Directory UMM :Data Elmu:jurnal:J-a:Journal of Economic Psychology:Vol21.Issue1.Feb2000:
Journal of Economic Psychology 21 (2000) 73±90
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Random utility maximiser seeks similar: An economic
analysis of commitment level in personal relationships
Samuel Cameron
a,*,1
, Alan Collins
b
a
Department of Social and Economic Studies, Richmond Building, University of Bradford, Richmond Road,
Bradford, West Yorkshire BD7 1DP, UK
b
Department of Economics, University of Portsmouth, Locksway Road, Southsea Hampshire PO4 8JF, UK
Received 5 March 1998; received in revised form 28 September 1998; accepted 10 September 1999
Abstract
This paper presents the ®rst attempts by economists to estimate a random utility maximisation model for the choice of desired involvement level in heterosexual relationships. A
sample of newspaper `personal' advertisements is used to estimate a multinomial logit. Age is
found to reduce the net probabiblity of seeking a casual relationship. A number of variables
are found to be signi®cant determinants of declared entry level. Ó 2000 Elsevier Science B.V.
All rights reserved.
PsycINFO classi®cation: 2980
JEL classi®cation: J12
Keywords: Partner age; Relationship; Entry level; Partner search; Personal ads
*
Corresponding author. Tel.:+44-1274-234-772.
E-mail address: [email protected] (S. Cameron).
1
Present address: Development and Project Planning Centre, Pemberton Building, University of
Bradford, Bradford, West Yorkshire BD7 1DP, UK.
0167-4870/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 4 8 7 0 ( 9 9 ) 0 0 0 3 7 - 9
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
``The sentiment of love is, in itself, agreeable to the person who feels it. It soothes and
composes the breast, seems to favour the vital motions, and to promote the healthful
state of the human constitution; and it is rendered still more delightful by the consciousness of the gratitude and satisfaction which it must excite in him who is the object of it.
Their mutual regard renders them happy in one another, and sympathy with this mutual
regard, makes them agreeable to every other person.''
[Adam Smith ± Theory of Moral Sentiments, 1759]
1. Introduction
Economists inspired by Becker (1973, 1974) have (see Grossbard-Shechtman, 1995; Bergstrom, 1996) investigated family formation and related topics
such as extramarital aairs (Fair, 1978). However there has not been explicit
consideration of the process of partner selection with the exception of the
early work of May (1954) and the illuminating work of Lemennicier (1988)
who also gives some descriptive statistics on personal advertisements. The
problem of matching relationship partners, at the aggregate level, has been
modelled mathematically in the important work of Bergstrom and Bagnoli
(1993) and Burdett and Coles (1997) and the micro matching problem was
earlier studied by Gale and Shapley (1962). The focus of Burdett and Coles is
on equilibrium in the aggregate market. The degree of reduction from the
salient characteristics of the real world is strong, as the model is basically a
straightforward analogue of the labour market where employers and workers
pair according to productivity. A single real number index `pizazz' is used to
represent the attributes being oered. Individuals meet at periodic intervals
to observe each other's `pizazz' with a view to either marrying or not.
From our perspective, the principal shortcoming in the Burdett and Coles
world is the neglect of the multidimensionality of the implicit contracts
formed by couples who pair with a view to marriage. In this area, it is not
always easy to separate the search process from the end state. Economists
have ignored the choice of `entry level' to the process being signalled by a
partner seeker, for example those using personal ads. in newspapers, oer
such things as `friendship possibly leading to relationship', or `seeks soulmate', or `daodil seeks vase', or `young female seeks solvent older male'. 2
Lemennicier (1988), using French advertisements, looks at requests for
characteristics such as beauty, sense of humour, aection, height and weight
2
The phrases cited have all been seen, by the authors, in personal advertisements, although not
necessarily in the sample used here.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
75
but he does not look at the process of emitting signals about the nature of
relationship sought. The neglect of these signals is partly because of the focus
on the companionate heterosexual marriage as a status quo that economists
have simply accepted (see e.g. Posner, 1992). This is increasingly questionable
as the average amount of time spent by individuals in an of®cially contracted
male plus female plus children relationship is declining in modern society due
to a number of factors. Divorce is an obvious one but there are also factors
leading to an expanded pre-marriage phase. In 1995, in the UK, 70% of
women had lived with their future husband before marriage compared with
5% in the mid-1960s. Of men aged 16±59, in 1995, 21% were described as
single never married (source: Population Trends 80, 1995). In the empirical
part of the paper we examine, using personal advertisements, stated preferences about the entry level of relationship sought. We estimate a multinomial
logit model for a four-way split between long-term, casual, platonic, and
ambiguously de®ned relationships. This is the ®rst ever estimation of this
kind of model as Lemennicier's (1988) work on personal advertisements did
not extend into econometric estimation.
2. Economic analysis of entry level choice in personal advertisements
Individuals are assumed to maximise stable underlying utility functions,
for interaction with partners, subject to constraints. A partner must ®rst be
selected from the available pool, and once their willingness to engage in
evaluation of the product (i.e. the potential relationship) is established,
search is then conducted over their attributes.
The underlying utility function may be characterised as follows:
U f S; M; X ;
1
where S is sexual services de®ned broadly to include any sexual arousal or
grati®cation received from interaction with a partner, M the companionship broadly de®ned to include non-sexual exchange, and X is the composite variable representing all other things, which obviously spans private
goods and public goods which might bring scale economies in sharing.
This is a general formulation of mate search which encompasses homosexuality and has, as the extreme case of public goodness in X, the
production and rearing of children, whether or not these are genetically
linked to the partners. We assume continuous substitutability and convexity
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
between S and M, at least over certain ranges of the utility function. The
constraints are primarily related to time and search costs in procuring S
and M.
A rudimentary diagrammatic exposition is provided in Fig. 1, which is a
simple indierence curve presentation. There will be an equilibrium choice of
partner where the marginal choice of substitution between S and M equals
the marginal rate of transformation, given by procurement costs. We assume
that the utility function is invariant with respect to intrinsic endowments of
the searcher. Utility may alter with age due to biological transformations in
individuals, however, we adopt a Becker and Stigler (1977) type assumption
that individuals have the same lifetime utility function. Differences between
underlying preference sets are therefore assumed to be randomly distributed
errors.
Systematic dierences in observed behaviour will therefore be attributed to
dierences in the constraints. Ceteris paribus, a more conventionally attractive individual (i.e. in a Burdett and Cole world, this would relate to a
high level of pizazz) will have the second budget line shown in Fig. 1. In
equilibrium they will have more S; whether or not they have more M depends
Fig. 1. Partner choice.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
77
on the precise nature of their utility function. 3 Conversely, having a child
from a previous relationship will shift the budget constraint and lead to lower
levels of S and M. The shift is a composite of reductions in time availability
and potential as a partner prospect. To attain the equilibrium position, the
individual must attract a pool of potential partners.
3. A speci®c model of entry level signalling for personal adverts
Fig. 2 is a revision of the analysis of Fig. 1 in terms of zones which connote
the speci®c entry levels analysed here. Basically, there is a probability that the
advert of an individual will be construed as signalling one of the four states:
platonic, ambiguous, long-term, or casual. The probability depends on tangency within one of the zones. Platonic is a corner solution on the M axis.
The remaining states are ranked according to the S/M ratio; for a given level
of S, the highest M is denoted `long-term', the next highest is denoted `ambiguous', whilst the lowest is denoted `casual'. The graph shows initial
equilibrium (E1 ) in the ambiguous zone for the indifference curve I1 given the
budget constraint BL1 . Let us suppose that the same individual was suddenly
blessed with more S related resources, then the budget constraint shifts to
BL2 giving us the new equilibrium (E2 ) on the indifference curve I2 . This
results in a change of status to casual from ambiguous. In a stochastic environment, the shift in S related resources obviously raises the probability of
casual over ambiguous (most appropriately, for the later modelling, the log
odds ratio). Obviously, homothetic preferences would mean that an overall
shift in the resource constraint would never lead to a change in the zonal log
odds ratios. We assume non-homothetic preferences, hence, the converse will
generally occur.
3
A referee has queried the use of `pizazz' or `sexiness' as shifting only the S element and not the M
element. There seems to us to be no actual hard evidence as to whether perceived attractivness is correlated
with companionship qualities. In a state of imperfect knowledge, individuals may use the perceived S of an
in individual as a proxy for other things like earnings power which could in¯uence the volume of M.
However, the evidence in Hammermesh and Biddle (1994) for a link between labour market success and
perceived attractiveness is very weak. In any case, this presentation assumes all such other factors to be
held constant when the choice is being made. Further, this is purely an illustrative diagram and the reader
is, of course, free to consider any possible scenario which they feel to be more apposite.
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 2. Commitment levels.
4. Data
Economists working in the area of personal relationships, such as Becker,
have not attempted to obtain explicit statements of preferences over partners
with the exception of May (1954) and Lemennicier (1988) who used a modest
size sample of French newspaper advertisements n 135.
Others have not been quite so neglectful as economists. A variety of
psychologists have been using the personal advertisements columns in
newspapers and magazines to test the propositions of `evolutionary biology'
(e.g. Kenrick and Trost, 1989; Thiessen, Young & Burroughs, 1993; Wiederman, 1993). They code the verbal text of the ads. into quantitative information (primarily dummy variables) to represent such things as stipulated
desire for wealthy, attractive partners, and oers of own attributes and assets. Personal advertisements are a fruitful source for economists working in
this area. It is possible to construct variables for the entry level stipulated, by
the placer of the advert, through evaluating the intent implicit in various
words.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
79
As already indicated we use a fourfold categorisation. The classi®cation
into casual, long-term, platonic and ambiguous groups was based on the
presence of keywords. Casual was based on explicit reference to a primarily
sexual partner. Long-term is coded on the basis of an explicit stipulation of
this, or a desire for sexual exclusivity, including mentions of marriage. Platonic is coded on the basis of a request for friendship with an explicit reference to non-sexual liaison, or an implicit deterrent to sexual overtures e.g.
`strictly ballroom'. Obviously these data are not devoid of ambiguity as they
have to be constructed from verbalisations which are subject to dierent
interpretations. In an attempt to overcome this, we adopt the standard
procedures of the specialist literature by using independent coding by one of
the authors and another researcher, who then conferred on anomalies, and
arrived at a consensus.
The data are derived from quantifying the text of 259 personal advertisements in the `Encounters' page in the English national newspaper `Sunday
Times' over the period from the 7th August 1994 to the 9th October 1994.
The variable de®nitions and names are given in Table 1. The pricing structure
of £11.75 per line plus £11.75 for a box number was used to construct the
PRICE variable. AGE is estimated as a mid-point if verbal information only
is given e.g. ``mid-thirties'' 35 although in many cases actual age is given. It
is well known that some individuals understate their age but this is of no
consequence for the analysis, so long as this deliberate error is independent of
other characteristics. Financial characteristics oered and sought are used to
create dummies based on the appearance of key phrases e.g. ``wealthy gent
Table 1
Variable names and de®nitions
Variable
De®nition
PRICE
cost of advert. in pounds
AGE
declared age of advertiser in years
FEMALE
1 if advertiser female 0 male
CHILDREN
1 if declares having children
FINOFF
1 oers ®nance
FINSOU
1 seeks ®nance
PHYSOWN
scale (0±5) of description of own physical characteristics
PHYSOU
scale (0±5) of description of desired partner physical characteristics
SOPHOWN
1 if declares `sophisiticated' leisure interests
SOPHSOU
1 if requires `sophisticated' leisure interests in partner
EXPOWN
1 if declares expensive leisure interests
EXPSOU
1 if requires expensive leisure interests in partner
All dummies are coded to 0 otherwise.
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
seeks ...'' or `solvent'. Physical characteristics are coded on a scale of 0±5
depending on the number of words used. For these variables, the number of
words is a proxy for the importance of physical attributes to the advertiser.
For the `expensive' tastes variables keywords such as `yachting' were used to
code as 1. For `sophisticated' tastes, items such as art, theatre were used to
code as 1. The variable which is most likely to be strategically misrepresented
is the declaration of having children. The frequency of declaration of children
is implausibly low given the age of the placers. Declaring children is a signal
to the potential respondent of additional dimensions of the relationship.
Potential respondents will be aware that those who do not declare children
may have them, in which case this facet will feature in the strategic interaction, by telephone, or face to face meeting, which follows taking up an advert. This aspect of interaction cannot be modelled with these data.
The means of the variables by group are shown in Table 2. These suggest
that certain variables are likely to be of use in discriminating between groups.
Seekers of long-term relationships spend much more on specifying their
transaction, as shown by price of advert, whilst those seeking platonic relationships spend much less. Seekers of platonic states are notably older than
the rest and considerably more likely to be women. The distribution of declaring children is skewed heavily to the long-term state seekers as we would
expect. Those seeking casual relationships display a much greater emphasis
on physical aspects of the relationship.
Table 2
Variable means by relationship type relationship type
Variable
Casual
Long-term
Platonic
Ambiguous
PRICE
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
N
102.13
39.9
0.37
0.01
0.68
0.297
2.176
1.19
0.198
0.055
0.10989
0.19780
91
108.61
41.9
0.5
0.128
0.577
0.372
1.487
0.705
0.179
0.0256
0.0512
0.192
78
88.8
48.3
0.76
0
0.52
0.36
1
0
0.24
0.04
0.2
0.36
25
100.15
42.5
0.41
0.015
0.71
0.29
1.57
0.74
0.25
0.123
0.077
0.23
65
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
81
5. Speci®cation and estimation
The data for analysis consist of variation across the individuals seeking
dierent relationship states but we have no measurement of characteristics of
the states. We therefore assume that each of the four relationship states has
utility:
Ui Vi ei ;
2
where U is utility, i the relationship state, V the systematic component, and e
is a random disturbance term representing unmeasured variation in tastes,
and the attributes of the relationship state. V consists of the variables identi®ed above. Individuals will choose the relationship state which ranks
highest in utility terms.
Assuming that the e's are independent and identically distributed, following a Weibull distribution, the model can be estimated as a multinomial
logit (see Cramer, 1991).
For the purposes of estimation, the model has to be normalised by setting
a base category for which the coecients are zero. There are therefore
i ÿ 1 3 sets of coecients for any such normalisation, and six sets of
pairwise coecients in all. The coecients of the model show the impact of a
variable on the log odds ratio for the pairing of the base category and the
category to which the coecients belong. Whilst the `t' ratios of these coef®cients provide some insight into the model, the values of the coef®cients
themselves are of limited use. A change in the value of a variable may increase the log odds of casual over long-term but, at the same time, decrease
the log odds of casual over the other states. The relationship of a state
prediction to a variable can therefore be non-monotonic. Interpretation of
the impact of the coef®cients therefore requires evaluation at some values of
the regressors. As most of the variables are dummies the usual procedure of
interpretation at the means is of limited usefulness. Accordingly we also
present simulations below for changes in the continuous variable age for
various combinations of the other variables.
Given the complexity of the model, in terms of the four states, and the six
sets of log odds, it is not easy to produce a standard list of expected signs and
magnitudes for the variables. Hence, we focus on highlighting some broad
relationships for the role of price of advertisement and age of the advertiser.
The price variable serves as a proxy for the search eort of the partner seeker.
One would, therefore, expect that more search eort be expended on seeking a
longer term partner than a casual partner, since the speci®cation of a more
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Table 3
Multinomial logit estimates of the relationship choice modela
Variables
INT
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
PRICE
State: Long-term
Base category: Casual
Coecients
ÿ1.38
(1.1)
0.02
(1.27)
0.24
(0.57)
2.65
(2.36)
ÿ0.25
(0.63)
0.07
(0.17)
ÿ0.47
(3.35)
ÿ0.46
(2.43)
ÿ0.73
(1.28)
0.32
(0.28)
ÿ2.01
(2)
0.77
(1.25)
0.01
(2.34)
Platonic
Casual
ÿ4.3
(2.1)
0.09
(2.73)
1.1
(1.62)
12.45
(0.02)
0.6
(1)
ÿ0.33
(0.5)
ÿ0.67
(2.39)
ÿ13.01
(0.09)
0.2
(0.24)
ÿ2.69
(1.55)
1.6
(1.19)
0.51
(0.55)
ÿ0.002
(0.15)
Ambiguous
Casual
ÿ1.62
(1.42)
0.04
(1.69)
0.28
(0.64)
0.7
(0.48)
0.54
(1.25)
ÿ0.29
(0.65)
ÿ0.24
(1.8)
ÿ0.46
(2.4)
ÿ0.69
(1.12)
2.28
(2.22)
ÿ2.47
(2.41)
0.88
(1.39)
0.003
(0.41)
259
15
ÿ275.0633
ÿ337.0999
N
Iterations
Log-likelihood
Restricted
(Slopes 0)
Log-L
Chi-squared
(36)
Pseudo R
squared
124.0732
0.184
Predicted
Actual
0
1
2
3
Total
0
1
2
3
Total
63
23
3
22
111
13
46
8
21
88
2
5
10
2
19
13
4
4
20
41
91
78
25
65
259
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
83
Table 3 (Continued)
Variables
State: Long-term
Base category: Casual
INT
1.38
(1.1)
ÿ0.025
(1.16)
ÿ0.3
(0.72)
ÿ2.59
(2.31)
0.32
(0.79)
0.02
(0.04)
0.44
(3.19)
0.49
(2.6)
0.94
(1.61)
ÿ0.51
(0.44)
2.4
(2.36)
ÿ1.16
(1.82)
ÿ0.015
(2.37)
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
PRICE
a
Platonic
Casual
ÿ2.95
(1.47)
0.067
(2.07)
0.84
(1.26)
ÿ15.56
(0.02)
0.87
(1.45)
ÿ0.36
(0.58)
ÿ0.22
(0.79)
ÿ12.43
(0.09)
1
(1.23)
ÿ3.08
(1.69)
3.71
(2.64)
ÿ0.37
(0.43)
ÿ0.016
(1.23)
Ambiguous
Casual
ÿ2.03
(1.03)
0.041
(1.31)
0.91
(1.35)
ÿ13.08
(0.02)
0.21
(0.36)
0.15
(0.23)
ÿ0.47
(1.71)
ÿ12.29
(0.09)
0.96
(1.14)
ÿ4.95
(2.8)
4.06
(2.87)
ÿ0.48
(0.56)
ÿ0.0064
(0.48)
Notes: Absolute t ratios in parentheses.
durable partnership is substantially higher in terms of detail. Regarding age,
older partner seekers have already established more clearly de®ned preferences, and acquired relationship-speci®c human capital from previous relationships, such that they are better able to discern compatibility. Accordingly,
we would expect a decline in the propensity to signal casualness. An alternative explanation is that older people are considered less attractive, something that may aect women faster than men (see Grossbard-Shectman, 1982).
6. Results
The results of estimating the model are shown in Table 3. The predicted frequencies are given by rounding to 1 from maximum probability.
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
All six pair ranking estimates of the V coef®cients and `t' ratios are
shown. 4
Comparing actual and predicted classi®cations, the percent correctly
classi®ed with the share of the state in the total sample in brackets are, for
casual 69.2 (35.1), long-term 59 (30.1), platonic 40 (9.7) and ambiguous 30.8
(25.1).
Age is a signi®cant positive discriminator of platonic from long-term and
casual. Gender proves to be a weak discriminating variable. For platonic
over casual, a positive in¯uence of being female is obtained at almost the 5%
level on a one-tailed test. The declaration of children is a signi®cant positive
predictor of long-term relationship seeking. The oer and demand for ®nancial characteristics proves not to be capable of in¯uencing classi®cation.
An emphasis on physical aspects of the relationship is a strong negative
predictor of long-term and platonic preferences.
Marginal eects (partial dierentials of probability with respect to X) can
be calculated for the two continuous variables, PRICE and AGE. Evaluating
these at the (full) sample means for casual gives absolute `t' ratios of 1.61 for
age and 1.55 for price. The corresponding marginal effects are a fall in the
casual probability of 0.007 for one year older and 0.002 for a one pound
increase in price. For long-term relationships, the `t' ratios for marginal effects, at the sample means are 0.48 for AGE and 2.34 for PRICE. The corresponding marginal effects are 0.0019 for AGE and 0.00295 for PRICE.
Statistical signi®cance, and the estimated elasticities, do not by themselves
provide clear insights into the meaningfulness of the results. One approach to
doing so is to simulate the impact of a variable change, under various different scenarios for the advertisers in the sample. Accordingly, we generated
Figs. 3±8 which simulate the distribution of probabilities amongst the categories for dierent set-ups as age goes from 25 to 50. In all cases, ageing
notably reduces the probability of seeking casual relationships. This fall is
generally redistributed to the ambiguous category rather than long-term relationships. The modal characteristics for the full sample were used for the
categorical variables, and the sample mean for PRICE, were used initially.
The impact of declaring a child is enormous, increasing the probability of
seeking long-term commitment by 0.48 for a 25-year-old woman and 0.46 for
a 35-year-old woman. Switching to a stronger orientation on physical char-
4
For the base categories shown the log likelihood converged at similar values. However, using
PLATONIC as the base category resulted in a failure to achieve convergence.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 3. Impact of age on choice for females without children declared.
Fig. 4. Impact of age on choice for females with children declared.
85
86
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 5. Impact of age on choice for females with child declared.
acteristics is associated with, in the absence of a child, a very high prediction
of casual.
The logit equation framework imposes interaction on the variables, in the
model, without the need for explcit recourse to interaction terms formed by
multiplying the variables together. For example, if one wishes to focus on
male±female dierences the impact of any individual variable will dier by
an amount due to the combined factors of the size of the FEMALE coef®cient and the combination of values of the other variables. Allowing for
parameter shifts across sex also runs into the problem of data sparsity as we
would then have some quite small samples within the fourfold classi®cation
within which there are quite infrequent occurences of 1 within some of the
dummy variables. The practice of only allowing the intercept parameter to
vary is a pragmatic solution often adopted even in models where there is no
inbuilt interaction. Nevertheless, following the suggestions of a referee, we
experimented with some further speci®cations (not reported) in an attempt
to bring out more clearly some of the expected results. A cut-down model
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
87
Fig. 6. Impact of age on choice for males without child declared.
featuring only age, children and the interaction of these yielded almost totally insigni®cant results on the parameters. Going to the opposite extreme,
estimation allowing all parameters to vary by gender resulted in similarly
dissapointing results. Adding a children±gender interaction term to the results shown in Table 3 failed to produce a `t' ratio of more than 0.5 in
absolute terms in any case. The most interesting variation was obtained by
adding interaction terms, with the female dummy, for the ®nance and
physical characteristics variables. The main result here was that an emphasis
on own physical characteristics by females reduced the likelihoods of their
choosing platonic or ambiguous in favour of casual and choosing ambiguous
in favour of long-term. Although the ®rst two results just given are what we
might expect, in terms of rational search behaviour, the latter is somewhat
contradictory. There are also some parameter changes for seeking ®nance;
this reduces the likelihood of women choosing casual in favour of platonic
or ambiguous. All the other parameter shifts were insigni®cant in this
augmented model.
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S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 7. Impact of age on choice for females without child declared.
Although the additional experimentation discussed above is not reported
in full detail because of the lack of statistically signi®cant coecients, this
does not mean that the results are devoid of substantive signi®cance. One
might argue that such variability indicates a lack of reliability due to a sample
size that is small relative to the spread of categorical responses. It is dicult
to establish a priori if this is true and we would obviously hope for larger
replicatory studies in the future to shed light on this.
7. Summary and conclusion
This paper has presented an economic analysis of declared preferences for
involvement level in personal relationships. This has been implemented empirically on a sample of `personal advertisements'. The random utility maximization model was found to have good predictive power and uncovered a
number of signi®cant relationships with the explanatory variables. A dra-
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
89
Fig. 8. Impact of age on choice for males with child declared.
matic decline in the pursuit of casualness with age was demonstrated. The
declaration of the presence of a child has an overwhelming in¯uence on the
choice of a long-term relationship. The pursuit of long-term relationships was
found to be signi®cantly related to resources expended in this mode of
partner search.
One might feel inclined to question the generalisability of these results.
Clearly, those in the sample are a self-selected group who have explicitly
chosen newsaper advertising as a means of searching for a partner. In this
rather obvious sense they are unlike the general population. However, this
does not necessarily limit the validity of this work which is concerned with
the examination of strategy and the expression of preferences. It would be
rash to conclude that advertisers are desperate lonely people with atypical
strategies or preferences especially given the growing resort to marketised
partner search due to economic factors emphasised earlier in this paper.
Further, the works cited in Section 4 suggest that advertisers have quite
similar characteristics to non-advertisers. Obviously, future research is
90
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
needed replicating this work using data from other advertising sources and
direct survey methods.
References
Becker, G. S. (1973). A theory of marriage: Part one. Journal of Political Economy, 81 (4), 813±846.
Becker, G. S. (1974). A theory of marriage: Part two. Journal of Political Economy, 82 (2), S11±S26.
Becker, G. S., & Stigler, G. J. (1977). De gustibus non est disputandum. American Economic Review, 68
(1), 76±90.
Bergstrom, A. (1996). Economics in a family way. Journal of Economic Literature, 34 (4), 1903±1934.
Bergstrom, A., & Bagnoli, M. (1993). Courtship as a waiting game. Journal of Political Economy, 101 (1),
185±203.
Burdett, K., & Coles, M. G. (1997). Marriage and class. Quarterly Journal of Economics, 112 (1), 141±168.
Cramer, J. S. (1991). The logit model. London: Edward Arnold.
Fair, R. (1978). A theory of extramarital aairs. Journal of Political Economy, 86 (1), 45±61.
Gale, D., & Shapley, L. (1962). College admissions and the stability of marriage. American Mathematical
Monthly, 69, 9±15.
Grossbard-Shechtman, A. 1982. A theory of marriage formality. Economic Development and Cultural
Change, 30, July, 813±830.
Grossbard-Shechtman, A. 1995. Marriage market models. In K. Ierulli & M. Tomassi, The new economics
of human behavior. Cambridge, UK: Cambridge University Press.
Hammermesh, D. S., & Biddle, J. E. (1994). Beauty and the labor market. American Economic Review, 84
(5), 1174±1194.
Kenrick, D. T., & Trost, M. R. (1989). A reproductive exchange model of heterosexual relationships. In C.
Hendrick, Review of personality and social psychology (vol. 10, pp. 92±118). Newbury Park, CA: Sage.
Lemennicier, B. 1988. Le marche du mariage et de la famille. Paris: Presses Universitaires de France.
May, K. O. (1954). Intransitivity, utility and the aggregation of preference patterns. Econometrica, 22 (1),
1±13.
Posner, R. A. (1992). Sex and reason. Cambridge, MA: Harvard University Press.
Thiessen, D., Young, R. K., & Burroughs, R. (1993). Lonely hearts advertisements re¯ect sexually
dimorphic mating strategies. Ethology and Sociobiology, 14 (3), 209±229.
Wiederman, M. W. (1993). Evolved gender dierences in mate preferences: Evidence from personal ads.
Ethology and Sociobiology, 14 (5), 331±351.
www.elsevier.com/locate/joep
Random utility maximiser seeks similar: An economic
analysis of commitment level in personal relationships
Samuel Cameron
a,*,1
, Alan Collins
b
a
Department of Social and Economic Studies, Richmond Building, University of Bradford, Richmond Road,
Bradford, West Yorkshire BD7 1DP, UK
b
Department of Economics, University of Portsmouth, Locksway Road, Southsea Hampshire PO4 8JF, UK
Received 5 March 1998; received in revised form 28 September 1998; accepted 10 September 1999
Abstract
This paper presents the ®rst attempts by economists to estimate a random utility maximisation model for the choice of desired involvement level in heterosexual relationships. A
sample of newspaper `personal' advertisements is used to estimate a multinomial logit. Age is
found to reduce the net probabiblity of seeking a casual relationship. A number of variables
are found to be signi®cant determinants of declared entry level. Ó 2000 Elsevier Science B.V.
All rights reserved.
PsycINFO classi®cation: 2980
JEL classi®cation: J12
Keywords: Partner age; Relationship; Entry level; Partner search; Personal ads
*
Corresponding author. Tel.:+44-1274-234-772.
E-mail address: [email protected] (S. Cameron).
1
Present address: Development and Project Planning Centre, Pemberton Building, University of
Bradford, Bradford, West Yorkshire BD7 1DP, UK.
0167-4870/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 4 8 7 0 ( 9 9 ) 0 0 0 3 7 - 9
74
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
``The sentiment of love is, in itself, agreeable to the person who feels it. It soothes and
composes the breast, seems to favour the vital motions, and to promote the healthful
state of the human constitution; and it is rendered still more delightful by the consciousness of the gratitude and satisfaction which it must excite in him who is the object of it.
Their mutual regard renders them happy in one another, and sympathy with this mutual
regard, makes them agreeable to every other person.''
[Adam Smith ± Theory of Moral Sentiments, 1759]
1. Introduction
Economists inspired by Becker (1973, 1974) have (see Grossbard-Shechtman, 1995; Bergstrom, 1996) investigated family formation and related topics
such as extramarital aairs (Fair, 1978). However there has not been explicit
consideration of the process of partner selection with the exception of the
early work of May (1954) and the illuminating work of Lemennicier (1988)
who also gives some descriptive statistics on personal advertisements. The
problem of matching relationship partners, at the aggregate level, has been
modelled mathematically in the important work of Bergstrom and Bagnoli
(1993) and Burdett and Coles (1997) and the micro matching problem was
earlier studied by Gale and Shapley (1962). The focus of Burdett and Coles is
on equilibrium in the aggregate market. The degree of reduction from the
salient characteristics of the real world is strong, as the model is basically a
straightforward analogue of the labour market where employers and workers
pair according to productivity. A single real number index `pizazz' is used to
represent the attributes being oered. Individuals meet at periodic intervals
to observe each other's `pizazz' with a view to either marrying or not.
From our perspective, the principal shortcoming in the Burdett and Coles
world is the neglect of the multidimensionality of the implicit contracts
formed by couples who pair with a view to marriage. In this area, it is not
always easy to separate the search process from the end state. Economists
have ignored the choice of `entry level' to the process being signalled by a
partner seeker, for example those using personal ads. in newspapers, oer
such things as `friendship possibly leading to relationship', or `seeks soulmate', or `daodil seeks vase', or `young female seeks solvent older male'. 2
Lemennicier (1988), using French advertisements, looks at requests for
characteristics such as beauty, sense of humour, aection, height and weight
2
The phrases cited have all been seen, by the authors, in personal advertisements, although not
necessarily in the sample used here.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
75
but he does not look at the process of emitting signals about the nature of
relationship sought. The neglect of these signals is partly because of the focus
on the companionate heterosexual marriage as a status quo that economists
have simply accepted (see e.g. Posner, 1992). This is increasingly questionable
as the average amount of time spent by individuals in an of®cially contracted
male plus female plus children relationship is declining in modern society due
to a number of factors. Divorce is an obvious one but there are also factors
leading to an expanded pre-marriage phase. In 1995, in the UK, 70% of
women had lived with their future husband before marriage compared with
5% in the mid-1960s. Of men aged 16±59, in 1995, 21% were described as
single never married (source: Population Trends 80, 1995). In the empirical
part of the paper we examine, using personal advertisements, stated preferences about the entry level of relationship sought. We estimate a multinomial
logit model for a four-way split between long-term, casual, platonic, and
ambiguously de®ned relationships. This is the ®rst ever estimation of this
kind of model as Lemennicier's (1988) work on personal advertisements did
not extend into econometric estimation.
2. Economic analysis of entry level choice in personal advertisements
Individuals are assumed to maximise stable underlying utility functions,
for interaction with partners, subject to constraints. A partner must ®rst be
selected from the available pool, and once their willingness to engage in
evaluation of the product (i.e. the potential relationship) is established,
search is then conducted over their attributes.
The underlying utility function may be characterised as follows:
U f S; M; X ;
1
where S is sexual services de®ned broadly to include any sexual arousal or
grati®cation received from interaction with a partner, M the companionship broadly de®ned to include non-sexual exchange, and X is the composite variable representing all other things, which obviously spans private
goods and public goods which might bring scale economies in sharing.
This is a general formulation of mate search which encompasses homosexuality and has, as the extreme case of public goodness in X, the
production and rearing of children, whether or not these are genetically
linked to the partners. We assume continuous substitutability and convexity
76
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
between S and M, at least over certain ranges of the utility function. The
constraints are primarily related to time and search costs in procuring S
and M.
A rudimentary diagrammatic exposition is provided in Fig. 1, which is a
simple indierence curve presentation. There will be an equilibrium choice of
partner where the marginal choice of substitution between S and M equals
the marginal rate of transformation, given by procurement costs. We assume
that the utility function is invariant with respect to intrinsic endowments of
the searcher. Utility may alter with age due to biological transformations in
individuals, however, we adopt a Becker and Stigler (1977) type assumption
that individuals have the same lifetime utility function. Differences between
underlying preference sets are therefore assumed to be randomly distributed
errors.
Systematic dierences in observed behaviour will therefore be attributed to
dierences in the constraints. Ceteris paribus, a more conventionally attractive individual (i.e. in a Burdett and Cole world, this would relate to a
high level of pizazz) will have the second budget line shown in Fig. 1. In
equilibrium they will have more S; whether or not they have more M depends
Fig. 1. Partner choice.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
77
on the precise nature of their utility function. 3 Conversely, having a child
from a previous relationship will shift the budget constraint and lead to lower
levels of S and M. The shift is a composite of reductions in time availability
and potential as a partner prospect. To attain the equilibrium position, the
individual must attract a pool of potential partners.
3. A speci®c model of entry level signalling for personal adverts
Fig. 2 is a revision of the analysis of Fig. 1 in terms of zones which connote
the speci®c entry levels analysed here. Basically, there is a probability that the
advert of an individual will be construed as signalling one of the four states:
platonic, ambiguous, long-term, or casual. The probability depends on tangency within one of the zones. Platonic is a corner solution on the M axis.
The remaining states are ranked according to the S/M ratio; for a given level
of S, the highest M is denoted `long-term', the next highest is denoted `ambiguous', whilst the lowest is denoted `casual'. The graph shows initial
equilibrium (E1 ) in the ambiguous zone for the indifference curve I1 given the
budget constraint BL1 . Let us suppose that the same individual was suddenly
blessed with more S related resources, then the budget constraint shifts to
BL2 giving us the new equilibrium (E2 ) on the indifference curve I2 . This
results in a change of status to casual from ambiguous. In a stochastic environment, the shift in S related resources obviously raises the probability of
casual over ambiguous (most appropriately, for the later modelling, the log
odds ratio). Obviously, homothetic preferences would mean that an overall
shift in the resource constraint would never lead to a change in the zonal log
odds ratios. We assume non-homothetic preferences, hence, the converse will
generally occur.
3
A referee has queried the use of `pizazz' or `sexiness' as shifting only the S element and not the M
element. There seems to us to be no actual hard evidence as to whether perceived attractivness is correlated
with companionship qualities. In a state of imperfect knowledge, individuals may use the perceived S of an
in individual as a proxy for other things like earnings power which could in¯uence the volume of M.
However, the evidence in Hammermesh and Biddle (1994) for a link between labour market success and
perceived attractiveness is very weak. In any case, this presentation assumes all such other factors to be
held constant when the choice is being made. Further, this is purely an illustrative diagram and the reader
is, of course, free to consider any possible scenario which they feel to be more apposite.
78
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 2. Commitment levels.
4. Data
Economists working in the area of personal relationships, such as Becker,
have not attempted to obtain explicit statements of preferences over partners
with the exception of May (1954) and Lemennicier (1988) who used a modest
size sample of French newspaper advertisements n 135.
Others have not been quite so neglectful as economists. A variety of
psychologists have been using the personal advertisements columns in
newspapers and magazines to test the propositions of `evolutionary biology'
(e.g. Kenrick and Trost, 1989; Thiessen, Young & Burroughs, 1993; Wiederman, 1993). They code the verbal text of the ads. into quantitative information (primarily dummy variables) to represent such things as stipulated
desire for wealthy, attractive partners, and oers of own attributes and assets. Personal advertisements are a fruitful source for economists working in
this area. It is possible to construct variables for the entry level stipulated, by
the placer of the advert, through evaluating the intent implicit in various
words.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
79
As already indicated we use a fourfold categorisation. The classi®cation
into casual, long-term, platonic and ambiguous groups was based on the
presence of keywords. Casual was based on explicit reference to a primarily
sexual partner. Long-term is coded on the basis of an explicit stipulation of
this, or a desire for sexual exclusivity, including mentions of marriage. Platonic is coded on the basis of a request for friendship with an explicit reference to non-sexual liaison, or an implicit deterrent to sexual overtures e.g.
`strictly ballroom'. Obviously these data are not devoid of ambiguity as they
have to be constructed from verbalisations which are subject to dierent
interpretations. In an attempt to overcome this, we adopt the standard
procedures of the specialist literature by using independent coding by one of
the authors and another researcher, who then conferred on anomalies, and
arrived at a consensus.
The data are derived from quantifying the text of 259 personal advertisements in the `Encounters' page in the English national newspaper `Sunday
Times' over the period from the 7th August 1994 to the 9th October 1994.
The variable de®nitions and names are given in Table 1. The pricing structure
of £11.75 per line plus £11.75 for a box number was used to construct the
PRICE variable. AGE is estimated as a mid-point if verbal information only
is given e.g. ``mid-thirties'' 35 although in many cases actual age is given. It
is well known that some individuals understate their age but this is of no
consequence for the analysis, so long as this deliberate error is independent of
other characteristics. Financial characteristics oered and sought are used to
create dummies based on the appearance of key phrases e.g. ``wealthy gent
Table 1
Variable names and de®nitions
Variable
De®nition
PRICE
cost of advert. in pounds
AGE
declared age of advertiser in years
FEMALE
1 if advertiser female 0 male
CHILDREN
1 if declares having children
FINOFF
1 oers ®nance
FINSOU
1 seeks ®nance
PHYSOWN
scale (0±5) of description of own physical characteristics
PHYSOU
scale (0±5) of description of desired partner physical characteristics
SOPHOWN
1 if declares `sophisiticated' leisure interests
SOPHSOU
1 if requires `sophisticated' leisure interests in partner
EXPOWN
1 if declares expensive leisure interests
EXPSOU
1 if requires expensive leisure interests in partner
All dummies are coded to 0 otherwise.
80
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
seeks ...'' or `solvent'. Physical characteristics are coded on a scale of 0±5
depending on the number of words used. For these variables, the number of
words is a proxy for the importance of physical attributes to the advertiser.
For the `expensive' tastes variables keywords such as `yachting' were used to
code as 1. For `sophisticated' tastes, items such as art, theatre were used to
code as 1. The variable which is most likely to be strategically misrepresented
is the declaration of having children. The frequency of declaration of children
is implausibly low given the age of the placers. Declaring children is a signal
to the potential respondent of additional dimensions of the relationship.
Potential respondents will be aware that those who do not declare children
may have them, in which case this facet will feature in the strategic interaction, by telephone, or face to face meeting, which follows taking up an advert. This aspect of interaction cannot be modelled with these data.
The means of the variables by group are shown in Table 2. These suggest
that certain variables are likely to be of use in discriminating between groups.
Seekers of long-term relationships spend much more on specifying their
transaction, as shown by price of advert, whilst those seeking platonic relationships spend much less. Seekers of platonic states are notably older than
the rest and considerably more likely to be women. The distribution of declaring children is skewed heavily to the long-term state seekers as we would
expect. Those seeking casual relationships display a much greater emphasis
on physical aspects of the relationship.
Table 2
Variable means by relationship type relationship type
Variable
Casual
Long-term
Platonic
Ambiguous
PRICE
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
N
102.13
39.9
0.37
0.01
0.68
0.297
2.176
1.19
0.198
0.055
0.10989
0.19780
91
108.61
41.9
0.5
0.128
0.577
0.372
1.487
0.705
0.179
0.0256
0.0512
0.192
78
88.8
48.3
0.76
0
0.52
0.36
1
0
0.24
0.04
0.2
0.36
25
100.15
42.5
0.41
0.015
0.71
0.29
1.57
0.74
0.25
0.123
0.077
0.23
65
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
81
5. Speci®cation and estimation
The data for analysis consist of variation across the individuals seeking
dierent relationship states but we have no measurement of characteristics of
the states. We therefore assume that each of the four relationship states has
utility:
Ui Vi ei ;
2
where U is utility, i the relationship state, V the systematic component, and e
is a random disturbance term representing unmeasured variation in tastes,
and the attributes of the relationship state. V consists of the variables identi®ed above. Individuals will choose the relationship state which ranks
highest in utility terms.
Assuming that the e's are independent and identically distributed, following a Weibull distribution, the model can be estimated as a multinomial
logit (see Cramer, 1991).
For the purposes of estimation, the model has to be normalised by setting
a base category for which the coecients are zero. There are therefore
i ÿ 1 3 sets of coecients for any such normalisation, and six sets of
pairwise coecients in all. The coecients of the model show the impact of a
variable on the log odds ratio for the pairing of the base category and the
category to which the coecients belong. Whilst the `t' ratios of these coef®cients provide some insight into the model, the values of the coef®cients
themselves are of limited use. A change in the value of a variable may increase the log odds of casual over long-term but, at the same time, decrease
the log odds of casual over the other states. The relationship of a state
prediction to a variable can therefore be non-monotonic. Interpretation of
the impact of the coef®cients therefore requires evaluation at some values of
the regressors. As most of the variables are dummies the usual procedure of
interpretation at the means is of limited usefulness. Accordingly we also
present simulations below for changes in the continuous variable age for
various combinations of the other variables.
Given the complexity of the model, in terms of the four states, and the six
sets of log odds, it is not easy to produce a standard list of expected signs and
magnitudes for the variables. Hence, we focus on highlighting some broad
relationships for the role of price of advertisement and age of the advertiser.
The price variable serves as a proxy for the search eort of the partner seeker.
One would, therefore, expect that more search eort be expended on seeking a
longer term partner than a casual partner, since the speci®cation of a more
82
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Table 3
Multinomial logit estimates of the relationship choice modela
Variables
INT
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
PRICE
State: Long-term
Base category: Casual
Coecients
ÿ1.38
(1.1)
0.02
(1.27)
0.24
(0.57)
2.65
(2.36)
ÿ0.25
(0.63)
0.07
(0.17)
ÿ0.47
(3.35)
ÿ0.46
(2.43)
ÿ0.73
(1.28)
0.32
(0.28)
ÿ2.01
(2)
0.77
(1.25)
0.01
(2.34)
Platonic
Casual
ÿ4.3
(2.1)
0.09
(2.73)
1.1
(1.62)
12.45
(0.02)
0.6
(1)
ÿ0.33
(0.5)
ÿ0.67
(2.39)
ÿ13.01
(0.09)
0.2
(0.24)
ÿ2.69
(1.55)
1.6
(1.19)
0.51
(0.55)
ÿ0.002
(0.15)
Ambiguous
Casual
ÿ1.62
(1.42)
0.04
(1.69)
0.28
(0.64)
0.7
(0.48)
0.54
(1.25)
ÿ0.29
(0.65)
ÿ0.24
(1.8)
ÿ0.46
(2.4)
ÿ0.69
(1.12)
2.28
(2.22)
ÿ2.47
(2.41)
0.88
(1.39)
0.003
(0.41)
259
15
ÿ275.0633
ÿ337.0999
N
Iterations
Log-likelihood
Restricted
(Slopes 0)
Log-L
Chi-squared
(36)
Pseudo R
squared
124.0732
0.184
Predicted
Actual
0
1
2
3
Total
0
1
2
3
Total
63
23
3
22
111
13
46
8
21
88
2
5
10
2
19
13
4
4
20
41
91
78
25
65
259
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
83
Table 3 (Continued)
Variables
State: Long-term
Base category: Casual
INT
1.38
(1.1)
ÿ0.025
(1.16)
ÿ0.3
(0.72)
ÿ2.59
(2.31)
0.32
(0.79)
0.02
(0.04)
0.44
(3.19)
0.49
(2.6)
0.94
(1.61)
ÿ0.51
(0.44)
2.4
(2.36)
ÿ1.16
(1.82)
ÿ0.015
(2.37)
AGE
FEMALE
CHILDREN
FINOFF
FINSOU
PHYOWN
PHYSOU
SOPHOWN
SOPHSOU
EXPSOU
EXPOWN
PRICE
a
Platonic
Casual
ÿ2.95
(1.47)
0.067
(2.07)
0.84
(1.26)
ÿ15.56
(0.02)
0.87
(1.45)
ÿ0.36
(0.58)
ÿ0.22
(0.79)
ÿ12.43
(0.09)
1
(1.23)
ÿ3.08
(1.69)
3.71
(2.64)
ÿ0.37
(0.43)
ÿ0.016
(1.23)
Ambiguous
Casual
ÿ2.03
(1.03)
0.041
(1.31)
0.91
(1.35)
ÿ13.08
(0.02)
0.21
(0.36)
0.15
(0.23)
ÿ0.47
(1.71)
ÿ12.29
(0.09)
0.96
(1.14)
ÿ4.95
(2.8)
4.06
(2.87)
ÿ0.48
(0.56)
ÿ0.0064
(0.48)
Notes: Absolute t ratios in parentheses.
durable partnership is substantially higher in terms of detail. Regarding age,
older partner seekers have already established more clearly de®ned preferences, and acquired relationship-speci®c human capital from previous relationships, such that they are better able to discern compatibility. Accordingly,
we would expect a decline in the propensity to signal casualness. An alternative explanation is that older people are considered less attractive, something that may aect women faster than men (see Grossbard-Shectman, 1982).
6. Results
The results of estimating the model are shown in Table 3. The predicted frequencies are given by rounding to 1 from maximum probability.
84
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
All six pair ranking estimates of the V coef®cients and `t' ratios are
shown. 4
Comparing actual and predicted classi®cations, the percent correctly
classi®ed with the share of the state in the total sample in brackets are, for
casual 69.2 (35.1), long-term 59 (30.1), platonic 40 (9.7) and ambiguous 30.8
(25.1).
Age is a signi®cant positive discriminator of platonic from long-term and
casual. Gender proves to be a weak discriminating variable. For platonic
over casual, a positive in¯uence of being female is obtained at almost the 5%
level on a one-tailed test. The declaration of children is a signi®cant positive
predictor of long-term relationship seeking. The oer and demand for ®nancial characteristics proves not to be capable of in¯uencing classi®cation.
An emphasis on physical aspects of the relationship is a strong negative
predictor of long-term and platonic preferences.
Marginal eects (partial dierentials of probability with respect to X) can
be calculated for the two continuous variables, PRICE and AGE. Evaluating
these at the (full) sample means for casual gives absolute `t' ratios of 1.61 for
age and 1.55 for price. The corresponding marginal effects are a fall in the
casual probability of 0.007 for one year older and 0.002 for a one pound
increase in price. For long-term relationships, the `t' ratios for marginal effects, at the sample means are 0.48 for AGE and 2.34 for PRICE. The corresponding marginal effects are 0.0019 for AGE and 0.00295 for PRICE.
Statistical signi®cance, and the estimated elasticities, do not by themselves
provide clear insights into the meaningfulness of the results. One approach to
doing so is to simulate the impact of a variable change, under various different scenarios for the advertisers in the sample. Accordingly, we generated
Figs. 3±8 which simulate the distribution of probabilities amongst the categories for dierent set-ups as age goes from 25 to 50. In all cases, ageing
notably reduces the probability of seeking casual relationships. This fall is
generally redistributed to the ambiguous category rather than long-term relationships. The modal characteristics for the full sample were used for the
categorical variables, and the sample mean for PRICE, were used initially.
The impact of declaring a child is enormous, increasing the probability of
seeking long-term commitment by 0.48 for a 25-year-old woman and 0.46 for
a 35-year-old woman. Switching to a stronger orientation on physical char-
4
For the base categories shown the log likelihood converged at similar values. However, using
PLATONIC as the base category resulted in a failure to achieve convergence.
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 3. Impact of age on choice for females without children declared.
Fig. 4. Impact of age on choice for females with children declared.
85
86
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 5. Impact of age on choice for females with child declared.
acteristics is associated with, in the absence of a child, a very high prediction
of casual.
The logit equation framework imposes interaction on the variables, in the
model, without the need for explcit recourse to interaction terms formed by
multiplying the variables together. For example, if one wishes to focus on
male±female dierences the impact of any individual variable will dier by
an amount due to the combined factors of the size of the FEMALE coef®cient and the combination of values of the other variables. Allowing for
parameter shifts across sex also runs into the problem of data sparsity as we
would then have some quite small samples within the fourfold classi®cation
within which there are quite infrequent occurences of 1 within some of the
dummy variables. The practice of only allowing the intercept parameter to
vary is a pragmatic solution often adopted even in models where there is no
inbuilt interaction. Nevertheless, following the suggestions of a referee, we
experimented with some further speci®cations (not reported) in an attempt
to bring out more clearly some of the expected results. A cut-down model
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
87
Fig. 6. Impact of age on choice for males without child declared.
featuring only age, children and the interaction of these yielded almost totally insigni®cant results on the parameters. Going to the opposite extreme,
estimation allowing all parameters to vary by gender resulted in similarly
dissapointing results. Adding a children±gender interaction term to the results shown in Table 3 failed to produce a `t' ratio of more than 0.5 in
absolute terms in any case. The most interesting variation was obtained by
adding interaction terms, with the female dummy, for the ®nance and
physical characteristics variables. The main result here was that an emphasis
on own physical characteristics by females reduced the likelihoods of their
choosing platonic or ambiguous in favour of casual and choosing ambiguous
in favour of long-term. Although the ®rst two results just given are what we
might expect, in terms of rational search behaviour, the latter is somewhat
contradictory. There are also some parameter changes for seeking ®nance;
this reduces the likelihood of women choosing casual in favour of platonic
or ambiguous. All the other parameter shifts were insigni®cant in this
augmented model.
88
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
Fig. 7. Impact of age on choice for females without child declared.
Although the additional experimentation discussed above is not reported
in full detail because of the lack of statistically signi®cant coecients, this
does not mean that the results are devoid of substantive signi®cance. One
might argue that such variability indicates a lack of reliability due to a sample
size that is small relative to the spread of categorical responses. It is dicult
to establish a priori if this is true and we would obviously hope for larger
replicatory studies in the future to shed light on this.
7. Summary and conclusion
This paper has presented an economic analysis of declared preferences for
involvement level in personal relationships. This has been implemented empirically on a sample of `personal advertisements'. The random utility maximization model was found to have good predictive power and uncovered a
number of signi®cant relationships with the explanatory variables. A dra-
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
89
Fig. 8. Impact of age on choice for males with child declared.
matic decline in the pursuit of casualness with age was demonstrated. The
declaration of the presence of a child has an overwhelming in¯uence on the
choice of a long-term relationship. The pursuit of long-term relationships was
found to be signi®cantly related to resources expended in this mode of
partner search.
One might feel inclined to question the generalisability of these results.
Clearly, those in the sample are a self-selected group who have explicitly
chosen newsaper advertising as a means of searching for a partner. In this
rather obvious sense they are unlike the general population. However, this
does not necessarily limit the validity of this work which is concerned with
the examination of strategy and the expression of preferences. It would be
rash to conclude that advertisers are desperate lonely people with atypical
strategies or preferences especially given the growing resort to marketised
partner search due to economic factors emphasised earlier in this paper.
Further, the works cited in Section 4 suggest that advertisers have quite
similar characteristics to non-advertisers. Obviously, future research is
90
S. Cameron, A. Collins / Journal of Economic Psychology 21 (2000) 73±90
needed replicating this work using data from other advertising sources and
direct survey methods.
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