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We propose a simple framework for analyzing a continuum of monetary policy rules characterized by differing degrees of credibility, in which commitment and discretion become special cases of what we call quasi-commitment. The monetary policy authority is assumed to formulate optimal commitment plans, to be tempted to renege on them, and to succumb to this temptation with a constant exogenous probability known to the private sector. By interpreting this probability as a continuous measure of the (lack of) credibility of the monetary policy authority, we investigate the welfare effect of a marginal increase in credibility. Our main finding is that, in a simple model of the monetary transmission mechanism, most of the gains from commitment accrue at relatively low levels of credibility.

As first pointed out by Kydland and Prescott (1977), “economic planning is not a game against nature but, rather, a game against rational economic agents.” When agents are rational and forward-looking, economic planners face constraints that depend on their own current and future choices, as forecasted by the private sector. Optimal policy therefore needs to internalize the effect of those choices on current private behavior. Consider for example the case of a central bank confronting a trade-off between inflation and unemployment, in which current inflation also depends on expectations of future inflation.1 In this environment, the credible announcement of a future policy tightening, in excess of that needed to curb forecasted inflationary pressures, lowers inflation expectations, thereby easing today's trade-off. Optimal policy should therefore exhaust the net marginal benefit of this announcement. This strategy, however, is time-inconsistent. The same tightening that was once desirable to announce, due to its moderating effect on expectations, becomes regrettable as soon as it delivers the promised recession. For this reason, a benevolent policymaker will be expected to renege on her announcement and avoid the recession. Yet, the credibility of that announcement is a necessary prerequisite for the optimal policy to be feasible. This highlights an important tension between the optimality of the commitment plan and the ex post incentive to abandon it. On the one hand, central banks can reap the benefits of commitment only if the private sector knows (with probability one) that they will not deviate from their announced plans. Yet, in the absence of a commitment technology, there is no reason for the private sector to believe that deviations will not occur. Moreover, this tension is exacerbated by the binary nature of the choice facing the public. It can either believe the central bank, or not. In this paper, we propose a way of endowing private agents with the benefit of the doubt. We assume that a new central banker, call her jj, is appointed with a constant and exogenous probability αα every period. When j takes office (in period τjτj), she reneges on the promises of her predecessor and commits to a new policy plan that is optimal as of period τjτj. Agents understand the possibility and the nature of this change and form expectations accordingly. As a result, the private sector is constantly doubtful of the reliability of outstanding promises. Think of this as an economy with access to a limited commitment technology. Thanks to this technology, policymakers can guarantee their own promises. However, they cannot influence the behavior of their successors, who are therefore expected to formulate their own policy plan. Given this expectation, a new policymaker's best response is indeed to reoptimize upon taking office. Once in office though, incumbents will play the commitment strategy for the duration of their mandate. We refer to the resulting equilibrium, and to the limited commitment technology that supports it, as quasi-commitment. Note that with quasi-commitment, even if reoptimizations can be arbitrarily frequent, they are not a source of gains for the policy authority. Since agents anticipate them to happen with the correct probability, on average there is no room “to exploit temporarily given inflationary expectations for brief output gains” (McCallum, 1999). This implies that quasi-commitment cannot improve on the (full) commitment solution to the planning problem, since it imposes a restriction on the menu of credible promises available to the planner. However, quasi-commitment converges to full commitment for α→0α→0. It also converges to discretion when α→1α→1. In this framework therefore, we can welfare-rank a continuum of intermediate cases between commitment and discretion, and investigate to what extent our imperfect commitment technology can approximate the optimal equilibrium. As described above, quasi-commitment is a useful modeling device to escape the strict binary logic of the debate on “commitment vs. discretion”, and to connect those two extreme modes of policymaking by a continuum of policy “rules”. In this context, we find it particularly suggestive to interpret αα as a measure of the credibility of the central bank, that is of “the extent to which beliefs about the current and future course of economic policy are consistent with the program originally announced by policymakers” (Blackburn and Christensen, 1989). In our model, the public always contemplates the possibility that the current policy plan will be abandoned. The higher the probability attributed to this event, the higher the mismatch between the public's perceptions and the plan being implemented by the incumbent policymaker, the lower her credibility.2 Credibility thus becomes a continuous variable, measuring the probability that a central bank “matches deeds to words.” This is precisely the notion of credibility advocated by Blinder (1998). Our definition of credibility is quite distinct from the ones previously proposed in the literature. In particular, we do not interpret credibility in terms of the relative weight on output in the central bank's loss function (Rogoff, 1985), or in terms of the discrepancy between inflation expectations and the central bank's inflation target (Faust and Svensson, 2000), but rather in terms of the expected durability of policy commitments. In this sense, our notion of credibility is closely related to an empirical measure of actual central bank independence proposed by Cukierman (1992), the observed turnover rate of central bank governors.3 Moreover, by assuming that private agents are perfectly informed about the nature and objectives of monetary policy, we rule out reputational equilibria based on the public's uncertainty about the preferences of different types of central bankers, of the kind studied for example by Barro (1986) and Rogoff (1989). We also view our approach to credibility as an alternative to the one built on the game theoretic apparatus of Abreu et al., 1986 and Abreu et al., 1990.4 Differently from that literature, we do not explore the set of competitive equilibria that can be sustained by punishing governments that renege on their promises. In fact, we bypass this issue completely by assuming that policymakers have access to a commitment technology that guarantees (some of) their promises. In our model, credibility is not the attribute of a particular policy plan, the plan which policymakers optimally choose not to deviate from when behaving sequentially. Rather it is a quality of the central bank as perceived by the public. In the reputation literature, policy plans are either sustainable or not, mainly as a function of how harsh a punishment the private sector is able to inflict on a deviating policymaker. Optimal policy therefore never implies deviations from the announced plan (Phelan, 2001). Under quasi-commitment on the contrary, different central banks enjoy different levels of credibility, depending on the commitment technology available to them. Therefore, deviations from pre-announced plans are indeed observed in equilibrium, even if they do not generate any systematic surprise for the public. In this sense, quasi-commitment assumes a given level of policy credibility, rather than explaining its origin. Nevertheless, we do not regard this as a shortcoming of the model, since its focus is on the consequences of marginal increases in credibility, rather than on its premises. Just as Calvo pricing is widely regarded as a useful starting point to explore the consequences of sticky prices, even if its time-dependent microfoundations are only suggestive of actual pricing behavior, so we propose quasi-commitment as a modeling device to explore decision-making procedures intermediate between discretion and commitment, along a dimension that can be usefully interpreted as credibility. The papers in the literature that are closest to ours are Flood and Isard (1988) and Roberds (1987).5 The former identifies conditions under which commitment to a simple rule can be improved upon by the addition of a provision for discretionary optimization in the face of “big” shocks.6 Our framework can easily be adapted to interpret αα as the probability of an extreme draw of the exogenous i.i.d. shocks that buffet the economy. Under this interpretation, policymakers are given free reign in the face of “big” shocks, but differently from Flood and Isard (1988), this optimally results in a new commitment rather than in a reversion to discretion. Roberds (1987) presents a technical apparatus very similar to the one described below. He solves a model in which policy is set by a sequence of administrations whose turnover is determined by i.i.d. Bernoulli draws. Thanks in part to the better understanding of optimal policy problems available today, our solution method is more transparent and more widely applicable than Roberds’ (1987), accommodating systems that include nontrivial dynamics for the endogenous state variables and singularities in the contemporaneous relations. On the other hand, we do not treat here the case of asymmetric information between policymakers and the public, which in Roberds’ (1987, Section 4) framework gives rise to an interesting class of equilibria with delayed information. Finally, and much more importantly in our view, this paper provides a novel interpretation of the frequency of administration turnover as a measure of policy credibility. As a result, we can exploit the technical apparatus first proposed by Roberds (1987), and further developed here, to address important questions in the still open debate on “rules vs. discretion.” The remainder of the paper is organized as follows. In Section 2, we introduce a simple New Keynesian model of the monetary transmission mechanism, which will serve as a laboratory for the study of quasi-commitment. This study is undertaken in Section 3. First, we solve the model analytically, to provide some intuition on the key steps involved in finding a quasi-commitment equilibrium. Second, we illustrate the dynamic behavior of the economy in a calibrated version of the model, under different assumptions on the degree of credibility enjoyed by its monetary authority. Finally, in Section 4, we study the distribution of the gains from commitment across different levels of credibility. Section 5 concludes.

This paper introduced the notion of quasi-commitment, a decision-making framework with limited commitment in which policymakers renege on their announced optimal plans with a constant, exogenous probability every period. Assuming that private agents know the probability of renegotiation, and form expectations on the future course of policy accordingly, we can interpret the expected duration of the announced plans as a continuous measure of whether policymakers match deeds to words. This is the notion of credibility proposed by Blinder (1998). We apply this framework to a calibrated version of a forward-looking model of the monetary transmission mechanism, and study the effect of credibility on welfare. Our main finding is that most of the gains from commitment accrue at relatively low levels of credibility. In our benchmark calibration a commitment expected to last for one year is enough to bridge 90% of the welfare gap between discretion and commitment. Moreover, we show that the presence of an average inflation bias significantly accentuates the nonlinearity of the relationship between credibility and welfare. These findings are important, because they imply that policymakers do not need to convince the public that they will honor their promises forever to reap most of the benefits of commitment. They also suggest a possible explanation for the often remarked obsession of central bankers with their credibility (Blinder, 1998). In our world, an even minor loss in credibility can have significant welfare effects. This paper represents a preliminary study of the behavior of a particular model economy under quasi-commitment. The robustness of our results across different models of the monetary transmission mechanism is an open question, that warrants further investigation. In fact, progress in this direction can be accomplished with a relatively modest effort, given that our solution method has been devised for a general class of DSGE models. Finally, endogenizing the probability of a change in regime seems an obvious step to increase the empirical plausibility of the model. We could think of two ways of accomplishing this, which we see as complementary. On the one hand, we could allow central bankers to invest in their credibility, for example by refusing to reoptimize when given the option. This would be justified only as long as the private sector could learn about the new frequency of reoptimizations. Comparing the costs of the transition, when inflation expectations are still high, with the long-run gains associated with the higher level of credibility, would produce a normative analysis of the transition from low to high credibility regimes. On the other hand, we could assume that the probability of a reoptimization depends on the state of the economy as in Flood and Isard (1988). For example, we could make this probability a function of the vector of predetermined Lagrange multipliers, which measure the temptation to disregard the associated constraints and reoptimize. Even though maybe desirable on the grounds of realism, these extensions would come at the cost of foregoing the linear quadratic structure that makes the model tractable. For this reason, the quasi-commitment framework with exogenous reoptimizations provides a useful first step in the direction of expanding the menu of policy choices beyond discretion and commitment.