Koszegi and Rabin (2006, 2007) develop a model of expectations-based reference-dependent preferences, in which the agent experiences prospect-theory inspired "gain-loss utility" by comparing his actual consumption to all his previously expected consumption outcomes. Koszegi and Rabin (2009) generalize the static model to a dynamic setting by assuming that the agent experiences both contemporaneous gain-loss utility over present consumption and prospective gain-loss utility over changes in expectations about future consumption. Moreover, the authors generalize the outcome-wise "static comparison" of gain-loss utility to a percentile-wise "ordered comparison," in which the agent compares consumption outcomes at each percentile. This paper generalizes the static comparison slightly differently to, what I call, a "separated comparison." Under the separated comparison, the agent compares each consumption outcome but experiences gain-loss utility only over uncertainty that has been realized, by considering it separately from remaining future uncertainty. Effectively, the separated comparison modifies the static comparison by considering potential non-independence of the prior and updated expectations about future consumption. Thus, it reduces to the static comparison for independent prior and updated expectations and is zero if these happen to be the same. Moreover, it yields simple, tractable, and well-behaved equilibria in a wide class of economic models, because it preserves an outcome-wise nature, which makes it linear and dynamically similar to contemporaneous gain-loss utility.
Pagel, Michaela. "Prospective Gain-Loss Utility: Ordered versus Separated Comparison." Journal of Economic Behavior & Organization 168 (December 2019): 62-75.
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