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

Chatelain, Jean-Bernard and Ralf, Kirsten (2017): A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Ramsey optimal policy, Stackelberg dynamic game, algorithm, forcing variables, augmented linear quadratic regulator.
• 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

Amman, H. (1996). Numerical methods for linear-quadratic models. in Amman H.M., Kendrick D.A. and Rust J. (editors) Handbook of Computational Economics, Elsevier, Amsterdam, 1, 587-618.

Anderson E.W., Hansen L.P., McGrattan E.R. and Sargent T.J. (1996). Mechanics of Forming and Estimating Dynamic Linear Economies. in Amman H.M., Kendrick D.A. and Rust J. (editors) Handbook of Computational Economics, Elsevier, Amsterdam, 1, 171-252.

Bryson A.E. and Ho Y.C. (1975). Applied Optimal Control, John Wiley and Sons, New York.

Chatelain J.B. and Ralf K. (2016). Countercyclical versus Procyclical Taylor Principles. Econstor working papers.

Chatelain J.B. and Ralf K. (2017a). Can We Identify the Fed's Preferences? Econstor working papers.

Chatelain J.B. and Ralf K. (2017b). Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy. Econstor working papers.

Kalman R.E. (1960). Contributions to the Theory of Optimal Control. Boletin de la Sociedad Matematica Mexicana, 5, pp.102-109.

Ljungqvist L. and Sargent T.J. (2012). Recursive Macroeconomic Theory. 3rd edition. The MIT Press. Cambridge, Massaschussets.

Miller M. and Salmon M. (1985). Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies, Economic Journal, 95 supplement: conference papers, 124-137.

Simon H.A. (1956). Dynamic Programming under Uncertainty with a Quadratic Criterion Function. Econometrica, 24(1), 74-81.

Taylor, J. B. (1999). The robustness and efficiency of monetary policy rules as guidelines for interest rate setting by the European Central Bank. Journal of Monetary Economics, 43(3), 655-679.