Are rational explosive solutions learnable?

•Study E-stability properties of explosive solutions in models with lagged endogenous variables.•Explosive solutions are E-stable and strongly E-stable under realistic parameterizations.•Establish convergence of least squares learning process to explosive solutions.•In the Cagan model, money supply feedback rule gives rise to a learnable explosive solution.•Simulations illustrate convergence to the explosive solution for prices.

It is commonly believed that rational explosive solutions are unstable or fragile under adaptive learning. Contrary to this belief, the paper shows that under realistic parameterizations, rational explosive solutions are both E-stable and strongly E-stable in a class of models with lagged endogenous variables. It also establishes the convergence of least squares learning process to explosive solutions. Taking a simple Cagan model of inflation as an application, the paper shows that money supply feedback rule gives rise to a rational explosive solution for prices which is learnable in real time. This provides a new potential explanation for historical high inflation. Finally, E-stability results for non-MSV explosive solutions are provided.