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 = +

Four Solutions First-Best Allocation maximize g households welfare subject to resource constraint o Cheating (Time-Inconsistent) Solution: government would like to deviate from her previous policy at the second period when k has been accumulated, because she always has incentive to reduce distortion by only taxing k &s Precommitment Solution: Open Loop Solution in the Stackelburghk Game Time Consistent Solution: Subgame, Perfect Equilibrium Welfare Comparison >2>3>

Four Solutions ❖ First-Best Allocation: maximize household’s welfare subject to resource constraint. ❖ Cheating (Time-Inconsistent) Solution: government would like to deviate from her previous policy at the second period when k has been accumulated, because she always has incentive to reduce distortion by only taxing k. ❖ Precommitment Solution: Open￾Loop Solution in the Stackelburgh Game. ❖ Time Consistent Solution: Subgame Perfect Equilibrium. ❖ Welfare Comparison: 1 > 2 > 3 > 4

What causes Time Inconsistency insufficient Policy Instruments: One can easily find that there is no time inconsistency in the second model if the government is allowed to levy lump-sum tax (or proportional income tax? ). However, this explanation seems not satisfactory since it can't explain why time inconsistency rises in the first model Persson and Tabellini(1994)argue that Ti is due to the sequential nature of policy-making. This, again, is only partially correct Now most economists believe that TI 3 is induced by the heterogeneity of i interests, or equivalently some externality. This is first pointed out by Chari, Kehoe and Prescott(1989). Be

What Causes Time Inconsistency • Insufficient Policy Instruments: One can easily find that there is no time inconsistency in the second model if the government is allowed to levy lump-sum tax (or proportional income tax?). However, this explanation seems not satisfactory since it can’t explain why time inconsistency rises in the first model. • Persson and Tabellini (1994) argue that TI is due to the sequential nature of policy-making. This, again, is only partially correct. • Now most economists believe that TI is induced by the heterogeneity of interests, or equivalently, some externality. This is first pointed out by Chari, Kehoe and Prescott (1989)

Atomistic Assumption wIthout loss of generality, we can write down a"semi-indirect utility function?" for the ith household vlk.KT Precommitment Solution(the first equation is the households behavior and the second is the government's choice) ay ak av 0 0 Time Consistent Solution(the first equation is the households behavior and the second is the government's choice) 0 ak 0∑ l aT Clearly the discrepancy lies in atomistic i agents, or similarly, the externality of F aggregate capital K

Atomistic Assumption ❖ Without loss of generality, we can write down a “semi-indirect utility function” for the ith household: v (k ,K, ) i i • Precommitment Solution (the first equation is the households’ behavior and the second is the government’s choice): 0 = 0           +     =   i i i i i K v K v k v   • Time Consistent Solution (the first equation is the households’ behavior and the second is the government’s choice): 0 = 0   =   i i i i v k v  • Clearly the discrepancy lies in atomistic agents, or similarly, the externality of aggregate capital K

Application for Monetary Policy 2 One can easily find that time inconsistency in our first model lies in the phillips curve . However, the microfoundation of the phillips curve again lies in the heterogeneity of interests everyone hopes others to underforecast inflation &So, the phillips curve and consequently the time inconsistency problem no longer 9 exist in communist world 复9大学 To conclude, time inconsistency seems to be a general outcome from the world with heterogeneous interests

Application for Monetary Policy ❖ One can easily find that time inconsistency in our first model lies in the Phillips Curve. ❖ However, the microfoundation of the Phillips Curve again lies in the heterogeneity of interests: everyone hopes others to underforecast inflation. ❖ So, the Phillips Curve and consequently the time inconsistency problem no longer exist in a “communist world”. ❖ To conclude, time inconsistency seems to be a general outcome from the world with heterogeneous interests

A Formal Model to stud Time Inconsistent Monetary Product Market Policy .Monopolistic Competition: Price W/A s One cash good and one credit good. p part of goods are determined at the begin of each period, i.e. the price, Psi, is sticky during one period. The flexible price is denoted by P &s Aggregate price is Pi. dP /dPi=1-H srhtousehplplse +hn+yin(n, )I s. GAM=Wn,+r B+M-P Cl-2 C2+l+D M1≥B1CnA1=M1+B 复9大学经 Given prices, households choose M, B and ng RP P2C2,(1) P (2) P Clearly the Precommitment Solution follows Friedman rule. ie.R=1. For Time Consistent Solution, Government chooses G ex-ante, or equivalently pt, subject to(1) and(2)

A Formal Model to Study Time Inconsistent Monetary Policy ❖ Product Market: ❖ Monopolistic Competition: Price = W/λ ❖ One cash good and one credit good. μ part of goods are determined at the begin of each period, i.e. the price, Ps i , is sticky during one period. The flexible price is denoted by Pf i . ❖ Aggregate price is Pi . dPi / dPf i = 1-μ. ❖ Households  : ( ) t t t t t t t t t t t t t t t t t t t t t t t M P C A M B GA W n R B M P C P C T D C C n st  = + = + + − − + + + + − +  = 1 1 1 1 1 2 2 0 1 2 max  ln ln  ln 1 . . • Given prices, households choose M, B and n. (1) Rt P1t C1t = P2t C2t (2) 1 1 1 2 2 2 2 2 t f t t t t t t t P P C C C P W n C =  − − =  − • Clearly the Precommitment Solution follows Friedman Rule, i.e., R = 1. For Time Consistent Solution, Government chooses G ex-ante, or equivalently Pf , subject to (1) and (2)