The Signaling Effect of Raising Inflation∗ Jean Barth´elemy Eric Mengus December 13, 2016 Abstract This paper argues that central bankers should temporarily raise inflation when antic- ipating liquidity traps to signal their credibility to forward guidance policies. As stable inflation in normal times either stems from central banker's credibility, e.g. through reputation, or from his aversion to inflation, the private sector is unable to infer the cen- tral banker's type from observing stable inflation, jeopardizing the efficiency of forward guidance policy. We show that this signaling motive can justify temporary deviations of inflation from target well above 2% but also that the low inflation volatility during the Great Moderation was insufficient to ensure fully efficient forward guidance when needed. Keywords: Forward Guidance, Inflation, Signaling. JEL Classification: E31, E52, E65. ∗Barth´elemy: Sciences Po, Department of Economics, 28 rue des Saints P`eres 75007 Paris, France and Banque de France, 31 rue Croix des Petits-Champs 75049 PARIS cedex 01. Email: jean.barthelemy@ sciencespo.fr. Mengus: HEC Paris, Economics and Decision Sciences Department, 1 rue de la Lib´eration, 78350 Jouy-en-Josas, France. Email: [email protected]. We thank Philippe Andrade, Marco Bassetto, Nicolas Coeurdacier, Gaetano Gaballo, Serguei Guriev, Emeric Henry, Josef Hollmayr, Eric Leeper, Olivier Loisel, Beno^ıt Mojon, Silvana Tenreyro, Jean Tirole, Fran¸cois Velde and Mirko Wiederholt for helpful comments as well as seminar participants at Banque de France, Chicago Fed, Indiana University, Sciences Po, T2M (Paris) and SED Meeting (Toulouse). All remaining errors are ours. 1 1 Introduction When the economy hits the zero lower bound (ZLB, thereafter) on nominal interest rates,1 monetary policy can still stimulate the economy by promising exceptional policy accommoda- tion in the future to generate an inflationary boom after the deflationary shock disappears - the so-called forward guidance (see Krugman, 1998; Eggertsson and Woodford, 2003; Werning, 2012). Yet, to be effective such a promise has to be credible to the private sector. The reputation acquired in achieving price stability prior to the 2008 crisis may have been, however, inadequate to ensure the credibility of forward guidance. The observed stable and low inflation { sometimes referred to as the Great Moderation { may have been interpreted as the consequence of a strict aversion of central bankers against any departure from the inflation target (as for the conservative central banker in Rogoff(1985)). And so, paradoxically, better inflation stabilization may have casted doubts about the capacity of the central bankers to tolerate the ex-post inflationary consequences of forward guidance, thus jeopardizing its ex- ante efficiency.2 In recent forward guidance experiences, inflation expectations remained well anchored reflecting the stronger credibility of central banks' inflation targets. In contrast, there is only scarce evidence of the credibility of forward guidance. Announcements of forward guidance policies, even if they led to a large decline in interest rates expectations, were not necessarily understood as a commitment to exceptional policy accommodation in the future but rather as bad news about future shocks (Campbell et al., 2012; Del Negro et al., 2013; Campbell et al., 2016). In addition, some evidence point out that private agents have been uncertain about and actually disagreed on the degree of extra policy accommodation contained in forward guidance announcements (see Andrade et al., 2015). But if this uncertainty on the central banker's actual willingness to follow through on his promises plagues the efficiency of forward guidance, are there any means for a central banker who can follow through on forward guidance to signal himself? In this paper, we provide a theory of why forward guidance announcements may be more or less efficient due to uncertainty on the central banker's objectives and why, in order to reduce this uncertainty, the central bank may have to temporarily raise inflation when the risk of a liquidity trap is looming. To this purpose, we study optimal monetary policy when private agents are uncertain about the central banker's preferences that determine his cred- ibility to implement an inflationary boom after a liquidity trap. More specifically, we link 1The lower bound on nominal interest rates may be slightly below zero as we have already observed slightly negative rates in Switzerland or in the euro area. Therefore, it can be also mentioned as the Effective Lower Bound. 2This is connected to Del Negro et al.(2013) and the \forward guidance puzzle". Other papers put forward alternative limits to forward guidance efficiency such as the discounted Euler equation as in McKay et al. (2015) or Gabaix(2016). We show that our signaling mechanism is robust to considering such a discounted Euler equation. 2 central banker's preference to the sustainability of the Ramsey outcome through the threat of reversion to the discretionary outcome. We determine whether standard monetary policy instruments can be used as a signal to ensure the credibility of forward guidance { and so, its efficiency. Our main result is normative: the central bank has to ensure its credibility before falling into a liquidity trap and, to this purpose, the central bank has to temporarily raise inflation to signal its willingness to follow through on forward guidance policy once the economy actually falls into a liquidity trap. Our paper has also some positive implications: we show that the low inflation volatility during the Great Moderation was insufficient to gen- erate a sufficient signal that would have ensured the efficiency of forward guidance once in a liquidity trap as observed during the Great Recession. But why signal through inflation? Forward guidance policies are least likely to be fol- lowed through by inflation-averse central bankers. And so, a central banker that intends to follow through on his promise has every incentive to be distinguished from such conservative inflation-averse central bankers. And because conservative central bankers are inclined to sta- bilize inflation in normal times, increasing inflation is the only available tool so as to ensure credibility before a liquidity trap occurs. Importantly, this signaling motive implies to raise inflation temporarily and prior to liquidity traps.3 To formalize that argument, we consider a new Keynesian model facing a period of neg- ative natural interest rate that pushes the economy into a liquidity trap. Section2 presents the model under perfect information and proves that an intermediate but strictly positive weight on the output gap stabilization objective in central banker's preferences is necessary to sustain the Ramsey allocation when introducing reputation concerns. Such a central banker optimally follow through forward guidance policy if he anticipates to face either the stabi- lization bias (due to cost-push shocks) or the inflation bias (due to inefficient steady-state) after the liquidity trap. In both cases, the value of maintaining credibility to deal with future biases makes forward guidance sustainable for the benevolent central banker. However, such a central banker will conduct a policy that is similar to the one conducted by the conservative central banker in normal times. We then introduce asymmetric information on the weight of the output gap stabilization objective (Section3) and limit the central banker's types to two: either he maximizes social welfare (the benevolent central banker) or he only takes inflation into account in his objective function (the conservative central banker) and therefore is not able to sustain forward guidance in the benchmark model. Our main insight is that inflation before the liquidity trap occurs can be used as a signaling device for the benevolent central banker. First, signaling is not possible during a liquidity 3Equivalently, this implies to deviate from the long-term inflation target in the short-run. This differs from Coibion et al.(2012) and more generally the buffer stock view of raising inflation due to liquidity traps, where inflation has to be permanently higher and, in particular, after liquidity traps occur. 3 trap as the policy instrument is constrained by the zero lower bound. Thus, if signaling is optimal, it must take place prior to the liquidity trap. Second, as inflation is the only variable entering into the conservative central banker's objective function, it is also the only means to distinguish between the benevolent central banker and the conservative one as the latter will not be inclined to mimic the former. The benevolent central banker then optimally sets inflation at the rate at which the conservative central banker would be indifferent between mimicking the benevolent central banker and adopting a conservative monetary policy.4 In the end, the central banker should raise inflation as a signaling device only when the risk of a liquidity trap is looming: the signaling level of inflation increases with the probability, the intensity and the length of liquidity traps. Importantly, signaling may arise because the two central bankers put different weights on the output gap stabilization objective. On the one hand, the positive weight puts by the benevolent central banker ensures his credibility to sustain forward guidance policy, as in the perfect information case, and therefore provides for a signaling motive to him. On the other hand, the difference in weights in the central banker's preferences plays the role of a Spence- Mirrlees condition in the signaling problem by triggering a differential cost of inflation prior to the liquidity trap between the two central bankers. When the benevolent central banker does not signal his type, the efficiency of forward guidance is determined by the private sector's beliefs on the actual implementation of forward guidance. We show that the efficiency of forward guidance increases with these beliefs, and so, can be arbitrarily low, thus capturing the \forward guidance puzzle", as described by Del Ne- gro et al.(2013). This dependence on private agents' beliefs leads to a hump-shaped optimal policy.