Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models
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Citation (published version)Zhongjun Qu, Denis Tkachenko. "Using Arbitrary Precision Arithmetic to Sharpen Identification Analysis for DSGE Models."
This paper is at the intersection of macroeconomics and modern computer arithmetic. It seeks to apply arbitrary precision arithmetic to resolve practical di¢ culties arising in the iden- ti cation analysis of log linearized DSGE models. The main focus is on methods in Qu and Tkachenko (2012, 2017) since the framework appears to be the most comprehensive to date. Working with this arithmetic, we develop the following three-step procedure for analyzing local and global identi cation. (1) The DSGE model solution algorithm is modi ed so that all the relevant objects are computed as multiprecision entities allowing for indeterminacy. (2) The rank condition and the Kullback-Leibler distance are computed using arbitrary precision Gauss- Legendre quadrature. (3) Minimization is carried out by combining double precision global and arbitrary precision local search algorithms, where the criterion for convergence is set based on the chosen precision level, so that it can be e¤ectively examined whether the minimized value equals zero. In an application to a model featuring monetary and scal policy interactions (Leeper, 1991 and Tan and Walker, 2015), we nd that the arithmetic removes all ambiguity in the analysis. As a result, we reach clear conclusions showing observational equivalence both within the same policy regime and across di¤erent policy regimes under generic parameter val- ues. We further illustrate the application of the method to medium scale DSGE models by considering the model of Schmitt-Grohé and Uribe (2012), where the use of extended precision again helps remove ambiguity in cases where near observational equivalence is detected.