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Citing as: Marcucci E, Gatta V (2013). Intra-agent heterogeneity in urban freight distribution: the case of own-account op -
erators. International Journal Of Transport Economics, vol. XL/2, p. 267-286
Intra-agent heterogeneity in urban freight distribution: the
case of own-account operators
Edoardo Marcucci
DIPES/CREI, University of Roma Tre, Rome, Italy, edoardo.marcucci@uniroma3.it
Valerio Gatta
DIPES/CREI, University of Roma Tre, Rome, Italy
ABSTRACT
Urban freight distribution policies aim to improve the efficiency of deliveries of goods in cities.
Local policy makers intervene on rooted, complex and pre-existent relationships. Various are the agents,
both collaborating and competing, involved in providing and buying freight distribution services.
Retailers, transport providers and own-account agents are among the most important actors; they are all po-
tentially characterized both by inter and intra agent heterogeneity in preferences. Heterogeneity in prefer-
ences, whenever present, has relevant implications for policy intervention.
There is a knowledge gap related to the peculiarities of these agents’ preferences and behavior, notwith-
standing some recent attempts to bridge it, that call for a thorough agent-specific analysis.
This paper focuses on urban freight distribution with specific reference to the impact that variations of policy
characteristics (e.g. time windows, number of loading and unloading bays, entrance fees, etc.) might cause
on own-account agents’ behavior. It is important to underline that, de facto, own-account agents are among
the least studied operators in this context. This lack of attention is mostly attributable to the toil needed to
acquire relevant data to study their preferences and behavior. This lack of knowledge has favored the birth
of a widely accepted presumption concerning their inefficiency that, in turn, has produced specifically tar-
geted policies often hindering their activities.
This paper reports the empirical results of a study conducted in the limited traffic zone in Rome's city center
in 2009 thanks to a Volvo Research Foundation grant. The analysis is based on a comprehensive and repre-
sentative data set including: 1) general information on the respondent, 2) company characteristics, and 3)
stated ranking exercises. The ranking data were subsequently transformed in choice data. The paper de -
scribes own-account operators’ preferences as they emerge from the stated ranking exercises and proposes
a systematic comparison among them via willingness to pay measures. The compared estimates are de -
rived under different assumptions concerning agents’ preference heterogeneity. More in detail we discuss re-
sults assuming: 1) no heterogeneity (multinomial logit), 2) covariates-explained heterogeneity (multinomial
logit including interactions with relevant socio-economic variables), 3) flexible heterogeneity (investigating
the systematic and stochastic components of the utility function).
Heterogeneity analysis, apart from relevant theoretical implications, has important policy repercussions in as
much as it impacts on the willingness to pay measures of the policies implemented. An appropriate treat-
ment of heterogeneity is therefore functional to obtaining undistorted and reliable policy forecasts to be fed
to micro simulation models used to support the decision-making process.
The paper: 1) addresses methodologically relevant issues, 2) uses a new, detailed and significant data set,
3) tackles policy relevant questions, 4) provides worthwhile information for policy-makers. The estimation of
willingness to pay / willingness to accept measures for hypothetical policies sets a benchmark for policy
makers and researchers alike.
Keywords: urban freight distribution; own-account; preference heterogeneity, freight policy evaluation.
1
1. Introduction
Urban freight distribution (UFD) policies aim to improve the efficiency of deliveries of
goods in cities. Local policy makers intervene on rooted, complex pre-existent relation-
ships. Various are the agents, both collaborating and competing, involved in providing
and buying freight distribution services.
Retailers, transport providers and own-account agents are among the most important
actors in UFD. Recent researches show that these actors are characterized both by inter
and intra agent preference heterogeneity (Marcucci and Gatta, 2013; Gatta and
Marcucci, 2013; Stathopoulos et al., 2012; Massiani, 2008). These considerations
potentially bear relevant implications for policy intervention. In fact, the distortions an
inappropriate treatment of heterogeneity, once its presence is relevant, might have on
policy decisions are substantial.
Current UFD literature still lacks a thorough investigation of the specific preferences,
needs, and concerns of these agents. This circumstance is prevalently attributable to the
scarcity of appropriate data. In fact, few studies have tackled this specific research issue
from an agent-specific perspective, notwithstanding the widely recognized need to
analyze the potentially diversified policy effects (Ogden, 1992).
These considerations assume a particular role when studying the complex environment
within which UFD agents operate. Present research calls for a focus at the agent-
specific level (Liedtke et al. 2006). Policy interventions in freight transport, in general,
and in UFD, in particular, often produce undesired results when behavioral and
contextual aspects are not explicitly considered.
This paper focuses on UFD agent-specific policy analysis. It aims at filling a knowledge
gap by studying own-account operators, which are, among the most important agents
involved in UFD, the least investigated. Daunting data acquisition problems are at the
base of this limited attention. This has ingenerated the widely accepted and mostly
unjustified presumption concerning the relative inefficiency of own-account operators
(Danielis et al., 2010) that has also induced the implementation of penalizing policies
specifically aimed at this agent category. Why would one study own-account operators if
their number should be reduced given their (untested) inefficiency? Danielis et al. (2010)
have recently questioned own-account allegedly inferior efficiency and underlined the
highly diversified situation among freight sectors and supply chains. Newly acquired
evidence suggests policy-makers should not adopt blunt policy instruments expecting a
homogeneous response. In fact, our results confirm the presence of substantial
preference heterogeneity among own-account operators and warn against a simplistic
study of preferences given the biases this might cause.
The paper reports the results of a study conducted in the limited traffic zone (LTZ) in
Rome's city center. The analysis uses a detailed data set including: 1) general
information about respondents; 2) company's characteristics; 3) stated ranking exercises
(SRE). In the SRE interviewees were presented with alternative policy scenarios and
had to rank them according to their preferences. The ranking data were subsequently
appropriately transformed into choice data.
Own-account operators’ preferences, as it emerges from the SRE, are derived under
different assumptions concerning agents’ preference heterogeneity. A systematic
2
comparison is performed via willingness to pay (WTP) and willingness to accept (WTA)
to account for different assumptions on both the deterministic and stochastic part of
utility in a random utility maximization context (Marcucci and Gatta, 2012). This
approach allows interesting insights on the implications distorted forecasts might have
on micro simulation models used for ex-ante policy impact evaluation.
Various manifestations of heterogeneity are investigated and tested in this paper. More
in detail, we discuss results assuming: 1) no heterogeneity according to a multinomial
logit (MNL) specification, 2) covariates-explained heterogeneity using MNL plus
interactions with relevant socio-economic variables (MNLSE), 3) flexible heterogeneity
considering the model which provides the best fit to the data, in this case, the latent
class (LC) specification. The econometric analysis supports the existence of 2 distinct
classes of people in the sample.
The practical implications deriving from the different ways used to search for intra-agent
heterogeneity are compared using WTP/WTA measures that help identifying markedly
different welfare effects the alternative policies might provoke.
The rest of the paper is structured as follows. Section 2 reports a brief overview of the
relevant literature concerning agent-type analysis for UFD. Section 3 succinctly
describes the study context, while section 4 reports the development of the survey
instrument and comment the data. The econometric results are reported in section 5.
Section 6 concludes and addresses future research efforts.
2. Literature review
Freight transport literature has recently witnessed a concomitant upsurge of interesting,
detailed and articulated reviews describing, from different perspectives, the development
of several modeling approaches, the current state of the art and the most likely
evolutions (Nuzzolo et al., forthcoming; Melo, forthcoming).
Nuzzolo et al. (forthcoming), when reviewing short distance freight transport modeling,
underline that, in recent years, the main driver of model development has been the need
to find solutions for the forecasting and management of freight vehicles flows in urban
areas. The various contributions have been flanked by numerous papers proposing
alternative classification methodologies. Starting from Ogden (1992) who proposed a
classification based on quantities moved (commodity-based) and on vehicles (truck-
based), one can move to Regan and Garrido (2001) who suggested a classification
focusing on the model structure used to identify the two approaches reported above both
leading to the construction of freight origin–destination matrixes. Regan and Garrido
(2001) illustrate and discuss gravity models (derived from the passenger modeling
tradition) and input-output models (derived from a macro-economic modeling approach
also including spatial price equilibrium models that are, indeed, more suitable for
modeling extra-urban freight movements). Furthermore, Ambrosini and Routhier (2004)
report a detailed classification of various freight policy-oriented models applied in
different European countries while Chow et al. (2010) review the recent advances in
freight forecasting models focusing, in particular, on data needs and interpreting urban
freight models as a component of two broader modeling classes: logistic and routing
3
models. Comi et al. (2012) suggest a classification of demand models based on short-
term assessment and decision-making support capabilities. More in detail, Comi et al.
(2012) discuss the recent and sophisticated model class deriving from the integration of
two previously distinct research streams: one aimed at simulating the level and spatial
distribution of commodity flows within cities (intra-city origin destination matrixes) and the
second focusing on route choice and traffic assignment.
Melo (forthcoming) adopts a different classification strategy. A relevant reflection
concerns the fact that freight transport models are usually developed at a national or
international scale (Pendyala et al., 2000; Regan and Garrido, 2001; WSP, 2002; ME&P,
2002a; ME&P, 2002b; de Jong et al., 2004; Tavasszy, 2006; Yang et al., 2010) in
contrast with what happens for passenger ones. Data availability and interest in long
trips are the most important explanatory variables of the scarce development of freight
models dealing with the urban scale. Melo concentrates on the identification of the most
relevant freight modeling examples developed for the urban level (e.g. Boerkamps and
Binsbergen, 1999; Regan and Garrido, 2001; Taniguchi et al., 2003; ME&P, 2002;
Groothedde, 2005; Yang et al., 2010) where models categorical separation is based on
the ‘commodity versus vehicle movements’ or ‘aggregate versus disaggregate’
approach.
An additional categorization proposed relates to the systemic or operational nature of the
models developed thus distinguishing whether the modeler’s aim mostly focuses on a
planning or operational level (Paglione, 2006). Systemic models are suitable for the: a)
strategic level, concerned with system design and evaluation; b) tactical level, centered
on operations planning and control (see Crainic et al., 2009). Systemic models usually
reflect public objectives, related to stakeholders’ well-being, life quality, and mobility. On
the other hand, operational models are characterized by a narrower scope often focused
on specific stakeholders groups (usually private suppliers and transport providers) and
their activities and objectives, primarily aimed at improving distribution efficiency and
profits.
A series of recent papers (Stathopoulos et al., 2012; Marcucci and Gatta 2013, Gatta
and Marcucci, 2013) have reported and discussed new and interesting findings deriving
from a behavioral approach to UFD. Among the first contributions in this emergent
stream of research one recalls Hensher and Figliozzi (2007) that persuasively claim that
standard approaches underestimate the complexity of freight movements at different
geographical scales thus missing potentially relevant motivations capable of explaining
agents’ behavior within current scenarios. Stakeholders’ utility maximization is explicitly
considered in behavioral models that represent a sub-set of disaggregate freight models.
The appropriate estimation of these models relies on the correct identification of key
decision-makers. Notwithstanding this might sound obvious, in the case of freight, it de
facto represents a very controversial and daunting issue. Understanding who actually
decides about freight choice movements is not an easy task since there are many actors
potentially influencing the final decision. The development of an agent-based modeling
framework capable of describing and forecasting the behavior of specific actors
necessitates an a priori identification of a decision maker for each given action
considered necessary for freight transportation (Liedtke and Schepperle, 2004;
Marcucci, forthcoming).
Agent-based micro models are, according to several authors (Gray, 1982; Wisetjindawat
et al., 2006; de Jong and Ben-Akiva, 2007; Hensher and Figliozzi, 2007; Samimi et al.,
4
2009; Yang et al., 2009; Roorda et al., 2010) an appropriate instrument to model UFD.
In fact, policies impacting on fuel prices, land use patterns and pricing strategies modify
the comparative convenience of different UFD options. Joint consideration of policy
instruments and the attributes influencing freight behavior is fundamental to understand
and correctly predict the impacts policies might produce on market outcomes (Puckett
and Greaves, 2009).
Policy makers need to identify incentives/disincentives with a relevant impact and
quantify the effects they would produce by comparing them with what occurs in the
reference scenario faced by the agents. The three most important issues a behavioral
model for freight transportation has to deal with are: 1) pinpointing the decision makers
involved, 2) clarifying operational constraints and 3) understanding inter-agent
interactions. This paper focuses on the first point, that is, the role and preference of own-
account operators which, in the context studied, play a relevant role (Danielis et al.,
2011).
3. The study context: the roman freight limited traffic zone
The data used in this paper were collected between March and December in 2009
thanks to a Volvo Research Foundation grant (Volvo Report, 2010). In the late eighties
the LTZ in Rome’s historical center was first introduced. A 5km2 area was restricted to
non-residents’ vehicles and bans on traffic, now applying both to passenger and freight,
were imposed. A specific regulation characterizes the LTZ area; only Euro 1 and more
fuel-efficient vehicles are allowed to enter. Free access is awarded only to residents; all
other vehicles pay an access fee. The scheme is enforced, during daytime, using
cameras and each vehicle pays a 565 € per year fee. Time windows regulations
selectively apply to entrants. Own-account operators are specifically targeted and
substantial exemptions apply to third party freight operators. The regulatory framework
is designed to: (1) foster the adoption of third party freight transport providers; (2)
discourage lengthy parking; (3) reduce the number of vehicles entering the LTZ area.
Time windows are, regrettably, not systematically enforced.
4. Study context and survey instrument description
Back in the ‘90s Ogden (1992) already underlined that receivers, carriers and forwarders
are the most important stakeholders to consider in UFD analysis. The survey instrument
was developed to study: carriers, retailers and own-account operators. The first two
operators have been studied in the literature. Stathopoulos et al. (2011), on the base of
stakeholder consultations, suggest investigating own-account operators too. The first
step in developing a survey instrument with this intent, is to define, select and customize
the attributes to be used for preference elicitation exercises.
The stakeholders’ consultation conducted allowed for realistic attribute definition and
contextualization. Section 4.1 highlights and motivates the attribute selection process.
Ex-ante joint policy acceptability was the most important attribute selection criterion
used. Subsequently, the paper describes how each attribute was: 1) defined; 2)
structured in levels; 3) assigned specific ranges; 4) progressively differentiated by agent
type. Attribute selection was initially guided by previous stakeholder surveys.
5
4.1. Attributes included in the Stated Ranking Exercise
Each alternative in the SRE is described by a set of attributes that take several levels
and span for different variation ranges when the alternatives are presented to
respondents1. The attributes were derived from three sources: a) literature survey; b)
previous studies on freight distribution in Rome; c) focus groups with representative
stakeholders. We conducted an extensive review on city logistics literature especially
focusing on those papers adopting an agent-based approach.
Attribute selection started with reviewing previous studies on city logistics conducted in
Rome (STA, 2001; Filippi and Campagna, 2008). Stakeholder surveys were also very
useful in reaching a final decision2. All stakeholders considered the attributes selected
relevant. The attributes, finally piloted with operators, were: 1) number of loading and
unloading bays (LUB); 2) probability to find loading/unloading bays free (PLUBF); 3)
entrance fees (EF); 4) time windows (TW). All these attributes have been considered as
possible components of a policy-package (Marcucci et al., 2012).
4.2. Agent-type differentiations
Given the limited budget available for the interviews an efficient design strategy was
adopted. Attributes have progressively been differentiated by respondent-type (own-
account; retailers; transport providers) after the piloting phase. Relevant and pertinent to
own-account operators is the inclusion of the TW attribute.
In fact, after stakeholders’ consultations, it was evident that own-account operators alone
are de facto facing TW restrictions. The SRE contained three policy options including the
status quo (SQ) alternative. Agents were asked to rank policies according to their
preferences. Table 1 reports an example of a SRE task.
Table 1 - Example of a SRE task
Attribute Policy 1 Policy 2 Status Quo
LUB 400 800 400
PLUBF 20% 10% 10%
EF 1000 €200 €600 €
TW 20:00-10:00/
14:00-16:00 04:00/ 20:00 20:00-10:00/
14:00-16:00
Policy
ranking
The levels of the attributes were considered plausible, policy relevant and easy to
implement. The attributes, levels, and ranges used are reported in Table 2.
1 Please refer to Stathopoulos et al. (2011) for a clear motivation of choosing stated ranking as an elicitation
mechanism.
2 An important phase of focus groups with experts focused on the definition of policies capable of mitigating
the identified UFD problems. Volvo Report (2010) provides a detailed overview of stakeholders survey
results as well as of attributes used in the SRE.
6
Table 2 - Attribute levels and ranges used in the SRE
Attribute Number
of levels
Range of attribute
(status quo underscored)
LUB 3 400, 800, 1200
PLUBF 3 10%, 20%, 30%
TW 3
1) OPEN from 18:00 to 08:00 e from 14:00 to
16:00;
2) OPEN from 20:00 to 10:00 e from 14:00 to
16:00;
3) OPEN from 04:00 to 20:00
EF 5 200€, 400€, 600€, 800€, 1000€
It is important to note that for the TW attribute the two hypothetical variations imply the
same amount of hours of allowed entrance to the LTZ as the SQ situation. The
difference between the levels considered consists not in the quantity of hours available
for entering the LTZ but, rather, in the specific hours added or subtracted to the SQ.
In particular TW1 subtracts two hours (08:00-10:00) in the morning (the most frequently
used to perform deliveries and, thus, the most preferred) and adds the same quantity in
the afternoon (18:00-20:00). It is assumed that TW1 will have a negative impact on
utility. TW3, on the contrary, subtracts 8 hours during the night (20:00- 04:00) and adds
the same amount during the day in two different time slots (10:00-14:00 and 16:00-
20:00) thus de facto making entrance always possible during working hours. It is
assumed that TW3 will have a positive impact on utility.
4.3. Data description
The results reported are part of a larger research project financed both by Volvo
Research Foundation aimed at UFD policy definition and implementation. A total of 252
interviews were administered but only 229 were finally used after discarding pilot
interviews. The sample is composed of 73 own-account operators, the only one used in
this paper, 90 retailers and 66 transport providers.
5. Econometric results
In this section we report the econometric results, for own-account operators using the
data sample elicited via the SRE described3.
The econometric strategy adopted in this paper focuses on detecting intra-agent
preference heterogeneity. As suggested by Marcucci and Gatta (2012) the search for
heterogeneity might be performed in different ways. In fact, heterogeneity can be
explored by investigating the systematic, stochastic or systematic and stochastic
3 For a detailed discussion of the methodological framework and possible applications of discrete choice models to
similar context. See, for example, Marcucci (2011); Gatta (2006).
7
components of the utility function. Each search endeavor can be performed with a
varying level of sophistication independently of which part of the utility function is
studied.
When investigating the systematic part of utility one could adopt the following model
specifications: 1) MNLSE, 2) Mixed Logit (ML), 3) LC.
On the other hand, when focusing on the stochastic part of utility the researcher could
specify the following models: 1) Error Component (EC), 2) Covariance Heterogeneity
(COVHET).
If, finally, one aims at investigating heterogeneity in both the systematic and stochastic
part of the utility function, the model specification that could be used to this end is a ML
with an EC component (MLEC).
The results obtained applying the search strategy to the available sample are reported in
what follows.
We first adopt a simple MNL model assuming perfect preference homogeneity as a
benchmark (M1). With reference to (M1) one notices that both LUB and PLUBF are not
statistically significant while EF and TW are significant and with the expected sign (see
Table 3). (M1) also includes two alternative specific constants (ASCs) for the unlabeled
hypothetical cases (ASC_Alt1, ASC_Alt2) whose coefficients represent the overall
alternative impact on own-account utility when all the coefficients of the other attributes
are zero. In our case, results show that, there is an a priori evaluation against the SQ.
The overall model fit is acceptable (adj-rho2 = 0.14). From a policy perspective it is
important to calculate which are the WTP/WTA for attributes’ variations. In particular, the
only WTP/WTA values that could be calculated are those related to the TW attribute
since this is, for this specification, the only statistically significant attribute along with EF.
The agents interviewed are willing to pay 197 € for TW3 while are willing to accept TW1
for 228 €.
Assuming preference homogeneity would induce the analyst to conclude that the
sampled agents are not willing to pay neither for LUB nor for PLUBF. This issue will be
further discussed in the following paragraphs.
Table 3 – MNL model estimates (M1)
Variable Coefficient St.Err. T-Stat WTP/WTA*
LUB -0.067 0.057 -1.18 -
PLUBF -0.008 0.052 -0.16 -
EF -0.768 0.052 -14.65 -
TW1 -0.875 0.080 -10.91 -228 [-265, -193]
TW3 0.756 0.079 9.63 197 [160, 237]
ASC_Alt1 0.936 0.151 6.20 -
ASC_Alt2 0.784 0.128 6.14 -
8
* in brackets the confidence intervals using Krinsky-Robb method with 10.000 pseudo-random
draws from the unconditional distribution of the estimated parameters.
A MNLSE specification represents a first attempt to investigate heterogeneity. This naïve
approach to heterogeneity assumes socio-economic variables are capable of
differentiating attributes’ impact among agents (M2). The MNLSE specification produces
a better fit to the data with a statistically improved adj-rho2 = 0.17. Also in this case it is
interesting to note that both LUB and PLUBF are not statistically significant and,
therefore, a naïve treatment of heterogeneity would also induce the analyst to assume
agents are not willing to pay neither for LUB nor for PLUBF. This issue will be further
investigated in what follows.
The socio-economic variables tested for explaining heterogeneity among agents are: 1)
number of employees (NOE), 2) shop dimension (SD), 3) frequency of deliveries (FOD),
4) freight sector (FS), 5) own-account level (OAL), that is, self-stated percentage of own-
account transportation performed with reference to the total amount of deliveries4, 6)
EURO vehicle standard (EVS), 7) number of deliveries (NOD). The first five socio-
economic variables have produced, at least partially, some statistically significant results
that are reported in table 4 below.
Table 4 – MNLSE model estimates (M2)
Variable Coefficient St.Err. T-Stat
LUB -0.054 0.058 -0.95
PLUBF -0.038 0.054 -0.70
EF -0.097 0.208 -0.47
TW1 -0.783 0.155 -5.04
TW3 0.446 0.117 3.82
EF_FS3 -1.836 0.410 -4.48
EF_NOE 0.028 0.010 2.73
EF_SD -0.318 0.093 -3.41
TW1_FOD 0.137 0.058 2.36
TW1_OAL1 -0.422 0.158 -2.66
TW1_OAL2 -0.699 0.141 -4.96
TW1_FS3 0.684 0.291 2.35
TW2_OAL1 0.444 0.173 2.57
TW2_OAL2 0.635 0.160 3.98
ASC_Alt1 0.968 0.155 6.23
ASC_Alt2 0.799 0.131 6.10
4 Since, de facto, there are no operators that only self-produce the transportation services they need, we used this
information in the estimation process. In particular, this variable was used to categorize the operators in three classes.
When the self-production percentage of the transportation services needed is, for example, at least 80% of the total the
variable takes the value of 1, whereas it takes the value of 2 when the self-production is between 30% and 80%, and 3
in the remaining cases (1 = strong own-account characterization; 2 = medium own-account characterization; 3 = low
own-account characterization).
9
(M2) results suggest the presence of some form of intra-agent heterogeneity. In fact,
without going too much into details, one sees that: 1) agents belonging to Sector 35 are
more sensitive to EF variations while less sensitive to TW1; 2) an increase in the number
of employees and/or in the frequency of deliveries both produce a reduction of the
sensitiveness to EF variations; 3) increasing shop dimension positively impact on EF
sensitivity; 4) agents’ medium or strong own-account characterization (see footnote n° 4)
provokes a higher negative sensitivity to TW1 (undesirable TW level) and, inversely a
higher positive sensitivity to TW3 (desirable TW level).
A further sophistication in the search for heterogeneity can be achieved by assuming an
underlying distribution of the agents’ preference parameters. ML is similar to LC even if it
embodies several important differences (Greene and Hensher, 2003). One of the large
virtues of ML is that in the simulated likelihood function (see Gourieroux et al., 1994 and
Train, 2003 for a discussion of maximum simulated likelihood estimation of this model)
one is not limited to using the normal distribution since the components of the
deterministic part of the utility may be drawn from different distributions. We would use
this model to investigate the presence of continuous forms of heterogeneity and test
non-normal continuous parameter distributions. However, in this case, ML did not
produce a better fit to the data and only one standard deviation was found to be
statistically significant.
At this point one could be tempted to revert to the simple MNLSE where only some
socio-economic variables explain heterogeneity in own-account operators’ preferences.
Nevertheless, following Marcucci and Gatta (2012), one last attempt, when investigating
the deterministic part of the utility, is in order. In other words, one has to check whether
there is a form of discrete mixture of heterogeneity among agents by estimating a LC
model (M3). The finite mixture approach to conditional logit models is developed and
latent classes are used to promote an understanding of systematic heterogeneity (Boxall
and Adamowicz, 2002). This helps uncovering unobserved heterogeneity in a population
and finding substantively meaningful groups of people that are similar in their responses
to measured variables (Muthén, 2004).
(M3) is reported in Table 5. The two main points that need underlining relate to: 1) the
detection of discrete heterogeneity among agents such that two different latent classes
are identified; 2) PLUBF is now statistically significant for one of the two latent classes
estimated notwithstanding it was never so in any of the previous model specifications.
Table 5 – LC model estimates (M3)
Variable CLASS 1 CLASS 2
Coefficient T-Stat WTP/WTA Coefficient T-Stat WTP/WTA
LUB -0.078 -0.63 - 0.074 1.42 -
PLUBF 0.103 0.78 - 0.120 2.50 27 [6, 49]
EF -1.293 -9.05 - -0.878 -26.43 -
TW1 -3.016 -9.26 -466 [-536, -406] -0.238 -3.76 -54 [-80, -27]
TW3 2.328 8.72 360 [305, 425] 0.447 7.83 102 [78, 126]
5 The macro sectors are: 1) food (fresh, canned, drinks, tobacco, bars, hotels and restaurants); 2) personal and house
hygiene (detergents, pharmaceuticals, cosmetics, perfumes, watches, barbers, etc.); 3) stationery (e.g. paper,
newspapers, toys, books, CDs etc.); 4) house accessories (e.g. dish washers, computers, telephones, metal products
etc.); 5) car accessories (e.g. vehicle components, vehicles, gasoline, etc.); 6) services (e.g. laundry, flowers, live
animals, accessories and animal food, etc.); 7) clothing (cloth, leather, etc.); 8) construction (e.g. cement, scaffold,
chemical products, etc.); 9) other (all that was not included in previous categories).
10
ASC_Alt1 1.035 3.53 - 0.333 2.09 -
ASC_Alt2 0.890 3.74 - 0.135 1.04 -
* in brackets the confidence intervals using Krinsky-Robb method with 10.000 pseudo-random draws from the unconditional
distribution of the estimated parameters.
(M3) represents a significant improvement with respect to (M2) in terms of fit to the data
(Adj Rho2 = 0.24). The two classes detected among the agents sampled are quite
distinct in terms of preferences. In fact, whereas class 1 (C1, with class probability equal
to 50%) is more sensitive, in relative terms, to TW variations whereas for class 2 (C2) EF
is the most important attribute with a role also played by PLUBF. In fact, looking at WTP
and WTA estimates one can notice that agents in (C1) are ready to pay 360€ for TW3
and to accept 466€ for TW1 while agents belonging to (C2) have substantially lower
values for both WTP and WTA measures respectively equal to 102€ and 54€. Moreover,
for (C2) PLUBF is now relevant in explaining choice suggesting that there is a class
within the sample that considers PLUBF a relevant attribute. More in detail, this class of
agents are ready to pay 27€ for an increase in 10% base points of finding a loading and
unloading bay free. This WTP has a magnitude not comparable to other variables but
still, should it not be explicitly considered, would provoke a distortion of the estimates.
We further investigated heterogeneity by searching the stochastic part of utility via EC
and COVHET model specifications. None of the two models estimated provided
statistically significant results and, consequently, no improvement in explanatory power.
This suggests there is no heterogeneity in the stochastic part of utility among the
sampled agents. These results imply that the search for heterogeneity in both the
stochastic and deterministic part of the utility (e.g. MLEC) is superfluous.
To sum up the results obtained one could say that heterogeneity has to be investigated
systematically and following a well-defined search strategy. Abandoning attribute
investigation beforehand is not a recommendable strategy. In fact, one could have
stopped searching for heterogeneity after estimating a ML model in which no significant
standard deviations are detected for the attributes considered and thus reverting to a
simple MNL model. However, this would have provoked two major problems. On one
side one would have not discovered the presence of a discrete form of heterogeneity
among agents (C1 and C2) and, on the other, the PLUBF attribute would have been
erroneously considered irrelevant in the decision making process. The measures of
these potential distortions are reported in Table 6.
Table 6 – WTP/WTA model comparison
Variable MNL LC MNL distorsion
C1 C2 C1 C2 Total
(weight: conditional class membership prob.)
TW1 WTA: 228€ WTA: 466€ WTA: 54€ -91€ +108€ 199€
TW3 WTP: 197€ WTP: 360€ WTP: 102€ -62€ +59€ 121€
PLUBF WTP: 0€ WTP: 0€ WTP: 27€ 0€ -17€ 17€
From a public perspective, using a simple MNL specification for WTP/WTA measures
determination, would induce adopting inefficient policy measures. In fact, taking the case
11
of TW1 as an example, if using a MNL specification the local policy makers would
assume own-account operators need an EF reduction of 228€ to accept the restrictive
measure. However, this action, taking the unconditional class membership probabilities,
would imply an overestimation of the WTA for (C2) (+ 174€) and an underestimation for
(C1) (-240€) with a total efficiency loss of around 414€6. Taking, instead, the conditional
class membership probabilities one notices that there is a 38% probability of belonging
to (C1) and 62% to (C2). Assuming these probabilities as relevant for the agents
sampled, the distortions deriving from the erroneous heterogeneity assumptions would
induce an overall loss of efficiency equal to 199€. An error of similar amount would be
induced for TW3.
6. Summary, conclusions and future research
This paper has investigated own-account operators’ preferences for UFD policy
interventions. It helps bridging a knowledge gap in UFD research literature by
investigating intra-agent heterogeneity. The paper is based on an original and detailed
dataset that overcomes data availability issues that typically constrain research efforts in
this specific domain. Data were collected in 2009 in Rome’s LTZ.
Notwithstanding the limited number of sampled agents the results obtained suggest the
presence of relevant intra-agent heterogeneity. More in detail, the search strategy
adopted allowed for the identification of a naïve form of heterogeneity by simply using
some socio-economic variables. However, more interesting from a policy perspective, is
the discovery of two latent classes within the agents sampled and the relevance in
explaining heterogeneity of an attribute (PLUBF) that was never statistically relevant in
any previous model specification. The policy implications of the model mis-specification
are quantified by calculating WTP/WTA measures and their respective confidence
intervals.
The restricted number of observations, due to the limited budget available, represents a
limitation. Should further funds be secured in the future, an extension in the coverage of
the own-account population will be performed. An increase in the available data would
also allow for more detailed investigations concerning both freight sectors as well as the
level of own-account characterization.
One main conclusion that evidently emerges from the research conducted is that local
policy-makers should not expect homogeneous responses to the policies implemented.
No one-policy-fits-all seems applicable to the LTZ in Rome.
Acknowledgements: The Authors would like to acknowledge: 1) Volvo Research Foundation and
Italian Ministry of University and Research for funding; 2) the precious work of Amanda
Stathopoulos and Eva Valeri who actively participated in all project phases and helped shaping
many of the search strategies both during the project as well as afterwards during estimation; 3)
two anonymous Referees for their valuable comments that helped improving the paper.
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