Convenciones específicas para la ejecución del formato.

This section compares the Bayesian update and the equilibrium action in both cases of exogeneous and endogeneous information. Figure 2.5 il- lustrates the weight assigned to the central bank’s disclosure both in the first-order expectation of the demand shock g and in the equilibrium pric- ing rule as a function of the degree of transparencyσ2

withξ= 0.1andσ2

η =σε2 = 0.25.6

For the case of exogeneous information, the dash-dotted and dotted lines represent the weight assigned toDiin the Bayesian update (Ω12in equation

(2.6)) and in the equilibrium price rule (γ2 in equation (2.9)), respectively.

We see that both weights increase with the degree of transparency: higher transparency increases the degree of common knowledge of central bank’s disclosure and its focal role for price setting. The weight in the pricing rule is also larger than that in the Bayesian update (γ2|σ2

φ >Ω12|σ2φ,∀σ 2 φ).

For the case of endogeneous information, the solid line represents Ω12

in the first-order expectation (2.14) and the dashed line γ2 in the optimal

pricing equation (2.15). As in the case of exogeneous information, firms overreact to the central bank’s disclosure in the sense that the weight as- signed to it in the pricing rule (γ2) is larger than that in the Bayesian up-

date (Ω12). But with endogeneous information, the effect of central bank’s

transparency (σ2

φ) on firms’ estimation is ambiguous: while a reduction in

the degree of transparency (that is to say an increase of the idiosyncratic noise) reduces the accuracy of the disclosure, it increases the precision of the average disclosureD as firms respond less strongly to it. Ω12 does not

monotonously increase in the degree of transparency. When σ2

φ falls, the

degree of common knowledge of the central bank’s disclosureDi increases

and the weight assigned to it in the pricing rule (γ2) rises. The impact of a

fall inσ2

φon the precision of the disclosureDi (and consequently onΩ12) is

twofold. On the one hand, the precision of disclosure increases because the idiosyncratic noise is reduced. On the other hand, as firms respond more strongly to the disclosure, the precision of both central bank’s information and disclosure decreases. The combination of both mechanisms gives rise to the ambiguous effect of transparency onΩ12that is particular to the model

with endogeneous information.

The next section addresses the effect of transparency on the accuracy of prices and central bank’s information as indicators of the state of the econ- omy.

6_{We use the methodology of Ulrich Doraszelski to solve this nonlinear model. We are}

grateful to him for making his codes available. See Doraszelski and Markovich (2005) for example.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 σ_φ2 γ₂: exogneous γ2: endogneous Ω12: exogneous Ω₁₂: endogneous

Figure 2.5: Bayesian update and equilibrium action

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 σ_φ2 Var[E(g|p)−g] or Var[E(g|I)−g]

ξ=0.1: info value of prices

ξ=0.25: info value of prices

ξ=0.5: info value of prices

ξ=0.1: info value of cb’s observation

ξ=0.25: info value of cb’s observation

ξ=0.5: info value of cb’s observation

Figure 2.6: Informative value of prices and central bank’s observation

2.4.4

Information value of prices and precision of central

bank’s information

Figure 2.6 illustrates the accuracy of prices and central bank’s informa- tion as indicators of economic conditions. The computation is done with

σ2

η = σε2 = 0.25. The information value is evaluated as the variance of the

error of demand shock estimations conditional either on the price levelpor on central bank’s informationD.

The information value of the price levelpis given by Var[E(g|p)−g] =VarhE³g|g+ γ2 1−γ2 η´−gi= γ 2 2 γ2 1 σ2η = γ2 2 (1−γ2)2 ση2,

while the information value of the central bank’s observationDis given by Var[E(g|D)−g] =VarhE³g|g+ 1 1−γ2 η´−gi= 1 γ2 1 σ2η = 1 (1−γ2)2 ση2.

The figure 2.6 shows that the information about the state of the economy contained in the price level and in central bank’s observation decreases with the degree of central bank’s transparency. In the limit of opacity, γ2 con-

verges to zero (firms don’t react to the disclosure) and the price level be- comes a perfect indicator for the demand shockg. The accuracy of central bank’s observation also increases with opacity. But as the central bank ob- serves the price level with an error termη, it is always less accurate than the price level itself.

The accuracy of the price level as an indicator for economic conditions decreases with the weight assigned to central bank’s disclosure. This weight is high either when the idiosyncratic noise of the disclosure is low (high degree of transparency or common knowledge) or when strategic comple- mentarities are strong (ξ small). The degree of strategic complementarities affects the information value of prices because it drives the overreaction to central bank’s disclosure. When complementarities are high (dotted lines), the central bank’s disclosure is given a large weight in the pricing rule. This increases the impact of the noiseηon the price level.

This clearly highlights the endogeneous nature of central bank’s infor- mation. The more effectively the central bank influences the pricing be- haviour of firms (γ2 large), the less accurate is its estimation of demand

shocks.