Scarcity of Safe Assets, In‡ation, and the Policy Trap
David Andolfatto and Stephen Williamson
Federal Reserve Bank of St. Louis
June 2015
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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Disclaimer
The views expressed are ours and do not necessarily re‡ect o¢ cial
positions of the Federal Reserve Bank of St. Louis, the Federal Reserve
System, or the Board of Governors.
Andolfatto-Williamson ()
Asset Scarcity
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Observations and Central Bank Behavior
Observations:
short-term nominal interest rates have been close to zero since late
2008.
standard monetary models: Friedman rule associated with de‡ation.
at least since 2010, the in‡ation rate in the U.S. has varied roughly
between 1% and 3%, so in‡ation is low, but not as low as you might
think.
real interest rates have been persistently low since the Great Recession.
How do central banks think about in‡ation, and in‡ation control?
Phillips curve.
Taylor rule – when in‡ation is high (low), raise (lower) the nominal
interest rate.
Andolfatto-Williamson ()
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June 2015
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Ideas
Why is the real interest rate on government debt low?
Maybe this re‡ects a shortage of government debt.
Government debt has an important role in …nancial markets – used as
collateral and directly in exchange.
Why a scarcity?
Financial crisis, sovereign debt problems a¤ected substitutes for U.S.
government debt.
New …nancial regulations – e.g. Basel III liquidity coverage ratio.
What are the implications of a government debt shortage?
matters for asset prices and in‡ation.
matters for how monetary policy works – e¤ects of open market
operations, optimal policy, operating characteristics of standard policy
rules.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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Plan
Model: Money, government bonds, credit, and a role for all assets in
transactions.
Suboptimal …scal policy creates government debt shortage – monetary
policy can matter in di¤erent ways.
What is optimal policy?
How do Taylor rules behave in this environment?
Standard case – Benhabib et al. (2001) problem, i.e. zero lower bound
is a policy trap.
Government debt shortage creates other problems.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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References
Money literature: Williamson (2012, 2014a,2014b) – Lagos-Wright
(2005).
Cash-in-Advance: Lucas-Stokey (1987).
Taylor rules: Benhabib et al. (2001).
Andolfatto-Williamson ()
Asset Scarcity
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Model
continuum of households with unit mass. Each household has
preferences
∞
E0
∑β
t =0
t
Z 1
0
u (ct (i ))di
γnt ,
ct (i ) is consumption of i th consumer in the household, i 2 [0, 1].
nt is the labor supply of the worker in the household – one unit of the
perishable consumption good produced with each unit of labor
supplied.
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Timing Within a Period
Household enters each period with money and bonds.
Trade on a competitive asset market.
Worker/sellers in households produce output, and choose one of two
segmented markets on which to sell it.
Market 1: only money accepted in exchange – a technological
constraint on means of payment.
Market 2: money, bonds, and within-period credit accepted.
Individual consumer: Must go either to market 1 (probability θ ) or
market 2 (probability 1 θ ) and consume on the spot.
Household knows where each consumer in the household is going, and
allocates the household’s portfolio accordingly, to maximize household
welfare – consumers then can’t share consumption within the
household.
Large household can be interpreted as standing in for banking
arrangements, collateral, etc.
Andolfatto-Williamson ()
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Household’s Problem
∞
max E0
∑ βt
θu (ct1 ) + (1
θ )u (ct2 )
γnt ,
t =0
subject to
θct1 + qt bt2 + qt bta+1 + mt2
bta+1
(1
pt 1
(mt + bta + btg ) + τ t ,
pt
0,
θ )ct2 = bt2 + mt2 + κ t ,
θct1 + qt (1 θ )ct2 + mt +1 + btg+1 + qt bta+1
pt 1
=
(mt + bta + btg ) + τ t + nt + qt κ t κ t .
pt
Andolfatto-Williamson ()
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Fiscal Authority and Central Bank
Consolidated government budget constraints:
m̄0 + q0 b̄0 = τ 0
m̄t
pt 1
m̄t
pt
1
+ qt b̄t
pt 1
b̄t
pt
1
= τ t , t = 1, 2, 3, ...,
Fiscal policy rule: Real quantity of consolidated government debt
exogeneous:
Vt = qt b̄t + m̄t
Central bank: Chooses qt , then carries out appropriate open market
operations.
Andolfatto-Williamson ()
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June 2015
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Equilibrium
State: (Vt , κ t , qt ) – …scal policy, credit limit, monetary policy.
Solve:
γ + βEt
u 0 (ct1+1 )
= 0,
π t +1
u 0 (ct2 )
qt u 0 (ct1 ) = 0,
u 0 (ct2 )
γ = 0 and Vt + qt κ t
u 0 (ct2 )
γ
θct1 + (1
θ )qt ct2 ,
0 and Vt + qt κ t = θct1 + (1
θ )qt ct2 ,
or
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Liquidity Premia
qt =
u 0 (ct2 )
γ
| {z }
liquidity premium
1=
u 0 (ct1 )
γ
| {z }
u 0 (ct1+1 )
[nominal bond]
βEt
π t +1 u 0 (ct1 )
|
{z
}
liquidity premium
sta =
u 0 (ct2 )
γ
| {z }
fundamental
u 0 (ct1+1 )
βEt
[money]
π t +1 u 0 (ct1 )
|
{z
}
liquidity premium
Andolfatto-Williamson ()
fundamental
βEt
|
u 0 (ct1+1 )
[real bond]
u 0 (ct1 )
{z
}
fundamental
Asset Scarcity
June 2015
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Unconstrained Equilibrium
Quasilinear preferences implies we can solve period-by-period.
u 0 (ct2 )
γ = 0, i.e. ct2 = c (no ine¢ ciency in market 2)
γ
u 0 (ct1 ) = ,
qt
πt =
β
.
qt
sta = qt βEt
Vt + q t κ t
θct1 + (1
1
qt + 1
,
θ )qt c (Ricardian – gov’t debt irrelevant)
Friedman rule (qt = 1) is optimal.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
13 / 20
Constrained Equilibrium
u 0 (ct2 )
qt u 0 (ct1 ) = 0,
Vt + qt κ t = θct1 + (1
πt =
θ )qt ct2
βu 0 (ct1 )
γ
Not Ricardian.
qt falls (nominal interest rate rises – open market sale): ct1 falls, ct2
rises, in‡ation rate rises, gdp rises, welfare rises for qt close to 1.
Constrained in period t i¤
u 0 ( Vt + κ t )
> 1,
γ
and qt su¢ ciently large.
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Credit Constraints and Government Debt
Suppose κ t declines – interpret as a …nancial crisis shock, lowering
the credit limit.
If asset market constraint binds, ct1 , ct2 , hours worked, and output
decline, in‡ation rate rises.
If this is permanent, real interest rate falls.
What’s the optimal policy response? Zero lower bound is not optimal,
as government debt is important in supporting some types of
exchange.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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Liquidity Trap
ct1 = ct2 = yt = Vt + κ t
πt =
βu 0 (Vt + κ t )
γ
In‡ation depends on the ine¢ ciency wedge, which is also determining
the liquidity premium on government debt.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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Taylor Rule
1
= max[π tα (π )1
qt
α
xt , 1 ]
π = target gross in‡ation rate; α > 0; xt is adjustment for real
interest rate
We know at the outset this is suboptimal.
Consider four di¤erent rules:
xt
xt
xt
xt
= constant.
= current real interest rate.
constant, replace π t with π t +1 – forward-looking rule.
constant, replace π t with π t 1 – backward-looking rule.
When there are dynamics, look only at deterministic cases, where
Vt = V , κ t = κ.
Consider how α > 1 (Taylor principle), or α < 1 matters.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
17 / 20
Taylor rule in the Unconstrained Case
Results in line with Benhabib et al. (2001).
xt =
1
β
implies period-by-period solution.
α > 1 implies two equilibria, one with π t = π , one with π t = β
(liquidity trap).
α < 1 implies unique equilibrium with π t = π .
xt = endogenous real rate:
α > 1 implies a continuum of dynamic equilibria converging to the
liquidity trap in …nite time.
α < 1 implies a continuum of dynamic equilibria converging to
π t = π steady state.
forward looking rule – turns the endogenous real rate case on its head.
backward looking rule – same as endogenous real rate.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
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Figure 1: Taylor Rule Equilibrium, Unconstrained, α > 1,
Endogenous Real Interest Rate
πt+1
πt
B
πtα(π∗)1−α
A
(0,0)
β
π2
π1
π0
πt
Figure 2: Taylor Rule Equilibrium, Unconstrained, α < 1,
Endogenous Real Interest Rate
πt+1
πt
πtα(π∗)1−α
A
β
(0,0)
π0
π1
π∗
πt
Taylor rule in the Constrained Case
Key problem is accounting for the endogenous real rate (in the short
run and long run).
Two approaches:
1
xt a function of the exogenous variables such that, in the desired
steady state, xt = gross real interest rate. Problems:
Taylor rule now much more complicated.
Multiplicity – examples in which there can be a liquidity trap steady
state, and other equilibria with a positive nominal interest rate and
π 6= π .
2
xt = actual real interest rate – yields same properties as in the
unconstrained case. Problem:
same multiplicity problems as in the unconstrained case.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
19 / 20
Conclusions and Other Ideas
Need to understand sign reversal: Can’t have permanently higher
in‡ation without permanently higher nominal interest rates.
When at the zero lower bound, this is not just a long-run issue.
Less-aggressive Taylor rules at least can give convergence to an
in‡ation target in the long run.
Problem of how to adjust for endogenous (even in the long run) real
interest rates: if a good measure of the real interest rate is not
available, …rst-di¤erence Taylor rules could work.
Phillips curve reasoning can be used to justify tightening, or lifto¤
from zero – doing the right thing for the wrong reason.
Andolfatto-Williamson ()
Asset Scarcity
June 2015
20 / 20