Supply Shocks, Private Sector Information and Monetary Policy:
Is There Inevitably a Stabilization Trade-Off ?
Jonathan G. James
University of Wales Swansea
and
Phillip Lawler†
University of Wales Swansea
Abstract
We assume that, while the central bank has an information advantage in respect of aggregate
productivity shocks, the private sector has superior knowledge of local disturbances. It is shown
that there is no policy trade-off between inflation and employment stability: moreover
macroeconomic outcomes are independent of the weight assigned to inflation by the central bank.
Keywords: Supply shocks; Private expectations; Stabilization trade-off
Classification: E58
† Corresponding Author. Department of Economics, University of Wales Swansea, Singleton
Park, Swansea SA2
p.lawler@swan.ac.uk
8PP,
United
Kingdom.
Fax:
+44-1792-295-872.
E-mail:
1. Introduction
In much of the literature relating to optimal monetary policy design, supply shocks play a
crucial role. Given the standard assumption that the central bank can observe the realized value of
such shocks, and is able to react to them in terms of its policy setting, a trade-off between
inflation and employment stabilization is faced. The policy choice made in the light of any given
shock, and the resulting macroeconomic equilibrium, will then be determined by the central
bank’s preferences, in particular the weight which it attaches to employment, relative to inflation,
stability. The policy trade-off inherent in such shocks, and the consequent dependence of
macroeconomic outcomes on central bank objectives, underlies the ‘higher level’ trade-off
between credibility and flexibility which Rogoff’s (1985) seminal analysis of optimal monetary
policy delegation highlights. It is also central to most of the subsequent developments of Rogoff’s
theme: see, for example, Lohmann (1992); Walsh (1995); Svensson (1997); Beetsma and Jensen
(1998); Muscatelli (1998); Lawler (2000); and Faust and Svensson (2001). The present paper reexamines the informational assumptions which underlie this literature: in so doing, it identifies
circumstances under which there is no policy trade-off. Instead, an appropriately formulated
monetary policy is able to achieve perfect stabilization of both inflation and employment.
A key aspect of the conventional approach to modeling supply shocks is the informational
asymmetry assumed to be present. While, as noted, the central bank is taken to observe the
realization of such shocks prior to implementing policy, in contrast the private sector is typically
assumed to have no information concerning their value before making its own decisions, such as
the appropriate setting of the nominal wage. Although widely employed, this characterization of
the information structure is not immune to criticism. Given that supply shocks are invariably
represented as random disturbances to production technology, it might be contended that agents
within individual firms are likely to have an informational advantage over the central bank with
respect to their own production/cost functions, an argument which is recognized in papers by
Tarkka and Mayes (1999) and Jensen (2000). A possible response to this objection to the standard
approach is to point out, as Jensen himself does, that while individual firms may have superior
information in respect of their own production technology, the central bank is likely to be better
informed with regard to supply conditions at the aggregate level. Certainly, such an assertion is
consistent with Romer and Romer’s (2000) finding that, for the U.S., the Federal Reserve’s
forecasts are more accurate than those of the private sector. Nonetheless, acceptance of this
argument does not, in itself, imply that the conventional treatment of supply shocks, with its
associated informational assumptions, adequately represents a situation in which, while the
1
central bank may have superior information in respect of the aggregate value of such shocks,
agents within individual firms have better knowledge of production/cost conditions at the local
level.
This issue is considered in the following analysis using a model in which economy-wide
aggregate supply shocks are the aggregation of those arising within individual firms, the latter
comprising both an element which is common to all firms and a firm-specific component. While
agents within any individual firm can directly observe the disturbance to which it is subject, they
can form only an imperfect estimate of its aggregate counterpart: the central bank, on the other
hand, has full knowledge of the latter. Incorporating these informational assumptions within a
framework characterized by contractual wage setting, we demonstrate that they have very
different implications from those which follow from the standard approach. As already noted, we
find there is no policy trade-off in respect of inflation and employment outcomes, with the central
bank able to stabilize both variables perfectly: moreover, this conclusion is independent of the
relative weights attached to its two policy targets by the central bank.
2. The model
The principal relationships of the framework are set out below, with all variables other than the
inflation rate expressed as logarithms, and where unimportant constants have been suppressed:
yi   li  i ,
i     i
(1)
lid  (1   )1 (wi  p  i )
(2)
lis  0
(3)
y d   (m  p)
(4)
  l 2   2 ,
1
l   li di
0
(5)
There is a continuum of perfectly competitive firms, uniformly distributed over the unit interval,
each producing a single homogeneous good. For representative firm i the relationship between
output, yis , and labor input, li , is described by Eq.(1), where  i represents a random productivity
disturbance comprising two independently distributed components. The first,  ~ N (0, 2 ) , is
common to all firms and thus corresponds to an aggregate shock; the second,  i ~ N (0, 2 ) , is a
2
firm-specific element with the property
1
  di  0 . The profit-maximizing demand for labor by
0
i
firm i is then identified by Eq. (2), where wi represents firm i's nominal wage and p is the price of
output. Labor is assumed to be immobile between firms, with the desired supply of labor to firm i,
lis , perfectly inelastic and normalized for convenience at zero, as described by Eq.(3). Aggregate
demand for output, y d , is represented by Eq.(4) as a function of the real money stock, i.e. the
nominal money supply deflated by the price level. Monetary policy is delegated to a central bank
whose objective function is described by Eq.(5), with the deviation of aggregate employment, l,
from the level associated with labor-market clearing and of inflation,  , from zero as its
arguments. The central bank’s inflation and employment objectives reflect those of society;
however, the parameter  , representing the relative weight attached to inflation stabilization by
the central bank, is potentially different from that in the social loss function. It is assumed that the
specific form of the central bank’s objective function is public knowledge.1
Reflecting the discretionary policy environment assumed, the central bank implements
monetary policy after the wage determination process is complete and with knowledge of the
aggregate outcome of wage setting within individual firms. As is standard in the literature
analyzing the issue of optimal monetary policy delegation, the central bank is assumed to observe
the actual realization of the aggregate productivity shock before choosing its setting of m. At the
level of the individual firm, the nominal wage is set with the objective of achieving the marketclearing employment level2, i.e. li  0 ; the chosen value of wi is then embodied in a single-period
contract, with employment demand-determined within the period. Crucially, wi is determined
after  i has been observed; however, agents within firm i are unable to distinguish between the
aggregate and firm-specific components of the disturbance. With the appropriate setting of the
nominal wage dependent on the composition of  i , prior to making their choice of wi wage
setters must form an estimate of  based on their observation of  i . Given the properties of 
and  i , the best estimate of  , conditional on the observed value of  i is :
1
Hence the analysis abstracts from the issues arising from uncertainty with regard to central bank
preferences: see, for example, the aforementioned papers by Beetsma and Jensen (1998) and Muscatelli
(1998). For an overview in the context of the wider issue of central bank transparency, see Geraats (2002).
2
Because the desired employment level within each firm is consistent with the central bank’s objective for
aggregate employment, there is no inflation bias in the model. This feature is discussed further in the
concluding section.
3
E ( | i )   i ,
where    2 ( 2   2 )
(6)
The sequence of events described above can be summarized by the following time line:
productivity
shocks realized
nominal wages set
 i observed by agents
within firm i:
expectations formed
employment and price
level determined
the central bank observes
 , w: monetary
policy implemented
The informational structure assumed is consistent with the view that, while the informationgathering and forecasting resources available to central banks will generally mean that they have
an informational advantage in respect of wider macroeconomic conditions (see the
aforementioned paper by Romer and Romer, 2000, for a statement of this position), individual
firms are likely to be better informed with regard to shocks to their own production technology.
Moreover, we emphasize that our principal conclusions do not depend on the assumption that
agents within firm i have perfect information concerning  i before wages are set, but are
consistent with observational errors at the local level providing such errors net out in the
aggregate.
To conclude this section, we note that the dichotomy drawn in our own framework between
information concerning purely local variables and that relating to aggregate outcomes is
reminiscent of that present in Lucas’s (1973) model. While Lucas assumes individual suppliers to
make inferences of the general price level on the basis of observations of their own product price,
our approach takes agents within each firm to use information concerning the productivity
disturbance to which their own firm is subject to estimate the corresponding aggregate shock (and
consequent price level).3
3. Macroeconomic Equilibrium
As a first step in solving for the equilibrium of the model, we use the aggregate counterparts of
Eqs. (1) and (2), noting
1
  di   , together with the aggregate demand relationship, Eq.(4), to
0
i
Important differences between Lucas’s analysis and our own derive from Lucas’s focus on demand
shocks and, additionally, our interest in stabilization policy.
3
4
determine the price level as a function of the nominal money stock, the average nominal wage,
1
w   wi di , and  :
0
p  [   (1   )]1[ (1   )m   w  ]
(7)
Using this expression in combination with the aggregate version of Eq.(2) identifies the
corresponding expression for aggregate employment, l :
l  [   (1   )]1[ (m  w)  (1   ) ]
(8)
The central bank’s optimal policy response to aggregate productivity shocks is now found by
substituting Eqs. (7) and (8) into Eq.(5)4 and minimizing the resulting expression over m:
m   1[1  (1   )2  ]1[   (1   ) ]w  [1    (1   ) ] 
(9)
The trade-off between price level/inflation and employment stabilization to which productivity
shocks give rise is implicit in Eqs. (7) and (8). Underlying this trade-off is the fact that, for any
non-zero realization of  , greater employment stability requires a corresponding adjustment in
the real wage: given w, such an adjustment can be accomplished only by an appropriate
movement in the price level. The central bank’s setting of the money supply, represented by
Eq.(9), then achieves its optimal price level-employment combination, contingent upon the given
values of w and  . The consequent values of p and l are:
p  [1  (1   ) 2  ]1 (w   )
(10)
l  [1  (1   )2  ]1 (1   ) (w   )
(11)
Of course, the average nominal wage is itself endogenously determined as the aggregate
outcome of wage decisions at the individual firm level: hence, to fully determine macroeconomic
equilibrium we must identify w. Given the objective of agents within firm i of maintaining
employment at its market-clearing level, it follows from Eq.(2) that wi will be set such that
wi  i  E ( p | i ) . Hence, using Eq.(10)5 and the property that E ( | i )   i :
4
5
For notational simplicity we set p1  0 , implying   p .
With p  
5
wi  [1  (1   )2  ]1{[1    (1   )2  ]i  E(w | i )}
(12)
1
  di   :
Aggregating the expression over all firms, noting
0
i
w  [1  (1   )2  ]1{[1    (1   )2  ]  E (w)}
(13)
where E is used to denote an average expectation across firms: hence, E (w) represents the
1
average expectation of the average nominal wage, i.e. E (w)   E (w | i )di . To determine E (w) ,
0
the expectation of Eq.(13), conditional on  i , is taken then aggregated over firms:
E (w)  [1  (1   )2  ]1{[1    (1   )2  ]  E 2 (w)}
(14)
where E 2 (w)  E ( E (w)) . To derive a closed-form solution for w requires taking successively
higher order expectations of (13). Continuous substitution then yields:6

w  [1  (1   ) 2  ]1[1    (1   ) 2  ] {[1  (1   ) 2  ]1 } j
(15)
j 0
With
  1,
the
infinite
sum
is
bounded,
with
its
value
given
by
[1    (1   ) 2  ]1[1  (1   ) 2  ] . Hence it follows:
w 
(16)
Substitution of this solution for w into Eqs. (10) and (11) identifies the key finding of this note,
summarized in the following Proposition:
Proposition: Given the informational structure assumed, the interaction between private sector
wage setting and the central bank’s choice of monetary policy stabilizes both the price level and
employment perfectly at their socially optimal values. This outcome is independent of the relative
weight,  , attached to inflation by the central bank.
To interpret this result and, in particular, to highlight the central role played by active
stabilization policy in generating it, it is instructive to first consider the case of a non-activist
monetary policy, in which m is independent of  . With a constant setting of m, aggregate
productivity shocks will inevitably be reflected in fluctuations in the price level. Although agents
6
A full derivation of Eq.(15), together with other key results, is presented in an Appendix, available from
the authors on request.
6
within individual firms are able to make an inference with regard to the aggregate component of
any shock to which their firm is subject, the average expectation of  systematically
underestimates its true value: specifically E ( )   . The consequence of this is that the impact
of non-zero realizations of  on the price level is also systematically underestimated, implying
the average real wage is inconsistent with labor market clearing at the aggregate level: thus
aggregate employment departs from its socially optimal value.7
In contrast, an activist monetary policy which neutralizes the impact of aggregate productivity
shocks on the price level renders private sector expectational errors in respect of  irrelevant.
Given price level certainty, wage setters have no need to distinguish between the firm-specific
and the aggregate components of any disturbance to which their firm is subject. Consequently, the
nominal wage set within each individual firm is consistent with labor market clearing, ensuring
this is also true at the aggregate level. 8 Clearly, the central bank does not face any trade-off
between its two objectives. On the contrary, achieving price level stability is an essential element
in stabilizing employment. Reflecting this, achievement of the social optimum is independent of
the relative weight which the central bank places on its inflation goal.9
4. Concluding remarks
This note has examined the consequences of modifying the informational assumptions which
characterize much monetary policy analysis. Specifically, while recognizing that the central bank
is likely to have an informational advantage in respect of aggregate productivity disturbances,
agents within individual firms were assumed to be better informed about shocks to their own
production technology. In this context, it was demonstrated that the central bank does not face a
trade-off between its inflation and employment objectives. Instead, stabilizing the price level is
integral to achieving employment stability.
7
Solving the model for a constant setting of m, using the methodology employed above to determine the
average nominal wage, the variance of aggregate employment  l2 is found to be:
 l2  [ (1   )   (1   )] 2 (1   ) 2  2
8
The consistency between private sector expectations and monetary policy can be understood in the
following way. Wage setters within each firm observe the value of the shock to which their own firm is
subject and, given the expectation E ( p | i )  0 , set the nominal wage such that wi  i : hence w   .
The optimal policy for the central bank is then to set m such that p  0 , thus confirming private sector
expectations and ensuring l  0 . We are indebted to a referee for this interpretation.
9
Providing only that  is strictly positive. It can be shown that   0 is associated with an indeterminate
price level.
7
An important aspect of our findings was that the relative weight attached to inflation in the
central bank’s objective function is of no significance for the ability of monetary policy to
achieve the social optimum. This conclusion would not be robust, however, to the presence of an
inflation bias. Such a bias might arise if, for example, labor supply were restricted by union
actions designed to raise the real wage above its market-clearing value. In this instance, monetary
policy would stabilize inflation perfectly but at some positive value declining in  . Hence a
central bank which attached an infinite relative weight to inflation stabilization would eliminate
the inflation bias completely. The crucial implication of our analysis in this context is that this
would not be at the expense of greater employment variability. Thus, our framework provides one
possible means of explaining the findings of Alesina and Summers’ (1993) empirical study,10 that
while there exists a significant negative relationship across a range of countries between average
inflation and a measure of central bank independence, there is no systematic relationship between
the latter and the variance of employment.
10
Additional to that suggested in James and Lawler (2006).
8
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