Equilibrium Selection in Pure Bubble Models by Dividend Injection

Abstract

Rational ``pure bubble'' models admit multiple (often a continuum of) equilibria, making predictions and policy analysis fragile. We show that if the fundamental equilibrium features a low interest rate relative to growth ($R<G$), then a bubbly equilibrium with $R=G$ exists. We propose an equilibrium selection device based on \emph{dividend injection}: endowing the bubble asset with a small dividend stream that grows more slowly than the aggregate economy. This perturbation eliminates the fundamental steady state and all equilibrium paths converging to it, thereby resolving indeterminacy. We illustrate the general applicability of dividend injection in overlapping-generations and infinite-horizon models, with or without production and financial frictions. In particular, we argue that the widely applied ``stochastic bubble'' model of Blanchard (1979) and Weil (1987) is implausible.