Publications des chercheurs de PSE

This paper compares Ramsey optimal policy for the new-Keynesian model with public debt with its .scal theory of the price level (FTPL) equilibrium. Both the fiscal theory of the price level and Ramsey optimal policy implies that a de.cit shock is instantaneously followed by an increase of in.ation and output gap. But each optimal policy parameters belongs in di¤erent sets with respect to FTPL. The optimal .scal rule parameter implies local stability of public debt dynamics ("passive fiscal policy"). The optimal Taylor rule parameter for in.ation is larger than one. The optimal Taylor rule parameter for output gap is negative, because of the intertemporal substitution e¤ect of interest rate on output gap. Both Taylor rule optimal parameters implies the local stability of inflation and output gap dynamics.

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.

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.

We consider a frictionless constant endowment economy based on Leeper (1991). In this economy, it is shown that, under an ad-hoc monetary rule and an ad-hoc fiscal rule, there are two equilibria. One has active monetary policy and passive fiscal policy, while the other has passive monetary policy and active fiscal policy. We consider an extended set-up in which the policy maker minimizes a loss function under quasi-commitment, as in Schaumburg and Tambalotti (2007). Under this formulation there exists a unique Ramsey equilibrium, with an interest rate peg and a passive fiscal policy.

This paper compares different implementations of monetary policy in a new- Keynesian setting. We can show that a shift from Ramsey optimal policy under short term commitment (based on a negative-feed back mechanism) to a Taylor rule (based on a positive-feed back mechanism) corresponds to a Hopfbifurcation with opposite policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when policy targets (inflation and out put gap) a reforward-looking variables in the new-Keynesian theory.

With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a single Riccati 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.

With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a single Riccati 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. JEL classi…cation numbers: C61, C62, C73, E47, E52, E61, E63.

This paper is a study of the history of the transplant of mathematical tools using negative feedback for macroeconomic stabilization policy from 1948 to 1975 and the subsequent break of the use of control for stabilization policy which occurred from 1975 to 1993. New-classical macroeconomists selected a subset of the tools of control that favored their support of rules against discretionary stabilization policy. The Lucas critique and Kydland and Prescott's time-inconsistency were overstatements that led to the "dark ages" of the prevalence of the stabilization-policy-ineffectiveness idea. These overstatements were later revised following the success of the Taylor (1993) rule.

This paper compares different implementations of monetary policy in a new-Keynesian setting. We can show that a shift from Ramsey optimal policy under short-term commitment (based on a negative feedback mechanism) to a Taylor rule (based on a positive feedback mechanism) corresponds to a Hopf bifurcation with opposite policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when policy targets (inflation and output gap) are forward-looking variables in the new-Keynesian theory.

Giannoni and Woodford (2003) found that the equilibrium determined by commitment to a super-inertial rule (where the sum of the parameters of lags of interest rate exceed ones and does not depend on the auto-correlation of shocks) corresponds to the unique bounded solution of Ramsey optimal policy for the new-Keynesian model. By contrast, this note demonstrates that commitment to an inertial rule (where the sum of the parameters of lags of interest rate is below one and only depends on the auto-correlation of shocks) corresponds to the unique bounded solution.