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Heterogeneity assumptions in the specification of bargaining models: a study of household level trade-offs between commuting time and salary


With many real world decisions being made in conjunction with other decision makers, or single agent decisions having an influence on other members of the decision maker’s immediate entourage, there is strong interest in studying the relative weight assigned to different agents in such contexts. In the present paper, we focus on the case of one member of a two person household being asked to make choices affecting the travel time and salary of both members. We highlight the presence of significant heterogeneity across individuals not just in their underlying sensitivities, but also in the relative weight they assign to their partner, and show how this weight varies across attributes. This is in contrast to existing work which uses weights assigned to individual agents at the level of the overall utility rather than for individual attributes. We also show clear evidence of a risk of confounding between heterogeneity in marginal sensitivities and heterogeneity in the weights assigned to each member. We show how this can lead to misleading model results, and argue that this may also explain past results showing bargaining or weight parameters outside the usual [0,1] range in more traditional joint decision making contexts. In terms of substantive results, we find that male respondents place more weight on their partner’s travel time, while female respondents place more weight on their partner’s salary.

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Fig. 1
Fig. 2


  1. A household containing two individuals, living as partners.

  2. It can be seen that a model with attribute specific λ p parameters is equivalent to a model estimating β 1 and β 2, a point we will return to later in the paper.

  3. We are grateful to an anonymous referee for highlighting this.

  4. The survey thus works with travel time per trip and salary per month. We acknowledge the different units of these two components and the potential shortcomings of this from a microeconomic theory perspective. However, from a behavioural perspective, salary is paid per month and travel time is experienced per journey, and this was the approach taken in the study—see also Swärdh and Algers (2009)

  5. The 2005 exchange is approximately £ 0.07 per SEK1.

  6. We thank an anonymous referee for this comment.

  7. While \(\mu_{\ln(\beta_{f,{\text{L-Sal}}})}\) in Table 2 relates to the mean of the underlying Normal distribution for the salary coefficient for female respondents, μL-Sal represents the resulting mean of the Lognormal distribution, with σL-Sal giving the resulting standard deviation. The means and standard deviations for the Lognormal distribution can be obtained as simple transforms of the parameters for the underlying Normal distribution reported in Table 2, using the formulae reported in Train (2009, page 150).

  8. Looking at model 1, we have that the ratio between the log-salary and time coefficients is equal to 22.69. This then needs to divided by a respondent’s salary to get the implied WTA. For example, the lowest male salary is SEK3,750, giving a willingness to accept 0.006 minutes per additional Krona. For a respondent at the highest male salary, in this case SEK75,000, the WTA is much lower, at 0.0003 minutes per additional Krona.

  9. Note that efforts to study differences between λ TT and λ L-Sal were only moderately successful in models 3 and 4.


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The authors are indebted to Danny Campbell for important contributions in the early stages of the work leading to this paper, and for his guidance to the first author during her PhD studies. The authors are also grateful to Staffan Algers for making the survey data available, and to Amanda Stathopoulos for translating the survey from Swedish—without their help, this work would not have been possible. The authors would also like to acknowledge the input of Nesha Beharry-Borg in early stages of this research. Earlier versions of this paper were presented at the European Transport Conference 2010 held in Glasgow and the Transportation Research Board (TRB) 91st Annual Meeting 2012 held in Washington, D.C. The authors are grateful for the comments received at these conferences, which provided insightful suggestions for revisions, as well as the comments of three anonymous referees received on an earlier version.

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O’Neill, V., Hess, S. Heterogeneity assumptions in the specification of bargaining models: a study of household level trade-offs between commuting time and salary. Transportation 41, 745–763 (2014).

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  • Household decisions
  • Distributional assumptions
  • Random coefficients
  • Joint decisions
  • Bargaining coefficient