Microeconomic Interpretation of MATSim for Benefit-Cost Analysis [original]

CHAPTER 51

Microeconomic Interpretation of MATSim for

Benefit-Cost Analysis

Benjamin Kickh¨

ofer and Kai Nagel

This chapter explains how MATSim’s agent-based framework can be interpreted from a micro-

economic perspective and how it can be used for the economic evaluation of transport policies,

e.g., for BCA (Benfit-Cost Analysis). The text of this chapter is partly taken from Kickh¨

ofer (2014,

Section 2.3).

Typically, the process of economic policy evaluation consists of three steps: First, forecasting

changes in the system by modeling users’ reactions to a policy (Section 51.1). Second, assigning

some (potentially monetary) valuation to these changes (Section 51.2). And third, applying an

appropriate aggregation rule (Section 51.3). As will be shown in the next sections, these steps are

neither completely independent nor completely dependent on each other.

51.1 Revisiting MATSim’s Behavioral Simulation

Estimating policy intervention benefits relies on a sound descriptive model able to predict indi-

viduals’ related behavioral changes. As explained in Section 1.2, agents in MATSim optimize their

mobility behavior over several iterations by reacting to the behavior of other agents. Even if one as-

sumes homogeneous individual preferences in the behavioral parameters of their utility functions

(see Section 3.4), activity locations and activity patterns of agents typically differ, meaning that

the simulation deals with heterogeneous decision makers. It thus seems reasonable to interpret the

simulation from a discrete choice modeling perspective (see Chapter 49). Another attractive rea-

son to use this interpretation lies in the well-established approaches to estimate user benefits and

system welfare changes in discrete choice models.

How to cite this book chapter:

Kickh¨

ofer, B and Nagel, K. 2016. Microeconomic Interpretation of MATSim for Benefit-Cost Analysis.

In: Horni, A, Nagel, K and Axhausen, K W. (eds.) The Multi-Agent Transport Simulation MATSim,

Pp. 353–364. London: Ubiquity Press. DOI: http://dx.doi.org/10.5334/baw.51. License: CC-BY 4.0

354 The Multi-Agent Transport Simulation MATSim

As shown by Nagel and Fl¨

otter¨

od (2012, also see Chapter 47 and Section 49.1.1), the MATSim

choice model is equivalent to a standard MNL model under the following two conditions: first,

valid choice sets have been found for all individuals; second, the score of each plan has con-

verged to its expectation value (self-consistent state). An approximation of this can be reached

by switching innovation off (Section 4.5.3) and forcing scores to convergence (Section 3.3.4, also

see Section 49.1.1). Still, the following methodological issues remain:

1. Choice set incomplete: The maximum number of plans Jin each agent’s choice set is

limited by memory constraints; the choice set for decision making is, hence, unlikely to be

complete.

2. Plans correlation from innovation: Plans might be correlated. This is very likely if they are

modified or replaced by best-response re-planning modules (e.g., the route choice module),

since they always have a tendency to generate the same answer. However, random muta-

tions, in general, also tend to result in correlated plans, since the concept of a mutation

implies only a small move away from the parent. This violates the required IIA (Inde-

pendence from Irrelevant Alternatives) property of the choice set necessary for a MNL

model.

3. Plans correlation from plans removal: The current MATSimimplementation has a tendency

to retain similar, i.e., correlated, plans when the number of plans has grown beyond J, because

the current default plans remover deletes the plan with the lowest score, which is also typically

most different from other plans. As a result, normally only very similar plans—with very

similar scores—remain in the choice set.

These three issues can lead to biased behavior, which would have consequences for economic

evaluation. Possible solutions for these shortcomings are discussed in Section 49.2, and again, from

a different angle, in Section 97.3. For the rest of this chapter, it will be assumed that the above issues

are solved, and that a consistent solution has been found for the system states before and after the

policy change. However, the following text briefly discusses possible impacts of the above issues on

policy appraisal results, to facilitate better understanding.

51.2 Valuing Human Behavior at the Individual Level

Following de Jong et al. (2007), a major advantage of the agent-based approach is a seamless

integration of (i) forecasting behavioral changes as a reaction to changes in the system, and (ii)

the subsequent economic evaluation. In this section, it is shown how estimated agent-specific pref-

erences, which determine behavior, can directly be used for deriving individual VTTSs and how

they need to be modified for running a MATSim simulation to obtain individual utility differences

resulting from a policy change. The next Section 51.3 will then focus on how these individual

utility changes can be used to derive an indicator of overall welfare change for the considered

population.

51.2.1 The Utility of Time

The MATSim scoring function of plan (= alternative) iconsisting of q=0..N−1 activities and

trips has been introduced in Chapter 3 in the following form:

U=X

Uact,q(tdur,q,...) +X

Utrav,q(ttrav,q,...) , (51.1)

Microeconomic Interpretation of MATSim for Benefit-Cost Analysis 355

where monetary payments (e.g., tolls) are included in Utrav,qand the index iwas dropped for

notational convenience.1

An approximate argument about optimal time allocation can be made as follows: Assume

the constraint T−Pqtdur,q−Pqttrav,q=0, i.e., that the time per day is limited by T=24h, dur-

ing which all trips and activities need to be completed. Let us now also assume that all travel times

are fixed; i.e., we ignore the possible optimization from departure time or mode switches and con-

centrate on the activity time allocation problem. Optimizing under this constraint leads to the

Lagrangian

L=X

Uact,q(tdur,q,...) +X

Utrav,q(ttrav,q,...) +µ·(T−X

tdur,q−X

ttrav,q) , (51.2)

where µis the Lagrangian multiplier corresponding to the time constraint.2

Solving the optimization problem leads to

=∂L

∂tdur,q

=U0

act,q(tdur,q,...) −µ (∀q)(51.3)

and the time constraint equation from above, where U0

act,q:=∂Uact,q/∂tdur,q. Equation (51.3)

states that, at the optimum and without further constraints, the tdur,qneed be selected for all

activities qsuch that all U0

dur,q(tdur,q,...) are the same and equal to µ.

Equation (51.2) can also be seen as a linearized version of the indirect utility function; for ex-

ample, reducing travel duration by 1tqaffects not only Utrav,q, but will also lead to a utility change

of µ·1tqfrom the constraint, which can be interpreted as the linearized utility effect of spending

that time otherwise.3In consequence, the marginal utility of time spent traveling reads

∂L

∂ttrav,q

=U0

trav,q(ttrav,q,...) −µ . (51.4)

µis the marginal utility of time as a resource—the marginal utility generated by increasing T,

i.e., by making the day longer than 24 hours. The marginal utility of time spent traveling is thus

determined by µ, modified by “any enjoyment or dislike of the travel itself” (Small, 2012).

To get a handle on the MATSim utility function in Equation (51.1), µand U0

trav,qneed to be

obtained separately: µin order to calibrate U0

act,qas in Equation (51.3) and U0

trav,qto calibrate the

direct utility of time spent traveling, the offset to the marginal utility of time as a resource. This

will be further discussed in Section 51.2.4.

51.2.2 The Utility of Money

Time allocation theory (DeSerpa, 1971; Jara-D´

ıaz and Guevara, 2003) makes a similar argument

for money, with a budget constraint similar to the time constraint. Just as the time constraint leads

to a marginal utility of time as a resource, the budget constraint leads to a marginal utility of money

as a resource.

1Strictly speaking, at this point, it would make more sense to stay with the scores Sthat MATSim generates.

Section 51.2.5 discusses the relation between MATSimscores S, systematic utility Vand total utility Uin more detail.

However, since the following text uses terms like “marginal utility of time” or “marginal utility of money”, equations

are also noted using Uinstead of S.

2This should not be confused with the scale parameter from discrete choice theory; here, to be consistent with time

allocation theory, µrepresents the marginal utility of time as a resource and corresponds to βdur in Chapter 3.

3A reminder: the indirect utility function describes utility as a function of the value of the constraint that emerges

when, for each value of the constraint, utility is maximized.

356 The Multi-Agent Transport Simulation MATSim

However, MATSimdoes currently not include such a monetary budget constraint. It is also ques-

tionable whether it should be introduced: the typical theoretical argument assumes the possibility

of increasing one’s income by working more hours. It is questionable if this functions in European

countries, where work contracts typically include a fixed number of working hours, which cannot

easily be changed. Hence, an alternative derivation of the marginal utility of money is necessary.

Assume that Utrav,qincludes a change in the monetary budget, λ·1m, e.g., invoked by fares or

tolls. Then ∂U

∂m=∂Utrav,q

∂m=λ, (51.5)

that is, reducing the monetary budget by 1mreduces the utility by λ·1m. We will therefore inter-

pret λas the marginal utility of money.4Taking the first derivative of Lwith respect to mwould

lead to the same result.

In contrast to the marginal utility of time above, we do not break down the marginal utility of

spending money for travel into a marginal utility of money as a resource, and an offset for spending

money on a particular purpose (for an example of this decomposition, see, e.g. Munizaga et al.,

2008). Because there is no monetary budget constraint, there is also no neutral Lagrange multiplier

that would give the marginal utility of money as a resource.

This, however, leads to the problem that if there are multiple monetary channels, they may have

different marginal utilities of money. For example, the marginal utility of toll payments is larger

than the marginal utility of payments for fuel—i.e., people find it less irritating to pay for fuel than

to pay tolls (see, e.g., Vrtic et al., 2008). That is, each monetary channel, such as fuel cost, toll, public

transport fare, or a toll refund, may lead to different preference estimates.

To our knowledge, there is no best solution to this problem in the literature. For the time being,

we work with forcing all alternatives’ cost-related parameters to a uniform value in preference es-

timation. However, choice modelers typically avoid limiting the model’s degrees of freedom in this

way, since it suppresses some information contained in the data.5It is therefore often impossible

to obtain necessary parameter estimates from the literature. Where raw data is available, the same

model can be re-estimated with a uniform marginal utility of money across alternatives (see, e.g.,

Kickh¨

ofer et al., 2011; Tirachini et al., 2014).

Also, Small (2012) points out that the “neutral” marginal utility of money as a resource is difficult

to estimate; for example, it is not the marginal utility of income. As an alternative research avenue,

we could hypothesize that a measure’s monetary channels are included in the choice experiment.

For example, a travel time improvement in a value-of-time study could come together with a hy-

pothetical income tax increase, or with a hypothetical toll. A rudimentary version of this actually

takes place in Switzerland, where large infrastructure investments are bundled with tax increases

that pay for them before they are put to public vote (see, e.g., BAV, 2013).

51.2.3 Value of Time

The VTTSof trip qis now defined as the marginal utility of time spent traveling (Equation (51.4)),

divided by the marginal utility of money (Equation (51.5)), i.e.,

VTTSq=∂L/∂ttrav,q

∂L/∂m,(51.6)

4This constant, potentially person-specific, implies that income effects (Herriges and Kling, 1999; Daly et al., 2008;

Dagsvik and Karlstr¨

om, 2005; Jara-D´

ıaz and Videla, 1989) do not play a role, i.e., that changes in expenses resulting

from transport policies are not strong enough to change λ. In microeconomic theory, λis the usual variable for the

marginal utility of money and corresponds to βmin Chapter 3.

5J. de Dios Ort´

uzar, personal communication.

Microeconomic Interpretation of MATSim for Benefit-Cost Analysis 357

where we are using the indirect utility function since we assume that the traveler compares optimal

allocations before and after the change.

With ∂L/∂ttrav,q=U0

trav,q−µfrom Equation (51.2) one obtains

VTTSq= −U0

trav,q

λ+µ

λ,(51.7)

µ/λ is sometimes called the value of time as a resource.

51.2.4 From Estimated to MATSim Parameters

As stated above, most value of time studies do not separately estimate µ,λ, and U0

trav,q(∀q). Assume

that an MNL estimation of behavioral parameters from a mode choice survey between car and PT

uses the following utility functions:

Ucar,q=ˆ

βtrav,car ·tcar,q+ˆ

βm·1mcar,q

Upt,q=ˆ

β0+ˆ

βtrav,pt ·tpt,q+ˆ

βm·1mpt,q,(51.8)

where tcar,q,tpt,q,1mcar,qand 1mpt,qare, respectively, travel times and monetary costs in the

different modes, and ˆ

βxare the corresponding parameter estimates As explained in Section 51.2.2,

βm(the same as λabove) is assumed to be the same for all modes, or more precisely, for all types

of expenditure.

According to Equation (51.4), the marginal utility of time spent traveling needs to be split into

two components:

1. The marginal utility of time as resource, which needs to be used for U0

act(tdur,q,...) (∀q)in

Equation (51.3).

2. The direct marginal utility of time spent traveling, which needs to be used for

trav,q(ttrav,q,...).

We do not know of any good way to perform this split; Kickh¨

ofer et al. (2011) and Kickh¨

ofer

(2014) use the least negative ˆ

βtrav,mode for µ(i.e., βdur) and then re-calculate all other direct

marginal utilities of travel time relative to that. As indicated in Section 3.4 of this book, this is

currently the preferred procedure.

51.2.5 From Simulation Output to Evaluation

At the end of the simulation run, each agent nhas a number of plans i=1..J, each of them as-

sociated with a score Sn,i, computed according to Equation (51.1). For economic evaluation, the

question arises how to aggregate these Sn,iinto an agent-value Sn, which can then be interpreted

as a utility Un. Possibilities include using:

•the logsum of the agent’s plans scores, i.e., lnPieSi

•the score of the agent’s last executed plan,

•the average of the agent’s plans scores, or

•the highest score of the agent’s plans.

51.2.5.1 Using the Logsum of the Agent’s Plans Scores

In literature, the logsum term

logsumn=lnX

eVi

358 The Multi-Agent Transport Simulation MATSim

has been proposed for applied welfare analysis with Discrete Choice Models (Small and Rosen,

1981; de Jong et al., 2006; Kohli and Daly, 2006; de Jong et al., 2007). Under the assumption of a

correctly specified model and choice set, the logsum term represents the EMU (Expected Max-

imum Utility) for a user with several options i=1..Jin her choice set and the systematic utility

of each option iis Vi. It is the expectation value, given that a random (Gumbel-distributed) εiis

added to each Vi, and that the individual chooses the alternative with the highest Ui=Vi+εi.6In

this interpretation, the (expected/average) MATSim score Siis equated with the systematic part of

the utility Vi.

However, as described in the previous Section 51.1, the use of MATSim as choice set generator

yields issues with incompleteness of the choice set and with similarity of daily plans. In the current

MATSim implementation, the maximum error occurs when all plans are copies of the best plan,

rather than a diversity of plans. An upper bound of this error can be approximated as follows.

Without loss of generality, assume that i=1 is the plan with the largest systematic utility. Then

logsumn=EMUn=ln

i=1

eVi≤ln

i=1

eV1=ln(J·eV1)=lnJ+lneV1=V1+lnJ.

At the same time, obviously

logsumn=EMUn=ln

i=1

eVi≥lneV1=V1.

Overall,

V1≤logsumn≤V1+lnJ.

That is, for a choice set with Ialternatives, the true logsum value lies between the systematic utility

of the best option, V1, and V1+lnJ.

51.2.5.2 Using the Score of the Agent’s Last Executed Plan

Using, for each agent, the logsum over the scores of all plans implies that all these plans are valid

behavioral choices. An alternative would be to simply use the score of the last executed plan. The

behavioral interpretation consistent with this procedure is that there is no additional relevant ran-

domness beyond what MATSim generates intrinsically. There has been no systematic work in this

direction in the MATSim context, but such an approach might be justified in conjunction with

the idea of explicitly generating the missing εn,ifor each person-alternative-pair n,i, then always

selecting the best plan, as described in Section 97.4.6.

51.2.5.3 Using the Average of the Agent’s Plans Scores

In principle, it is also possible to use

Sn=1

i=1

Sn,i·Pn,i,(51.9)

where Pn,iis the probability of plan ifor agent n. This can, however, only be justified when the

choice probabilities, Pn,i, are interpreted like mixed strategies from game theory, i.e., that sam-

pling from these probabilities is the true agent behavior. In principle, we cannot see why such an

6At this point, we assume that Viis absorbing the scale parameter.

Microeconomic Interpretation of MATSim for Benefit-Cost Analysis 359

interpretation should be plausible—except that it is statistically the same as Section 51.2.5.2 with

the advantage of having less variance. Note, however, that the approach is intertwined with the

choice model. If, e.g., Pn,iis one for the plan with the highest score and zero for all other plans,

then Section 51.2.5.2 and Equation (51.9) are identical.

51.2.5.4 Using the Highest Score of the Agent’s Plans

Alternatively, one could simply use the highest score that the agent has in its plan. This would only

make sense if true behavior is assumed to always select the plan with the highest score. Again, this

should then also be expressed by the choice model, i.e., using the highest score only makes sense

when the agent always selects the plan with the highest score, in which case the result becomes the

same as Section 51.2.5.2 and 51.2.5.3.

51.2.5.5 More Complicated Variants

Section 49.1.2 discusses the idea that MATSim’s typical choice model might be described by a

mixture-of-logit model. In that model, ni remains fixed per agent nand alternative i, but other

attributes such as the network conditions vary from one iteration to the next. In Equation (49.5),

ηni denotes these random, but simulation-generated, deviations from the average conditions; let

us add an index kfor the iteration number, i.e., write ηk

ni. That is, it is postulated that a real person

would know both ni and ηk

ni, but the simulation only knows the latter (through the MATSim

score). Equation (49.5) then just describes the resulting choice distribution from what MATSim

often does, i.e., apply a logit model to scores that are not averaged.

At least for ηk

ni that are uncorrelated from one iteration to the next it is, however, clear that this

will not result in optimal average agent behavior – the agent may be pushed towards some choice by

a random fluctuation of the ηk

ni, but obtaining a much lower score from that choice in the average.

Overall, the agent would be better off by first averaging the score of each alternative over many

iterations, and then basing her choice on those scores. This goes back to the converged scores of

Section 49.1.1.

Calculating benefits from a mixture-of-logit interpretation becomes thus rather involved: we

postulate that the agent sees the full MATSim score, plus some private s; that she optimizes based

on the sum of these two; that the MATSim simulation, however, does not know the s and thus

has to sample from the logit model; but that the economic utility has to include the effect of the s

although we do not know them, as in Section 51.2.5.1. Overall, thus, assigning utility values to such

behavior as described by Equation (49.5) requires a better understanding of underlying behavioral

rationality. Section 97.4.6 discusses this further.

51.2.5.6 Summary

Overall, there seem to be two consistent strategies to aggregate various plan scores of an agent n

into one value:

•If the choice model is a logit model, then using the logsum term over all plan scores as the

agent’s utility Uiis consistent with the choice model.

•If the choice model is such that the plan with the highest score is selected, then using that score

as the agent’s utility Uiis consistent with the choice model.

In both cases, the choice model needs to be consistent with the behavioral assumption about the

agent, i.e., in the first case it needs to be assumed that the model does not know the true agent

choice beyond the choice probabilities and the model system thus has to repeatedly sample from

these probabilities. In the second case it needs to be assumed that the randomness has already been

“frozen” into the score computation (see Section 97.4.6) and the agent thus selects the plan with

the highest score.

360 The Multi-Agent Transport Simulation MATSim

In both cases, the calculated individual score differences that result from a policy measure can

be directly used in order to identify winners and losers.

Some economists claim that the modeler’s task of providing information for decision support

ends at this point (Ahlheim and Rose, 1989). However, in practice, some (monetary) valuation of

the resulting behavioral changes is often required. The next section reviews different possibilities

to monetize and aggregate individual utility differences in the MATSim context.

51.3 Aggregating Individual Values

After having obtained the individual changes in terms of utility, it is often necessary to convert

these utility changes into monetary terms for economic evaluation, e.g., in BCA. Unfortunately,

no “correct” monetization or aggregation approach exists for individual utility differences. This is

reflected by the ongoing discussion7between transport policy appraisal experts:

1. The first stream argues in favor of a consistency in values used in demand modeling and ap-

praisal (Grant-Muller et al. (2001, p.255), Bickel et al. (2006, p.S4 and p.S8), and Proost8).

Values from literature should only be used if behavioral model values are not available. These

researchers are, however, aware that this procedure potentially limits the comparability of

projects in different regions of the same state, or in different member states of the EU (Euro-

pean Union). In consequence, additional indicators such as absolute time savings per income

group should also be reported to address equity issues.

2. In contrast to the above, Mackie and Worlsley (2013, p.12) state, that in the United King-

dom, “standard [VTTS] values per minute would be used across incomes, modes and regions.

Therefore, their practice is to use behavioral information for modeling but standard values

for appraisal.” Also Daly (2013) distinguishes between “valuation”, i.e., people’s willingness-

to-pay (or accept) for marginal changes, and “appraisal”, i.e., what these changes are worth

from a societal point of view.

3. Fowkes (2010), OECD (2006), and G¨

uhnemann9argue slightly differently, but in the same

direction: modeling and evaluation should be based on the best heterogeneous preferences

available; in the evaluation, additional weights should be introduced, e.g., to counter the ef-

fect of decreasing marginal utilities of money, or increasing VTTS with income, respectively.

These weights would, thus, define the underlying equity concept of the appraisal method.

4. However, as Ahlheim and Rose (1989) point out, no approach to empirically determine these

weights is available without assuming some arbitrary a-priori specification. In consequence,

every interpersonal comparison of utility changes requires some normative decision and the

weights need therefore to be determined on a political level.

One goal of this section 51.3 is to show the impact of a possible integration between behav-

ioral modeling and economic evaluation in the same agent-based framework. First, a conversion

into income equivalents, and second, a conversion into time equivalents (possibly followed by some

conversion into money terms).10 The choice of the procedure depends on a (normative) decision

whether one EUR or one hshould be valued equally across individuals. It is, therefore, important

7A similar overview on this discussion is given by B¨

orjesson and Eliasson (2014).

8S. Proost, personal communication.

9A. G¨

uhnemann, personal communication.

10 Kickh¨

ofer (2014) shows that the choice of the monetization and aggregation procedure can have major impact on

the results when heterogeneity is assumed in user preferences.

Microeconomic Interpretation of MATSim for Benefit-Cost Analysis 361

that decision makers and modelers who deal with economic evaluation understand the possible

effects of that choice; simply going with the most common approach may not be advisable.

51.3.1 Income Equivalents

Basic Approach The most common approach used in welfare economics to convert utility

changes into money terms is to calculate the monetary amount 1Ynthat one would need to give

or take from individual nto offset the impact of the policy on the utility level 1Un. According to

Equation (51.1), it is calculated as

1Yn= −1Un

λn

.(51.10)

Note that the marginal utility of money, λn, might be person-specific, e.g., dependent on the

person’s income.

The monetary amount −1Ynfrom above represents individual Consumer Surplus. Its absolute

value is, in the absence of income effects (see Footnote 4 in Section 51.2.1), equal to the Compen-

sating Variation and the Equivalent Variation (Daly et al., 2008). The overall welfare change 1W

for the population with individuals n=1..Nis then calculated by

1W= −

n=1

1Yn.(51.11)

Equity The above approach is often criticized for equity reasons: if the marginal utility of money

is—in the behavioral model—assumed to decrease with income, and these values are directly (with-

out additional weights) used in economic evaluation, rich people will have a stronger impact in

the evaluation process than poor people. In turn, this might lead, e.g., to investments in expensive

high-speed trains on major corridors rather than affordable train services for everyone. In terms

of equity and public acceptance, such specification in the appraisal method might not be desirable.

To counter this effect in economic evaluation, the use of standard or equity values is proposed in

the literature. In this context, Jara-D´

ıaz (2007, p.106ff) introduces the social utility of money and

the social price of time. For a more general overview of possible solutions how to address equity

issues, see Rizzi and Steinmetz (2015).

A rather ad-hoc but simple possibility is to replace the person-specific marginal utility of money,

λn, with a population average,

λ:=1

λn,(51.12)

and then

1Yn= −1Un

λ.(51.13)

Following the argument by Fowkes (2010), OECD (2006) and G¨

uhnemann et al. (2011) mentioned

above (Item 3), this would be one particular way to introduce the necessary weights. Alternatively,

one could think of fixing the social weight of every person to 1.0, and derive the social price of all

attributes included in the generalized costs from there (Jara-D´

ıaz, 2007, p.108f).

51.3.2 Time Equivalents

Another option to derive a monetary measure of welfare changes is composed of two steps: First, a

conversion of individual utility changes into equivalent hours of time as a resource (Jara-D´

ıaz et al.,

2008; Mackie et al., 2001). This would be the number of hours 1Tnthat one would need to give or

362 The Multi-Agent Transport Simulation MATSim

take from individual nto offset the policy impact on the utility level 1Un. Second, a monetization

of the resulting numbers through an arbitrary conversion factor, i.e., the monetary value of one

hour for the individual or for society.

In the MATSim sense, one could first calculate the corresponding time equivalent by

1Tn= −1Un

µn

.(51.14)

Similar to the marginal utility of money, also the marginal utility of time as a resource, µn, might

be person-specific.

One option would be simply provide time equivalents, i.e., the BCA would return time equiva-

lents per invested monetary unit. In many situations, however, it is desirable to convert all impacts

of a policy into monetary terms, i.e., to compute,

1Yn=αn·1Tn,(51.15)

and to compare 1Ynwith investment or changes in external costs. The following options are then

possibilities for αn:

•The obtained time equivalents 1Tncould be converted in monetary terms using the person-

specific resource values of time, i.e.,

αn=µn

λn

.(51.16)

This would obviously result in the same monetary amount as the income equivalent approach

from Equation (51.10).

•Following Mackie and Worlsley (2013), one could argue that the resource value of time should

be the same for every individual, and, thus, use some average value for monetization, e.g.,

αn≡α=1

n=1

µn

λn

•As another alternative, one could average over the marginal utility of money only, i.e.,

λ=1

λn

and then

αn=µn

λ.(51.17)

This would highlight that some persons are more pressed for time than others, while, at the

same time, using an equal value for the marginal utility of money. Clearly, this gives the same

result as Equations (51.12) and (51.13). It does, however, lend itself to a clearer interpretation:

first, all utility differences are converted to a comparable scale, i.e., time as a resource (Equation

51.14). Then, these times are converted to a monetary scale, using a conversion factor which

includes the pressure for time (i.e., the person-specific µn) but assumes an average marginal

utility of money.

In all cases, the overall welfare change 1Wfor the population with individuals n=1..Nis then

calculated identically to Equation (51.11), i.e., by 1W= −PN

n=11Yn.

Microeconomic Interpretation of MATSim for Benefit-Cost Analysis 363

51.3.3 Income vs Time Equivalents: Discussion

The sections above show how to monetize and aggregate individual utility differences though

income equivalents or time equivalents. To summarize:

•Income equivalents put emphasis on the individual willingness-to-pay, whereas time equiva-

lents focus on time pressure.

•The aggregation of income equivalents yields the overall equivalent monetary cash flow that

would be generated by the project for the population considered. That is, one EUR is valued

equally across individuals.

•The aggregation of time equivalents yields the overall equivalent lifetime hours that would be

generated by the project for the population considered. That is, one hour of lifetime is valued

equally across individuals.

•A monetization of time equivalents using person- and activity-specific resource values of time

leads to the same total benefit as directly aggregating income equivalents.

•A monetization of time equivalents using some average value of time as a resource, therefore

generally leads to a different total benefit than directly aggregating income equivalents. Such

an approach maintains the equal value for one hof lifetime.

51.3.4 Conclusion and Recommendations

Scoring Function A correct scoring function is central to correct MATSim functioning. The

mathematics and understanding of that scoring function need to be derived from time allocation

theory in economics. In particular, any marginal utility of travel time needs to be split into the

marginal utility of time as a resource (µin the text above, and βdur in Section 3.4) and an addi-

tional direct marginal utility of time spent traveling (U0

trav,qin the text above, and βtrav,mode,qin

Section 3.4).

Since most discrete choice models estimate the sum of these two, definition is required about

how to split up this sum. A somewhat ad-hoc way to achieve this is to find the mode with the

largest (=least negative) marginal utility of time and use that value for the marginal utility of time

as a resource. That reference mode’s direct marginal utility of time spent traveling is then zero; all

other modes’ direct marginal utilities of time spent traveling are relative to that of the reference

mode.

If one is interested in monetization, i.e., converting utility values into monetary terms, then ad-

ditionally the marginal utility of money as a resource (λin the text above, and βmin Section 3.4)

needs to be known. Our current approach to obtain an approximation to λis to force all monetary

preferences in the estimation of a choice model to a unique value. If this is not possible, then one

has to make a normative decision which monetary channel is considered most “neutral”, i.e., most

similar to an “unearned income” channel.

Choice Model and Score Aggregation MATSimagents normally have more than one plan; each

plan has a score. There are two consistent approaches to come up with a utility value from those

scores:

•Using a MNL choice model that makes probabilistic draws from those plans using their scores:

The correct aggregation is then the logsum of all scores.

•Using a choice model that selects the plan with the highest score: The correct aggregation is

then to use the score of that plan.