Time flips and price dips: Modeling preference reversals between intertemporal choice and pricing

Subjective value and preference for delayed prospects are measured in multiple ways, including both choices between options and price equivalents. However, these methods diverge in their conclusions, resulting in preference reversals that parallel those observed in risky choice. To reconcile these reversals under a common theory of value, we develop a dynamic model of pricing that incorporates anchoring and dynamic adjustment of pricing judgments. To do so, we first present and evaluate several predictions made by a price accumulation model in the context of intertemporal value -- such as the effects of delay and payoff manipulations and the skew of price responses. Next, using a neural network approach to fit the data in a likelihood-free way, we applied this model to both pricing and choice data to understand why people select smaller-sooner options in choice but assign higher bids to larger-later options. We show that intertemporal choice-price preference reversals can be explained by the dynamic anchoring process that is present in pricing but not in choice. This approach is then extended to the domain of delayed losses, showing that anchoring rather than endowment or some other effect is primarily responsible for preference reversals. Furthermore, loss aversion manifests in shallower discounting rates in choice and stronger anchoring effects in pricing for delayed monetary losses relative to monetary gains. Put together, we show that preference reversals between intertemporal choice can be explained by a dynamic anchoring process that is present in pricing but not choice.