FORMA DE DISCUSIÓN DE RESULTADOS

This section analyzes the welfare effect of public information when the central bank does not influence the economy except with its information disclosure. The aim of this section is to illustrate the much debated result by M-S where information disclosure is the only task of the central bank. Since the central bank does not implement any action, we set I = 0 and rewrite the pricing rule (3.2) as

pi =Ei[(1−ξ)p+ξg]. (3.4)

One may worry about the fact that the central bank does not offset de- mand shocks in the present economy and claim that this is not optimal. However, the aim of this chapter is not to address the merits of having a central bank stabilizing the economy but to compare the welfare effect of disclosure in the case where the central bank does not stabilize the econ- omy to the case where it does. So, the present section must be seen as a benchmark case that replicates the results by M-S and allows a better suited comparison.

We describe the information structure in the next section. Then, we dis- cuss the optimal information disclosure first when the central bank chooses between full transparency and opacity (i.e. the central bank either perfectly reveals its opinion or totally withholds it), and second when the central bank can choose its optimal degree of transparency (i.e. the central bank speaks with some ambiguity).

3.3.1

Information structure

Each firm sets its price according to its information about the demand shock g and the expectations of other firms about it (the so-called higher- order expectations). The demand shock is drawn from a uniform distribu- tion over the real line: g ∈ R. Each firm receives a private signal about the

demand shock. The private signal is centred on the true value ofg and has a normally distributed error term:

gi =g+εi withεi ∼N(0, σε2).

Firms additionally get a signal disclosed by the central bank. The central bank itself receives a signal on the demand shock that is centred on its true value and has a normally distributed error term:

D=g+η withη∼N(0, σ2η).

The central bank provides firms with its assessment of the demand shock. As discussed in the introduction, there are different ways for the central bank to communicate. Indeed, the central bank may be fully transparent by disclosing a public signal Dcommon knowledge among firms. Or the central bank may also be opaque and withhold its information. This is the case where the central bank provides each firm with an individual signal whose idiosyncratic noise is infinite. One can imagine any intermediate situation where the central bank provides firms with more or less equivocal information. For the sake of generality, we write the signal disclosed by the central bank and received by firmias

Di =g+η+φi withφi ∼N(0, σφ2).

The individual noise φi captures the degree of transparency of a central

bank. Under transparency, every firm gets the same univocal signal (when

σ2

φ = 0), while under opacity, the individual signal got by each firm is so

noisy that its interpretation is impossible (σ2

φ → ∞).

3.3.2

Equilibrium

The economy described above is similar to that of chapter 2 section 2.3. We refer to this section for the resolution of the equilibrium behaviour of firms and recall the main results for convenience.

tral bank’s disclosure and is given by p = γ1g+γ2D with γ1 = ξσ2 η +σφ2 σ2 ε +ξσ2η+σφ2 γ2 = σ2 ε σ2 ε +ξσ2η+σφ2 .

The corresponding unconditional expected social loss can be written as E(L) =γ₁2σε2+γ22σφ2+λγ22ση2. (3.5)

We present the optimal disclosure strategy in the subsequent sections. Since the optimal disclosure has been derived in the previous chapter, we simply recall the main results.

3.3.3

Transparencyversus

opacity

As discussed in section 2.3.4, transparency is welfare improving when the loss under opacityLOis larger than the loss under transparencyLT. The

welfare analysis of transparency yields the following proposition:

Proposition 1: When the central bank’s unique task is information disclo-

sure, full transparency is preferable to opacity when

λ−2ξ < σ 2 ε σ2 η . (3.6)

It turns out that transparency is welfare detrimental whenever public in- formation is too noisy relative to private information (σ2

ηlarge), when strate-

gic complementarities are rather strong (ξ small), and when the weight as- signed to output gap stabilization (λ) is large.

3.3.4

Optimal degree of transparency

Again, we report the optimal degree of transparency analyzed in sec- tion 2.3.5. Deriving the optimal degree of transparency in the framework

described above, we get the following proposition:

Proposition 2: When the central bank’s unique task is information disclo-

sure, the optimal degree of transparency is given by

σ2∗

φ = max[0,(2λ−3ξ)σ2η −σε2]. (3.7)

.

This analysis calls for partial transparency when central bank’s informa- tion is rather noisy (σ2

η large), when the degree of strategic complementari-

ties is high (ξsmall), and when the weight assigned to output gap stabiliza- tion (λ) is large.