Consumer surplus for random regret minimisation models

ABSTRACT

This paper is the first to develop a measure of consumer surplus for the Random Regret Minimisation (RRM) model. Following a not so well-known approach proposed two decades ago, we measure (changes in) consumer surplus by studying (changes in) observed behaviour, i.e. the choice probability, in response to price (changes). We interpret the choice probability as a well-behaved approximation of the probabilistic demand curve and accordingly measure the consumer surplus as the area underneath this demand curve. The developed welfare measure enables researchers to assign a measure of consumer surplus to specific alternatives in the context of a given choice set. Moreover, we are able to value changes in the non-price attributes of a specific alternative. We illustrate how differences in consumer surplus between random regret and random utility models follow directly from the differences in their behavioural premises.

KEYWORDS:

• Random regret minimisation
• consumer surplus
• welfare
• probabilistic demand function
• context dependency

Acknowledgments

The authors gratefully acknowledge support from the Netherlands Organisation for Scientific Research (NWO), in the form of VIDI-grant 016-125-305.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Some readers may be familiar with Regret Theory (Loomes and Sugden 1982). The RRM model is distinctively different from Regret Theory, since it does not focus on choices under risk and uncertainty. Regret Theory is operationalised by means of utility differences between alternatives and it aims to capture violations of Expected Utility theory predominantly in the context of binary lotteries. The RRM model is instead concerned with differences in attributes, and aims to (non-linearly) capture choice set composition effects in multinomial and riskless choice situations. As a result, it links more closely with extremeness aversion (Simonson and Tversky 1992) than with Regret Theory.

2. The Hicksian equivalent variation (EV) takes the new utility level as the point of departure and examines how much compensation an individual requires to forego an improvement. McFadden (1981) also denotes the CV and EV as measures of willingness to pay and willingness to accept.

3. Williams’ (1977) measure is already defined in monetary terms due to the use of a generalized cost approach.

4. Technically, if the absolute value of prices affect the choice probabilities, then this is an indication of an income effect (Jara-Diaz and Videla 1989).

5. Adding to every alternative in the choice set does not affect choice probabilities since choice probabilities are entirely defined by utility differences.

6. The non-linear specification of the RRM model enables estimation of a dispersion parameter in the logit framework (van Cranenburgh et al. 2015). The researcher can ensure that regret equals zero when all alternatives in the choice set are equivalent by subtracting a constant of size (J -1) · M · ln(2), but this constant is obsolete.

7. RUM and RRM are behaviourally equivalent for binary choices, including welfare implications (Chorus 2010).

8. We treat changes in travel time in isolation. That is, we reduce (or increase) the travel time of alternative A by five minutes and evaluate the change in consumer surplus for alternative A. We then go back to the initial situation and repeat the same process for alternatives B and C.

9. In the design nine unique choice cards are included. Each of the choice cards includes three alternatives which can be improved or deteriorated in terms of average travel time. This provides a total of twenty-seven cases to evaluate.

10. The recently proposed muRRM model (van Cranenburgh et al. 2015) does potentially lead to larger differences in model fit. This is due to its ability to capture a wide range of levels of regret aversion.

11. Note that when some attributes of alternative i are improved and others deteriorated it is impossible to set bounds on changes in total surplus.

12. Alternative i has a zero choice probability in deriving this subsequent consumer surplus, since it has been made very unpopular, but is not removed from the choice set.

Additional information

Funding

Nederlandse Organisatie voor Wetenschappelijk Onderzoek [grant number VIDI-grant 016-125-305].