Monetary Policy Switching to Avoid a Liquidity Trap Siddhartha Chattopadhyay Vinod Gupta School of Management IIT Kharagpur Betty C. Daniel Department of Economics University at Albany SUNY September 28, 2012 Chattopadhyay & Daniel () Liquidity Trap September 28, 2012 1 / 31
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Monetary Policy Switching to Avoid a Liquidity Trap
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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
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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
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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)
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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
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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
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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
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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
arrows of motion point away
∂ [Et (πt+1)− πt ]
∂πt=1− β
β> 0
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Graph of Phase Diagram with Optimal Interest RateSaddlepath
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Optimal Interest RateTwo Problems
equilibrium indeterminacy
no feedback on endogenous variablesyields model with saddlepath
liquidity trap for large adverse demand shock
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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
Chattopadhyay & Daniel () Liquidity Trap September 28, 2012 11 / 31
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
arrows of motion point away
∂ [Et (yt+1)− yt ]∂yt
= σ
(κ
β+ φy
)> 0
Chattopadhyay & Daniel () Liquidity Trap September 28, 2012 12 / 31
Phase Diagram with Taylor RuleGlobally Unstable
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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
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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
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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
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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
Chattopadhyay & Daniel () Liquidity Trap September 28, 2012 17 / 31
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
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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
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Policy-Switching Rule: Choice of inflation targetSmall Adverse Demand Shock
)3 standard Taylor Rule which eliminates sunspots and stabilizes output inface of demand shocks
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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
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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
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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%
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Policy-SwitchingLarge Adverse Demand Shock
Impulse response under inflation target to keep nominalinterest constant:
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Policy-SwitchingLarge Adverse Demand Shock
Excessive fluctuations (annualized):
output: 93.05% per annuminflation: 25.50% per annum
Unacceptable welfare loss
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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
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The Sticky Price New-Keynesian DSGE ModelLarge Adverse Demand Shock
Impulse response under inflation target which allows nominalinterest to fall but remain positive
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Smaller welfare loss than policy of fixed nominal interest rate
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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
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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
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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
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