A test of the rational expectations hypothesis using data from a natural experiment

Abstract

Data on contestants’ choices in Italian Game Show Affari Tuoi are analysed in a way that separates the effect of risk attitude (preferences) from that of beliefs concerning the amount of money that will be offered to contestants in future rounds. This separate identification is possible by virtue of the fact that, at a certain stage of the game, beliefs are not relevant, and risk attitude is the sole determinant of choice. The rational expectations hypothesis is tested by comparing the estimated belief function with the ‘true’ offer function which is estimated extraneously using data on offers actually made to contestants. We find a close correspondence, leading us to accept the rational expectations hypothesis. The importance of belief formation is confirmed by the estimation of a mixture model which establishes that the vast majority of contestants are forward looking as opposed to myopic.

Keywords:

• beliefs
• discrete choice models
• extraneous estimators
• natural experiments
• rational expectations
• risky choice

JEL Classification:

• C15
• C23
• C25
• D81

Acknowledgements

We are grateful to Glenn Harrison, John Hey, Franco Peracchi and Arthur van Soest for their valuable suggestions. The authors would also like to thank the Editor and two anonymous referees for their comments that led to a significant improvement in the article. Usual disclaimers apply. Dataset is available from the authors on request.

Notes

¹ See, among the others, Friend and Blume (1975), Gertner (1993), Metrick (1995), Beetsma and Shotman (2001) and Hartley et al. (2005) for an analysis of individual risk attitude through TV games.

² For a more detailed description of the data set used in this article, see Botti et al. (2007, 2008).

³ Blavatskyy and Pogrebna (2010) focus attention on the swap in Affari Tuoi.

⁴ We have also used a Constant Relative Risk Aversion (CRRA) and an Expo-power specification, assuming nonzero lifetime wealth as a parameter to be estimated, along similar lines to Andersen et al. (2006). We find that the estimate of the lifetime wealth parameter is not significantly different from zero. However, the use of these specifications never significantly improves the fit over the CARA specification (cf. Andersen et al., 2006; Post et al., 2008; de Roos and Sarafidis, 2010). The various results are available from the authors upon request.

⁵ Here, and throughout this article, we measure money amounts in units of €1000.

⁶ This hypothesis has been used in a similar context by Botti et al. (2008) and in different contexts by Araña and León (2006).

⁷ In view of the constraint , the parameter that is in fact estimated is ψ where . After estimation of ψ, an estimate of is deduced, and a SE is found using the delta method (Oehlert, 1992). Other parameters that are constrained such as and are estimated using similar techniques.

⁸ Parameters representing SDs of error terms, and tremble probabilities, are clearly constrained to be nonnegative, and the hypothesis under test is one for which the parameter of interest is on the boundary of the parameter space. Many authors have acknowledged the problems that arise in this situation (see, e.g. Hey and Orme, 1994, footnote 17; Moffatt and Peters, 2001). There is usually a simple remedy: for a test with size 0.05, the 0.10 column from tables should be consulted to obtain the appropriate critical value. This remedy has been prescribed in a more general context by Godfrey (1988, p. 94).

⁹ Bone et al. (2003) investigate the possibility that people might not be forward-looking in a dynamic setting, and provide explanations for those who do not comply with a forward-looking behaviour.

¹⁰ See Mulino et al. (2009) and de Roos and Sarafidis (2010) for a more detailed explanation.

¹¹ We know of no reason to presume that one type of individual trembles more than the other.

¹² For the Vuong tests performed here, we use a correction for the degrees of freedom that corresponds to the Schwarz's Bayesian Information Criterion.

¹³ Establishing the ways in which agents process information in order to form expectations of others’ actions is extremely important in many applications such as financial analysis. See, for example, Tabak (2009).