Inﬂation Targeting

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Lars E.O. Svensson

Sveriges Riksbank

Norges Bank, June 2010

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1 Introduction: Inflation targeting

1 An announced numerical inflation target

2 Forecast targeting, flexible inflation targeting: Choose policy rate path so forecast of inflation and real economy “looks good”

(stabilizes inflation around target and resource utilization around normal)

3 A high degree of transparency and accountability 2 History and macroeconomic effects

Starts 1990 in NZ, now about 25 countries

Effects on inflation, inflation expectations, and output

Success: Flexible, resilient, and robust monetary-policy regime

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3 Theory

Central role of projections

Policy choice: Choice of interest-rate path,notpolicy function, in feasible set of projections

Targeting rules

Implementation of policy and equilibrium determination Uncertainty: State of the economy (additive), the transmission mechanism (model, multiplicative)

Judgment

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4 Practice

Publishing a policy-rate path

Case studies: The Riksbank and Norges Bank Preconditions for emerging-market economics 5 Future

Price-level targeting

Inflation targeting and financial stability: Lessons from the financial crisis

6 Conclusions

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Inflation targeting starts 1990 in New Zealand Bundesbank inflation targeter in disguise?

Now about 10 advanced and 15 emerging-market and developing countries

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Country Date Country Date New Zealand 1990 q1 Korea 2001 m1

Canada 1991 m2 Mexico 2001 m1

United Kingdom 1992 m10 Iceland 2001 m3

Sweden 1993 m1 Norway 2001 m3

Finland 1993 m2 Hungary 2001 m6

Australia 1993 m4 Peru 2002 m1

Spain 1995 m1 Philippines 2002 m1 Israel 1997 m6 Guatemala 2005 m1 Czech Republic 1997 m12 Slovakia 2005 m1 Poland 1998 m10 Indonesia 2005 m7

Brazil 1999 m6 Romania 2005 m8

Chile 1999 m9 Turkey 2006 m1

Colombia 1999 m9 Serbia 2006 m9 South Africa 2000 m2 Ghana 2007 m5

Thailand 2000 m5

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Effects on inflation, inflation expectations, and output for advanced and emerging-market countries

Success: Flexible, robust, and resilient monetary-policy regime

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Linear quadratic model (approximation around stochastic steady state) X_t+1

Hx_t+₁jt

=A Xt

x_t +Bi_t+ ^C

0 ε_t+1 (1)

Xtpredetermined,xtforward-lookingvariables,it(policy)instruments

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Yttargetvariables, typicallyYt (π_t π ,yt y¯t, ...)⁰

Yt =D 2 4 X_t

xt

i_t 3

5 [D_X Dx D_i] 2 4 X_t

xt

i_t 3

5 (2)

Intertemporal loss function E_t

∑

∞ τ=0

δ^τL_t+τ (0<δ <1) (3) Period loss

Lt Y⁰_tΛYt (4)

Λweight matrix, typicallyΛ Diag(1,λ, ...) L_t = (π_t π )²+λ(y_t y¯_t)²

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Optimization under commitment in a timeless perspective, solution:

xt

i_t = F Xt

Ξt 1

Fx

F_i

Xt

Ξt 1 (5) X_t+1

Ξt = M X_t Ξt 1

+ ^C

0 ε_t+1 (6)

Y_t = D I 0 F

X_t Ξt 1

D˜ X_t

Ξt 1 (7) ΞtLagrange multipliers for lower block of (1)

Optimal instrument rule (optimal policy function), i_t=F_i X_t

Ξt 1 (8)

Certainty equivalence:

MatricesFandMdepend onA,B,H,D,Λ, andδ, but not onC

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Standard theory of (optimal) monetary policy:

Central bank commits to some (optimal) policy functionF_i Private sector combines policy function with model, solves for rational-expectations equilibrium

Notin practice:

Inflation-targeting central bank chooses and announces current policy rate, indicates or announces path of future policy rate, publishes forecast of inflation and the real economy

Private sector responds to this information, and the actual equilibrium results

Forecasts and projections of the policy rate, inflation, and the real economy take center stage

How to model and understand?

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All inflation-targeting central banks not well described by this theory

Theory is idealization (like consumption theory of actual consumer behavior)

Theory of mature inflation targeting, potential best-practice inflation targeting

Actual inflation targeting, w/ one innovation after the other, moving in this direction

Some inflation-targeting central banks may be pretty close

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Some misunderstandings to be avoided:

Two things that inflation targeting is not

Notstrictinflation targeting, notL_t= (π_t π )². Alwaysflexibleinflation targeting.

Not simple policy rule, such thatit =α(π_t π )or i_t i_t ₁= α(π_t π ).

Instead, inflation targeting implies that central banks respond to much more information, namely all information that affects the forecast of inflation and the real economy (resource utilization)

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u^t f^u^t⁺^τ,tg^∞τ=0projection(conditional mean forecast) in periodt Projection modelfor the projections(X^t,x^t,i^t,Y^t)in periodt (ε_t+_τ,t=0 forτ 1)

X_t+τ+1,t

Hx_t+τ+_1,t =A X_t+τ,t

xt+τ,t +Bit+τ,t (9)

Y_t+τ,t =D 2 4 X_t+_τ,t

x_t+τ,t

it+τ,t

3

5 (10)

Xt,t=X_t_j_t (11)

X_t_j_testimate of predetermined variables in periodt(allows for imperfectly observed state of the economy)

T(X_t_j_t)feasible set of projectionsfor givenX_t_j_t, the set of projections (X^t,x^t,i^t,Y^t)that satisfy (9)-(11)

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Policy problem int: Determine optimal projection(X^ˆ^t, ˆx^t, ˆı^t, ˆY^t) that minimizes intertemporal forecast loss function,

L(Y^t) =

∑

∞ τ=0

δ^τL_t+τ,t (0<δ 1), (12) subject to(X^t,x^t,i^t,Y^t)2 T(X_t_j_t)

Period forecast loss

L_t+τ,t Y_t+τ,t0ΛYt+τ,t (13) Optimization under commitment in timeless perspective,

modified loss function (Svensson-Woodford 05) mini^t,Y^t L(Y^t) +¹

δΞ⁰_t ₁H(x_t,t x_t,t ₁) s.t.(X^t,x^t,i^t,Y^t)2 T(X_t_j_t) (14)

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Alternative implementation of timeless perspective (Giannoni-Woodford 02, Svensson-Woodford 05):

Restrictioninstead of modified loss function xt,t =Fx X_t_j_t

Ξt 1 (15)

T(X_t_j_t,Ξt 1), therestrictedfeasible set of projections, the subset of the feasible set of projectionsT(X_t_j_t)that satisfy (15) for givenX_t_j_t andΞt 1

Optimal policy projection is also the solution to the problem mini^t,Y^t L(Y^t)subject to(X^t,x^t,i^t,Y^t)2 T(X_t_j_t,Ξt 1) (16)

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L(Y^t) =

∑

∞ τ=₀

δ^τ(π_t+τ,t π )²+λ

∑

∞ τ=₀

δ^τ(y_t+τ,t y¯_t+τ,t)² (17) Sums of discounted squared inflation and output gaps (forecasts)

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General targeting rule (Giannoni-Woodford 09, Svensson 99)

∑

b s= a

gsYt+s+τ,t =0 (τ 0)

Simplest New Keynesian model (Svensson-Woodford 05) πt+τ,t π +^λ

κ[(yt+τ,t y¯t+τ,t) (y_t+τ 1,t y¯_t+τ 1,t)] =0 Simple, robust, and practical way to characterize optimal policy in small models

Complex in larger models

Arguably, for practical policy, policymakers need to look at graphs only

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Determination of equilibrium?

Periodt:

Central bank chooses and announces forecast(X^ˆ^t, ˆx^t, ˆı^t, ˆY^t)and setsit=ıˆt,t

Private sector believes forecast:x_t+₁jt =xt+1,t

Private sector determinesx_tgivenx_t₊₁_j_t,X_t, andi_t: Hx_t₊₁_j_t = A₂₁X_t+A₂₂x_t+B₂i_t

x_t = A₂₂¹(Hx_t₊₁_j_t A₂₁X_t B₂i_t) Periodt+1:

Private sector determinesX_t+1givenX_t,x_t,i_t, andε_t+1

X_t+₁ =A₁₁Xt+A₁₂xt+B₁it+Cε_t+₁

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Determinacy/uniqueness of rational-expectations equilibrium?

Implicit out-of-equilibrium commitment (Svensson-Woodford 05), for instance,

i_t =ˆı_t,t+ϕ(π_t π_t,t)

Svensson-Woodford 05: ϕ>1 (Taylor Principle) ensures determinacy

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Main point of theory:

Central bank doesnotchoose and communicate apolicy function, i_t = f_XX_t+f_xx_t

it = fπ(πt π ) +fy(yt y¯t)

Instead, central bank chooses and communicates apolicy-rate path,

i^t fⁱt+τ,tg^∞_τ=⁽^T0⁾

mini^t,Y^t L(Y^t)subject to(X^t,x^t,i^t,Y^t)2 T(X_t_j_t, ...)

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The discretion equilibrium

Degrees of commitment (Schaumburg and Tambalotti 07)

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Uncertainty about the state of the economy (additive uncertainty, certainty equivalence) (Svensson-Woodford 03)

Uncertainty about the model/transmission mechanism (multiplicative uncertainty, not certainty equivalence) (Onatski-Williams 03, Svensson-Williams 07 MJLQ)

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Time-varying add factors/deviations

(Reifschneider-Stockton-Wilcox 97, Svensson 05)

FOMC Bluebook 02: “Policymaker perfect-foresight projections”

Use judgment in Greenbook, optimal policy in FRB/US (Svensson-Tetlow 05)

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RBNZ: Towards more flexible inflation targeting Away from a fixed policy horizon

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RBNZ (1997), Norges Bank (2005), Riksbank (2007), Czech National Bank (2008)

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Policy options, July 2009

a. Alternative repo-rate paths Percent, quarterly averages

-1.0 0.0 1.0 2.0 3.0 4.0 5.0

08 09 10 11 12

Main Low High

c. CPIF Annual percentage change

0.0 1.0 2.0 3.0 4.0

08 09 10 11 12

Main Low High

b. Mean squared gaps

Main Low

High

0.0 5.0 10.0 15.0

0.00 0.02 0.04 0.06 0.08 0.10

CPIF

Output

d. Output gap Percent

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0

08 09 10 11 12

Main Low High

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Policy options, February 2010

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Mean squared gaps:Simple theory Main scenario

(i^t,Y^t)2 T(X_t_j_t, ...) Loss for main scenario (δ=0)

L(Y^t) T+1

∑^Tτ=₀(π_t+τ,t π )²

T+1 +λ∑^Tτ=₀(y_t+τ,t y¯_t+τ,t)² (T+1)

= MSG(π^t) +λMSG(y^t)

Alternative feasible interest-rate scenarios, variations(di^t,dY^t), (i^t+di^t,Y^t+dY^t)2 T(X_t_j_t, ...)

If(i^t,Y^t)optimal,

L(Y^t) L(Y^t+dY^t)

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Policy options, March 2005

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The application of judgment, February 2009

a. Repo rate Percent

0 1 2 3 4 5

03 04 05 06 07 08 09 10 11 12 Outcome

BVAR Ramses Riksbank

c. GDP growth Annual percentage change

-3 -1 1 3 5 7

03 04 05 06 07 08 09 10 11 12 Outcome BVAR Ramses Riksbank

d. Output gap Percent

-4 -2 0 2 4

03 04 05 06 07 08 09 10 11 12 Outcome

BVAR Ramses Riksbank b. CPIF Annual percentage change

-1 1 3 5 7

03 04 05 06 07 08 09 10 11 12 Outcome

BVAR Ramses Riksbank

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Price-level targeting

Inflation targeting and financial stability: Lessons from the financial crisis