Taylor Projection: A New Solution Method for Dynamic General Equilibrium Models

Abstract

This article presents a new solution method for dynamic equilibrium models. The solution is approximated by polynomials that zero the residual function and its derivatives at a given point x0. The algorithm is essentially a type of projection but is significantly faster, since the problem is highly sparse and can be easily solved by a Newton solver. The obtained solution is accurate locally in the neighborhood of x0. Importantly, a local solution can be obtained at any point of the state space. This makes it possible to solve models at points that are further away from the steady state.

Rare Disasters, the Natural Interest Rate and Monetary Policy

“…We set up a NK model with stochastic trend growth and disaster shocks as in Gourio (2012), Isoré and Szczerbowicz (2017) and Fernández-Villaverde and Levintal (2018). The economy comprises a representative household supplying labor and deciding the optimal level of consumption and investment, while firms combine capital and labor to produce the single consumption good.…”

“…The modeling of disasters closely follows Fernández-Villaverde and Levintal (2018). Private investment is subject to adjustment costs (see next subsection for a detailed description), with the law of motion of capital being:…”

“…The firms' side of the model is completely standard and borrowed from Fernández-Villaverde and Levintal (2018). Perfectly competitive final good producers combine i intermediate goods according to…”

“…As in Fernández-Villaverde and Levintal (2018) the central bank sets the interest rate according to the following rule:…”

“…where variables with a superscript f are detrended, variables with a ˜ are detrended, andẑ t = zt z t−1 is the growth rate of productivity. Fernández-Villaverde and Levintal (2018), following the literature on asset prices (see e.g. Lucas, 1978;Lettau, 2003;Gourio, 2012;van Binsbergen et al, 2012;Nakamura et al, 2013;Isoré and Szczerbowicz, 2017), show that the price of a one-period risk-free bond can be defined as:…”