Solving Linear DSGE Models with Bernoulli Iterations

This paper presents and compares Bernoulli iterative approaches for solving linear DSGE models. The methods are compared using 99 different models from the macroeconomic model data base (MMB) and different parameterizations of the monetary policy rule in the medium-scale new Keynesian model of Smets and Wouters (Am Econ Rev 97(3):586–606, 2007. https://doi.org/10.1257/aer.97.3.586 ) iteratively. I find that Bernoulli methods providing similar accuracy as measured by the forward error of the solution at a somewhat higher computation burden to the standard method of Dynare when solving DSGE models. The method, however, has convergence properties useful when a specific solution, e.g., unique stable, is sought and can be combined with other iterative methods, such as the Newton method, lending themselves especially to refining solutions—either when standard methods fail or when one moves through a parameter space iteratively—as I show in applications of the methods.