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

This algorithm extends Ljungqvist and Sargent (2012) algorithm of Stackelberg dynamic game to the case of dynamic stochastic general equilibrium models including exogenous forcing variables. It is based Anderson, Hansen, McGrattan, Sargent (1996) discounted augmented linear quadratic regulator. It adds an intermediate step in solving a Sylvester equation. Forward-looking variables are also optimally anchored on forcing variables. This simple algorithm calls for already programmed routines for Ricatti, Sylvester and Inverse matrix in Matlab and Scilab. A final step using a change of basis vector computes a vector auto regressive representation including Ramsey optimal policy rule function of lagged observable variables, when the exogenous forcing variables are not observable. C61, C62, C73, E47, E52, E61, E63.

Mots clés: Ramsey optimal policy; Stackelberg dynamic game; algorithm; forcing variables; augmented linear quadratic regulator

Domaines: Economies et finances

Jean-Bernard Chatelain, Kirsten Ralf. A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables. 2017. ⟨hal-01577606v1⟩