Time inconsistency and reputation in monetary policy : a strategic modelling in continuous time

Jingyuan LI, Guoqiang TIAN

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

Abstract

This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational equilibria, we give the conditions under which the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for nonstochastic settings even with a finite horizon. We provide the conditions for the existence of stationary sequentially strong rational equilibrium, and also completely characterize the existence of stationary sequentially weak rational equilibrium. We show that, under the assumption of the public's weak rational expectation or the certainty setting, the government will keep the inflation at zero if and only if a(1 ¡ µ) < 2. This inequality is satisfied if the rate of the aggregate output gain from the unanticipated inflation, a, is small (less than 2) or the government puts more weight on stabilizing output than on stabilizing inflation (µ > 1). Furthermore, we investigate the robustness of the sequentially strong rational equilibrium behavior solution by showing that the imposed assumption is reasonable.
Original languageEnglish
Pages (from-to)697-710
Number of pages14
JournalActa Mathematica Scientia
Volume28B
Issue number3
DOIs
Publication statusPublished - 1 Jul 2008
Externally publishedYes

Fingerprint

Monetary Policy
Inconsistency
Continuous Time
Modeling
horizon
Rational Expectations
Optimal Stopping
Finite Horizon
stopping
Trigger
Inflation
Horizon
actuators
Robustness
If and only if
Reputation
Zero

Keywords

  • Time inconsistency
  • optimal stopping
  • stochastically stable equilibrium

Cite this

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title = "Time inconsistency and reputation in monetary policy : a strategic modelling in continuous time",
abstract = "This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational equilibria, we give the conditions under which the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for nonstochastic settings even with a finite horizon. We provide the conditions for the existence of stationary sequentially strong rational equilibrium, and also completely characterize the existence of stationary sequentially weak rational equilibrium. We show that, under the assumption of the public's weak rational expectation or the certainty setting, the government will keep the inflation at zero if and only if a(1 ¡ µ) < 2. This inequality is satisfied if the rate of the aggregate output gain from the unanticipated inflation, a, is small (less than 2) or the government puts more weight on stabilizing output than on stabilizing inflation (µ > 1). Furthermore, we investigate the robustness of the sequentially strong rational equilibrium behavior solution by showing that the imposed assumption is reasonable.",
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Time inconsistency and reputation in monetary policy : a strategic modelling in continuous time. / LI, Jingyuan; TIAN, Guoqiang.

In: Acta Mathematica Scientia, Vol. 28B, No. 3, 01.07.2008, p. 697-710.

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

TY - JOUR

T1 - Time inconsistency and reputation in monetary policy : a strategic modelling in continuous time

AU - LI, Jingyuan

AU - TIAN, Guoqiang

PY - 2008/7/1

Y1 - 2008/7/1

N2 - This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational equilibria, we give the conditions under which the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for nonstochastic settings even with a finite horizon. We provide the conditions for the existence of stationary sequentially strong rational equilibrium, and also completely characterize the existence of stationary sequentially weak rational equilibrium. We show that, under the assumption of the public's weak rational expectation or the certainty setting, the government will keep the inflation at zero if and only if a(1 ¡ µ) < 2. This inequality is satisfied if the rate of the aggregate output gain from the unanticipated inflation, a, is small (less than 2) or the government puts more weight on stabilizing output than on stabilizing inflation (µ > 1). Furthermore, we investigate the robustness of the sequentially strong rational equilibrium behavior solution by showing that the imposed assumption is reasonable.

AB - This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational equilibria, we give the conditions under which the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for nonstochastic settings even with a finite horizon. We provide the conditions for the existence of stationary sequentially strong rational equilibrium, and also completely characterize the existence of stationary sequentially weak rational equilibrium. We show that, under the assumption of the public's weak rational expectation or the certainty setting, the government will keep the inflation at zero if and only if a(1 ¡ µ) < 2. This inequality is satisfied if the rate of the aggregate output gain from the unanticipated inflation, a, is small (less than 2) or the government puts more weight on stabilizing output than on stabilizing inflation (µ > 1). Furthermore, we investigate the robustness of the sequentially strong rational equilibrium behavior solution by showing that the imposed assumption is reasonable.

KW - Time inconsistency

KW - optimal stopping

KW - stochastically stable equilibrium

UR - http://commons.ln.edu.hk/sw_master/2726

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DO - 10.1016/S0252-9602(08)60071-5

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VL - 28B

SP - 697

EP - 710

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

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IS - 3

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