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Empirical Economics

Erschienen in:

28.06.2017

A dual theory approach to estimating risk preferences in the parimutuel betting market

verfasst von: Niko Suhonen, Jani Saastamoinen, Mika Linden

Erschienen in: Empirical Economics | Ausgabe 3/2018

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Abstract

This paper introduces an alternative empirical approach to estimating risk preferences in the parimutuel betting market using a dual theory model which is amended to include bettors’ misperceptions of probabilities. We replicate previous empirical results and test our alternative empirical approach using parimutuel horse race betting data. Our results suggest that while bettors are risk-averse, they are also prone to misperceiving probabilities by overweighting low probabilities and underweighting high probabilities. As an application, these results replicate the choice patterns consistent with the Allais paradox.

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More recently, Gandhi and Serrano-Padial (2014) and Chiappori et al. (2012) propose an empirical model where the heterogeneity of risk preferences explains bettors’ behaviour.

We also attempted to estimate more complex models (CARA with Prelec’s (1998) one-parameter and two-parameter weighting functions) applied by Jullien and Salanié (2000). Unfortunately, Stata 13 could not compute numerical derivatives for these models.

Zank (2010) shows that the listed properties are necessary but not sufficient.

However, it should be noted that DT is more general by nature.

Additionally, Gonzalez and Wu (1999) suggest a rank-dependent utility model which contains a utility function for risk and a two-parameter probability weighting function in which one parameter measures the discrimination of probabilities and the other measures the attractiveness of gambling.

In general, if utility is convex in the outcome space, it corresponds to concave utility in the probability space and vice versa (Yaari 1987).

As a robustness check, we also estimated a two-parametric function alternative suggested by Lattimore et al. (1992). The results were qualitatively the same as the ones obtained with Prelec’s specification (1998).

This is, in general, a rank-dependent utility. For an illustrative generalization of experiments for the Allais paradoxes and the rank-dependent utility, see Peel et al. (2008).

Note that the approach also satisfies other variants of these experiments. For instance, Kahneman and Tversky (1979): \(A_1 =(1,2400)\succ B_1 =(0.01,0;0.33,2500;0.6,2400)\) and \(A_2 =(0.34,2400;0.66,0)\prec B_2 =(0.33,2500;0.67,0)\), and \(A_1 =(0.1,0;0.9,3000)\succ B_1 =(0.45,6000;0.55,0)\) and \(A_2 =(0.002,3000;0.998,0)\prec B_2 =(0.001,6000;0.999,0).\)

Using the probability weighting parameter \(\alpha \) did not make any qualitative difference to the results.

This conclusion has been challenged also by Snowberg and Wolfers (2010).

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Titel: A dual theory approach to estimating risk preferences in the parimutuel betting market
verfasst von: Niko Suhonen
Jani Saastamoinen
Mika Linden
Publikationsdatum: 28.06.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 3/2018
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-017-1258-x

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