝑡1
𝑏)/2+(𝑝0
𝑏−𝑝1
𝑏)/2] ×
|∆𝑥| is the change in consumer surplus,
[𝑝1
𝑏−𝑟𝑐1
𝑏]× |∆𝑥| is the change in producer surplus on option 𝑏,
[−(𝑝𝑎−𝑟𝑐𝑎)] × |∆𝑥| is the change in producer surplus on option 𝑎.
That is, after including an implicit utility difference according to Eq. 4 into the resource
consumption calculation, it yields the same result as the welfare calculation using consumer
and producer surplus. Or, in other words, the insights provided by the welfare computation
including the rule-of-half were used to retrofit the calculation according to resource con-
sumption in such a way that the result is in line with basic consumer theory.
4.2 Consequences of including the implicit utility into the resource consumption
calculation
The implicit utility difference of switching, and therefore its contribution to the economic
benefit, is
positive if 𝑝𝑏+𝑡𝑏>𝑝𝑎+𝑡𝑎,
negative if 𝑝𝑏+𝑡𝑏<𝑝𝑎+𝑡𝑎.
As a tendency,
a further improvement of an already fast and cheap (train or car) connection will
generate less benefits than with the existing approach, and
an improvement of a slow and expensive (train or car) connection will generate
more benefits than with the existing approach.
That is, including the implicit utility into the German national assessment exercise will, as a
tendency, increase the benefit-cost-ratio for measures that improve below average elements
of the infrastructure to the average. And similarly, it will, as a tendency, decrease the bene-
fit-cost-ratio for measures that improve already above average infrastructure elements.
Improvements here refer to improvements in travel time and travel cost, but Eq. 5 implies
that the analysis would hold for improvements in all considered attributes.
4.3 Advantages and disadvantages
The welfare computation is much simplified if one assumes that a and b are competitive
markets. In that situation, pa − rca and pb − rcb can both be approximated by zero, which
simplifies the computation significantly. The computation according to resource consump-
tion, however, remains at the same level of complexity. This may justify the application of
the welfare computation in situations where the competitive market assumption is assumed
to hold.
If, however, the competitive markets assumption is not applicable, then both computation
paths have a similar level of complexity. In consequence, when there is a tradition of using
the resource consumption approach, the only argument for a move to the standard welfare
approach seems to be international consistency. On the other hand, when staying with the
resource consumption approach, then the existing computational modules, including intui-
tion for most of their numbers, can be kept, and just a term is added. Also, the term has a
plausible interpretation: It is the utility difference of switching to the improved infrastruc-
ture. This becomes, in fact, particularly clear when considering completely new (“induced”)
traffic, i.e. not just a switch from another mode. Here, the utility difference is exactly the
implicit benefit from doing an activity at another location (see Sec. 4.4).
Another advantage of the resource consumption approach, after the correction, is that one
does not need the producer surplus, ps. Clearly, computationally this is just the same as
p − rc, i.e. the difference between the charged price and the resource cost. However, in the
German tradition, there exist already models for p and rc, since p is the out-of-pocket price
that is already used in the mode choice models, and rc is the old resource cost. For ps, in
contrast, there is, e.g., debate of how to include taxes, that is, if “gains to private firms” are
to be accounted in the same way as “gains to government”, or not.
4.4 “Induced” traffic
A welcome consequence of the above retrofitting of the resource consumption approach is
that it also works for so-called induced traffic, i.e. activated traffic demand that was latent
before the infrastructure improvement (more trips, longer trips, completely new trips). On
the one hand, this is to be expected, since the rule-of-half approximates the utility effects of
changes from any alternative, including the alternative of not having made a trip before. On
the other hand, it is instructive to go through the calculation. According to Eq. 4,
∆𝑈𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 =[𝑝𝑏
+𝑡𝑏
] × |∆𝑥|,
since 𝑡𝑎 and 𝑝𝑎 are zero since no trip takes place for that option.
That is, the implicit utility difference for the average new user is exactly as large as the
generalized cost of the travel for the average new user. In other words, the equation yields
an estimate for the implicit utility of additional mobility. As stated, from the perspective of
the rule-of-half this is not a surprise. From the perspective of the German national assess-
ment exercise, it provides a straightforward solution to a situation that is difficult to resolve
otherwise, because in (the basic version of) the resource consumption calculation, any addi-
tional travel just leads to increased resource consumption and thus a negative benefit.
4.5 Additional attributes besides price and travel time
Eq. 4 only includes price and travel time. When looking at the derivation, however, it
should be clear that additional attributes, for example unreliability, can be easily added.
One could also use different monetization approaches for options a vs. b, if the measure-
ment for unreliability underneath is different. The equation then becomes
∆𝑈𝑖𝑚𝑝𝑙𝑖𝑐𝑖𝑡 =[−(𝑝𝑎
+∑𝛽𝑖𝑎∗𝑧𝑖𝑎
𝑖)+(𝑝𝑏
+∑𝛽𝑖𝑏∗𝑧𝑖𝑏
𝑖)] × |∆𝑥|, (5)
where the zi are the various attributes, and the βi are their monetization factors.
5. Partial inclusion of the consumer surplus — The German standardized
assessment for public transit investments
Practitioners have been aware of the problem for a long time. In particular, it was consid-
ered counter-intuitive that persons switching to an improved train connection might reduce
the benefits of a measure (cf. example in Sec. 2). In order to improve upon this, a version of
the rule-of-half was introduced into the process (ITP and VWI, 2006; BVU and ITP, 2010).
What was done is equivalent to using the rule-of-half for the travel times but staying with
resource consumption for the production costs. The result is discussed in Sec. A.
The “story” for this is quite plausible: One the one hand, there is the consumer, and she
reaps the consumer surplus. On the other hand, there is the “producing economy”, and it
needs to spend resources to produce the service. However, the result is not the same as from
the standard welfare computation.
6. Discussion
Different switchers are treated differently in the 2003/2010 BVWP procedure (BVU et al.,
2003; BVU and ITP, 2010).
Passengers switching from road to rail are treated according to the rule-of-half
with respect to travel time (BVU and ITP, 2010). All other attributes are treated
according to resource consumption.
Similarly, induced rail traffic is treated according to the rule-of-half with respect
to the time component (BVU and ITP, 2010).
Passengers switching from rail to road are treated according to resource con-
sumption. It seems that this would imply that the average travel time gain from rail
to road should be counted as a benefit, but this is effectively not included since the
corresponding benefits component (denoted “NE” = Nutzen der Erreichbarkeit) is
computed for existing car users only.
Passengers switching to road are not included into the traffic assignment.
Induced road traffic is treated according to a parameterized approach without
explicitly computing its volumes (STASA et al., 2000).
Freight mode switches in both directions are computed according to resource con-
sumption. Travel time improvements induce mode switches for freight, but the
value of time of freight is set to zero in the benefits calculation.
Freight switching to road is not included into the traffic assignment.
It is assumed that there is no induced freight traffic.
Overall, these different treatments make it difficult to keep track of all the different cases,
and thus to keep the approach consistent. Furthermore, they are a hindrance with respect to
future developments. For example, induced traffic cannot be included into the road assign-
ment, since the additional congestion effects are already contained in the parameterization.
This, however, would make any detailed emissions calculations for those users impossible.
– The approach presented in this paper makes it possible to treat mode switchers and in-
duced traffic explicitly: They would switch according to the mode choice or induced de-
mand model, they would be included into the respective modal assignments, and their ef-
fect would be computed in a plausible way by including the implicit utility difference into
the resource consumption computation. Extra parameterizations and special rules would no
longer be necessary, simplifying the conceptual approach and thus making it more transpar-
ent.
A concern might be that more emphasis should be put on strategic or system aspects
(Rothengatter, 2000; Wissenschaftlicher Beirat, 2010). The present paper is not meant as a
counter-argument to this. Nevertheless, we believe that the cost-benefit-analysis part of the
assessment should be comprehensible and transparent, and an understanding in how far a
procedure is similar or different to other procedures contributes to that. This is what the
present paper concentrates on.
7. Conclusion
The objective of this paper was to propose a way to adapt the current German national CBA
approach for infrastructure projects, which is based on resource consumption, to the inter-
national evaluation standard of welfare computations, in particular to the approximation
based on the rule-of-half. As shown in our calculations, adding an implicit benefit compo-
nent to the resource consumption leads to the equivalence of both approaches. We also
analysed the practical consequences of including these implicit user benefits for the as-
sessment results. With the inclusion of that benefit component, the current evaluation pro-
cedure could largely be kept, while illogical and counterintuitive effects in conjunction with
mode switchers or induced traffic would be avoided.
Acknowledgments
T. Beckers helped by insisting that it should be possible to put the issue into one diagram
(which eventually emerged in the form of Fig. 5). Discussions with H.-U. Mann and P.
Rieken clarified many issues. We also acknowledge a helpful discussion with C. Winkler.
The project was funded in part by German National Science Foundation (DFG) grant NA
682/3-1 ‘Detailed evaluation of transport measures using microsimulation’. Work on this
paper was also motivated by the participation of the authors in the German Federal Ministry
of Transport, Building and Urban Development (BMVBS) project FE 960974/2011: ‘Re-
view and further development of the assessment methodology with a focus on the benefits
components of the benefit-cost-analysis of the German national transport assessment exer-
cise’.
A. German standardized assessment (Standardisierte Bewertung)
Figs. 7 and 8 show an example where the “German standardized assessment” is not con-
sistent with the welfare approach:
Assume 𝑝𝑠𝑎=𝑝𝑠𝑏=0, i.e. prices are competitive and thus there is no producer
surplus.
In consequence, the surplus calculation would only yield the consumer surplus.
Yet there may still be a difference in the resource consumption, yielding a (posi-
tive or negative) contribution in the resource consumption calculation.
Figure 7: Areas that are considered for the benefits calculation in the German stand-
ardized assessment for public transit investments (“standardisierte Bewertung”; see
ITP and VWI, 2006) and in the intermediate revision of the CBA numbers of the
German national assessment exercise (“Bedarfsplanüberprüfung”, see BVU and ITP,
2010). Again, a “+” in the shape means that a larger shape increases the benefit; a “−”
in the shape means that a larger shape reduces the benefit.
Figure 8: “Standardized assessment”, full comparison
What is the explanation for this difference? It might be easiest to understand this from a
comparison with a standard welfare computation, similar to Sec. 3.6. Adding up the areas in
Fig. 8 leads to
[𝑟𝑐𝑎+𝑝𝑠𝑎+𝑡𝑎] × |∆𝑥|=[𝑟𝑐𝑏+𝑝𝑠𝑏+𝑡1
𝑏]× |∆𝑥| + 𝐶𝑆 + 𝐺𝑟𝑖𝑑
or
𝐶𝑆+[𝑝𝑠𝑏−𝑝𝑠𝑎] × |∆𝑥|
=[(𝑟𝑐𝑎−𝑟𝑐𝑏+𝑡0
𝑏−𝑡1
𝑏
2)−𝑡0
𝑏−𝑡1
𝑏
2+(𝑡𝑎−𝑡1
𝑏)−[(𝑝𝑎+𝑡𝑎)−(𝑝𝑏+𝑡𝑏
)]] × |∆𝑥|
or
∆𝑊𝑒𝑙𝑓𝑎𝑟𝑒=𝐺𝑆𝐴𝐶+(𝑝𝑏−𝑝𝑎)× |∆𝑥|,
where 𝑡𝑏
=(𝑡0
𝑏+𝑡1
𝑏)/2 was used, and GSAC means “German standardized assessment
computation”.
That is, while the resource consumption calculation needs to be corrected by [−(𝑝𝑎
+
𝑡𝑎
)+(𝑝𝑏
+𝑡𝑏
)] × |∆𝑥| (Eq. 4), the “standardized assessment” only needs to be corrected
by (−𝑝𝑎+𝑝𝑏)× |∆𝑥| in order to be consistent with the standard welfare computation2.
The consequences of moving the German standardized assessment to the welfare computa-
tion approach would be the following:
Projects where 𝑝𝑏>𝑝𝑎 would improve their benefits-cost-ratio.
Projects where 𝑝𝑏<𝑝𝑎 would decrease their benefits-cost-ratio.
That is, changing the German standardized assessment computation to the welfare compu-
tation approach would, as a tendency, increase the benefit-cost-ratio for improvements of
infrastructure elements that charge above average user prices. And similarly it would, as a
tendency, decrease the benefit-cost-ratio for improvements of infrastructure elements that
charge below average user prices.
A bigger problem may be that the German “standardized assessment” approach still pro-
duces implausible results for induced traffic. Consumer surplus with respect to travel time
is calculated correctly. However, the additional resource cost is deducted from the benefit.
The welfare calculation, in contrast, would include the difference between the additional
resource cost and a (higher) price as positive benefit.
2 or by −(𝑝𝑎
+𝑝𝑏
)×∆𝑥 if one assumes that prices change
8. Abstract
The German evaluation procedure for the Federal Transport Infrastructure Plan (‘Bun-
desverkehrswegeplan’) is a large-scale and comprehensive modeling, simulation, and eval-
uation effort. An important component of the evaluation procedure is a cost-benefit analy-
sis, based on the concept of resource consumption. This concept means that new transport
infrastructure causes changes in the consumption of time, money, safety, environment, etc.
In this paper, we show that — assuming elastic demand for the facility under consideration
— the current approach is not in line with basic consumer theory. This stems from incon-
sistencies between the behavioral model and the evaluation method: ignoring unobserved
attributes of the different transport modes in the evaluation can lead to quite different eco-
nomic gains than when these attributes are considered. Current practice in other EU coun-
tries avoids this problem typically by applying the so-called rule-of-half, or by directly
deriving the logsum term from the underlying logit model. However, a change in the Ger-
man assessment procedure towards one of these best-practice approaches for the upcoming
Federal Transport Infrastructure Plan in 2015 seems politically not feasible. We therefore
propose an easily applicable procedure to include the logic of the rule-of-half into the exist-
ing evaluation approach. We show that the resulting calculation yields the same result as
the rule-of-half while maintaining the rest of the former evaluation method. Finally, we
discuss how another German assessment scheme for urban public transit projects, which is
currently under revision, fits into the proposed procedure.
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