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.
翻译:本文研究的是,在休克不受约束的情况下,计算出来的动态模型的无症状趋同。大多数动态经济模型缺乏封闭式解决办法。因此,使用了数字方法的近似解决办法。由于研究者无法直接评估确切的政策功能和相关确切可能性,因此,必须使几乎无症状的可能性 -- -- 以及了解趋同条件 -- -- 与确切可能性相趋同,以便证明和证实其使用。在这方面,Fernandez-Villaverde、Rubio-Ramirez和Santos(2006年)表明,当休克得到紧凑支持时,这种可能性是趋同的。然而,紧凑式支持意味着休克是被捆绑起来的,这不是大多数动态经济模型(例如通常分布式的冲击)所满足的假设。本文为文献中使用的大多数动态模型提供了理论上的理由,展示了从数字模拟到精确变量计量的近似值的趋同条件,从而提供了使可能性趋同的条件。