I'm a long-time proponent of using the limit of the equilibrium of an (analogous) finite-horizon model as the horizon goes to infinity as a selection criterion to eliminate multiple equilibria in infinite-horizon models. I spelled out the argument in detail in "Multiple equilibria in dynamic rational expectations models: A critical review," Eur. Ec. Rev., (50), 2006. Steve Williamson is I think correct: getting the finite-horizon terminal condition requires an extra assumption. But I think there are good reasons to add that assumption-or something like it.