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Lecture 8

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.

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Lecture 8

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  1. Lecture 8 Central Banks - The Issue of Credibility and Reputation

  2. 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

  3. 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

  4. 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)

  5. 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

  6. 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

  7. 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

  8. Stackelberg Game G d nd End P s ns G G nd d nd d P P s ns ns s

  9. 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

  10. 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.

  11. Time consistency • Objective function V=V(x1,x2, 1, 2) • xs are targets and s are instruments • x1=f1(1) • x2=f2(x1, 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. 2same as period 1

  12. Period 2 optimisation in time consistent case

  13. Rational expectations and time inconsistency

  14. Optimising in period 1 for period 2

  15. But optimising in period 2 for period 2

  16. Inflation - Unemployment illustration  A C B U

  17. Barro and Gordon

  18. Three types of policies • Discretionary policy - Nash • Policy rule • Cheating policy

  19. Discretionary policy

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

  21. Cheating policy

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

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

  24. Temptation to cheat

  25. Cost of cheating

  26. Costs and benefits of commitment b2/2a Best enforceable rule b2/2a(1+r) rb/a(2+r) Ideal rule 0 b/a  Enforceable range

  27. Minimum cost rule

  28. 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

  29. 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

  30. Information asymmetry • Private sector assigns a probability pt each period that the government is strong • pt 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

  31. 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.

  32. 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

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