Residential location preferences and relative power in threemember households: a choice experiment
Marcucci Edoardo, DIPES, University of Roma Tre, Rome, Italy
Stathopoulos Amanda, DISES, University of Trieste, Trieste, Italy
Danielis Romeo, DISES, University of Trieste, Trieste, Italy
Rotaris Lucia, DISES, University of Trieste, Trieste, Italy
IATBR The 12th International Conference on Travel Behaviour Research
Jaipur, Rajasthan - India - December 13-18, 2009
Abstract
Microeconomics studies group behaviour by using the unitary model. However, there is growing evidence that
there can be significant differences between choices made by single individuals and those made by the same
individuals when choosing collectively. This study investigates the differences between individual and joint
decision-making in the context of residential location choice. It is widely recognized that household location
choices involve several members of a household with heterogeneous preferences and influence power.
Nonetheless little is known about group decision-making processes in practice. In particular, there is only scant
evidence on how preferences differ among family members and to what extent individual preferences can be
aggregated to achieve an approximation of joint choices. The study evaluates whether there are differences in
single members’ preferences. Furthermore, relative power is inferred by measuring similarity between ex ante
single preferences and ex post joint choice outcomes. We also quantify the implicit bias generated by relying on
the unitary household approach. These issues are tested by employing a two-stage conjoint choice experiment
administered to a sample of 53 Italian families. This work proposes a novel extension of the commonly used
dyadic interaction approach to consider the role of adolescents in household decision-making.
Keywords: Unitary household, stated choice experiments, residential location, agent interaction and relative
influence, discrete choice models, MNL, MMNL.
1
Introduction
Empirical studies, employing Stated Preference (SP) techniques to study group behaviour have, with
few exceptions, ignored potentially important issues inherent in multi-person choices. The lack of
consideration behind the choice of an “appropriate” unit of analysis1 may well generate biased welfare
estimates and erroneous policy predictions (Molin et al. 1999, Adamowich et al. 2005). Several recent
studies have questioned the practice of treating group preferences as coincident with those of single
members. This issue should be tested rather than assumed. There is clear evidence of both preference
disparity between family members and dissimilarities between choices made individually and jointly
(Lampietti, 1998; Dosman and Adamowich 2006; Bateman and Munro 2005a; Hensher et al. 2008,
Beharry-Borg et al. 2009). This paper tests the differences between single preferences, considering
three distinct household member-types, and joint choices of residential location.
Family housing decisions are studied by adopting a two-stage conjoint choice experiment. Our
approach allows us to compare individual choices with joint household ones and specifically to
explore the following issues:
First of all we test for preference heterogeneity among family member-types.
Second, we asses the validity of the unitary model or, equivalently, of the representative member
hypothesis. We control whether the joint household decisions can be better approximated by any
among the single member-types or, alternatively, by the average family member (pooled model).
Third, for the instances where the representative member hypothesis fails, we estimate the bias
implied by the “wrong” choice of survey subjects.
These three hypotheses are tested by administering a two stage conjoint SP experiment. This
methodology represents a novel extension of the, nowadays common, dyadic interaction approach. In
fact, we also consider the role adolescents play in household residential choice.
The paper is organized as follows. In the next section we review the literature on household decisions.
Section 3 describes the base model of group choices and enunciates the hypotheses tested. Data and
sample description are reported in section 4. Econometric results are presented in section 5. Section 6
concludes.
1
This is testified by the commonly adopted representative member hypothesis where information is gathered from a single
individual.
2
2
Research on household decisions
2.1 Microeconomics of household choices
Microeconomic analysis of family decisions originates from the consensus household model of
Samuelson (1956). Indeed, it is recognized that the household, not the individual, represents the basic
consumption unit. A later contribution is Becker’s rational choice approach to family-life. Even
intimate decisions such as marriage, divorce, and family size are supposedly reached through
weighing the pros and cons of alternative actions (Becker 1993). Becker treats the family much like a
tiny specialized factory engaging in household production of Z-goods like children, prestige and
health (Becker 1973). Over the last two decades, however, there has been a growing recognition that
the unitary household model does not appropriately reflect the reality of household decision-making.
The assumptions of the beckerian unitary household model (ranging from the single utility function to
the single time and budget constraints) have failed numerous empirical tests (Thomas 1990, Browning
and Chiappori 1998). Game theoretic bargaining models have challenged the unitary approach.
Household behaviour is the outcome of the interaction between heterogeneous members with distinct
preferences (Manser and Brown 1980, McElroy and Homey 1981). In fact, only by treating each
member as an independent heterogeneous entity can some form of bargaining take place. In essence,
classic utility theory is not rejected per se but is inadequate for the analysis of household behaviour
(Browning and Chiappori 1998). In recent years, activity based analysis has produced rich
developments of empirically based interactive models (Golob and McNally 1997, Gliebe and
Koppelman 2002). In addition to such daily activity behaviour, concerning the coordination of
activities among members, one can also observe relevant group-based decision-making in long-term
decisions. Several studies analyse group decisions regarding residential choices (Molin et al. 1999),
labour choices (Chiappori et al. 1998) car ownership (Hensher et al. 2008) and vacation choices (Kang
and Hsu 2005). The following sections deal with two essential features of empirical household
decision-making research, namely, sampling strategies and influence analysis.
2.2 Sampling strategies for household analysis
When studying household choices it is standard practice, in SP studies, to ignore differences in
preferences and power among members. It is possible to classify several strategies and their
implications for the estimates derived thereby. Generally, empirical research adopts the following
procedures:
1. Randomly interview a single member with no further attention to the appropriateness of the
chosen respondent under the hypothesis that her choice is sufficiently similar to that of the
family or, she is able to impose her choice on the household.
3
2. Interview a single targeted member following a specific procedure to individuate the most
suitable respondent (for instance, interview the member that pays the bills supposing that this
is an appropriate method to recognize the person making the decisions).
3. Interview a single member that is asked to represent the preferences of the whole group.
4. Interview (only) the whole household based on the hypothesis that the choice is group-based
and that only collective choices adequately represent real world ones.
5. Interview/compare both single and group-based preferences to verify the validity of the
previous approaches and select the most adequate unit of analysis.
The first approach, namely an indistinct choice of respondent, assumes that any member-type is
adequately qualified to represent the preference structure of the family as a whole. This approach has
become standard practice in SP choice modelling of residential location choice. It is equivalent to
assuming that either differences among members are so small that they can be overlooked or they
cancel out in the aggregate (Adamowicz et al. 2005). Alternatively, if one assumes the household to
choose on the basis of a single utility function, then one can simply study the preferences of any
member to gain an understanding of the household as a whole2 (for a testing see Lundberg, et al. 1997,
Browning and Chiappori 1998). Overall there is no explicit selection procedure to find the most
suitable respondent, neither is there any effort to distinguish single and joint responses.
The second approach is generally considered more accurate. It implies using a proxy to individuate the
member considered the most influential or singularly responsible for a certain decision (Blood and
Wolfe 1960). One, de facto, assumes that there might be heterogeneity and power asymmetry but that
a careful choice of the respondent can assure a correct representation of the household3. Since there is
experimental evidence supporting the view that families make influential decisions jointly (Davis and
Rigeaux 1974, Munsinger et al. 1975) one can arguably question the univocal and clear identification
of the individual responsible for the decision. What is more, traditional indicators, such as relative
income, may prove distorted proxies of the ability to influence choices (see Dosman and Adamowicz
2006 for an empirical testing of these points).
Based on these assumptions one might adopt the third method for choosing a respondent, namely ask
the respondent to represent the preferences of other member-types. Empirical findings show that, on
the contrary, the ability of any one member to correctly assess the preferences of others is, in general,
rather weak (Corfman and Lehmann 1987, Menon et al. 1995, Dellaert et al. 1998). Corfman
establishes that there is a lack of agreement among members when it comes to determining influence
2
Arsenio et al. provide an illuminating example of this approach “Each respondent was an adult who was asked to represent
the household since this is the unit of decision making in the case of residential choice and the environmental attributes
would impact on all household member.” (2005, p. 19).
3
An example of this procedure is reported in Jin et al. (2005, p 5) where the authors say: “The head of the household was
identified as the person in charge of the daily expenditures and other (younger) family members.”.
4
over joint choices (1989). Moreover, Dellaert et al. (1999) show how components of a household
detain a limited ability to predict their own and others influence over joint choices.
The fourth approach suggests, based on the findings by Molin et al. (1999), to sample the whole
group. This is expected to provide estimates with higher predictive accuracy. Applications in the
residential literature include Ortùzar and Rodrıguez (2002), Pérez et al. (2003) and Galilea and
Ortùzar (2005). This approach, however, produces no information concerning household components’
likings. This hampers the comparative analysis of power differences within the family and does not
make explicit disagreements and concessions.
In line with the fifth approach, this paper investigates the gap between individual and joint
preferences. Past research indicates that there are large differences between individual and joint choice
outcomes (Arora and Allenby 1999; Corfman and Lehmann 1993; Dellaert et al. 1999). Recent
contributions use an experimental approach to model the differences between individual and joint
choices (Bateman and Munro 2005b, de Palma et al. 2008, Carlsson et al. 2009, Beharry-Borg et al.
2009). On the whole these findings indicate that individual choice data are not sufficient to produce
representative and robust estimates of joint family decisions (Menasco and Curry 1989; Molin, et al.
1997; 1999, Arora and Allenby 1999, Aribarg et al. 2002, Dosman and Adamowicz 2006, Puckett and
Hensher 2006). There are simply more factors to consider such as influence, altruism, roles and
resources at play that contribute towards shaping the final joint decision.
2.3 From dyads to triads
Past research on household decision-making has, almost exclusively, focused on dyads alone
considered as the (only) relevant household decision-making unit (among others, Arora and Allenby
1999, Bateman and Munro 2006, Beharry-Borg et al. 2009). For instance in Beharry-Borg et al. (2009)
the dyadic couple is described as the basic decision-making unit. Understanding the role of third party
influences, such as adolescents or other family members, on decision strategies is essential to gain a
broader view of the relevant unit of analysis. Decision-making in households, in fact, is influenced by
the mere presence of children. This suggests joint family choices are qualitatively different from
atomistic ones (Filiatrault and Ritchie 1980). Spiro (1983) finds that the presence of children
influences the use of persuasive techniques in the couple. There is also empirical evidence against the
unitary household model in location choice among childless dyadic households (Mok 2006). However,
the author notes that in the presence of children there is not sufficient evidence to reject the parent
income-pooling hypothesis.
2.4 Decision-making in residential household choices
It is difficult to generalize findings from one context to another given that the level of interest,
participation and influence among members are all shaped by the specific decision situation.
5
The work by Molin et al. (1999; 2001) is the closest to the present study. For example, Molin et al.
(2001) capture preference heterogeneity among household members by individually interviewing each
member of the 147 households participating in the study; whereas Molin et al. (1999) compare
interactive group responses to conventional conjoint (single agents) to investigate the differences
between individual and group preferences. The studies show that group-based models are better
predictors of household residential location choices than traditional approaches. The Authors also
propose a method to measure the relative influence of each member on the household decision
outcome.
SP methods represent a valid option to investigate residential location choices. This study belongs to
the relatively small group of works employing an experimental SP approach. The main contribution is
the combination of this experimental approach with two novel features of non-market SP evaluation.
That is, we focus on the choice of dwelling and apply a group-based approach. The adoption of an
experimental method avoids “yes saying” responses that ignore actual trade-offs and merely produces
declarative responses containing no valuable information. Conjoint choice analysis (CCA) examines
the trade-offs people make among attributes to assess the weight they assign to each of them4.
Residential location choice has often been considered an ideal choice context to elicit agents’
preferences for housing attributes. The motivations for this research strategy are due to the: 1) more
direct perception of the issue at hand since the interview is explicitly connected to the present living
situation; 2) realistic simulation of the decision-making mechanism agents adopt when choosing a
dwelling; 3) credible evaluation of attribute variations.
2.5 Relative power analysis
Research suggests that a large proportion of the relevant decisions made by families are joint efforts
by two or more family members (Samuelson 1956, Davis and Rigeaux 1974). Various scientists from
different fields have analyzed decision-making in households composed of non-identical individuals.
Especially, research in marketing has modelled influence strategies in family decision-making (Davis
1970, Shuptrine and Samuelson 1976). A common approach to measure the influence exerted by a
member is to compare her initial preferences to the group’s decision outcome. The degree of similarity
between the first and the latter is taken as an indicator of the extent of influence (Corfman 1989,
Corfman and Lehmann 1987). Recent empirical research conducted by Aribarg et al. (2002), Arora
and Allenby (1999), and Arora (2006) present useful modelling approaches to measure individual
influence at the attribute level in the context of group decision-making. This development is essential
4
Examples of experimental choice studies on accessibility and environmental factors are profile based studies like Molin et
al. (1999), ranking exercises such as Galilea and Ortùzar, (2005), Hunt et al (1994), Perez et al. (2003), Ortùzar and
Rodrıguez (2002) Arsenio et al (2006), or a comparison between methods like Wardman and Bristow (2008).
6
Corfman states that: “Predictions and reports on relative influence made by spouses and observers are probably not valid
indicators of relative influence. They may contain other useful information, but they are not objective measures.” (Corfman,
1989, p 663).
6
given the growing importance of techniques based on choices between goods and services with
bundled characteristics.
The issue of obtaining accurate information concerning relative influence in family decision-making is
still hotly debated and remains, mostly, unresolved. In the related literature, an array of methods has
been suggested to evaluate the role of personal relationships and interaction. These are almost
exclusively based on a questionnaire SP logic. In fact, data obtained from observed behaviour does not
allow the detection of interaction effects. Research efforts such as Kirchelers’ Diary method (1995)
and Arora and Allenby’s attribute-specific influence measure (1999) are simply based on self-declared
power measures. However, the literature has questioned this method of measuring power6. Moreover
past research reveals a limited ability of single members to assess other member’s preferences
(Corfman and Lehmann, 1987; Dellaert et al. 1998; Menon et al. 1995). Analysing the role of children
in influencing decisions is especially complex. The papers considering it, generally based on declared
influence, show that the children are aware of their influencing power while the parents, in general,
underestimate it (Flurry and Burns 2005). One needs to devise a method to uncover the unobservable
so to obtain adequate SP data on household interaction. Authors such as Katz (1997) and Manski
(2000) suggest that an experimental approach is needed to identify the heterogeneity of preferences
and disentangle the intricacy of household decision-making7. Experiments have the advantage of
allowing the researcher to produce data suitable to perform controlled tests of a theory.
3
Model and hypotheses
3.1 Base model of group choices
The various alternatives are described by a utility function of a general form. The model is kept simple
to allow a meaningful comparison between individual and joint preferences. The impact of socioeconomic interactions is not treated in the present work due to the considerable difficulties in
computing them along with interaction effects and not because we regard their potential effects as
marginal. On the contrary, a follow-up paper under way will explicitly address this specific issue. The
general utility function used is the following:
U jk = !1 jn SQ + !2 j RENT + ! 3 j ACC + ! 4 j AIR + !5 j NOISE + " j Z + #
(1)
Ujk is the overall utility of the jth participant for k attributes in the experiment proposed to the four
member-types (mother [M], father [D], adolescent [A] and joint-family-decision [F]). β1jn is the
7
In the words of Manski, “Empirical analysis of social interactions would particularly benefit from performance of welldesigned experiments in controlled environments and from careful solicitation of persons' subjective perceptions of the
interactions in which they participate.” (2000, p 117).
7
coefficient of the constant capturing the intrinsic preference of the jth respondent for alternative n. β2jβ5j and θj are coefficients whereas Z is the matrix of socio-economic characteristics of respondent j.
The variables to be estimated are the SQ (codified as a dummy = 1 when the current housing is
chosen), RENT (measured in euro), ACC (measuring the access time in minutes), AIR (identifying the
level of air pollution) and NOISE (level of noise).
While MNL is the most commonly used choice model, nonetheless it exhibits well-known restrictions
that limit realism, particularly in cases where individuals have diverse preferences and behavioural
attitudes (Hensher et al. 2005, Train 2003). This fact may not be overlooked given the aim of
assessing the preferences of different household members. In a MNL setting all member-types are
assumed to exhibit a zero degree of random preference heterogeneity. In other words, the vector of βs
merely reflects a sample mean. What is more, MNL assumes that individuals’ unobserved utility is
uncorrelated across alternatives and over repeated choices. In brief the factors explaining the
unobserved utility are assumed to be perfectly random.
Mixed multinomial logit (MMNL) represents a major breakthrough in discrete choice modelling
(Train 1998, Hensher and Greene 2003). As implied by the name, MMNL is effectively a mixture of
logits. The point of departure is a basic MNL that is brought to accommodate heterogeneity by
iteratively taking draws of the estimated coefficients from a predefined underlying (mixing)
distribution (e.g. normal, lognormal, triangular, etc.). This procedure is repeated numerous times and
the outcomes averaged to produce the desired results.
3.2 Hypotheses testing for individual and triadic group choices
At this stage we can consider response heterogeneity more rigorously. Binary comparison of the
responses allows us to test the hypothesis of preference equality for single attributes. More formally
we have:
H1: the preferences regarding single attributes will not be identical for the different members. The null
hypotheses for this proposition should thus be rejected:
!10 : " kD = " kM = " kA
(2)
Does the utility function of single respondents differ from the pooled or post-discussion group utility?
By analyzing the coefficients of the members and comparing them to family responses one can
understand to what extent family members agree on the relevance of the different attributes in line
with sampling approach n°2 (see par. 2.2). Alternatively, one may test the null that it is the pooled
choices to reveal the correct preference structure in line with sampling approach n°1. If the pooled
answer correctly represents household utility then randomly selecting mothers, fathers and adolescents
would not generate particularly biased results. On the other hand if a specific single member
8
adequately represents family preferences then the representative member assumption cannot not be
rejected and interviewing only that specific member would cause no distortion. This implies that
interviewing both single member-types as well as the family would not be resource-efficient.
H2: we control if the preferences of the pooled sample are an adequate representation of the
preferences of the single sub-samples. In other words we test the H2 hypothesis by using a market
segment test. We want to reject the null of preference equality assumed by randomly interviewing
respondents and ignoring member-type issues.
H 02 : ! kPooled = ! kA + ! kM + ! kD
(3)
H3: we check whose single member-type preferences are the most representative of the joint family.
This test will help individuating the most suitable respondent to interview for the aim of the study.
Family
H a3 : ! k
Family
H b3 : ! k
= ! kA
= ! kM
(4)
Family
H c3 : ! k
= ! kD
Based on these tests we will also estimate the bias implied by each hypotheses.
4
Data and sample description
4.1 Development of the stated choice experiment
4.1.1 Description of survey instrument
A SP experiment was administered to measure individual and household preferences for residential
location. It was based on a pivoted design that presented two alternative housing bundles and the
status quo situation. The hypothetical housing alternatives are related to the respondent-specific status
quo and, more precisely, levels are expressed both in percentage around the RP (Revealed Preference)
values as well as in discrete variations for the environmental attributes. The experiment was unlabeled.
The reference status quo alternative is based on the levels stated by the respondents (see Appendix).
This procedure was adopted since the arrival point for different respondents was not necessarily the
same8. The status quo is inserted also to increase the degree of realism and to avoid artificially
boosting the part worth utilities of the remaining attributes.
8
This situation off course generates different travel times among members.
9
4.1.2 Attributes and levels
The levels of the attributes for the experiment are drawn from recent literature on residential choice.
We include four attributes that are considered to be among the most influential in choosing a housing
situation. The final selection consists of rent, air pollution, noise and accessibility to work or school
Table 1 illustrates these attributes and the levels used to describe them.
Table 1. Attributes and levels
Rent
Air pollution
1
20 % lower than current
1
Very low level of emissions
2
10 % lower than current
2
Acceptable level of emissions
3
Same as current
3
Quite high emissions
4
10 % higher than current
4
Very high emissions
5
20 % higher than current
Accessibility
Noise
1
Half the time to reach work/school
1
Quiet house
2
Same distance as currently
2
Low level of noise
3
50 % more time to reach work/school
3
Quite noisy
4
Very noisy
A full profile, fractional factorial design was used to combine the attributes and levels. In the case of
three alternatives, each having four attributes with three to five attribute levels each, the total number
of combinations is 5×3×42=240. Since it is impossible to show the full design to a single respondent
the design was subdivided in 15 blocks where each choice set consisted of 16 choice tasks. Given the
sample of 53 respondents of each member-type, the design was “covered” more than three times for
each member-type. Four tasks were holdouts, designed to test for monotonicity (2 tasks) and stability
in behaviour (2 tasks). These were not used for estimation.
4.2 Sequential survey administration
A two-step methodology was used to complete interviews with three-component families consisting of
fathers, mothers, adolescents as well as family (all members responding together). The choice tasks
combined four attributes characterizing the residential localization denoted by a short definition. The
conjoint design guarantees that choices take place between different profiles rather than single
attributes thus avoiding abstract rating or ranking exercises. A summary of the explanatory variables is
given in the Appendix. The study involved the following three steps:
Step 1 (pre-interview / individual task): The interviewees answered questions on individual
and family socio-demographic characteristics, attitudes and present housing conditions. Each
member conducted the interview without the presence of other members to avoid external
influence.
10
Step 2 (interview / individual task): The first round of choice tasks was individual. The aim of
this step was to uncover each member’s preferences. Respondents were instructed to choose
on the basis of their own preferences only. More in detail, they were told, “In this part of the
study we are interested in your opinion. We would like you to choose the housing alternative
that you prefer the most.”
Step 3 (interview / group task): The second round brought the members together and
discussion was encouraged in order to reach a joint decision. The families, in this step, were
instructed to jointly select an alternative and, more specifically, they were told, “We would
like you to choose the housing alternative that you all can agree on among the following.”
Five university students, adequately instructed, interviewed 53 households. The interviews were faceto-face computer assisted (CAPI) and carried out in the home of the respondents. The students were
trained in interview administration and instructed to find families living together and including, at
least, one adolescent 9.
4.3 Description of sample
The sample consisted of 53 Italian households, implying that 212 interviews were carried out in total
(4 member-types). The majority was located in the city of Rome and in the Friuli-Venezia-Giulia
region. Most families included three (53% of the sample) or four (37%) members: mother, father and
son/daughter. In families with more than 3 members, only 1 adolescent was interviewed. We consider
this sampling approach, implicitly adopting a “representative child” hypothesis, a reasonable trade-off
between accuracy and complexity (Kato and Matsumoto 2009). Most households (59%) stated a
family income within the range of €30.000 - €60.000. The age of the respondents ranged from 11 to 70
years where the average age of adolescents was 22, 50 for mothers and 54 for fathers. On average the
parents had a similar level of education with 32% having concluded at least one year of university.
The work status is slightly different for men and women. The former was more represented in
freelance positions while the latter were over-represented in employee positions. Among adolescents
47% were female. An overview of the characteristics of the respondents is given in the Appendix.
When asked if they would approve of stricter traffic regulations the mothers gave the strongest support
(43%) while 38% of adolescents and 34% of the fathers said yes. It is interesting to note the perception
and acceptance heterogeneity among members. At the aggregate level few among the respondents saw
their residential location as not acceptable on a likert-type scale regarding noise and air pollution. The
mothers and fathers had a similar opinion of current air pollution while adolescents found it both
higher and more acceptable than the parents. The current noise level was seen as more severe among
mothers and less so for adolescents. The mothers also described the current level of noise as less
9
Such a sampling procedure is not ideal from a statistical standpoint but proved a necessity due to the nature of the
interviews and is in line with the procedure employed by Hensher et al. (2008).
11
acceptable compared to the other components. Considering accessibility to work/school the mode
choice was quite different between members: adolescents walk (15%) and drive (43%), fathers drive
(60%) while mothers mostly drive (47%) or use public transport (26%). The fathers had a slightly
longer trip to work in line with previous research (Blumen 1994). Although spending more time in
commuting the fathers found the mean travel time to be more acceptable than adolescents did.
5
Econometric results
5.1 MNL specification
A MNL was estimated as a reference model. Results are reported in Table 2. All estimations were
performed using Nlogit 4.0 (Greene 2007). In the first column of the table the variables are listed. A
separate model for each member-type and for the joint household choice was estimated. For each
model we report the value of the coefficients and t -statistics. Coefficients (βSQ, βACC, βRENT, βAIR,
βNOISE) are all statistically significant and have the expected signs. The MNL is estimated using the
absolute values for time and rent. The stated levels of air pollution and noise are used to pivot the
environmental coefficients. The SQ variable is coded 1 for the current housing and 0 otherwise. As
such it expresses the desire to remain in the current housing situation along with the general influence
of omitted variables (Train 2003).
Table 2. MNL model results
Family
Variable
Coeff.
SQ
0,717
Rent
-0,007
Acc
-0,069
Air
-0,947
Noise
-0,242
Scale
1
Summary statistics
LL*
-2314,894
LL(const.)
-3726,493
McFadden
.725
Rsq
Adolescent
Mother
Father
t-ratio
Coeff.
t-ratio
Coeff.
t-ratio
Coeff.
t-stat
7,2
-9,6
-8,3
-12,1
-3,1
fixed
0,542
-0,004
-0,051
-0,459
-0,187
0,676
8,2
-8,9
-9,2
-10,3
-3,9
18,5
0,457
-0,007
-0,039
-0,958
-0,225
0,925
5,1
-9,9
-5,3
-13,1
-3,3
18,7
0,407
-0,004
-0,028
-0,722
-0,152
0,724
6
-7,6
-5,9
-13,1
-2,9
18,8
The results reported are comparable among them since they were scale corrected using the nested logit
“trick” (Hensher and Bradley 1993). Data indicate the adolescent is the most interested in status quo
and accessibility. In line with results obtained by Molin et al. (2001), we believe that a plausible
explanation of the high preference of the adolescent for the status quo might be that he/she has strong
links with friends living in the immediate surroundings. Likewise the importance of accessibility is
high for the adolescent. On the other hand the concern for the environmental aspects (noise and
12
pollution) was, along with rent, most pronounced for mothers, whereas fathers are characterised by
relatively low values of the βs for all attributes10.
5.2 MMNL and individual specific MMNL specification
Several studies have applied mixed multinomial logit (MMNL) to measure variation from unobserved
sources. The MMNL specification was used allowing status quo, accessibility and air pollution to vary
randomly across respondents and assumed to be normally distributed (Train et al. 1998). To avoid
artificially suppressing heterogeneity no constraints were imposed on the distributions. The standard
deviation of the noise parameter was not statistically significant in any of the models estimated.
WTP/WTA identification requires a fixed βRENT.
Table 3. Random parameters models
Family
Adolescent
Mother
Father
Variable
Coeff.
t-ratio
Coeff.
t-ratio
Coeff.
t-ratio
Coeff.
t-ratio
Rent (non r)
-0,014
-8,5
-0,009
-8,1
-0,014
-8,8
-0,009
-7,3
Noise(non r)
-0,983
-6,0
-0,771
-6,2
-1,155
-6,9
-0,745
-5,4
SQ (r.n)
1,427
5,0
1,150
5,4
1,179
3,8
1,140
4,4
SQ (st dev)
1,610
5,9
1,096
4,4
1,940
6,3
1,554
5,8
Acc (r.n)
-0,163
-6,6
-0,151
-6,2
-0,122
-5,0
-0,111
-5,7
Acc(st dev)
0,051
1,9
0,065
3,0
0,070
2,7
0,056
3,1
Air (r.n)
-1,957
-7,7
-1,131
-6,4
-1,693
-8,4
-1,674
-8,1
Air (st dev)
0,777
4,3
0,698
4,3
0,449
1,8
0,668
4,2
Summary statistics
LL*
-287,505
-348,225
-300,531
-325,775
LL (const.)
-698,717
-698,717
-698,717
-698,717
Rsq
.467
.367
.468
.414
RsqAdj
.463
.363
.464
.410
The results reported in Table 3 indicate that the introduction of housing attributes with random
parameters improves the statistical fit compared to the MNL specification. All parameters in the model
have the expected signs and are statistically significant. The standard deviation for each of the mixed
coefficients was statistically significant at the 5% level. This indicates the presence of heterogeneity
among all member-types regarding travel time, air pollution and the status quo. The results indicate
that there is no underlying unitary preference structure in our sample.
10
The scale factor for fathers is as low as that of the adolescent. This implies that the standard deviation of the observation is
relatively high and there is a high degree of noise in the data. The mother is more akin to the response of the family with a
high scale factor.
13
5.3 WTP/WTA estimates
The calculations of the WTP/WTA measures for the attributes show that there is no specific influence
deriving from the model adopted. In fact the results of the MNL specification are generally in line
with those derived from the MMNL specification with the only exception being accessibility. Daily
WTP/WTA measures are reported for facilitating interpretation since monthly rent is used as the
numeraire (Table 4).
Table 4. WTP/WTA results
MNL
RPL
Family
Adol.
Mother
Father
Family
Adol.
Mother
Father
SQ (€/level)
-4,07
-4,86
-3,11
-4,61
-3,33
-4,08
-2,79
-4,17
Accessibility (€/hour)
23,08
27,11
14,94
17,33
22,74
32,15
17,23
24,37
Air pollution (€/level)
3,12
2,42
3,37
4,40
4,56
4,01
4,00
6,13
Noise (€/level)
1,99
2,16
2,03
2,04
2,29
2,73
2,73
2,73
Notes: the WTA estimate is referred to the SQ while the remaining attributes are described as WTP, All values are
referred to a daily WTP/WTA.
In the MNL specification, notwithstanding the fact that the mothers had the highest environmental
coefficients, the fathers show a higher WTP for both noise and air pollution. Adolescents are
characterised by a strikingly high WTP for accessibility and a relatively high WTA for the status quo.
In the MMNL specification, similar results are obtained. WTP for accessibility coefficients are, on
average, greater than in the MNL specification. The other noteworthy aspects are fathers’ increased
interest in air pollution, noise and status quo. The apparent loss of intensity in mothers’ preferences is
due to the pronounced interest this group has for rent, used as denominator in the WTP/WTA
measures. Despite this, mothers appear to be the best predictor of the joint choice outcome.
5.3.1 Member and individual specific differences in WTP/WTA
In this paragraph we report the results for individual specific WTP/WTA estimates which are useful to
compare the distribution of the various coefficients around the mean and show their relative
dispersion. At the individual level the status quo attribute is, in general, not statistically different from
zero and in line with the general ex ante expectation that not all the interviewees have a strong and
common view of the status quo situation. As noticed earlier adolescents have the highest WTP for
accessibility as the kernel density confirms. Fathers, in this case represent the joint family choice
better, although mothers are also proximate. In other words the family outcome is de facto an average
of the fathers and mothers WTP. All the coefficients are statistically significant and different from
zero with the exception of the mothers; they are positive, as one would expect, notwithstanding the
fact that no restrictions on the βs signs were imposed.
14
Regarding WTP for decreasing the level of air pollution one notices that mothers have an extremely
homogeneous evaluation of air pollution albeit with a lower mean value with respect to other membertypes. Adolescents’ evaluations of air pollution are in line with those of the family while fathers have
both the highest average values and the most spread out distribution. The WTP data show adolescents
to be the least reliable proxy for understanding family preferences (several β’s are non significant and
some are even negative). Notwithstanding this, their final values are the most similar to that of the
family. This is probably the average of fathers’ and mothers’ preferences.
Figure 1. Kernel – Conditional distributions of marginal WTP
15
Heterogeneity in the sample indicate considerable preference differences both among member-types as
well as within them. Thus, we implicitly consider the H1 hypothesis rejected. In more detail, in the
case of air pollution, mothers could well be treated by adopting a “representative mother” hypothesis.
On the contrary, adolescents and fathers are both distinctly different from mothers for this attribute
and there is evidence of substantial disagreement within these groups.
5.4 Similarity and relative power
Similarity is a proxy for relative power. Similarity between a member-type ex-ante preferences and the
joint ex-post ones implies that this member-type has a higher relative power over the joint decision. In
fact, this implies that the other household members must accept a larger deviation from her (his)
preferred choice outcomes. This logic is commonly used in studying dyadic decisions where there is
no ambiguity as to who prevails. However, with more than two participants, identification of the
source of relative power is more complex. In fact, an intermediate position between two extremes
could be explained in two different ways. It may indicate power equality or, on the contrary, it may be
due to the dominance of a member that happens to lie in the middle of the extreme preferences.
Table 5. Standard deviation between Family and single members (MMNL normal dist.)
Adolescent
Mother
Father
WTP sq
0,387
-0,260
0,431
WTP acc
-1,431
0,826
-0,231
WTP air
0,358
0,324
-1,132
Table notes: The absolute values reported are the delta between the family and each
member-type WTP/WTA βs in terms of standard deviations of individual estimates. The
sign represents the distance (positive or negative) that the family has compared to each
single member.
The data reported can be used as a formal description of the proximity of each member-type to the
joint choice outcomes. For example, fathers are more willing to pay for accessibility (24,37 €) than the
family as a whole (22,37 €) but they are also the best single member-type predictors for this attribute.
In fact, the WTP standard deviation of fathers from the family is the smallest (-0,23 above) compared
16
to mothers (0,82 below) and adolescents who are 1,43 standard deviations above the family (see Table
5). Considering air pollution one can observe that fathers are furthest away from family preferences
(1,13 stnd. dev. above). Instead, mothers and adolescents have similar positions (0,32-0,36 stnd. dev.)
but below family estimates.
In general relative power analysis can be complicated in the case of three-member families. This is
due to the intricate identification of the source of power. In fact to determine the relative power of
each member-type we cannot solely rely on similarity but also need to account for ex-ante preference
intensity. An emblematic example of this point, in our sample, is adolescents’ influence over air
pollution. Despite the fact that adolescents show a limited interest for this attribute according to the
previous measure of similarity adopted, one could mistakenly interpret this as a result of relative
power. However, we are convinced that the final result is most probably due to a reconciliation
between fathers’ and mothers’ distinctly different preferences averaging out over adolescents’
intermediate position.
5.5 Representative member hypotheses
To test the representative member hypothesis one should assess whether the utility functions of single
respondents differ from the pooled or post-discussion group utility. SP studies typically interview
single members to gather “representative” information regarding collective preferences. The
shortcomings of the representative member assumption are revealed in two specifications. Firstly we
test the null that the pooled choices correctly reveal the preference structure expressed in the joint
choice (H2). Secondly we analyse the coefficients of member-types and compare them to family
responses. This allows us to discover to what extent they agree on the priorities for the different
attributes (H3a, H3b, H3c). For H2 a log-likelihood ratio test shows that the pooled version of the
sample is not a statistically valid representation of individual answers 11. For H3a, H3b, H3c looking at
the box-plot reported in figure 2 one can appreciate the difference in WTP/WTA distribution among
member-types.
11
Indeed the test of the equality between the pooled model against the sum of individual models yields a test statistic of
36,16 to be compared against the critical χ2 value (at 95%) of 25.
17
Figure 2. Box-plot of Individual specific WTP/WTA
Notes: sq is referred to the status quo value, acc indicates accessibility and air
stands for air pollution. The unit of measurement is the monthly WTP/WTA
18
Mothers’ WTP for access and air pollution abatement are both quite concentrated around the mean
and, at the same time, similar to those of the family.
5.6 Quantifying the bias of the “representative member” hypotheses
In this paragraph we illustrate the potential bias induced by an uncritical adoption of the representative
member hypothesis. These considerations might be extremely important for policy evaluations. We
compare the family WTP/WTA values, derived from the MMNL, with those of each member-type as
well as with the pooled sample.
Figure 3. Illustration of WTP/WTA bias based on MMNL WTP
The use of a randomly selected sample of family member-types would provoke an up-ward bias for
accessibility (1,27 €). For the other attributes there is no relevant distortion.
On the other hand the comparison between single member-types and the family data reported give us
an idea of the entity of the over- or under-estimation bias introduced were we to use the targeted
sample strategy. For instance in the case of studying accessibility by targeting mothers we would
underestimate the WTP for accessibility by 5,50 € per hour. By targeting adolescents for accessibility
one would over-estimate by 9,41 € per hour. Based on our results only noise could be aptly studied by
targeting any member-type.
6
Summary and conclusions
The representative member hypothesis has, since long, been the cornerstone of household analysis. Its
validity has only recently been questioned. In fact, analysts have generally treated the household as if
it were an individual, a single economic unit without much interest as to what went on within it.
19
Theory building and policy definition assumed households to have a single set of preferences. Were
this true, inquiring the preferences of a single individual would be sufficient to model family ones.
This approach is acceptable if either the representative member adequately describes other members’
preferences or if he/she holds the power over a certain decision. Research findings, in the last decades,
cast doubts over these assumptions. What is more, families make influential decisions jointly. This
makes it difficult to locate an individual that is solely responsible for the decision (Davis and Rigeaux,
1974). Traditional indicators, such as relative income, may not be good proxies for ability to influence
choices. Past empirical research point to large differences between individual and joint choices (Arora
and Allenby 1999, Corfman and Lehmann 1993, Dellaert et al. 1998, Molin et al. 1999, Beharry-Borg
et al. 2009). When families decide jointly in the presence of heterogeneity we need to consider novel
methods to detect preference disparity. Lastly, if single members were able to describe the preferences
of the family, then we might still be able to salvage the traditional representative member approach.
However, studies find a weak ability to assess other members’ preferences (Corfman and Lehmann
1987, Menon et al. 1995) and a limited capacity to predict own influence over joint choice (Dellaert et
al. 1998). So, what is done in this paper to analyze interactive family decision-making keeping these
critical comments in mind?
The paper tests three hypotheses. We first reject the hypothesis that there is no significant preference
heterogeneity both among and within different member-types. Subsequently, we also reject the
hypothesis that either a specific member-type or the average member can adequately represent
household preferences for each of the attributes. Finally, we quantify the WTP/WTA bias inherent in
the uncritical adoption of the representative member hypothesis. This is illustrated for both the specific
and average member-type hypotheses.
Future research will: explore more cost efficient and empirically robust sampling strategies; develop
advanced methodologies to study relative power in a triadic context; research and identify agentspecific, choice-specific and latent variables to segment the respondents.
7
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