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Instrument-Based Vs. Target-Based Rules

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Instrument-Based Vs. Target-Based Rules Instrument-Based vs. Target-Based Rules Marina Halac Pierre Yared Yale University Columbia University January 2020 Motivation Should central bank incentives be based on instruments or targets? • Instruments: interest rate, exchange rate, money growth • Targets: inflation, price level, output growth Global central banks have moved towards inflation targets • 26 central banks since 1990, 14 EMs • But many EMs continue fixed exchange rate regimes This paper: Do target-based rules dominate instrument-based ones? What We Do Monetary model to study instrument-based vs. target based rules • Rule is optimal mechanism in setting with non-contractible information Elucidate benefits of each class, when one is preferred over the other • Compare performance as a function of the environment Characterize optimal unconstrained or hybrid rule • Examine how combining instruments and targets can improve welfare Preview of Model Canonical New Keynesian model with demand shocks Central bank (CB) lacks commitment, has private forecast of demand • Inflation/output depends on monetary policy and realized demand Incentives: Socially costly punishments (money burning); no transfers • Instrument-based rule: Punishment depends on interest rate • Target-based rule: Punishment depends on inflation Main Results In each class, optimal rule is a maximally enforced threshold • Instrument-based: Punish interest rates below a threshold • Target-based: Punish inflation above a threshold Target-based dominate instrument-based iff CB info is precise enough • More appealing on the margin if CB commitment problem is less severe Optimal hybrid rule improves with a simple implementation • Instrument threshold that is relaxed when target threshold is satisfied • E.g., interest rate rule which switches to inflation target once violated Related Literature Optimal monetary policy institutions • Rogoff 1985, Bernanke-Mishkin 1997, McCallum-Nelson 2005, Svensson 2005, Giannoni-Woodford 2017 • This paper: Mechanism design to characterize and compare rules Commitment vs. flexibility in policymaking • Athey-Atkeson-Kehoe 2005, Amador-Werning-Angeletos 2006, Halac-Yared 2014,19 • This paper: Condition incentives on outcome in addition to action Delegation in principal-agent setting • Holmstrom 1977,84, Alonso-Matouschek 2008, Amador-Bagwell 2013 • This paper: Condition incentives on outcome in addition to action Model New Keynesian model: πt = βEtπt+1 + κxt (Phillips Curve) xt = Etxt+1 − ζ(it − Etπt+1) − θt/κ (Euler Equation) θt i.i.d. with Eθt = 0 (Demand Shock) Social welfare at t = 0: 1 2 2 X (κxt) π E βt ακx − γ − t −1 t 2 2 t=0 Substituting with Phillips curve: ( 1 " 2 2 #) X (πt − βEtπt+1) π E απ + βt −γ − t −1 0 2 2 t=0 Timing L H 1. CB privately observes signal st = fs ; s g • Where sH = −sL = ∆ and each signal has equal probability 2. CB publicly chooses interest rate it 2 3. Aggregate demand θt is publicly observed, where θtjst ∼ N st; σ 2 2 • Unconditional distribution has E(θt) = 0 and V ar(θt) = σ + ∆ 4. Expectations are formed, output gap and inflation are realized 5. CB punished according to rule: Pt 2 [0; P ] based on it and/or πt Markov Perfect Equilibrium Focus on Markov CB strategy, conditioning on st only and not history • Constant future expectations (Eπ, Ex) on- and off-path Given expectations, CB's choice of it implies choice of µt: µt ≡ (β + κζ)Eπ + κEx − κζit Therefore, πt = µt − θt Eπ = Eµ µ − θ − βEµ x = t t t κ Welfare Social welfare from timeless perspective: E [U(µ, θ; Eµ) − P (µ, µ − θ)] [µ − θ − βEµ] 2 (µ − θ)2 where U(µ, θ; Eµ) = −γ − 2 2 Given Eµ, CB of type sj chooses µj to maximize j j j j Esj α µ − θ − βEµ + U(µ ; θ; Eµ) − P (µ ; µ − θ) Thus, CB is better informed but biased relative to society: First best policy: µ = s; implying Eπ = Ex = 0 α + γβEµ Flexible policy: µ = s + implying Eπ > 0, Ex > 0 1 + γ Classes of Rules Compare different classes of rules • Instrument-based: P (µ, µ − θ) depends only on µ • Target-based: P (µ, µ − θ) depends only on µ − θ Compare as we vary info precision keeping E(θ) and V ar(θ) fixed • Uninformative signal: σ ! pV ar(θ) and ∆ ! 0 • Perfect signal: σ ! 0 and ∆ ! pV ar(θ) Assumptions: 1. Types are close: α=(1 + γ) ≥ 2∆ I Implies both types prefer higher action than either type's first best α2 1 2. Large maximum punishment: P ≥ 1+γ 2φ(1j0;1) I Implies sufficient breadth of incentives to use in relationship Optimal Instrument-Based Rule X 1 max E U(µj; θ; Eµ) − P jjsj µL,µH ;P L;P H 2 j=L;H subject to, for j = L; H, E αµj + U(µj; θ; Eµ) − P jjsj ≥ E αµ−j + U(µ−j; θ; Eµ) − P −jjsj j j j j j E αµ + U(µ ; θ; Eµ) − P js ≥ max E αµe + U(µ,e θ; Eµ) − P js µe P j 2 [0; P ] Optimal Instrument-Based Rule Proposition: Optimal rule implemented with maximally-enforced instrument threshold µ∗ = 0. • If µ ≤ µ∗, P (µ) = 0. Otherwise P (µ) = P Proof: Solve relaxed problem with only L's private info constraint • Optimal mechanism admits µL = µH = µ∗ = 0, P L = P H = 0 Mechanism deters CB from choosing excessively expansionary policy • Enforcement constraint non-binding, punishment occurs off path Optimal Target-Based Rule X 1 max E U(µj; θ; Eµ) − P (µj − θ)jsj µL,µH ;P (π) 2 j=L;H subject to, for j = L; H, j j µ 2 arg max E αµe + U(µ,e θ; Eµ) − P (µe − θ)js µe P (π) 2 0; P for all π Optimal Target-Based Rule Proposition: Optimal rule implemented with maximally-enforced target threshold π∗. • If π ≤ π∗, P (π) = 0. Otherwise P (π) = P Proof: Solve relaxed problem using a first-order approach j j • Given normal shocks, CB's FOC yields µ = s + δ for some δ T 0 • Social welfare depends on δ and is independent of type Mechanism deters CB from choosing excessively expansionary policy • α+γβEµ δ 2 0; 1+γ : below flexible, above first best (to limit punishment) • E(π) = δ < π∗: CB undershoots cap (to limit punishment) Role of Precision of Private Information Consider increasing precision σ−1 while keeping V ar(θ) unchanged Social welfare is unchanged under optimal instrument-based rule: V ar(θ) −(1 + γ) 2 but it increases under optimal target-based rule: σ2 δ2 −(1 + γ) − 1 + γ(1 − β)2 − Pr π > π∗jσ2 P 2 2 Welfare at the extremes: • Perfect signal (σ ! 0, ∆ ! pV ar(θ)): target-based dominates • Uninformative (σ ! pV ar(θ), ∆ ! 0): instrument-based dominates Optimal Class of Rules Proposition: Take instrument-based and target-based rules and consider changing σ while keeping V ar(θ) unchanged • There exists σ∗ > 0 s.t target-based strictly optimal if σ < σ∗, instrument-based strictly optimal if σ > σ∗. • σ∗ is decreasing in CB's bias α and increasing in punishment P Low α and high P reduce punishment frequency in target-based rule • While not affecting welfare under instrument-based rule When does inflation-targeting dominate interest rate rule? • CB has highly superior non-contractible information • CB is not very biased, suffers large sanctions Optimal Hybrid Rule X 1 max E U(µj; θ; Eµ) − P j(θ)jsj µL,µH ;P L(θ);P H (θ) 2 j=L;H subject to, for j = L; H, E αµj + U(µj; θ; Eµ) − P j(θ)jsj ≥ E αµ−j + U(µ−j; θ; Eµ) − P −j(θ)jsj j j j j j E αµ + U(µ ; θ; Eµ) − P (θ)js ≥ max E αµe + U(µ,e θ; Eµ) − P js µe P j(θ) 2 [0; P ] for all θ Optimal Hybrid Rule Proposition: Optimal rule implemented with maximally-enforced hybrid threshold fµ∗; µ∗∗; π∗(µ)g. • If µ ≤ µ∗, P (µ, θ) = 0 • If µ 2 (µ∗; µ∗∗], P (µ, θ) = 0 if π ≤ π∗(µ). Otherwise P (µ, θ) = P • If µ > µ∗∗, P (µ, θ) = P Proof: Solve relaxed problem with only L's private info constraint • Solution yields µL = µ∗ < µH = µ∗∗ Optimal rule admits simple implementation, strictly improves welfare • Interest rate rule switches to inflation target if violated • " flexibility vs. instrument-based, # punishment vs. target-based Discussion: Other Instruments and Targets Results apply to output gap/price level target instead of inflation • Follows from divine coincidence Results apply to open economy: ∗ it = it + Et(∆et+1) (UIP) • CB choice of ∆et+1 is equivalent to choice of it • Optimal instrument-based rule is cap on exchange rate devaluation Results apply to model with money growth ∆mt = πt + xt − ηit − xt−1 + ηit−1 • Optimal instrument-based rule is cap on money growth rate Extension: Continuum of Types 2 2 Suppose CB's signal is st ∼ N 0; ∆ , with θtjst ∼ N st; σ 2 2 • Unconditional distribution has E(θt) = 0 and V ar(θt) = σ + ∆ • Let β = 1: Zero expected output gap, no expected inflation externality I Allows focus on welfare implications of local perturbations Proposition: Optimal instrument-based and target-based rules take the same implementation as under binary types. There exists σ∗ > 0 s.t. target-based preferred if σ < σ∗, instrument-based if σ > σ∗ Target-based identical to two-type case. Instrument-based different: • Types s < s∗ and s > s∗∗ choose flexible action; s 2 [s∗; s∗∗] bunched • Moreover, types s > s∗∗ break threshold and are punished • Welfare increases with precision, but main result still valid Extension: Persistent Shocks Suppose θt−1 shifts mean of θt • Signal st also shifted by Et−1(θt) • Implication: Action µt can be renormalized by Et−1(θt) Proposition: Optimal instrument-based and target-based rules take the same implementation as under i.i.d shocks.
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