This paper addresses the issue of monetary policy transparency in a context of model uncertainty by adapting the robust control approach. We find that even if the desire of robustness induces an aggressive response of union and central bank, the central bank should reveal its preference about model robustness.central bank transparency

Eleftherios SPYROMITROS

Li QIN

English

Research Papers in Economics

Central bank transparency about model uncertainty and wage
setters 
Eleftherios SPYROMITROS Li QIN
Louis Pasteur University , Strasbourg, BETA Louis Pasteur University , Strasbourg, BETA
Abstract
This paper addresses the issue of monetary policy transparency in a context of model
uncertainty by adapting the robust control approach. We find that even if the desire of
robustness induces an aggressive response of union and central bank, the central bank should
reveal its preference about model robustness.
We would like to thank an anonymous referee and Moïse Sidiropoulos for their helpful comments.
Citation: SPYROMITROS, Eleftherios and Li QIN, (2006) "Central bank transparency about model uncertainty and wage
setters." Economics Bulletin, Vol. 5, No. 18 pp. 1-5
Submitted: October 14, 2006.  Accepted: November 2, 2006.
URL: http://economicsbulletin.vanderbilt.edu/2006/volume5/EB-06E50022A.pdf1 Introduction
Central bank transparency has been one of the major developments in central banking over
the past decade. In the existing studies, policymakers are assumed to know the true model
of the economy and observe accurately all relevant macroeconomic variables. However, the
reality is much more complex. The policymaker’s choice is made in the face of tremendous
uncertainty about the true structure of the economy and the impact of policy actions to
the economy. This complexity means the policymaker may be unsure about his model.
The resulting question is how model uncertainty a￿ects the optimal choice of central bank
transparency.
Recently, monetary policy decision making in presence of uncertainty has received much
attention in the literature (Onatski and Williams, 2003; Giordani and S￿derlind, 2004;
Walsh, 2004). Taking into account possible model misspeci￿cation, the central bank views
its model as an approximation of the model corresponding with the true structure of econ-
omy. In this context, we identify two sources of uncertainty: ￿rst, uncertainty concerning
central bank preferences about model robustness by which we mean a lack of transparency
and second, model uncertainty which comes from ignorance of the true structure of the
economy.
The paper adapts the robust control approach (Hansen and Sargent, 2004) to a model
that studies the interaction between a monopoly union and the central bank. Contrary
to intuition, we show that an increase in preference for model robustness induces more
wage claims and thus a higher in￿ation. Nevertheless, transparency about central bank
preferences concerning model robustness is desirable.
2 The model
We consider a two stages game between a monopoly union and a central bank. First, the
monopoly union ￿xes the log of the nominal wage w and second, the in￿ation rate is ￿xed
by the central bank.
The central bank cares about in￿ation and employment but also views its model as
an approximation. We apply robust control techniques developed by Hansen and Sargent
(2004) and we model uncertainty about the process that governs the unemployment rate
as follows:
u = aW + h (1)
where W = w − π is the log real wage. Without loss of generality, we assume that
a = 1. In the spirit of Hansen and Sargent (2004), h represent model misspeci￿cation
errors introducing ambiguity to the model. More precisely, it can be considered as a
deterministic disturbance controlled by a ￿ctitious ￿evil agent￿ who aims to maximize the
policymaker’s loss. The parameter η is assumed to be the budget allocated from the central
bank to the evil agent in order to create misspeci￿cation. Thus, the budget constraint for
the evil agent is h2 ≤ η2.
The latter restriction together with Eq.(1) de￿ne a set of models which the central bank
considers as being possible outcomes.
1The policy maker sets the in￿ation rate to maximize the value of its utility function,
while the evil agent sets its controls to minimize the central bank’s utility, given the con-
straints on misspeci￿cation. To introduce this ambiguity into the decision making problem,
we replace the standard quadratic utility function of the central bank by an uncertainty
averse quadratic utility function :
max
π
min
h
Vcb = −λπ
2 − u
2 + θh
2 (2)
subject to the model with misspeci￿cations in Eq.(1). λ > 0 is a parameter which
measures the weight policymakers assigned to in￿ation stabilization with respect to out-
put stabilization and θ ∈ (1,∞]1 is a parameter which re￿ects the degree of the model
robustness or a penalty parameter restraining the minimization of misspeci￿cations errors
h. Thus, the design of a robust control policy becomes a min-max problem subject to the
linear constraint (1) where the central bank acts as a Stackelberg leader against the evil
agent.
Concerning the labor market of the economy, we suppose that all the workers are
organized in a single union which chooses their nominal wage w to minimize the following
loss function
V = W −
B
2
u
2; B > 0 (3)
The parameter B denotes the union’s relative concern for unemployment.
2.1 Equilibrium
The reaction function of the central bank can be derived from the resolution of the min-max
problem of the central bank as:
π =
θ
1 + (1 + λ)(θ − 1)
w (4)
h =
λ
1 + (1 + λ)(θ − 1)
w (5)
At stage one, we analyze wage setting in the economy by minimizing union’s loss func-
tion subject to the reaction function of central bank as follows:
V =
"
w −
θ
1 + (1 + λ)(θ − 1)
w

−
B
2

w −
θ
1 + (1 + λ)(θ − 1)
w + ht
2#
(6)
Hence, the solution of the problem is :
w =
(θ − 1)[θ + λ(θ − 1)]
λBθ2 (7)
From equation (7), we get the following proposition:
1The second order condition of Eq.(2) with respect to h shows that the evil agent’s problem is well
de￿ned and concave i￿ θ > 1 . Thus, θ = 1 is a lower bound for θ or a breakdown point. (see Hansen and
Sargent, 2004)
2Proposition 1 An increase in the degree of model robustness θ raises wages and the in-
￿ation rate.
Proof. Taking ￿rst order condition of equation (7) with respect to θ it is straightfor-
ward to ￿nd that
∂w
∂θ
=
θ + 2λ(θ − 1)
λBθ3 > 0 (8)
∂π
∂θ
=
1
λBθ2 > 0 (9)
The intuition behind this result is that in a less uncertain economic environment (a more
robust monetary policy) trade unions will be more aggressive about their wage claims.
An increase in the degree of model robustness diminishes the perception of the union
concerning the impact of a wage increase on in￿ation and unemployment, leading thus to
an increase in wage claims. In response to the increasing wage claims, the central bank
raises the in￿ation rate.
2.2 Uncertainty about the degree of robustness
We suppose that the trade union is not perfectly informed about θ , the degree of model
robustness, when it ￿xes w. Equation (10) speci￿es the stochastic behavior of the parameter
θ
θ = ¯ θ + µ,with Eµ = 0 and Eµ
2 = σ
2
µ (10)
This implies that the union is correct on average, but may be mistaken when making
guesses about the central bank preferences for robustness in individual cases or at certain
points in time. σ2
µ measures the degree of opacity of the central banker. We assume that a
more transparent decision process reduces σ2
µ. Taking into account uncertainty about the
central bank’s preference for robustness, the union maximizes the following function:
EV = E
"
w −
θ
1 + (1 + λ)(θ − 1)
w

−
B
2

w −
θ
1 + (1 + λ)(θ − 1)
w + ht
2#
(11)
and the solution of this problem is:
w =
(1 + λ)
 ¯ θ2 + σ2
µ − 2¯ θ + 1

+
 ¯ θ − 1

λB
 ¯ θ2 + σ2
µ
 (12)
An immediate consequence of the above equation is the following proposition:
Proposition 2 Uncertainty about the central bank’s preference for robustness θ raises
wages, average in￿ation and unemployment.
3Proof. It is easy to verify from the following equation that wages increase with σ2
µ.
∂w
∂σ2
µ
=
¯ θ + λ
 
2¯ θ − 1

λB
 ¯ θ2 + σ2
µ
2 > 0 (13)
Similarly, an increase in σ2
µ causes higher average in￿ation and unemployment
∂π
∂σ2
µ
=
θ
1 + (1 + λ)(θ − 1)
¯ θ + λ
 
2¯ θ − 1

λB
 ¯ θ2 + σ2
µ
2 > 0
∂u
∂σ2
µ
=
θ
1 + (1 + λ)(θ − 1)
¯ θ + λ
 
2¯ θ − 1

B
 ¯ θ2 + σ2
µ
2 > 0
The intuition behind this result is that the trade union does not know the exact value
of the degree of robustness and its perception about this value increases in this uncertain
economic environment leading to an increase in wages, average in￿ation and unemploy-
ment. More precisely, higher opacity about the degree of robustness may be followed by
an aggressive response from the trade union which anticipates an increase in the value of
θ.
Next we analyze, in the sense of Gruner (2002), the impact of more uncertainty about
the degree of robustness θ on in￿ation uncertainty σ2
π. The latter is de￿ned as σ2
π =
E

(π − ¯ π)
2
.
Using a second order Taylor approximation yields
σ
2
π =
1
λ2B2
σ2
µ
¯ θ2  
4¯ θ − 5

− σ2
µ

¯ θ6 with ¯ θ
2  
4¯ θ − 5

> σ
2
µ (14)
Taking the ￿rst order condition of (14) with respect to σ2
µ, we get
∂σ2
π
∂σ2
µ
=
¯ θ2  
4¯ θ − 5

− 2σ2
µ
λ2B2¯ θ6 (15)
This derivative is positive i￿
¯ θ2  
4¯ θ − 5

2
> σ
2
µ (16)
Hence we have:
Proposition 3 In￿ation uncertainty increases with uncertainty about central bank’s pref-
erence for robustness θ when the latter is low. It increases when uncertainty about θ is
high.
Proof. see above.
43 Discussion
Gr￿ner (2002) argued that limited central bank transparency was favorable. Our analysis,
in this context of economic uncertainty, shows that the central bank should reveal its
preference about the degree of model robustness. In spite of the fact that a preference for
higher model robustness leads to higher wage claims, an increase in the central banker’s
transparency about the preference of model robustness reduces in￿ation and nominal wage
claims. As a consequence, unemployment is diminished when monetary policy is more
transparent.
References
[1] Onatski, A. and Williams, N., 2003. Modeling model uncertainty. Journal of the Eu-
ropean Economic Association, 1 (5), 1087-1122.
[2] Walsh, E., C., 2004. Robust optimal instrument rules and robust control: An equiva-
lence result. Manuscript, University of California, Santa Cruz.
[3] Giordani, P. and Soderlind, P., 2004. Solution of macromodels with Hansen-Sargent
robust policies: some extensions. Journal of Economic Dynamics and Control, Elsevier,
vol. 28(12), 2367-2397.
[4] Gruner, H., P., 2002. How much should central bank talk? A new argument. Economics
Letters 77, 195-198.
[5] Hansen, L., P. and Sargent J., T., 2004. Robust control and economic model uncer-
tainty. Princeton University Press.
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Central bank transparency about model uncertainty and wage setters

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