The signaling role of policy actions

Journal of Monetary Economics 57 (2010) 682–695

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Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme

The signaling role of policy actions$ Romain Baeriswyl a,, Camille Cornand b a b

Munich Graduate School of Economics and Swiss National Bank, Boersenstrasse 15, P.O. Box, CH-8022 Zurich, Switzerland CNRS - BETA and University of Strasbourg, France

a r t i c l e i n f o

abstract

Article history: Received 13 July 2007 Received in revised form 31 May 2010 Accepted 4 June 2010 Available online 12 June 2010

In an economy affected by shocks that are imperfectly known, the monetary instrument takes on a dual stabilizing role: as a policy response that directly influences the economy and as a vehicle for information that reveals the central bank’s assessment to firms. Because mark-up shocks cannot be neutralized by monetary policy, providing firms with more information about these shocks exacerbates their reaction and creates a larger distortion. Recognizing the signaling role of its instrument, the central bank distorts its policy response in order to optimally shape firms’ beliefs. While providing firms with more information is always detrimental to the output gap, it has a more subtle effect on price dispersion depending on whether information is provided through the transparency channel or through the signaling channel. Although more transparency is always detrimental to welfare, the information that is conveyed by the monetary instrument improves welfare when firms’ coordination is highly valuable. & 2010 Elsevier B.V. All rights reserved.

1. Introduction In the ongoing debate on the social value of public information, most of the literature considers information as being disclosed by means of an explicit and official statement made by an institution such as a central bank.1 However, taking a policy action also conveys information as an implicit communication. For instance, the implementation of monetary policy reveals to the market the economic assessment of the central bank and discloses public information even in the absence of an explicit statement. Consequently, the response of a policy maker takes a dual role: as an action that directly influences economic outcomes and as a vehicle for information that influences the beliefs of market participants. A policy maker should naturally account for the signaling role of its policy action when determining the optimal action to take. Although there is a growing pool of literature on the desirability of central bank transparency, it has largely abstracted from the interaction between the choice to be transparent and the optimal design of monetary policy.2 To illustrate the signaling role of the policy action, we consider the optimal conduct of monetary policy in an economy where monetary frictions are caused by imperfect information. In this environment, communication turns out to be an essential component in designing an optimal monetary policy because it drives the degree of information imperfection and

$ An earlier version of this paper was presented at the conference on ‘‘Monetary Policy, Transparency, and Credibility’’ at the Federal Reserve Bank of San Francisco, March 2007.  Corresponding author. Tel.: + 41 44 631 31 21. E-mail address: [email protected] (R. Baeriswyl). 1 See Geraats (2002) for an overview and the literature in the vein of Morris and Shin (2002) seminal beauty-contest paper, for instance Hellwig (2005) and Lorenzoni (2010). 2 Some exceptions are Angeletos et al. (2006), Hellwig et al. (2006), and Walsh (2007) who analyze the signaling role of policy choices on market participants in different contexts.

0304-3932/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2010.06.001

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the real effects of policy choices. The central bank may disclose more information to the private sector through two channels. First, the central bank explicitly discloses more information when it becomes more transparent with respect to its economic assessment or its monetary instrument; this is the form of communication with which the literature usually deals. Second, for a given level of transparency, the central bank may implicitly disclose more information about its economic assessment through the signaling role of its monetary policy whenever the market’s interpretation of it is ambiguous.3 The central bank thus determines its monetary policy action by optimally balancing both its direct impact on the economy and the information it conveys to market participants. In particular, if the central bank wishes to withhold information from the markets, it should adjust its monetary policy so as not to release too much information through its policy action. The economy is hit by two types of disturbances, namely, a stochastic labor supply shock that induces parallel variations in both the efficient and the equilibrium level of output, and a stochastic mark-up shock that induces variations in the equilibrium level of output but leaves the efficient level unaffected. Providing better information reduces frictions and helps economic agents reach the equilibrium level of output that would prevail in a frictionless economy. As Angeletos and Pavan (2007) emphasize, providing more information improves welfare to the extent that the equilibrium and the efficient level of output are symmetrically affected by shocks. Consequently, withholding information about the mark-up shock reduces the output gap because it prevents the economy from moving too closely to the frictionless equilibrium level of output and, thereby, from deviating too much from the efficient level.4 In cases where firms perfectly observe the monetary instrument but where the central bank does not disclose any explicit announcement about its economic assessment, firms cannot properly decipher the rationale behind the policy action. The central bank can exploit this ambiguity by distorting its response to labor supply and mark-up shocks in order to optimally shape firms’ beliefs. Because the central bank seeks to maximize the welfare of the representative agent, the welfare loss increases with both the output gap and price dispersion. Providing firms with more information on mark-up shocks systematically exacerbates the output gap. As a result, when the output gap is relatively more costly, the central bank strengthens its response to labor supply shocks to reduce the amount of information about mark-up shocks that is conveyed by its chosen monetary instrument. However, providing firms with more information has a more subtle effect on price dispersion depending on whether information is provided through the transparency channel or through the signaling channel. On the one hand, providing firms with more information through the transparency channel is always detrimental to welfare because it impairs the trade-off between output gap and price dispersion. This suggests that the result of Cukierman (2001), which emphasizes the benefit of opacity for the trade-off between employment and inflation caused by mark-up shocks, carries over into a framework where price dispersion matters, even if one would expect transparency to favor firms’ coordination. On the other hand, providing firms with more information through the signaling role of the monetary instrument, for a given level of transparency, enhances firms’ coordination and improves welfare when price dispersion is relatively more costly. In this case, the central bank weakens its response to labor supply shocks to make its instrument more informative about mark-up shocks and to reduce price dispersion. The fact that more public information enhances firms’ coordination has been stressed by Hellwig (2005) and Woodford (2005). Briefly, while more transparency is always detrimental to welfare, disclosing more information to firms through the signaling role of the monetary instrument improves welfare when coordination is socially highly valuable.5 The paper is structured as follows. Section 2 presents the economy. Section 3 derives the optimal monetary policy for benchmark cases with homogeneous information; it highlights the welfare effect of information with respect to labor supply and mark-up shocks. Section 4 presents the optimal monetary policy under heterogeneous information as a function of the communication strategy of the central bank. Finally, Section 5 concludes.

2. The economy The economy is derived from a small-scale general equilibrium model with flexible prices, populated by a representative household, a continuum of monopolistic competitive firms, and a central bank. Two types of stochastic shocks hit the economy: a labor supply shock and a mark-up shock. The nominal aggregate demand is determined by the central bank, which maximizes the utility of the representative household. Apart from the informational structure, the analysis is based on the model developed by Adam (2007). 3 Empirically, the signaling role of monetary policy has been well documented by Romer and Romer (2000). Using US data, they show that ‘‘the Federal Reserve’s actions signal its information’’ and that ‘‘commercial forecasters raise their expectations of inflation in response to contractionary Federal Reserve actions [y]’’ (p. 430). 4 Angeletos and La’O (2010) also emphasize the welfare effect of information about mark-up shocks within a micro-founded business cycle model. 5 Although the current analysis is based on the methodology developed by Morris and Shin (2002), the detrimental effect of transparency has little to do with the overreaction of firms to a noisy announcement by the central bank. Information about mark-up shocks is indeed detrimental to welfare even if it is perfect. In that respect, the current analysis departs from Walsh (2007), who also accounts for the signaling role of the monetary instrument but highlights the detrimental effect of firms’ reaction to the central bank’s noisy information about mark-up shocks. In his framework, transparency improves welfare when the central bank obtains more accurate information on mark-up shocks.

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2.1. Representative household The representative household chooses its aggregate composite good Y and labor supply L in order to maximize its utility subject to its budget constraint, UðYÞnVðLÞ, s:t:

WL þ P ¼ PY þT:

W denotes the competitive wage, P the profits the household gets from firms, and T the nominal transfer from the central bank. The parameter n is a stochastic labor supply shock with EðnÞ ¼ 1, that induces variations in the efficient level of output. Y is the composite good defined by the Dixit–Stiglitz aggregator "Z #y=ðy1Þ 1

Y¼

0

ðYi Þðy1Þ=y di

,

where y 4 1 is the parameter of price elasticity of demand and where Yi is the good produced by firm i. y is stochastic with EðyÞ ¼ y and induces variations in the desired mark-up of firms and thereby in the equilibrium level of prices and of the R1 output. P is the appropriate price index which solves PY ¼ 0 Pi Yi di. 2.2. Firms Each firm i produces a single differentiated good Yi with one unit of labor Li according to the simple production function Li ¼ Yi : The profit maximization problem of firm i is given by maxE½ð1 þ iÞPi Yi ðPi ÞWY i ðPi ÞjGi , Pi

where i is an output subsidy that offsets the efficiency detrimental effect of the mark-up and Gi is the information set of firm i. Linearizing the first order condition of firm i’s problem around its steady state delivers pi ¼ Ei ½p þ xðyy Þ þu,

ð1Þ

where Ei is the expectation operator conditional on firm i’s information Gi and where small letters indicate percentage deviation from the steady state. The pricing rule (1) states that firms set their price as a function of their expectations of the overall price level p, the real output gap y y*, and the mark-up shock u. The deviation of the efficient level of output y* from its steady state is determined by the stochastic labor supply shifter n. The parameter x ¼ U 00 ðY ÞY =UuðY Þ þ V 00 ðY ÞY =VuðY Þ determines the sensitivity of the optimal price to the output gap and is increasing in the risk aversion of the household. The optimal pricing also depends on the expected value of the mark-up shock u given by u ¼ ðyy Þ=ðy ðy 1ÞÞ, where y is the price elasticity of demand at its steady state level. Firms find it optimal to increase their price when the price elasticity of demand y falls below its steady state value y . Using the fact that the nominal aggregate demand q can be expressed as q= y+p, the pricing rule (1) can be rewritten as pi ¼ Ei ½ð1xÞp þ xqxy þu:

ð2Þ

x determines whether prices are strategic complements or substitutes. Prices are realistically assumed to be strategic complements, i.e., 0 o x r1: each firm tends to rise its own price when it expects other firms to do so. The labor supply shock and the mark-up shock are assumed to be normally and independently distributed with the following properties: y  Nð0, s2y Þ, u  Nð0, s2u Þ:

2.3. Informational structure Monetary frictions arise because of information imperfections. This is reminiscent of insight by Phelps (1970), which states that information imperfections play a crucial role in the monetary transmission mechanism.6 6 The recent revival of interest in Phelps (1970) insight includes the work of Adam (2007), Hellwig (2002), Mankiw and Reis (2002), and Woodford (2003). These authors emphasize the realistic dynamics of models relying on information imperfections when firms’ prices are strategic complements.

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2.3.1. Information of the central bank The central bank receives a signal in private on both the labor supply and the mark-up shock. Each signal deviates from the true value of the shock by an error term, which is normally distributed: ycb ¼ y þ Z

with Z  Nð0, s2Z Þ,

ucb ¼ u þ m

with m  Nð0, s2m Þ,

where Z and m are independently distributed. 2.3.2. Information of firms Two sources of information imperfections with respect to firms are introduced. On the one hand, following Mankiw and Reis (2002), information spreads slowly through the economy. According to this assumption of information stickiness, only a fraction a of firms are informed about the current economic development, while the remaining fraction 1a of firms do not receive any contemporaneous information update at all. As emphasized in Section 3, this first source of frictions allows to solve the problem of price level indeterminacy and to derive the optimal monetary policy. On the other hand, the information received by the fraction a of informed firms is noisy and heterogeneous, which entails fundamental and strategic uncertainty. The information received by the informed atype firms is threefold. First, each informed atype firm i receives a private signal on the mark-up shock ui, which may be interpreted as a private estimate. The private signal of each firm deviates from the true mark-up shock by an error term, which is normally distributed: ui ¼ u þ ri

with ri  Nð0, s2r Þ,

where ri is identically and independently distributed across atype firms. Second, the atype firms eventually observe the monetary instrument implemented by the central bank. The signal released by the central bank on its instrument can be generally expressed as qi ¼ q þ ji

with ji  Nð0, s2j Þ:

Whenever the central bank is transparent with respect to its monetary instrument (s2j ¼ 0), the nominal level of aggregate demand q is common knowledge among the informed atype firms. By contrast, whenever the central bank is opaque in this respect (s2j -1), firms cannot observe the instrument. By making its instrument public, the central bank gives an indication to firms about its own beliefs on the state of the economy. However, firms are unable to properly understand the central bank’s assessment of the economy: because the central bank responds to two shocks, the monetary instrument does not allow firms to decipher the rationale behind the implemented policy unless the central bank discloses more information. Third, whenever the central bank is transparent with respect to its monetary instrument, the atype firms eventually observe an additional public signal that completely eliminates the informational asymmetry between itself and the atype firms. A fully transparent central bank directly discloses its signal on the efficient level of output y*cb so that the atype firms are able to properly interpret the rationale for the monetary instrument.7 The signal released by the central bank on its economic assessment can be generally expressed as ycb,i ¼ ycb þ fi ,

with fi  Nð0, s2f Þ:

The case of transparency with respect to its economic assessment is captured by s2f ¼ 0, and the case of opacity is captured by s2f -1. 2.4. The central bank The central bank seeks to maximize the expected utility of the representative household by adjusting its monetary instrument, the nominal demand q, conditional on its own information. With our informational setup, the second-order approximation of the welfare of the representative household implies that the central bank seeks to minimize the following unconditional expected loss "  # y 1a 2  2 2 2 2 2 2 2 EðLÞ ¼ minE ðyy Þ þ p þ aðg1 sj þ g2 sf þ g3 sr Þ , ð3Þ q

x

a

subject to the pricing equation of firms (2).8 The coefficients g1 , g2 , and g3 are the weights assigned in equilibrium by firms to their signals on, respectively, the monetary instrument, the central bank’s disclosure, and the mark-up shock, as defined 7 One may think of different types of announcement that would reveal the central bank’s signals to firms. In practice, the publication of inflation forecasts and/or targets appears to be the main form of announcement adopted by transparent central banks. 8 For more details, see Appendix A available online, which derives the approximation of the welfare of the representative household according to the informational structure of the economy.

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in Section 4.1. The cost of the price dispersion increases relative to that of the output gap with the price elasticity of demand y (with more competition). Because both fundamental shocks and error terms are independently normally distributed, and because the welfare function is quadratic, the optimal instrument rule of the central bank that determines the nominal aggregate demand q is a linear combination of its signals and can be written as q ¼ z1 ðy þ ZÞ þ z2 ðu þ mÞ:

z1 and z2 describe how the central bank sets the nominal aggregate demand in response to its signal on both shocks. 2.5. Timing of events The sequence of events is as follows. First, the communication strategy of the central bank is determined and is common knowledge among firms.9 Second, the nature draws the labor supply shock y* and the mark-up shock u. The central bank observes both shocks with an error term and sets its monetary instrument q. According to its communication strategy, the central bank may reveal its instrument to the public and may make an explicit announcement y*cb. Based on their private signal on the mark-up shock ui and—when available—on the monetary instrument qi as well as on the announcement of the central bank y*cb,i, firms then simultaneously determine their price. Finally, the household demands products for consumption, and production takes place. 3. Homogeneous information The mechanism of the model is illustrated within benchmark information settings under homogeneous information. First, it is shown that in a frictionless economy, the optimal monetary policy is indeterminate. Second, information stickiness is introduced for resolving the indeterminacy problem and for illustrating the welfare effect of information about mark-up shocks. 3.1. Perfect information The case of perfect information is captured when there is no information stickiness (a ¼ 1) and when the error terms are zero: s2Z ¼ 0, s2m ¼ 0, and s2r ¼ 0. With perfect information, there is no price dispersion across firms because all firms set the same price, and the monetary policy problem becomes

EðLÞ ¼ minE½ðyy Þ2 

ð4Þ

q

s:t:

p ¼ qy þ

1

x

u,

ð5Þ

q ¼ yþ p:

ð6Þ 

Plugging (6) into (5) shows that an output gap (and a loss) appears whenever there is a mark-up shock: yy ¼ u=x. Because there is no friction on the price level (or p does not enter the loss function (4)), the optimal monetary policy is indeterminate: 1 q ¼ y  u þ p:

x

The nominal aggregate demand q can be arbitrarily chosen by the central bank, leading the price level p to take on the corresponding value. The unconditional expected loss is given by

EðLÞ ¼

s2u x2

ð7Þ

and is independent from the policy implemented by the central bank. 3.2. Perfect sticky-information In order to solve the indeterminacy problem of monetary policy that arises in the frictionless economy, sticky information as described in Section 2.3.2 is introduced. In this setup, only a fraction 0 o a o1 of firms are assumed to get an information update; the other 1a firms remain completely uninformed. However, the error terms of the central bank and of the atype firms remain zero: s2Z ¼ 0, s2m ¼ 0, and s2r ¼ 0. With perfect sticky-information the monetary policy problem 9 The choice of the communication strategy occurs before the central bank observes its signals on the shocks. We abstract here from the discussion on whether it is optimal for the central bank to rely on its signals to choose its communication strategy and how firms would accordingly adjust their beliefs.

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of the central bank becomes "

EðLÞ ¼ minE ðyy Þ2 þ q

s:t:

p¼

a 1a þ ax

y 1a 2 p x a

687

# ð8Þ

ðxqxy þ uÞ,

q ¼ y þ p: Solving the problem (8) delivers the optimal monetary policy q ¼ y 

aðy 1Þ 1a þ ayx

u

and yields a price level and an output gap given by p ¼ au=ð1a þ ayxÞ and yy ¼ ay u=ð1a þ ayxÞ, which implies an unconditional expected loss equal to

EðLÞ ¼

ay s2u : xð1a þ ayxÞ

The optimal monetary policy indicates that labor supply shocks are perfectly accommodated by the central bank. The monetary instrument simultaneously closes the output gap and eliminates price deviations induced by labor supply shocks independently of the share a of informed firms. By contrast, mark-up shocks cannot be neutralized by the central bank. Increasing the share a of informed firms strengthens the aggregate reaction to mark-up shocks. As a result, the response of the central bank to mark-up shocks strengthens (@q=@a o0), and the price level and the output gap deviations increase, all of which lead to a larger unconditional expected loss. Therefore, improving information among firms is detrimental to welfare. While information about mark-up shocks is privately desirable according to the optimal pricing rule of firms (2), it is socially undesirable because of the inefficiency wedges it creates.10 The loss associated with mark-up distortions increases with the price elasticity of demand y . Therefore, the central bank responds more aggressively to mark-up shocks when the price elasticity of demand increases (@q=@y o0) and perfectly stabilizes the price level for infinite price elasticity.

4. Heterogeneous information Let us now consider the more realistic case where firms have heterogeneous information. First, the general equilibrium of the economy is established, and then the optimal monetary policy is derived according to three communication strategies of the central bank.

4.1. Equilibrium This section solves the perfect Bayesian equilibrium and derives the optimal behavior of firms according to their information set on the monetary instrument and on the central bank’s assessment of the economy. The information set of atype firms is composed of a private signal on the mark-up shock ui, a signal on the nominal aggregate demand qi, and a signal on the central bank‘s assessment of the labor supply shock y* cb,i. For setting its optimal price according to (2), each atype firm solves the inference problem E½q,y ,ycb ,ujqi ,ycb,i ,ui  that is defined by 0 1  0 1 O11 O12 O13 0 q  0 1 1  q qi i B C B y  C O O O B C 21 22 23  B C B C B  C C EB   qi ,ycb,i ,ui C ¼ X@ ycb,i A ¼ B ð9Þ B O31 O32 O33 C@ ycb,i A, @ ycb  A @ A  u u i i O41 O42 O43 u  with X ¼ Vuo V1 oo , where Vuo is the covariance matrix of the unobserved expected variables and the observed signals and Voo is the covariance matrix of the observed signals themselves. It is important to see from the covariance 10 At the limit, when a converges to 1, the output gap and the unconditional expected loss are identical as under perfect information. However, the price level and the monetary policy are determinate at the limit.

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matrix 0 B B B Vuo ¼ B B @

z21 ðs2y þ s2Z Þ þ z22 ðs2u þ s2m Þ z1 ðs2y þ s2Z Þ z2 s2u z1 s2y

s2y

z1 ðs2y þ s2Z Þ

s2y þ s2Z

2 u

z2 s

0

1

C 0 C C C 0 C A

s2u

that firms rationally use their signals to form their expectations. For instance, the covariance between the mark-up shock and the monetary instrument z2 s2u highlights the signaling role that the monetary instrument plays in the formation of firms’ rational expectations.11 Following Morris and Shin (2002), atype firms set their price according to the following linear pricing rule: pi ¼ g1 qi þ g2 ycb,i þ g3 ui : The equilibrium response of atype firms to their signals is given by the system of simultaneous equations12:

g1 ¼

að1xÞðg2 O31 þ g3 O41 Þ þ xðO11 O21 Þ þ O41 , 1að1xÞO11

g2 ¼

að1xÞðg1 O12 þ g3 O42 Þ þ xðO12 O22 Þ þ O42 , 1að1xÞO32

g3 ¼

að1xÞðg1 O13 þ g2 O33 Þ þ xðO13 O23 Þ þ O43 : 1að1xÞO43

ð10Þ

The central bank chooses its monetary instrument to minimize the expected loss (3) subject to (10) given the precision of its information. In the following sections, we derive the optimal monetary policy for three communication strategies employed by a central bank. First, transparency refers to the case where there is no information asymmetry between the central bank and informed atype firms. Second, opacity describes the case where the central bank does not disclose any information with respect to its monetary instrument and its economic assessment. Third, intermediate transparency depicts the most interesting situation, where the central bank is transparent with respect to its monetary instrument but does not disclose any additional information about its economic assessment. While the current section presents the equilibrium for any degree of information stickiness a, in the remainder of the paper, we concentrate on the limiting case, where the share of informed firms a goes to one. This allows us to solve the indeterminacy problem that occurs in the absence of stickiness while focusing on the heterogeneous nature of information as frictions. 4.2. Optimal monetary policy under transparency Under transparency, the informed atype firms perfectly observe the monetary instrument q and the central bank‘s assessment of the labor supply shock ycb * . Because there are two shocks affecting the economy, the combination of both observations removes the informational asymmetry between the central bank and the atype firms. Transparency is modeled with perfect firms’ signals on the monetary instrument q and on the central bank‘s announcement y*cb, that is, with s2j ¼ s2f ¼ 0.13 Solving the monetary policy problem under transparency and taking the limit when a converges to one delivers the optimal coefficients of monetary policy14:

z1,T ¼

s2y 2 y

s þ s2Z

z2,T ¼ 

,

y 1 s2u : yx s2u þ s2m

11 Since firms know how the central bank responds to mark-up shocks, i.e., z2 is common knowledge, they use their signal on the monetary instrument to infer mark-up shocks as well as their private signal on mark-up shocks to infer the monetary instrument. However, when the monetary instrument is perfectly observable, signals on labor supply and mark-up shocks do not contain any information that is relevant to infer the instrument and O12 ¼ O13 ¼ 0. 12 See Appendix B available online for the derivation. 13 We consider the case of a credible central bank and abstract from the discussion on whether it would be optimal for the central bank to cheat the private sector by disclosing a falsified economic assessment. 14 Appendix C available online presents the optimal monetary policy under transparency for general values of a.

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As z1,T and z2,T indicate, the central bank accommodates variations in the efficient level of output but implements a restrictive policy in response to mark-up shocks. The strength of central bank’s response to mark-up shocks increases with the precision of its information s2m , with the price elasticity of demand y , and with the degree of strategic complementarities 1x. Implementing the optimal monetary policy under transparency yields an unconditional expected loss given by

EðLT Þ ¼ AT þ BT þ CT þDT , where AT ¼

BT ¼

CT ¼

s2u x2

,

s2y s2Z , s2y þ s2Z 2xs2u s2m s2r ðs2u þ s2m Þ

x2 ðs2r ðs2u þ s2m Þ þ xs2u s2m Þ2

s2u s2m s2r ,

and DT ¼

yxs2u s2m 2

x ðs2r ðs2u þ s2m Þ þ xs2u s2m Þ2

s2u s2m s2r :

The unconditional expected loss can be split into the output gap component (AT, BT, and CT) and the price dispersion component (DT). AT stands for the loss under perfect information, as derived in Section 3.1. BT is the incremental loss due to the output gap that arises when the central bank is unable to perfectly accommodate the labor supply shock because of its imperfect information. CT captures the mitigation of the output gap that arises owing to uncertainty surrounding the markup shock. CT increases in absolute value with the inaccuracy of firms’ private information s2r , with the inaccuracy of central bank information s2m , and with the degree of strategic complementarities 1x. When firms’ private information and central 2 bank information is totally noisy, CT perfectly offsets AT, that is, lims2r , s2m -1 CT ¼ s2u =x . The loss associated with the price dispersion DT increases when firms respond more strongly to their private signals because of more inaccurate central bank information s2m or stronger strategic complementarities 1x. The price dispersion also becomes more costly when the economy is more competitive, that is, when the price elasticity of demand y increases. The precision of firms’ private information has, however, an ambiguous effect on price dispersion: @DT =@s2r 4 03s2r o xs2u s2m =ðs2u þ s2m Þ. When firms’ private information is highly precise, reducing the precision of that information increases price dispersion because firms tend to assign a large weight to it. By contrast, when the precision of firms’ private information is sufficiently low, reducing its precision further reduces price dispersion because firms respond less strongly to it. Overall, the uncertainty surrounding the mark-up shock improves welfare ðCT þ DT o 0Þ when the weight assigned to the output gap is relatively large, that is, when the price elasticity of demand y is low. The positive effect of the uncertainty surrounding the mark-up shocks on the output gap CT dominates the negative effect of the uncertainty on the price dispersion DT when y o t, where t ¼ 2 þ ðs2u þ s2m Þs2r =xs2u s2m . Similarly, we have CT + DT =0 when y ¼ t, and CT þ DT 4 0 when y 4 t. 4.3. Optimal monetary policy under opacity Under opacity, the informed atype firms do not observe the monetary instrument q or the central bank‘s assessment of the labor supply shock y*cb. They only get their private signal on the mark-up shock ui. The case of opacity is modeled with infinite noise on firms’ signal on the monetary instrument and on the central bank‘s assessment, i.e., s2j , s2f -1. Solving the monetary policy problem under opacity and taking the limit when a converges to one delivers the optimal coefficients of monetary policy15:

z1,O ¼

s2y 2 y

s þ s2Z

z2,O ¼ 

, ðy 1Þs2r s4u

sm sr þ xs2u Þ2 þ s2r s2u ðxy s2u þ s2r Þ 2ð 2

:

As under transparency, z1,O indicates that the central bank tries to fully accommodate variations in the efficient level of output according to the precision of its signal. The central bank’s response to mark-up shocks z2,O is always restrictive and 15

Appendix D available online presents the optimal monetary policy under opacity for general values of a.

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strengthens with the precision of its information s2m , with the price elasticity of demand y , and with the degree of strategic complementarities 1x. The effect of the precision of firms’ private information s2r is not monotone on the response to 2 mark-up shocks: @jz2,O j=@s2r 403s4r o x s4u s2m =ðs2u þ s2m Þ. As already mentioned, the strength of the central bank’s response to mark-up shocks increases with the weight assigned to the price dispersion (y ). Similarly, the central bank responds more strongly when the price dispersion across firms is relatively high. This arises when the inaccuracy of firms’ private information is intermediate. When firms’ private information is either perfectly accurate (s2r ¼ 0) or perfectly noisy (s2r -1), there is no price dispersion, and the central bank does not respond to mark-up shocks. Implementing the optimal monetary policy under opacity yields an unconditional expected loss given by

EðLO Þ ¼ AO þ BO þ CO þ DO , where AO ¼

BO ¼

CO ¼

s2u x2

,

s2y s2Z , s2y þ s2Z s2u

x2

2

þ

x2 s4m s4u þ2xs2m s2r s2u ðs2m þ y s2u Þ þ ðs2m þ s2u Þðs2m þ y s2u Þs4r ðs2m ðxs2u þ s2r Þ2 þ ðxy s2u þ s2r Þs2u s2r Þ2

s6u ,

and DO ¼

yxðs2r ðs2u þ s2m Þ þ xs2u s2m Þ2 s2u 2

x ðs2m ðxs2u þ s2r Þ2 þðxy s2u þ s2r Þs2u s2r Þ2

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Similarly to the case of transparency, AO stands for the loss under perfect information, and BO stands for the incremental output gap that arises when the central bank is unable to perfectly accommodate the labor supply shock because of its imperfect information. When firms’ private information is totally noisy, CO, the welfare effect on the output gap of 2 uncertainty on mark-up shocks, perfectly offsets AO, that is, lims2r -1 CO ¼ s2u =x . The analysis of the combined effect of the uncertainty surrounding the mark-up shock on the output gap and on the price dispersion under opacity shows that the positive welfare effect of uncertainty on the output gap dominates the negative effect on the price dispersion (CO þDO o0) when y o t. Both the positive and negative effects cancel out (CO + DO =0) when y ¼ t, and the negative effect on price dispersion dominates the positive effect on the output gap ðCO þ DO 4 0Þ when y 4 t. Note that this result is the same as under transparency. 4.4. Unconditional expected loss under transparency vs. opacity The effect of transparency versus opacity on the unconditional expected loss induced by labor supply and mark-up shocks is now analyzed. 4.4.1. Loss induced by labor supply shocks The unconditional expected loss induced by labor supply shocks is independent of the disclosure strategy of the central bank; that is, BT = BO. This result may a priori look surprising in regard to the analysis by Angeletos and Pavan (2007). The latter show that the accuracy of information with respect to labor supply shocks improves welfare while the commonality of information may decrease welfare if it destabilizes the weight assigned to competing signals. One would thus expect the disclosure regime to affect how the economy reacts to labor supply shocks. However, the current framework presents two particularities that rationalize the irrelevance of disclosure. First, the central bank accommodates labor supply shocks with its instrument up to the accuracy of its information. Second, firms do not get any private signal on labor supply shocks. Therefore, the central bank’s announcement neither impairs the stabilizing role of its monetary instrument nor destabilizes firms’ responses. Expecting the central bank to accommodate labor supply shocks, firms indeed choose not to respond to them. 4.4.2. Loss induced by mark-up shocks By contrast, the central bank‘s disclosure strategy matters in the case of losses associated with mark-up shocks because they cannot be neutralized by the central bank. The unconditional expected loss under opacity is always smaller than or equal to the loss under transparency: CO þ DO r CT þDT . In the particular case where y ¼ t, the loss is equal under both disclosure regimes (CT + DT =CO + DO = 0). When y o t, opacity is superior to transparency in terms of welfare because it yields a lower output gap (CO o CT ). By reducing firms’ uncertainty, transparency enhances the reaction of firms to mark-up shocks, which exacerbates the output gap. When y 4 t, opacity is superior to transparency because it yields a lower price dispersion (DO o DT ). It is surprising that transparency leads to a larger price dispersion than opacity when the price elasticity of demand is high. One would

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indeed expect firms to better coordinate with more public information, as suggested in analyses by Hellwig (2005) and Woodford (2005). However, under opacity, the central bank can better exploit firms’ uncertainty to mitigate the price dispersion, as its policy response is stronger in this context than under transparency. Cukierman (2001) highlights that limiting transparency allows the central bank to optimally trade off inflation against employment. The current analysis shows that his result transcends his specific setting and also applies when the output gap is traded off against price dispersion. Fig. 1 illustrates the conduct of monetary policy under both disclosure regimes as a function of the price elasticity of demand y (with x ¼ 0:25, s2y ¼ s2u ¼ s2r ¼ 1, and s2Z ¼ s2m ¼ 0:2). Fig. 1a presents the optimal monetary policy response to mark-up shocks z2 . The strength of the policy response increases with the price elasticity of demand, as the price dispersion becomes more detrimental to welfare. When the output gap is relatively costly (y is small), the response of the central bank under opacity is naturally weaker than under transparency because firms have less information about markup shocks. However, as the price elasticity of demand increases, the central bank further strengthens its policy response under opacity to mitigate the reaction of firms to their private signal and thereby the price dispersion.16 Fig. 1b illustrates that, under transparency, the reaction of firms to their private signal g3 is independent of y . By contrast, under opacity, the strong response that the central bank implements when y is large weakens firms’ reaction to their private signal (g3,O o g3,T if y 4 t). However, the stronger policy response of the central bank under opacity, which aims at mitigating price dispersion (see Fig. 1e), causes a larger output gap than under transparency when y 4 t (see Fig. 1d). Finally, Fig. 1f and c show that the welfare effect of the uncertainty surrounding the mark-up shock C +D and the unconditional expected loss EðLÞ are always superior under opacity than under transparency. 4.5. Optimal monetary policy under intermediate transparency Intermediate transparency refers to the most interesting case, where the monetary instrument is perfectly observed by the atype firms, and the central bank does not make any explicit announcement about its economic assessment. Intermediate transparency is modeled with a perfect signal on the monetary instrument q, but with an infinitely noisy signal for firms on the central bank‘s assessment ycb * , that is, s2j ¼ 0 and s2f -1. By implementing its monetary instrument, the central bank implicitly discloses information to firms about its economic assessment. However, in the absence of an additional announcement, firms cannot unambiguously decipher the rationale behind the implemented instrument. For instance, the central bank may implement an expansionary instrument either because of a positive labor supply shock or because of a negative mark-up shock. The central bank can thus exploit this ambiguity by adjusting its response to labor supply and mark-up shocks in order to control the information that is conveyed by its instrument and to optimally shape firms’ beliefs with respect to mark-up shocks. Fig. 2 illustrates the optimal conduct of monetary policy for the three communication strategies, that is, transparency, opacity, and intermediate transparency, as a function of the price elasticity of demand y (with x ¼ 0:25, s2y ¼ s2u ¼ s2r ¼ 1, and s2Z ¼ s2m ¼ 0:2). Fig. 2a and b depict the optimal monetary policy coefficients of the central bank z1 and z2 in response to labor supply and mark-up shocks. The optimal policy response to labor supply shocks is identical under transparency and opacity regimes and is independent of the degree of price elasticity y , as derived in Sections 4.2 and 4.3. Because firms do not observe the monetary instrument under opacity, and because its interpretation is unambiguous under transparency, the central bank simply accommodates the labor supply shocks given the accuracy of its signal. By contrast, under intermediate transparency, the central bank strongly distorts its response to the labor supply shocks in order to optimally shape firms’ expectations and trade off the output gap against price dispersion. When the price elasticity of demand is low and thus the relative weight assigned to the output gap is high, the central bank finds it optimal to strengthen its response to labor supply shocks in order to enhance firms’ uncertainty with respect to mark-up shocks and to reduce the output gap. On the contrary, when the price elasticity of demand is high, the central bank finds it optimal to weaken its response to labor supply shocks in order to improve firms’ coordination by reducing their uncertainty with respect to mark-up shocks. 4.5.1. Accuracy of firms’ information How does the optimal monetary policy under intermediate transparency shape the accuracy of firms’ information? The accuracy of firms’ information is interpreted as the variance of firms’ expectations on mark-up shocks conditional on their signals normalized by the variance of mark-up shocks: Eðujqi ,ycb,i ,ui Þ2 =s2u 2 ½0,1.17 Fig. 2c illustrates the accuracy of firms’ information on mark-up shocks for the alternative disclosure regimes. Obviously, the accuracy of firms’ information is lower under opacity (dotted line) than under transparency (solid line); it is independent of the monetary instrument in both cases. The accuracy of firms’ information in the case of intermediate transparency (dashed line) is confined between the low accuracy of opacity and the high accuracy of transparency. 16

The policy response under transparency z2,T is equal to the response under opacity z2,O if y ¼ t þ xs2u =s2r . This measure is equal to zero when firms have no information at all about the mark-up shocks, increases with more accurate information, and is equal to 1 when firms’ information is perfect. 17

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Fig. 1. Optimal monetary policy and welfare effects under transparency and opacity. Opacity is always superior to transparency because it yields a smaller output gap when y o t and a lower price dispersion when y 4 t owing to the strong central bank’s response: (a) policy response to mark-up shocks, (b) firms’ response to private signal, (c) unconditional expected loss, (d) output gap induced by uncertainty on mark-up shocks, (e) price dispersion induced by uncertainty on mark-up shocks, and (f) loss induced by uncertainty on mark-up shocks.

However, because the policy response to mark-up shocks is tightened with the increasing price elasticity of demand, the monetary instrument conveys more information on mark-up shocks, and, as a result, the accuracy of firms’ information increases. The monetary instrument thus takes on a dual role: as a policy response that directly influences the economy and as a vehicle for information that shapes firms’ beliefs. Recognizing the signaling role of its policy action, the central bank implements the monetary instrument that optimally balances both effects.

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Fig. 2. Optimal monetary policy and welfare effects under transparency, opacity, and intermediate transparency. When the output gap is relatively costly, the central bank strengthens its response to labor supply shocks under intermediate transparency to reduce the information about mark-up shocks conveyed by its instrument. The opposite holds when the price dispersion is relatively costly: (a) policy response to labor supply shocks, (b) policy response to mark-up shocks, (c) firms’ information on mark-up shocks, (d) loss induced by labor supply shocks, (e) loss induced by uncertainty on mark-up shocks, and (f) unconditional expected loss.

To highlight the effect of the optimal policy response on firms’ beliefs, compare the accuracy of firms’ information under the intermediate transparency disclosure regime when the central bank implements (i) the policy response that is optimal under intermediate transparency (dashed line), (ii) the policy response under opacity (thin dotted line labeled OP), and (iii) the policy response under transparency (thin solid line labeled TP). The optimal monetary policy under intermediate transparency tends to reduce the accuracy of firms’ information when the output gap is relatively costly (y small) and tends to increase it when the price dispersion is relatively costly (y large).

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A stronger response of the central bank to labor supply shocks reduces the amount of information about mark-up shocks that is conveyed by the monetary instrument, while a weaker response increases the amount of this information. 4.5.2. Benefits and costs of shaping firms’ beliefs What are the benefits that the central bank reaps by shaping firms’ beliefs and the costs associated with the distortion of its policy? First, shaping firms’ beliefs helps the central bank to better stabilize mark-up shocks, as Fig. 2e illustrates. When the output gap is relatively costly (y o t), reducing the accuracy of firms’ information increases the welfare effect of the uncertainty surrounding mark-up shocks (C+ D). Conversely, when the price dispersion is relatively costly (y 4 t), improving the accuracy (and commonality) of information allows firms to better coordinate. The welfare gain associated with the stabilization of mark-up shocks that the central bank reaps through shaping firms’ beliefs under the intermediate transparency disclosure regime is captured by the difference between the welfare effect of uncertainty when the central bank implements (i) the optimal monetary policy under intermediate transparency (dashed line) and (ii) the opaque or the transparent policy (labeled OP and TP). Second, the distortion of the policy response to labor supply shocks entails costs in terms of welfare. Fig. 2d illustrates the loss associated with labor supply shocks B. Under transparency and opacity, the loss is solely determined by the accuracy of the central bank’s response, as there is no distortion. Under intermediate transparency, the central bank undermines the stabilization of the labor supply shock, as it distorts its policy response. 4.5.3. Welfare effects of the accuracy of firms’ information The analysis above presents two apparently contradictory welfare effects associated with the accuracy of firms’ information. On the one hand, the comparative welfare analysis under transparency versus opacity shows that providing firms with more information is detrimental to welfare. On the other hand, under intermediate transparency, the central bank finds it optimal to distort its policy response in order to increase the accuracy of firms’ information when the price elasticity of demand is high. Therefore, it is not generally true that more accurate firms’ information about mark-up shocks is always detrimental to welfare. There are two ways in which the central bank can provide firms with more accurate information. The accuracy of firms’ information may increase either because the central bank becomes more transparent (falling noises s2j and s2f ) or because the information that is conveyed by the monetary instrument increases (for a given level of noises s2j and s2f ).18 When the output gap is relatively costly (y o t), providing firms with more information about mark-up shocks is always detrimental because it exacerbates firms’ reaction to them and, as a result, the inefficiency wedges. However, when the price dispersion is relatively costly (y 4 t), providing firms with more information is detrimental only to the extent that it exacerbates the reaction of firms to their private signal. While transparency exacerbates the price dispersion, as discussed in Section 4.4.2, providing firms with more information about mark-up shocks through the strategic use of the monetary instrument enhances firms’ coordination and improves welfare when the price elasticity of demand is high. More generally, providing firms with more information by reducing the idiosyncratic noise of firms’ signals on either the monetary instrument q or the central bank’s disclosure ycb * never improves welfare: @EðLÞ=@s2j r 0 and @EðLÞ=@s2f r 0. The unconditional expected loss under intermediate transparency is therefore always larger than or equal to the loss under opacity but smaller than or equal to the loss under transparency. However, providing firms with more information about mark-up shocks through the signaling role of the monetary instrument improves welfare when coordination is highly valuable. This result shows that the way in which disclosure intertwines with the policy action influences the welfare effect of information. 5. Conclusion In an economy affected by shocks that are imperfectly known, the communication of the central bank intertwines with the design of the optimal monetary policy. As discussed in the extreme cases of transparency and opacity, the optimal monetary policy is a function of firms’ beliefs and is thereby a function of the communication strategy of the central bank. Moreover, the realistic case of intermediate transparency also shows that firms’ beliefs can be shaped by monetary policy whenever the interpretation of the monetary policy is ambiguous. The monetary instrument thus takes on a dual stabilizing role: as a policy response that directly influences the economy and as a vehicle for information that (partially) reveals the central bank’s assessment of the economy to firms. Because mark-up shocks cannot be neutralized by monetary policy, providing firms with more information about these shocks exacerbates their reaction and creates a larger distortion. The central bank faces a trade-off because its monetary instrument, which aims at stabilizing the economy, may detrimentally shape firms’ beliefs. Consequently, the central bank distorts its policy response to labor supply and mark-up shocks to optimally control the information it conveys. 18 From an inference perspective as defined in (9), note that an increase in transparency exclusively affects the covariance matrix Voo while the signaling role of monetary policy also affects the matrix Vuo.

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The analysis also emphasizes that the welfare effect of the information released by the central bank depends on how this information interacts with the optimal monetary instrument. Providing firms with more information about mark-up shocks is always detrimental to the output gap. However, it has a more subtle effect on price dispersion, depending on whether information is provided through the transparency channel or through the signaling channel. Providing firms with more information through the transparency channel is detrimental to price dispersion because it impairs the output gap-price dispersion trade-off that the central bank faces. On the contrary, the information that is conveyed by the distorted monetary instrument improves welfare when firms’ coordination is highly valuable. Public information generally does not necessarily improve firms’ coordination; rather, its effect depends on how it interacts with the policy action.

Acknowledgments The authors thank Marios Angeletos, Laurent Clerc, Alex Cukierman, Richard Dennis, Petra Geraats, Marvin Goodfriend, Charles Goodhart, Frank Heinemann, Christian Hellwig, Gerhard Illing, Hubert Kempf, Andrew Levin, Olivier Loisel, Hyun Shin, Carl Walsh, and John Williams for useful comments at various stages of the project. The authors also thank three anonymous referees and the editor, Robert King, for valuable comments. Remaining errors are the authors’ own. The views expressed in this paper do not necessarily reflect those of the Swiss National Bank. Romain Baeriswyl gratefully acknowledges financial support from the German Research Foundation (DFG) through GRK 801. Camille Cornand thanks the FMG at the LSE for hospitality and gratefully acknowledges financial support from the U.K. ESRC and the ANR-DFG joint program. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2010.06.001.

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