Abstract
In experiments of decision-making under risk, structural mixture models allow us to take a menu of theories about decision-making to the data, estimating the fraction of people who behave according to each model. While studies using mixture models typically focus only on how prevalent each of these theories is in people’s decisions, they can also be used to assess how much better this menu of theories organizes people’s utility than does just one theory on its own. I develop a framework for calculating and comparing two kinds of rationalizable opportunity cost from these mixture models. The first is associated with model mis-classification: How much worse off is a decision-maker if they are forced to behave according to model A, when they are in fact a model B type? The second relates to the mixture model’s probabilistic choice rule: How much worse off are subjects because they make probabilistic, rather than deterministic, choices? If the first quantity dominates, then one can conclude that model a constitutes an economically significant departure from model B in the utility domain. On the other hand, if the second cost dominates, then models a and B have similar utility implications. I demonstrate this framework on data from an existing experiment on decision-making under risk.
Highlights
Experimental and behavioral economists have largely embraced the idea that there could be more than one process driving behavior in our experiments
Whether it be decision-making under risk (e.g., [1,2]), discounting [3], or choice bracketing [4], to name but a few, we have generally found that our data are better modeled using mixture models [1], rather than assuming that one model of decision-making is generating all of our data
Harrison and Rutström [1] assume that decisions in their experiment are made using either an Expected Utility objective function, or a Prospect Theory objective function, and estimate that approximately 51% of decisions were made using an Expected Utility objective function, and the Mixture models can differ in the assumption about the level of mixing
Summary
Experimental and behavioral economists have largely embraced the idea that there could be more than one process driving behavior in our experiments. If their preferences are EU, buying insurance is optimal for all values of p If they are instead making decisions according to the RDEU model, they could be better off by the height of the blue curve, which is the difference in certainty equivalents. Subjects’ rationalizable opportunity costs of the RDEU model are generally small when compared to the absolute welfare costs of probabilistic choice: for the Hey [8] experiment, while RDEU decisions may look quite different to EU decisions, Rank Dependent Expected Utility is not substantially different to Expected Utility
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