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Jean-bernard Chatelain and Kirsten Ralf
''The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks''
( 2020, Vol. 40 No.2 )
With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a Ricatti equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock.
Keywords: Ramsey optimal policy, Stackelberg dynamic game, algorithm, forcing variables, augmented linear quadratic regulator, new-Keynesian Phillips curve.
JEL: C6 - Mathematical Methods and Programming: General
E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit: General
Manuscript Received : May 05 2020 Manuscript Accepted : Jun 24 2020

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