A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables

Economics Bulletin, 39(4), 2429-2440 (2019)

12 Pages Posted: 29 Aug 2017 Last revised: 28 Oct 2019

See all articles by Jean-Bernard Chatelain

Jean-Bernard Chatelain

Paris School of Economics, Université Paris 1 Panthéon Sorbonne

Kirsten Ralf

Ecole Supérieure du Commerce Extérieur (ESCE)

Date Written: October 25, 2019

Abstract

This article presents an algorithm that extends Ljungqvist and Sargent's (2012) dynamic Stackelberg game to the case of dynamic stochastic general equilibrium models including forcing variables. Its first step is the solution of the discounted augmented linear quadratic regulator as in Hansen and Sargent (2007). It then computes the optimal initial anchor of "jump" variables such as inflation. We demonstrate that it is of no use to compute non-observable Lagrange multipliers for all periods in order to obtain impulse response functions and welfare. The algorithm presented, however, enables the computation of a history-dependent representation of a Ramsey policy rule that can be implemented by policy makers and estimated within a vector auto-regressive model. The policy instruments depend on the lagged values of the policy instruments and of the private sector's predetermined and "jump" variables. The algorithm is applied on the new-Keynesian Phillips curve as a monetary policy transmission mechanism.

Keywords: Ramsey optimal policy, algorithm, forcing variables, augmented linear quadratic regulator, new-Keynesian Phillips curve

JEL Classification: C61, C62, E47, E52, E58, E60, E61

Suggested Citation

Chatelain, Jean-Bernard and Ralf, Kirsten, A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables (October 25, 2019). Economics Bulletin, 39(4), 2429-2440 (2019), Available at SSRN: https://ssrn.com/abstract=3026988 or http://dx.doi.org/10.2139/ssrn.3026988

Jean-Bernard Chatelain (Contact Author)

Paris School of Economics, Université Paris 1 Panthéon Sorbonne ( email )

48 Boulevard Jourdan
Paris, 75014 75014
France

HOME PAGE: http://www.parisschoolofeconomics.eu/fr/chatelain-jean-bernard/

Kirsten Ralf

Ecole Supérieure du Commerce Extérieur (ESCE) ( email )

10 Rue Sextius Michel
Paris, 75015
France

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