Money and Banking Essay (Richard Mash - Time consistency) PDF

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‘Although in theory Walsh’s optimal contract for central bankers is to be preferred to Rogoff’s conservative central banker in solving the problem of inflation bias, the Rogoff solution is more robust to the practical problems associated with the conduct of monetary policy.’ Discuss...

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For Gareth Anderson Money and Banking ‘Although in theory Walsh’s optimal contract for central bankers is to be preferred to Rogoff’s conservative central banker in solving the problem of inflation bias, the Rogoff solution is more robust to the practical problems associated with the conduct of monetary policy.’ Discuss Inflation bias is a phenomenon that occurs when a central bank operating under discretion sets an output target that is above the natural level of output. The central bank is then unable to commit to optimal policy and inflation exceeds its optimal level. Two of the possible solutions to this problem are the creation of a state-dependent contract, as described by Walsh (1995), for central bankers that incentivises attaining the optimal level of inflation; and the appointment of a conservative central banker that is more averse to inflation, as described by Rogoff (1985). Theoretically, the Rogoff solution faces the problem that the conservative central banker is too averse to inflation for the purposes of stabilisation policy, a problem which is not shared by the optimal Walsh contract. However, numerous practical difficulties exist in implementing such contracts. That said, there is a difference between difficulty in implementing policy and difficulty in conducting monetary policy once either of the solutions is in place. While the Walsh contract is more difficult to implement, once in place it is more robust than the conservative central banker in dealing with macroeconomic volatility and resolving the inflation bias. The model of inflation bias described by Barro and Gordon (1983) explains inflation bias as the result of an output target that is too high. The model assumes a Lucas supply function as follows:

y = y n +a( π −π ) +e e

Where y n is the natural level of output as determined by labour and capital that are assumed to be fixed; e is the level of the supply shock with mean 0. A quantity theory of inflation is assumed to hold such that the policymaker can set the rate of inflation through varying the money supply according to the relation

π =Δ m+ v Where v is the error in policymaking (this essay will assume no error and thus v=0). Expectations are assumed to be formed prior to the monetary policy decision and the realisation of the supply shock. Furthermore, the monetary policy decision is made after the realisation of the supply shock such that there is an active stabilisationary role for monetary policy. In setting monetary policy the central bank aims to minimise the following squared loss function:

1 1 V = λ ( y − y n−k )2 + π 2 2 2 The loss function states that the inflation target is zero while the output target is central bank’s optimal level of inflation (conditional on e) is e

a λ π + aλ ( k−e) (1) 2 1+a λ 2

π=

y n +k . The

Under rational expectations, individuals will predict the central bank’s maximising behaviour and set their own inflation expectations accordingly 2

π e =E ( π )=

e

a λ π +aλk (2) 1+ a2 λ

For Gareth Anderson Money and Banking (since E(e)=0) Substituting (2) in (1) to find

π d , the inflation rate under central-bank discretion,

( 1+aλa λ )e

π d=aλk−

2

Thus inflation is positive with an expected value of This phenomenon is the inflation bias.

aλk and exceeds the social optimum of zero.

The conservative central banker is a proposed solution to the inflation bias. The central banker as theorised by Rogoff has a modified loss function of

1 2 2 1 V R = λ ( y − y n−k ) + ( 1+δ ) π 2 2 Such that the inflation term is weighted by 1+δ , where δ is a measure of the conservativeness of the central banker. Minimising this loss function as in (1) above yields the level of expected inflation π eR :

0< π eR =

aλk...