شهرت و اعتبار بانک مرکزی در یک مدل آینده نگر

This paper examines whether reputation concerns can induce the central bank to implement the time-inconsistent optimal monetary policy in the standard New Keynesian model. Interestingly, the forward-looking nature of this model enables us to account for the coordination of the private agents on the punishment length of their trigger strategy. Our results suggest that both the inflation bias and the stabilization bias can be overcome by a reputation-concerned central bank for the calibrations used in the literature. These results enable us to endogenize Woodford's timeless perspective and tend to weaken the case for recent monetary policy delegation proposals.

Optimal monetary policy is known to be potentially time-inconsistent since the seminal work of Kydland and Prescott (1977). The best known illustration of this time-inconsistency problem is Barro and Gordon's (1983a) inflation bias which arises when the central bank seeks to stabilize output above its potential level. Barro and Gordon (1983b) show, however, that reputation considerations can then make the optimal monetary policy sustainable under a simple trigger-strategy assumption. An alternative way to overcome this inflation bias, proposed by Rogoff (1985), is to delegate monetary policy to a conservative central banker. Now whether because they are conservative or concerned for their reputation, nowadays central bankers do not seem in practice to aim at stabilizing output above its potential level, so that the inflation bias is arguably no longer a relevant issue in the current low-inflation environment. The time-inconsistency problem of optimal monetary policy has, however, aroused renewed interest in recent years with the development of stochastic forward-looking models. As first shown by Clarida et al. (1999) and Woodford (1999), these models give indeed rise to a ‘stabilization bias’1 by making optimal monetary policy time-inconsistent even when the central bank does not seek to stabilize output above its potential level. In the standard New Keynesian model for instance, the Phillips curve makes the current inflation rate depend on the current output gap, the expected future inflation rate and the current cost-push shock. The occurrence of cost-push shocks therefore prevents the central bank from achieving the complete and permanent stabilization of both the inflation rate and the output gap. In this context, the optimal monetary policy reaction to a one-off cost-push shock lasts actually longer than the shock itself, so as to make the expected future inflation rate depend on the current cost-push shock, in order to improve the trade-off between stabilizing the current inflation rate and stabilizing the current output gap. This inertial or history-dependent monetary policy is optimal because it enables the central bank to spread the burden of the adjustment to the shock over time, but time-inconsistent because the central bank will want to revert to a neutral stance as soon as the shock disappears. The literature has already come up with a number of monetary policy delegation schemes as remedies for this stabilization bias: Jensen (2002b) proposes to introduce a nominal income growth stabilization objective, Söderström (2005) a money growth stabilization objective, Svensson and Woodford (2005) a state-contingent linear inflation contract, Vestin (2006) a price level stabilization objective, Walsh (2003b) an output gap smoothing objective and Woodford (2003b) an interest-rate smoothing objective, into the loss function assigned to the central bank. All these monetary policy delegation schemes are designed in such a way that the central bank minimizing its assigned loss function under discretion conducts a monetary policy that coincides, or is close to, the time-inconsistent socially optimal monetary policy described above. But to our knowledge there is so far no study on central bank reputation as a way to overcome the stabilization bias (except Kurozumi, 2007, discussed below). Such a study would, however, be welcome since these monetary policy delegation proposals might prove unnecessary if reputation concerns alone could induce the central bank to implement the time-inconsistent socially optimal monetary policy.2 This paper aims at filling this gap in the literature by considering the issue of central bank reputation in a forward-looking model, namely the standard New Keynesian model chosen for its popularity and analytical tractability. We define the reputation of the central bank as its ability to influence the private agents’ expectations and make this ability depend on the central bank's monetary policy track record through a simple trigger-strategy assumption (i.e. credibility is gained by matching deeds with words), thus explicitly modelling a simple argument expressed e.g. by Walsh (2006).3 The consideration of trigger strategies is particularly interesting in the standard New Keynesian model—as in most other forward-looking models—for two reasons. First, numerical calibrations of this model enable us to conclude unambiguously about the sustainability of the optimal monetary policy for a given punishment length. By contrast, ‘qualitative models’ usually lead to inconclusive results since the optimal monetary policy (and more generally any time-inconsistent monetary policy superior to the discretionary monetary policy) is necessarily non-sustainable when the discount factor is close enough to zero and sustainable when the discount factor is close enough to one and the punishment is long enough, as implied by the folk theorem. Second, the forward-looking nature of this model is shown to greatly facilitate the coordination of the atomistic private sector on the punishment length—except in the particular case of serially uncorrelated cost-push shocks. By contrast, this coordination is usually left unexplained in non-forward-looking models. The results obtained suggest that both the inflation bias and the stabilization bias can be overcome by a reputation-concerned central bank for the calibrations used in the literature, provided that the punishment length is at least of the order of a few years. These results tend therefore to weaken the case for the recent monetary policy delegation proposals mentioned above. They moreover enable us to endogenize Woodford's (1999) ‘timeless perspective’, so that we also view our paper as a first step in addressing some concerns about the lack of a proper treatment of monetary policy credibility in Woodford's (2003a) influential book.4 Before proceeding, let us briefly mention four closely related papers. The first and second papers are Ireland (1997) and Kurozumi (2007), which apply Chari and Kehoe's (1990) method to study the sustainable monetary policies in a non-stochastic micro-founded model with an inflation bias for the former and a stabilization bias for the latter. The main difference between these papers and ours is that we consider a specific trigger strategy whose punishment is not the worst possible, in particular because it is (in our view, more realistically) of finite length—technically speaking, considering a finite punishment length is indeed our main original contribution. The third paper is Currie and Levine (1993, Chapter 5), which extends Barro and Gordon's (1983b) framework to a general linear stochastic forward-looking model. There are two main differences between this paper and ours. First, we consider a finite punishment length. Second, we use a micro-founded model, so that we have to make sure that our relaxation of the rational-expectations assumption does not affect the reduced form of this model. The fourth paper is Haubrich and Ritter (2000), which considers the option to wait for a more favourable situation to switch from discretion to commitment or vice versa in a stochastic non-micro-founded model where the central bank can commit and renege at a fixed cost. Again, there are two main differences between this paper and ours. First, we use a micro-founded model. Second, no option to wait can arise in our analysis since we consider a trigger strategy that forbids the central bank to choose when to switch from discretion to commitment, and since we focus on the condition for the central bank never to switch from commitment to discretion (i.e. not to switch from commitment to discretion in the most tempting situation), rather than on the condition for the central bank not to switch from commitment to discretion in a given situation. The remainder of the article is organized as follows. Section 1 presents the forward-looking model considered and assesses the size of the corresponding inflation and stabilization biases. Section 2 introduces the concept of central bank reputation into this model and examines whether reputation concerns may enable the central bank to overcome these biases. We then shortly conclude and provide a technical appendix.

This paper examines whether reputation concerns can induce a central bank to implement the time-inconsistent optimal monetary policy in the standard New Keynesian model. Our analysis rests on a simple trigger-strategy assumption in an infinite-horizon repeated game with complete information. This trigger-strategy assumption appears relevant in our framework as the forward-looking nature of our standard New Keynesian model greatly facilitates the coordination of firms on the punishment length—except in the particular case of serially uncorrelated cost-push shocks. Our results suggest that the inflation bias and the stabilization bias can be overcome for the calibrations used in the literature.20 These results enable us to endogenize the precommitment equilibrium and therefore Woodford's (1999) timeless-perspective equilibrium as well, since the latter corresponds to the limit of the former as the commitment date becomes infinitely distant in the past. Moreover, they tend to weaken the case for monetary policy delegation shortly presented in the Introduction of this article. Examining the issue of central bank reputation in a stochastic forward-looking model with a finite punishment length raises some practical difficulties. In this paper we have overcome these difficulties for the standard New Keynesian model by focusing on the most tempting situation for the central bank, thus determining a necessary and sufficient condition for the central bank never to deviate from the precommitment equilibrium, rather than a necessary and sufficient condition for the central bank not to deviate from this equilibrium in a given situation. This method could be generalized to other stochastic forward-looking models for which it should provide a useful indicator of whether to consider the discretionary equilibrium or the timeless-perspective equilibrium in the presence of a sizeable stabilization bias. In particular, applying our method to a New Keynesian model with a Phillips curve that, like ours, features both expected future inflation and past inflation and a social loss function that, unlike ours, penalizes inflation volatility rather than quasi-differenced inflation volatility21 would be interesting for two reasons: first, because the stabilization bias may be larger in such a model than in our model with γ=0γ=0, as shown by Dennis and Söderström (2006), even though this bias disappears in the limit case of a purely backward-looking Phillips curve; second, because the stabilization bias remains sizeable when information and/or transmission lags22 are introduced into this model, as shown by Dennis and Söderström (2006) and Lam and Pelgrin (2004).23