Random utility maximiser seeks similar: An economic
analysis of commitment level in personal relationships
Samuel Camerona,*,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 max-imisation 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
www.elsevier.com/locate/joep
*Corresponding author. Tel.:+44-1274-234-772.
E-mail address:[email protected] (S. Cameron).
1Present address: Development and Project Planning Centre, Pemberton Building, University of
Bradford, Bradford, West Yorkshire BD7 1DP, UK.
``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 conscious-ness 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-Shecht-man, 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 soul-mate', 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
2The phrases cited have all been seen, by the authors, in personal advertisements, although not
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 quothat 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 prefer-ences 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
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 betweenS 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 at-tractive 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 moreS; whether or not they have moreMdepends
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 ofSand 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 tan-gency within one of the zones. Platonic is a corner solution on the M axis. The remaining states are ranked according to theS/Mratio; for a given level ofS, the highest Mis denoted `long-term', the next highest is denoted `am-biguous', 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 en-vironment, the shift inSrelated 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 theSelement and not theM
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 n135.
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; Wie-derman, 1993). They code the verbal text of the ads. into quantitative in-formation (primarily dummy variables) to represent such things as stipulated desire for wealthy, attractive partners, and oers of own attributes and as-sets. 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.
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. Pla-tonic is coded on the basis of a request for friendship with an explicit ref-erence 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 adver-tisements 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 female0 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
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 interac-tion, by telephone, or face to face meeting, which follows taking up an ad-vert. 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 rela-tionships spend much less. Seekers of platonic states are notably older than the rest and considerably more likely to be women. The distribution of de-claring 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
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:
UiViei; 2
whereUis utility,ithe relationship state,Vthe systematic component, ande
is a random disturbance term representing unmeasured variation in tastes, and the attributes of the relationship state.Vconsists of the variables iden-ti®ed above. Individuals will choose the relationship state which ranks highest in utility terms.
Assuming that the e's are independent and identically distributed, fol-lowing 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 iÿ13 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 coefcoef-®cients themselves are of limited use. A change in the value of a variable may in-crease the log odds of casual over long-term but, at the same time, dein-crease 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.
Table 3
Multinomial logit estimates of the relationship choice modela
durable partnership is substantially higher in terms of detail. Regarding age, older partner seekers have already established more clearly de®ned prefer-ences, and acquired relationship-speci®c human capital from previous rela-tionships, such that they are better able to discern compatibility. Accordingly, we would expect a decline in the propensity to signal casualness. An alter-native explanation is that older people are considered less attractive, some-thing 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 pre-dicted frequencies are given by rounding to 1 from maximum probability.
Table 3 (Continued)
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 ef-fects, at the sample means are 0.48 for AGE and 2.34 for PRICE. The cor-responding 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 dif-ferent scenarios for the advertisers in the sample. Accordingly, we generated Figs. 3±8 which simulate the distribution of probabilities amongst the cate-gories 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 re-lationships. 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-4For the base categories shown the log likelihood converged at similar values. However, using
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
featuring only age, children and the interaction of these yielded almost to-tally 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 re-sults 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.
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 em-pirically on a sample of `personal advertisements'. The random utility max-imization model was found to have good predictive power and uncovered a number of signi®cant relationships with the explanatory variables. A
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
needed replicating this work using data from other advertising sources and direct survey methods.
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