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

Jean-Bernard Chatelain (1, 2) , Kirsten Ralf (3)

1 PJSE - Paris Jourdan Sciences Economiques
2 PSE - Paris School of Economics
3 Ecole Supérieure du Commerce Extérieur - ESCE, INSEEC U. Research Center

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.

Mots clés: forcing variables; new-Keynesian Phillips curve; Stackelberg dynamic game; augmented linear quadratic regulator; Ramsey optimal policy; algorithm

Domaines: Economies et finances; Économie et finance quantitative [q-fin]; Optimisation et contrôle [math.OC]

Jean-Bernard Chatelain, Kirsten Ralf. A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables. Economics Bulletin, 2019, 39 (4), pp.2429-2440. ⟨hal-01577606v3⟩