6.2 The model
6.2.3 Central bank’s policy objective
The policy objective describes the goals the central bank pursues by con- ducting monetary policy. Following most of the literature on monetary pol- icy analysis, we assume that the policy objective consists in minimizing the weighted sum of the deviation of inflation π and output gap cfrom their
0 0.2 0.4 0.6 0.8 1 alpha 5 10 15 20 period 0 0.2 0.4 0.6 0.8 1 Delta 0 0.2 0.4 0.6 0.8 alpha
Figure 6.2: Gradual impact on inflation over time
respective target values.15 Once the target values are normalized to zero,
the welfare loss of the central bank in any periodt has the quadratic form
π2
t +λc2t, where λis a positive relative weight on output deviation. In any
period zero, the goal of the central bank is to minimize the discounted sum of welfare losses min I E0 ∞ X t=0 βt b(π2t +λc2t), (6.13)
owing to its instrumentI, whereβbis the central bank’s discount factor. The
policy objective guides the policy maker through the choice of the optimal policy. One may think of two ways of rationalizing the central bank’s objec- tive (6.13). Indeed, this objective can be motivated either by a pragmatic or by a microfounded welfare theoretical perspective.16
The pragmatic approach rationalizes objective (6.13) by stressing two well-known features. First, monetary policy is recognized to play a cru- cial role in the determination of inflation. Central bankers are also aware that inflation involves real costs for the economy as a whole. While Fischer and Modigliani (1978) classify potential costs of inflation according to the indexation of the economy,17 De Long (1997) argues that the experience of
15See Walsh (2003a).
16See Clarida et al. (1999) section 2.2.
17For instance, Fischer and Modigliani (1978) propose an overview of the potential costs
of inflation. They classify the costs of inflation according to the extent to which the economy is indexed to inflation. In a fully indexed economy, the real effects of inflation are limited to seigniorage, diversion of resources to transactions, and menu costs. Yet, when inflation is
the 1970s awakened central bankers to the costs of high inflation.18 Hence,
the central bank should keep inflation under control. Second, as described by Phillips curves, monetary policy may influence the real economy in the short run. Models incorporate a combination of long-run monetary neu- trality and short-run nominal inertia, such that monetary policy has a po- tentially significant role in stabilizing the economy. Resting on these two common ideas, the policy objective has been motivated in the literature in a very intuitive way that clearly captures both central bank’s tasks: the con- trol of inflation and the stabilization of output gap.
It is worth noting that the policy objective (6.13) has been recently ra- tionalized into fully microfounded models motivating the policy objective from the utility of a representative household. Indeed, by deriving microe- conomic foundations of monetary policy analysis, one can show that the welfare maximization of a representative agent calls for stabilization of both the output gap (because of the concavity of household’s utility function and Jensen’s inequality) and the relative price distortion across goods (because price dispersion leads to inefficient substitution between goods).19 While
this result is robust, the determinants of the variance of relative price distor- tion depend on the price setting scheme.
In the Calvo sticky-price model, Woodford (2003b) shows that the rel- ative price distortion is related to the inflation squared. Since firms set their price at different periods, price dispersion will be low when the op- timal price path remains constant over time,i.e. when inflation is minimal. It turns out that the optimal approximated welfare of the representative household yields a policy objective in the form of (6.13).
Ball et al. (2005) derive the microfounded policy objective a central bank should adopt in the case of sticky information. Since prices are flexible in this economy, relative prices are distorted if agents do not share the same information. In this context, the central bank should commit to a determin- istic path for the price level in order to insure common information among private agents. Whether the deterministic path is stationary, explosive, or
unanticipated or not fully indexed, the list of potential costs is much longer and includes – to mention but a few – redistributive effects, forecast imprecision, and distortion of relative prices.
18See also Shiller (1996).
oscillatory is irrelevant in terms of welfare.20
However, the microfounded approach of central bank policy objective has at least two limitations. First, these models do not seem to capture the real costs of inflation as perceived by real world experiment. For instance, in the sticky-price model, apart from its impact on relative price distortion, inflation per se is costless. Second, the use of a representative household may be misleading in deriving the welfare analysis related to monetary pol- icy issues as it ignores the disparate effect of monetary policy across society members. For instance, redistributive effects or forecast imprecisions are absent from microfounded models. The microeconomic derivation of the objective function is on a knife-edge: economists like their models to have microeconomic foundations but microfounded objectives miss the real ef- fects and costs of inflation as described by Fischer and Modigliani (1978), Shiller (1996), and De Long (1997).
Therefore, in this chapter, we adopt the pragmatic approach as in most of the literature. The central bank is assumed to care about inflation instead of relative price distortion. We focus on the inflation targeting objective (6.13) whatever the economy we refer to, even if it could be regarded as microe- conomically inconsistent in the case of sticky information. This approach is nevertheless consistent with concerns of central banks in the conduct of monetary policy in reality.21