We theoretically explore long-run stagnation at the zero lower bound in a representative agent framework. We analytically compare expectations-driven stagnation to a secular stagnation episode and find contrasting policy implications for changes in government spending, supply shocks and neo-Fisherian policies. On the other hand, a minimum wage policy is expansionary and robust to the source of stagnation. Using Bayesian methods, we estimate a DSGE model that can accommodate two competing hypotheses of long-run stagnation in Japan. We document that equilibrium selection under indeterminacy matters in accounting for model fit.