monetary policy switching to avoid a liquidity trap

Monetary Policy Switching to Avoid aLiquidity Trap

Siddhartha ChattopadhyayVinod Gupta School of Management

IIT Kharagpur

Betty C. DanielDepartment of EconomicsUniversity at Albany —SUNY

September 28, 2012

Chattopadhyay & Daniel () Liquidity Trap September 28, 2012 1 / 31

MotivationLiquidity Trap

Large negative demand shock can send nominal interest rate to zero

Conventional monetary policy loses ability to stimulateEquilibrium values for inflation and output become indeterminate

Design monetary policy switching to

Stimulate economy following a large negative demand shockWhile avoiding a liquidity trapAnd avoiding indeterminacy


Other LiteraturePolicy in Liquidity Trap

Bernanke, Reinhart (2004), Bernanke, Reinhart, Sack (2004):keeping long-term interest expectation low through non-standardpolicy alternatives

Svensson (2003): raising inflation expectation by currencydepreciation

Krugman (1998): permanent increase in money supplyEggertson and Woodford (2003): optimal policy with price leveltarget

Adam and Billi (2006): optimal policy commitment under zerolower bound

Nakov (2008): optimal policy with truncated Taylor rule


The Sticky Price New-Keynesian DSGE ModelWoodford (2003), Walsh (2010)

Expectational IS:

Et (yt+1) = yt + σ [ı̂t − Et (πt+1)] + ut , σ ≥ 1 (1)

Sticky Price Phillips curve:

πt = βEt (πt+1) + κyt , κ ∈ (0,∞) (2)


Optimal Monetary PolicyWoodford (2003)

Loss function:

Lt =12Et

∞

∑j=0

βj(π2t+j + λy2t+j

), β ∈ (0, 1) ,λ ∈ [0,∞) (3)

Optimal policy chooses ı̂ tominimize (3)subject to

IS equation (1)Phillips Curve equation (2)feasibility: it ≥ 0


Optimal Policy (cont)Optimal Interest Rate

Monetary authority sets

ı̂ is interest deviation from long-run equilibriumı̄ is long-run equilibrium interestoptimal policy

ı̂t = it − ι = −σ−1ut

yt = πt = Lt = 0


Phase Diagram

∆y = 0 curve

equation

Et (yt+1)− yt = σı̂t − ut −σ

β(πt − κyt ) = 0

positive slopeyt = κ−1πt

arrows of motion point away

∂ [Et (yt+1)− yt ]∂yt

=σ

βκ > 0


Phase Diagram (cont)

∆π = 0 curve

Equation

Et (πt+1)− πt =1β[(1− β)πt − κyt ] = 0

positive slope, but flatter than slope of ∆y = 0 curve

yt =1− β

κπt


∂ [Et (πt+1)− πt ]

∂πt=1− β

β> 0


Graph of Phase Diagram with Optimal Interest RateSaddlepath


Optimal Interest RateTwo Problems

equilibrium indeterminacy

no feedback on endogenous variablesyields model with saddlepath

liquidity trap for large adverse demand shock


Taylor Rule

Taylor Rule with Taylor principle eliminates indeterminacy

Taylor Rule: interest rate responds to endogenous variables

ı̂t = −σ−1ut + φππt + φy yt

Taylor principle (Bullard and Mitra, 2002): responsiveness must belarge enough

φπ + φy

(1− β

κ

)− 1 > 0


Phase Diagram with Taylor Rule

∆y = 0 curve

equation

Et (yt+1)− yt = σ[φππt + φy yt

]− σ

β(πt − κyt ) = 0

slope less than ∆π = 0 if Taylor Principle satisfied (we’ll draw asnegative)

yt =1− βφπ

κ + βφyπt


∂ [Et (yt+1)− yt ]∂yt

= σ

(κ

β+ φy

)> 0


Phase Diagram with Taylor RuleGlobally Unstable


Liquidity Trap

Globally unstable model solves equilibrium indeterminacy for positiveinterest rates

Does not solve liquidity trap problem

Large adverse demand shock (ut > σι)

1 monetary authority reduces nominal interest rate close to zero yieldingliquidity trap

2 set φπ = φy = 0 yielding indeterminacy and sunspots

our proposed switching policy solves both


Taylor Rule with Time-varying Intercept

Woodford (2003):

Nominal interest rate deviation is sum of real interest deviation andinflation deviation

ı̂t = r̂t + π̂t

Woodford’s optimal monetary policy allows time-varying real interestrate

natural rate of interestr̂t = −σ−1ut

inflation deviation is set to zero

π̂t = 0


Evidence for Time-Varying Inflation Target

Kozicki and Tinsley (2001), Rudebusch and Wu (2004), Gurkaynak,Sack and Swanson (2005) and Ireland (2007):

significant variation in inflation target in post-war USTaylor rule with time-varying inflation target better capture interestrate movement of USexpectation theory of term structure works better for US undertime-varying inflation target


Introduce Time-varying Inflation Target into Taylor Rule

Our Taylor rule:

ı̂t = −σ−1ut + φπ (πt − π∗t ) + φy (yt − y ∗t ) ,

Time-varying short-run inflation target where monetary authoritychooses π∗t , and makes it highly persistent

π∗t+1 = ρππ∗t

ρπ < 1, but close to unity

Output target must be consistent implying

y ∗t =π∗t − βEt

(π∗t+1

)κ


Taylor Rule with Time-varying Inflation Target

Substitute time-varying inflation and output targets into Taylor Rule

it = ı̄− zπ∗t − σ−1ut + φππt + φy yt

where,

z = φπ + φy

(1− ρπ β

κ

)− 1 > 1

Taylor principle

requires z > 0assures sunspot-free determinate equilibrium


Equililbrium with Our Taylor Rule

Output:

yt =1− ρπ β

β (λ1 − ρπ) (λ2 − ρπ)σzπ∗t

Inflation:πt =

κ

β (λ1 − ρπ) (λ2 − ρπ)σzπ∗t

Nominal interest rate

it = ı̄− zπ∗t − σ−1ut + φππt + φy yt

= ı̄− σ−1ut + qzπ∗t (4)

Taylor principle with ρπ high enough ⇒

q =

[φπκ + φy (1− ρπ β)

β (λ1 − ρπ) (λ2 − ρπ)σ− 1

]> 0


Policy-Switching Rule: Choice of inflation targetSmall Adverse Demand Shock

Monetary authority follows zero inflation target policy (π∗t = 0)1 minimizes loss (yt = πt = Lt = 0)2 policy feasible

(it = ı̄− σ−1ut ≥ 0

)3 standard Taylor Rule which eliminates sunspots and stabilizes output inface of demand shocks


Policy-Switching with Large Adverse Demand ShockLarge Adverse Demand Shock

Monetary authority switches to positive inflation target

Inflation target large enough to keep nominal interest rate fixed at ι

π∗t =σ−1utzq

To maintain inflation target going forward need

ρπ = ρu

whereut = ρuut−1


Monetary Transmission Mechanism

Negative demand shock reduces output and inflationMonetary authority wants to reduce the interest rate to reduce the realrate and stimulate economyWhen the demand shock is too large, nominal interest rate would fallbelow zero

Our policy reduces the real interest rate by raising inflationaryexpectations

Raise inflation targetPromise to keep it high for a long period of time by promising highpersistenceWith suffi cient persistence, output and inflation rise even if the nominalinterest rate does not fall

Promise of persistence requires the inflation target to remain higheven after the demand distrubance has fallen suffi ciently that atraditional Taylor Rule could stimulate

Policy is dynamically inconsistentRequires ability to commit to a rule


Parameterization

Adam and Billi (2006):

σ = 1, β = 0.99, κ = 0.057, ρπ = ρu = ρ = 0.8

φπ = 1.5, φy = 0.5

Large adverse demand shock:

u0 = 1.04% > σı̄ = 1.01%


Policy-SwitchingLarge Adverse Demand Shock

Impulse response under inflation target to keep nominalinterest constant:


Policy-SwitchingLarge Adverse Demand Shock

Excessive fluctuations (annualized):

output: 93.05% per annuminflation: 25.50% per annum

Unacceptable welfare loss


Policy-Switching with Alternative Inflation TargetLarge Adverse Demand Shock

Monetary Authority Switches to Positive Inflation Target

Allow nominal interest rate to fallInflation target just high enough to keep nominal interest rate positive

i0 = ι− η0 > 0

withi0 ≥ 0

⇒π∗0 =

σ−1u0 − η0zq

andπ∗t = ρtππ∗0


The Sticky Price New-Keynesian DSGE ModelLarge Adverse Demand Shock

Impulse response under inflation target which allows nominalinterest to fall but remain positive


Monetary Policy SwitchingLarge Adverse Demand Shock

Reasonable fluctuations (annualized):

output: 2.69% per annuminflation: 0.73% per annum

Smaller welfare loss than policy of fixed nominal interest rate


Comparison of Our Switching Policy with Standard TaylorRule in Liquidity Trap

Large adverse demand shock

Our switching policy

Reduce nominal interest rate and raise inflation targetStimulates output and inflationRetain positive responsiveness of interest to output and inflation inTaylor Rule so retain determinacy

Standard policy of reducing nominal interest to zero with fixed inflationtarget

Cannot reduce nominal interest rate enough to stimulate enoughLose responsiveness of interest to output and inflation so losedeterminacy


Policy RobustnessSticky Information Phillips Curve

Introduce policy into Sticky Information Phillips Curve (Mankiw andReis, 2002, 2006, 2010)

Similar results

Avoid liquidity trap stimulating both output and inflationPeak effect on inflation delayed due to delay in information about newinflation target


Conclusion

Zero inflation target is an optimal policy under small demand shock

Switch to positive inflation target policy under large adverse demandshock

credible implementation avoids liquidity trap when persistence is highenoughrobust as supported both the sticky price and sticky information model

Costs and benefits

our switching policy stimulates at cost of inflation biasstandard policy has period of indeterminacy and insuffi cient stimulus


monetary policy switching to avoid a liquidity trap

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