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
q
Uact,q(tdur,q,...) +X
q
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
q
Uact,q(tdur,q,...) +X
q
Utrav,q(ttrav,q,...) +µ·(T−X
q
tdur,q−X
q
ttrav,q) , (51.2)
where µis the Lagrangian multiplier corresponding to the time constraint.2
Solving the optimization problem leads to
0!
=∂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,
ˆ
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
U0
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
i
eVi
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