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

Chatelain, Jean-Bernard and Ralf, Kirsten (2019): A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables. Published in: Economics Bulletin , Vol. 4, No. 39 (25 October 2019): pp. 2429-2440.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Ramsey optimal policy, Stackelberg dynamic game, algorithm, forcing variables, augmented linear quadratic regulator, new-Keynesian Phillips curve.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E47 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E61 - Policy Objectives ; Policy Designs and Consistency ; Policy Coordination; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E63 - Comparative or Joint Analysis of Fiscal and Monetary Policy ; Stabilization ; Treasury Policy

References

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