Truthfulness of Central Bank Announcemen

Truthfulness of Central Bank Announcements

Julian A. Parra

University of Cambridge Central Bank of Colombia (PhD Dissertation - Paper 2)

September 2009

Abstract

To evaluate the impact of central bank transparency, previous literature has assumed that the policymaker commits to truthful communication. However, by manipulating in‡ation expectations economic volatility might be reduced. This paper analyses the truthfulness with which a central bank communicates in‡ation targets or forecasts. It shows that, for a standard model, there is no rational expectations equilibrium with in‡ation announcements when the policymaker has incentives to misrepresent private information. This problem is solved by announcing late in the period, when in‡ation expectations are already formed but there is not yet information about future shocks. In this case, there are no incentives to mislead the public and in‡ation announcements are still informative about the central bank’s intentions for future periods. Therefore, an equilibrium does exist and truth-telling is optimal for the central bank and welfare-improving for society. Based on the implications of the model, empirical data is examined and no evidence is found against the truthfulness of annual in‡ation targets.

JEL Classi…cation: E52, E58, D82 Keywords: central bank announcements, monetary policy, transparency

jap58@cam.ac.uk, jparrapo@banrep.gov.co. I am especially grateful to my research supervisor, Dr. Petra M. Geraats, for her advice and to the Central Bank of Colombia for its …nancial support. I am also grateful to J. Roberto Parra-Segura and Paul Baker for their helpful comments and to participants in macroeconomics workshops at the University of Cambridge. Any views expressed and errors are entirely mine.

1 Introduction

The increasing amount of information released to the public by central banks brings attention to the in‡uence of policy announcements on the formation of in‡ation expectations. To evaluate the economic impact of monetary policy transparency, it has been common practice to assume that the central bank commits to making truthful in‡ation announcements. The present paper, instead, analyses the scenario in which the policymaker strategically communicates information about in‡ation targets or forecasts so as to maximise society’s welfare. By manipulating in‡ation expectations the central bank might potentially o¤set the e¤ects of aggregate shocks on in‡ation, and therefore truth-telling may not be the best strategy. This paper shows that, for a standard setup, there is no rational expectations equilibrium with in‡ation announcements when the policymaker intends to misrepresent private information. This problem can be overcome by announcing late, when in‡ation expectations of the period of announcement are already formed but there is not yet information about future shocks. In this case, there are no incentives to mislead the public and in‡ation announcements reveal useful information about the central bank’s intentions for future periods. As a result, an equilibrium exists and truth-telling improves social welfare and is also the optimal strategy for the central bank.

Over the last two decades, as central banks have become more independent, transparency and communication with the public have gained relevance in the conduct of monetary policy. Whereas secrecy was conventional 20 years ago, today it is the norm that the public be informed of the central bank’s decisions. This trend in monetary policy has been recently documented in multiple papers (e.g. Dincer and Eichengreen, 2007; Geraats, 2009). Moreover, signi…cant amount of theoretical and empirical research has been conducted to determine if transparency is bene…cial from an economic point of view. 1

As concluded by Geraats (2006), theoretical arguments bring about three main results of the e¤ects of central bank transparency on the public perception of monetary policy. First, transparency improves the predictability of monetary policy because it reduces uncertainty about the state of the economy and the central bank’s intentions. Second, transparency induces reputation building because it increases the sensitivity of in‡ation expectations to unanticipated policy actions. Third, by allowing the public to check the consistency of policy actions and outcomes with formal policy objectives, transparency enhances credibility and reduces long-run in‡ation expectations volatility. Based on these results, most of the recent economic literature highlights the economic desirability of transparency (e.g. Geraats, 2005; Svensson, 2006; Demertzis and Hughes Hallett, 2007).

1 See Eij¢nger and Van der Cruijsen (2007) for a survey of literature on central bank transparency.

Another part of earlier literature has also pointed out that transparency may be undesirable because its bene…ts come at the cost of ‡exibility, and hence the central bank’s ability to stabilise the economy is reduced (e.g. Jensen 2002). Cukierman (2001), for instance, explores the impact of transparency in two di¤erent models, one with the conventional expectations-augmented Phillips curve and the other with a monetary transmission mechanism of a Neo-Keynesian type. The result obtained, for both models, is that transparency is detrimental to society’s welfare because disclosing information about upcoming aggregate shocks increases variability of short-run in‡ation expectations and, consequently, in‡ation and output volatility.

In assessing the impact of monetary policy transparency it is common practice to assume that the monetary authority commits to truthful announcements. With the purpose of …nding out whether transparency is bene…cial or not, society’s welfare is compared for opacity versus limited or full transparency. Under opacity the central bank does not disclose any private information. In contrast, under transparency, the

central bank’s private information is partially or fully revealed. 2 If transparency yields a higher level of welfare, we can conclude that society prefers it over secrecy. Nevertheless, it does not imply that the central bank’s commitment to truthful communication is credible. The policymaker may still have incentives to misrepresent private information because in that way economic volatility can be reduced. When faced with in‡ationary shocks, for instance, the central bank might try to deceive agents into believing that the intended in‡ation target is lower than it actually is, such that the e¤ect of shocks on in‡ation is o¤set by the e¤ect of in‡ation expectations.

The question arises whether the central bank is able to improve society’s welfare by manipulating in‡ation expectations. The present paper shows that, for a multiple- period model with a stochastic expectations augmented Phillips curve, there is no equilibrium under rational expectations when the central bank communicates in‡a- tion targets or forecasts with the purpose of reducing economic volatility by misleading in‡ation expectations. The intuition behind this result is as follows. Private agents use the announcement to extract information about the central bank’s intentions. Since the policymaker knows that the in‡ation announcement in‡uences in‡ation expectations, she …nds it optimal to misrepresent private information so as to o¤set the e¤ect of anticipated shocks on in‡ation. As rational agents foresee this situation, they incorporate the announcement into their information set but take into account the intention of the central bank to misrepresent. The policymaker anticipates this reaction and increases the degree of misrepresentation. But again, private agents also anticipate this and adjust their in‡ation expectations accordingly... and so on. As section 3 shows, this process does not converge to a rational expectations equilibrium with in‡ation announcements.

Canzoneri (1985) was the …rst to call attention to the lack of credibility of mone- 2 Examples of partial transparency can be found in Jensen (2002) and Walsh (2007). The former

sets up a model in which the control error of monetary policy may be partially revealed. The latter assumes that the central bank announces in a manner such that just a fraction of …rms receives the information. Misrepresentation of private information is not considered in any of these papers.

tary policy announcements when the central bank has private information, speci…cally, the policymaker’s forecast of the money demand shock. Therefore, private agents are unable to know with certainty whether an expansionary policy is a result of a perceived increase in money demand or an attempt to stimulate output above potential. As a result, monetary policy announcements cannot be trusted because the central bank has incentives to lie in order to achieve better outcomes.

A similar conclusion is reached by Stein (1989) in a cheap-talk game in which the central bank’s exchange rate target is not known to the public and, in contrast to Can- zoneri’s (1985) paper, the monetary policy announcements are made before expectations are formed. Stein points out that the central bank is unable to credibly communicate its intentions by making precise announcements despite the fact that it would be better o¤ by announcing its true target compared to making no announcements. Stein (1989) and Gar…nkel and Oh (1995) show a way to overcome this problem. The central bank can partially reveal its private information when it announces the range in which such information lies, rather than announcing a speci…c value. The ranges from which the central bank picks the one to announce have to be large enough to discourage lying. If the central bank wants to lie it has to claim that its private information is in a di¤erent range and therefore the policymaker would have to signi…cantly increase the degree of her misrepresentation. Imprecise announcements may make truth-telling preferable over such signi…cant misrepresentations.

A common feature in the three above-mentioned papers is that the credibility problem of central bank announcements arises from the fact that one of the monetary authority’s goals is inconsistent with the steady-state level and therefore, there is time inconsistency as described originally by Kydland and Prescott (1977) and Barro and Gordon (1983). In the present paper, in contrast, the central bank does not pursue any time-inconsistent policy and, despite this fact, it is still unable to credibly communicate its intentions. The source of the problem, as mentioned above, is the fact that the central bank intends to o¤set volatility that stems from economic shocks by manipulating in‡ation expectations. In this way, the paper points out the existence of di¢culties with regard to credibility of in‡ation announcements even when there is no in‡ation bias in central bank preferences. Furthermore, imprecise in‡ation announcements would be an impractical solution to this problem since the optimal sizes of ranges would have to vary every period according to the central bank’s forecasts of economic shocks which might not be known to the public.

In more recent literature, the possibility that the central bank strategically sets the level of the in‡ation announcement is proposed by Walsh (1998, p.363) and it is later incorporated into several papers. 3 A common feature of these papers is to assume that, as Walsh originally does, the policymaker is exogenously penalised for the deviation of actual in‡ation from the announcement and that the central bank’s loss function includes an additional term which is increasing in the square of this deviation.

3 See, for instance, Walsh (1999), Mahadeva and Sterne (2002) and the …rst paper of the present dissertation.

Penalisation could, for instance, take the form of public embarrassment or, in a more formal way, a request for the resignation of the central bank governor. In these cases, the monetary policy game converges to an equilibrium because when the degree of misrepresentation is large, the central bank faces a severe punishment as well. In contrast, no exogenous penalisations are assumed in the present paper and all of the incentives that make transparency desirable or undesirable arise endogenously from the model.

This paper suggests that the central bank can …nd a way to communicate its intentions. The policymaker may announce in‡ation targets in a previous period to the one for which the target applies, when there is no yet information to predict future shocks and when it is late to incorporate new information into private sector in‡ation

expectations that a¤ect in‡ation of the period of announcement. 4 Without accurate information about upcoming shocks, there is not much opportunity to o¤set their e¤ect on economic volatility and hence only the incentives to truthfully communicate the central bank’s intentions remain. By disclosing information about its actual future target, the central bank improves future coordination between monetary policy and in‡ation expectations.

The analysis applies to di¤erent types of central bank announcements. The paper particularly focuses on short-run in‡ation targets and output and in‡ation forecasts. However, in the case of forecasts it would be very restrictive to assume that they are always released before the policymaker can be well informed about upcoming shocks since, in practice, new updated forecasts can be published as the time to observe the actual outcome approaches. In this case, an alternative solution is explored. The central bank may announce output and in‡ation forecasts at a late stage in the same period for which they apply. In this way forecasts can be accurate, because they incorporate information about anticipated shocks, but released when it is late to be incorporated into in‡ation expectations of the same period. Nevertheless, they are still useful because they are informative about the intentions of the policymaker for future periods.

Based on the implications of the model and in order to provide a …rst step for future empirical research, the paper examines the data on annual in‡ation target setting and …nds no evidence against the hypothesis that central banks announce truthfully rather than strategically.

The remainder of the paper is organised as follows. Section 2 presents the model. Equilibrium is discussed in Section 3. Section 4 examines the empirical data. Section

5 concludes. Certain technical details are left to the appendix.

4 In countries with low and stable in‡ation, the in‡ation target is constant and therefore known well in advance. In in‡ation-targeting countries that are currently disin‡ating and change their in‡ation

targets every year (Colombia, Indonesia, Philippines, Romania and Turkey) the target for a reference year is known, on average, 5 quarters before the reference year starts. It does not imply, however, that under some special circumstances e.g. a global in‡ationary shock, the target cannot be revised later.

2 The Model

The model is a game between the central bank and the public. The former minimises in‡ation and output volatility and the latter intends to forecast in‡ation as accurately as possible. Every period, the central bank makes an announcement t and, later in the same period, picks the monetary instrument m t so as to minimise the expected value of the loss function

(1) where y t is the deviation of output with respect to its natural level, t is in‡ation, t

t =y t +( t

is the implicit in‡ation target, > 0 is the relative weight on output stabilisation and the subscript t denotes the time period. Uncertainty about central bank preferences is modelled as uncertainty about the implicit target as in Tarkka and Mayes (1999) and Geraats (2005). Both papers analyse the impact on macroeconomic performance when the policymaker commits to truthfully revealing in‡ation and/or output forecasts, and hence there is economic transparency, as de…ned by Geraats (2002).

The implicit target changes over time as follows

(2) where 0 is the long-run in‡ation target, which is exogenously given,

t1 + (1

2 (0; 1) and

t is independently distributed with E [ t ] = 0 and V ar [ t ]= . t is drawn at the beginning of the period and is only known to the central bank. For simplicity it is

assumed that t is uncorrelated with other disturbances in the model. Equation (2) captures the empirical evidence that, as shown by paper 2 of this dissertation and Mahadeva and Sterne (2002), in countries with moderate to high in‡ation, there is persistence in short-run in‡ation targets. 5

In order to simplify the assessment of social welfare it is assumed that the central bank’s loss function is equal to society’s loss. It should be noted that this assumption implies that changes in the implicit target will be a result of changes in the perceived optimal rate of in‡ation rather than a result of political pressure on the central bank by particular groups. As can be seen, (1) implies no in‡ation bias in the central bank’s intentions.

Aggregate supply is described by an expectations-augmented Phillips equation:

(3) where e

e t = t +y t +s t

t represents in‡ation expectations and s t is an aggregate supply shock. Aggre- gate demand is equal to the monetary instrument m t plus an aggregate demand shock

y t =m t +d t

5 In the theoretical model of the …rst paper, the optimal short-run target was found to follow t = 0 + 1 t1 + (1

1 ) 0 and realised in‡ation t = 2 + 3 t1 + (1 3 ) 0 + t where j , j 2 f0; 1; 2; 3g are constant parameters and is a control error. Using these two equations, their respective one-period-lagged versions and assuming there is no in‡ation bias ( 0 = 2 = 0), it can be

shown that t can be expressed as in (2) with = 3 .

The variable m t can be regarded as related to the negative of the interest rate or, alternatively, to the growth rate of the money supply. Aggregate shocks " t 2 fs t ;d t g

are separated into three di¤erent components, " p t which is anticipated by both the central bank and the public, " b t which is anticipated only by the central bank, and " u t

b which is unanticipated by both the central bank and the public, where " u t =" t +" t +" t : Each component is independently distributed with zero mean and V ar " k

= " k , for k

2 fp; b; ug. This separation allows for the analysis of di¤erent situations as particular cases of the model. For instance, when the central bank has perfect information " u t = 0, 8t and 2

" u = 0; and when both the central bank and the public are equally informed " b t = 0, 8t and 2 " b = 0. For ease of exposition, we collect the part of aggregated shocks

that is anticipated by the central bank into a single term, such that " cb t p =" t +" b t and

" cb = 2 " p + 2 " b . The timing for every period t is as follows:

(0) At the beginning of the period, t is drawn. It is only known to the central bank. (1) The central bank makes an in‡ation announcement t for period t. (2) Private agents form in‡ation expectations e

(3) The central bank sets the monetary instrument m t . (4) Shocks s t ,d t and in‡ation t are realised.

3 Equilibrium

The model is solved by backward induction. In the third stage, the central bank sets the monetary instrument so as to minimise its expected loss function (1) subject to (3) and (4) and taking private sector in‡ation expectations as given. The solution to this problem implies

Substituting (4) and (5) into (3) yields

Using (6) and rational expectations implies

(7) where I p

t =E[ t jI t ]+s t

t denotes the information set of private agents when they form in‡ation expectations, I p

;" t ;E" t ; " k ; tl ;y tl ;m tl for " 2 fs; dg, k 2 fp; b; ug and l 2 f1; 2; :::; t 1g.

0 ;E

t ];

3.1 Symmetric information

As a benchmark, the model is …rst solved for the case in which private information held by the central bank is truthfully revealed to the public and hence I p

t includes t , s b t and d b t . From equations (4)-(7) we can obtain the following expressions for in‡ation

expectations, realised in‡ation and the output gap, respectively:

(10) Substituting expressions (9) and (10) into (1) and taking the unconditional expected

cb y u

t = s t +d t

value we …nd that for any period t, the expected loss function for the symmetric information (SI) case is

(11) Society’s loss is increasing in the economic volatility associated with the variance of the

E SI

= (1 + ) d u + s cb + s u

unanticipated demand shock and the variance of all of the components of the aggregate supply shock.

3.2 Asymmetric information

This section analyses the model described by equations in section 2, allowing for the possibility that the central bank may be better informed than the private sector about the implicit in‡ation target and about demand and supply shocks. Three scenarios are considered. The …rst one corresponds to the model with no in‡ation announcements. By comparing this case to the one with symmetric information, we determine a su¢- cient condition under which transparency is preferred over secrecy. The second scenario incorporates in‡ation announcements into the model and shows that there is no rational expectations equilibrium with in‡ation announcements when the central bank has incentives to misrepresent private information. The third scenario provides a solution to this problem. It analyses the case in which the central bank communicates information about in‡ation targets and forecasts when in‡ation expectations of the period of announcement are already formed but there is not yet information about shocks of future periods. In this case an equilibrium exists and in‡ation announcements are still informative about the central bank’s intentions for future periods.

3.2.1 No in‡ation announcements Let us begin with the case in which there are no announcements (N A) in a two-period

setup. In the second period, since private agents do not know 2 , they have to estimate its value from their information set I p

2 that includes the in‡ation outcome 1 , the monetary instrument m 1 and the output gap y 1 . This implies, using equations (4)-(7),

2 = b 2j2 +s 2 (12)

2 = 2 +s 2 +

b 2j2

2 +s 2 +s 2 +d 2 (13)

2 b 2j2

2 +s 2 +d 2 (14)

E ( 2 jI 2 ). For simplicity of notation we will henceforth denote by br T jt the expected value of any variable r T conditional on the information set available to

where p b

2j2

the public in period t, (i.e. p br

E (r T jI t )). Notice that even if private agents could perfectly estimate the implicit target ( b 2j2 = 2 ), equations (12)-(14) would not be equal to (8)-(10) because there would still be asymmetric information about s b

T jt

t . Using equation (2) for periods one and two, it can be seen that

2 = 0 + 1 + 2 (15) Taking the expected value conditional on I p

2 gives

(16) To estimate 6

b 2j2 = 0 + b 1j2

1 , the public constructs three signal variables using 1 ,y 1 , and m 1 . Substituting expressions (13)-(16) into (1) and taking the unconditional expected value produces

1 ). Comparing (11) and (17), it can be seen that with asymmetric information uncertainty about the

where 1 is the mean square error of b 1j2 , (i.e. 1 E b 1j2

2 implicit target ( 2 +

1 ) increases the expected loss but the e¤ect of the supply shock s b 2 on economic volatility is mitigated. The …nal result, on the expected loss, of these

two contrary e¤ects is formally analysed below in Proposition 1. In period one the central bank takes into account that its policy instrument m 1 a¤ects the estimator of the implicit target in period two. Therefore, the central bank picks m 1 with two purposes; …rst, to reduce the volatility that stems from shocks in the same period, and second, to reduce uncertainty about its intentions in period two. In the third stage of period one, the problem for the central bank is minimising

E 1 jI cb 1(3) + [(1 + ) ( 2 d u + 2 s p )+ 2 s u ]

h io (18) +

2 (0; 1) is the discount factor and I cb 1(3) represents the information set of the central bank in period one at the moment of deciding upon the

with respect to m 1 , where

The public is not able to perfectly infer p 1 from I 2 because the problem implies a system of three equations, one from each variable 1 ,y 1 and m 1 in …ve unknowns s b 1 ,s u 1 ,d b 1 ,d u 1 and 1 . Appendix A analyses the solution for period one and shows the three equations of the system, (49)-(51).

monetary instrument, i.e. in the third stage. Solving this problem implies cumbersome and non-illuminating algebra. For the purpose of this paper it is su¢cient to know that, as shown in Appendix A, the solution implies

1 = 0 +s 1 +c 1 d 1 +c 2 s 1 +c 31 +s 1 +d 1 (19)

d b b 1 u = 1 +c 1 1 (1 c 2 )s 1 +c 31 +d 1 (20) where c 1 ,c 2 and c 3 are constant parameters. Comparing equations (13)-(14) to (19)-

(20), it can be seen that unlike period two, in‡ation and the output gap in period one are a¤ected by the anticipated demand shock d b (Appendix A proves that c

1 > 0). As explained by Geraats (2000), a central bank that operates under opaqueness, restrains its stabilisation e¤orts to make the monetary instrument a better signal of its intentions. In the second and last period, there is no concern about improving the public’s knowledge of the central bank’s intentions for the future, and therefore there are no restrictions in setting monetary policy so as to fully respond to anticipated demand shocks. In period one, as mentioned above, there exist two di¤erent and not entirely

compatible purposes for choosing m 1 , and therefore ‡exibility of monetary policy is reduced. In period one, it is optimal to allow d b 1 to have some e¤ect on the economy in order to pass on to the public some information about this shock and, in that way, to

reduce 1 i.e. the mean square error of the estimator b 1j2 .

From the same equations, (13)-(14) and (19)-(20), we can also state that with no announcements (N A), asymmetric information about the implicit target a¤ects neither expected in‡ation nor the expected output gap, E NA t =E SI t = 0 and Ey NA

=Ey t = 0 for t 2 f1; 2g. However, as can be inferred from Proposition 1 below, uncertainty about the implicit target a¤ects volatility in the economy and may either increase or reduce social welfare with respect to the symmetric information case.

SI t

Proposition 1 When there is asymmetric information about the implicit target t and the supply shock s b

t , (i) If volatility that stems from uncertainty about the implicit target shock ( 2 ) is

large enough relative to volatility caused by the e¤ect on in‡ation expectations of revealing the supply shock s b , society’s welfare with symmetric information is higher than that with no announcements. Therefore, full transparency is socially

bene…cial. Formally, E SI

>E t for t 2 f1; 2g, if

(21) (ii) For the limiting case in which the implicit target shock t does not vary over time

( 2 = 0), it is better for the policymaker to be opaque i.e. E NA t 2 =0 E SI t for t 2 f1; 2g.

Proof. First notice that since E SI t does not depend on decisions from previous periods then (11) applies to any period t. Also recall that 2 = s 2 cb s p + 2 s b . Part (i): Assume that (21) holds. By comparing (11) and (17), E NA 2 >E SI 2 . To compare the expected loss in period one, let m 1 be the solution to the minimisation of (18) when the central bank does not care about the future (i.e.

= 0). For this particular case,

1 (m 1 ) = (1 + ) d u + s p + s u +

s b + (22)

By de…nition E NA 1 (m 1 )

E NA 1 . Comparing (22) to (11), we can see that

E NA (m )>E SI (if and only if (21) holds). Therefore, E NA >E SI 1 1 1 1 1 . Part (ii): Note that since private agents know E [ ], by making 2 t = 0 we are eliminating uncertainty about t , and therefore information from the past is no longer useful to private agents. Solving the one-period model is enough to obtain the solution for any period. The expected loss is

2 =0 = (1 + ) d u + s p + s u +

s b (23)

The statement in the proposition follows from comparing (23) to (11). Part (i) of Proposition 1 points out that if the informational advantage of the central

bank about the supply shock is small relative to uncertainty about the central bank’s intentions (and hence 2 s 2 b is small relative to ), it is better for the policymaker to

be transparent because the cost of disclosing her private information about the supply shock would be smaller than the bene…t from communicating the implicit in‡ation target. Since condition (21) is su¢cient but not necessary, we cannot directly state that if it is not satis…ed then secrecy outperforms transparency. However, as remarked by part (ii), when the variance of the implicit target shock t approaches zero, the central bank prefers secrecy over full transparency.

So far, to analyse the impact of in‡ation announcements on society’s welfare we have assumed that the central bank either commits to truthfully reveal all of its private information or discloses nothing. However, using the results above we can show that partial transparency is preferred to both secrecy and full transparency. It is not di¢cult

to see that if, rather than making 2 = 0, we assume that t varies over time but is known to the public, the expected loss does not change and hence it is equal to the right-hand side of (23). Therefore, from part (ii) of Proposition 1 we can state that it is a better strategy for the policymaker to commit to reveal only the implicit target rather than all of its private information because the latter includes information about the supply shock which increases in‡ation expectations volatility. This is in the spirit of Geraats (2007) who concludes that the optimal communication strategy for the central bank is to be clear about the in‡ation target but ambiguous about supply shocks. In order to see that revealing only the implicit target is preferred over secrecy we can

verify that E NA t 2 =0 E NA t for t 2 f1; 2g by comparing (23) to (17) and (22).

The next section explores the strategic aspect of central bank in‡ation announcements. By manipulating in‡ation expectations, the central bank might reduce economic volatility, and therefore it has incentives to misrepresent private information.

3.2.2 Announcements As mentioned in section 1, Stein (1989) remarks that the central bank is unable to

communicate its private information by making precise announcements. He points out that if the central bank’s announcement were believed by the public, the policymaker would misrepresent private information, and therefore the announcement would turn out to be noncredible.

Using the model described in section 2 this section analyses, as Stein does, the credibility problem of announcements when the central bank has incentives to misrepresent private information and, unlike Stein, extends the analysis to formally incorporate the possibility that the public tries to extract some information from the in‡ation announcement, even if the central banks acts strategically. If private agents know that the central bank has incentives to lie, they will not take the announcement at face value, but they can still try to use it to enhance their information set. The result obtained, as shown below, is that there is no rational expectations equilibrium for the model with in‡ation announcements. Since the central bank knows the private sector’s reaction, the policymaker adjusts the announcement accordingly so as to be able to still deceive private agents; but they also foresee this new adjustment and the central bank again anticipates their new reaction and so on... ad in…nitum and without convergence to an equilibrium with in‡ation announcements.

In order to distinguish between the case in which there are announcements from that in which there are not, the next de…nition indicates when a public statement provides useful information to forecast in‡ation, and hence can be regarded as an in‡ation announcement.

A public statement made by the central bank in period t is an in‡ation announcement t only if it is correlated with any piece of information that is not known to private agents but is relevant to forecast in‡ation in the same period or in future periods.

De…nition 1.

If, for instance, the policymaker announced s p t , it would be equivalent to the case with no announcements as s p t is already known by private agents, and hence publishing its

value does not provide any additional information in forecasting in‡ation. Given De…nition 1, we look for an answer to the question whether there is a rational expectations equilibrium in the model with announcements. The present section shows that there is no equilibrium in a one-period setup. Appendix B shows that if this equilibrium existed in a multi-period setup, it would be equal to that for the one- period model. The intuition is that in this equilibrium, the central bank’s expected loss value does not provide any additional information in forecasting in‡ation. Given De…nition 1, we look for an answer to the question whether there is a rational expectations equilibrium in the model with announcements. The present section shows that there is no equilibrium in a one-period setup. Appendix B shows that if this equilibrium existed in a multi-period setup, it would be equal to that for the one- period model. The intuition is that in this equilibrium, the central bank’s expected loss

form in‡ation expectations e . Using (6) and rational expectations implies that t e t =

E p [ t jI t ]+Es t jI t . The in‡ation announcement t is incorporated into I t so we need to distinguish the private agents’ estimator before and after knowing t . Let br t(0)

cb p

be the estimator of any variable r t conditional on the information set available to the public in period t, before knowing t

i.e. before the …rst stage. Taking into account the private sector’s information set and for analytical convenience, we can express e t in the following form:

(24) In the …rst stage, the central bank minimises (1) with respect to t , which a¤ects the

t(0) +E t b t(0) j t + s t +Es t j t

loss function through its e¤ect on in‡ation expectations. Substituting (3)-(5) into (1) and taking the expected value conditional on the information set of the central bank yields

E cb 2 u

t jI t(1) = (1 + ) d + s u +

t +s t (25)

2 e cb 2

where I cb t(1) represents the information set of the central bank in the …rst stage.

We do not yet know the explicit functional form of (24). Assuming that t b t(0) and s b t are normally distributed, it is shown below that E t b t(0) j t and E s b t j t

are linear functions in p t , b t(0) and s t . Therefore, we can consistently assume that minimising (25) implies a solution for t that is linear in t ,s b t p ,s t and b t(0) and that, accordingly, e

t takes the form

(26) where a i for i 2 f0; ; s;

t =a 0 +a t +a s s t +a b t(0)

g are constants to be determined. Using (26), minimising (25) implies

a 0 (1 + a s )s t s b t + (1 a ) b t(0) t =

b t(0)

for a 6= 0. Equation (27) shows that t is correlated with both the forecast error t

b b t(0) and s t which are unobserved variables to the public, and hence following De…nition

1 we can state that t is an in‡ation announcement. Substituting (27) into (26) implies

e t = t s cb t and then substituting this result into (6) yields t = t +s u t +d u t . The announcement t intends to in‡uence in‡ation expectations in such a way that

7 This is unlike the expected loss for the case with no announcements in which, as shown in section 3.2.1, the decision about the monetary instrument in period one (m 1 ) a¤ects the expected loss of

period two.

their e¤ect on in‡ation o¤sets the e¤ect of the anticipated supply shock s cb t . Therefore, realised in‡ation deviates from the implicit target only as a result of unanticipated shocks.

In order to determine parameters in equation (26) we proceed as follows. Since private agents know that the central bank announces t following (27), they can construct

a signal x ( t ), x p (

0 +a t + (1 + a s )s t (1 a ) b t(0) = t b t(0) s t (28) The right-hand side of the equality represents a noisy signal of t b t(0) and s b t because

private agents are not able to perfectly separate one variable from the other. The left- hand side provides the way in which this signal can be constructed by using variables that are known to the public. Finding E b

b t(0) j t and E s t j t represents a signal extraction problem as described by Harvey and De Rossi (2006, p. 970). Notice that since the forecast error t b t(0) only depends on t and past information, it is

uncorrelated with s b t . From a standard lemma on the multivariate normal distribution (Harvey, 1989, p. 165), the estimators are

E t b t(0) j t =x( t )

1+ 2 sb 2 (0; 1) can be interpreted as a signal-to-noise ratio and =M SE [ b t (0) ] M SE b t(0) is the mean square error of the estimator b t(0) . The higher (lower) the variance 2

s b relative to the M SE b t(0) , the noisier (better) the signal x ( t ) for estimating b

b t(0) but the better (noisier) for estimating s t . Substituting (28)-(30) into (24) and comparing the result to (26) we obtain the following system of equations:

The only equilibrium to this system requires that a = 0, which implies that, from (27), t is unde…ned. 8 Making a = 0, means that agents do not include t as a relevant variable to forecast in‡ation. Taking into account De…nition 1, this only occurs when there is no in‡ation announcement, and therefore it does not exist a rational expectations equilibrium with in‡ation announcements in this monetary policy game.

This problem does not arise under commitment to truthful communications. When the central bank commits to publish its actual in‡ation target or in‡ation forecast every period at stage one, private agents directly incorporate the announcement into their

8 Note that since

2 (0; 1) and > 0,

information set with no need to anticipate any strategic behaviour on the policymaker’s part. In the case of the in‡ation target, private agents simply assume that the central

bank is truthfully revealing the implicit target, and therefore they set b t(2) = t . Simi- larly, in the case of an in‡ation forecast, private agents trust the in‡ation announcement and set e

t = t . How can the public verify that the central bank is indeed ful…lling this commitment? It is di¢cult to do so because the in‡ation outcome and changes in

the monetary instrument depend on central bank preferences and forecasts of shocks that cannot be directly observed. To show its willingness to stick to the commitment, the central bank has to release, in addition to the in‡ation target or forecast, enough information to allow agents to determine that the in‡ation announcement is not af- fected by any intention to manipulate expectations. For instance, some central banks (e.g. Colombia, Hungary, UK) include in their in‡ation reports some in‡ation forecasts calculated by other (national or international) independent organisations.

3.2.3 Late in‡ation announcements To solve the inability of the central bank to communicate its intentions, the policymaker

can make in‡ation announcements ‘late’ in the period, when in‡ation expectations of the same period are already formed but there is not yet information about future shocks. With no information about upcoming shocks, it is not possible to know with certainty the direction that in‡ation expectations of future periods should take to reduce future economic volatility. In this case, misleading expectations would only increase expected volatility, and hence there are no incentives to misrepresent private information. De- spite being announced at a late stage of the period, in‡ation announcements are still useful because they are informative about the central bank’s future intentions, and therefore they enhance communication with the public and improves the predictability of monetary policy.

In practice in‡ation targets are known, in general, before the reference period for which they apply. 9 We then assume that an in‡ation target t , for period t, is announced at a late stage in period t

1. This assumption is important to obtain the condition derived in the empirical section for late in‡ation announcements (no correlation between

t and t ). However, the results presented in this section would not change if, instead, we assume that the in‡ation target is announced late in the same period for which it applies.

As commented in section 1, in the case of forecasts it would be restrictive to assume that they are always released before information about upcoming shocks is available since, in practice, updated forecasts can be published as the time to observe the actual outcome approaches. In order to allow for the possibility that in‡ation announcements may incorporate anticipated information about aggregate shocks, we assume that a forecast t for period t, is announced at a late stage in the same period.

9 As commented in footnote 4, in countries with low in‡ation the in‡ation target is constant and known well in advance. In countries with moderate to high in‡ation, which change their in‡ation

targets every year, the annual target is known, on average, 5 quarters before the reference year starts.

The game is analysed in a two-period setup. In terms of the timing for every single period, we are switching places between the …rst and the second stage. The timing now is described as follows (cf. section 2) 10

(0) At the beginning of the period, t is drawn. It is only known to the central bank. (1) Private agents form in‡ation expectations e

(2) The central bank announces t+1jt , an in‡ation target for period t + 1 or t , an in‡ation forecast for period t.

(3) The central bank sets the monetary instrument m t . (4) Shocks s t ,d t and in‡ation t are realised.

Let us …rst focus on the case in which the central bank announces in‡ation targets. Notice that the timing above implies that the public’s information set in period t does not include the in‡ation announcement made in the same period, t+1jt , but includes the one made in the previous period, tjt 1 . To keep this fact in mind, we will write

I p t; t jt 1 when referring to the public’s information set in t. In the second period, the monetary instrument is set following (5). Because it is the last period, there is no in‡ation target announcement at the second stage. In‡ation

expectations are based on I p

2 ; 2j1 . Using (6) and rational expectations, we can express

2 =E 2 jI 2 ; 2j1 +s 2 (31) At the moment of announcing 2j1 , the central bank is not able to anticipate shocks of

period two. Therefore, as con…rmed below, private agents can consistently assume that there is truthful communication and that it is possible to obtain the best estimation of

2 from 2j1 . Then private agents follow

(32) Substituting (4)-(6), (31) and (32) into (1) and taking the expected value conditional

E 2 jI 2 ; 2j1 = 2j1

on the information available to the central bank we obtain

E cb 2 2 u p

2 jI 2(0) = (1 + ) d + s u +

cb 2

2j1 +s 2 2 +s 2 (33)

where I cb 2(0) represents the information set of the central bank at the beginning of period two. In the third stage of period one the central bank minimises

cb E cb

1 +E 2 jI 2(0) jI 1(3)

10 Alternatively, the stage for the in‡ation announcement could be the third one and the result would be the same.

with respect to m cb

1 . Since, from (33), E 2 jI 2(0) does not depend on m 1 , the policy reaction takes the same form again (equation (5)). In the second stage, expectations

are already formed, and therefore cannot be a¤ected by the in‡ation announcement 2j1 . As a result, 1 does not depend on 2j1 either. Consequently, just 2 is relevant for the decision in the second stage. In this stage, the central bank minimises

E cb 2 2 2 jI 1(2) = (1 + ) d u + s p

with respect to 2j1 . The solution to this problem implies

) 0 (34) The in‡ation target announced 2j1 , turns out to be the best possible estimation of the

2j1 =

implicit target for period two, which is the right-hand side of (34) since the central bank cannot anticipate 2 in period one. It should be noted that although (34) corresponds to truthful communication because the central bank is publishing its actual estimation of the implicit target for the next period, it is not equivalent to full transparency because no private information is disclosed at the beginning of the period despite the fact that it is available to the central bank and relevant to forecast in‡ation in the same period.

In periods one and two, in‡ation expectations, realised in‡ation and the output gap follow

Notice that equations (35)-(36) are similar to those for the case with no announcements (N A), (12)-(14). They would be equal if in the N A case there were perfect information about the implicit target of period t

1, so that the implicit target forecast error of period t would be t

b tjt = t . As in the N A case, with late announcements (LA) neither expected in‡ation nor the expected output gap are a¤ected by in‡ation announcements. For any period t 2 f1; 2g, E LA t = 0 and E y LA t = 0. However, more interesting results are obtained when comparing the LA case to the other cases

(SI and N A) in terms of economic volatility, and hence in terms of social welfare. The expected loss function for t 2 f1; 2g is

= (1 + ) d u + s p + s u +

s b + (38)

Let us start by assuming again that the central bank can …nd a mechanism to credibly commit to full transparency. The question arises whether the policymaker prefers revealing all of its private information at the beginning of the period as compared to making late announcements. Proposition 2 gives us the condition under which the former is preferred over the latter.

Proposition 2 When there is asymmetric information about the implicit target t and

1, an in‡ation target for period t,

the supply shock s b t and the central bank announces, late in period t

(i) If, and only if, volatility that stems from uncertainty about the implicit target shock ( 2 ) is large enough relative to volatility caused by the e¤ect on in‡ation

expectations of revealing s b t , society’s welfare with symmetric information is higher than that with late announcements, and therefore full transparency is socially preferred to late announcements. Formally, E LA t >E SI t for t 2 f1; 2g, if and only if (21) holds.

(ii) Society is better o¤ with late announcements than with no announcements, i.e.

E LA t

E NA t for t 2 f1; 2g.

Proof. Part (i): By comparing (11) to (38).

Part (ii): By comparing (17) to (38), E LA

2 E NA 2 . With regard to period one, as in the proof for Proposition 1, let m 1 be the solution to the minimisation of

(18) when LA = 0. By comparing (22) to (38), E

1 (m 1 )=E 1 . By de…nition

E NA (m )

E NA . Therefore E LA

E 1 NA 1 1 1 1 .

Although late in‡ation announcements communicate the implicit target of period t

1 and, in that way, the estimation of the target in period t is enhanced, the latter cannot yet be perfectly forecasted because there is still uncertainty about t . From part (i) of Proposition 2 we can state that if the policymaker is able to credibly commit to full transparency and if volatility that stems from uncertainty about t is signi…cant relative to volatility caused by disclosing private information about the supply shock

s b t , the central bank prefers full transparency over late in‡ation announcements. If, instead, volatility that stems from revealing s b

t is large enough, the central bank prefers late in‡ation announcements. Nonetheless, partial transparency remains a better strategy. If the policymaker can credibly commit to reveal only the implicit target at the

beginning of each period, society is better o¤ than with late in‡ation announcements, as can be seen by comparing (23) to (38). 11

On the other hand, if the central bank cannot …nd a mechanism to credibly commit to reveal private information at the beginning of the period, then we are more interested in comparing the case with late in‡ation announcements to the one with no in‡ation announcements. Part (ii) of Proposition 2 shows that society prefers the former to the latter. The intuition behind this result is as follows. Without in‡ation announcements

there is only one policy instrument (m 1 ) for the two purposes mentioned in section 3.2.1, namely, (I) reducing volatility that stems from economic shocks in the …rst period and (II) reducing volatility that stems from uncertainty about the central bank’s intentions

11 Recall that (23) applies as well to the case in which we assume that varies over time but is known to the public.

in the second period and, accordingly, giving a good signal of 2 . Since these two purposes are not entirely compatible, giving the public the best possible estimation of

2 would have to be done at the cost of not responding optimally to shocks in period one. In contrast, with late announcements the central bank has one additional instrument,

the in‡ation announcement 2j1 , to reveal the best estimation of the implicit target 2 without compromising its ability to respond to shocks in the …rst period.

Appendix C shows that it is straightforward to extend the model to the in…nite horizon. Results are the same, namely, the in‡ation announcement is the best possible estimation of the implicit target of the next period; in‡ation expectations, realised in‡ation and the output gap follow (35)-(36); and the expected loss function for any period t is equal to (38).

Now consider the case in which the central bank announces, at a late stage of period one, an in‡ation forecast for the same period. In this case some additional issues arise. If the actual in‡ation forecast is the only announcement, it is not possible

Truthfulness of Central Bank Announcemen