Advanced Macroeconmic Theory

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How might delegation to a conservative central banker help overcome the inflationary bias to monetary policy? Demonstrate this result formally or graphically. [8 Marks]

In much of the literature on Central Bank Independence CBI, independence is often not distinguished carefully from conservativeness. In fact, most of the legal indicators for CBI give a central bank a higher score if price stability is the (primary) objective of the central bank concerned, while it, of course, implies less goal independence. The reason for doing so is that in the theoretical set-up both independence and conservativeness matter for the inflation performance. We can exemplify this as follows. It is assumed that policy-makers seek to minimize the following loss function, which represents the preferences of the society: Eqn 1

Where yt is output, y* denotes desired output and x is government's weight on output stabilization ( > 0). Output is driven by a simplified Lucas supply function:

Eqn 2
Where π is actual inflation, πe is expected inflation, and is a random shock with zero mean and a variance of . Policymakers minimize (Eqn 1) on a period by period basis, taking the inflation expectations as given. With rational expectations, inflation turns out to be:

Eqn 3

The first term at the right hand side of (Eqn 3) is the inflationary bias. A country with a high inflationary bias has a credibility problem, as economic subjects realize government's incentives for surprise inflation. The second term in (Eqn 3) reflects the degree to which stabilization of output shocks influence inflation. Suppose now that a 'conservative' central banker is put in charge of monetary policy. Conservative means that the central banker is more inflation-averse than government. The loss function of the central banker can therefore be written as: Eqn4

Where, denotes the additional inflation aversion of the central banker. The preferences of the central banker do not matter, unless (s) he is able to determine monetary policy. In other words, the central bank should be able to pursue monetary policy without (much) government interference. This can simply be modeled as follows (Eijffinger and Hoeberichts, 1998):

Eqn 5

Where “ ” denotes the degree of central bank independence, i.e. to which extent the central banker's loss function affects monetary policy-making. If ( = 1), the central bank fully determines monetary policy M. With rational expectations and minimizing government's loss function, inflation will be:

Eqn6

Comparing Eqn 3 and Eqn 6 one can immediately see that the inflationary bias (the first term at the right hand of the equations) is lower for positive values of “y” and . In other words, delegating monetary policy to an independent and ‘conservative’ central bank will yield a lower level of inflation. There is an optimal level of independence cum conservativeness ( *) under certain assumptions, this is shown graphically in Figure 1. It also follows from Eqn6 that both independence and the inflation aversion of the central bank matter. If the central banker would have the same inflation aversion as government (i.e. = 0), the independence does not matter. And similarly, if the central bank is fully under the spell of government (i.e. = 0), The conservativeness of the central bank does not matter. There are various combinations of “ ” and that may yield the same outcome, including the optimal one. Ceteris paribus an increase in the bank’s conservativeness or independence will lead to a more inflation-averse monetary policy.

L

*
Type equation here. Figure 1: The optimal level of central bank independence and conservativeness.

Rogoff also proposed a solution to inflation bias: appoint a conservative central banker i.e. a central banker who attaches greater weight to...
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