  This paper studies the asymptotic convergence of computed dynamic models when
the shock is unbounded. Most dynamic economic models lack a closed-form
solution. As such, approximate solutions by numerical methods are utilized.
Since the researcher cannot directly evaluate the exact policy function and the
associated exact likelihood, it is imperative that the approximate likelihood
asymptotically converges -- as well as to know the conditions of convergence --
to the exact likelihood, in order to justify and validate its usage. In this
regard, Fernandez-Villaverde, Rubio-Ramirez, and Santos (2006) show convergence
of the likelihood, when the shock has compact support. However, compact support
implies that the shock is bounded, which is not an assumption met in most
dynamic economic models, e.g., with normally distributed shocks. This paper
provides theoretical justification for most dynamic models used in the
literature by showing the conditions for convergence of the approximate
invariant measure obtained from numerical simulations to the exact invariant
measure, thus providing the conditions for convergence of the likelihood.
