Solving and estimating linearized DSGE models with VARMA shock processes and filtered data

Solving Linear DSGE Models with Bernoulli Iterations

“…of Meyer-Gohde and Saecker (2022) in this respect. Increasing the weight towards the Bernoulli increment (with p = 1/3) increases the number of models for the combined Newton-Bernoulli algorithms converged -both with and without line searches.…”

“…where X B restricts x to be greater or equal to one, see above, and X N restricts x to be between zero and two (see Meyer-Gohde and Saecker, 2022).…”

“…Table 3 summarizes the results. The first column of results counts the number of models for which the method in question converged to the unique stable solution, highlighting the well-known (Higham and Kim, 2001;Meyer-Gohde and Saecker, 2022) drawback of Newton methods, namely the unpredictability of which solution the algorithm will converge to. This problem is not faced by the baseline Bernoulli method, as is to be expected following theorem 1 above, which converged for all models in the MMB.…”

“…1 methods to be formulated such that they converge to the minimal solvent (solution with the smallest eigenvalues in magnitude) allow them to perform favorably compared with QZ-based methods -particularly when combined with Newton methods and their asymptotic quadratic convergence. Precisely this iterative characteristic also enables the methods I introduce to linear DSGE models to correct insufficiently accurate solutions of economic consequence as presented in Meyer-Gohde (2022).…”

“…Initial ValueAll Bernoulli iterations need an initial value, P 0 . In contrast to Newton methods, seeMeyer-Gohde and Saecker (2022), the baseline Bernoulli method has strong convergence results, see the next subsection, and hence this initial value is of lesser importance. Yet many of the algorithms presented above combine Bernoulli and Newton methods and are subject to this concern.…”