复旦大学：《宏观经济学》课程教学讲义（PPT）Topics in Macroeconomic Policy：Time Inconsistency in Monetary and Fiscal Policies

Topics in Macroeconomic Policy Time Inconsistency in Monetary and Fiscal Policies 复9大学经学院

Topics in Macroeconomic Policy: Time Inconsistency in Monetary and Fiscal Policies

Time Inconsistency in Monetary Policy 90 Central Bank's Object 2 ∑ u t+s mn BE +6-+s =0 2 st u - 丌:)+E which yields L+.+ 1+6 Note that this solution deviates from agents' expectation, or equivalently central bank's ex-ante commitment. This is the ne time inconsistent problem found by 4 Kydland-Prescott(1977, JPE)and Barro Gordon(1983, JPE)

( ) ( ) t e t t t T s t s t s t s st u u u E       = − − +       + − = + + . . 2 2 min 0 2 2 Central Bank’s Object: which yields     + − + + = 1 t e t t u Note that this solution deviates from agents’ expectation, or equivalently, central bank’s ex-ante commitment. This is the time inconsistent problem found by Kydland-Prescott (1977, JPE) and Barro￾Gordon (1983, JPE). Time Inconsistency in Monetary Policy

Agents' Response Update Expectation B& Find Rational Expectation (Fixed Point Problem) ++ 1+O u The Consequent Equilibrium Inflation becomes u t O 1+6 Note that this time consistent solution is inferior to the solution 复9大学经学院 with zero inflation commitment

Agents’ Response: Update Expectation ❖ Find Rational Expectation (Fixed Point Problem): u e t   1  = −         + − + + −  = −      1 1 1 t e t t e t t t u E E • The Consequent Equilibrium Inflation becomes t u  t    + = − + 1 1 1 • Note that this time consistent solution is inferior to the solution with zero inflation commitment

Four Solutions First-Best Allocation: government is allowed to manipulate agents g expectation to achieve zero unemployment and inflation . Cheating (Time-Inconsistent) Solution: government would like to deviate from her precommitment because she always has incentive to reduce unemployment by unexpected inflation &Precommitment Solution government is assumed to commit to her ex-ante announced policy &s Time Consistent Solution government is unable to commit to her policy 复9大学经学院 wElfare Comparison

❖ First-Best Allocation: government is allowed to manipulate agents’ expectation to achieve zero unemployment and inflation. ❖ Cheating (Time-Inconsistent) Solution: government would like to deviate from her precommitment, because she always has incentive to reduce unemployment by unexpected inflation. ❖ Precommitment Solution: government is assumed to commit to her ex-ante announced policy. ❖ Time Consistent Solution: government is unable to commit to her policy. ❖ Welfare Comparison: 1 > 2 > 3 > 4 Four Solutions

Time Inconsistency in Fiscal Policy s The following model, developed a 0 by Fischer(1981, JEDC), is a benchmark to start with ☆ Household's behavior max(c, C2, 4, g) Subject to +k==k+-r This yields households response function Ig) k 8 A benevolent government would like 3 to maximize households' welfare.45 subject to g=ckk+rzl

Time Inconsistency in Fiscal Policy ❖ The following model, developed by Fischer (1981, JEDC), is a benchmark to start with. ❖ Household’s Behavior maxU(c ,c ,l, g) 1 2 Subject to c k y c ( )Rk ( )zl k l + = = 1− + 1− 1 2 This yields households’ response function c ( g) c ( g) k( g) l( g) k l k l k l k l , , , , , , , , 1 2         • A benevolent government would like to maximize households’ welfare, subject to g k zl k l = +