A robust reference-dependent model for speculative bubbles

- We assume loss-averse preferences to resolve the non-robustness issue of rational bubbles.
- Our model of bubbles is able to handle a silent market with unobservable prices.
- Strong bubbles in our model are robust to moderate perturbations in parameters.
- Results on the bubble size and the bubble frequency in the classical setting are preserved.
- Reference points are endogenously formed and prices are also endogenously determined.

We present a robust model of speculative bubbles by introducing loss-averse reference-dependent preferences by Koszegi and Rabin (2006) into the framework of Allen et al. (1993), where in equilibrium, asymmetrically-informed rational investors buy overvalued assets, hoping to sell them to less informed agents before the crash occurs. With reference-dependent preferences, the asset price may not necessarily be observable to agents when there is no trade. However, this is never the case with classical preferences, as shown in the paper. Incorporating the classical model as a special case, we generalize the notion of bubbles to allow for the analysis in the case of a silent market with unobservable prices, and our model is able to generate strong bubbles robust to moderate perturbations in parameters without the need for stronger conditions as suggested in previous literature. Assuming for simplicity that dividends can only take on two values, we construct an example of a robust reference-dependent bubble which is not robust in the classical setting, and we also show that the positive results regarding the limit of the bubble size and bubble frequency in the classical setting are preserved in our framework. Our main results and economic implications remain valid in more general settings.