Lecture 8 Central Banks - The Issue of Credibility and Reputation

This lecture addresses two issues: Credibility The distinction between rules and discretion a) credible commitments b) rules can be learned by private agents, discretion cannot

Lucas v Tinbergen Tinbergen paradigm - discretionary policy can be used to meet set objectives. If there are n targets we need n independent instruments to satisfy targets Lucas critique - very act of discretion undermines its effectiveness A modest policy of rules would be more effective

The Leader - Follower paradigm Lucas approach treats the economy as a collection of optimising agents But the government is also an optimising agent The government can be treated as a leader private agents are followers Leader-follower game (Stackelberg)

Illustration of leader - follower game At each date a speculator can raise domestic currency which is sold for foreign currency. He pays a fixed charge of c per transaction Assume that there is a limit to which the speculator can sell in each period - transactions or liquidation costs If a devaluation occurs the benefit is π per unit of domestic currency

leader - follower continued If a devaluation occurs - profit is π - ct; t=1,2,.. and ct is the opportunity cost Government has reserves of $R It is forced to devalue when it runs out of reserves

Assumptions For a given level of reserves, the government prefers maintaining the exchange rate to devaluation For a given exchange rate it prefers more reserves to less 2 < $R < 3 π/2 < c < π

Stackelberg Game G d nd End P sns GG d ndd P s ns P s

Possible equilibrium Speculators will sell until the government decides to devalue Thus the government devalues immediately delaying devaluation can occur only until t=3 But suppose government can pre-commit not to devalue until all reserves are gone devaluation does not occur

Conclusions Solution concepts matter. Nash, Stackelberg, perfect equilibrium etc. Even if it is accepted that the government is a leader, the inability to make self binding commitments may reduce the leaders power without binding commitments there may be more than one solution.

Time consistency Objective function V=V(x 1,x 2, 1, 2 ) xs are targets and s are instruments x 1 =f 1 ( 1 ) x 2 =f 2 (x 1, 2, 1 ) In period 1 maximise w.r.t. 1 In period 1 maximise w.r.t. 2 In period 2 maximise w.r.t. 2 same as period 1

Period 2 optimisation in time consistent case

Rational expectations and time inconsistency

Optimising in period 1 for period 2

But optimising in period 2 for period 2

Inflation - Unemployment illustration U A B C

Barro and Gordon

Three types of policies Discretionary policy - Nash Policy rule Cheating policy

Discretionary policy

Policy rule Ex-ante optimal policy time inconsistent but if CB can pre-commit = e = 0 = * cost z = 0 = z*

Cheating policy

Ranking of policies Cheating is first best policy rule is second best discretion is third best

Enforcement rules Credibility enhancing t-1 = e t-1 distrust and Nash enforcing t-1 e t-1 Thus the gain from cheating (reneging) must be judged against the costs of loss of reputation

Temptation to cheat

Cost of cheating

Costs and benefits of commitment b 2 /2a b 2 /2a(1+r) Enforceable range Best enforceable rule 0 Ideal rule b/a rb/a(2+r)

Minimum cost rule

Insights The most important insight is that a superior policy to Nash is enforceable when reputation is a criterion A policy is only credible if people can see that the costs of cheating is greater than the benefits The most limiting aspect of the study is that reputation effects last only for 1 period

Backus and Driffil Modification of Barro-Gordon result with introduction of asymmetric information Agents are unaware of CB or governments cost function parameters Let e = {0,1} weak government inflates - plays =1 strong government is sound money - plays =0

Information asymmetry Private sector assigns a probability p t each period that the government is strong p t is revised periodically First, government avoids inflating = e =0 Government still plays =0 but private sector assigns >0 At some point the government plays =1

Conclusion Contrary to Barro-Gordon there will exist a period during which a zero inflation policy is credible because it pays even a weak government to build up a stock of good reputation.

Insights Two-sided uncertainty leads to Stackelberg warfare Strong private sector may induce a stronger government to be tougher than necessary to convince them that they are strong Even a strong government may abandon =0 if costs of disinflation are large