復(fù)旦經(jīng)濟(jì)學(xué)院的平衡和成長3個(gè)英文

1、Topics in Macroeconomic Policy: Time Inconsistencyin Monetary and Fiscal PoliciesCentral Banks Object:which yieldsNote that this solution deviates from agents expectation, or equivalently, central banks ex-ante commitment. This is the time inconsistent problem found by Kydland-Prescott (1977, JPE) a

2、nd Barro-Gordon (1983, JPE).Time Inconsistency in Monetary PolicyAgents Response: Update ExpectationFind Rational Expectation (Fixed Point Problem):The Consequent Equilibrium Inflation esNote that this time consistent solution is inferior to the solution with zero inflation commitment.First-Best All

3、ocation: government is allowed to manipulate agents expectation to achieve zero unemployment and inflation.Cheating (Time-Inconsistent) Solution: government would like to deviate from her mitment, because she always has incentive to reduce unemployment by unexpected inflation. mitment Solution: gove

4、rnment 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 4Four SolutionsTime Inconsistency in Fiscal PolicyThe following model, developed by Fischer (1981, JEDC), is a benchmark to start with.Househol

5、ds BehaviorSubject toThis yields households response functionA benevolent government would like to maximize households welfare, subject toFour SolutionsFirst-Best Allocation: maximize households welfare subject to resource constraint.Cheating (Time-Inconsistent) Solution: government would like to de

6、viate 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. mitment Solution: Open-Loop Solution in the Stackelburgh Game.Time Consistent Solution: Subgame Perfect Equilibrium.Welfare Comparison: 1 2 3 4What

7、 Causes Time InconsistencyInsufficient 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 e tax?). However, this explanation seems not satisfactory since it cant explain why time inconsist

8、ency 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 pointe

9、d out by Chari, Kehoe and Prescott (1989).Atomistic AssumptionWithout loss of generality, we can write down a “semi-indirect utility function” for the ith household: mitment Solution (the first equation is the households behavior and the second is the governments choice):Time Consistent Solution (th

10、e first equation is the households behavior and the second is the governments choice):Clearly the discrepancy lies in atomistic agents, or similarly, the externality of aggregate capital K.Application for Monetary PolicyOne can easily find that time inconsistency in our first model lies in the Phill

11、ips 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 se

12、ems to be a general e from the world with heterogeneous interests.A Formal Model to Study Time Inconsistent Monetary PolicyProduct Market:Monopolistic Competition: Price = W/One cash good and one credit good. part of goods are determined at the begin of each period, i.e. the price, Psi, is sticky du

13、ring one period. The flexible price is denoted by Pfi.Aggregate price is Pi. dPi/ dPfi = 1-.Households:Given prices, households choose M, B and n.Clearly the mitment Solution follows Friedman Rule, i.e., R = 1. For Time Consistent Solution, Government chooses G ex-ante, or equivalently Pf, subject t

14、o (1) and (2).We claim that for some condition, TC Solution is equivalent to mitment Solution. Method: Evaluate marginal returns to Pf, denoted by L, at R = 1 with tight CIA. Check if R = 1 can be sustained by Pf = Pe.For the right derivative L+, i.e. Pf Pe, we have C1 = 1/P1 from CIA constraint, M

15、has been normalized to 1. Differentiating (2) yields Here we use the following equation: since we evaluate derivative at Pe = Pf = P and P1 = P2 = P. For the left derivative L-, i.e. Pf Pe, we have C1P1 = C2P2 from (1). Differentiation yieldsSubstitute (4) and (5) into (3) yieldsHere we use C1=C2 in

16、 the equilibrium. So L+ 0 if 0. To conclude, if . Intuitively, high price stickiness induces incentive of inflation, the underlying mechanism is the same as Phillips Curve.Specifically, “A benefit of expansionary monetary policy is that it leads to an increase in demand for goods whose prices are fi

17、xed. This increase in demand tends to raise employment.” Note that inefficient low employment is due to monopolistic competition. “A principal cost of EMP is that it tends to reduce employment in the cash good sector”. Finally, “It is possible that the reduction in employment in the cash good sector

18、 is so large that overall employment and welfare fall.” Quoted from Albanesi, Chari and Christiano (2003, pp. 136).Note 1: This result is sensitive to the modeling of money demand.Note 2: We only study the local optimum (global optimum has been checked numerically).Note 3: Here Time Consistent Solut

19、ion is (implicitly) contingent upon Pf, so ACC call the solution “Markov Equilibrium”. This equilibrium is unique under some restrictions. Assume CD production technology, with capital output elasticity and fixed labor (normalized to 1). Public spending is financed by capital e tax:A Formal Model to

20、 Study Time Inconsistent Fiscal PolicyGiven g and balanced budget, households Behavior is the following:To obtain analytical solution, here we assume 100% depreciation. Solving this problem recursively, we haveBy deduction, one can obtain:It is clear that future taxation affects current saving decis

21、ion. Specifically, at time t, government takes into consideration the impact of t+1 upon kt+1. However, at time t+1, optimal taxation plan would change since kt+1 is fixed and the impact of t+1 disappear.Maximizing value function (static problem?) yields TC solution. mitment (Ramsey) Solution cant b

22、e solved analytically (bellman problem?).Next we consider proportional e tax:By the same procedure, one can obtain:Note that by proportional e tax, there is no distortion in marginal returns of capital.By deduction, one can obtain:It is clear that future taxation doesnt affect current saving decisio

23、n. So one can expect that Ramsey solution is time consistentThis is a classical model, but the above result was recently emphasized by Klein, Krusell and Rios-Rull (2002/3).To conclude, time consistent taxation plan is contingent upon current state variable, capital k. That is why KKR call it “Marko

24、v equilibrium” (TC solution is also called close-loop solution.). In the above simple model with proportional e tax, time consistent solution or Markov equilibrium turns out to be irrelevant to k. So it is equivalent to mitment (open-loop) solution.Finally, the result is sensitive to preference assu

25、mption. If utility is not logarithm, TC solution is not equal to mitment solution since e effect cant be offset by substitution effect.To Be Better Off: Some IllustrationsTrigger Strategy: By the Folk Theorem, the best e can be an equilibrium if the discount rate is sufficiently low in a infinite ho

26、rizon model (how about finite horizon?).A possible strategy:One can check that if F and are sufficiently large, zero inflation will be a subgame perfect equilibrium. Note the concept of perfection: you not only need to check deviations from the equilibrium path, but also need to check zero inflation

27、 is the best response of government along off-equilibrium path. Weakness: How to select an equilibrium from so many possible candidates? This is a typical problem in game theory.Contract ApproachGovernment construct a contract to punish central bank for inflationTime Consistent Solution isClearly if

28、 government sets = -u, zero expected inflation can be achieved, which is the first-best e. This result was first pointed out by Walsh (1995, AER). Has the time inconsistency problem been killed by this simple incentive contract? The answer is, unfortunately, negative.First note that the above result

29、 is crucially dependent upon the linear Phillips Curve. Without this ad-hoc assumption, it would be impossible to derive any feasible incentive contract.Second, contract implicitly removes time inconsistency to another level, i.e. who insures the governments commitment to the contract?Stories about

30、Central BankerA straightforward way to kill inflation is to delegate central banker to a person with infinite aversion to inflation, i.e. = .If there is no such a person, we can delegate central banker to a person with higher (than social level). One can easily show that this can moderate time inconsistency problem. This approach was pointed out by Rogoff (1985, QJE).Clearly public expectation towards inflation is closely