Deflationary Bubbles

In an attempt to clean up an unruly literature, we specify the necessary and sufficient conditions for household optimality in a model where money is the only financial asset and provide the relevant proofs. We use our results to analyse when deflationary bubbles can and cannot exist. Our findings are in contrast to the results in several prominent contributions to the literature. We argue for particular specifications of the no-Ponzi-game restrictions on the household's and government's intertemporal budget constraints in a model with money and bonds. Using the restriction on the household we derive the necessary and sufficient conditions for household optimality. The resulting equilibrium terminal conditions are then used to demonstrate that the existence of bonds does not affect when deflationary bubbles can and cannot occur. This result differs from that in other recent works.