Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain

Abstract

, Ivie, MECD and FEDER funds under the projects SEJ-2007-62656 and ECO2012-36719. Rafael Valero acknowledges support from MECD under the FPU program. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

The Empirical Implications of the Interest-Rate Lower Bound

“…The model is solved for a minimum state variable solution using a projection method similar to Christiano and Fisher 2000and Judd, Maliar, Maliar, and Valero (2014), and the details of the method are provided in a Technical Appendix. 3 Because we are estimating the model, it might be tempting to use a computationally-efficient solution algorithm that respects the nonlinearity in the Taylor rule but log-linearizes the remaining equilibrium conditions.…”

Non-intrusive reduced order modelling of the Navier–Stokes equations

“…To cope with the curse of dimensionality, as we know, the Smolyak sparse grid method [25] is an efficient method of integrating/interpolating multidimensional functions based on a univariate quadrature rule. This sparse grid method has been widely applied in various applications [26,27,28], including numerical integration [29], partial differential equations [30], economics [31,32], stochastic natural convection problems [33], sensitivity analysis [34], portfolio problems [35] and high dimensional interpolation [36].…”

Self-Justified Equilibria: Existence and Computation

“…To solve for self-justied equlibria in general, we need to repeatedly approximate and interpolate multi-variate policy function on irregularly-shapedthat is, non-hypercubic domains. In such environments, standard grid-based methods such as Smolyak (see, e.g., Krueger and Kubler (2004) and Judd et al (2014)) or adaptive sparse grids (see, e.g., Brumm and Scheidegger (2017) and Brumm et al (2015)), will fail. To this end, we will follow closely Scheidegger and Bilionis (2017) and use Gaussian process regression (GPR) (see, e.g., Rasmussen and Williams (2005) and Sec.…”