This paper considers some of the questions raised by the fact that people's behaviour—including their behaviour in experimental environments—has a stochastic component. The nature of this component may be crucial to the interpretation of the patterns of data we observe and the choice of statistical criteria for favouring one hypothesis at the expense of others. However, it is arguable that insufficient consideration has been given to the way(s) in which the stochastic element is modelled. The paper aims to explore some of the issues involved.

There is an odd contradiction about much of the empirical (experimental) literature: The data is analysed using statistical tools which presuppose that there is some noise or randomness in the data, but the source and possible nature of the noise are rarely explicitly discussed. This paper argues that the noise should be brought out into the open, and its nature and implications openly discussed. Whether the statistical analysis involves testing or estimation, the analysis inevitably is built upon some assumed stochastic structure to the noise. Different assumptions justify different analyses, which means that the appropriate type of analysis depends crucially on the stochastic nature of the noise. This paper explores such issues and argues that ignoring the noise can be dangerous.

The structural Quantal Response Equilibrium (QRE) generalizes the Nash equilibrium by augmenting payoffs with random elements that are not removed in some limit. This approach has been widely used both as a theoretical framework to study comparative statics of games and as an econometric framework to analyze experimental and field data. The framework of structural QRE is flexible: it can be applied to arbitrary finite games and incorporate very general error structures. Restrictions on the error structure are needed, however, to place testable restrictions on the data (Haile et al., 2004). This paper proposes a reduced-form approach, based on quantal response functions that replace the best-response functions underlying the Nash equilibrium. We define a regular QRE as a fixed point of quantal response functions that satisfies four axioms: continuity, interiority, responsiveness, and monotonicity. We show that these conditions are not vacuous and demonstrate with an example that they imply economically sensible restrictions on data consistent with laboratory observations. The reduced-form approach allows for a richer set of regular quantal response functions, which has proven useful for estimation purposes.

Data from a risky choice experiment are used to estimate a fully parametric stochastic model of risky choice. As is usual with such analyses, Expected Utility Theory is rejected in favour of a form of Rank Dependent Theory. Then an estimate of the risk aversion parameter is deduced for each subject, and this is used to construct a measure of the “closeness to indifference” of each subject in each choice problem. This measure is then used as an explanatory variable in a random effects model of decision time, with other explanatory variables being the complexity of the problem, the financial incentives, and the amount of experience accumulated at the time of performing the task. The most interesting finding is that significantly more effort is allocated to problems in which subjects are close to indifference. This presents us with another reason (in addition to statistical information considerations) why such tasks should play a prominent role in experiments.