International Choice Modelling Conference, International Choice Modelling Conference 2017

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Discrete choice analysis of multidimensional risk attitude
Nathalie Picard, André de Palma, Sophie Dantan

Last modified: 28 March 2017

Abstract


Individual risk attitude has been studied theoretically and empirically for decades in the economics, psychology and transportation literatures. Traditionally, empirical studies are conducted in specific areas: accidents, route choice, natural catastrophes, climate change, financial investments, or health decisions – the list is far from being exhaustive. Large and small risks, or small, medium and large probabilities are traditionally treated in different models; and using different tools. One important question is whether if the same individual may be risk averse for some decisions and risk lover for other decisions. For example, buy lottery tickets on the one hand, and buy health insurance or an insurance for a washing machine, on the other hand. The notions of mental accounting and background risk may partially explain such behaviors.

Specialized questionnaires aim at studying risk attitude, usually in a given context. Indeed, the European MiFID I and II Directive make it compulsory for European banks to assess the level of risk aversion of their clients. They stipulate that no question outside the context of finance should be asked in a financial risk questionnaire. We think that, given the state of the knowledge, this is a wise decision.

In this paper, we analyze the determinants of risk attitude using a similar methodology in two different contexts (transportation and finance), and the correlation between risk aversions in these two contexts. The sign of this correlation is not obvious a priori. One may expect positive correlation and speak about risk averse individuals in general. In this case, an individual would both buy stocks and do skydiving. One may also expect risk compensation: In this case the same individual would drive formula 1 cars but would only buy financial instruments with safe returns.

We also use three different sources of data. The first source is a 20 minutes on-line questionnaire, dedicated to the analysis of risk aversion both in the financial context and in the transportation context. This questionnaire was competed by students at Ecole Poytechnique, the French most prestigious elite institution. Since 2004, about 300 students responded the questionnaire each year, and 3 of them, chosen randomly, received a “prize”. The prize just implemented one of the lottery chosen randomly. Since payment was a function of their replies, we expect answers to be reliable.

The second source of data, MIMETTIC, is an online transportation survey conducted on more than 4,000 respondents. It takes advantage of our experience with a telephone transportation survey conducted on 5,000 respondents, to improve our methodology. In both cases, questions were asked in the context of Paris area.

The third source of data is a risk questionnaire conducted by a financial company on more than 7000 investors, in the financial context. In this case, the incitation to give sincere answers is to receive a relevant financial advice.

All our questionnaires contain questions about socio-economic attributes, as well as series of lottery questions. Each lottery question involves the choice between a safe and a risky alternative. In the context of transportation the safe alternative is a route with a safe travel time, while in finance it is an investment with a guaranteed return. The risky question, in transportation is a route with a risky travel time, while in finance it is an investment with a risky returns. The risky alternative involves a known good outcome and a known bad outcome, occurring with known probabilities p and (1-p), respectively. In the risky alternative, the expected travel time (resp. return) is lower (resp. larger) than the travel time (resp. return) of the safe alternative.

We analyze the data using a method based on the ordered Probit, consistently with the tree structure of our series of lottery questions. This leads to an ordinal as well as to different cardinal measures of risk aversion. Such an approach is consistent with expected and with non-expected utility theory.

Estimates in transportation show that risk aversion is larger for transit users, blue collars and for business appointments.

Estimates in finance show that women are more risk averse than men and that respondents who are married with a marriage contract are particularly risk averse.

In both contexts, absolute risk aversion seems roughly constant, but the distribution of risk aversion parameter is dramatically different in the two contexts.

The simplest models are estimated in the context of expected utility, using an ordered probit model. Extensions consider other dimensions of risk attitude, namely loss aversion (related to schedule delay cost in the case of transport) and perception biases, on the probabilities which are modelled with probability weighting functions). The individual-specific values and determinants of loss aversion and probability weighting parameters are estimated simultaneously with risk aversion, combining latent variables techniques with ordered probit models.


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