Kenichiro McAlinn, Kosaku Takanashi
arXiv 11 Mar 2021 · Econometrics
arXiv:2103.06483 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 72% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Santos and Peralta-Alva (2005) Accuracy of simulations for stochastic dynamic models | 1.000 | 8 | 4 | 100% |
| 2 | Fernandez-Villaverde, Rubio-Ramirez, and Santos (2006) Convergence Properties of the Likelihood of Computed Dynamic Models | 0.928 | 10 | 4 | 80% |
| 3 | Futia (1982) Invariant distributions and the limiting behavior of Markovian economic models | 0.644 | 2 | 2 | 100% |
| 4 | Dudley (2002) Real analysis and probability, volume 74 of Cambridge Studies in Advanced Mathematics | 0.405 | 1 | 1 | 100% |
| 5 | Kamihigashi and Stachurski (2016) Seeking ergodicity in dynamic economies | 0.405 | 1 | 1 | 100% |
| 6 | Kamihigashi (2007) Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks | 0.405 | 1 | 1 | 100% |
| 7 | Munkres (2000) Topology | 0.405 | 1 | 1 | 100% |
| 8 | Nishimura and Stachurski (2005) Stability of Optimal growth models: a new approach | 0.405 | 1 | 1 | 100% |
| 9 | Smets and Wouters (2007) Shocks and frictions in US business cycles: A Bayesian DSGE approach | 0.405 | 1 | 1 | 100% |
| 10 | Stachurski (2002) Stochastic Optimal growth with unbounded shock | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 12 scored citations.